Fatigue Damage Tolerance of Bainitic and Pearlitic

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Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear

Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves Jin-Yeon Kim,Laurence J.Jacobs,a͒and Jianmin QuG.W.Woodruff School of Mechanical Engineering,Georgia Institute of Technology,Atlanta,Georgia30332-0405Jerrol W.LittlesPratt&Whitney,Materials and Processes Engineering,400Main Street,M/S114-40,East Hartford,Connecticut06108͑Received10February2006;revised14June2006;accepted16June2006͒This research develops a robust experimental procedure to track the evolution of fatigue damage ina nickel-base superalloy with the acoustic nonlinearity parameter,␤,and demonstrates itseffectiveness by making repeatable measurements of␤in multiple specimens,subjected to both high-and low-cycle fatigue.The measurement procedure developed in this research is robust in that it is based on conventional piezoelectric contact transducers,which are readily available off the shelf,and it offers the potential forﬁeld applications.In addition,the measurement procedure enables the user to isolate sample nonlinearity from measurement system nonlinearity.The experimental results show that there is a signiﬁcant increase in␤linked to the high plasticity of low-cycle fatigue,and illustrate how these nonlinear ultrasonic measurements quantitatively characterize the damage state of a specimen in the early stages of fatigue.The high-cycle fatigue results are less deﬁnitive͑the increase in␤is not as substantial͒due to increased uncertainties involved in the high-cycle fatigue tests,but still show a clear relationship between␤and remaining fatigue life.One application of the measured␤versus fatigue-life data is to potentially serve as a master curve for life prediction based on nonlinear ultrasonic measurements.©2006Acoustical Society of America.͓DOI:10.1121/1.2221557͔PACS number͑s͒:43.25.Zx,43.25.Dc,43.25.Ba͓MFH͔Pages:1266–1273I.INTRODUCTIONRecent experimental studies and new physical models are demonstrating the potential of nonlinear ultrasonics͑or the second-harmonic generation technique͒to quantitatively detect and characterize fatigue damage in metals.1–10This fatigue damageﬁrst appears in the form of dislocation sub-structures,such as veins and persistent slip bands͑PSBs͒, and these PSBs accumulate at grain boundaries to produce strain localization and,thenﬁnally,microcrack initiation with increasing fatigue cycles.These dislocations͑and re-sulting microplastic deformation͒do not cause a large change in the linear macroscopic properties͑such as elastic moduli,sound speed,and attenuation͒of a material;the changes in the linear ultrasonic values are not large enough to be accurately measured with conventional linear ultrasonic techniques.However,the accumulation of dislocations throughout the continuum͑with increasing fatigue͒will cause a nonlinear distortion in an ultrasonic wave propagat-ing in the material,and thus generate higher harmonic com-ponents in an initially monochromatic ultrasonic wave sig-nal.For this reason,nonlinear ultrasonic͑acoustic͒waves can be used to quantify the presence and the density of dis-locations in a metallic material,and thus measure fatigue damage in a quantitative fashion.In addition,nonlinear ul-trasonics has the potential to promote an understanding of the evolution and accumulation of the dislocation substruc-tures in the very early stages of fatigue.To date,a number of investigators1–8have applied non-linear ultrasonic techniques to assess fatigue damage in dif-ferent materials under relatively controlled laboratory condi-tions.Yost and Cantrell1and Cantrell and Yost6 experimentally observed changes of the acoustic nonlinearity parameter,and attributed the changes to the effects of fatigue-induced dislocations.Frouin et al.5,8performed in situ nonlinear ultrasonic measurements during fatigue test-ing,and related the measured increase in the acoustic non-linearity parameter—in the vicinity of the fracture surface—to an increase in the dislocation density.Among these studies,only Frouin et al.8reported using nonlinear ultrasonic results to track fatigue damage throughout the en-tire fatigue life of a specimen.Oneﬁeld application of non-linear ultrasonics examined fatigue damage in stainless-steel turbine blades.7In spite of the recognized potential of non-linear ultrasonics,there are very few examples of its success-ful application to monitor fatigue damage.This is probably due to instrumentation issues that make accurate and consis-tent nonlinear ultrasonic measurements difﬁcult,plus a lack ofﬂexibility in the measurement setup needed to interrogate real fatigue test specimens.A critical next step—for the in-corporation of nonlinear ultrasonic techniques into life-prediction strategies of structural components—is a system-a͒Also at:School of Civil and Environmental Engineering,Georgia Institute of Technology,Atlanta,GA30332-0355;electronic mail: laurence.jacobs@atic study that quantiﬁes the robustness,accuracy,and validity of nonlinear ultrasonics to detect the early stages of fatigue damage͑prior to crack initiation͒in metallic materi-als.Of particular interest is the development of an experi-mental procedure with the capability of performingﬁeld in-spections of an absolute and repeatable nature.The objective of the current research is to develop a robust experimental procedure to track the evolution of fa-tigue damage in metallic materials with the acoustic nonlin-earity parameter,␤.The effectiveness of this proposed mea-surement procedure is demonstrated by making repeatable acoustic measurements of␤,in nickel-base superalloy speci-mens,subjected to three types of damage:Quasi-static monotonic,low-,and high-cycle fatigue.These nonlinear ul-trasonic measurements are used to track the evolution of damage in multiple specimens with a series of interrupted mechanical tests—ﬁrst by making a baseline measurement of ␤in an undamaged specimen,then introducing some damage into the specimen,repeating the measurement of␤in thissame͑unloaded͒specimen,then introducing more damage into the specimen,and repeating the procedure.It is important to note that the acoustic nonlinearity pa-rameter,␤,is an absolute material constant,which can be related to the higher-order elastic constants,of a material;the ␤parameter is a directly measurable acoustic parameter that is linked to the state of material damage.As a result,nonlin-ear ultrasonics is unparalleled in its potential to provide a robust and quantitative characterization of fatigue damage in in-service structural components.However,the acoustic non-linearity associated with fatigue damage is very small,and can be easily overwhelmed by a number of other factors ͑especially instrumentation nonlinearity͒inherent to the mea-surement procedure.Therefore,a critical contribution of this research is a systematic experimental procedure that can identify and remove spurious sources of nonlinearity,isolat-ing only those contributions due to the material and associ-ated damage.II.GENERATION OF HIGHER HARMONICS AND THE ACOUSTIC NONLINEARITY PARAMETER,␤The equations of motion of a solid element,in the ab-sence of body forces,are written in material coordinates,X, as␳ץ2u iץt2=ץ␴ijץX j,͑1͒where t is time,␳is the mass density,u i is the displacement vector,and␴ij is the stress tensor.The stress in a nonlinear ͑fatigued͒solid can,in general,be written as␴ij=␴ij0+A ijkl ץu kץX l+12A ijklmnץu kץX lץu mץX n+¯,͑2͒where␴ij0is the residual stress in the material,and A ijkl and A ijklmn are the Huang coefficients,9which are related to the second-and third-order elastic constants by A ijkl=␴jl0␦ik +C¯ijkl and A ijklmn=C¯ijklmn+C¯jlmn␦ik+C¯ijnl␦km+C¯jnkl␦im.C¯ijkl and C¯ijklmn are modified by fatigue damage͑dislocation substructures͒9from their initial values,C ijkl and C ijklmn.11Expressions for the modified elastic constants during fatigue have been presented in terms of the residual stress and plastic strain.12The density of a material undergoing finite deforma-tion is given by␳=␳0/det F where␳0is the constant den-sity in the unstressed configuration and F is the deforma-tion gradient tensor,defined as F ij=␦ij+ץu j/ץX i. Substituting Eq.͑2͒into Eq.͑1͒,and considering one-dimensional wave propagation of a longitudinal wave in an isotropic solid,one getsץ2u1ץt2=c2ץ2u1ץX12ͩ1+␤ץu1ץX1ͪ,͑3͒where c=ͱ͑C¯1111+␴110͒/␳is the longitudinal wave speed and␤is the acoustic nonlinearity parameter defined as␤=C¯111111+3C¯1111C¯1111+␴110.͑4͒It is well known that the second-order elastic constant͓C¯1111 in Eq.͑4͔͒changes very little,and that the residual stress ͑␴110͒is relatively small compared to the elastic constants. Therefore,it is the third-order elastic constant͓C¯111111in Eq.͑4͔͒which causes the increase in the acoustic nonlin-earity parameter,␤,during fatigue.Consider a time-harmonic plane͑displacement͒wave A1cos͑kX1−␻t͒,where A1is the amplitude,k is the wave number,and␻is the angular frequency.Assuming that the nonlinearity in the solid is small,the solution to Eq.͑3͒for this time-harmonic wave is obtained by a perturbation analy-sis as13u1=−18␤k2A12X1+A1cos͑kX1−␻t͒+18␤k2A12X1cos͓2͑kX1−␻t͔͒+¯=A0+A1cos͑kX1−␻t͒+A2cos͓2͑kX1−␻t͔͒+¯.͑5͒It is noted that the amplitude of the second-harmonic dis-placement is proportional to the acoustic nonlinearity param-eter and a subharmonic;that is,the static displacement is induced by the material nonlinearity.14The acoustic nonlin-earity parameter is determined experimentally by measuring the absolute amplitudes of the fundamental͑A1͒and the second-harmonic͑A2͒displacement signals,or␤=8A2k2X1A12.͑6͒Finally,note that Eq.͑6͒neglects the effect of attenua-tion losses that may be present in the fundamental and second-harmonic.If the difference in attenuation rates at the fundamental and the second-harmonic frequencies is large, then a correction factor must be included in the measurement of␤.The speciﬁc superalloy examined in this research is IN100,which is produced by powder metallurgy and has a veryﬁne grain structure.Attenuation measurements are made in IN100through the range of1–15MHz before fa-tigue tests.These results show that the attenuations at the fundamental and the second-harmonic frequencies are about0.14Neper/cm and0.34Neper/cm,respectively,which cor-respond to a maximum correction of less than2%in␤.Fur-thermore,the fatigue specimens show no noticeable change in attenuation in the frequency range considered here,so no attenuation corrections are made for the following␤calcu-lations.III.EXPERIMENTAL PROCEDUREA.Measurement system and procedureFigure1shows a schematic of the proposed nonlinear ultrasonic measurement system.A tone burst signal of7–9 cycles͑depending on the specimen thickness͒at5.3MHz is generated by a function generator͑80MHz Agilent33250A͒and is fed into a high-power gated ampliﬁer͑Ritec RAM-10000͒.In order to ensure one-dimensional wave propaga-tion in a single direction͑only right or left propagating͒,the exact number of cycles of the tone burst is selected as the maximum number of cycles that canﬁt within the thickness of the specimen—the spatial length of the tone burst is less than the specimen thickness.This eliminates any possible spurious͑apparent͒higher harmonics generated by the inter-ference of the incident and reﬂected wavefronts,as well as the effects of boundary conditions.The ampliﬁed high-voltage signal passes through a4dB attenuator͑pad͒and a 50⍀termination to suppress the transient behavior due to the mismatch in electrical impedances between the ampliﬁer and the mercial narrow-band PZT͑Lead Zir-conate Titanate͒-base piezoelectric transducers,with center frequencies of5MHz and10MHz,are used as a transmitter and a receiver,respectively.The transducers are coupled to the specimen with light lubrication oil.A specialﬁxture is designed to keep both the transmitting and receiving trans-ducers aligned on the same centerline axis,and to also allow for the removal of either transducer͑transmitter or receiver͒without disturbing the coupling͑and position͒of the other; this capacity is critical for the calibration procedure de-scribed next.The receiver is terminated with a50⍀passive load to have the same terminal load in the calibration.Both voltage and current signals of the transmitted ultrasonic waves are recorded and averaged256times with an oscillo-scope,and then transferred to a computer for further signal processing.Then,diffraction corrections are made to the measured fundamental and the second-harmonic signal am-plitudes.The calibration procedure for the͑piezoelectric͒receiv-ing transducer is based on the principle of self-reciprocity,15 and is employed in order to obtain a conversion transfer function͑from the measured electrical signal to the absolute amplitude of the particle displacement͒,and to compensate for any͑small͒variations in the coupling of the receiving transducer.Note that this calibration is performed prior to every nonlinear measurement,with the transmitter transducer removed.A50MHz pulser/receiver͑Panametrics,5072PR͒is used to transmit͑through the receiver transducer͒a wide-band ultrasonic pulse through the specimen.The current and voltage signals of the incident and the reﬂected pulse from the bottom surface of the specimen that is kept stress-free ͑when the transmitter is removed͒,are measured and used to calculate a transfer function that converts the measured cur-rent signal to the particle displacement of the incident wave at the receiver.15Finally,the pulse-inversion technique16,17is applied to accentuate the contribution of the even͑second͒harmonic signal,while reducing the dominance of the fundamental contribution.The pulse-inversion technique is very efﬁcient in extracting this second-harmonic amplitude by canceling out the odd harmonics͑which are mainly due to the instru-mentation͒;the even harmonic signal is extracted by adding two180°out-of-phase input signals.18Figure2illustrates the pulse-inversion technique by showing both the0°phase,and the180°out-of-phase͑inverted͒signals,the respective Fou-rier spectra before and after addition͑in the time domain͒, and the second-harmonic signal extracted.For the actual pro-cedure,ﬁrst,two transmitted time domain signals with180°out-of-phase inputs are measured consecutively with all other conditions unchanged.A function generator performs phase inversion of the input pulse.Then,two separately mea-sured output signals are combined in the time domain,ex-tracting the second-harmonic signal.Note that this combina-tion is performed with two raw signals without introducing any adjustments,such as time shifts or amplitude modiﬁca-tion.Figure2clearly demonstrates how the fundamental fre-quency contribution is completely canceled out,leaving only the second-harmonic contribution.Note that the remaining subharmonic component͑at zero frequency͒corresponds to theﬁrst term in Eq.͑5͒,and appears as a result of the static displacement induced by the acoustic radiation;this compo-nent should have an amplitude proportional to the amplitude of the second-harmonic,19but it is not systematically ana-lyzed in this study.The frequency spectra of the signal origi-nally transmitted,and the extracted signal shown in Fig.2͑b͒are independently calculated with a rectangular window.Fi-nally,to obtain a more accurate estimation of the amplitudes of the fundamental and second-harmonics,the signals are digitallyﬁltered in the frequency domain and inverse Fourier transformed.An additional advantage of using the pulse-inversion technique is that one can readily monitor the shape of the second-harmonic signal.Since the amplitude of the second-harmonic signal produced by material nonlinearity is very small in comparison to the amplitude of thefundamen-FIG.1.͑Color online͒Experimental setup.tal,small variations in coupling—that are usually accompa-nied by spurious interface nonlinearity—can have a signiﬁ-cant inﬂuence on the repeatability of the proposed measurement procedure.Experience shows that the shape of this second-harmonic signal is an excellent indicator of the quality of the transducer to specimen coupling.Figure 3illustrates the linear relationship that exists be-tween the measured absolute amplitudes of the second-harmonic and the squared fundamental ͑both displacements ͒,as a function of increasing input voltage amplitude.These absolute displacement amplitudes are calculated using the transfer function described previously.Figure 3shows the results of two independent measurements on the same speci-men,where the transducers and the couplant are completely removed,and then reattached and recalibrated for the second measurement.It is seen that the slopes from these two inde-pendent measurements are nearly constant,which conﬁrms that the measurements are repeatable,and that removal andreplacement of the transducers ͑and couplant ͒will not have a dominant ͑negative ͒inﬂuence on the results.The variability ͑error bars ͒due to measurement error is determined by av-eraging ﬁve measurements on the same undamaged speci-men,and results in a variability of ±0.45on all ␤values reported henceforth.Finally,Fig.3can be used as a guide for the required input voltage needed to avoid inconsistencies caused by a low fundamental amplitude.20The measurement system is calibrated by measuring ␤in borosilicate.It is known that borosilicate has a very low degree of nonlinearity,and researchers 21have shown that the ratio of the second-harmonic amplitude to the fundamental amplitude is on the order of −120dB ͑this unpublished ref-erence value illustrates that the ␤of borosilicate is almost zero ͒.A ␤of 9.0is measured in borosilicate using the pro-posed measurement procedure,and this nonzero value of ␤is believed to be associated with the inherent nonlinearity of the transmitting piezoelectric transducers used in the mea-surement system.This is in agreement with previous researchers 22who examined the nonlinear properties of PZT ͑polarized K1͒and measured its ␤to be on the order of 8.0.Therefore,a ␤of 9.0will be used to calibrate the measure-ment system by subtracting this value from all measured ␤values.Although such a calibration method neglects the in-teractions between different frequencies in a nonlinear sys-tem,it can be easily argued that the effects of such interac-tions on ␤are higher ordered.This is further veriﬁed by performing a ␤measurement on fused silica.The directly measured value of ␤for fused silica is 21.0.After calibration ͑subtracting 9.0͒,a ␤of 12.0is obtained for fused silica,which is in agreement with published values.23The good agreement between these results and published values,plus the consistency and repeatability of the results reported in Sec.IV ,validate the accuracy of the proposed procedure as a working method to track changes in ␤as a function of fatigue life in multiple specimens.B.SpecimensThree different types of specimens are used;each type machined from IN100cylindrical rods—128mm longandFIG.2.͑a ͒Typical time domain signals:Thin continuous and dotted lines are the transmitted signals with 0ؠphase ͑uninverted ͒and 180ؠout-of-phase ͑inverted ͒inputs,respectively.The thick line is the second-harmonic signal extracted by the pulse-inversion technique.͑b ͒Fourier spectra of the origi-nal transmitted signal ͑fundamental ͒and the second-harmonic signal ex-tracted by the pulse-inversion technique,demonstrating that the second-harmonic amplitude can be measured without being inﬂuenced by the large fundamentalamplitude.FIG.3.͑Color online ͒Second-harmonic amplitude ͑A 2͒versus the ampli-tude of the fundamental squared ͓͑A 1͒2͔for increasing input voltage ob-tained from two independent measurements.27mm in diameter.Note that the surface ﬁnishes on all specimens in this study are “as-machined.”The ﬁrst type is a standard fatigue specimen with a constant rectangular cross section—a constant gauge width of 12.5mm and a thickness of 6.4mm.One of these specimens is used for the low-cycle fatigue tests,and one is used for the high-cycle fatigue tests.The second specimen has an hour-glass shape ͑starting from a width of 12.5mm and a constant thickness of 6.4mm ͒with a varying cross section that gradually reduces to create a region of higher stress at its center;this specimen is used exclusively for the high-cycle fatigue tests.The third speci-men is a nonstandard rectangular bar specimen;it is simply a 120mm long by 14.3mm wide rectangular bar—having a constant thickness of 4.7mm.This specimen is used for both the monotonic and low-cycle fatigue tests,and for a concur-rent set of Rayleigh wave measurements.24IV.EXPERIMENTAL RESULTS AND DISCUSSION A.Monotonic load resultsFirst,consider a quasi-static monotonically loaded ͑non-standard rectangular bar ͒specimen.This specimen is used to validate the repeatability of a set of nonlinear ultrasonic mea-surements made on a specimen subjected to an interrupted mechanical test—a test specimen that is mechanically loaded,removed to make a set of nonlinear ultrasonic mea-surements,and then the procedure is repeated at speciﬁed intervals,typically until the specimen fails.In this monotonic test,the specimen is loaded ͑at a rate of 890N/s ͒to a ﬁrst-load equivalent to 125%of the yield stress ͑absolute strain of 7.463%͒,and then is unloaded at the same rate.The nonlin-ear ultrasonic measurements are then performed on the un-loaded specimen.The same procedure is repeated for in-creasing maximum loads equivalent to 135%and 145%of yield stress ͑strains of 10.66%and 13.77%,respectively ͒.These calibrated results are presented in Fig.4,and note that these measured acoustic nonlinearity parameters,␤,are ab-solute values.It is important to note that the ␤value of 23.1—measured in the undamaged specimen ͑before anymechanical load is applied ͒—is a measure of the intrinsic nonlinearity of the undamaged IN100material;and that the nonlinearity associated with the transmitting piezoelectric transducers ͑␤=9.0͒has already been subtracted from this and all other values.Figure 4shows that there is a signiﬁcant increase in ␤with increasing plastic stress;the increase is largest from the unloaded ͑undamaged ͒state to 125%yield stress,and then the increase is less substantial at the higher stresses.This observed behavior of a large increase in the acoustic nonlinear parameter,once the specimen is loaded above its yield stress,makes sense because dislocations ͑or microplasticity ͒create signiﬁcant material nonlinearity;the literature reports that the second-͑order ͒harmonic ampli-tudes associated with dislocations should be larger than the intrinsic material nonlinearity due to the elastic lattice anharmonicity.25Most importantly,the results in Fig.4show that the proposed measurement procedure is capable of mak-ing an absolute measurement of the evolution of the acoustic nonlinear parameter,␤͑as a function of stress in this case ͒in these interrupted mechanical tests on an IN100specimen.B.Low-cycle fatigue resultsLow-cycle fatigue in this paper refers to a fatigue test where the maximum stress is above yield,so there is plastic deformation even at the beginning of the fatigue test.Of equal importance is that cyclic loading promotes the forma-tion of dislocation dipoles,which is the strongest source of nonlinearity among a list of potential sources.6,9,10The fre-quency of cyclic loading is 0.5Hz,R ͑=␴min /␴max ͒is zero ͑strain controlled ͒,the maximum stress level is 105%of the yield stress ͑strain of 0.48%͒,and the fatigue tests are inter-rupted to perform the nonlinear ultrasonic measurements at different numbers of fatigue cycles.Three different speci-mens are tested,and there will be some level of variability associated with the initial microstructure of each specimen.As a result,the measured acoustic nonlinearity parameters will be normalized by the value measured in each undam-aged specimen ͑␤0͒,before any mechanical load is applied.This normalization procedure ͑which will be repeated for the high-cycle fatigue results ͒removes some of the variability associated with the initial microstructures of each specimen,enables a direct comparison of the evolution of the acoustic nonlinearity of all the specimens tested,and normalizes the nonlinearity associated with the transmitting piezoelectric transducers.The evolution of the normalized acoustic non-linearity parameter ͑␤/␤0͒,as a function of normalized fa-tigue life ͑fatigue cycle normalized to the total number of cycles,where 100%means the total fatigue life ͒,together with a best-ﬁt curve,is shown in Fig.5.Note that the speci-mens failed at 12,640,13,012,and 50,221cycles ͑the third specimen is the standard fatigue specimen;while the ﬁrst two are the nonstandard rectangular bars ͒and the ͑calibrated ͒␤0measured in each specimen is 21.4,22.2,and 22.4,re-spectively.Figure 5shows a rapid increase in ␤/␤0͑up to 30%͒during the ﬁrst 40%of fatigue life,which demonstrates that these nonlinear ultrasonic measurements can be used to quantitatively characterize the damage state of thismaterialFIG.4.͑Color online ͒Monotonic load results—acoustic nonlinearity pa-rameter ␤versus applied stress ͑or strain ͒level.in the early stages of fatigue life.This is somewhat different from other experimental results,5which show a slower initial increase in ␤.The difference in behavior is most likely due to the high maximum stress ͑strain ͒level beyond the yield stress ͑strain ͒,and a signiﬁcant amount of plasticity—due to the dislocation motions—probably starts accumulating in the specimen from the ﬁrst loading cycle,which reduces the time period for dislocation reassociation at the beginning of fatigue.The measurement data show increasing scatter with increasing number fatigue cycles,which is most likely due to a combination of two factors:The intrinsic material behavior,and issues with the measurement procedure.There is an in-herent randomness in the progression of fatigue damage dur-ing fatigue testing ͑more so in high-cycle fatigue,as dis-cussed in the next section ͒,which should manifest itself as a corresponding randomness in the resulting acoustic nonlin-earity.There is a somewhat unrelated issue with the measure-ment procedure in the later stages of fatigue—the surface deformation associated with the increased plasticity makes it difﬁcult to consistently couple the transducers to the speci-men surface.Finally,note that a best-ﬁt curve,such as the one developed in Fig.5͑but based on a larger number of specimen and data points ͒,has the potential to serve as a master curve for life prediction based on nonlinear ultrasonic measurements.A companion study makes nonlinear ultrasonic measure-ments with Rayleigh surface waves on the ﬁrst two speci-mens;the procedure used to make these ͑relative ͒nonlinear Rayleigh wave measurements is reported elsewhere.24Figure 6shows a comparison of the best-ﬁt curve from Fig.5͑lon-gitudinal waves ͒with those from the nonlinear Rayleigh wave measurements.There is excellent agreement with these two sets of results,demonstrating that both longitudinal and Rayleigh waves can be used to track nonlinear material be-havior.Note that the sharp drop in the acoustic nonlinearity ͑the single data point in Fig.6͒,at 87%of fatigue life forSpecimen No.1,is most likely due to the emergence of surface-breaking microcracks whose depths are larger than the wavelength of the second-harmonic.24C.High-cycle fatigue resultsHigh-cycle fatigue in this study refers to fatigue tests where the maximum stress level is below yield;in this case,the maximum stress is 95%of yield stress,the frequency of cyclic loading is 1Hz,and R ͑=␴min /␴max ͒is zero ͑load controlled ͒.Five different fatigue specimens are tested,with failure occurring at 55,432,102,392,203,220,328,341,and 350,985cycles.As with the monotonic and low-cycle fatigue tests,these fatigue tests are interrupted to perform the non-linear ultrasonic tests.Figure 7shows the change in the nor-malized acoustic nonlinearity parameter ͑␤/␤0͒over the nor-malized fatigue life of each specimen.Note that the ͑calibrated ͒␤0measured in each specimen is 22.1,21.3,19.8,22.4,and 21.2,respectively.FIG.5.Low-cycle fatigue results—normalized acoustic nonlinearity param-eter ␤/␤0as a function of the percentage of fatigue life for three different fatigue specimens.The continuous line is the best-ﬁt curve obtained from the discrete experimentaldata.parison of longitudinal and Rayleigh wave ͑Ref.24͒results showing the normalized acoustic nonlinearity parameter ␤/␤0as a function of the percentage of fatigue life for the low-cycle fatigueresults.FIG.7.High-cycle fatigue results—normalized acoustic nonlinearity param-eter ␤/␤0as a function of the percentage of fatigue life for ﬁve different fatigue specimens.The continuous line is the best-ﬁt curve obtained from the discrete experimental data.。

无损探伤英汉对照

NDT 英汉无损检测词汇abortion ---n.故障｀失灵｀失事abortive----v.失败abruption n 裂断｀中断。

断路absolute adj 绝对的｀纯粹的absolute sensitivity 绝对灵敏度absolute value 绝对值absorb 吸收`减震absorbance 吸收absorb dose 吸收计量absorbent 吸声材料，吸收体。

吸收性的。

Abutment joint 平接缝`对接缝。

对接。

AC yoke demagnetization 交流磁轭去磁，交流磁轭退磁AC yoke magnetization 交流磁轭磁化。

accept n 接受acceptable defect level 缺陷合格等级。

Acceptable emergency dose 容许的事故计量。

acceptable quality level(AQC)指验收等级，象指验收表准。

acceptance 接收，验收。

认可，肯定Acceptance certificate 验收证明书Acceptance criterion 验收准则` 验收Accessory device 辅助装置Accessory equipment 附属设备Accident 偶然事故，偶然损伤。

Accident condition 事故情况Accident error 偶然错误。

Accident prevention 安全措施Accidental exposure 偶然曝光Accidental radiation injury偶然辐射伤害。

Accumulate dose 总剂量，累计剂量。

Accumulator battery 蓄电池Accumulator cell 蓄电池Acetic acid 醋酸，乙酸。

ACDS（acoustic crack detection system）声裂纹检测系统，声裂纹检测装置，声裂纹检测仪。

道岔术语中英文对照

道岔术语中、英文对照中文名称英文对照一、道岔turnout道岔和交叉turnout and crossings单开道岔simple turnout对称道岔bilateral turnout三开道岔symmetrical double turnout/three-throw turnout/tandem turnout 菱形交叉diamond crossing交分道岔slip switch复式交分道岔double slip switch单式交分道岔single slip switch单渡线Single crossover渡线Crossover交叉渡线scissors crossover套线overlapping of lines套线道岔mixed gauge turnout左开道岔Left hand turnout右开道岔right hand turnout高速道岔high-speed turnout提速道岔speed-up turnout普速道岔conventional turnout二、转辙器Switch可弯式尖轨转辙器flexible switch间隔铁式尖轨转辙器loose heel switch转辙角switch angle三、导曲线（连接部分）lead curve四、辙叉Frog高锰钢（整铸）辙叉solid manganese steel frog钢轨组合辙叉bolted rigid frog可动心轨辙叉movable-point frog钝角辙叉obtuse frog锐角辙叉end frog曲线辙叉curved frog辙叉角frog angle辙叉号数frog number辙叉心轨理论尖端theoretical point of switch rail辙叉趾端toe end of frog辙叉跟端heel end of frog辙叉趾长toe length of frog1/10辙叉跟长heel length of frog辙叉趾宽toe length of frog辙叉跟宽heel length of frog辙叉咽喉throat of frog五、轨件Rail基本轨stock rail直基本轨straight stock rail曲基本轨curved stock rail尖轨switch rail直线尖轨straight switch rail曲线尖轨curved switch rail护轨guard rail ，check rail翼轨wing rail心轨point rail ， nose rail异形轨compromise rail矮形轨flat-web-section rail特种断面钢轨special section rail长心轨long point rail短心轨short point rail导轨guide rail/closure rail淬火轨quenched rail绝缘轨insulated rail可动心轨swing nose rail无缝钢轨continuous welded rail（CWR）轨缝joint gap钢轨接头rail joint绝缘接头insulated joint胶结接头glued joint焊接接头welded joint冻接接头frozen joint异形接头compromise joint六、板件Plate轨撑垫板tie plate of rail brace接头平垫板joint flat tie plate辙跟垫板switch heel tie plate支距扣板offset fastening plate垫板tie plate七、轨枕Sleeper木枕wooden sleeper混凝土枕concrete sleeper2/10岔枕switch sleeper八、零部件Components工件workpiece易损件wear parts备件spare parts扣件rail fastenings弹条Clip弹性扣件elastic rail fastenings尖轨补强板reinforcing bar轨撑rail brace支撑块support block支座条bearer strap低紧扣件low restrain fastening道钉track spike间隔铁filler限位器position-limited device滑床板slide plate鱼尾板Fishplate道岔拉杆switch rod ， stretcher bar道岔连杆connecting bar ， following stretcher bar钢轨伸缩调节器expansion joint导电销conductive pin调整楔adjusting wedge辙跟内轨撑rail brace inside of switch heel辙跟外轨撑rail brace outside of switch heel双头螺柱double head bolt轨距块gauge block调整片adjustment shim长方头螺栓rectangle head bolt接头夹板fish plate ， joint bar接头螺栓fish bolt ， tract bolt螺纹道钉screw spike轨撑rail brace补强板reinforcing bar顶铁Iron/stud/Distance block调整片adjustable shim绝缘垫片insulated shim轨距块是扣轨肢的，顶铁是顶轨腰的，间隔铁一般是和钢轨轨头下颚和轨肢上颚相接触的。

Damage tolerance and classic fatigue life prediction of a helicopter main rotor blade

Damage tolerance and classic fatigue life prediction of a helicopter main rotor bladeA.R.Shahani .S.MohammadiReceived:25April 2015/Accepted:24November 2015/Published online:30November 2015ÓSpringer Science+Business Media Dordrecht 2015Abstract Fatigue life of the main rotor blade of a helicopter is investigated from two different approaches.The blade is comprised of many different parts such as spar,skin,abrasive strip,doublers,box beam doublers,etc.and it undergoes complex random load spectra.A ﬁnite element analysis is carried out to assess the stress distribution in the blade parts.Then,using the Miner’s rule the fatigue life of the blade is calculated following a classic life estimation method under random loading.At the next step,damage tolerance approach is used for life estimation of the blade.Fatigue crack growth properties and threshold stress intensity range of the spar is obtained based on ASTM E647test method.Then,crack growth analysis is done using Zencrack software.In order to calculate the length of the smallest growing cracks and their fatigue crack growth life,no crack growth and slow crack growth approaches are used.A comprehensive investigation is carried out on the effect of initial crack length and aspect ratio on growth or no growth of paring the obtained fatigue life from two different approaches,some conclusive results are drawn.Keywords Helicopter fatigue life ÁBlade lifeestimation ÁDamage tolerance ÁFracture mechanics ÁFatigue crack growth1IntroductionEurocopter investigations about helicopter accidents show that 77%of accidents occur by environmental factors and usage,17%is due to maintenance errors and 0.3%is due to poor design [1].The results of comprehensive review of the failure investigations carried out within Agusta Westland over the last 30years show that fatigue accounts for approximately 55%of all failures in helicopter components [2].In a military helicopter crash investigated by Amura et al.[3],one of the blades had been separated in the air.Visual examination of the fracture surface of the blade indicated fatigue crack growth followed by ductile overload separation.Wanhill et al.[4]discussed ﬁve helicopter accidents with evidence of material and/or design deﬁciencies.It was concluded that most of helicopter accidents are due to problems concerning ﬂight operations,ground duties (mission planning and preparation),training and instructions.Design of helicopters against fatigue phenomenon is a particularly important and complex problem,due to the peculiar load spectra,composed by a high number of low-amplitude cycles [5].In order to calculate fatigue life of the helicopter parts three factorA.R.Shahani ÁS.Mohammadi (&)Department of Applied Mechanics,Faculty of Mechanical Engineering,K.N.Toosi University of Technology,Pardis Street,Mollasadra Avenue,Vanak Square,P.O.Box 19395-1999,Tehran,Iran e-mail:mec.mohammadi@Meccanica (2016)51:1869–1886DOI 10.1007/s11012-015-0339-1should be recognized[6].Theﬁrst factor is the fatigue strength of the part,the second one is the expected loading and stresses and the last factor is the frequency of occurrence of these loads and stresses.Deﬁning the ﬂight loads accurately is impossible at theﬁrst step and therefore previous loading information are completely important for design purpose.The fatigue design methodology most commonly applied by the helicopter community is based on the safe-life philosophy[7].In the safe life approach the aim is to ensure that crack initiation does not happen during the service life of the structures[8].In this method,S–N curves are used as basic tools.These curves are derived by using test specimens under constant amplitude loading[9].Safe life approach uses a cumulative damage model such as Miner’s linear cumulative damage rule[10]in order to predict a safe period of performance[11].In the paper presented by Och[12],a short investigation about successful fatigue life prediction methods in MBB model heli-copter,considering its dynamic parts,is done.Three steps are considered for predicting fatigue life of the helicopter parts:loads prediction,fatigue strength and applying damage hypothesis in order to relate two previous steps.In the paper presented by Wolfe et al.[13],test and fatigue criteria requirements for United States heli-copters were described emphasizing dynamic parts. For dynamic parts,the army considered safe life method for test and veriﬁcation.Miner’s rule and army special spectrum loading was applied for calculating life.The minimum required life for the helicopter dynamic parts was considered to be4500–5000h.Alli [14]presented some of the helicopter design require-ments in his article.For example,safe life designed parts should have a minimum life of5000h or if the main parts of the helicopter is damaged due to projectile impact,they should have the capability of sustaining that damage at least for30min.Baraniecki and Kaniewska[15],presented a methodology for predicting fatigue life of a structural element of MI-24 helicopter(swash plate lever arm)with the aid of strain gauges,which were used to deﬁne the realﬂight loads. Estimation of the fatigue life was done with the aid of MSC fatigue computer program and according to the Palmgren’s–Miner’s cumulation damage rule.In1980,a research has been done on a helicopter pitch link using the safe life approach.Due to large scattered lives obtained by different researchers for the same problem,using other fatigue life analysis methods was felt more necessary.In the same year, the United States Army presented a criteria which has required the six nine(0.999999)reliability for dynamic parts of helicopter during its design and application life.In1983,Sikorsky has signed a contract with United States air force for HH-53 helicopter structures fatigue analysis by damage tolerance approach[16].Since1989the Airworthiness Regulation evolved towards the application of Dam-age Tolerance principles to rotorcraft.Under the impulse of the FAA,the regulatory change to FAR 29.571[8]was approved in1989(Amdt.29-28), requiring tolerance toﬂaws and damages and opening the way to the application to rotorcraft of the Damage Tolerance(DT)design philosophy.According to FAR 29.571,helicopter fatigue analysis should be done by one of the damage tolerance,ﬂaw tolerance or fail-safe approaches.Applying damage tolerance approach to helicopter dynamic components is highly desirable but is more difﬁcult compared to aircraft structures[17].One reason is the number of degrees of freedom of helicopter which enables it toﬂy and the other is rapid accumulation of loading cycles[3].Rotor components are subjected to a load spectra dominated by many high R-ratio low-amplitude cycles,inter-spersed with a number of low values minima(start stop cycle).Standard load sequences have also been deﬁned,like Helix and Felix[18],Rotorix[19]and Asterix[20].Accumulation of cyclic loads is hap-pened at such a high rate that fracture mechanics techniques must be applied to very small initialﬂaws to obtain acceptable in-service inspection intervals [21].High-strength materials used in the available designs is the next problem.This kind of materials usually has a good performance for safe life design but they may not have desirable characteristics of fatigue crack growth[22].In addition,high-strength materials are often sensitive to corrosion fatigue and stress corrosion cracking[23].In a helicopter design,if a good procedure is taken,it is possible to have a combination of components which some of them are designed by the safe life method and the others by the fracture mechanics approach[24].In the article presented by Forth et al.[25],different fatigue life methods were tested and assessed for fatigue design and maintenance of a hypothetical axes clamp of a helicopter.Theﬁnal result was that damagetolerance design method is applicable for the heli-copters.Lincoln et al.[26],investigated results of damage tolerance analysis of HH-53helicopter per-formed by Sikorsky.In this article,initial ﬂaw length were considered to be 0.254mm.But,for some components,despite choosing 0.127mm for initial ﬂaw length,inspection intervals were very short.In the article presented by Everett and Elber [27],for computing total fatigue life by a crack growth analysis,it was considered that a very small initial crack (0.001–0.050mm)does exist in the test coupon.It was shown that performed analysis predicts the total fatigue life of 4340steel test coupon under constant amplitude and Felix/28helicopter standard load spec-trum with good accuracy.Shaniavski [28]investigated fatigue crack growth of aluminum longerons of Mi-8helicopter rotor blades during the operation.Meso-beach-marks were used to estimate the fatigue crack growth period in one of the damaged longerons with the least crack size.Cook et al.[29]investigated the capabilities of existing crack growth models for predicting crack growth behavior in two different materials which are used in helicopter industry using test specimens and different loading sequences.One of the conclusions that were drawn was that predictions for helicopter loading sequences tests are very sensi-tive to small changes in the crack growth near threshold data.In the article presented by Forth et al.[30],capability of application of damage tolerance approach to dynamic systems was evaluated by performing a simple variability study on damage tolerance of a helicopter rotor pitch link using NASGRO 4.11code.Effect of different parameters uncertainty on compo-nents damage tolerance was investigated.It was concluded that in dynamic systems,loading sequence has the highest effect on damage tolerance manage-ment.In the article presented by Citarella and Apicella [31],a probabilistic foundation of damage tolerant design for metallic aircraft structures was developed.Giglio et al.[32]applied no crack growth method to a helicopter tail rotor hub.In this method,if stress intensity factor of no growth cracks under external variable load can be determined and also threshold stress intensity factor range (D K th)for the same cracks can be calculated,safety factor against crack growthcould be obtained from g ¼D K thD K .In order to apply the above-mentioned method to the tail rotor hub,a 0.2mm radius length defect was considered in theplace of maximum stress and perpendicular to the maximum principal stress direction.The obtained safety factor for three considered loading condition were more than unity.So,the analyzed component,with considered hypothetical ﬂaw was in a safe condition.Agusta Westland [33]applied ﬂaw toler-ance methods to AB139two engine helicopter,successfully and complete conformity with FAR 29.571[8]standard were obtained.For metal dynamic parts,no crack growth method was used to conﬁrm ﬂaw tolerance strength of these parts in addition to safe life approach.For four components of ﬁve evaluated parts in Adams article [34],it was concluded that classic slow crack growth damage tolerance method lead to very short inspection intervals or its application is more complicated in comparison to ﬂaw tolerance method.One of the results that was obtained in the test and analysis program used for EH-101helicopter fuselage damage tolerance evaluation,were that because of very short and disappointing inspection intervals,ﬂaw tolerance approach is more suitable for main loading path of the EH-101helicopter,in comparison to damage tolerance approach [35].In this article,fatigue life of a helicopter main rotor blade is analyzed by the safe-life and damage toler-ance approaches.At the ﬁrst step,the blade model was created considering all of its details.32parts were modeled and then connected together to form the blade complete model.After that,all the forces applied to the blade were calculated in hover situation and applied to the blade to obtain the stresses.Then,stress analysis was made and stress spectrum was derived for each main part of the blade using standard load spectrum,Felix.At the next step,the blade fatigue life was calculated using a classic life estimation method considering Miner’s rule.Then,fatigue crack growth properties and threshold stress intensity range of the blade spar was obtained based on ASTM E647test standard.Finally,crack growth analysis for the main parts of the blade was done by using Zencrack software.In order to calculate the length of the smallest growing cracks and their fatigue crack growth life,no crack growth and slow crack growth approaches were used.A comprehensive investigation was carried out on the effect of initial crack length and aspect ratio on growth or no growth of cracks in the spar and skin of the blade.For the growing initial cracks,fatigue crack growth life and inspectionperiods were obtained for different aspect ratios.The fatigue lives of the spar and skin derived from different methods were compared together and some conclusive results were drawn.2Finite element analysis of the bladeIn this part,ﬁnite element modeling of the helicopter rotor blade is carried out and the results are presented.2.1Finite element modeling of the helicopterrotor blade Blade modeling was carried out using ABAQUS/6.10software in a three-dimensional manner considering all of its details.32parts were modeled and then connected using merge technique to form the blade complete model.The created model for the helicopter rotor blade is shown in Fig.1.The main load bearing part of the blade is the spar which is made from an aluminum alloy.There are 14doublers near the blade root in order to increase its strength in this region.In order to prevent the blade abrasion,a steel abrasive strip is installed on the leading edge of it.In the core of the blade,honeycomb structure is used,which despite of low weight,it causes a signiﬁcant bending strength increase in the blade.In addition,it plays an important role in impact energy absorption.The blade compo-nents are shown in Fig.2.The blade complete model was meshed using tetrahedral elements.The number of elements of the complete model is 995,480elements.At the blade root,all degrees of freedom of the nodes which areattached to the shaft and the grip pad was restricted.Effect of the blade rotation was applied to the blade in terms of centrifugal load.One of the most important tasks during structural analysis and fatigue life estimation of each component is computing loads as accurate as possible.The loads which act on the helicopter rotor blade are divided into two groups [36]:the loads which act vertically on the blade,and the loads which act along the blade length.Vertical loads consist of aerodynamic loads,blade weight,normal inertia loading due to vertical accel-eration,aerodynamic losses which come from blade ﬂapping and its curvature and structural losses which is a function of mechanical and blades material characteristics.The load which acts along the blade length (horizontal load)is centrifugal force.In this article,for obtaining lift distribution along the blade length,the combination of momentum theory and blade element theory was used.In order to obtain the loads of the blade,the following steps were considered:1.The distribution of angle of attack along the blade length,which is needed for the helicopter to remain in the hovering mode,were obtained using a Matlab code.Vertical drag force effect and blade tip losses were considered during this procedure,too.2.The blade was divided into 10elements in its longitudinal direction and considering the distri-bution of the angle of attack obtained in the previous step,the pressure distribution on each element was obtained.3.A centrifugal force was applied to the blade along its longitudinaldirection.Fig.1The helicopter rotor blade model created in abaqus4.The weight force was applied to the blade,deﬁning the acceleration of gravity in proper direction.2.2Finite element resultsIn this part,the results of the blade ﬁnite element analysis are presented.The maximum deformation of the blade for the 6.69m length blade of rotational speed of 294rpm was obtained to be 18.29cm in hover mode which occurs at the blade tip.In order to obtain more accurate results for the stresses,sub-modeling technique was used.In fact,a sub-model was extracted from the blade in the region near the critical zone of stress in such a manner that the cut boundaries do not affect the stress distribution inside the sub-model.The result of the stress analysis of the blade and the sub-model location is shown in Fig.3.The sub-model was cut from the critical region of the blade where highest stresses occur.The considered sub-model and the related ﬁne mesh are presented in Fig.4.Stress analysis of the sub-model is presented in Fig.5.For each main load bearing part of the blade,the distribution of different stress components in their critical point was investigated.The point of maximum Von-Mises stress was considered to be the critical point for each blade part.The magnitude of differentcomponents of stress at the critical point of the blade parts are presented in Table 1.In Table 1,Smises is the Von-Mises stress and Sprincipal,max is the principal stress.S11,S22and S33are the normal stress components and S12,S13and S23are the shear stress components.As it is clear from Table 1,the normal stress in the longitudinal direction of the blade (S33)is much more than the other stress components.3Helicopter blade fatigue analysis from the classic approach In this part,helicopter blade fatigue life is calculated from the classic approach.The fatigue life was calculated adopting a three dimensional method.In the mentioned method,Von-mises stress was used for obtaining stress spectrum and calculating fatigue life of the blade.In the other words,in three dimensional method,considering the von-mises stress in hover situation and using the stress spectrum which is presented in Felix,the stress spectrum of the blade was obtained.Then,using this stress spectrum,the fatigue life was calculated applying the following procedure.As mentioned before,blade stress analysis is done for hover situation and in order to obtain the magni-tude of stress corresponding to differentmissionsFig.2Main load bearing parts of the bladeFig.3Stress analysis of theblade and the sub-modellocationFig.4The considered sub-model in the critical regionof the bladeFig.5The results of sub-model stress analysisTable1Maximum value of the stresses at the helicopter blade parts(MPa)S11S22S33S12S13S23 Part name Smises Sprincipal,max1Box beam102.5102.50.96 2.5298.8 1.271017 2Skin133.1125.8-1.8-0.5114.80.1537.3 2.7presented in Felix for blade parts,the magnitude of Felix mean stresses and stress amplitudes should be multiplied byr Hover ðÞactual r ave ;Hover ðÞFelix.Fatigue life relationships areusually presented for completely reversed stress.The completely reversed equivalent stress (r ae )corre-sponding to a stress state with mean stress of r m and stress amplitude of r a is a stress that gives the same life as that stress state and can be obtained as:r ae ¼r a1Àr mutð1ÞIn order to obtain fatigue life at a deﬁned stress state,Basquin’s equation is employed [38]:r ae ¼r 0f 2N f ÀÁbð2Þin which,r ae is an equivalent completely reversed stress corresponding to stress state (r m ,r a ),2N f is the number of stress ranges before failure,r 0f is the fatigue strength coefﬁcient and b is the fatigue strength exponent.The most important components of the blade are the spar and skin and in this article,fatigue lives are calculated for these parts.Von-Mises stress distribu-tion of the spar is shown in Fig.6.Maximum Von-Mises stress location in the spar is near the blade root and its magnitude is 102.5Mpa.Spar is made from AA 2014T6which is one of the most commonly used metals in aerospace industry.For this alloy,fatigue strength coefﬁcient and fatigue strength exponent are 776MPa and -0.091,respec-tively [37].In order to calculate fatigue life of the spar,Miner cumulative rule [10]is used.At ﬁrst,for eachstress state of (r m ,r a ),an equivalent completely reversed stress is calculated,using Eq.(1).Then,the life corresponding to the obtained equivalent com-pletely reversed stress (N)is calculated using Eq.(2).Now,if,for example,the number of cycles which is applied to the blade at a speciﬁed stress state in the stress spectrum is n ,its corresponding fraction of damage can be calculated as:D ¼n Nð3ÞFinally,the number of cycles which makes the summation of the fraction of damages equal to one would be reported as the fatigue life [38].Von Mises stress is the stress component which is used during the life calculation.Similar procedure that was considered for calculating fatigue life of the spar was assigned for the blade skin,too.The fatigue life of the spar and skin is calculated by using a Matlab code and the results are presented in Table 2.To obtain the fatigue life in terms of ﬂight hour,considering that the blade rotation velocity is 294rpm,we have:life h ðÞ¼life cycles ðÞ294Â60ð4Þ4Fatigue crack growth modeling of the helicopter blade In this part,fatigue crack growth modeling of the blade is presented.In this article,crack growth analysisisFig.6Von Mises stress distribution in the sparperformed assuming linear elastic fracture mechanics (LEFM),and load interaction effects are neglected.Felix standard load spectrum [18]is used in this analysis.4.1Crack growth modeling of the sparIn this part,at ﬁrst,fatigue crack growth properties of the spar are obtained using the tests.Then,the smallest crack which can grow in the spar is investigated and fatigue crack growth analysis is carried out using Zencrack software [39].Zencrack is a 3D crack analysis tool able to read in an uncracked ﬁnite element model and to produce a cracked ﬁnite element model.Stress intensity factors are calculated automat-ically from the results of the cracked ﬁnite element analysis.Some of the previous researches ([40,41])have used Zencrack for simulating crack propagation and obtaining fatigue crack growth life.4.1.1Material characterizationIn this part,fatigue crack growth properties and threshold stress intensity range of the spar is obtained conducting tests according to ASTM E647standard [42].The tests are performed using compact tension (CT)specimens with sharp pre-cracks produced by fatigue cycling.The main test is performable in k-increase and k-decrease methods.In k-increase method,the load amplitude is kept constant during the test and stress intensity value is increased due to increasing the crack length.This method is properwhen dadN !10À8m =cycle.In the k-decrease method,stress intensity value is decreased during the test by continuous or step by step decreasing the load.In thecase of dadN 10À8m =cycle,k-decrease method is good.In order to obtain fatigue crack growth proper-ties (Paris constants)of the spar,k-increase method is used,and,threshold stress intensity range of the spar is obtained by the k-decrease method.In Fig.7,bladeparts and the CT specimen which was cut from the spar are shown.Figure 8shows the CT specimen during the test.In order to obtain fatigue crack growth properties of the spar,three specimens were cut from it and were tested.The results of the performed tests are shown in Fig.9.As it is clear,the test results are in good agreement with each other.Fatigue crack growth properties (Paris constants)of the spar (m ,C )were obtained to be (3.41,5.6e -11).Because the load ratio of more than 90%of the applied loads in Felix is 0.5,the tests were conducted in the mentioned load ratio.In the next step,for obtaining the threshold stress intensity range of the spar,k-decrease test method was performed.This procedure was started by cycling at a D K and Kmax level equal to or greater than the terminal precracking values.Subsequently,forces were decreased in a blockwise manner as the crack grows,and test data were recorded until the lowest D K or crack growth rate of interest was achieved.TheTable 2Calculated fatigue life of the spar and skin from the three dimensional classic approachFatigue life (cycles)Fatigue life (h)Spar 6.145e09348,344Skin1.361e087718Fig.7Blade parts and the CTspecimenFig.8CT specimens during the testreduction in P max of adjacent force blocks shall not exceed 10%of the previous P max .Based on ASTM E647[42]test method,the best-ﬁt straight line from a linear regression of log da/dN versus log D K using a minimum of ﬁve da/dN,D K data points of approxi-mately equal spacing between growth rates of 10-9and 10-10m/cycle should be determined.D K -value that corresponds to a growth rate of 10-10m/cycle using the above ﬁtted line is deﬁned as D K th (threshold stress intensity factor)according to the operational deﬁnition of the ASTM E647[42]test method.Stress intensity range versus crack length is shown in Fig.10.As is shown,the stress intensity range is increased in each constant load block because of crack growth.The threshold stress intensity factor of the spar was calculated from the test to be2:94MPa ﬃﬃﬃﬃm p .4.1.2The crack growth threshold in the spar Initial crack was considered to be a semi elliptical crack and was put at the critical point of the spar which has the maximum principal stress (Fig.11).The crack faces were considered to be perpendicular to thelongitudinal direction of the blade which corresponds to the maximum principal stress direction,too.For each initial crack length,different aspect ratios were considered and the effect of the aspect ratio on the crack growth was investigated.Aspect ratio (AR)is the ratio of the crack depth to its surface half-length.Zencrack calculates the stress intensity factor at each step of crack growth.The obtained stress intensity factors corresponds to hover ﬂight mode (K hover ),because the ﬁnite element analysis was performed for hover situation.For the helicopter blade in the critical ﬂight situation (autorotation)the mag-nitude of the stresses changes between 2.778and -0.56times the hover stresses [18].So,the largest stress intensity factor range of the blade could be obtained as:D K max ¼K hover Â2:778À0ðÞ¼2:778K hoverð5ÞIn autorotation,the lowest limit of stress intensity factor was considered to be zero,because the load ratio is negative.The length of the smallest crack which may grow was obtained by equating Eq.(5)with the spar threshold stress intensity factor (D K th).The spar is made from 2014Temp T6aluminum alloy and its threshold stress intensity factor was obtained to be2:94MPa ﬃﬃﬃﬃm p .So,we have:D K max ¼D K th !2:778K hover ¼2:94!K hover¼2:942:778¼1:058MPa ﬃﬃﬃﬃm p Now,using Zencrack results,it should be checked which cracks in the spar produce a stress intensityfactor equal to or more than 1:058MPa ﬃﬃﬃﬃm p .Different initial crack lengths,2c i ,in the range of 0.2–1mm with various aspect ratios were considered and in each case growth or no growth of them were investigated.The obtained results for investigating growth or no growth of different initial cracks in the spar is presented in Fig.12.As can be seen,for initial crack lengths lower than 0.2mm,crack growth does not occur,regardless of the aspect ratio (considering that the autorotation maneuver is happened).For larger initial cracks,growth or no growth of the crack depends on the aspect ratio.As an example,for a 0.3mm initial crack,growth occurs when the aspect ratio is equal to or greater than 0.65.Autorotation maneuver is rarely happened for helicopters.So,growth or no growth of the cracks should be checked based on the other criticaly = 3.4139x -10.252-7.7-7.5-7.3-7.1-6.9-6.7-6.50.830.93 1.03l o g (d a /d N )Log (Dk)test1test2test3the ﬁƩed lineFig.9The results of the performed tests on the spar。

Damage tolerance approach for probabilistic pitting corrosion fatigue life prediction

Damage tolerance approach for probabilistic pittingcorrosion fatigue life predictionPan Shi,Sankaran Mahadevan *Department of Civil and Environmental Engineering,Vanderbilt University,Box 6077-B,306Jacobs Hall,Nashville,TN 37235,USAReceived 27December 1999;received in revised form 20August 2000;accepted 5October 2000AbstractThe fatigue damage process induced by pitting corrosion is composed of seven stages:pitting nucleation,pit growth,transition from pit growth to short crack,short crack growth,transition from short crack to long crack,long crack growth,and fracture.A comprehensive mechanics-based probabilistic model for pitting corrosion fatigue life prediction by including all the seven stages is presented in this paper.An analytical ®rst-order reliability method (FORM)and Monte Carlo simulation are implemented with the proposed model.Probabilistic sensitivity analysis is performed using the analytical FORM approach as well as through parametric studies.A numerical example is implemented for the application of the proposed method for the corrosion fatigue life prediction of aluminum alloys.The cumulative dis-tribution function of the fatigue life is obtained and the e ect of several important random variables and their scatter on the fatigue life estimation is investigated.Ó2001Elsevier Science Ltd.All rights reserved.Keywords:Corrosion;Pitting;Fatigue;Crack growth;Damage;Life prediction;Probability;Reliability1.IntroductionIn recent years,a number of research studies have been conducted worldwide in the ®eld of aging aircraft and their attendant problems.In 1991,statistics showed that 31%of the US ¯eet exceeded the design goals and that by the year 2000,about 60%of the worldwide ¯eet of US manufactured aircraft would be 20or more years old.It is therefore necessary to re-evaluate the service life of the large ¯eet of aging aircraft based on their condition and service environment.There are three di erent approaches for ensuring the safety of an aircraft structure.The ``safe-life''approach requires that the component be safe under the prescribed load for a given number of service cycles.The ``fail-safe''approach requires that the entire structure be capable of damage without cata-strophic failure of the entire structure.The ``damage tolerance''approach assumes that the structure contains an initial ¯aw or defect that will grow under service usage.The crack propagation is investigated to ensure that the time for crack growth to a critical size takes much longer than the required service lifeofEngineering Fracture Mechanics 68(2001)1493±1507/locate/engfracmech*Corresponding author.Tel.:+1-615-322-3040;fax:+1-615-322-3365.E-mail address:mahas1@ (S.Mahadevan).0013-7944/01/$-see front matter Ó2001Elsevier Science Ltd.All rights reserved.PII:S 0013-7944(01)00041-81494P.Shi,S.Mahadevan/Engineering Fracture Mechanics68(2001)1493±1507the structure.In this paper,the damage process due to pitting corrosion fatigue is investigated and the time for corrosion fatigue life is evaluated using probabilistic analysis in the context of the damage tolerance approach.Corrosion(pitting)leading to fatigue crack nucleation and crack growth is considered to be among the most signi®cant degradation mechanisms in aging structures.Especially in aircraft,widespread corrosion pits on the surface and hidden within the fuselage joints are an important cause for multiple site damage, since fatigue cracks are observed to nucleate and propagate from these corrosion pits.A mechanics-based probabilistic model for the nucleation and propagation of corrosion pits is presented in this paper for corrosion fatigue life prediction.A seven-stage conceptual model was identi®ed by Goswami and Hoeppner[1]from the onset of cor-rosion to fatigue fracture.The electrochemical e ects in pit formation and the role of pitting in fatigue and corrosion fatigue crack nucleation behavior were considered in that model.But the model was only based on conceptual arguments and no computational implementation was described.A three-stage probabilistic model has been proposed by Harlow and Wei[2]to predict the corrosion fatigue life.The computed fatigue life is considered to be the sum of three periods:the time required for crack initiation,the time for a surface crack to grow into a through crack and the time for the through crack to grow to a prescribed critical length.However,this model does not consider the stage of pit nu-cleation and short crack e ects.Harlow and Wei[3]also proposed a probabilistic model for the growth of corrosion pit induced by constituent particles.The model addressed the relationship between the pit growth and the clustered ca-thodic particles and estimated the size of the pit at a given time.This model is useful for the prediction of the time required for the pit growth to crack nucleation.A transition model for pitting to corrosion fatigue crack nucleation was®rst proposed by Kondo[4],and further discussed by Chen et al.[5].In the corrosion fatigue process,pitting predominates in the early stages and is replaced by fatigue crack growth,based on two criteria:stress intensity factor and the competition between pit growth and crack growth.Moreover,several research studies have been reported on short crack growth by Piascik and Willard[6], Newman[7],Kaynak et al.[8]and Dolley and Wei[9].In most cases,it was found that the short crack growth rates exceed those of long cracks.Di erent models have been proposed to describe the short crack growth process.As reviewed above,deterministic and probabilistic models of varying degrees of accuracy are available for various stages of the corrosion fatigue life.However,these models only consider the separate stages and do not simulate the entire progressive damage process for corrosion fatigue.This paper proposes a com-prehensive methodology that quantitatively incorporates all the seven stages of corrosion fatigue life,in-cludes the uncertainties in each stage to develop a probabilistic life prediction technique,and quanti®es the sensitivity of the overall life to the uncertainties in each stage.In the proposed method,the pitting corrosion fatigue consists of seven stages:1.pit nucleation,2.pit growth,3.transition from pitting to fatigue crack nucleation,4.short crack growth,5.transition from short crack to long crack,6.long crack growth,7.fracture.The total fatigue life is the sum of four critical phases:time to pit nucleation(stage1),time for pit growth to short crack nucleation(stage2),time for short crack growth(stage4)and time for long crack growth(stage6).Three additional stages(stage3,5and7)are considered for the transition between these four phases.In this paper,the probabilistic model addresses the randomness in the parameters a ecting the nucle-ation/growth processes in all the seven stages,and incorporates them in a damage tolerance methodology to compute the corrosion fatigue life.The appropriate mathematical models,which are based on mechanical and probabilistic considerations, are developed to describe the damage accumulation in each of the seven stages.The main hurdle lies in the determination of the statistical information about the random variables a ecting the damage accumulation process in each stage.The appropriate selection of the distribution parameters of these random variables needs experimental testing and statistical analysis.Moreover,these statistical data will be di erent for various materials.In this paper,for illustration purposes,only2024-T3aluminum alloy is considered and the corresponding parameters are chosen using the existing information in the literature.The limit states for this probabilistic model are developed to compute the cumulative distribution function(CDF)of the corrosion fatigue life.The random variables involved in the model are a mixture of discrete and continuous variables.Classical®rst-order reliability method(FORM)and second-order reli-ability method(SORM)methods can only handle continuous variables and therefore have di culty in handling this problem.For accuracy,robustness,and validation purposes,Monte Carlo simulation may be used.The obtained CDF of the corrosion fatigue life may be used to de®ne the suitable inspection intervals and the repairs for aging structures.For the purpose of illustrating the e ect of di erent random variables on the corrosion fatigue life,the coe cients of variation(COV)and distribution types of the random variables are varied for di erent parameters and their e ects on corrosion fatigue life are investigated.Thus,a comprehensive seven-stage model is developed in this paper for quantitative simulation of the pitting corrosion fatigue damage process,with the following features:(a)It provides a quantitative basis for life prediction;(b)t includes the uncertainties in the damage growth process;and(c)it provides quanti-tative sensitivity information on the parameters associated with di erent stages of damage growth.2.Model descriptionThe main tasks in the development of the model are:(i)to identify the mechanical and probabilistic damage processes in all the seven stages,and(ii)to choose the appropriate deterministic and random variables involved.The damage process considered here consists mainly of pitting nucleation,pit growth, short crack growth and long crack growth in aluminum alloys.Since the rivet holes of the fuselage lap joints are the critical locations for pit nucleation,the damage process is assumed to start at the surface of the rivet holes.The material of interest is assumed to be2024-T3aluminum alloy,which is widely used inaircraft structures.The total fatigue life may be represented by the sum of the following four phases(Fig.1):Fig.1.Seven stages of pitting corrosion fatigue life.P.Shi,S.Mahadevan/Engineering Fracture Mechanics68(2001)1493±15071495t f t pn t pg t sc t lc 1 where t pn is the time for pit nucleation,t pg is the time for pit growth,t sc is the time for short crack growth,t lc is the time for long crack growth.The four time periods are functions of several deterministic and random variables,which are described below.The objective of the proposed method is to compute the CDF of the corrosion fatigue life.The failure probability at some speci®ed time t needs to be computed in order to plot the CDF curve.The failure probability may be expressed as:P f t P t f6t P t fÀt60 2 2.1.Corrosion pit nucleationThis is the®rst stage in the damage process model.It is related to the electrochemical processes during corrosion which result in the nucleation of a corrosion pit.The time to pit nucleation depends on factors such as electrolytes,loads,materials etc,which are not well understood yet.The proposed method therefore assumes the time to pitting nucleation t pn as a random variable.Di erent distribution types for this random variable may be assumed to compare their e ects on the CDF of life.For illustrative purposes,lognormal and Weibull distributions are used in this paper.The assumed distribution random parameters are shown in Table3.2.2.Corrosion pit growth modelThe second stage relates to pit growth,which initiates at the constituent particles and involves elec-trochemical processes a ected by clusters of particles.The surfaces of rivet holes in the lap joints in the aircraft structure are the critical locations for the corrosion pit nucleation.The pits are formed by the localized galvanic corrosion near the exposed constituent particles.As the pits grow,the exposed particles will interact and contribute to the pit growth.The model used here considers the e ect of the clustered particles on the pit growth and incorporates it into the computation of time for pit growth.The phase terminates when the pit grows to a critical size leading to the transition to crack nucleation.The corre-sponding mechanical model has been investigated by Harlow and Wei[3].The constituent particle in an aluminum alloy can be considered as cathodic or anodic relative to the matrix.Among these two particles,cathodic particles are essential for pit growth.It has been shown that the constituent particles are clustered[11,12],using well-established techniques for spatial point processes. Therefore,it is essential to consider the in¯uence of clusters of the constituent particles.In the proposed model,the clustered particles are related to the pitting current coe cient.The number of cathodic particles in a cluster is assumed to be a random variable with a discrete Pareto distribution.This distribution is found to provide the best®t for the empirical data compared to other commonly used discrete distributions. The probability mass function is expressed as:p k P N c k 0:725kÀ2:41k P1 3 where N c is the number of clustered particles.In this model,the pit is assumed to grow at a constant volumetric rate according to FaradayÕs Law:d V d tMI P0 knF qexpÀD HRT41496P.Shi,S.Mahadevan/Engineering Fracture Mechanics68(2001)1493±1507where M is the molecular weight of the material,N is the valence,F is Faraday constant,q is the density,D H is the activation energy,R is the universal gas constant,T is the absolute temperature,and I P0is the pitting current coe cient,which is dependent on the clustered particles.The shape of the pit is geometrically quite complex.As an approximation,the shape will be assumed to be half of a prolate spheroid.Then,the volume of the pit can be expressed asV 23p ca 25where c and a are half lengths of the major and minor axes,respectively.The time-dependent behavior of c and a in Eq.(5)are essential to the pit growth model in Eq.(4).As suggested by Harlow and Wei [3],there are three possible approaches for this problem:constant aspect ratio,discrete time-dependent aspect ratio,and continuous time-dependent aspect ratio.The latter two approaches are quite complex and di cult to implement.As a trade-o between simplicity and accuracy,the constant aspect ratio is chosen asac u k ;k >0;u k 61 6 where u k is assumed to be constant over time but dependent on the cathodic particle cluster size k .Esti-mation of the aspect ratio u k is complex and no methods have yet been presented to derive an explicit expression for u k .In this paper,for illustration purposes,we assume u k 1,so that the pit is bining Eq.(5)with Eq.(6),V 23p c 37Applying Faraday Õs law,V 23p c 3Àc 30 MI P0nF qexp ÀD H RTt 8Then,the time for pit growth is derived ast pg2p nF q 3MI P0 kc 3ci Àc 30 e D H =RT9where c ci is the critical pit size leading to crack nucleation,obtained as in the next subsection and c 0is theinitial pit size.Eq.(9)indicates that the time for pit growth is dependent on the clustered cathodic particles.2.3.Determination of critical pit size:transition from pitting to fatigue crack nucleationThe third stage is the transition from pit growth to fatigue crack nucleation,where mechanical e ects such as the stress intensity factor come into play.The nucleation of the fatigue crack is controlled by the competition between the processes of pit growth and crack growth.Two criteria may be used to describe the transition process [4,5]:(1)The stress intensity factor for the equivalent surface crack growth for the pit reaches the threshold stress intensity factor for the fatigue crack growth.(2)The corrosion fatigue crack growth rate exceeds the pit growth rate.In the discussion below,the models for pit growth and corrosion short crack growth are investigated to derive the transition ing the ®rst criteria,D K pit D K crack10Since the crack-nucleating pits are small compared to the radius of the rivet holes,they may be con-sidered as surface cracks in the edge of the semi-in®nite plate subjected to the maximum stress k t D r at the circular hole.Then the pit equivalent stress intensity factor may be expressed asP.Shi,S.Mahadevan /Engineering Fracture Mechanics 68(2001)1493±15071497D K pit 1:12k t D rp cpU11U Z p=2sin2h c=a 2cos2h 1=2d h 12where k t represents the stress concentration factor of the circular hole,D r represents the remote stress range,and U is the shape factor determined by u k.In this transition stage,the pit is assumed to be a hemisphere,as discussed in Section2.2,and the volume of the pit may be expressed by Eq.(7).Then,the volume growth rate may be expressed asd V d t d2p3c3d t 2p c2d cd tC P 13For simplicity,we assumeC P MI P0 knF qexpÀD HRT14Then,the pit growth rate may be expressed asd c d tC P2p c15Next,the short crack growth rate needs to be considered in order to apply the second criterion of the transition.A simple power law model is used to model the short crack growth,but the parameter involved is di erent from the long crack growth model.(The model will be discussed in detail in the next subsection.)d ad NC scD K m sc 16where C sc is a material constant and m sc is the growth exponent.Note that a in this equation and in the following stages refers to crack size,and is not to be confused with pit size parameter a in Eqs.(5),(6)and (12).Since the corrosion fatigue crack growth rate of the2024-T3aluminum alloy is independent of frequency f[6],Eq.(16)may be expressed asd ad tC scD K m sc f 17Equating the two growth rates in Eqs.(15)and(17),and substituting Eq.(11),the critical pit size for transition to short crack growth stage may be obtained as:a ciC P2p C sc f2= msc 4 U1:12k t D rpp2msc= m sc 418Upon obtaining the transition pit size,the time for pit growth to this size can be computed from Eq.(9). If the pit is small when a crack emanates,then the remaining fatigue life will be long,due to the long period of short crack growth before transition to long crack growth.If the pit is large at crack initiation, then the remaining life is shortened.These two cases are controlled by the term c ci in Eq.(9),which is the transition size from pit to short crack.The two cases are shown in Table1,using the data for the numerical example in Section4.1498P.Shi,S.Mahadevan/Engineering Fracture Mechanics68(2001)1493±15072.4.Short crack growthThe fourth stage is the short crack growth stage involving chemical and microstructural factors and their interactions.The applications in which fracture mechanics has been used in actual practice have usually considered long cracks.However,the important e ect of short crack growth on fatigue life prediction has received more and more attention in recent years.Many studies have found that the growth rate of short cracks exceeds the corresponding growth rate of long cracks,and that short cracks grow at stress intensities below the long crack threshold.It is questionable to apply the Paris law crack growth model,which is used widely in long crack range,to the small crack growth,which is not only a microstructural but also a chemical process.Although much research has been done in this area,it has been di cult to derive an explicit formula for short crack growth,especially in corrosive environment.A probabilistic model is presented here to account for the uncertainties in describing the relationship between the stress intensity factor and the growth rate.The empirical formula has a form similar to Paris law.However,the parameters involved are random variables dependent on experimental data.Then,the short crack growth model may be expressed asd ad NC scD K m sc19For short crack growth,it is assumed that the short crack is a surface crack semi-circular in shape in an in®nite plate with a circular rivet hole.Then the stress intensity factor is given byD K b D rp c p 20 where b 2:2=p k t ,and k t is the stress concentration factor resulting from circular rivet holes.Substituting Eq.(20)in Eq.(17),d ad tC sc 2:2k tD r = p p m sc f 21Then,the time for growth of short crack to the transition size to long crack growth is given by:t sc22À m sc fC sc 2:2k t D r = p p m sc a 1À m sc =2 thÀa 1À m sc =2ci 22where a th is the transition size from a short crack to a long crack,which is discussed in the next subsection.2.5.Transition from short crack growth to long crack growthExperimental and analytical approaches have been proposed to determine the transition size a th from short crack growth to long crack growth [8,9].An analytical approach equating the growth rates in the short crack and long crack stages,similar to the earlier transition between pit and short crack,has been mentioned by Kaynak et al.[8]for En7A steel.For 2024-T3aluminum alloys,Dolley and Wei [9]have reported a th to be in a range of 0.5and 5mm,and have considered 1mm as a reasonable average.Table 1The e ect of pit size on the corrosion fatigue life Transition size from pitting to crack nucleation c ci (mm)Pit growth time (days)Short crack growth time (days)0.056966900.15543860P.Shi,S.Mahadevan /Engineering Fracture Mechanics 68(2001)1493±15071499Therefore,in this paper,a th is treated as a random variable with a mean value of 1mm.The e ect of its scatter is studied in the numerical example.2.6.Long crack growth The widely used Paris law may be used in this stage to estimate the time for long crack growth,expressed asd ad NC lcD K m lc23where C lc is the material constant for long crack,and m lc is the growth exponent for long crack.The stress intensity factor may simply be expressed asD K b D rp a p 24 where b k t ,because of the e ect of the circular hole in the in®nite plate considered.Similar to Eq.(22),the time for long crack growth is expressed ast lc 2lc lc t p m lc a 1À m lc =2 f Àa 1À m lc =2th 25where a f is the speci®ed critical size for corrosion fatigue.A crack size beyond this value is considered be a failure or in need of repair.2.7.FractureA speci®ed crack size is considered to be the failure criterion at this stage.It is not the actual crack size at which the structure will fracture but a size considered to be unacceptable or to be in need of repair.Es-pecially in the case of multiple sites,the failure condition is more complicated,and the collective e ect of the various single crack sites has to be considered.The selection of this speci®ed value is dependent on practical considerations.In the numerical example,the critical crack length is assumed to be a deterministic value of 6mm.3.Probabilistic analysisFollowing the terminology of limit-state-based reliability methods [10],failure is de®ned as the corrosion fatigue life t f being less than a desired value t f .The corresponding performance function or the limit state function is written asg x t f Àt26where x is the vector of random variables.Eq.(26)is a nonlinear performance function of a group of random variables based on the four critical stages discussed in the Section 2.In the space of the random variables,the limit state function is the boundary between the safe and unsafe regions.g x >0denotes the safe state,g x <0denotes the failure state,and g x 0denotes the limit state.As discussed earlier in Eq.(2),it is seen that the failure probability at any speci®ed time t is equal to the CDF value of corrosion fatigue life.The CDF in Eq.(2)is di cult to evaluate using numerical integration,but can be estimated through simulation or analytical approximations [13].A commonly used approach for reliability estimation is to use1500P.Shi,S.Mahadevan /Engineering Fracture Mechanics 68(2001)1493±1507analytical methods,which construct ®rst-order or second-order approximations to the limit state.The FORM has been widely used.The FORM method is illustrated using Fig.2with two random variables y 1and y 2.y 1and y 2are un-correlated standard normal variables.The original variables x ,which may in general be correlated and nonnormal,are transformed to the y -space using well-known transformations [14,15].The exact probability of failure is the integral of the joint probability density function over the failure domain g y <0 .The ®rst-order Taylor series approximation to the limit state surface g 0 is applied at the point which has the minimum distance from the origin in the y -space.A reliability index b is de®ned as the minimum distance from the origin to the limit state in this space.The point of minimum distance from the origin to the limit state represents the worst combination of the random variables and is therefore called the most probable failure point (MPP)or design point.The computation of the reliability index then becomes an optimization problem to locate the MPP on the limit-state surface.The Rackwitz±Fiessler [15]algorithm can be used to recursively search for the MPP as:y k 1 1r g y k 2r g y k ty k Àg y k n o r g y kn o 27 where fr g y k g is the gradient of the performance function at y k ,the k th iteration point.After the reliability index b is calculated,the ®rst-order approximation to the failure probability is obtained as:P f U Àb28This method is simple to use,and is found to converge fast in many cases.In case the performance function is highly nonlinear,SORM are also available [16±18],in which the curvature of the limit state is used to construct a second-order approximation to the failure probability estimate.Since all the random variables do not have equal in¯uence on the reliability,probabilistic sensitivity factors may be used to quantify the in¯uence of each basic random variable.With reference to Fig.2,these are obtained as the components of the unit gradient vector a r g y =jr g y j at the MPP of the limit state in the standard normal space.The sensitivity index can be used to improve computational e ciency.Variables with very low sensitivities can be treated as deterministic at their mean values.This signi®cantly reduces the amount of computation,because,in many practical problems,only a few variables may have a signi®cant e ect on the probability offailure.Fig.2.First-order reliability approximation.P.Shi,S.Mahadevan /Engineering Fracture Mechanics 68(2001)1493±150715011502P.Shi,S.Mahadevan/Engineering Fracture Mechanics68(2001)1493±1507In the proposed pitting corrosion fatigue life model,some random variables are continuous and some are discrete.FORM/SORM analysis is suitable for continuous random variables.However,since the present problem has only one discrete random variable(k,the number of clustered particles),the failure probability in Eq.(2)may be expressed asXP f tP f t f6t j k i g P k k i 29i P1where P k k i may be obtained from Eq.(3),and P f t fÀt60j k i g may be computed using FORM/ SORM.In the numerical example in Section4,the summation in Eq.(29)is terminated at i 20,since the contribution of the terms for i>20is not signi®cant.Corresponding to Eq.(29),the sensitivity vector is expressed by a weighted sum asXaf a j k ig P k k i 30i P1where a j k i is the sensitivity vector when k is equal to i.Another commonly used probabilistic approach is the Monte Carlo simulation method.The simulation method generates many samples of the random variables and evaluate whether the performance function is violated in each simulation.A large number of simulations are needed to obtain a relatively accurate result for low failure probability.Though it is quite time consuming,simulation is robust,accurate and easy to implement.It can handle both discrete and continuous random variables.E cient sampling and variance reduction techniques have been developed to improve the performance of the Monte Carlo method.In corrosion fatigue life prediction,the random variables are a mixture of discrete and continuous variables.For a single pit analysis,the limit state function evaluation is not complicated.Therefore,the Monte Carlo method is an appropriate tool to handle this problem.In this paper,both FORM and Monte Carlo simulation method are used and compared.4.Numerical exampleThe structure is idealized as an in®nite plate with a circular rivet hole.The material considered is an aluminum alloy.A corrosive environment is assumed and pit corrosion occurs on the surface of the hole. The deterministic parameters used in the numerical example are listed in Table2.Most of the deterministicTable2Deterministic variable for corrosion fatigue lifeVariable ValueDensity q(gm/m3)2:7Â10 6Valence n3Molecular weight M(gm)27FaradayÕs constant F(C/mol)96514Activation energy D H(kJ/mol)50Universal gas constant R(J/mol K)8.314Temperature T(K)293Applied stress D r(MPa)90Frequency f(cycles/day)10Stress concentration factor k t 2.6Short crack growth exponent m sc 3.3Long crack growth exponent m lc 3.3Speci®ed critical crack size a f(m)6:0Â10À3。

飞机常见缺陷英文描述

缺陷 Defect1. Common Structure结构缺陷术语凹坑（1） dent凹槽（2） notch变形（3） deform划痕（4） nick点腐蚀（5） pitting断裂（6） broken腐蚀（7） corrode划伤（8） scratch裂纹（9） crack毛刺（10） butt磨损（11） chafe凸起（12） protrude凹陷（13） sag粗糙（14） rough漆层剥落（15） finish missing 褪色（16） fade积水（17） entrapped water mon metallic defect:一般性金属材料缺陷：氧化（18） oxidize划伤（8） scratch扭曲（19） distort跷起（20） not in contour穿孔（21） puncture碎屑（22） chip腐蚀（7） corrode磨损（11） chafe变形（3） deform风蚀/风化（23） erode裂纹（9） crack2) Common non-metallic defect:一般性非金属材料缺陷：发霉（24） mildew分层（25） delaminate风蚀/风化（23） erode裂纹（9） crack老化（26） deteriorate起皱（27） wrinkle受潮（28） saturated撕裂（29） tear穿孔（21） puncture变色（16） fade陈旧（30） worn脱胶（31） adhere.设备及零部件分为1） Plumbing defect 管路缺陷凹坑（1） dent爆裂（32） burst擦伤（11） chafe滑丝（33） cross thread扭曲（34） twist渗漏（35） leak堵塞（36） obstruct2) Wiring defect 线路缺陷腐蚀（7） corrode磨损（11） chafe相碰（37） contact断丝（38） fray熔断（39） fused弯曲（40） bend3) Mechanical linkage defect 传动机构缺陷断丝（38） fray松弛（） slack扭结（34） twist磨损（11） chafe脱开（41） disconnect4） Fastener defect 紧固件缺陷丢失（42） missing松动/松脱（43） loose腐蚀（7） corrode磨损（11） chafe未关（扣）紧（44） not secure5). Sealant 封严脱胶（31） adhere老化（26） deteriorate不均匀（45） inconsistent6). Wheel Assembly 轮胎见线（46） exposed cords磨平（47） bald扎伤（21） puncture气压不足（48） insufficient-air-pressure7). Life Limited Parts 时寿件过期（49） expire8). Placard and Marking 标牌/标识模糊（50） illegible缺损（51） damage丢失（42） missing翘起（52） lifting9). Slide/life Vest 滑梯/救生衣散包（53） not properly packed变形（54） not properly sealed 4．general defect terms 一般性缺陷术语脏（55） dirty陈旧（30） worn断裂（56） fracture磨损（11） chafe超标（57） exceed-the-limit丢失（42） missing腐蚀（7） corrode裂纹（9） crack空行程/无效行程（58） backlash卡阻/阻塞（59） block鼓起（60） bulge污染（61） contaminate不一致（62） disagree（电池/气瓶）被释放（63） discharge装错（64） dislocate失效（65） fail摆动（66） fluctuate抖动（67） flutter不够/不足（68） insufficient不工作（69） inoperative（不）亮（70） (not) illuminate干扰（71） interfere扭结/缠结（72） kink走向错误（73） misrouted漏装（74） not installed相磨（75） rubbing干涩/缺乏润滑（76） un-lubricated不能复位（77） will-not-reset氧气oxygen氧气面罩oxygen mask流量控制flow control充气控制inflation control热补偿thermal compensator机组氧气瓶crew oxygen cylinder氧气发生器oxygen generator氧气压力指示oxygen pressure indicator旅客氧气面罩passenger oxygen mask机组氧气面罩crew oxygen mask氧气系统组件oxygen system module氧气系统面板oxygen system panel安全销safety pin压力调节器pressure regulator氧气指示继电器oxygen indicator relay高度压力电门altitude press switch机组氧气传感器crew oxygen transducer乘务员服务组件attendant service unit厕所服务组件lavatory unit旅客服务组件passenger service unit超压释放活门overpressure relief valve同意放行dispatch approved 或released因为due 或because因停场时间不足due time short没有备件lack parts 或no spare parts available 或no parts in stock待件wait for parts申请保留apply for reservation保留故障defer defect保留项目defer item保留期限due time关闭保留项目close deferred item撤消保留项目rescind deferred item参考/按……更换……（件），测试……1. 根据工卡3821040001，更换电子/电气冷却供气风扇气滤，通电测试正常。

Fatigue crack propagation of 444 stainless steel welded joints in air and in 3%NaCl aqueous solution

Fatigue crack propagation of 444stainless steel weldedjoints in air and in 3%NaCl aqueous solutionMasayuki Akita a ,Masaki Nakajima b ,Keiro Tokajia,*,Toshihiro ShimizubaDepartment of Mechanical and Systems Engineering,Faculty of Engineering,Gifu University,1-1Yanagido,Gifu 501-1193,JapanbDepartment of Mechanical Engineering,Toyota College of Technology,2-1Eisei-cho,Toyota 471-8525,JapanReceived 10May 2004;accepted 1October 2004Available online 8December 2004AbstractFatigue crack propagation (FCP)was studied on ferritic stainless steel welded joints in air and in 3%NaCl aqueous solution.In air,when the crack propagated normal to the weld line,FCP rates decreased temporarily as it reached the heat aﬀected zone (HAZ)and then increased monotonously.When the crack propagated within HAZ and the weld metal,FCP rates were lower than those of the base metal.After allowing for crack closure,the FCP data of all the welded specimens became similar and coincided with those of the base metal.In 3%NaCl aqueous solution,all the welded specimens still showed enhanced FCP rates at high eﬀective stress intensity factor range region,where extensive intergranular and quasi-cleavage fractures were seen.Ó2004Elsevier Ltd.All rights reserved.Keywords:Ferrous metals and alloys;Welding;Fatigue1.IntroductionFerritic stainless steels posses an excellent resistance to stress corrosion cracking (SCC),while they had poor toughness and as-welded ductility.In recent years,new ferritic stainless steels with extremely reduced (C +N)content have been developed,in which toughness and weldability are signiﬁcantly improved [1,2].Of various joining methods,welding is widely used in machine components and structures.To ensure their safety and reliability,evaluation on the fatigue properties of welded joints is particularly important because they are very sensitive to fatigue loading.Although studies on corrosion fatigue behaviour [3]and fatigue crack ini-tiation and small crack growth [4]have been indicated in ferritic stainless steels themselves,there have been very limited studies on the fatigue behaviour of welded joints.Only a few studies on the toughness of welded joints have been reported [2,5].In addition,since stainless steels are mostly used in applications where corrosion resistance is required,it is also necessary to understand their fatigue behaviour in corrosive environments.In the present study,fatigue crack propagation (FCP)behaviour for large cracks was studied on welded joints of a ferritic stainless steel,type 444,in air and in 3%NaCl aqueous solution.The obtained results were discussed on the basis of residual stress,crack closure behaviour and fracture surface analysis.2.Experimental details 2.1.Material and specimensThe base metal is a ferritic stainless steel,type 444(18Cr–2Mo)whose chemical composition (mass %)is C:0.004,Si:0.06,Mn:0.1,P:0.024,S:0.006,Ni:0.11,Nb:0.17,Cr:18.72,Mo:1.81,V:0.06,N:0.068.The0261-3069/$-see front matter Ó2004Elsevier Ltd.All rights reserved.doi:10.1016/j.matdes.2004.10.004*Corresponding author.Tel.:+81582932500;fax:+81582301892.E-mail address:tokaji@cc.gifu-u.ac.jp (K.Tokaji)./locate/matdesMaterials and Design 27(2006)92–99Materials &Designmaterial was used in the as-received condition.The mechanical properties for two directions parallel and perpendicular to the rolling direction(L and T direc-tions,respectively)are listed in Table1.The proof stress and tensile strength in the T-direction are slightly higher than those in the L-direction.Fig.1shows the conﬁguration of compact type(CT) specimens used in FCP experiment.As illustrated schemat-ically in Fig.2,three types of welded CT specimens were evaluated:the specimens of which starter notch was intro-duced perpendicular to the weld line(N-specimen,Fig. 2(a)),within the heat aﬀected zone(HAZ)(H-specimen, Fig.2(b)),and within the weld metal(W-specimen,Fig. 2(c)).Since the welding direction was parallel to the T-direc-tion,the FCP direction was the L-direction in the N-speci-mens,while the T-direction in the H and W specimens. 2.2.Welding conditionWelding was performed by the tungsten–inert gaswelding method(TIG)with a root opening of1.6mm, an X-shape groove,the voltage of20V and three weld-ing passes on both sides.Theﬁller metal was a309L austenitic stainless steel.The microstructures in the base metal,HAZ and the weld metal are represented in Fig.3.The microstructure of the base metal consists of ferritic grains with the aver-age size of approximately56l m(Fig.3(a)).In HAZ,the microstructure also consists of ferritic grains,but a pro-nounced grain growth takes place,resulting in the aver-age size of123l m(Fig.3(b)).On the other hand,the weld metal has a complicated microstructure:dendrite or acicular microstructure(Fig.3(c)).Hardness was measured using a Vickers hardness tes-ter and the obtained results were162HV,172HV and 194HV for the base metal,HAZ and the weld metal, respectively.2.3.ProceduresFCP tests were performed at a stress ratio,R,of0.05 using a19.6kN capacity electro-hydraulic fatigueTable1Mechanical properties of base metalDirection0.2%Proof stressr0.2(MPa)Tensile strengthr B(MPa)Breaking strength onﬁnal area r T(MPa)Elongationu(%)Reduction of areaw(%)L29344514803483T31046013523181M.Akita et al./Materials and Design27(2006)92–9993testing machine operating at a frequency of 1Hz.Test environments employed were laboratory air and 3%NaCl aqueous solution.The solution was kept at 30°C and circulated between the corrosion cell attached to the specimen surface and a reserved tank by using a pump.Crack length was monitored with a travelling micro-scope with a resolution of 10l m and crack closure was measured by an unloading elastic compliance method [6]using a strain gauge mounted on the back face of the specimen.After experiment,fracture surfaces were examined in detail using a scanning electron microscope (SEM).3.Results3.1.Residual stress distributionResidual stress in the welded specimens was measured by the X-ray diﬀraction method.Fig.4shows the distribu-tion of residual stresses normal to the FCP direction in the N-specimens.Residual stresses are approximately from À110to À480MPa at the top surface (the side of the ﬁrstpass),while À100to À500MPa at the bottom surface (the opposite side of the second pass).Compressive residual stresses decrease as the distance from the notch root in-creases toward the weld zone.From this measured resid-ual stress distributions,it is believed that large tensile residual stresses would be present in the weld metal.Residual stresses normal to the weld line were also measured in HAZ,which were approximately À300MPa (compression)at the top surface,while 100MPa (tension)at the bottom surface,regardless of the dis-tance from the weld zone.3.2.FCP behaviour of base metalAs described previously,the FCP direction is the L-direction in N-specimens,while the T-direction in H and W specimens,thus FCP behaviour for the base me-tal was evaluated using CT-specimens of both T–L and L–T orientations.Fig.5(a)represents the relationship between FCP rate,d a /d N ,and stress intensity factor range,D K ,for the base metal in air and in 3%NaCl aqueous solution.As can be seen in the ﬁgure,the eﬀect of orientation is not seen at high D K region in both environments,but the FCP rates for the L–T orientation are faster than those for the T–L orientation at low D K region.It is worth noting that the FCP behaviour for both orienta-tions is aﬀected by corrosive environment at D K P 15MPa m 1/2,where the FCP rates in 3%NaCl aqueous solution are signiﬁcantly faster than those in air.When the FCP data are characterized in terms of the eﬀective stress intensity factor,D K eﬀ(Fig.5(b)),the dif-ference in FCP rate between both orientations observed in the d a /d N –D K relationship disappears.This indicates that crack closure played a signiﬁcant role in FCP behaviour.Based on observation of crack path and frac-ture surface analysis,fracture surface roughness was considerably larger in the T–L orientation than in the L–T orientation at low D K region,thus it is believed that the diﬀerence in crack closure was induced from fracture surface roughness.It should be noted that the enhanced FCP rates in 3%NaCl aqueous solution observed in the d a /d N –D K relationships are still seen.This indicates that there ex-ists an environmental eﬀect on FCP behaviour.As anFig.3.Microstructures:(a)base metal,(b)heat aﬀected zone (HAZ),(c)weld metal.94M.Akita et al./Materials and Design 27(2006)92–99example,Fig.6reveals SEM micrographs of fracture surfaces in air and 3%NaCl aqueous solution.At low D K region,the appearance of fracture surfaces is similar in both environments,but at high D K region some inter-granular fracture can be seen on the fracture surface in 3%NaCl aqueous solution.3.3.FCP behaviour of welded jointsThe FCP behaviour for the N,H and W specimens is shown in Figs.7–9,respectively.For comparison,the FCP behaviour for the base metal is also included in those ﬁgures.N-specimen (Fig.7)In air,the FCP rates are nearly the same as those for the base metal in low D K region.With increasing crack growth,ﬂuctuation of FCP rate becomes pronounced and FCP rates decrease temporar-ily around D K =20MPa m 1/2,then increase and tend to approach the FCP behaviour for the base metal.Such a complicated FCP behaviour appears to be due to resid-ual stress and hardness changes induced by welding.In 3%NaCl aqueous solution,the FCP rates are con-siderably lower than those for the base metal and ﬂuctu-ation of FCP rate is not seen,being due to a higher initial D K level employed in the experiment.Fig.6.SEM micrographs showing fracture surfaces of base metal.M.Akita et al./Materials and Design 27(2006)92–9995H-specimen(Fig.8)In air,the FCP rates are lower than those for the base metal,particularly in low D K re-gion and with increasing D K gradually approach and then coincide with the FCP rates for the base metal at high D K region.This indicates a higher FCP resistance of HAZ than the base metal.In3%NaCl aqueous solution,the FCP rates are fas-ter than those in air,which becomes more pronounced with increasing D K.When compared with the data for the base metal,the FCP rates are lower in the entire D K region,particularly remarkable at low D K region.W-specimen(Fig.9)The overall FCP behaviour is similar to that of H-specimens.In air,the FCP rates are considerably lower than those for the base metal in low D K region,then gradually approach and eventually coincide with the FCP rates for the base metal at high D K region.This also indicates a higher FCP resistance of the weld metal than the base metal.In3%NaCl aqueous solution,the FCP rates are nearly consistent with those in air at low D K region, but become faster with increasing D K.When compared with the data for the base metal,the FCP rates are sig-niﬁcantly lower in low D K region and then rapidly in-crease and coincide with the FCP rates at high D K region.3.4.Fracture surface analysisSEM micrographs of fracture surfaces in air are shown in Fig.10.As can be seen in theﬁgure,the oper-ative micromechanisms are the same in all the welded specimens:ductile transgranular at low D K region,while striation at high D K region.On the other hand,fracture micromechanisms oper-ated in3%NaCl aqueous solution were diﬀerent from those in air and will be discussed later.4.Discussion4.1.Factors inﬂuencing FCP behaviour of welded joints in airAs seen in Fig.7,in air the N-specimens showedﬂuc-tuations of FCP rate and a remarkable decrease in FCP rate around D K=20MPa m1/2.It has been well known that residual stress plays a signiﬁcant role in the FCP behaviour of welded joints.Fig.11represents the FCP behaviour and residual stress distribution in the N-spec-imens as a function of crack length in both environ-ments.It should be noted that the remarkable decrease of FCP rate in air occurs as the crack reaches HAZ. On the other hand,compressive residual stresses de-crease monotonously with increasing crack length,indi-cating that the residual stress distribution does not correspond to the remarkable decrease in FCP rate just before reaching HAZ.The similar results have been re-ported in laser welded butt joints,which was due to a sudden hardness change at the boundary between the base metal and HAZ[7].At low D K region,in spite of the presence of compressive residual stresses,the FCP rates for the welded specimens are nearly the same as those for the base metal(see Fig.7),this is because the compressive residual stress of approximatelyÀ270 MPa was detected in the base metal,which is equivalent96M.Akita et al./Materials and Design27(2006)92–99to the compressive residual stresses in the welded specimens.The results in3%NaCl aqueous solution did not showcomplicated FCP behaviour as seen in air.This is due to a higher initial D K level employed in the experiment, thus the eﬀect of HAZ becomes relatively small.In the H and W specimens,the cracks propagated within HAZ and the weld metal,pres-sive residual stress of approximatelyÀ300MPa and ten-sile residual stress of100MPa were present at the top and bottom surfaces in HAZ,respectively.Residual stress in the weld metal could not be measured,but it is assumed that similar residual stresses would beFig.10.SEM micrographs showing fracture surfaces of all welded specimens in air.M.Akita et al./Materials and Design27(2006)92–9997present.Although it is not easy to understand the eﬀect of residual stress in such a case,pressive on one side and tensile on the opposite side,it seems that the FCP behaviour is aﬀected by compressive residual stress rather than tensile residual stress,because the absolute value of the former is signiﬁcantly larger than that of the latter.In addition to residual stress,deﬂection of crack path was much more pronounced in HAZ and the weld metal due to grain growth and solidiﬁcation microstructure,respectively,which also contributes the higher FCP resistance of HAZ and the weld metal than the base metal.4.2.FCP behaviour after allowing for crack closure The FCP behaviour characterized in terms of D K eﬀis shown in Fig.12.As can be seen in the ﬁgure,in air the d a /d N –D K eﬀrelationships for all the welded specimens are almost identical to that of the base metal.Therefore,the diﬀerences among the welded specimens and be-tween the welded specimens and the base metal observed in the d a /d N –D K relationships are attributed to crack closure that was induced by residual stress and fracture surface roughness.In 3%NaCl aqueous solution,the d a /d N –D K eﬀrela-tionships in all the welded specimens are nearly the same,thus the diﬀerence among the welded specimens observed in the d a /d N –D K relationships is also attrib-uted to crack closure.However,when compared with the d a /d N –D K eﬀrelationships in air,the FCP rates in 3%NaCl aqueous solution are signiﬁcantly faster in the region of D K eﬀ>15–20MPa m 1/2,which indicates that an environmental eﬀect exists in this region.4.3.Eﬀect of corrosive environment on FCP behaviour of welded jointsAs seen in Fig.12,the FCP rates of all the welded specimens were still faster at high D K eﬀregion in 3%NaCl aqueous solution,suggesting that operative micromechanisms would be diﬀerent from in air.Therefore,fracture surfaces were examined in detail using SEM.SEM micrographs of fracture surfaces at high D K region where the enhanced FCP rates were observed are shown in Fig.13.At low D K region where the same FCP rates were observed in both environments,the fracture surfaces in 3%NaCl aque-ous solution revealed ductile transgranular,which was the same as in air.At high D K region,however,a signiﬁcant fraction of intergranular fracture or quasi-cleavage fracture can be seen (Fig.13),indicat-ing clearly that diﬀerent fracture micromechanisms from in air have operated in 3%NaCl aqueous solution.SCC,hydrogen embrittlement and intergranular cor-rosion are believed to be the possible causes of brittle nature in 3%NaCl aqueous solution.However,the eﬀect of SCC would be negligible,because it has been indi-cated that ferritic stainless steels had very low suscepti-bility to SCC even in a highly concentrated chloride solution [8].In order to conﬁrm the resistance to SCC of the present 444stainless steel,SCC tests have been performed using CT-specimens in 3%NaCl aqueous solution,but SCC did not take place.On the other hand,it has been pointed out that hydrogen embrittlement oc-curred under cathodic potentials in high purity ferritic stainless steel [9].However,hydrogen embrittlement would not take place in the present case,because of a low hydrogen-produced environment,i.e.3%NaCl aqueous solution.Therefore,it is believed that inter-granular corrosion would be the cause for the enhanced FCP observed in 3%NaCl aqueous solution,because it has been indicated that HAZ became sensitive to inter-granular corrosion in ferritic stainless steel weldments [8],and thus welded joints would have increasing pro-pensity of intergranular fracture compared with the base metal.The weld metal is an austenitic stainless steel,type 309L,which also showed enhanced FCP at high D K eﬀregion.This would be attributed to hydrogen embrittle-ment of martensitic phase transformed from austenitic phase [10].Fig.13.SEM micrographs showing fracture surfaces of all welded specimens in the FCP regime enhanced by 3%NaCl aqueous solution.98M.Akita et al./Materials and Design 27(2006)92–995.ConclusionsFatigue crack propagation(FCP)behaviour for large cracks was studied on welded joints of a ferritic stainless steel,type444,in air and in3%NaCl aqueous solution.The obtained results were discussed on the basis of residual stress,crack closure behaviour and fracture surface analysis.The conclusions can be made as follows:(1)In air,the welded specimens of which FCP direc-tion was perpendicular to the weld line showed a complicated FCP behaviour with frequentﬂuctua-tions of FCP rate.When the crack reached HAZ, the FCP rates were signiﬁcantly decreased and then monotonously increased.When the cracks propa-gated within HAZ and the weld metal parallel to the weld line,the FCP rates for both specimens were almost identical and lower than those for the base metal in the entire D K region.(2)The FCP rates of all the welded specimens in3%NaCl aqueous solution were enhanced com-pared with those in air,being more pronounced with increasing D K.(3)In air,after allowing for crack closure,all thewelded specimens showed nearly the same FCP behaviour,indicating that the observed diﬀerences in the FCP rate characterized in terms of D K were attributed to crack closure.(4)The FCP rates in3%NaCl aqueous solution werestill faster at high D K eﬀregion than those in air after allowing for crack closure,where extensive inter-granular fracture or quasi-cleavage fracture was seen.AcknowledgementsThe authors thank Mr.Y.Asano,Mr.T.Hayakawa, Mr.M.Itoh and Ms.C.Ohmori for their experimental assistance.References[1]Nakazawa T,Suzuki S,Sunami T,Sogo Y.Application of high-purity ferritic stainless steel plates to welded structures.ASTM STP1980;706:99–122.[2]Redmond JD.Toughness of18Cr–2Mo stainless steel.ASTMSTP1980;706:123–44.[3]Kimura Y,Yagasaki Y,Kunio T.Initiation process of corrosionfatigue cracks in stainless steels.Trans Jpn Soc Mech Eng 1984;A50-1:33–40.[In Japanese].[4]Nakajima M,Akita M,Tokaji K,Shimizu T.Fatigue crackinitiation and early growth behavior of a ferritic stainless steel in laboratory air and in3%NaCl aqueous solution.JSME Int J,Ser A2003;46–4:575–81.[5]Krysiak KF.Weldability of the new generation of ferritic stainlesssteels-update.ASTM STP1980;706:221–40.[6]Kikukawa M,Jono M,Tanaka K,Takatani M.Measurement offatigue crack propagation and crack closure at low stress intensity level by unloading elastic compliance method.J Soc Mater Sci Jpn 1976;25:899–903.[In Japanese].[7]Minagi A,Tokaji K.Fatigue crack propagation of laser weldedbutt joints.Fracture mechanics:applications and challenges.In: Proceedings of the13th european conference on fracture (ECF13).San Sebastian,Spain;2000[CD-ROM].[8]Kowaka M.The corrosion behavior of ferritic stainless steels.JSoc Mater Sci Jpn1974;23:924–35.[In Japanese].[9]Koterazawa K,Uchida H,Ohshiba H.Eﬀect of tensile orientationon hydrogen embrittlement in single crystals of high purity ferritic stainless steel.J Soc Mater Sci Jpn1993;42:983–9.[In Japanese].[10]Endo K,Komai K,Murayama S.Inﬂuence of ClÀconcentrationon corrosion fatigue crack growth of an austenitic stainless steel.Trans Jpn Soc Mech Eng1982;48:1489–95.[In Japanese].M.Akita et al./Materials and Design27(2006)92–9999。

毕业设计外文参考文献

[1] 王起江，洪杰．超超临界电站锅炉用新型管材的研制[J]．宝钢技术，2008(5)：44-53．[2] 王起江，邹凤鸣．T91高压锅炉管的研制与应用[J]．发电设备，2005 (1)：43-47．[3] Fujio Abe．Bainitic and martensitic creep-resistant steels[J]．Solid State andMaterials Science，2004，8：305-311．[4] 马明编译．美国新的超临界机组考虑使用T/P92的原因[J]．电力建设，2006，27(11)：79-80．[5] 戴平．国产P91钢管道存在的问题及其解决[J]．广东电力，2008，21(8)：67-69．[6] 田党．关于难变形钢和合金管坯的二辊斜轧穿孔问题[J]．钢铁，1998，33(1)：33-36．[7] P J Ennis，A Czyrska-Filemonowicz．Recent advances in creep-resistant steelsfor power plant applications [J]．Sādhanā，2003，28：709–730．[8] 刘立民，朱洪，刘志国．法国T91、P91钢管性能评定[J]．电站系统工程，2002，18(1)：63-64．[9] 彭孙鸿．T91钢管在我国的应用前景[J]．宝钢技术，1997，6：48-50．[10] H.C. Furtado，L.H. de Almeida，I. Le May．Precipitation in 9Cr–1Mo steel aftercreep deformation[J]．Materials Characterization，2007，58：72–77．[11] 蒯春光，彭志方．T/P91钢在450-1200℃区间各相元素的分配特征及相稳定性[J]．金属学报，2008，44(8)：897-900.[12] 孙智，董小文，张绪平，等．奥氏体化温度对9Cr-1Mo-V-Nb钢组织与性能的影响[J]．金属热处理，2001，26(8)：12-14．[13] 刘靖，周立新，傅晨光，等．电站锅炉用T91钢热穿孔性能的研究[J]．钢管，2002，31(5)：9-11．[14] 彭孙鸿，尤夙志，姜明娟，等．热穿孔温度对T91持久强度的影响[J]．特殊钢，2001，22(2)：10-12．[15] 崔光珠，朱伏先，高德福，等．T91钢高温变形特性研究[J]．塑性工程学报，1999，6(2)：13-16．[16] 余勇，周晓岚，赵志毅，等．T91变形抗力模型建立及理论轧制压力计算[J]．宝钢技术，2006(3)：31-34．[17] Polcik P，Sailer T，Blum W，et al．On the microstructural development of thetempered martensitic Cr-steel P91 during long-term creep[J]．Materials Science and Engineering，1999，260：252-259．[18] Orlová A，Buršík J，Kucharová K，et al．Microstructural development duringhigh temperature creep of 9% Cr steel[J]．Materials Science and Engineering，1998，254：39-48．[19] Sasaki，Terufumi，Kobayashi，et al．Production and properties of seamlessmodified 9Cr-1Mo steel boiler tubes[R]．Kaw asaki Steel Technical Report，1991，25(4)：78-87．[20] Bendick W，Vaillant JC，Vandenberghe B，et al．Properties and workability ofnew creep strength enhanced steels as known grades 23, 24, 911 and 92[J]．International Journal of Pressure Vessels and Piping，2004，476：25-29．[21] 刘江南，王正品，束国刚，等．P91钢的形变强化行为[J]．金属热处理，2009，34(1)：28-32．[22] Tőkei Z S，Viefhaus H，Grabke H J．Initial stages of oxidation of a9CrMoV-steel: role of segregation and martensite laths[J]．Applied Surface Science，2000，165：23-33．[23] Rajendran P S，Sankar P，Khatak H S．Cyclic oxidation of P91 at 1073, 1123 and1173K[J]．High Temperature Materials and Processes，2004，23(3)：195-204．[24] Ahmed Shibli，Fred Starr．Some aspects of plant and research experience in theuse of new high strength martensitic steel P91[J]．International Journal of Pressure Vessels and Piping，2007，84：114-122．[25] J.C. Vaillant，B. Vandenberghe，B. Hahn，et al．T/P23, 24, 911 and 92: Newgrades for advanced coal-fired power plants—Properties and experience [J].International Journal of Pressure Vessels and Piping，2008，85：38-46．[26] Brett SJ．The creep strength of weak thick section modified 9Crforgings[C]．Proceedings of Baltica，2001，1：39-45．[27] U.Gampe，P.Seliger．Creep crack growth testing of P91 and P22bends[J]．International Journal of Pressure Vessels and Piping，2001，78：859-864．[28] L.Kunz，P.Lukáš．High temperature fatigure and cyclic creep of P91steel[J]．European Structural Integrity Society，2002，29：37-44．[29] B.Fournier，M.Sauzay，C.Caës，et al．Creep-fatigue-oxidation interactions ina 9Cr-1Mo martensitic steel[J]．International Journal of Pressure Vessels andPiping，2008，85：478-485．[30] 刘洪杰．电站锅炉用P91钢蠕变/疲劳交互作用的试验研究[J]．动力工程，2007，27(6)：990-995．[31] LIU Jiang-nan，JIE Wang-qi．Application of improved vacuum degassingtechnique to refinement of heat resistant steel P91[J]．Trans. Nonferrous Met.Soc. China，2005，15：291-294．[32] 苏俊，张铮，李进．P91高压锅炉管的开发[J]．钢管，2008，37(4)：33-37．[33] 郭元蓉，吴红．P91无缝钢管国产化研究进展[J]．钢管，2008，37(1)：22-27．[34] 王起江，邹凤鸣，张瑞，等．宝钢T91高压锅炉管性能试验与研究[J]．宝钢技术，2003，(4)：46-50．[35] Miyata K，Sawaragi Y．Effect of Mo and W on the phase stability of precipitatesin low Cr heat resistant steels[J]．ISIJ，2001，41：281-289．[36] Wachter O，Ennis PJ．Investigation of the properties of the 9% Cr steel of thetype 9Cr-0.5Mo-1.8W-V-Nb with respect to its application as a pipework and boiler steel operation at elevated temperatures[D]．Germany，1995．[37] Hättestrand M，Andrén H O．Evaluation of particle size distribution in a 9% Crsteel using EFTEM[J]．Micron，2001，32：789-797．[38] Sklenicka V，Kucharova K，Svoboda M，et al．Long-term creep behavior of9-12%Cr power plant steels [J]．Mater. Character，2003，51：35-48．[39] Strang A，Foldyna V，Lenert J，et al．Prediction of the long-term creep ruptureproperties of 9-12Cr power plant steels [C]．Proceedings of the 6th International Charles Parsons Turbine Conference，Dublin，2003，427-441．[40] Kimura K，Kushima H，Sawaka K．Long-term creep strength prediction of highCr ferritic creep resistant steels based on degradation mechanisms[C]．Proceedings of the 6th International Charles Parsons Turbine Conference，Dublin，2003，444-456．[41] 高巍，刘江南，王正品，等．P92钢塑性变形行为[J]．西安工业大学学报，2008，28(4)：356-359．[42] 田党，张根良，卜玉钦．二辊斜轧穿孔时高合金钢的变形分布和分层缺陷形成机制[J]．钢铁，1995，30(1)：40-45．[43] 刘新生，赵定国，崔成业．冷轧薄板中分层现象的研究[J]．钢铁，2008，43(5)：40-43．[44] 崔风平，赵乾，唐愈．铸坯内部缺陷对钢板分层形成的影响[J]．中国冶金，2008，18(2)：14-18．[45] 唐生斌．板材分层缺陷产生原因分析[J]．连铸，2003，4：32-34．[46] 洪小玲，肖荣仁，李端来．GH3030合金锻坯裂纹分析[J]．钢铁研究，2002，128(5)：11-12．[47] S.A.Sharadzenidze，E.A.Svetlitskii．High Quality Seamless Tubes[J]. Metallurg，1968，11：38-39．[48] 王建文．27SiMn钢管表面龟裂原因分析[J]．湖南冶金，2000，5：25-26．[49] 任建国，祁晓英，马学军，等．低合金钢热轧缺陷分析[J]．沈阳工业学院学报，1996，15(3)：35-37．[50] 卢居桂，安自亮，刘钰．夹杂物引起的石油套管缺陷分析[J]．天津冶金，2002，106(1)：27-29．[51] 田党．关于锥形辊穿孔机轧辊转速对毛管分层缺陷影响的讨论[J]．钢管，2006，35(4)：12-16．[52] 王永吉，陈大国，王世英，等．二辊斜轧穿孔轧辊转速对高合金钢毛管质量的影响[J]．钢铁，1985，20(2)：25-30．[53] 严智．高温合金穿孔工艺的研究[J]．特钢技术，1994，2：27-31．[54] 田党．高温合金无缝管材的研制与生产[J]．钢管，2002，31(3)：1-6．[55] 田党．关于毛管分层缺陷的试验研究[J]．轧钢，1997，6：7-10．[56] 田党．高温合金管坯在二辊斜轧穿孔机上的穿孔实践[J]．天津冶金，1996，4：25-28．[57] 田党．毛管分层缺陷形成过程的观察和分析[J]．天津冶金，1996，1：24-26．[58] 田党．高温合金毛管分层缺陷形成的过程[J]．钢管，1992，1：19-22．[59] 卢于逑，王先进．二辊斜轧穿孔中心金属断裂机理和穿孔变形工艺实质[J]．钢铁，1980，6：7-15．[60] 卢于逑，王先进．二辊斜轧穿孔圆坯断面的变形分布[J]．金属学报，1980，4：470-479．[61] 田党，张根良，卜玉钦．二辊斜轧穿孔时高温合金钢圆坯的变形分布及分层形成机制[J]．钢铁，1995，30(1)：40-46．[62] 田党，李群．关于锥形辊穿孔机的穿孔原理及应用问题的讨论[J]．钢管，2003，32(6)：1-4．[63] 赵咏秋，吴秀丽，陈菊芳．0Cr18Ni9Ti热轧荒管分层内裂原因分析[J]．物理测试，1999，2：33-35．[64] 张存信，冯晓庭，项炳和，等．不锈钢无缝管加工过程中断裂原因简析[J]．钢管，2008，37(3)：38-42．[65] 袁桂林，苏殿荣．GCr15钢管环状层裂在二辊斜轧穿孔过程中的发生和发展[J]．钢管，1983，3：15-18．[66] 张世文，刘仓理，李庆忠，等．初始应力状态对材料层裂破坏特性影响研究[J]．力学学报，2008，40(4)：535-542．[67] 侯凤桐．日本住友金属公司新开发的菌式穿孔机[J]．钢管技术，1985，2：57-59．[68] Chihiro HAYASHI，Tomio YAMAKAWA．Influences of Feed and Cross Angleon Inside Bore and Lamination Defects in Rotary Piercing for Materials with Poor Hot Workability [J]．ISIJ International，1997，37(2)：153-160．[69] 嵇国金，彭颖红，阮雪榆．有关金属体积成形中的韧性断裂准则[J]．金属成形工艺，1998，16(4)：36-37．[70] 郭达人编译．金属材料的断裂及其断口分析[J]．国外金属热处理，1996，17(4)：25-31．[71] 黄建科，董湘怀．金属成形中韧性断裂准则的细观损伤力学研究进展[J]．上海交通大学学报，2006，40(10)：1748-1753．[72] Oyane M，Sota T，Okintoto K，et al．Criteria for ductile fractures and theirapplications[J]．J Mech Work Tech，1980，4：65-81．[73] 郑长卿，张克实，周利．金属韧性破坏的细观力学及其应用研究[M]．北京：国防工业出版社，1995，28-32．[74] Venugopal Rao A，Ramakrishnan N，Krishna Kumar R．A comparativeevaluation of the theoretical failure criteria for workability in cold forging[J]．Journal of Materials Processing Technology，2003，142(1)：29-42．[75] Komori Kazutake．Effect of ductile fracture criteria on chevron crack formationand evolution in drawing[J]．International Journal of Mechanical Sciences，2003，45(1)：141-160．[76] Ozturk Fahrettin，Lee Daeyong．Analysis of forming limits using ductile fracturecriteria[J]．Journal of Materials Processing Technology，2004，147(3)：397-404．[77] Jeong Kim，Sung-Jong Kang，Beom-Soo Kang．A prediction of bursting failurein tube hydroforming processes based on ductile fracture criterion[J]．Int J Adv Manuf Technol，2003，22：357-362．[78] 虞松，陈军，阮雪榆．韧性断裂准则的试验与理论研究[J]．中国机械工程，2006，17(19)：2049-2052．[79] 胡庆安，程侠，邰卫华．金属材料断裂预测损伤破坏准则的应用[J]．长安大学学报，2007，27(4)：100-102．[80] 俞树荣，严志刚，曹睿，等．有限元软件模拟裂纹扩展的方法探讨[J]．甘肃科学学报，2003，15(4)：15-21．[81] 陈乃超，田冠玉，郑博．12Cr1MoV短期高温冲击断裂韧性及其参数的研究[J]．上海电力学院学报，2008，24(2)：178-181．[82] Ken-ichiro Mori，Hidenori Yoshimura，Kozo Osakada．Simplified three-dimensional simulation of rotary piercing of seamless pipe by rigid-plastic finite-element method[J]．Journal of Materials Processing Technology，1998，80-81：700-706．[83] Y van Chastel，Aliou Diop，Silvio Fanini，et al．Finite Element Modeling ofTube Piercing and Creation of a Crack[J]．Int J Mater Form，2008，Suppl 1：355-358．[84] Hyoung Wook Lee，Geun An Lee，Eung Kim，et al．Prediction of plug tipposition in rotary tube piercing mill using simulation and experiment[J]．International Journal of Modern Physics B，2008，22(31-32)：5787-5792．[85] S Fanini，A Ghiotti，S Bruschi．Evaluation of Fracture Initiation in theMannesmann Piercing Process[C]．The 10th ESAFORM Conference on Material Forming，2007，709-714．[86] Saurabh Dwivedi，Samuel H，Huang Jun Shi，et al．Yield prediction for seamlesstubing processes: a computational intelligence approach[J]．Int Adv Manuf Technol，2008，37：314-322．[87] Elisabetta Ceretti，Claudio Glaudio，Aldo Attanasio．3D Simulation andValidation of Tube Piercing Process[C]．NUMIFORM 07 Materials and Design: Modling, Simulation and Applications，2007，413-418．[88] Kazutake Komori．Simulation of Mannesmann piercing process by thethree-dimensional rigid-plastic finite-element method[J]．International Journal of Mechanical Sciences，2005，47：1838-1853．[89] Hayashi C，Yamakawa T．Influence of feed and cross angle on rotary forgingeffects and redundant shear deformation in rotary piercing process[J]．ISIJ International，1997，37：146-152．[90] 曾幼宗．斜轧穿孔工艺的有限元分析[J]．钢管，2004，33(3)：51-53．[91] 双远华，赖明道，张中元．斜轧穿孔过程金属流动的有限元模拟[J]．机械工程学报，2004，40(3)：140-144．[92] 双远华，赖明道，张中元．钢管斜轧过程应力应变与温度耦合模拟分析[J]．锻压技术，2003(6)：36-40．[93] 李胜衹，陈大宏，孙中建，等．二辊斜轧穿孔时圆管坯的变形与应力分布及其发展[J]．钢铁研究学报，2000，12(5)：26-30．[94] A Ghiotti，S Fanini，S Bruschi，et al．Modeling of the Mannesmanneffect[J]．CIRP Annals-Manufacturing Technology，2009，58：255-258．[95] E.I. Panov．Shear Stresses and Their Dependence on Different ProcessParameters in The Helical Rolling of Solid Semifinished Products[J]．Metallurgist，2005，49(7-8)：280-292．[96] E.I. Panov．Certain Aspects of The Stress-Strain State of Semifinished Productsin Helical Rolling[J]．Metallurgist，2003，47(11-12)：499-505．[97] E.I. Panov．Effect of thrust and tension on the radial stresses in helical rolling[J]．Metallurg，2004，4：50-57．[98] Z. Pater，J. Kazanecki，J. Bartnicki．Three dimensional thermo-mechanicalsimulation of the tube forming process in Diescher’s mill [J]．Journal of Materials Processing Technology，2006，177：167-170．[99] 双远华，陈惠琴，赖明道．斜轧管材生产中内部组织有限元模拟和预测[J]．中国有色金属学报，2001，11(2)：238-242．[100] 双远华，张中元，赖明道．热轧穿孔内部组织控轧的工业性试验研究[J]．钢铁，2002，37(6)：42-47．[101] J C Prince，R Maroño，F León．Thermomechanical analysis of a piercing mandrel for the production of seamless steel tubes[J]．J. Process Mechanical Engineering，2003，217：337-344．[102] W.A.Khudheyer，D.C.Barton，T.Z.Blazynski．A comparison between macroshear redundancy and loading effects in 2- and 3-roll rotary tube cone piercers[J]．Journal of Materials Processing Technology，1997，65：191-202．[103] A.N.Nikulin，V.V. Streletskii．Deformation of continuous cast metal during rotary rolling[J]．Metallurgist，2005，49(3-4)：97-101．[104] Kazutake Komori，Kouta Mizuno．Study on plastic deformation in cone-type rotary piercing process using model piercing mill for modeling clay[J]．Journal of Materials Processing Technology，2009，209：4994-5001．[105] 李连诗．钢管塑性变形原理(上册)[M]，北京：冶金工业出版社，1985：178-185．[106] 卢于逑．斜轧穿孔过程中应力和变形的分布和中心金属断裂机构的某些特点分析[D]．北京：北京钢铁学院，1963．[107] 卢于逑，王先进．二辊斜轧穿孔时圆坯断面的变形分布和发展[J]．金属学报，1980，16(4)：470-479．[108] 严泽生．现代热轧无缝钢管生产[M]．北京：冶金工业出版社，2009：175-195．[109] Takuda H，Mori K，Hatta N．The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals[J]．J Mater Process Technol，1999，95：116-121．[110] Takuda H，Mori K，Fujimoto H，et al．Prediction of the forming limit in bore-expanding of sheet metals using ductile fracture criteria[J]．J Mater Process Technol，1999，92-93：433-438．[111] Mori K，Takuda H．Prediction of forming limit in deep drawing of finite element simulation and criterion for ductile fracture[J]．Transaction of NAMRI/SME XXIV，1996，143-148．[112] Takuda H，Mori K，Takakura N，et al．Finite element analysis of limit strains in biaxial stretching of sheet metals allowing for ductile fracture[J]．Int J Mech Sci，2000，42：785-798．。

Fracture toughness and fatigue crack growth properties of the base metal and weld metal of a type 30

Fracture toughness and fatigue crack growth properties of the base metal and weld metal of a type 304stainless steel pipeline for LNG transmissionJong-Hyun Baek *,Young-Pyo Kim,Woo-Sik Kim,Young-Tai KhoR &D Center,Korea Gas Corporation,638-1,Il Dong,Ansan,Kyunggi-Do,425-790,South KoreaReceived 11November 2000;revised 26February 2001;accepted 26February 2001AbstractThe fatigue crack growth rate and CTOD tests on type 304stainless steel and weld metal were studied over the temperature range 21628C to room temperature.The girth weld metal specimens were fabricated using a combination of gas-tungsten-arc-welding and shielded-metal-arc-welding.The seam weld joint was made by submerged arc welding.Fracture toughness was evaluated through CTOD tests with three point bend specimens.The fatigue crack growth rate tests were conducted using compact tension specimens in accordance with ASTM E647.The CTOD values were affected by crack orientation with respect to the rolling direction,but orientation had no in¯uence on the fatigue crack growth rates.The fatigue crack growth rates and the CTOD values decreased with decreasing test temperature.q 2001Elsevier Science Ltd.All rights reserved.Keywords :Stainless steel;LNG,CTOD;Fatigue crack growth rate;Fracture toughness1.IntroductionDemand for clean and convenient natural gas has continuously increased.Natural gas is more ef®ciently stored and transported as lique®ed natural gas (LNG)below the liquefaction temperature because the volume of LNG is about 1/600of that in the gaseous form.The materials for storage and transmission of LNG should have good mechanical properties at low temperature because the boiling point of LNG is 21628C under 1atm.The structural materials for cryogenic application should exhibit high strength,ductility,fracture tough-ness,good weldability and fabrication [1±4].The AISI type 304austenitic stainless is widely used for LNG utilisation because of its good metallurgical and mechanical properties [2,3].Type 304austenitic stain-less pipes for LNG transmission are invariably joined by welding.The integrity of welded structures is considerably reduced by fatigue in the presence of weld metal defects such as incomplete fusion,gas pore,undercut and slag inclusion.The pipes for LNG transmission are subjected to repeated thermal stress as a result of temperature gradients and pressure ¯uctua-tion due to changes of operating conditions [2,3,5].The coef®cient of thermal expansion of 304austenitic stain-less is about one and a half times higher than that of carbon steel [6].The result of this could be increased distortion,buckling and fatigue fracture at the weld joint.There have been a large number of studies of the fatigue and fracture toughness of the weld metal and base metal of austenitic stainless steel [5±10].Little research,however,has been done on the fatigue and fracture toughness properties at LNG temperature under ®eld operating conditions.Mukai et al.,investi-gated the tensile and fatigue properties of base metal of austenitic stainless steel at temperature between 20and 21628C [2].The authors in Ref.[2]did not deal with fracture toughness of the base metal and mechanical properties of the weld metal.The elastic±plastic frac-ture mechanics approach to analysis of fatigue beha-viour of the weld metal has become a valuable method in establishing design criteria and structural integrity.Fatigue crack growth rate and CTOD tests to evaluate integrity using specimens machined from the welded 304austenitic stainless pipes over the temperature range from room temperature to 21628C are described and discussed in this paper.2.Experimental proceduresThe material used in this study was type 304austenitic stainless steel pipe for LNG transmission.The pipe,International Journal of Pressure Vessels and Piping 78(2001)351±3570308-0161/01/$-see front matter q 2001Elsevier Science Ltd.All rights reserved.PII:S0308-0161(01)00040-0/locate/ijpvp*Corresponding author.Tel.:182-31-400-7487;fax:182-31-416-9014.E-mail address:jhbaek@kogas.re.kr (J.-H.Baek).with a 26.9mm wall thickness and 406.4mm outer diameter,was seam-welded by submerged-arc-welding with ER308L ®ller metal.The girth welding was done by gas-tungsten-arc-welding with ®ller metal of ER308L up to the 4th pass followed by the shield-metal-arc-welding with E308L electrode for the remainingpasses.Details of the girth welding conditions are given in Table 1.Three CTOD tests were conducted at each temperature to evaluate the fracture toughness.Each CTOD test was carried out in accordance with BS 7448part 1using specimens of the B £2Brectangular type with 13mm thickness.Testing was carried out in three point bending under displacement control at a crosshead displacement rate of 1mm/min.Tensile tests were carried out at the same temperature as the CTOD tests.The compact tension specimens for fatigue crack growth tests were manufactured with a size of 52mm width (W)and 6.5mm thickness (B)according to ASTM E647.Fig.1shows the crack orientation of specimens in the welded pipe.The compact tension specimens with the notch perpendicular (LT)andJ.-H.Baek et al./International Journal of Pressure Vessels and Piping 78(2001)351±357352Table 1Girth welding condition Weld processesFiller metal Electrical properties Travel speed (cm/min)Heat input (kJ/cm)ElectrodeDia.Polarity Amp.Vol.GTAW (1±4th pass)ER308L 2.4DCSP 151±16017.5±19.618.3±36.4 4.3±10.3SMAW (5±10th pass)E308L 3.2DCRP87.4±98.630.0±33.24.6±8.818.0±42.8Table 2Chemical composition of the base metal and weld metal (wt%)Specimens C Mn P S Si Ni Cr Mo Nb Fe Cr eq Ni eq Base 0.096 1.540.040.0110.829.5616.050.090.02Bal.17.3712.65Seam 0.076 1.240.040.0160.928.6316.680.070.05Bal.18.1713.14Girth0.0250.740.040.0110.799.8916.680.090.05Bal.17.9913.00Fig.2.SEM photographs of the base and weld metal on the CTOD specimens at 21628C:(a)LT of base metal;(b)TL of base metal;(c)Seam weld metal;(d)Girth weldmetal.Fig.1.Schematic illustration of the direction of crack propagation.parallel(TL)to the rolling direction in the case of the base metal were also prepared.The notch in the girth weld(GW)and seam weld(SW)specimens was aligned parallel to the welding direction along the weld centre-line.All the specimens were extracted from the centre of the thickness of the pipe.The fatigue tests were performed at a frequency of20Hz with a maximum load of8.825kN under load control(R 0.1)by using a sinusoidal stress waveform.Changes in crack length(a)during the fatigue tests were measured by a clip gauge.Each test was started30min after holding the specimen at the speci®ed temperature.The tempera-ture¯uctuation was kept within^18C.3.Results and discussion3.1.Chemical composition and tensile propertiesThe chemical compositions of the base metal and weld metals are given in Table2.There were small differences in the Cr and Ni contents.The carbon content was the highest for the base metal at0.096%, while the girth weld had the lowest value of0.025%. Contents of sulphur and phosphorous were within the ASTM A312and AWS SFA5.4,5.9speci®cations.The Creq on the girth weld and seam weld was found from calculation to17.99,18.17and the Nieq was13.00, 13.14,respectively.Cr and Ni equivalent were cal-culated from the Eq.of Creq %Cr1%Mo11.5 x%Si10.5x%Nb and Nieq %Ni130£%C10.5 X%Mn.The effect of the temperature on the tensile and yield strength is shown in Table3.The tensile strength at21628C is about twice that at room tempera-ture[11]for both base and weld metal.The yield strengths were relatively insensitive to the test temperature [4].3.2.CTOD testsThe CTOD values are presented in Table 4.All values were calculated at maximum load as there was no pop-in and unstable crack propagation during tests. Fracture toughness of LT specimens,crack growth transverse to the plate rolling direction,showed higher toughness values than TL specimens in base metal.The CTOD values of seam weld metal are similar to those of girth weld metal at all test temperatures.Fig.2 shows fractographs of the fracture from CTOD speci-mens from the base and weld metals.There were differences in dimple size with test temperature in the base metal.The dimple size decreased from10±15m m (not presented here)to3±4m m(Fig.2a and b)as the temperature reduced from room temperature to21628C.J.-H.Baek et al./International Journal of Pressure Vessels and Piping78(2001)351±357353 Table3Strength properties of the base metal and weld metalTemp.(8C)Strength(MPa)Base metal(TL)Base metal(LT)Girth weld Seam weld 20YS288.73297.64300.94319.62UTS697.90695.33576.16580.712100YS350.73266.19322.68335.14UTS1211.381057.95985.891065.112162YS354.71373.12358.91322.51UTS1410.981411.551211.741236.27Temperature had little in¯uence on the weld metal dimple size.A spherical inclusion with a size of 1±2m m was examined in the dimples of the weld metal (Fig.2c and d).Examples of energy dispersive X-ray analysis on the inclusions of Fig.2c and d are shown in Fig. 3.These inclusions were determined as a compound of silicon,manganese,oxygen,aluminium and sulphur.J.-H.Baek et al./International Journal of Pressure Vessels and Piping 78(2001)351±357354Fig.4.The crack growth rates of the base metal and weld metals with variation of temperature:(a)TL of base metal;(b)LT of base metal;(c)Seam weld metal;(d)Girth weld metal.Table 4CTOD values of the base metal and weld metal (unit:mm)Temp.(8C)Base metal (TL)Base metal (LT)Girth weld Seam weld 20 1.110 1.153a 2.218 2.079a ±0.791a 0.9240.909a 1.195 1.8750.7950.971± 2.1450.7870.83321000.6580.762a 1.088 1.092a 0.4770.517a 0.5250.475a 0.786 1.1220.5390.4460.843 1.0650.5360.45421620.4560.444a0.4740.471a0.3400.386a0.4490.440a0.4270.4760.4560.4740.4490.4630.3620.396aAverage of CTOD values.3.3.Fatigue crack growth rateThe fatigue crack growth rate tests were conducted according to ASTM E647.For the compact tension speci-mens,the stress intensity factor range(D K)was obtained fromD KD PBWp21a12a 3=20:88614:64a213:32a2114:72a325:6a4where D P is the load amplitude,a a/W,a the distancebetween the crack tip and loading line,W the specimenwidth and B the specimen thickness[12].The fatiguecrack growth rate data are presented in Figs.4and5.Thefatigue crack growth obeys the Paris relation,d a=d NC D K m;where C and m are numerical constants[13].The crack growth rates of all the specimens except girthweld metal(GW)were fastest at room temperature(Fig.4).The crack growth rates at2100and21628C indi-cated similar behaviour for both the base metal and seam J.-H.Baek et al./International Journal of Pressure Vessels and Piping78(2001)351±357355 Fig.5.The crack growth rates on the different specimens at(a)room temperature and(b)21628C.Fig.6.SEM photographs of the base and weld metal on the fatigue specimens at21628C and50MPa-m1/2.(a)LT of base metal(b)TL of base metal(c)Seam weld metal(d)Girth weld metal.weld metal.In the case of the girth weld metal,the fatigue crack growth rate at 21008C suggested a higher resistance to crack growth than at room temperature and 21628C.The crack growth rates on the different specimens at room temperature and 21628C are plotted in Fig.5.The crack growth resistance under fatigue of the seam weld metal was the poorest at room temperature.At 21628C the crack growth rate of the girth weld metal was faster than any other specimens.There was no signi®cant difference in crack growth rate for LT and TL specimens of base metal but there was an obvious difference in CTOD values for LT and TL specimens.Fig.6shows fracture surfaces on the LT and TL specimens of the base metal and weld metals at D K of 50MPa m 1/2after fatigue cracking at 21628C.The fracture surface was smooth in the base metal of (Fig.6a and b)but many inclusions were observed in the weld metal of (Fig.6c and d).Examples of energy dispersive X-ray analysis on the inclusions of (Fig.6c and d)are shown in Fig.7.These inclusions were analyzed as a compound of silicon,manganese,oxygen,aluminium and sulphur.The presentation in terms of log C versus m calculated fromd a =d N C D K m ;is presented in Fig.8.The m values increased as temperature reduced from room temperature to 21628C while the C values decreased with decreasing temperature.The m value was about 3±4at room tempera-ture and increased to 4.3±6.4at 21628C.From Fig.8,it can be concluded that the fatigue crack growth rates on the material used in this study decrease with reducing tempera-ture in the range from room temperature to 21628C.4.ConclusionsFatigue crack growth rate and CTOD tests for type 304stainless steel and weld metal were studied over the temperature range from room temperature to 21628C.1.The CTOD values decreased with decreasing tempera-ture and the CTOD values of the base metal were higher than those of weld metals.2.The CTOD values were in¯uenced by the crack propaga-tion orientation relative to the rolling direction.3.The fatigue crack growth rates of base metal and weld metal decreased with decreasing test temperature,but the crack propagation rate was relatively insensitive to orien-tation in the base metal.4.The base metal possessed superior resistance to crack growth relative to weld metals over the entire tempera-ture range.References[1]Avery RE,Parsons D.Welding stainless and 9%nickel steel cryo-genic vessels.Weld J 1995;74(11):45±50.[2]Mukai K,Hoshino K,Fujioka T.Tensile and fatigue properties ofaustenitic stainless steels at LNG temperature.Tetsu-to-Hagane 1979;65:1756±65.[3]Tsuzaki K,Nakanishi E,Maki T,Tamura I.Low-cycle fatigue beha-vior in metastable austenitic steel accompanying deformation-induced martensitic transformation.ISIJ 1983;23:834±41.[4]Mills WJ.Fracture toughness of type 304and 316stainless steelsand their welds.International Materials Reviews 1997;42(2):45±82.J.-H.Baek et al./International Journal of Pressure Vessels and Piping 78(2001)351±357356Fig.7.Results of energy dispersive X-ray analysis on the inclusion of (Fig.6c and d).(a)Seam weld metal (b)Girth weldmetal.[5]Nakamura T,Tominaga M,Murase H,Nishiyama Y.Low cyclefatigue behavior of austenitic stainless steel at cryogenic temperature.Tetsu-to-Hagane1982;68:471±6.[6]Gordon J,Hanson A.An introduction to stainless steel.Metals Park,OH:ASM,1965p.137±8.[7]Ogawa R,Moris JW.Fatigue crack growth behavior in a nitrogen-strengthened high-manganese steel at cryogenic temperatures.ASTM STP1985;857:47.[8]Verkin BI,Grinberg NM,Serdyuk VA,Yakovenko LF.Low tempera-ture fatigue fracture of metals and alloys.Mater Sci Eng 1983;58:145±68.[9]Kawasaki T,Nakanishi S,Sawaki Y,Hatanaka K,Yokobori T.Fracture toughness and fatigue crack profagation in high strengthsteel from room temperature to21808C.Eng Frac Mech 1975;7:465±72.[10]Liaw PK,Logsdon WA.Fatigue crack growth threshold at cryogenictemperature:A review.Eng Frac Mech1985;22(4):585±94. [11]Matsumoto T,Satoh H,Wadayama Y,Hataya F.Mechanical proper-ties of fully austenitic weld deposits for cryogenic structures.Weld J 1987;66(4):120-s±6-s.[12]Strawley JE.Wide range stress intensity factor extressions for ASTME399standard fracture toughness specimens.Int J Fract 1976;12(6):475±6.[13]Paris PC,Gomez MP,Anderson WE.A rational analytic theory offatigue.The Trend Engng1961;13:9±14.J.-H.Baek et al./International Journal of Pressure Vessels and Piping78(2001)351±357357。

不锈钢的疲劳裂纹扩展有限元模拟-英文版(另有中文翻译)

Modeling of fatigue crack growth of stainless steel 304LFeifei Fan,Sergiy Kalnaus,Yanyao Jiang *Department of Mechanical Engineering (312),University of Nevada,Reno,NV 89557,USAa r t i c l e i n f o Article history:Received 7November 2007Received in revised form 9June 2008Keywords:Damage accumulation Fatigue crack growth Fatigue criteriona b s t r a c tAn effort is made to predict the crack growth of the stainless steel 304L based on a newly developed fatigue approach.The approach consists of two steps:(1)elastic–plastic ﬁnite element (FE)analysis of the component;and,(2)the application of a multiaxial fatigue cri-terion for the crack initiation and growth predictions based on the outputted stress–strain response from the FE analysis.The FE analysis is characterized by the implementation of an advanced cyclic plasticity theory that captures the important cyclic plasticity behavior of the material under the general loading conditions.The fatigue approach is based upon the notion that a material point fails when the accumulated fatigue damage reaches a cer-tain value and the rule is applicable for both crack initiation and growth.As a result,one set of material constants is used for both crack initiation and growth predictions.All the mate-rial constants are generated by testing smooth specimens.The approach is applied to Mode I crack growth of compact specimens subjected to constant amplitude loading with differ-ent R -ratios and two-step high–low sequence loading.The results show that the approach can properly model the experimentally observed crack growth behavior including the notch effect,the R -ratio effect,and the sequence loading effect.In addition,the early crack growth from a notch and the total fatigue life can be simulated with the approach and the predictions agree well with the experimental observations.Ó2008Elsevier Ltd.All rights reserved.1.IntroductionLoad-bearing engineering components are often sub-jected to cyclic loading and failure due to fatigue is of a great concern.Generally,fatigue process consists of three stages:initiation and early crack growth,stable crack growth,and ﬁnal fracture.Traditionally,the crack growth rate (d a /d N )is expressed as a function of the stress inten-sity factor range (D K )on a log–log scale.The stable crack growth results under constant amplitude loading with dif-ferent R -ratios (the minimum load over the maximum load over a loading cycle)are often represented by the Paris law (Paris and Erdogan,1963)and its modiﬁcations (Walker,1970;Kujawski,2001).Different materials behave differ-ently under constant amplitude fatigue loading.Some materials display a R -ratio effect:crack growth rate curves are coincided for the same R -ratio,but a higher R -ratio re-sults in a higher crack growth rate (Kumar and Garg,1988;Pippan et al.,2005;Wu et al.,1998;Zhao et al.,2008).Other metallic materials do not reveal any R -ratio effect,and the curves for constant amplitude loading overlap in a log–log scale (Crooker and Krause,1972;Kumar and Pan-dey,1990;Wang et al.,to appear ).The fatigue crack growth behavior under variable amplitude loading is another subject that has been studied for a number of years.The application of an overload (ten-sile load of high magnitude applied over one cycle pre-ceded and followed by constant amplitude loading)or change in the loading amplitude (so-called high–low se-quence loading experiments)can introduce profound effects on the fatigue crack growth.For most metallic materials,the application of the abovementioned loading schemes results in a crack growth rate retardation.Based on the linear elastic fracture mechanics (LEFM)concept,such a transient behavior is often modeled by using the stress intensity factor concept and by introducing correc-tion factors to the Paris law on the stable crack growth0167-6636/$-see front matter Ó2008Elsevier Ltd.All rights reserved.doi:10.1016/j.mechmat.2008.06.001*Corresponding author.Tel.:+17757844510;fax:+17757841701.E-mail address:yjiang@ (Y.Jiang).Mechanics of Materials 40(2008)961–973Contents lists available at ScienceDirectMechanics of Materialsj o u r n a l h o m e p a g e :/loc ate/mechmatregime.A model of such a type was introduced by Wheeler (1972)and can be viewed as a practical way of treating the effects of variable amplitude loading.Several modiﬁcations on Wheeler’s model have been proposed(Kim et al.,2004; Yuen and Taheri,2006;Zhao et al.,2008)targeting the par-ticular shapes of the crack growth curves for different materials subjected to variable amplitude loading.These models have little or no physical basis and the results of the crack growth experiments are needed in order to ob-tain a set ofﬁtting constants to calibrate the models.Since its introduction by Elber(1970),the crack closure concept is often used to explain crack growth behavior.The retardation in crack growth rate generated by a single ten-sile overload was explained by using the crack closure con-cept in Elber’s later study(Elber,1971).The concept of K op was introduced as a stress intensity factor corresponding to the crack opening load,and the effective stress intensity factor range from K op to K max was considered as a crack driving parameter.As a result,the contribution to crack propagation comes from a part of the total stress intensity factor range corresponding to the part of the cycle when the crack is open.Such an approach is used to explain the R-ratio and variable loading effects.However,the crack closure method has been under criticism based upon experimental observations(Lang and Marci,1999;Sada-nanda et al.,1999;Silva,2004;Feng et al.,2005)and numerical simulations(Jiang et al.,2005;Mercer and Nich-olas,1991;Zhao et al.,2004).Crack-tip blunting has been used to explain the crack advance(Gu and Ritchie,1999;Tvergaard,2004).The retardation caused by an overload is attributed mainly to the compressive residual stresses ahead of the crack tip, plasticity induced crack closure behind the crack tip,or the combination of these two.The initial acceleration in the crack growth immediately after the application of an overload was explained as a result of the tensile residual stress due to crack-tip blunting(Makabe et al.,2004).The ﬁnite element analysis was used to analyze the stress dis-tribution and the crack opening displacement which was related to the variable amplitude loading effects(Zhang et al.,1992;Ellyin and Wu,1999;Tvergaard,2006).Generally,a fatigue crack is nucleated at a notch due to the stress concentration.The so-called notch effect on short crack behavior exists and the crack growth rate may be higher or lower than that expected based on the stable growth.Extensive research has been carried out to study the crack initiation and early crack growth behavior from a notch.Around a notch,a transition zone exists and the fatigue crack growth rate may decelerate,accelerate,or non-propagate after the crack initiation under constant amplitude loading.In order to model the short crack growth behavior from a notch,efforts were concentrated on the‘‘effective stress intensity factor”near the notches (Sadanandam and Vasudevan,1997;Dong et al.,2003; Teh and Brennan,2005;Vena et al.,2006),notch tip plas-ticity(Li,2003;Hammouda et al.,2004),and the combina-tion of crack tip cyclic plasticity and the contact of the crack surfaces(Ding et al.,2007a).A recent effort by Jiang and co-workers(Ding et al., 2007a,b;Feng et al.,2005;Jiang and Feng,2004a)at-tempted to use a multiaxial fatigue criterion to unify the predictions of both crack initiation and crack growth.The notion is that both crack initiation and the subsequent crack growth are governed by the same fatigue criterion.A material point fails to form a crack once the accumula-tion of the fatigue damage reaches a certain critical value. The approach has been applied to1070steel with success. The predictions of the early crack growth from notches (Ding et al.,2007a;Jiang,Ding and Feng,2007),the stable crack growth(Feng et al.,2005;Jiang and Feng,2004a; Jiang,Ding,and Feng,2007),the overload effect(Jiang and Feng,2004a;Jiang,Ding,and Feng,2007),the R-ratio effect(Jiang and Feng,2004a;Jiang,Ding,and Feng, 2007),and the crack growth under direction-changing loading(Ding et al.,2007b)agreed well with the experi-mental observations.All the predictions of the crack growth were based on the material constants generated from testing the smooth specimens.In the present investigation,the aforementioned ap-proach is used to simulate the crack growth from the notched specimens made of the AISI304L austenitic stain-less steel.The notch effect on the early crack growth,the R-ratio effect,and the inﬂuence of the loading sequence are modeled.The stress analysis is conducted by using theﬁ-nite element method implementing a robust cyclic plastic-ity model.The predicted results are compared with the results of the crack growth experiments.2.Crack growth modelingIn the present investigation,the fatigue approach devel-oped by Jiang and co-workers(Jiang and Feng,2004a;Jiang et al.,2007)is used to model the crack growth of the stain-less steel304L.The approach is based on the assumption that any material point fails if the accumulation of the fa-tigue damage reaches a critical value on a material plane.A fresh crack surface will form on the material plane at the material point.Essentially,the approach consists of two major computational steps:a)Elastic–plasticﬁnite element(FE)stress analysis forthe determination of the stress and strain history atany material point of a component,and,b)Application of a multiaxial fatigue criterion utilizingthe stress and strain obtained from the previous stepfor the determination of crack initiation and crackgrowth.The following sub-sections describe the methods em-ployed in the current study.2.1.Cyclic plasticity model and multiaxial fatigue criterionEarlier studies indicate that an accurate stress analysis is the most critical part for the fatigue analysis of the mate-rial(Jiang and Kurath,1997a,b;Jiang and Zhang,2008; Kalnaus and Jiang,2008;Jiang et al.,2007).If the stresses and strains can be obtained with accuracy,fatigue life can be reasonably predicted by using a multiaxial fatigue criterion.The elastic–plastic stress analysis of a notched or cracked component requires the implementation of a962 F.Fan et al./Mechanics of Materials40(2008)961–973cyclic plasticity model into FE software package.The selec-tion of an appropriate cyclic plasticity model is crucial for an accurate stress analysis of a component subjected to cyclic loading.Cyclic plasticity deals with the non-linear stress–strain response of a material under repeated external loading.A cyclic plasticity model developed by Ohno and Wang (1993,1994)and Jiang and Sehitoglu (1996a,b)is used in the present FE simulations of the stress and strain response in a notched or cracked component.The model is based on the kinematic hardening rule of the Armstrong–Frederick type.Basic mathematical equations constituting the model are listed in Table 1.A detailed description of the plasticity model together with the procedures for the determination of material constants can be found in corresponding refer-ences (Jiang and Sehitoglu,1996a,b ).The choice of the cyc-lic plasticity model was based on its capability to describe the general cyclic material behavior including cyclic strain ratcheting and stress relaxation that occur in the material near the notch or crack tip.The plasticity model listed in Table 1was implemented into the general purpose FE package ABAQUS (2007)through the user deﬁned subroutine UMAT.A backward Euler algorithm is used in an explicit stress update algo-rithm.The algorithm reduces the plasticity model into a non-linear equation that can be solved by Newton’s meth-od.The corresponding consistent tangent operator is de-rived for the global equilibrium iteration,which ensures the quadratic convergence of the global Newton–Raphson equilibrium iteration procedure (Jiang et al.,2002).A critical plane multiaxial fatigue criterion developed by Jiang (2000)is used for the assessment of fatigue dam-age.The criterion can be mathematically expressed as follows,d D ¼r mrr 0À1m 1þr r fb r d e p þ1Àb s d cpð1ÞIn Eq.(1),D represents the fatigue damage on a material plane and b and m are material constants.r and s are the normal and shear stresses on a material plane,and e p and c p are the plastic strains corresponding to stresses r and s ,respectively.r 0and r f are the endurance limit and the true fracture stress of the material,respectively.r mr is a memory stress reﬂecting the loading magnitude.For constant amplitude loading,r mr is equal to the maximum equivalent von Mises stress in a loading cycle.The use ofMacCauley bracket hi ensures that when r mr 6r 0the fati-gue damage is zero.The critical plane is deﬁned as the material plane where the fatigue damage accumulation ﬁrst reaches a critical value,D 0.The Jiang multiaxial fatigue criterion has been success-fully applied to the fatigue predictions of a variety of mate-rials (Ding et al.,2007a,b;Feng et al.,2005;Gao et al.,to appear;Jiang,Ding,and Feng,2007;Jiang et al.,2007;Zhao and Jiang,2008).The incremental form of the criterion (Eq.(1))does not require a separate cycle counting method for general loading conditions.Any fatigue criterion making use of the stress/strain amplitude or range requires the deﬁnition of a loading cycle or reversal.Therefore,a cycle counting method is needed to deal with the variable ampli-tude loading.Although the rain-ﬂow cycle counting meth-od is widely accepted for counting the loading reversals/cycles,it is not well deﬁned for general multiaxial loading.The second feature of the criterion expressed by Eq.(1)is its capability to predict the cracking behavior.The Jiang fa-tigue criterion is a critical plane approach which is capable of predicting different cracking behavior through the intro-duction of constant b in Eq.(1).The value of constant b is selected to predict a particular mode of cracking based on the smooth specimen experiments.It has been shown (Jiang et al.,2007;Zhao and Jiang,2008)that the predic-tions of the cracking behavior based on the Jiang criterion are generally more accurate than the predictions based on the other multiaxial criteria such as the Fatemi–Socie mod-el (Fatemi and Socie,1988),the Smith–Waltson–Topper model (Smith et al.,1970)and the short-crack based crite-rion (Döring et al.,2006).Table 2lists the material constants used in the cyclic plasticity model and the fatigue model for stainless steelTable 1Cyclic plasticity model used in the ﬁnite element simulations Yield functionf ¼ðe S À~a Þ:ðe S À~aÞÀ2k 2¼0e S ¼deviatoric stress~a¼backstress k =yield stress in shear Flow lawd ~e p ¼1hh d ~S :~n i ~n ~n¼normal of yield surface h =plastic modulus function ~e p ¼plastic strain Hardening Rule~a¼P Mi ¼1~aði Þ~aði Þ¼i th backstress part d ~a ði Þ¼c ði Þr ði Þ~n À~a ði Þk k r ði Þ v ði Þþ1~a ði Þ~aði Þk k !dp M =number of backstress parts (i =1,2,3,...M )dp =equivalent plastic strain increment c (i ),r (i ),v (i )=material constantsTable 2Material constants for SS304L Cyclic plasticity constantsElasticity modulus E =200GPa Poisson’s ratio l =0.3k =115.5MPac (1)=1381.0,c (2)=507.0,c (3)=172.0,c (4)=65.0,c (5)=4.08r (1)=93.0MPa,r (2)=130.0MPa,r (3)=110.0MPa,r (4)=75.0MPa,r (5)=200.0MPa v (1)=v (2)=v (3)=v (4)=v (5)=8.0Fatigue constants r 0=270MPa;m =1.5;b =0.5;r f =800MPa;D 0=15000MJ/m 3F.Fan et al./Mechanics of Materials 40(2008)961–973963304L.The cyclic plasticity material constants were ob-tained from the cyclic stress–strain curve which was ob-tained from the experiments on the smooth specimens under fully reversed tension-compression loading.A com-plete description of procedure for determination of mate-rial constants can be found in corresponding references (Jiang and Sehitoglu,1996a,b ).The fatigue material con-stants were determined by comparing the fatigue data un-der fully reversed tension-compression and that under pure torsion (Jiang,2000).2.2.Finite element modelRound compact specimens with a thickness of 3.8mm were used in the crack growth experiments.The geometry and the dimensions of the specimen are shown in Fig.1.The crack growth experiments were conducted in ambient air.The specimens were subjected to constant amplitude loading with different R -ratios (the minimum load over the maximum load in a loading cycle)and high–low se-quence loading.All of the experiments started without a pre-crack,except two specimens tested under the follow-ing loading conditions:R =0.85,D P /2=0.54kN and R =À1,D P /2=5.0kN.More detailed information of the experiments and the experimental results were reported in a separate presentation.Due to the small thickness,plane-stress condition was assumed for the round compact specimen.Four-node plane-stress elements were used in FE mesh model.The FE mesh model shown in Fig.2was created by using the FE package HyperMesh (Altair HyperMesh,2004).Due to the symmetry in geometry and loading,only half of the specimen was modeled.To properly consider the high stress and strain gradients in the vicinity of the notch or crack tip,very ﬁne mesh size was used in these regions.The size of the smallest elements in the mesh model was 0.05mm.There were approximately 3058to 5067ele-ments used in the mesh model depending on the cracksize.The knife edges for the attachment of the open dis-placement gage in the specimen (Fig.1)were not modeled because the free end of the specimen does not affect the stress and strain of the material near the crack tip or notch.Referring to the coordinates system employed in Fig.2,the tensile external load,P ,is applied in the y direction uni-formly over nine nodes on the upper surface of the loading hole.To mimic the actual loading condition,the compres-sive load is applied in the negative y direction uniformly over nine nodes on the lower surface of the loading hole.The displacements in the x direction of the middle nodes on the upper edge of the loading hole are set to be zero.The displacements in the y direction for all the nodes on the plane in front of the crack tip or the root of the notch are set to be zero.In order to consider the possible contact between the upper and lower surfaces of a crack,the FE model incorpo-rates the contact pairs deﬁned in ABAQUS (2007).The crack surface of the lower symmetric half of the specimen is considered as a rigid surface which acts as the master surface.The corresponding crack surface of the upper half of the specimen serves as the slave surface.2.3.Determination of crack growth rateFor continuous crack growth under constant amplitude loading with small yielding,a simple formula was derived for the determination of the crack growth rate (Jiang and Feng,2004a ),d a d N ¼AD 0;ð2Þwhere,A ¼Zr 0D D ðr Þd r ;ð3Þr is the distance from the crack tip and r 0is the damaging zone size ahead of the crack tip where the fatigue damage is non-zero.D D (r )is the maximum fatigue damage per loading cycle with respect to all possible material planes at a given material point.D D (r )is determined by integrat-ing Eq.(1)over one loading cycle,D D ¼Icycler mrr 0À1m 1þr r fb r d e p þ1Àb s d cpð4ÞFig.1.Geometry and dimensions of the round compact specimen (all dimensions inmm).Fig.2.Finite element mesh model.964 F.Fan et al./Mechanics of Materials 40(2008)961–973for a given material point once the stress–strain response at the point is known.In Eq.(3),A denotes the damaging area enclosed by the D D(r)–r curve.Fig.3shows the distribution of D D(r)along the x-direc-tion for Specimen C01which was subjected to constant amplitude loading with R=0.1and D P/2=2.475kN. According to the fatigue criterion,Eq.(1),a material plane will accumulate fatigue damage when the memory stress is higher than the endurance limit and the material point experiences plastic deformation.For a cracked component, only the material near the crack tip accumulates fatigue damage.The values of D D(r)are determined along all ra-dial directions in a polar coordinate system with its origin being at the crack tip.The direction at which the crackgrowth rate is a maximum or the value of A is a maximum is the predicted cracking direction.The corresponding crack growth rate is the predicted crack growth rate.2.4.Crack initiation and early crack growth from notchThe approach described in the previous sub-sections as-sumes that a material point fails to form a fresh crack on the critical plane when the accumulation of the fatigue damage on the critical material plane reaches a critical va-lue,D0.The rule applies to the initiation of a crack and the crack extension after a crack has been formed.Therefore, the approach uniﬁes both the initiation and the subse-quent crack propagation stage.The distribution of the stress-plastic strainﬁeld in the vicinity of a notch root, however,inﬂuences the early crack growth,which should be properly considered.The deﬁnition of crack initiation used in the current study is different from that of the traditional way.The crack initiation of a fatigue crack is judged by using the fa-tigue criterion,Eq.(1).Once the fatigue damage on a mate-rial plane for the material point at the notch root reaches the critical fatigue damage,D0,the notched member is called to have initiated a fatigue crack.The FE stress analysis is conducted with the notched member for the designated loading condition.For a notched component,the maximum fatigue damage occurs at the notch root.The fatigue damage per loading cycle can be determined and it can be plotted as a distribution along the radial direction from the notch root.Fig.4shows an example for Specimen C20(R=0.2,D P/2=2.0kN,notched depth a n=7.38mm,notch radius=2.0mm).The distance,r,from the notch root is along the x-axis(refer to Fig.1).D D i denotes the fatigue damage per loading cycle on the critical plane during crack initiation.D D i is a function of the location of the material point.The maximum fatigue damage occurs at the notch root during crack initiation.The crack initiation life is predicted to be,N i¼D0D D in;ð5Þwhere N i is the predicted crack initiation life,D0is a mate-rial constant,and D D in is the fatigue damage per loading cycle on the critical plane at the root of the notch.D D in is D D i shown in Fig.4when r=0.During crack initiation,the fatigue damage is also accu-mulated in the vicinity of the notch root and should be considered in the determination of the crack growth near the notch.The area where the fatigue damage accumula-tion is non-zero during crack initiation(Fig.4)is referred to as the notch inﬂuencing zone(NIZ).For a specimen un-der a given loading condition,the NIZ can be determined by applying the fatigue criterion,Eq.(1),with the stress and strain histories outputted from the FE analysis.For Specimen C20shown in Fig.4,the NIZ size is approxi-mately0.85mm ahead of the notch root.For each material plane at any material point,the total fatigue damage at the end of the fatigue crack initiation is N i D D i.It should be reiterated that the discussion is based on the assumption that the material is stable in stress–strain response and the applied loading is constant ampli-tude.The crack growth rate within the NIZ can be deter-mined by using the following equation with the consideration of pre-existing fatigue damage accumulation (Ding et al.,2007a):d ad N¼AD0ÀN i D iðrÞ:ð6Þwhere A is the damage area enclosed by the D D(r)–r curve, as explained in Section2.3.In Eq.(6),N i and D D i(r)are re-lated to the fatigue damage accumulation during crack ini-tiation in the NIZ.For a given crack size within the NIZ the FE analysis is conducted.The distribution of the fatigue damage per loading cycle,D D(r),can be determined as a function of the distance from the crack tip,as shown in Fig.3.The enclosed area made by the D D(r)–r curve is A in Eq.(6).For any direction radiated from the crack tip, the direction which has the highest crack growth rate isF.Fan et al./Mechanics of Materials40(2008)961–973965the predicted cracking direction and the corresponding crack growth rate is the predicted crack growth rate.It can be seen that the difference between the crack growth rate determination near the notch(Eq.(6))and that away from the notch root(Eq.(2))lies in the consideration of the fatigue damage caused during the crack initiation stage.Generally,the stress–strain response becomes stabi-lized after a limited number of loading cycles.It was shown (Jiang and Feng,2004a)that the predicted crack growth re-sults obtained based on the stress–strain response from the10th loading cycle were very close to those based on the stabilized stress and strain response.Therefore,the FE analysis for a given notch or crack length under a desig-nated loading amplitude is conducted for10loading cycles. The stress and strain results at the10th loading cycle are used for the fatigue analysis.The stress and strain results obtained from analyzing the notched component during crack initiation will deter-mine the fatigue damage per loading cycle for each mate-rial plane at each material point.Eq.(5)is used to determine the crack initiation life.FE stress analyses are conducted with different crack lengths for a given loading condition.When the crack tip is within the notch inﬂuenc-ing zone,Eq.(6)is used for the crack rate determination.D D i(r)in Eq.(6)is the fatigue damage per loading cycle for a given material point during crack initiation.Once the crack grows out of the NIZ,Eq.(2)is used for the crack growth rate determination.In fact,D D i(r)is determined during crack initiation.As a result,Eq.(6)can be used for both situations since D D i(r)is zero for the material points out of the notch inﬂuencing zone.It should be noticed that the FE simulation is conducted cycle by cycle mimicking the real crack growth procedure. The crack initiation life is determinedﬁrst.The crack growth rates at several crack lengths are predicted by using the approach.Therefore,the prediction is the relationship between the crack growth rate,da/dN,and the crack length for a given notched component.With the crack initiation life obtained from using Eq.(5),the relationship between the crack length and the number of loading cycles can be established through a numerical integration.Simulations are also conducted for the high–low step loading conditions.In a high–low step loading experiment, an external load with higher loading amplitude is applied until a crack length reaches a certain value.The amplitude of the external load is switched to a lower value in the sec-ond loading step.In the simulations for the high–low load-ing sequence,one special consideration is made.The memory stress,r mr,in Eq.(1)is kept the same before and immediately after the change of the external load from a higher amplitude to a lower amplitude.After an extension of the crack in the second loading step,the memory stress returns to that under the lower constant amplitude loading.3.Results and discussion3.1.Crack growth experimentsThe material under consideration in the present study is AISI304L austenitic stainless steel which belongs to the class of metastable steels of300-series.Austenitic steels display a R-ratio effect when subjected to constant ampli-tude loading,as has been shown for AISI304(Mei and Morris,1990)and AL6-XN(Kalnaus et al.,2008).The experimental data used in the present investigation was the results of a series of experiments conducted by the authors.Fatigue crack growth experiments were performed using round compact specimens made of stainless steel 304L.The compact specimens were machined from an as-received cold rolled round bar.The bar had a diameter of41.28mm.The dimensions of the specimens are shown in Fig.1.The U-shaped notches were made through EDM (Electric Discharge Machining).The width of the slot in the specimen is0.2mm.One side of the specimen was pol-ished to facilitate the observation of the crack growth using an optical microscope with a magniﬁcation of40. The loading conditions included constant amplitude load-ing with R-ratios ranging fromÀ1to0.85and two-step high–low sequence loading.Detailed description of the experiments and the results were reported in a separated presentation.Fig.5shows the experimental results under constant amplitude loading with different R-ratios.Ten specimens were subjected to constant amplitude loading with different loading amplitudes and six R-ratios.Clearly, the R-ratio has an effect on the crack growth of the mate-rial.The notch effect is reﬂected in the crack growth results presented in Fig.5.It can be found that,except in the case of the specimen with a relatively large notch radius under R=À1loading,the notch effect on the crack growth is not signiﬁcant.For the R=À1case(Specimen C24,notch966 F.Fan et al./Mechanics of Materials40(2008)961–973。

Fatigue issues in aircraft maintenance and repairs

Int.J.Fatigue Vol.20,No.6,pp.413–431,1997©1998The Boeing Company.Published by Elsevier Science LtdPrinted in Great Britain 0142–1123/98/$19.00+.00PII:S0142-1123(97)00029-7Fatigue issues in aircraft maintenance and repairsUlf G.GoransonBoeing Commercial Airplane Group,Seattle,WA,USA (Received 10February 1997)Many design considerations are involved in ensuring structural integrity of Boeing jet transports,which have common design features validated by extensive analyses,tests,and service performance.Designing for continued structural integrity in the presence of damage such as fatigue or corrosion is an evolutionary process.Performance demands,increasing structural complexity,and aging ﬂeet reassessments have required development of standards suitable for application by large teams of engineers.This presentation is focused on such methods with special emphasis on practical fatigue reliability considerations.Durability evaluations are based on quantitative structural fatigue ratings which incorporate reliability considerations for test data reduction and ﬂeet performance predictions.Fatigue damage detection assessments are based on detection reliability estimates coupled to damage growth and residual strength evaluations.Data are presented to airline operators on detection check forms which permit efﬁcient maintenance planning to achieve required fatigue damage detection reliability levels.©1998The Boeing Company.Published by Elsevier Science Ltd.(Keywords:fatigue and damage tolerance;damage detection reliability;airline maintenance planning)OVERVIEWCriteria and procedures used in commercial jet trans-port design and manufacture over the last four decades have resulted in fail-safe/damage-tolerant structures with a credible safety record,Figure 1.Advancements in the capability to characterize structural performance by analysis have spurred adaptation of traditional fatigue and fracture mechanics technologies with large test and service databases to achieve development of technology standards over the last two decades.Major Boeing efforts have been focused on capturing lessons learned for future continuous design improvements with standardized durability and damage tolerancecheckingFigure 1Safety record –worldwide commercial jet ﬂeetThis paper was originally published in JIJF 19Supp.1,pp.3–21.413procedures similar to traditional strength checking pro-cedures.The challenge of successfully implementing technology standards hinges on a practical balance between simplicity and technical credibility aimed at providing structural engineers with useful and service/test validated analysis tools.This paper provides fundamental principles behind durability and damage tolerance technology standards,as well as examples of test and service validation.DESIGN CONSIDERATIONSStructural integrityTwo basic structural integrity issues must be addressed.The ﬁrst is to design and verify the ultimate strength of the undamaged structure for speciﬁed design maneuvers,gusts,ﬂutter,ground loads,and pressuriz-ation.The second is to design the structure to sustain fail-safe loads with limited damage for a period of service prior to detection and repair.All Boeing jet transports are designed to this fail-safe principle,which requires fail-safe load capability at all times and resto-ration of the structure to ultimate load capability after damage detection.The fail-safe load factor is 2.5g for maneuver design conditions,and an additional safety factor of 1.5is applied to obtain the ultimate load requirement.The fail-safe (limit)load levels are selec-ted to represent conditions that may occur once in a lifetime for a ﬂeet of airplanes.Design gust levels are based on a similar remote probability of occurrence criterion.Static strength design criteria existing today,414U.G.Goransonincluding the factor of safety,have worked well,and concerns about static overload failures have essentially been eliminated in present-day commercial airplanes.Several sources of damage must be evaluated to ensure structural safety during service.Both accidental damage and environmental deterioration are random events during the operational life of the airplane,and maintenance requirements must reﬂect inspectability for these types of damage.Fatigue damage is a cumulative process,and some cracking is expected in large ﬂeets designed to reach an economic life goal with high reliability.Consequently,supplemental fatigue damage inspections may be required for older airplanes.The inspectability and accessibility characteristics of the structure must be such that general visual methods of damage detection can be conﬁdently employed for most of the structure.Directed inspections involving sophisticated damage detection equipment may be acceptable in areas where inaccessibility dictates infrequent inspection.Structural durabilityInteraction between structural damage tolerance and durability characteristics must be recognized in the design,manufacturing,and operation of modern jet transports.Design evolution and maintenance require-ments are motivated by both safety and economic concerns.Damage tolerance is primarily governed by certiﬁcation requirements,while durability character-istics mainly inﬂuence the airplane cost of ownership and are dictated by the requirements of a competitive international market.There is no limit to the service life of damage-tolerant (fail-safe)airplane structures,provided the necessary inspections are carried out along with timely repairs and comprehensive corrosion pre-vention programs.Since operational efﬁciency is impacted by the cost and frequency of repair,durability may limit the productive life of the structure.Fatigue tests of components or the entire airframe are extremely valuable in the early life of a given model,but proof of quality stems from the accumulated experience of maturing ﬂeets,Figure 2.The Boeing Commercial Airplanes durability system was developed in the early 1970s to serve as a corporate memory of past design,Figure 3.Highlighted key parameters pro-vide the means of timely extension and transfer of experience to new design and/or operating usage.The Boeing ﬂeet is surveyed continuously and theinfor-Figure 2Boeing commercial jet ﬂeetsummary Figure 3Boeing technology standards developmentmation is summarized in terms of service-demonstrated fatigue lives of various components.Damage toleranceCertiﬁcation of commercial jet transports requires damage-tolerant designs in all instances where they can be used without unreasonable penalty.The technical capability has now evolved to use damage growth to determine inspection requirements,which in the past were based on service experience.Appropriate multiple site damage must be considered in both new design and structural reassessments of older models.Damage tolerance comprises three distinct elements of equal importance for achieving the desired level of safety:¼Damage limit –the maximum damage,including multiple secondary cracks,that the structure can sustain under limit load conditions;¼Damage growth –the interval of damage pro-gression,from the detection threshold to damage limit;it varies with the magnitude of operating loads,sequence of loads,and environmental inﬂuences;¼Inspection program –a sequence of inspections of a ﬂeet of airplanes with methods and intervals selec-ted to achieve timely detection of damage.These elements of damage tolerance are merged at Boeing Commercial Airplanes by a Damage Tolerance Rating (DTR)system to provide a quantitative measure of fatigue damage detection reliability,Figure 4.Figure 4Damage detection evaluation415Aircraft maintenance and repair STRUCTURAL DURABILITY ASSESSMENTS Fatigue ratings and allowablesLong-life structures are achieved by balancing detail design practices with the operating stress environment,Figure 5.Experience has shown that incompatibility between operating stresses and fatigue allowables causes 85%of the service problems.Standardizing the fatigue analysis process allows the service requirement analysis to be conducted independently of and prior to structural capability analysis.This design process pro-vides the following beneﬁts.¼Early attention directed toward fatigue prevention.¼Fatigue methods and allowables available to all structural engineers.¼Common quantiﬁable base for decision making.¼Emphasis on detail design to achieve minimum design service objectives.¼Trade studies leading to efﬁcient weight/cost designs.Structural conﬁgurations are selected to meet mini-mum design service objectives.This implies that some speciﬁc level of structural fatigue quality must be achieved,with the desired level of conﬁdence and reliability,to provide competitive economic structures with very limited cracking during the anticipated ser-vice life.Service life calculations are based on fatigue damage models representing known test and service experience.The focal point in the damage model is deﬁned by a Detail Fatigue Rating (DFR).A compre-hensive inventory of service and test-proven design allowables is based on a family of damage curves for various mean and alternating stress combinations uniquely deﬁned by given DFR values.Such DFRs permit quantitative compilation of the cumulative fatigue and design experience as shown in Figure 6.Analytical fatigue allowables are also available to structural engineers to modify existing conﬁgurations proven by test and ﬂeet experience,or to derive fatigue ratings for a completely new design.Base ratings are established for notches and mechanically fastened structures,and comprehensive libraries of modiﬁcation factors accounting for different design parameters such as the type of detail,amount of load transfer,fastening system,surface ﬁnish,and material alloy type are pro-vided.Figure 5Durability designevaluationFigure 6Normalized fatigue ratingsFatigue reliability considerationsThe structural design service objective is a minimum of 20years of airline operation with only a small percentile of the population subject to repair because of the initiation of detectable fatigue cracks.This per-centile varies from less than 5%for those structures that are easy to inspect and repair to extremely low percentiles for structures with difﬁcult access.To obtain these levels of reliability,every structural engin-eer is required to design for fatigue prevention.This requirement has necessitated the use of straightforward procedures that are easily applied at the design stage.The ‘scatter factor’approach to structural fatigue reliability has been used in the airplane industry for decades,and scatter factors such as 2and 4are well established.Therefore,in deference to structural engineer familiarity,this approach of using statistically and physically meaningful scatter factors has been retained.The two-parameter Weibull distribution is used for the structural life distribution mode.In this application structural life is deﬁned as the operational life to initiation of a fatigue crack of detectable size.The Weibull distribution was selected after considerable USAF-sponsored research in the late 1960s and early 1970s.Furthermore,the two-parameter model was chosen to recognize the conservative possibility of a detectable fatigue crack being present at zero life.Predeﬁned shape parameters are used for the design process.These parameter values were established after reviewing literally thousands of fatigue test results and determining that the parameter was material dependent,and in the case of high strength steel was also stress concentration dependent.Design scatter factors are based on shape parameters that range from 2.2for high strength steels to 4for aluminum.The scale parameter ␤deﬁnes the central tendency (characteristic)fatigue life of a structure and depends upon the quality of the structure and the stresses to which the structure is subjected during its operation.The characteristic fatigue life is either calculated by the designer or determined by testing.For design purposes,characteristic life is related to fatigue lives at higher levels of structural reliability via appropriate scatter factors.The fatigue design procedure is divided into two major steps.The ﬁrst step establishes a structure’s minimum design service objective in terms of oper-ational ﬂights with high structural reliability.The416U.G.Goransonsecond step determines the structural fatigue quality required to attain this design objective.Scatter factors are used in both steps.The ﬁrst step uses a factor known as the Fatigue Reliability Factor (FRF).This factor has been nor-malized so that a value of unity translates to a mini-mum level of reliability of 95%over the structure’s operational lifetime.FRF =1is limited to structures in which fatigue cracks are easily detected and repaired.Structural engineers are required to use FRFs that are increasingly greater than unity when establishing life goals for structures that are increasingly difﬁcult to inspect and repair.This simple approach results in the more difﬁcult structures being designed for longer lives.Therefore,at any time during an airplane’s oper-ational lifetime,a difﬁcult-to-inspect/repair structural part would have less expectation of fatigue cracking,i.e.higher reliability,than an easy-to-inspect/repair part.The second step of the fatigue design process requires fatigue allowables in order to determine the structural quality needed to achieve the economic design service objective.These allowables are usually referred to as SN curves,and they deﬁne the life of a structure at any given level of stress,Figure 7.Fatigue design allowables (DFR curves)identify for any level of operational stress a minimum fatigue life that can be comfortably exceeded by all but the weak-est extreme members of the structural population.These allowables are developed empirically from fatigue test results of structurally representative specimens subject to realistic operational loads.The fabrication and test-ing of specimens are carefully monitored and docu-mented and the test results veriﬁed before acceptance as valid data.Four separate ‘scatter factors’are used to reduce valid fatigue life data to reliable design allowables.As shown in Figure 8,these factors are as follows.¼Establish a lower bound interval estimate of central tendency fatigue life from the results of a limited number of test specimens.In keeping with long-established static strength allowables practice,the conﬁdence bound is set at the 95%level.¼Account for the degree of simpliﬁcation used in the fatigue test representation of the actual structural part and the real operational load conditions.¼Account for the inﬂuence of population size on fatigue life.This factor distinguishes betweentheFigure 7Fatigue damagemodelFigure 8Fatigue design allowables considerationsfatigue performances of typically small test speci-mens,which contain few potential crack initiation locations,and large full-scale structures with their multitude of potential sizes for initiation of the earliest fatigue cracks.¼Establish the structure’s design allowable fatigue life at the 95%reliability level;that is,the life at which 95%of the population of structures will be free of fatigue cracks of detectable size.The 95%reliability level was adopted for fatigue allowables as a simpli-ﬁcation of the A and B basis static strength allow-ables,which have been set for decades at reliability levels of 99%and 90%respectively.The fatigue design procedure can be simply summar-ized as follows.The structural engineer ﬁrst establishes a minimum design service objective for the structure per appropriate Design Requirements and Objectives document for each model.This design objective is then entered in an appropriate DFR curve and the design allowable stress determined.This stress is then com-pared to the actual stress that will be imposed on the structure during its operation,and a resultant fatigue margin is calculated by dividing the allowable stress by the operational stress.Clearly this margin must equal or exceed unity to attain the structure’s reliability and life goal requirements.Fatigue performance validation Technology standards.Since the early 1970s,Boeing has devoted extensive efforts to developing methods and allowables that enhance analysis capability for new and aging airplane structures,see Figure 3.(‘Allowables’are material properties and speciﬁc strength data used for design and analysis of airplane structures.)Signiﬁcant amounts of testing served as veriﬁcation and validation of technology standards development.This testing included coupon,component,and full-scale fatigue testing and teardown inspections.(‘Coupons’are small material test specimens used to determine allowables.)Durability standards were developed ﬁrst,followed by damage tolerance standards.These two standards were incorporated into the designs of the second gener-ation of Boeing jet transports,the 757and 767.The damage tolerance standards were utilized in the certiﬁ-cation of the 757and 767as damage tolerant.This damage tolerance was certiﬁed per the US Federal Aviation Administration (FAA)Federal Airworthiness Regulation 25.571,Amendment 25-45.The Boeing damage tolerance standards were also utilized in the417Aircraft maintenance andrepair Figure 9Major airframe fatigue testsSupplemental Inspection Documents of aging airplane programs for the Boeing 707,727,737,and 747.Since the early 1970s,corrosion has been recognized as one of the dominant factors in the inspection and maintenance activities of airline operations.Boeing has devoted extensive resources to the technology standards development in the areas of corrosion prevention and corrosion control.Expanded corrosion coverage,as a result of the corrosion standards development,has been incorporated into the production lines of all current production airplanes as well as the Aging Fleet Struc-tures Working Groups.These groups include represen-tatives from airframe manufacturers,airline operators,and regulatory agencies.Figure 9illustrates the signiﬁcance of durability standards development to the structural improvement process.For example,the second generation 757and 767were tested to twice their respective Design Service Objectives (DSOs)in ﬂight cycles;improved testing technology allowed this testing to be completed in less time than it took to test the ﬁrst generation 747to its one DSO in ﬂight cycles.More signiﬁcantly,the design changes identiﬁed in the 757and the 767fatigue testing in two DSO ﬂight cycles are far fewer than the design changes identiﬁed for the 747during fatigue testing for its one DSO in ﬂight cycles.This improve-ment was possible because durability technology stan-dards were incorporated into the original designs of both the 757and 767.Another measurement for the effectiveness of the design improvements is ‘maintenance labor hours per airplane’compared for the initial 10years of operation for each model,Figures 10and 11show signiﬁcant order of magnitude improvements between ﬁrst and second generation wide and standard bodyairplanes.Figure 10747/767service bulletin:labor hours after 10years of service to address corrosion andfatigueFigure 11727/737/757service bulletin:labor hours after 10years of service to address corrosion and fatigueThese improvements are a result of implementation of lessons learned from past design practices for new air-planes.Full-scale fatigue testing.Full-scale fatigue testing of airplanes is a major part of structural performance data development.In addition to providing the vali-dation of aircraft design concepts,full-scale fatigue testing is often used to identify any preventative main-tenance actions for the ﬂeet,if the fatigue testing is done at the time of certiﬁcation of a new model of jet transport (which is often the case at Boeing).Figure 12shows the minimum DSO in ﬂight cycles and the full-scale fatigue testing in ﬂight cycles.It may be seen from Figure 12that full-scale fatigue testing is generally accomplished to twice the minimum DSO,with two exceptions.The ﬁrst exception is the model 727,which was originally fatigue tested to its DSO of 60,000ﬂight cycles.However,approximately two years ago,a 727airplane with 47,000accumulated ﬂight cycles was acquired and the fuselage cyclic pressure tested to an additional 76,000cycles.The second exception is the model 747,which was also originally fatigue tested to the DSO of 20,000ﬂight cycles.As in the case of the 727,a 747airplane with 20,000accumulated ﬂight cycles was acquired and the fuselage cyclic pressure tested to an additional 20,000cycles.In addition,the fuselage sections 41and 42of the derivative model 747-400were cyclic pressure tested to 60,000cycles,representing three DSOs.Teardown inspections.Since the introduction of the 707,several teardown inspections andevaluationsFigure 12Full-scale fatigue test programs418U.G.Goransonof high-time airplanes have been conducted as part of a continuing assessment of airplane structure.These inspections permit a detailed examination of structural performance,and provide much useful information for forecasting future structural maintenance requirements.Sophisticated inspection techniques,capable of ﬁnding smaller cracks than typically found during routine air-line inspections,are used on the disassembled structure.Teardowns also provide an excellent database for calib-rating analysis tools,and developing structural modiﬁ-cations on future production airplanes,if required.Major teardown inspections supplementing normal ﬂeet surveillance activities have been conducted on several models:b 707wing plus center section 1965b 707wing 1968b 707wing plus center section and 1973fuselageb 707empennage 1978b 727forward fuselage 1978b 737wing plus center section,forward 1987fuselage,and empennage b 737aft fuselage 1988b 747wing and empennage 1989b 747fuselage 1991b 727wing and empennage 1994b 727fuselage 1995Concerns related to an increased number of airplanes being used beyond their original design life objectives have spurred further activities to obtain airframes retired from service for teardown inspections.Boeing will continue to monitor the aging ﬂeet to verify the effectiveness of preventative modiﬁcations incorporated as retroﬁt on older models and/or new model pro-duction improvements.Findings will be disseminated to operators by service bulletins as required and incor-porated in maintenance recommendations.Fleet surveys.The aging ﬂeet surveys by engin-eering teams were initiated in 1986to gain a better understanding of the condition of structures and sys-tems and to observe the effectiveness of corrosion prevention features and other corrosion control actions taken by the operators,Figure 13.All manufacturers continually review reported service data and other ﬁrst-hand information from customer airlines in order to promote safe and economic operation of the worldwide ﬂeet.These surveys were primarily prompted bytheFigure 13Boeing ﬂeet surveys projected upward trend in airplane age towards and beyond original design service objectives.The initial ﬂeet surveys showed that the majority of the airplanes were well maintained and in relatively good condition.However,there were a number of airplanes whose condition showed that ﬁnding cor-rosion discrepancies and repairing them was accepted practice and little or no attempt was made to apply any preventative measures.From the surveys and some similar incidents it became apparent that some airplanes were continually operating with signiﬁcant structural corrosion and that this was on the increase as airplanes age.This in turn could signiﬁcantly inﬂuence the fatigue cracking and damage tolerance capability of principal structural elements.Boeing formed a special Corrosion Task Force in 1988and held meetings with airline maintenance executives as a result of these sur-veys.Service-demonstrated fatigue lives.The commer-cial jet ﬂeet is used as a large group of specimens loaded in real-life environments to demonstrate service-demonstrated fatigue life and to predict future fatigue performance.This ﬂeet represents a database of over 8000delivered airplanes,with a total ﬂeet experience exceeding 150million ﬂight cycles,and daily utiliz-ation exceeding 23,000ﬂights,see Figure 2.Where a statistically signiﬁcant number of fatigue cracks have been reported in a ﬂeet,maximum likeli-hood estimates of the Weibull shape and scale para-meters are used to determine ﬂeet-demonstrated DFR values.This provides a means of relating service experience for one model to other models with different utilization characteristics.Signiﬁcant ﬂeet ﬁndings,often augmented by extensive teardown inspections,are used to modify fatigue methods and allowables described previously.When no fatigue cracks have been observed,a simpler approach based on the design shape parameter is used to estimate service-demon-strated lives.Such information provides a fundamental check and balance for the fatigue analysis system,and new design and/or redesign evaluations can be related to accumulated ﬂeet performance,Figure 14.DAMAGE TOLERANCE ASSESSMENTSJet transports are designed to be damage tolerant,a concept that evolved from the fail-safe design principle introduced in the 1950s.The ability to a analyze damaged structure has improved steadily throughmoreFigure 14Service-demonstrated fatigue lives419Aircraft maintenance and repairsophisticated application of fracture mechanics.Timelydetection of damage is the ultimate control in ensuring structural safety.However,traditional damage growth and residual strength evaluations have failed to incor-porate damage detection parameters that inﬂuence maintenance planning.The effects of accidental,environmental,and fatigue damage must be assessed to achieve a balanced inspec-tion program.Of these,fatigue damage,characterized by the initiation and subsequent growth of a crack,is the most amenable to rigorous analytical treatment. Major efforts during the last15years have focused on establishing quantitative damage detection rating sys-tems that measure the efﬁciency of inspection pro-grams.Extensive statistical evaluations of reported ser-vice data have resulted in estimates of damage detection reliability for different inspection methods. Fatigue damage detection is normally considered in terms of a single event involving inspection for a given size of crack with a speciﬁed method.However,airline maintenance practices consist of multiple inspection levels,varying inspection intervals,and different methods of inspection.In addition,fatigue cracking is generally found on more than one airplane in theﬂeet within a relatively short period of time.This multi-plicity of events signiﬁcantly inﬂuences the timely detection of fatigue damage and needs to be reﬂected in damage detection assessments.It must be shown that there is a high probability of detecting fatigue damage in theﬂeet before such damage reduces air-plane residual strength below speciﬁed levels.A DTR system suitable for ensuring timely detection of fatigue damage in theﬂeet was developed to accommodate these concepts,see Figures3and4.Elements of damage toleranceThe key objective for airplane structures designed to the damage tolerance concept has always been to carry regulatory fail-safe loads until detection and repair of any fatigue cracks,corrosion,or accidental damage occurring in service.The ability to analyze damaged structures has progressed signiﬁcantly during the last20years through the evolution of fracture mechanics.Assessments now consider residual strength, damage growth,interactive multiple damage sites and quantitative structural maintenance evaluations.Struc-tural maintenance is the cornerstone for ensuring con-tinued airworthiness of damage-tolerant structures. Residual strength.The maximum allowable dam-age that a structure can sustain at a critical fail-safe level is the key to the level of damage growth and inspection needed to ensure damage detection.Built-up airplane structures consist of multiple sheet,stiff-ener,and fastener elements.Interaction between these cracked and uncracked elements causes signiﬁcant redistribution of stresses.Failures are often precipitated by local exhaustion of plastic strain capability of the most critical elements,and/or net section failures involving a mixture of fracture mechanics and tran-sitional behavior in some elements,Figure15. Crack growth.The rate of damage propagation is a function of material properties,structural conﬁgur-ation,environment,crack length of primary and sec-ondary cracks,and operating stress exposure.Damage Figure15Residual strengthevaluationFigure16Crack growth evaluationdetection assessments require crack growth data from detection threshold lengths to the allowable damage determined by residual strength e of nor-malized damage models for calculating relative growth perﬂight,including load sequence effects,permits separation of the material,geometry,and stress para-meters,Figure16.Damage detection.Both accidental damage and most forms of environmental damage can be considered as random events that can occur at any time during the operational life of an airplane.Fatigue damage is characterized by cumulative progression relating to airplane usage measured inﬂights.Detection ratings have been developed for accidental and environmental damage.A quantitative fatigue damage detection rating system is known as the DTR system.Damage detection is a function ofﬂeet size,number of cracks,and number and type of inspections,Figure17.Figure17Damage detection。

FATIGUE DAMAGE AND FAILURE OF STEAM TURBINE ROTORS

Strength of Materials,Vol.42,No.1,2010FATIGUE DAMAGE AND FAILURE OF STEAM TURBINE ROTORSBY TORSIONAL VIBRATIONSA.P.Bovsunovskii,a O.Yu.Chernousenko,b E.V.Shtefan,c UDC620.178;534.1and D.A.Bashta cThe fatigue damage and failure of steam turbine rotors by torsional vibrations are investigated.Possible causes of the occurrence of torsional vibrations are discussed.Modeling of torsionalvibrations of the shafting of a steam turbine,which occur under its operating conditions,has beenperformed,and the cyclic strength of the shafting under these vibrations has been estimated.Keywords:rotor,torsional vibrations,cyclic damage,finite element modeling.The world experience of the long-term operation of turbine units of thermal and nuclear power stations allows the conclusion to be drawn that one of the causes of accidents and catastrophic failures of turbine rotors is fatigue damage accumulation due to torsional vibrations of shafting.This is indicated,e.g.,by accidents at a thermal power station in the USA(Tennessee,1974)[1],at the state district power station-4at Kashira in Russia(October 2002)[2]and at one of the overhauled power generating units of the Pridneprovskaya thermal power station in Ukraine(2007).In the first case,an accident resulted in the failure of a medium-low pressure rotor(Fig.1shows the lines along which the rotor fractured)and in the second case in the complete failure of the power generating unit No.3(K-300-240-1turbine)and in the partial failure of two neighboring power generating units.Fragments of rotors were found within a radius of several hundreds of meters from the station.In the last case,the turbine had to be urgently stopped because of the occurrence of strong vibration,which prevented it from failure because of a considerable fatigue damage of the rotor,as was found out later.It was concluded from the results of investigations of these accidents that one of the main causes was fatigue of the rotor metal as a result of cyclic torsion.Taking into account the potential hazard of this phenomenon for all steam turbines being in operation,the task was set to evaluate the degree of the fatigue damage of turbine unit shaftings due to torsional vibrations.To perform this task,it is necessary to ascertain the causes of the occurrence of torsional vibrations of shaftings during operation,to model vibrations under the action of operating load and to evaluate the fatigue properties of their materials in operation.The ascertainment of the causes of the occurrence of shafting vibrations made it possible to model structure loading conditions which approached the operating conditions.Since no monitoring of torsional vibrations of turbine rotors is performed at present,the causes of their occurrence can only be conjunctured.The results of a number of theoretical studies[2,3]indicate that the main cause of the occurrence of torsional vibrations of shaftings is the dynamic load acting on the turbine shaft on the turbogenerator side mainly under its abnormal operating conditions, particularly under short-circuit(SC)conditions,at the moments of connection to network with rough synchronization, because of the dynamic instability of the turbogenerator-network system and the nonuniformity of the electric field of the generator,etc.The only experimental work[4]on this problem,known to the authors,which was carried out on a smaller turbine unit model,confirms that SC on the generator really gives rise to shaft torsion vibrations of considerablea Pisarenko Institute of Problems of Strength,National Academy of Sciences of Ukraine,Kiev,Ukraine.b National Technical University of Ukraine“Kiev Polytechnic Institute,”Kiev,Ukraine.c National University of Food Technologies,Kiev,Ukraine.Translated from Problemy Prochnosti,No.1,pp.144–151,January–February,2010. Original article submitted July29,2009.1080039–2316/10/4201–0108©2010Springer Science+Business Media,Inc.amplitude.The SC duration in experiments is 0.03–0.26s.In spite of the short abnormal action on the turbine unit shafting on the generator side,it gives rise to its torsional vibrations of amplitude which is larger by a factor of 2.8than the nominal torque.In some works it is assumed that as a result of SC the torque amplitude may exceed the nominal torque by a factor of up to six [6].The second point is modeling and investigation of turbine shafting vibrations under the action of operating load and determination of the most stressed zones of the shafting.The main difficulty here is that the shafting of steam turbine (e.g.,K-200-130turbine)is a complex mechanical structure,which consists of three rotors joined by couplings.Each of the rotors is a component part the high-pressure,medium-pressure and low-pressure stages,at each of which the conditions of force and thermal action differ greatly.To investigate vibrations of such a complex mechanical system,we used a three-dimensional finite element model of shafting,which consisted of 50,000finite elements (Fig.2).The main attention was given to the investigation of shafting vibrations as a result of SC since this regime is,as our investigations showed,most hazardous.From the standpoint of mechanical loading,SC results in a strong reactionary-torque spike of short duration (acts in the direction opposite to the sense of rotor rotation).The nominal torques at the high-,medium-,and low-pressure stages were taken from the turbine operating conditions:M h =⋅0196.,MN m M m =⋅0291.,MN m and M l =⋅0163..MN m The reactionary torque M r acting on the turbogenerator side was taken to be 3and 6nominal torques (M nom ):ÌM r nom =3,ÌÌr nom =6,(1)where M M M M nom h m l =++.Figure 3shows some results of calculations of the first cycles of torsional vibrations of shafting under SC.In this particular case,the reactionary torque amplitude M M r l =3.As is evident,the force action in question is really able to excite considerable torsional vibrations of shafting with high cycle asymmetry.In this case,mainly vibrations of the first torsional mode are excited;higher vibration modes manifest themselves only slightly (in Fig.3,the second vibration mode of small amplitude can be seen).The SC duration has a considerable effect on vibrations.In our case.SC of longer duration caused shafting vibrations of smaller amplitude.At first sight this result seems paradoxical.However,spacial investigations,which were carried out on a system with one degree of freedom using a program worked out earlier [5],show that the amplitude of vibration of the mechanical system as a result of action of SC depends not so much on its duration as on the ratio of SC duration (T SC )to the natural period of the system (T NP ).The maximum of vibration amplitude is reachedatÒn SC NP =+(.),05(2)109Fig.1.Failure of the medium-low-pressure rotor of a steam turbine (Gallatin,Tennessee,USA).and the minimumatÒn SC NP =,(3)where n is an integer.As is seen from Fig.3,in the former case,theratio T SC NP ≈06.,i.e.,is close to 0.5,the torsional vibration amplitudes of shafting are close to the maximum value;in the latter case,T SC NP ≈29.,i.e.,is close to 3,therefore SC is able to excite only vibrations of relatively small amplitude.110Fig. 2.Finite element model of the shafting of K-200-130steam turbine.M hM mM lτa )of the shafting of K-200-130steam turbine at the SC duration T SC =0015.(a)and 0.078s (b).(The dashed lines denote the time variation of torque M .)τa M,τa M,abThus,there is an additional uncertainty factor in the problem of torsional vibrations of steam turbine shafting as a result of SC.Under real conditions,the SC duration is a random and un predictable quantity.It follows that these loading conditions can both cause considerable and dangerous shafting vibrations and not excite them at all.The third point is the estimation of the degree of fatigue damage of shaftings as a result of SC.This estimation requires,in addition to results of investigations of their torsional vibrations,data on the torsional cyclic strength of rotor steel with allowance for the influence of operation factors:temperature,cycle asymmetry,scale factor and the form of stressed state.Since there are no such data at present,a rough estimation of them has been performed on the basis of a fatigue curve for 25Kh1MFA rotor steel in case of symmetrical tension–compression [6].The curve was approximated by a power function of the form:σηηηa p c u b N N =++0()(),(4)where η0,ηp ,and ηu are the coefficients of the function (η01750=.,ηp =26694162.,and ηu =1562745216,.),c and b are exponents (c =−03114.and b =−08348.),and N is cycle life.The effect of the form of stressed state on the cyclic strength of 25Kh1MFA low-alloy carbon steel was taken into account on the basis of the second and fourth theories of strength since the ratio of torsional and tension-and-compression fatigue limits(κτ=−−1)for carbon steels is known [7]to be best described by the second theory of strength and for alloy steels the fourth theory of strength:τκηηηa sf a p c u b K K N N =++−II IV (()()).0(5)The coefficients taking into account the effect of the form of stressed state on the cyclic strength of steel were taken as κII =0794.and κIV =0577..The effect of mean cycle stress on the cyclic strength of steel was taken into account with the aid of K a coefficients,which were determined from appropriate Goodman and Herber limiting amplitude diagrams:K a m =−−−τψτττ11,(6)K a =−1(7)The influence of scale factor was estimated with the aid of the scale factor influence coefficient K sf ,which was determined from the data presented in [8].When calculating the cyclic strength of the shaft,whose diameter was over 300mm,the coefficient K sf was taken to be 0.58.The short-circuit conditions were modeled by reactionary torque spike of different duration and amplitude.Investigations of vibrations resulting from such loading show that the highest tangential stresses occur on the shafting of K-200-130turbine in two its sections:in the coupling zone between the medium-pressure and low-pressure rotors and in the shafting-to-turbogenerator joint zone.The mean cycle stresses in the case of first-mode torsional vibrations of shafting τm =82and 59MPa.The action of SC on the mechanical system gave rise to a damped vibration process.In the calculations,linear viscous damping was assumed,therefore the damped vibration process is described by an exponential function of the form:ττωδ=−a ft e t sin ,(8)where τa is the initial stress amplitude of the damped process,δis a logarithmic vibration decrement,which characterizes the rate of free-vibration damping,f and ωare the frequency and circular frequency of free vibrations of shafting respectively,t is time.111The amplitude of the i th cycle of the damped process is determined from the formula:ττδai a i e =−+()/.144(9)In the calculation of the cyclic strength of the shaft we used the linear theory of damage summation (Palmgren–Miner hypothesis):n N i fi i s =∑=11,(10)where n i is the number of loading cycles with stress amplitude τai ,N fi is cycle life in the case of cyclic loading with stress amplitude τai ,and s is the number of loading levels (blocks).In this work,summation of damages in each deformation cycle has been effected,i.e.,the number of loading blocks,s ,is equal to the number of damaging loading cycles.The degree of material damage is estimated by the parameter Π:ΠΠ==∑i i s ,1(11)where Πi is the degree of material damage in one vibration cycle.It is evident that the vibration damping level of a mechanical system has a great effect on the number of damaging loading cycles.In the general case,vibrational energy dissipation for such system as shafting under operating conditions is caused by energy loss in the material,structural energy dissipation and air damping,which is associated with interaction between vibrating elements and the steam-air medium.Analysis of the damping properties of a number of low-alloy carbon steels shows that the logarithmic decrement of torsional vibrations of 25Kh1MFA steel can hardly be under 0.8%.Therefore,the lower limit of the damping characteristic δwas taken in calculations to be 0.8,the upper limit of this quantity,which takes into account structural energy dissipation and air damping as well,being 1%.The degree of cyclic damage of shafting as a result of SC was calculated at two reactionary-to-nominal torque ratios(M r nom =3and M r nom =6)and at two SC durations (T SC =00155.and 0.078s).Table 1the results of of the degree of cyclic damage of the most stressed shafting zone,i.e.,the zone between the medium-pressure and low-pressure rotors,in the case of first-mode torsional vibrations.As can be seen,in most cases of loading considered and vibrating system parameters,a cyclic damage occurs in the shafting material,the highest level of which is observed at the SC duration T T SC NP =056.with a reactionary torque amplitude that is equal to six nominal ones.In this case,the degree of cyclic damage of rotor steel Π=0.56–4.24%according to different theories of strength.112TABLE 1.Degree of Cyclic Damage of the Shafting of K-200-13-3Turbine of the Thermal Power Station at Kurakhovo in the Coupling Zone between the Medium-and Low-pressure Rotors as a Result of One SC τà,MPa δ,%Degree of damage,ΠSecond theory(Goodman)Fourth theory (Goodman)Second theory (Herber)Fourth theory (Herber)ÒSC=0015.s (.)ÒÒSC NP =0561281.00.00100.00730.00020.00212140.81.00.01230.00980.04240.03390.00560.00450.01850.0148ÒSC =0079.s (.)ÒÒSC NP =29381.0000093 1.00.00010.001900.0003Note.All data are given for a mean cycle stress (τm )of 82MPa.The spread of values of the degree of cyclic damage,determined according to different theories,reaches an order of magnitude.This spread can be appreciably reduced,and the accuracy of prediction can be thereby increased through using directly data on the torsion fatigue properties of25Kh1MFA steel.In other cases of loading considered,the degree of cyclic damage of material is much lower;at T T=29.with a reactionary torqueSC NPamplitude that is equal to three nominal ones,it does not occur.Noteworthy is that the calculations of the degree of cyclic damage of shafting have been performed for one SC.The degree of damage during all service time of turbine unit is determined as the sum of degrees of shafting damage as a result of all SCs on turbogenerator.CONCLUSIONS1.Analysis of torsional vibrations of the shafting of K-200-13-3steam turbine,which occur as a result of SC on the turbogenerator,shows that in shafting elements there may be a fatigue damage,the level of which is determined in the general case by the torsional cyclic strength of the shafting material,reactionary torque parameters and vibration damping level in mechanical system.2.Taking into account the potential danger of the phenomenon and considerable uncertainty of loading parameters,it is necessary to organize in the future continuous monitoring of torque variation over shafting and to create on this basis an automated system for the estimation of the degree of cyclic damage of shafting by the action of operating dynamic torsional loads.REFERENCES1.L.D.Kramer and D.D.Randolph,“Analysis of the Tennessee valley authority,Gallatin unit N2turbinerotor burst,”in:ASME-MPC Symp.on Creep-Fatigue Interaction(1976),p.1.2.I.Sh.Zagretdinov,A.G.Kostyuk,A.D.Trukhnii,and P.R.Dolzhanskii,“Failure of the300MW turbineunit of the state district power station at Kashira:causes,consequences and conclusions,”Teploénergetika, No.5,5–15(2004).3. F.M.Detinko,G.A.Zagorodnaya,and V.M.Fastovskii,Strength and Vibrations of Electrical Machines[inRussian],Énergiya,Leningrad(1969).4.I.A.Glebov,E.Ya.Kazovskii,É.E.Ostroumov,and G.E.Rubisov,“Torques on turbine unit shaft onclearing short circuits,”Élektrichestvo,No.2,22–26(1978).5. A.P.Bovsunovskii,“Numerical study of vibrations of a nonlinear mechanical system simulating a crackedbody,”Strength Mater.,31,No.6,571–581(1999).6.RTM108.021.103-85.Parts of Stationary Steam Turbines.Low-Cycle Fatigue Design[in Russian],NPOTsKTI,Moscow(1985).7.V.T.Troshchenko and L.A.Sosnovskii,Fatigue Resistance of Metals and Alloys.A Handbook[inRussian],Naukova Dumka,Kiev(1987).8.I.V.Kudryavtsev and N.E.Naumchenkov,“Fatigue strength characteristics of steel25KhNZMFA inrelation to absolute dimensions and stress concentrations,”Strength Mater.,10,No.4,386–391(1978).113。

林木枯损量的专业英语名词

林木枯损量的专业英语名词In the realm of forestry and environmental science, the term "stand damage" is commonly used to describe the extent of damage to a forest or a group of trees. This concept encompasses various factors that can affect the health of trees, such as insect infestations, diseases, and natural disasters.The measurement of stand damage is crucial for assessing the overall health of a forest ecosystem. It involves quantifying the percentage of trees that have been affected, whether through partial or complete loss of foliage, structural damage, or death.One of the key indicators of stand damage is "mortality rate," which refers to the proportion of trees that have died within a given area. This metric is critical for understanding the severity of the damage and for planning remedial actions.Another important term is "defoliation," which describes the loss of leaves from trees. This can be a result of pests, disease, or environmental stress, and it can significantly impact the tree's ability to photosynthesize and grow.The term "crown dieback" is also used to describe the phenomenon where the tree's crown, or the uppermost part of the tree, begins to die due to various stressors. This can bean early sign of stand damage and requires attention.In the context of forest management, "thinning" is a practice that involves selectively removing trees to reduce stand density and improve the overall health and growth of the remaining trees. It can be a response to stand damage to prevent further deterioration.The "stand density index" (SDI) is a quantitative measure that assesses the density of a tree stand. A lower SDI may indicate over-crowding, which can lead to increased stand damage due to competition for resources.Lastly, "reforestation" is the process of replanting or regenerating a damaged forest stand. It is a proactive approach to mitigate the effects of stand damage and restore the ecosystem's balance.Understanding these terms is essential for professionals in the field of forestry, as they provide a framework for diagnosing and addressing issues related to stand damage.。

Truck Models for Improved Fatigue Life Predictions

Truck Models for Improved Fatigue Life Predictionsof Steel BridgesPiya Chotickai 1and Mark D.Bowman 2Abstract:A new fatigue load model has been developed based on weigh-in-motion ͑WIM ͒data collected from three different sites in Indiana.The recorded truck trafﬁc was simulated over analytical bridge models to investigate moment range responses of bridge structures under truck trafﬁc loadings.The bridge models included simple and two equally continuous spans.Based on Miner’s hypothesis,fatigue damage accumulations were computed for details at various locations on the bridge models and compared with the damage predicted for the 240-kN ͑54-kip ͒American Association of State Highway and Transportation Ofﬁcials ͑AASHTO ͒fatigue truck,a modiﬁed AASHTO fatigue truck with an equivalent effective gross weight,and other fatigue truck models.The results indicate that fatigue damage can be notably overestimated in short-span girders.Accordingly,two new fatigue trucks are developed in the present study.A new three-axle fatigue truck can be used to represent truck trafﬁc on typical highways,while a four-axle fatigue truck can better represent truck trafﬁc on heavy duty highways with a signiﬁcant percentage of the fatigue damage dominated by eight-to 11-axle trucks.DOI:10.1061/͑ASCE ͒1084-0702͑2006͒11:1͑71͒CE Database subject headings:Cyclic loads;Fatigue life;Damage;Trucks;Bridges,steel;Predictions .IntroductionSteel bridge structures are normally subjected to numerous repeated cyclic stresses due to truck trafﬁc.The damage accumu-lation caused by these cyclic stresses can initiate cracks and lead to the fatigue failure of a bridge member.To evaluate the cyclic performance of bridge structures,the fatigue resistance of the critical detail and a suitable cyclic load model are both needed.The stress-life approach in the American Association of State Highway and Transportation Ofﬁcials ͑AASHTO ͒load and resistance factor ͑LRFD ͒speciﬁcations AASHTO ͑1998͒is generally used in bridge applications to estimate the fatigue resistance.It utilizes a family of S -N curves to represent fatigue strength levels corresponding to various categories of fatigue details commonly used in the design and construction of steel bridge structures.These S -N curves were developed based on experimental research programs conducted through the auspices of the National Cooperative Highway Research Program ͑NCHRP ͒.The cyclic load model is also an important parameter in a fatigue evaluation.Based on Miner’s hypothesis ͑Miner 1945͒,an effective stress range is generally used to relate the variable amplitude fatigue behavior to a constant amplitude fatiguebehavior ͑Fisher et al.1998͒.The effective stress range can be obtained from a couple of alternatives,namely spectrum analysis using strain gage data and structural analysis using a suitable fatigue truck.For the ﬁrst alternative,the effective stress range can be determined from a root-mean-cube ͑RMC ͒value of the stress range spectrum obtained by decomposing a complex stress ͑strain ͒history with a suitable cycle counting procedure.This alternative tends to provide an accurate estimate of the actual bridge response under routine truck trafﬁc;however,signiﬁcant time and expense are required to acquire and evaluate the data.For the fatigue truck analysis,the effective stress range is computed from a structural analysis of a suitable bridge model with an applied load given in terms of an equivalent fatigue truck.An attractive feature of the method is that it can be conveniently used to determine an effective stress range occurring in bridge structures.Accuracy in an estimated value of the effective stress range is,obviously,dependent upon the conﬁguration of the fatigue truck.Ideally,the fatigue truck conﬁguration should be selected so that it will cause the same fatigue damage as actual truck trafﬁc for a given equivalent number of passages.Truck trafﬁc loadings are composed of a variety of axle weights,axle spacings,and gross vehicle weights of the truck population and can vary dramatically from site to site.Therefore,to accurately estimate the fatigue damage accumulation caused by random or variable truck loadings,it is essential to incorporate information on truck trafﬁc characteristics at an investigated site into the fatigue calculation.Current available fatigue truck models are reviewed in this paper.Weigh-in-motion ͑WIM ͒data collected from three sites in Indiana were investigated and used as applied loads on analytical bridge models.Fatigue damage accumulations were computed based on Miner’s hypothesis for the truck trafﬁc proﬁle con-structed using the WIM data.These damage accumulations were then compared with the fatigue damage predicted by the current available fatigue trucks and used as a basis in developing a new design of the fatigue trucks.1Graduate Research Assistant,School of Civil Engineering,Purdue Univ.,550Stadium Mall Dr.,West Lafayette,IN 47907-2051.E-mail:pchotick@ 2Professor of Civil Engineering,School of Civil Engineering,Purdue Univ.,550Stadium Mall Dr.,West Lafayette,IN 47907-2051͑corresponding author ͒.E-mail:bowmanmd@Note.Discussion open until June 1,2006.Separate discussions must be submitted for individual papers.To extend the closing date by one month,a written request must be ﬁled with the ASCE Managing Editor.The manuscript for this paper was submitted for review and possible publication on June 28,2004;approved on October 14,2004.This paper is part of the Journal of Bridge Engineering ,V ol.11,No.1,January 1,2006.©ASCE,ISSN 1084-0702/2006/1-71–80/$25.00.JOURNAL OF BRIDGE ENGINEERING ©ASCE /JANUARY/FEBRUARY 2006/71D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .Available Fatigue Truck ModelsA fatigue truck is typically used to represent truck trafﬁc at a given site with a variety of gross weights and axle conﬁgurations.The fatigue truck models provided in the AASHTO fatigue guide speciﬁcations ͑AASHTO 1990͒and those proposed by Laman and Nowak ͑1996͒were examined in the present study.The AASHTO fatigue guide speciﬁcations ͑AASHTO 1990͒provide a single fatigue truck that can be used for the fatigue evaluation.The AASHTO fatigue truck was developed based on a truck conﬁguration proposed by Schilling and Klippstein ͑1978͒.However,instead of using a 222-kN ͑50-kip ͒gross weight as proposed for the Schilling fatigue truck,the AASHTO guide speciﬁcations ͑AASHTO 1990͒stipulate a 240-kN ͑54-kip ͒gross weight of the fatigue truck for the fatigue strength evaluation.This gross vehicle weight represents the actual truck trafﬁc spectrum obtained from WIM studies ͑Synder et al.1985͒,including more than 27,000trucks and 30sites nationwide.Its conﬁguration was approximated based on the axle weight ratios and axle spacings of four-and ﬁve-axle trucks,which dominated a high percentage of the fatigue damage in typical bridges.The AASHTO fatigue truck has front and rear axle spacings of 4.27m ͑14ft ͒and 9.14m ͑30ft ͒,respectively,with a 1.83-m ͑6-ft ͒axle width,as shown in Fig.1.However,when a gross weight distribution at an investigated site is available,an effective gross weight determined from Eq.͑1͒can be used to modify the gross weight of the AASHTO fatigue truckW eq =͚͑f iW i3͒1ր3͑1͒where f i ϭfrequency of occurrence of trucks with a gross vehicle weight of W i .This effective weight must be distributed to each axle in the same proportion as noted Fig.1.By using this modi-ﬁcation,it is anticipated that a more accurate estimate of the fatigue damage accumulation can be obtained for a given man and Nowak ͑1996͒developed a fatigue load model based on WIM measurements at ﬁve steel bridge structures.The effective gross weights at these structures were in a range of 278to 347kN ͑62.4to 78.1kips ͒.A simulation technique was utilized to investigate moment range responses caused by actual trafﬁc ﬂow over analytical simple-beam bridge models.By using the S -N line approach and Miner’s rule,it was found that a high percentage of the fatigue damage in the monitored structures was dominated by 10-and 11-axle trucks.In addition,based on simulation results and an analysis of the WIM data,Laman and Nowak ͑1996͒proposed two new fatigue trucks ͑see Fig.2͒.The three-axle fatigue truck was suggested to be representative oftwo-to nine-axle trucks,while the four-axle truck was suggested for the 10-and 11-axle trucks.The damage accumulation caused by passages of these fatigue trucks is equivalent to the fatigue damage caused by the corresponding truck spectrum with an equivalent number of passages.It was demonstrated that for the WIM database developed in the study,these two fatigue trucks could provide a relatively accurate estimate of the fatigue damage accumulation over a range of bridge spans.Weigh-in-Motion DatabaseWIM sensors have been extensively used in recent years by highway and bridge engineers to monitor truck trafﬁc.A WIM system can be used to measure vehicle gross weights,axle weights,and axle spacings of the actual truck trafﬁc.Typically,the WIM sensor,such as a load cell or a piezoelectric strip,is installed directly in the roadway and is relatively unobtrusive.Consequently,an advantage of the technology is that it can be operated without being detected by roadway users.As a result,unlike static weigh stations that tend to be avoided by heavy trucks,unbiased truck trafﬁc data can be obtained ͑Moses et al.1987͒.The WIM data collected from three different sites in Indiana were included in a WIM database in the present study.Piezo-electric sensors were used for the WIM system at these three sites.A view of the WIM for one site is shown in Fig.3.The WIM sites were selected to represent a variety of truck trafﬁc characteristics that practicing engineers might encounter when performing a fatigue evaluation of bridge structures.Statistics of the WIM data were examined to evaluate the truck trafﬁc characteristic at these sites.Table 1summarizes the assigned nomenclature,site descrip-tion,recording period,number of sampled trucks,and effective gross weight of the WIM database.The highest and lowest effective gross weights of 327kN ͑73.5kips ͒and 188kN ͑42.3kips ͒were observed at Stations 001and 410,respectively.Meanwhile,an effective gross weight at Station 520was found to be 254kN ͑57kips ͒.These effective gross weights,computed using Eq.͑1͒,demonstrate the site-speciﬁc characteristic of truck trafﬁc loadings,and they illustrate that the effective weight can be considerably different from the 240-kN ͑54-kip ͒gross weight of the standard AASHTO fatigue truck.Station 001is located on U.S.Route 20along the heavy-duty corridor in northwest Indiana.The corridor provides an important route for steel producers and other manufacturers totransportFig.1.AASHTO fatigue truck ͑AASHTO 1990͒72/JOURNAL OF BRIDGE ENGINEERING ©ASCE /JANUARY/FEBRUARY 2006D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .cargos between northwest Indiana and the state of Michigan.With a special permit,the legal weight limit of trucks using this route is 596kN ͑134kips ͒,which is much heavier than the 356-kN ͑80-kip ͒legal limit for typical interstate and state highways.A common truck type traveling along this route is a multitrailer,multiaxle vehicle ͑see Fig.4͒.The eastbound truck trafﬁc data collected at Station 001in January 2002included a sample of 22,992trucks.A percentage distribution of trucks classiﬁed by the number of axles is provided in Table 2.It was found that approximately 45%of the truck trafﬁc was ﬁve-axle trucks,while eight-to 11-axle trucks accounted for 14%of the total truck trafﬁc.A gross weight distribution of the truck trafﬁc recorded at this station is shown in Fig.5͑a ͒.The maximum gross weight was found to be as high as 961kN ͑216kips ͒.The second WIM site,referred to as Station 410,is located on I-65in northwestern Indiana.The 4-day southbound truck trafﬁc data collected in August 2002included a sample of 21,856trucks.The gross weight distribution is presented in Fig.5͑b ͒.A maximum gross weight of 455kN ͑102.3kips ͒was observed.The majority of truck trafﬁc at this site are ﬁve-axle trucks,with approximately 84%of the total truckpopulation.man and Nowak fatigue trucks ͑Laman and Nowak 1996͒Fig.3.WIM sensors and control loops at Station 001D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .The third WIM site referred as Station 520is located on U.S.Route 50in southeastern Indiana.The eastbound truck trafﬁc data collected in May 2002included a sample of 16,696trucks.Fig.5͑c ͒shows a gross weight distribution of the recorded truck trafﬁc.The maximum recorded gross weight was found to be 713kN ͑160.3kips ͒.The highest percentage of truck trafﬁc at this station was dominated by two-axle trucks,approximately 47%of the total truck trafﬁc.Moreover,only 0.25%of the truck trafﬁc had more than ﬁve axles.Analysis Results of WIM DatabaseThe Palmgren–Miner’s hypothesis is one of the most widely used fatigue damage accumulation models.It assumes a linear damage accumulation and neglects sequence and mean stress effects.Therefore,the fatigue damage of each cycle in a stress history is independent.Based on Miner’s rule,the accumulated fatigue damage ͑D ͒is equal to the summation of the damage caused by each stress cycle,as shown in Eq.͑2͒D =͚i =1k⌬D i =͚i =1kn i N i͑2͒where N i and n i ϭfatigue resistance and the number of cyclesof the i th stress range,respectively.The stress history in bridge girders for each truck passage is complex due to a composition of static and dynamic responses.By utilizing the rainﬂow counting method ͑Committee on Fatigue and Fracture Reliability 1982͒,the stress history can be decomposed into primary and higher order stress ranges.The primary stress range is the maximum stress range in the stress history while the remaining reversals are the higher-orderstress ranges.Schilling ͑1984͒demonstrated that the fatigue damage accumulation of the complex stress cycles caused by an individual truck passage can be represented by the fatigue damage of the primary or maximum stress range with an equivalent number of cycles ͑N e ͒determined fromN e =1+ͩS r 1S rpͪm+ͩS r 2S rpͪm¯+ͩS riS rpͪm͑3͒where m ϭslope constant of the S -N line;S rp ϭmaximum stressrange;and S ri ϭhigher order stress range.The slop constant ͑m ͒is approximately equal to 3for all AASHTO fatigue category details ͑Keating and Fisher 1986͒.Although Eq.͑3͒is expressed in terms of stress ranges,it can also be calculated from moment ranges for linear elastic behavior based on the assumption that they are proportional.By using the concept of an equivalent number of cycles and Miner’s rule,the fatigue damage accumulation caused by each truck passage can be written as:D =͚1N i =N e S rp 310b͑4͒where N i ϭfatigue strength ͑cycles ͒corresponding to each stress range in a stress history;and b ϭintercept of S -N line for the detail being evaluated.A computer program was developed to simulate the actual truck trafﬁc ﬂow over analytical bridge models,including a simple-span and a two-span structure with equal span lengths.The simulated bridge spans ranged from 9to 37m ͑30to 120ft ͒with a 3.05-m ͑10-ft ͒increment.The WIM database developed for the three bridge sites was used for the input loading.Static moment ranges were monitored at the middle span of the simpleTable 1.Site Description Station Description ͑location ͒Monitored direction Period ͑start–end ͒Number of sampled trucksW eq ͑kN ͒001U.S.Route 20,Michigan City,Ind.Eastbound 1/1/02–1/31/0222,992327410I-65,Rensselaer,Ind.Southbound 8/1/02–8/4/0221,856188520U.S.Route 50,Versailles,Ind.Eastbound5/1/02–5/31/0216,696254Fig.4.Multiaxle truck on heavy-duty highwayD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .beam,the middle support of the continuous beam,and the middle span of the continuous beam.The moment cycles caused by each truck passage were decomposed using a rainﬂow counting method.The maximum moment range and equivalent number of cycles for each truck passage were then determined.This procedure was applied to all trucks in the WIM database.A sample of the simulation results is provided in Tables 3–5.The maximum moment range and effective moment range in 9-,18-,and 37-m ͑30-,60-,and 120-ft ͒bridge spans are included in the tables.The maximum moment range is the single greatest moment difference caused by the trucks within the loading spectrum,while the effective moment range is the effective weighted moment difference caused by the truck load spectrum.The latter value is given byM re =͚͑f iMr i3͒1ր3͑5͒where f i ϭfrequency of trucks within a particular moment range,Mr i .The results indicated that among the recorded truck trafﬁc data,Station 001had the highest effective moment ranges in all spans,followed by Stations 520and 410,respectively.This is consistent with an order of the effective gross weights observed at these three stations.An average of the equivalent numbers of cycles per passage of all trucks is presented in Fig.6for the three sites.This quantity was determined by taking the average of the values computed using Eq.͑3͒for each truck passage at the three sites.It is evident that the average number of cycles per truck passage at the middle span of the simple beam and the continuous beam approaches one when the span length exceeds 15m ͑50ft ͒.However,the average number of cycles at the middle support of continuous beams increases in spans above 12m ͑40ft ͒.The results also indicate that Station 520had a higher average number of cycles per passage at the middle support of the continuous beam than Station 410.This is because Station 520had a high percentage of two-and three-axle trucks,which tend to cause a higher equivalent number of cycles in long spans than trucks with a greater number of axles.On the other hand,Station 410had a somewhat higher average number of cycles at midspan of the simple beam and the continuous beam than Station 520.The primary reason for the difference is that ﬁve-axle trucks,the majority truck type at Station 410,tend to cause a greater number of cycles than two-and three-axle trucks at the middle span of short beam members.By employing Eq.͑4͒,the percent fatigue damage accumula-tion caused by each truck type was computed.Fig.7presents the percent fatigue damage caused by two-and three-axle,four-,and ﬁve-axle,and eight-to 11-axle trucks at midspan of a simple beam member.The results indicate that the summation of the fatigue damage caused by four-and ﬁve-axle trucks and eight-to 11-axle trucks contributed to more than 86%of the total damage accumulation at Station 001.Moreover,the eight-to 11-axle trucks caused more than 50%of the total fatigue damage at the middle span of simple beam in spans above 15m ͑50ft ͒.This percentage was relatively high given that a total number of these trucks was only 14%of the truck trafﬁc.In long bridge spans,the fatigue damage caused by eight-to 11-axle trucks tends to overcome the damage caused by four-and ﬁve-axle trucks.This is because the heavy loaded eight-to 11-axle trucks cause considerably higher moments than the four-and ﬁve-axle trucks in long spans.At Station 410,four-and ﬁve-axle trucks contributed to more than 95%of the total fatigue damage.A majority of the fatigue damage was dominated by four-and ﬁve-axle trucks at Station 520.They accounted for roughly 70%of the total fatigue damage,while two-and three-axle trucks caused approximately 30%of the fatigue damage at this station.The percent fatigue damage of the multiple axle trucks at the middle span and middle support of continuous-beam members was found to have a similar trend as depicted in Fig.7for simple-beam members.Table 2.Percent Truck Classiﬁed by Number of Axles Number of axles Station001410520227.918.1347.063 6.12 3.3812.694 2.22 2.748.71545.2184.1731.36 2.82 1.540.227 1.30.030.038 3.070.0109 6.820010 1.9900112.54Fig. 5.Histogram of gross truck weight:͑a ͒Station 001;͑b ͒Station 410;and ͑c ͒Station 520JOURNAL OF BRIDGE ENGINEERING ©ASCE /JANUARY/FEBRUARY 2006/75D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .Evaluation of Various Fatigue TrucksThe fatigue damage accumulations obtained from the simulation of the truck database were compared with the fatigue damage predicted by the 240-kN ͑54-kip ͒AASHTO fatigue truck,the modiﬁed AASHTO fatigue truck,and the Laman fatigue trucks.The effective gross vehicle weights computed from the WIM data were assigned for the gross weight of the modiﬁed AASHTO fatigue truck.To compare the fatigue damage accumulation caused by actual truck trafﬁc and the various fatigue trucks,a damage ratio is introduced as follows:Damage ratio =D actualD truck =͚ͩN ei S rpi 3NC ϫN t ϫS FT3ͪ=͚ͩN ei M rpi 3NC ϫN t ϫMr 3ͪ͑6͒where S rpi ϭprimary or maximum stress range of truck i ;S FT ϭstress range of the fatigue truck;M rpi ϭprimary or maximum moment range of truck i ;Mr ϭmoment range of the fatigue truck;N ei ϭequivalent number of cycles per passage of truck i ;NC ϭequivalent number of cycles per passage of the fatigue truck;and N t ϭtotal number of fatigue truck passages.The dam-age ratio is used in the comparison because it does not require information on the fatigue detail or category classiﬁcation;the detail expression is in the denominator of both damage terms and cancels out accordingly.By simulating the fatigue trucks over analytical bridge models,effective moment ranges and an equivalent number of cycles per passage of these fatigue trucks were determined.The damage ratio for each fatigue truck model was then computed.It should be noted that Laman and Nowak ͑1996͒provide a range of axle weights and axle spacings for the fatigue trucks ͑see Fig.2͒.Therefore,to obtain a conﬁguration of the Laman fatigue trucks for each station,an iterative procedure was utilized.Each range of axle weights and axle spacings was divided into more thanTable 3.Sample of Simulation Results of WIM Data at Station 001LocationSpan ͑m ͒Moment range ͑kN m ͒Maximum Effective Middle span of simple beam9969270182,473762376,5982,173Middle support of continuous beam 9616198181,323470373,0291,014Middle span of continuous beam 9913247182,488749376,6372,188Table 4.Sample of Simulation Results of WIM Data at Station 410LocationSpan ͑m ͒Moment range ͑kN m ͒Maximum Effective Middle span of simple beam9517164181,230425373,0781,233Middle support of continuous beam932811818698295371,437581Middle span of continuous beam9483154181,234416373,0901,248Table 5.Sample of Simulation Results of WIM Data at Station 520LocationSpan ͑m ͒Moment range ͑kN m ͒Maximum Effective Middle span of simple beam9766241181,955597374,6571,650Middle support of continuous beam9436158181,187408372,096776Middle span of continuous beam9762232181,961582374,6901,675Fig.6.Average number of cycles per passage:͑a ͒Station 001;͑b ͒Station 410;and ͑c ͒Station 52076/JOURNAL OF BRIDGE ENGINEERING ©ASCE /JANUARY/FEBRUARY 2006D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .10increments.During each iteration,one of the axle weights and axle spacings of the Laman fatigue trucks was modiﬁed within the range provided in Fig.2.The procedure continued until a minimum sum of squared error of the fatigue damage over a range of bridge spans was obtained.Fig.8shows the damage ratios computed for the loading spectrum gathered for each of the three stations when compared with the 240-kN ͑54-kip ͒fatigue truck and modiﬁed AASHTO fatigue truck.The moment ranges obtained from simulation and a number of cycles per passage provided in the AASHTO fatigue guide speciﬁcations ͑AASHTO 1990͒were used in the calculation.The results indicate that the modiﬁed AASHTO fatigue truck provides a notably better estimate of the fatigue damage accumulation than the original 240-kN ͑54-kip ͒AASHTO fatigue truck at all three stations ͑i.e.,values closer to unity ͒.The fatigue damage predicted by the 240-kN ͑54-kip ͒AASHTO fatigue truck is signiﬁcantly underestimated at Station 001and overestimated at Station 410.It can also be observed in Fig.8that the modiﬁed AASHTO fatigue truck does not provide an accurate estimate of the fatigue damage accumulation over the full range of the bridge spans investigated.The fatigue damage was signiﬁcantly overestimated in both simple and continuous beams with short span lengths at all stations.It also should be noted that the fatigue guide speciﬁcations ͑AASHTO 1990͒provide a number of cycles per passage in form of step functions for both simple and continuous beams with short span lengths.When the actual number of cyclesper passage of the modiﬁed AASHTO fatigue truck was used in the comparison,damage ratios of approximately 0.35,0.47,and 0.57were obtained in simple and continuous beams with a 9-m ͑30-ft ͒span length at Stations 001,410,and 520,respectively.A comparison of the fatigue damage caused by the actual truck trafﬁc and the Laman fatigue trucks are shown in Fig.9.The moment ranges and equivalent numbers of cycles per passage of the Laman fatigue trucks obtained from simulation were used in this ﬁgure.The results indicate that the Laman fatigue trucks provide a reasonable estimate of the fatigue damage accumulation at Station 001.The fatigue damage at Stations 001and 520is slightly overestimated in spans shorter than 18m ͑60ft ͒and slightly underestimated at the middle support of continuous beams in 18-to 30-m ͑60-to 100-ft ͒spans.The Laman fatigue trucks,however,overestimate fatigue damage in all span ranges at Station 410because the effective gross weight at this station is signiﬁcantly less than a minimum gross weight of the truck conﬁgurations provided in Fig.2.Proposed Fatigue TruckA new fatigue truck design was developed by utilizing an iterative procedure.During the iteration,both the axle weight ratios and the axle spacings of the fatigue truck were modiﬁed.The effective gross weights obtained from the WIM database were assigned for a gross weight of the fatigue trucks.Maximum momentranges,Fig.7.Percent fatigue damage accumulation at midspan of simple beam members:͑a ͒Station 001;͑b ͒Station 410;and ͑c ͒Station520Fig.8.Damage ratio of 240kN and modiﬁed AASHTO fatigue trucks:͑a ͒Station 001;͑b ͒Station 410;and ͑c ͒Station 520JOURNAL OF BRIDGE ENGINEERING ©ASCE /JANUARY/FEBRUARY 2006/77D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S o u t h e a s t U n i v e r s i t y o n 11/28/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。

铸铁摩擦磨损溃载荷

铸铁摩擦磨损溃载荷英文回答：Cast iron is a type of iron that has a high carbon content. This high carbon content makes cast iron very strong and durable, but it also makes it very brittle. As a result, cast iron is often used in applications where strength and durability are more important than toughness. One common application for cast iron is in the manufactureof engine blocks.The friction and wear properties of cast iron are important in many applications. The coefficient of friction of cast iron against steel is typically between 0.2 and 0.4. This coefficient of friction is relatively low, which makes cast iron a good choice for applications where low friction is desired. The wear resistance of cast iron is also good, which makes it a good choice for applications where wear is a concern.The fatigue strength of cast iron is relatively low. This means that cast iron is not as resistant to repeated loading as some other materials. As a result, cast iron is not typically used in applications where fatigue strengthis a concern.The ultimate tensile strength of cast iron is typically between 200,000 and 300,000 psi. This ultimate tensile strength is relatively high, which makes cast iron a good choice for applications where strength is important.The yield strength of cast iron is typically between 120,000 and 150,000 psi. This yield strength is relatively high, which makes cast iron a good choice for applications where strength is important.中文回答：铸铁是一种碳含量较高的铁。

(3)残损鉴定常用英语

残损鉴定常用英语海损理事书Average adjustment海损异议书Captain’s protest提出抗议To raise an objection提出含混申诉To make vague complaints停止仲裁To withhold business诉诸仲裁To resort to arbitration打官司To resort to litigation正确对待问题To view the matter in a proper light解决困难To straighten out difficulties消除误解To clarify misunderstanding帮助消除纠纷To help one get out of the mess找出和解办法To work out a compromise通融让步To stretch appoint部分赔偿To compensate partly抵消差额To offset the difference圆满解决To bring the case to a happy close表层top layers／surface在卸货过程中in the course of discharge during discharge右后角at aft starboard corner变黄、褐色discolored into dark yellow or dark brown愈向内愈严重The more inner the worse.结块become cakelike发出__气味giving out a ___ smell更有甚者so much the worse粘连成片／块agglomerated into slices / hard mass呈焦黑色in burnt black color位于__之前located in front of核计损失如下The loss is enumerated as follows鉴定损失如下the following is the ascertainment of loss我们对整批货物作了仔细检查发现We made an careful inspection of the whole shipment and found that整批货物经本局鉴定人员仔细检验，查得Our careful inspection of the whole shipment revealed/showed经向大副了解On inquiry ,the chief-mate said that在＿＿港装船时已发现有漏、湿的情况The leaky and the wetted bags came in his noticeduring loading at ＿＿＿port.提单上已有批注，经我局查阅属实There were exceptions made about the fact on the Bill of Loading. they have been verified to be true by us.提单上已有批注There was remarks about it on the Bill of Loading.拣取干、湿样品，分别测定其含氮量。

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U.S. DepartmentOf TransportationFederal RailroadAdministrationRR06-02February 2006 Fracture and Fatigue Damage Tolerance ofBainitic and Pearlitic Rail SteelsSUMMARYThe Federal Railroad Administration sponsored a research project to investigate the fracture and fatigue damage tolerance of baintic steels. Low carbon baintic steel shows promising potential, especially in critical components such as frogs and switches. The study examined the microstructure – fracture and fatigue damage tolerance relationships of bainitic rail steel in comparison with pearlitic rail steel. It was found that the bainitic microstructure consists of a mixture of tempered martensite and ferrite associated with intralath carbides. The pearlitic microstructure consists of fine lamellar aggregate of very soft and ductile ferrite and very hard carbide. The J6 bainitic steel studied in the present work has ultimate strength, yield strength and elongation to failure of about 1500MPa, 1100MPa and 13% respectively. These values are higher than those for pearlitic steel as shown in Figure 1. The bainitic steel exhibits a higher rate of crack deceleration in the second stage, as indicated by the lower slope of the fatigue crack propagation kinetics curve in comparison with the pearlitic steel. This attests to the superior fatigue damage tolerance of the bainitic rail steel and provides evidence to support the superior rolling fatigue damage tolerance of the bainitic rail steel reported in the literature.Figure 1. Microstructure - Mechanical properties andfatigue relationships of Bainitic and pearlitic rail steels.US Department of transportationFederal Railroad Administration Research Results RR06-02BACKGROUNDPearlitic steels obtain their strength from the fine grains of pearlite. However, there is a limit in the production of very fine grains in manufacturing and post-heat treatment processes. In contrast, bainitic steels derive their strength from ultra-fine structure with many dislocations that are harmless and confer high strength (1). The microstructure of bainitic steel is a metastable aggregate of ferrite and cementite produced from the transformation of austenite at temperatures below the pearlite range and above the martensite starting temperature. Failure analysis of rails has demonstrated that fatigue crack propagation and fracture is one of the major reasons of broken rail derailment and other severe accidents . For example, Orringer et al. (2) studied the fatigue crack propagation life of detail fracture in rails. Glowacki and Kuziak (3) have investigated the effect of coupled thermal-mechanical processes on the evolution of microstructure in rails. Fracture toughness and fatigue strength have been applied as criteria for characterizing the fatigue damage resistance of railway rails (4). The limitations of fracture toughness and fatigue strength criteria are obvious due to the diversified composition of rails and the complicated live bending stress, shear stress and residual stress conditions.The microstructure-properties relationships, plane strain fracture toughness, and fatigue crack growth of a J6 bainitic and a premium pearlitic rail steel were studied to gain fundamental understanding of the underlying mechanisms between these performance- related properties and the microstructure of the materials.REPRESENTIVE RESULTSFracture Toughness EvaluationThe general expression of the plane strain fracture toughness for a compact tension specimen used to compare the two rail steels is: (1) Where P is the load, B is the thickness, W is the distance from the center of the loading holes to the edge of the specimen, a is the total crack length (initial plus fatigue pre-crack) and f (a/W) is a geometrical correction factor. Thegeometrical correction factor, f(a/W), in Equation (1) can be expressed as : (2)2/3432))(1(])(6.5)(72.14)(32.13)(64.4886.0))[(2()(Wa W aW a W a W a W a Wa f −−+−++=The bainitic steel demonstrated elastic behavior and cleavage fracture; therefore ASTM Standard E 399 was used for the analysis. The data for all three samples tested along with their calculated values of K Ic based on Equation (1) are presented in Table 1.Table 1. Compact tension specimengeometry and test results for bainitic and pearlitic steels S a m p l ea (mm)f (a /W ) P m (kN) B (mm) K IcMPa √mBainitic Rail Steel #111.8910.66 6.6 9.14 51.43 #212.3911.48 6.3 9.14 52.87 #312.2911.136.4 9.14 51.44Average value of K Ic52Pearlitic Rail Steel #112.0910.98 5.7 9.14 45.75 #212.1911.25 4.7 9.14 38.74 #312.1911.854.39.1437.25 Average value of K Ic41W = 22.4 mm.a = total crack length P m = maximum loadP q = load at which K q is calculatedB = thicknessK q =stress intensity factor calculated from Equation 1K Ic = mode I fracture toughnessIn order to validate the calculated value of K as a true K Ic fracture toughness, the following conditions must be met:)(1Waf W B P K =a and B ≥ 2.5 (K Q /σy )2 (3)P max /P Q < 1.1 (4)For the bainitic steel, the value of 2.5 (K Q /σy )2= 205101520253035404550less than B, which is 9.14 mm and less than a, which is about 12 mm; therefore the condition of Equation 3 is met. In addition P max equals P Q so the condition of Equation 4 is met. Therefore these fracture tests for the bainitic steel yield a valid value of K Ic according to ASTM E399. Theaverage value of K Ic for the bainitic steel wasfound to be 52 MPa √m.The pearlitic steel also demonstrated elasticbehavior and cleavage fracture. Similarly ASTMStandard E 399 was used for the analysis of theplane strain fracture toughness, K Ic . The data forall three premium pearlitic steel samples testedalong with their calculated values of K Ic, basedon Equation 1, are also presented in Table 1.For the pearlitic steel, the value of 2.5 (K Q /σy )2 =2.5 (41/700)2 *1000 = 8.6 mm. This value is lessthan B, which is 9.14 mm, and less than a whichis about 12 mm, therefore the condition ofEquation 3 is met. In addition P max equals P Q, sothe condition of Equation 4 is met. Thereforethese fracture tests for the pearlitic steel yield avalid value of K Ic according to ASTM E399. Theaverage value of K Ic was found to be 41 MPa √mfor the premium pearlitic steel.0246810121416182022Crack Length a, (mm)E n e r g y R e l e a s e R a t e , J * (k J /m 2)Based on the plane strain fracture toughnessanalysis using compact tension specimens, thefracture toughness of the bainitic steel was found to be about 27% higher than that of the premium pearlitic steel. Fatigue Crack Growth AnalysisThe average crack length, a , versus the number of cycles, N, for both bainitic and pearlitic rail steel is shown in Figure 1. It can be seen from Figure 1 that the total fatigue lifetime of the bainitic steel is much higher than that of the pearlitic steel. This is based on the average of three macroscopically identical specimens from each material. The total average fatiguelifetime for the bainitic steel is about 78,000cycles, while that for pearlitic is about 11,000. Itis also shown that both initiation lifetime andpropagation lifetime for the bainitic steel ishigher than that for the pearlitic. The slopes ofthe curves in Figure 1 are taken as the averagecrack speed at each crack length.Energy Release RateThe potential energy, P, was calculated fromthe hysteresis loops recorded at intervals ofnumber of cycles. It is the area above theunloading curve at each crack length. On thisbasis, the relationship between the potentialenergy and the fatigue crack length, a , was established. The energy release rate J* was evaluated from the potential energy curve a is the crack length and B is the specimen thickness. Figure 2 illustrates the average energy release rate, J*, as a function of the crack length, a , for the bainitic and pearlitic rail steels. The value of J* increases with the increase of the crack length, a . The critical value of J* for the bainitic steel is about 40 kJ/m 2, while that for the pearlitic steel is about 13 kJ/m 2. This is the point where the onset of rapid crack growth is observed. The a c , andrespectively.Figure 2: Energy release rate, J*, versus the fatigue crack length, a. Fatigue Crack Growth Kinetics The crack speed versus the energy release rate J* for both the bainitic and pearlitic rail steel are shown in Figure 3. The crack deceleration in the case of the bainitic steel started after a J* value of about 10 kJ/m 2. This is indicative of material damage ahead of the crack tip. It can also be seen from Figure 4 that the first stage, or initiation stage, of fatigue crack propagation (FCP) kinetics is well developed in the bainitic steel, while that for the pearlitic is less pronounced. Under the same J*, the crack growth rate of pearlitic steel is higher than thatof bainitic steel, which means that bainitic rail steel has higher resistance to FCP. In order to analyze the fatigue crack growth behavior of the two materials the Paris Law was used, as defined in the following equation: (6) In this equation, da/dN is the crack speed and J* is the energy release rate, both obtained from Figure 3. The empirical constants, A and m are parameters that depend on the material properties, obtained from Figure 3. The average values of A and m for the bainitic steel are 1.0 x 10-8and 1.13 respectively, while those for the premium pearlitic steel are 3.04 x 10-12and 5.44. The influence of the value of m in the aboveequation is much greater than the influence of the constant A due to its role as an exponent rather than as a multiplicative factor. The lower value of m reflects the considerably lower crack speeds at the same value of J* for the bainitic steel, even with the much higher value of A. Figure 3 Crack growth rate, da/dN, versus energy release rate, J*. CONCLUSIONS Fracture toughness evaluation was conducted on bainitic and pearlitic rail steels using (½ T) compact tension specimens according to ASTM standard E399. It was found that the average K Ic for the bainitic rail steel is 52 MPa √m, while that of the premium pearlitic steel is 41 MPa √m. It was also found that the crack speed for the bainitic steel is lower than that for the pearlitic steel over the entire range of the energy release rate. The bainitic steel exhibits a higher rate of crack deceleration in the second stage, as indicated by the lower slope of the FCP curve in comparison with the pearlitic steel. This indicates the superior resistance of bainitic rail steel to FCP, i.e. higher fatigue damagetolerance. Also, ductile tearing and extensiveridge formation are associated with the stable crack propagation region of the bainitic steel. Pulled-up pearlite lamella, limited microcracks and micro-void coalescence can be found in the pearlitic steel. In general, the more ductile features of the bainitic steel reflect the crack deceleration and indicate a considerably high energy consuming process giving it its superior fracture and fatigue damage tolerance. *)log(log log m A da +=⎟⎞REFERENCES1. Sawley, K. J., Technology Digest, TD97-001, 1997.2. Orringer, O. et al. Risk/Benefit Assessment of Delayed Action Concept for Rail Inspection , DOT/FRA/ORD-99/03 DOT-VNTSC-FRA-99-7, FRA, Office of R& D, Washington D. C.1997.3. Glowacki, M. and R. Kuziak. Conf. Proc.COMPLAST 5 (Computational Plasticity), eds.D.R.J. Owen,E. Onate, E. Hinton, Barcelona, March 1997, 1313 - 1316. 1.E -081.E -071.E -061.E -051.E -0401020304E nergy Release Rate, J* (kJ/m2)C r a c k G r o w t h R a t e , d A /d N (m /c yc l e )0 4. Vitez, I., and B. Todic. ECF 9 - Reliability and Structural Integrity of Advanced Materials , Vol. I and II: 1992, .1291-1296.ACKNOWLEDGEMENTSHeshmat Aglan, professor at TuskegeeUniversity, performed this study. Mahmood Fateh, FRA Technical Representative, providedsupport through technical discussions. CONTACT Mahmood Fateh Federal Railroad Administration Office of Research and Development 1120 Vermont Avenue NW – Mail Stop 20 Washington, DC 20590 TEL: (202) 493-6361 FAX: (202) 493-6333 Mahmood.Fateh@J dN ⎠⎜⎝⎛。