Effect of surface stresses on CuO nanowire growth in the thermal oxidation

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基于圆孔扩张理论的桩基水平承载力计算方法

文章编号：1000-4750(2021)02-0232-10基于圆孔扩张理论的桩基水平承载力计算方法张小玲1,2，赵景玖1,2，孙毅龙1,2，许成顺1,2(1. 北京工业大学建筑工程学院，北京 100124；2. 北京工业大学城市与工程安全减灾教育部重点实验室，北京 100124)摘要：近年来，我国城市的基础设施建设规模不断扩大，桩基础是基础设施建设中常用的基础形式，其水平承载特性的分析计算是桩基设计中的重要问题。

基于Vesic 圆孔扩张理论，分析了水平荷载作用下桩侧土体的实际受力状态，推导了基于应力增量的桩侧土抗力的计算公式，进而提出了考虑摩擦效应的桩土相互作用的计算方法；并基于MATLAB 编写了相应的分析程序，通过开展案例分析，验证了该计算方法的有效性；最后基于所建立的桩基水平承载力的力学模型，探讨了荷载、桩径等因素对水平受荷桩的承载特性的影响规律。

关键词：桩土相互作用；Vesic 圆孔扩张理论；桩土摩擦效应；水平承载力；桩侧土抗力中图分类号：U443.15 文献标志码：A doi: 10.6052/j.issn.1000-4750.2020.04.0278AN ANALYSIS METHOD FOR THE HORIZONTAL BEARINGCAPACITY OF PILE FOUNDATION BASED ON THECAVITY EXPANSION THEORYZHANG Xiao-ling 1,2, ZHAO Jing-jiu 1,2, SUN Yi-long 1,2, XU Cheng-shun1,2(1. College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China;2. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China)Abstract: In recent years, the urban infrastructure construction in China has been constantly developing. The pile foundation is a common form of foundation in infrastructure construction. The calculation of the capacity of a pile foundation is an important subject in the foundation design. Based on the Vesic expansion theory, the actual stress state of the soil on the pile side under horizontal loading is presented. A calculation method of the soil resistance on the pile side in the form of stress increment is derived, and the mechanical method of the horizontal capacity of the pile foundation considering the pile-soil interaction is proposed. The corresponding analysis program was compiled based on MATLAB software and the validity of the proposed calculation method was verified by a comparison with experimental results. The effects of the load and the pile diameter on the mechanical behavior of the pile-soil interaction system was analyzed based on the proposed mechanical model for the horizontal bearing capacity of pile foundation.Key words: pile-soil interaction; Vesic cavity expansion theory; pile-soil friction effect; horizontal bearingcapacity; soil resistance on the pile side近年来，我国城市基础设施建设的规模不断扩大，建设水平不断提高，而桩基础作为这些重大基础设施的主要承载构件，其安全性和稳定性成为保障这些基础设施安全运营的关键因素。

Effect of Stress Concentration on Magnetic Flux Leakage Signals from Blind-Hole Defects in Stressed

Res Nondestr Eval(1996)8:83–100©1996Springer-Verlag New York Inc.Effect of Stress Concentration on Magnetic Flux Leakage Signals from Blind-Hole Defects in Stressed Pipeline Steel T.W.Krause,R.W.Little,R.Barnes,R.M.Donaldson,B.Ma,and D.L.Atherton Department of Physics,Queen’s University,Kingston,Ontario,K7L3N6,CanadaAbstract.Stress-dependent magneticﬂux leakage(MFL)signals of the normal surface compo-nent(radial)MFL signal from blind-hole defects in pipeline steel were investigated.Three different stress rigs with uniaxial stress andﬁeld conﬁgurations were used.A double-peak feature in the MFL signal was deﬁned quantitatively by a saddle amplitude,which was taken as the difference between the average of the double peaks and the corresponding saddle point.Results indicated that the saddle amplitude increased linearly with increasing tensile surface stress and decreased, or did not exist,for increasing compressive surface stress.The stress-dependent saddle amplitude was shown to increase with increasing defect depth.Finite-element calculations indicated that stress concentration also increased with increasing defect depth.The measurements and analy-sis demonstrate that the stress-dependent saddle amplitude behavior in the radial MFL signal is associated with surface-stress concentrations near the blind-hole defects.IntroductionMagneticﬂux leakage(MFL)techniques are commonly used for the in-line inspection of pipelines for metal loss defects such as corrosion pits[1].The in-service operating pressures of gas pipelines generate large circumferential stresses that may reach70%of the yield strength of the pipe.These in-service stresses affect theﬂux leakage patterns and have been studied previously[2]–[7].In the presence of stress,defects act as“stress raisers”[8].Dependent upon the defect depth[9],the defects may generate stress con-centrations that exceed the yield strength in their vicinity.Stress raising around defects also may lead to enhanced stress corrosion cracking[10].There are two effects that may contribute to the generation of the stress-dependent MFL signal:1)the bulk effect of stress on the magnetic properties[11]–[16]and2)the effect of the defect as a stress raiser that is also dependent on the depth of the defect [9].Metal loss resulting from increasing defect depth increases the level of magnetic saturation in the vicinity of the defect and,therefore,increases the MFL signal.Similarly, by affecting the stress-dependent magnetic properties of the steel in the vicinity of the defect,the application of a bulk stress also affects the peak-to-peak MFL(MFL pp) signal.Stress concentrations in the vicinity of the defect have a similar effect.From a previous consideration[17],under a bending stress the two-dimensional solution for a100%through-wall defect or hole generates a peak stress level at the edge of the84Krause et al. hole that is2.4times that of the nominal background stress[8,17].Finite-element calculations and stress measurements[17]indicate that,for the same bending stress,the stress concentration for a round-bottomed pit that is50%of the through-wall thickness is1.2times the nominal stress.For a plate under uniform tensile stress,the maximum stress at the edge of a full cylindrical through-hole is three times that of the nominal stress [8,18].Stress concentrations occur at the two edges of the defect that are tangential to the applied stress direction.An increase in the pipe wallﬂux density typically results in an increase in the MFL signal due to increased saturation of the steel in the defect region.The effect of stress on the MFL pp signal has been shown to increase for increasingﬂux densities in the range of 0.65to1.24T[9,13]–[16].It is expected,therefore,that stress concentration combined with increasingﬂux density may similarly affect the MFL signal.Observations of a double-peak feature that increases in amplitude with increasing applied tensile stress have been made for normal-surface component(radial)MFL signals for various uniaxial orientations of stress andﬁeld applied to pipeline steel[5,11].In particular,the amplitude of the double-peak feature(hereafter referred to as the saddle amplitude)has been observed to increase linearly with increasing levels of applied stress and has been associated with stress patterns around the defect itself[12,14].In this paper we provide evidence that strongly supports this claim.Further,it is demonstrated that the double-peak feature in the MFL signal may be associated primarily with stress concentrations that appear in the vicinity of the defect near the surface of the steel pipeline sample,and also that the stress concentration and resultant saddle amplitude in the MFL signal increase with increasing defect depth.Experimental ApparatusThe experimental apparatus is described in detail elsewhere[11,12].The apparatus used to measure the radial component of theﬂux leakageﬁeld from a defect on the same side of the sample as the measuring apparatus(near side)consisted of a Hall probe,an ampliﬁer to amplify the Hall signal,and a computer for data acquisition.The radialﬂux leakage signal was measured at scanned positions set at1-mm intervals(0.5mm for the semicircular pipe section)across the area of the defect.The radialﬂux leakage signal was taken as the average of100measurements taken at each position.Pipeline Sample and Stressing ApparatusSamples of pipeline steel used in this study were cut from a610-mm(24-in.)diameter X70steel pipe of9-mm wall thickness.Theﬁrst sample used was a102-mm(4-in.)wide semicircular section cut in the pipe hoop direction.Other samples used were4.27-m long axial strips that were also102mm(4in.)wide.The pipeline steel composition is given elsewhere[17].There were three separate experimental test rigs.Theﬁrst apparatus is the semi-circular hoop bending rig shown in Fig.1.The second and third apparatus use the single-strip beam-bending arrangement and the composite beam-bending arrangement,Magnetic Flux Leakage Signals from Blind-Hole Defects85Fig.1.The semicircular pipe section and bending stress rig for the production of surface stress in semicircular sections of pipe steel.both described elsewhere[11,12].Surface stresses up to±300MPa were applied using the three stress rigs.This is below the yield stress of the pipe steel,which is at500MPa. All three sets of apparatus have a13-mm diameter ball-milled external pit machined to50%of the steel wall thickness.The composite beam apparatus also has two more 13-mm diameter ball-milled external pits machined to depths of25and75%.An area of about40mm by40mm around the defect was stripped of its epoxy coating to expose the pipe steel.The defect area was magnetized to a maximum axialﬂux density of1.6T using ferrite magnets.For the semicircular pipe section,steel hingedﬁngers were used to couple theﬂux from the magnets into the steel pipe,while for the two beams,steel brushes shaped to the curvature of the beams coupledﬂux into the steel samples. Semicircular Pipe Section Stress RigIn theﬁrst stress rig,shown in Fig.1,a semicircular pipe section is held stationary by a ﬁxed clamp,while the other is connected to a movable clamp.The movable clamp is free to travel along a horizontal threaded rod as the rod is rotated with the handle,the result being the application of a hoop-bending stress.When the clamp is moved inward,tension is created on the outside and compression on the inside pipe surface,with the opposite being true if the clamp were to be moved outward.A“clamp position versus stress”calibration was obtained theoretically[17]and veriﬁed using strain gauges(placed well away from the defect region).86Krause et al. Single BeamThe single-strip beam is a102-mm wide strip of steel cut in the axial direction from the 610-mm diameter pipe with a thickness of9mm and a length of4.27m.The low rigidity of the single beam allows bending by simply hanging masses of about5kg from one end of the beam or supporting it at a raised height while the middle length of the beam is supported and the opposite end of the beam isﬁxed in position.Composite BeamThe third apparatus utilizes a composite beam and an arrangement to bend the beam [11,12].The composite beam is made from two axial strips of pipeline steel that are separated at aﬁxed distance of29mm by an alternatingﬁberglass–wood composite. The composite materials are bonded together with high-strength epoxy resin.Under a bending stress the neutral axis of the beam is outside the pipeline steel regions,so that nearly uniform stress is generated through the thickness of the steel walls.Because the composite beam is much more rigid,the beam is stressed by placing it parallel to a comparably rigid pipe section of equal length separated by a wood saddle in the middle. At one end the beam and pipe are held together by a clamp or chain,and at the other end the beam and pipe are pulled together by another clamp with a scissor jack.For tests using tensile stress the steel strip with the defect in it is on the side facing away from the rigid pipe,with the composite beam above the pipe.For compressive stress the steel strip is on the side facing toward the pipe and with the beam underneath the pipe,so that the detector can be placed on top of the beam.Stress CyclesThree different procedures of applyingﬁeld and stress are used to perform the mea-surements:1)the“normal cycle,”which involves magnetizing the beam with no applied stress and maintaining the appliedﬁeld during the stressing of the beam;2)the“opposite cycle,”which is similar to the“normal cycle”except that the magnetization is generated with theﬁeld in the opposite polarity;and3)the“after-cycle,”which involves removing the magnet before each stressing increment and then replacing it so that the beam is remagnetized after each change of stress.In all three methods,the defects are scanned at ﬁxed levels of stress.Of the three cycles,the after-cycle is the most similar to an actual pipeline pigging measurement.Measurements of the peak-to-peak magneticﬂux leakage(MFL pp)signal in the normal-cycle mode across a50%penetration round-bottomed blind-hole–simulated de-fect for various levels of applied tensile and compressive stress in the semicircular pipe section were performed using the hoop-bending stress rig shown in Fig.1.Starting from0MPa,tensile stress up to250MPa was applied followed by changes in stress to 250MPa compressive stress and,ﬁnally,back to a0-MPa stress level.The MFL signal was recorded at various levels of applied stress.The stress in the pipe section was ad-justed by varying the distance between the ends of the semicircular pipe section in the stress rig to various strain gauge calibrated settings.Magnetic Flux Leakage Signals from Blind-Hole Defects87 For the composite beam tensile stress scans were performed,ﬁrst for all three defects and stress cycles,and then followed by compressive stress scans,since a reorientation of the beam was required.No compressive stress scans were performed for the single beam.Variation of Pipeline Steel Flux DensityThe totalﬂux density within the semicircular pipe section was measured by removing the magnetizing system,noting theﬂux change,reversing the polarity of the magnetizer, applying it again,and noting theﬂux change again.The average of the twoﬂux readings was taken and theﬂux density within the pipe and was found to be1.54T.The totalﬂux density within the single-beam stress rig was determined in the same manner and was found to be1.6T.Two techniques were used to vary theﬂux density within the composite beam pipe wall and are described in detail elsewhere[9,13].Theﬁrst technique consisted of changing the size of the magnets used,and the second involved the application of partial shorting bars.The steel bars diverted some of theﬂux from the magnets and therefore reduced theﬂux density in the pipe wall.An integrating voltageﬂuxmeter,connected to a13-turn coil wound around one section of steel beam and through a hole in the center of the composite beam assembly,was used to determine theﬂux density within the pipe wall. The four pipe wallﬂux densities generated within the composite beam pipe wall using these two techniques were0.65T,0.84T,1.03T,and1.24T.AnalysisThe peak-to-peak radial component of the magneticﬂux leakage(MFL pp)signal is ob-tained by taking the difference between the maximum(positive)and minimum(negative) components of the MFL signal.Positive saddle amplitude values are obtained from the MFL signal by evaluating the difference between the average of the two positive peaks and the positive saddle point.Negative saddle amplitude values are obtained in the same manner,except that the negative double MFL peaks and the negative saddle point are used for the evaluation.Both the variation of the MFL pp signal and the saddle amplitude as functions of stress were investigated.Finite-Element CalculationsA three-dimensionalﬁnite-element method was used to model the stress pattern surround-ing the defect.Finite-element modeling was performed using the ANSYS Revision4.4 by Swanson Analysis Systems.A ten-node tetrahedral element with three directional degrees of freedom at each node was used to mesh the solid model.The volumes were deﬁned using a solid modeling approach,where the geometry of the object was described by specifying key points,lines,areas,and volumes.ANSYS thenﬁlled in the solid model with nodes and elements based on the user-deﬁned element shape and size.88Krause et al.Fig.2.(a)Surface and contour plots of the radial magneticﬂux leakage from the near side of a13-mm-diameter ball-milled50%defect in the semicircular pipe section under a tensile stress of250MPa during a normal cycle.Theﬁnite-element calculations modeled aﬂat plate with a ball-milled defect.The plate dimensions were taken as50mm×50mm with a thickness of9mm,which was the same as that of the pipeline steel samples.The radius of curvature of the ball-mill that generated the defect was taken as6.35mm.The full defect radius was,therefore,only attained at71%defect depth.This may have affected the calculations since the defect radius was changing continuously with respect to the mesh distribution up to71%of the wall thickness.Young’s modulus was taken as210GPa and Poisson’s ratio as0.28. Calculations were performed for a nominal stress of190MPa.ResultsSemicircular Pipe Section:MFL pp MeasurementsFigures2a and2b show surface and contour plots of the radial magneticﬂux density leakageﬁeld over the defect for tensile and compressive stresses of250MPa,respectively. Both scans are from the normal-cycle procedure using constant magnetization.The amplitude of a signal is obtained by taking the difference between the maximum andMagnetic Flux Leakage Signals from Blind-Hole Defects89Fig.2.(b)Surface and contour plots of the radial magneticﬂux leakage from the near side of a13-mm-diameter ball-milled pit in the semicircular pipe section under compressive stress at250MPa during a normal cycle.minimum values ofﬂux density over the area of the scan(MFL pp).The proﬁle of the contours is typical for all scans,with slight variations with changing paring the two scans,a more pronounced double-peak feature is observed for the tensile surface stress case than for the compressive surface stress case.The MFL pp signal as a function of stress for the semicircular pipe section under bending-hoop stress is shown in Fig.3.Starting at0MPa,the variation of the MFL pp signal with surface stress demonstrates an initial increase with the application of tensile stress followed by a decrease and a large hysteresis loop as the stress is cycled from 250MPa to−250MPa.Under a compressive stress the variation of the MFL pp signal is smaller,as is the hysteresis.Theﬁnal zero-stress MFL pp signal is greater than the initial starting point.Arrows indicate the order in which the data were taken.Variation of Saddle Amplitude with StressResults obtained from an analysis of the positive and negative saddle amplitudes as a function of surface stress in the normal cycle are shown for the semicircular pipe section in Fig.4.Positive and negative saddle amplitudes are present for the zero-stress case.90Krause et al.Fig.3.Peak-to-peak MFL signal from the near side as a function of surface stress in the normal cycle for a13-mm-diameter ball-milled50%defect on the semicircular pipe section under hoop-bending stress with an applied pipe wallﬂux density of1.54Tesla at0MPa.Since hysteresis is present,arrows indicate the direction in which the data were taken.The positive saddle amplitude increases linearly from a minimum at250MPa compressive stress to a maximum at200MPa tensile stress.Some hystersis is evident.In comparison, the negative saddle amplitude is smaller in magnitude,more hysteretic,and slightly less linear.For the single-beam stress rig,observations of a saddle amplitude that depended linearly on stress were made for there tensile surface stress measurements equal to and greater than200MPa measured in the normal cycle.In this rig a saddle was not observed for zero or applied compressive stresses.As in the semicircular pipe section,the magnitude of the positive saddle amplitudes was greater than the corresponding negative saddle amplitudes.The variations of the positive and negative saddle amplitudes with stress for the composite beam for the three defect depths in the normal cycle at1.24T are shown in Fig.5for tensile stress values.For the composite beam no saddle was observed for any zero or compressive stress values,which is in contrast to the semicircular pipe section where a saddle amplitude that was a decreasing function of increasing compressive stress was observed.This result is considered further in the discussion.The results for the composite beam indicate an increasing variation of saddle amplitude with stress forMagnetic Flux Leakage Signals from Blind-Hole Defects91Fig.4.Positive(•)and negative( )saddle amplitudes as functions of surface stress using the semi-circular pipeline apparatus with aﬁeld of1.54T during the normal cycle are plotted for the13-mm ball-milled50%defect.increasing defect depth.For the25and50%depth defects the positive saddle amplitudes are greater in magnitude than the negative saddle amplitude values for equivalent levels of stress,while at75%this difference is not as great.The dependence of the positive and negative saddle amplitudes upon stress in the composite beam for the three different defect depths for measurements performed in the after-cycle at1.24T are shown in Fig.6.In contrast to the normal-cycle measurements for the25and50%defects,the magnitude of the negative saddle amplitudes is greater than that of the positive saddle amplitudes,while there is no observed difference between the magnitudes for the75%defect.The rate of change of the saddle amplitude with stress is greatest for the75%defect and least for the25%defect.Stress-Dependent Saddle Amplitude SlopesLinear bestﬁts were applied to the saddle amplitude data as a function of stress for the three different stress rigs.The slopes of saddle amplitude variation with stress for the normal cycle in the three different stress rigs are shown in Table1.Several observations can be made for the normal-cycle stress applied in the three different stress rigs.These92Krause et al.Fig.5.Saddle amplitudes as a function of stress in the composite beam apparatus from13-mm ball-milled defects in aﬁeld of1.24T in the normal cycle are plotted for the25%defect for the positive( ) and negative( ),for the50%defect for the positive( )and negative( ),and for the75%defect for the positive( )and negative(•)saddle amplitudes.Table1.Bestﬁt slopes for normal-cycle MFL pp and saddle amplitude with different defect depths in the composite beam and50%defect in the semicircular pipe section and single beam.%MFL pp vs.Stress-dependent Stress-dependent+Sad.amp.−Sad.amp. Defect stress slope saddle amplitude saddle amplitude MFL pp slope MFL pp slope depth(10−12T/Pa)pos.(10−13T/Pa)neg.(10−13T/Pa)(=col.3/col.2)(=col.4/col.2) Composite Beam(B=1.24T)25% 1.6210.130.0650% 5.1760.140.1275%11.019.119.50.1740.177 Semicircular Pipe Section(B=1.54T)50%—118——Single Beam(B=1.6T)50% 2.3 1.68±39±30.350.43Fig.6.Saddle amplitudes as a function of stress in the composite beam apparatus from13-mm ball-milled defects in aﬁeld of1.24T in the after-cycle are plotted for the25%defect for the positive( ) and negative( ),for the50%defect for the positive( )and negative( ),and for the75%defect for the positive( )and negative(•)saddle amplitudes.are:1)the slope directions of the positive and negative saddles as a function of stress are all positive;2)the rate of change of saddle amplitude as a function of stress for all three stress rigs is of the same order of magnitude,in contrast to the MFL pp signal variations with stress,which demonstrate little correlation between the three different stress rigs: 3)the magnitude of the saddle amplitudes obtained from the positive saddle curves is greater than the corresponding negative saddle curves in the normal cycle;4)no change in the saddle amplitudes was observed under compressive stress for bending stress applied in the axial direction in both the single and composite beams;5)the magnitudes of the saddle amplitudes for the semicircular pipe section are approximately four times greater than those observed for the single and composite beams,and do not go to zero even with the largest application of compressive stress;and6)there is a general increase in the positive and negative saddle amplitude slopes with increasing defect depth.The slopes obtained from the after-cycle and opposite-cycle also demonstrate an increasing saddle amplitude slope with increasing defect depth,although increased in-tercepts for the25and50%defects for the negative saddle amplitude variation are observed.This increase can be seen for the after-cycle in a comparison of Figs.5and6. The sum of the positive and negative saddle amplitude slopes(the total saddle amplitudeFig.7.The sum of positive and negative saddle amplitude stress slopes plotted as a function of% defect depth for the normal cycle( ),after-cycle,( )and opposite cycle( )in the composite beam (B=1.24T).The solid and dashed curves are lines to guide the eye.slope)obtained from the three stress cycle results are plotted as a function of percent defect depth in Fig.7.The total saddle amplitude slope is plotted as a function ofﬂux density for the after-cycle in Fig.8.For all three cycles the results indicated an increasing total saddle am-plitude with increasingﬂux density.The stress concentration factor is a constant for constant defect depth and,therefore, may be related to the slope of the saddle amplitude variation with stress.However,for the zero-stress case,the radialﬂux leakage signal demonstrates a considerable increase with increasing defect depth[19,20].Therefore,to perform a comparison of the variation of the saddle amplitude with stress for different defect depths with calculated values of the stress concentration,it is necessary to normalize the stress-dependent saddle amplitude slopes by their respective zero-stress MFL pp signals.A comparison of the normalized saddle amplitude slopes with the maximum and surface maximum stress concentrations obtained fromﬁnite-element calculations is shown in Fig.9.The stress-dependent saddle amplitude slopes have been averaged over the three cycles,normalized by their respective zero stress MFL pp signals,and scaled to the calculated maximum surface stress at75% defect depth.The normalized and scaled saddle amplitude slopes have beenﬁtted in Fig.9with anFig.8.Sum of positive and negative saddle amplitude stress slopes plotted as a function of pipe wall ﬂux density for the after-cycle( )in the composite beam(B=1.24T).The solid curve is simply a line to guide the eye.empirical formulation given byA=a sinh(bD),(1)where A is the sum of the positive and negative saddle amplitude slopes,D is the percent defect depth,and a and b areﬁtting parameters given by(a,b)=(0.71,0.018). Equation(1)holds in the limit of a0%defect since the total saddle amplitude A goes to zero as the MFL pp signal goes to zero.Theﬁnite-element calculations indicate that both the maximum and surface maximum stress concentration are increasing functions of percent defect depth.Starting at0%defect depth,the maximum stress concentration increases more rapidly than both the surface maximum and the normalized and scaled saddle amplitude slope values.Slower increases in theﬁnite-element calculations are observed in the vicinity of70%,which corresponds with the defect depth in theﬁnite-element model where the radius of the defect reaches its maximum of6.35mm.After90%the surface maximum concentration becomes the maximum stress concentration.The hyperbolic sine function,Eq.(1),coincides with the ﬁnite-element calculations above75%defect depth and with the theoretical fractional change in stress concentration at100%defect depth.Fig.9.Normalized change in maximum stress( )and maximum surface stress(⊕)as a function of%defect depth as obtained fromﬁnite-element calculations.The total saddle amplitude stress slopes ( )for the composite beam normalized by their respective zero-stress MFL pp signals and averaged over the three different stress cycles have been scaled to the maximum surface stress(SurfaceσMAX)ﬁnite-element calculations at75%defect depth.The dashed lines are spline curves through the pointsobtained from theﬁnite-element calculations and the solid line is a bestﬁt of the empirical relation,Eq.(1).DiscussionSemicircular Pipe Section:MFL pp MeasurementsThe application of a bending stress in the semicircular pipe section complicates the prediction of the magneticﬂux leakage stress behavior of the pipe since,if the upper surface of the pipe with the near-side defect is under tensile stress,then the inner surface will be under compressive stress.A further complication in this system is the direction of the magnetic easy axis with respect to the direction of the applied stress.The magnetic easy axis is at90◦to the direction of the applied stress,and,therefore,the magnetic properties of the pipeline steel are different[21]from those where the stress and easy axis are aligned in the same direction[22].Geometric properties of the semicircular pipe stress rig also may play a role in affecting the stress-dependent variation of the MFL pp signal,since the radius of curvature and therefore the length of theﬂux path in the semicircular pipe section changes as a function of stress with respect to theﬁxed length of the magnetizer.Furthermore,different levels of pipe wallﬂux density at equivalent stress levels for increasing and decreasing applied stresses may arise because of hystereticﬂux coupling in the hingedﬁnger–semicircular stress system.This may explain the severe hysteresis observed in the radial MFL pp signal for the semicircular pipe section under tensile stress shown in Fig.3.The application of a hoop-bending stress that is either tensile or compressive results in an overall decrease of the MFL pp signal for either surface tensile or surface compressive applied stress.However,there is an initial increase of the MFL pp signal under a surface tensile stress of50MPa.This may be attributed to the presence of a residual compres-sive surface stress present within the pipe.This suggestion is supported by spring-back measurements observed when the pipe section was cut in half[22].Stress-Dependent Saddle Amplitude:Stress Concentration FactorsThe variation of the MFL pp signal with stress appears to be associated primarily with the bulk effects of stress[9],[11]–[13]and pipe wallﬂux density[9,13]on the magnetic properties of steel in the general vicinity of the defect.However,we propose that the double-peak feature in the MFL pp signal and the variation of the saddle amplitude with stress is associated with the near-surface variation of stress in the immediate vicinity of the defect,which acts as a local stress raiser[17].Measurements of the MFL pp signal with almost uniform bulk stress in the composite beam stress rig indicate an increase of the MFL pp signal with increasing uniaxial tensile stress[9,13].Similarly,the variation of the saddle amplitude as a function of stress at the near-side surface of the defect demonstrated the same positive dependence.The rate of change of the saddle amplitude as a function of stress was also of the same order of magnitude in all three apparatus.Since it is the surface stress in all three apparatus that is monitored,we associate the saddle amplitude behavior as a function of stress with the corresponding variation of surface stress in the pipeline steel in the vicinity of the defect.Normalization of the stress-dependent saddle amplitude variation by the stress-de-pendent MFL pp slope for the case of the composite beam is shown in Table1.The results indicate that the saddle amplitude increases with defect depth faster than the stress-dependent MFL pp signal.Also shown in Table1are the positive and negative saddle amplitude slopes for the single beam normalized by the stress-dependent MFL pp slope for the50%defect.The values for the normalized saddle amplitude slopes obtained in this manner are more than twice those obtained for the50%defect in the composite beam. Normalization of the semicircular pipe section stress-dependent saddle amplitude by the corresponding MFL pp stress-dependent signal generates a nonlinear stress variation since the MFL pp signal varies nonlinearly over the applied tension–compression stress cycle.As was shown elsewhere[9,13],the single and composite beams demonstrate a compressive stress dependence,while no saddle amplitude is observed in this applied stress region.These results demonstrate that the variation of the MFL pp signal as a function of the bulk stress effect cannot explain the observed stress-dependent variation of the saddle amplitude.Furthermore,the slope of the saddle amplitude as a function of measured surface stress for the50%defect in the three different stress rigs,two of which are under a bending surface stress,are all of the same order.These points indicate。

ReducingInternalStresses

Reducing Internal StressesSpecialChem - Nov 3, 2004Edward M. Petrie, Member of SpecialChem Technical Expert Team. IntroductionInternal stresses within the adhesive or sealant joint can significantly reduce the inherent adhesive strength. Internal stresses can occur on setting or curing, but they may also develop due to the joint's aging in service. For example, internal stresses could occur by bending forces or by dimensional change of the substrate due to absorption of moisture or aging. This article will focus on internal stresses that occur during the setting process. These stresses are difficult to foresee and avoid. They are common to all adhesive and sealant joints and detract from the ultimate strength of the joint even before it is placed into service.Figure 1 qualitatively illustrates the various forces that are at work to yield the measured bond strength. Internal stresses are a significant factor in why the theoretical (maximum) adhesion values are never realized in practice. In fact, the bond strength measured on well prepared lap-shear specimens is basically the inherent bulk strength of the adhesive material minus the internal stresses.Figure 1: Relationship between the forces involved in adhesion. 1 This chart is qualitative, not quantitative; no significance is attached to the relative lengths of the linesInternal stresses are primarily due to different physical characteristics of both the adhesive and substrate, such as coefficient of thermal expansion, modulus of elasticity, and shrinkage during cure. There are many sources of internal stress, but the four most common are:1. stress concentration points at an interface due primarily to imperfections in the adhesive or at the interface,2. stress due to differences in thermal expansion coefficients of the adhesive and substrate (mainly associated with adhesives that cure at temperatures different than their normal service temperatures),3. stress resulting from non-thermally induced dimensional change in the substrate, and4. stress due to shrinkage of the adhesive or sealant as it cures.Proper internal stress management is required to minimize internal stresses and achieve reliable joints with high adhesive strength. This paper is intended to describe the sources of the most common internal stresses and to recommend corrective action that the formulator and/or end-user can take to minimize strength degradation caused by these forces. Localized StressesLocalized stress concentrations within the joint may occur due to irregularities (voids, defects,etc.) within the adhesive or at the adhesive - substrate interface. These irregularities are usually due to poor wetting of the adhesive on the substrate or faults within the adhesive such as voids.Loss of theoretical adhesive strength arise from the action of internal stress concentrations caused by trapped gas and voids. Griffith 2 showed that adhesive joints may fail at relatively low stress if cracks, air bubbles, voids, inclusions, or other surface defects are present. If the gas pockets or voids in the surface depressions of the substrate are all nearly in the same plane and not far apart (as is shown in Figure 2 top), cracks can rapidly propagate from one void to the next. However, a variable degree of roughness (such as shown in Figure 2 bottom) provides barriers to spontaneous crack propagation. Therefore, not only is surface roughening important, but the degree and type of roughness may be important as well.Figure 2: Effect of surface roughness on coplanarity of gas bubbles. Upper adherend is smooth and gas bubbles are in the same plane; lower adherend has roughness and gasbubbles are in several planes.It has also been shown 3that a concentration of stress can occur at the point on the free meniscus surface of the adhesive (edge of the bond-line). This stress concentration increases in value as the contact angle, , increases. At the same time, the region in which themaximum stress concentration occurs will move toward the adhesive-adherend interface. These results are illustrated in Figure 3 for a lap joint in shear with a contact angle, , rangingfrom 0 to 90 degrees.For contact angles less than about 30 degrees (i.e., for good wetting) the maximum stress occurs in the free surface of the adhesive away from the edges, and the stress concentration is not much greater than unity. For larger contact angles, the maximum stress occurs at the edges, designated by "A" (i.e., at the actual interface between adhesive and substrate). The stress concentration factor increases until, for a value of = 90 degrees (non-wetting), it isgreater than 2.5. Thus, poor wetting will be associated with a weak-spot at the edge of the interface with a consequent likelihood of premature failure at this region.Localized stresses, such as those mentioned above, can generally be reduced by formulating an adhesive that (1) flows well without starving the joint area and (2) wets the substrate surface. The proper degree of flow can be achieved by controlling the viscosity of the base polymer or with additives such as thixotropes and fillers. Efficient surface wetting can be achieved by using a base polymer with low surface energy, or by increasing the surface energy of the substrate via prebond surface treatment. 4Another method of reducing stress concentration from voids and other defects is to introduce a toughening agent into the adhesive formulation. The toughening agent will provide a stress relief mechanism to interrupt the growth of cracks. An example of a toughening agents for structural epoxy adhesives are carboxy terminated butadiene nitrile elastomers and other discrete elastomeric or thermoplastic particles. The benefits of toughening agents in epoxyand other adhesive systems have been described in previous SpecialChem4Adhesive articles. 5,6Figure 3: Maximum stress concentration in a lap joint. Poor wetting of the adherend produces maximum stress concentration at point of contact of adhesive, adherend, and atmosphere. Stresses Due to Thermal Expansion DifferencesThe most common cause of internal stress is due to the difference in the thermal expansion coefficients of the adhesive and the substrate. These stresses must be especially considered when the adhesive or sealant solidifies at a temperature that is different from the normal temperature that it will be exposed to in service. The thermal expansion coefficients for some common polymeric adhesives and metal substrates can be more than an order of magnitude apart. This means that the bulk adhesive will travel more than 10 times as far as the substrate when the temperature changes, thereby causing stress at the interface.The stresses produced by thermal expansion differences can be significant. Take for example an annular journal bearing where a polyamide-imide sleeve is bonded to the internal diameter of a stainless steel housing (Figure 4). Further, assume that the adhesive used is one that cures at 125°C (e.g., a one-component epoxy). At the cure temperature, all substrates and the gelled adhesive are in equilibrium. However, after the cure is complete and when the temperature begins to reduce as the system approaches ambient conditions, stresses in the adhesive develop because the polyamide-imide substrate wants to shrink to a greater extent than the steel. At ambient room temperature, these stresses may be significant but not high enough to cause adhesive failure. Now further assume that the bonded bearing is to be placed in service with operating temperatures that will vary between 125°C and -40°C. At 125°C the internal stresses due to the miss-match in thermal expansion are reduced to zero, since we are back at the equilibrium condition (assuming that there was no shrinkage in the adhesive as it cured or other stresses in the joint). In fact at temperature greater than 125°C an adhesive may not even be necessary because of an interference fit. However, when the service temperature reaches -40°C, the thermal expansion differences create internal stress in addition to those already present due to curing. Thus, a failure could easily occur.A similar example is evident by noting the test results of a typical elevated temperature cured joint as a function of test temperature, Figure 5. Notice that the bond strength actually increases with temperature to a maximum, and then it falls-off with further increasing temperatures. This is similar to the case above where the internal stresses are actuallyreduced by the service or test temperature. At some elevated temperature, the internal stresses are completely relieved and the bond strength reaches a maximum. The test temperature at which this occurs is usually very close to the curing temperature. At higher test temperatures, additional stresses develop or the effects of thermal degradation become evident, and the bond strength then decreases with increasing test temperature.Figure 4: Journal bearing application. Outer cylinder (stainless steel) is bonded to inner cylinder (polyamide-imide) with an epoxy adhesive. Exposure to low temperatures causes significant stress on the bond due to difference in coefficient of thermal expansions.Figure 5: Plot of strength of an aluminum joint (bonded at elevated temperatures with anepoxy adhesive) as a function of test temperature.The above examples illustrate why the external forces exerted on the bond joint by the test procedure can be either positive or negative as shown in Figure 1. When the external stress acts to neutralize the internal stress, the measured bond strength can increase. External stress can also add to the internal stress (as in the case of the specimen in Figure 4 when tested at -40°C) and result in a total stress level that results in catastrophic failure.The effect of differing thermal expansion coefficients on internal stress generated during cure is discussed in the preceding paragraphs. However, thermal stresses could easily occur during the joint's service life. If the temperature is uniform throughout the bond, the approximate stress on a thin rigid bond may be calculated from the following relationship 7:where:S = shear stress on the adhesive due to differential thermal expansion rates of theadherends, without consideration for adhesive strain;E1, E2 = Young's moduli of the adherends;T = temperature differential between zero stress temperature and service; temperature; (zero stress condition usually exists at the cure temperature.)k1, k2 = thermal expansion coefficients of adherendsIf the substrates are assumed to be unyielding, and the adhesive is relatively flexible and thick, the greatest stress on the adhesive - occurring at the ends of the joint - may be approximated from the following relationship:where:S = greatest shear stress in the adhesive due to differential thermal expansion of the adherends, without consideration for adherend strain;G = shear modulus of the adhesive;d = thickness of the adhesive;L = length of the joint.These theoretical expressions are approximations in that they exclude the strain capability of either the adhesive or the adherends. Such strain would tend to relieve some of the stress. The values calculated would be greater than the actual stress and, therefore, conservative. There are several possible solutions to the expansion miss-match problem. One can use a resilient adhesive that deforms with the substrate during temperature change thus relieving the internal stress. The penalty here is possible creep of the adhesives, and highly deformable adhesives usually have low cohesive strength. If the adhesive is rigid (modulus of 1,000,000 psi), internal stress levels due to mismatch in thermal expansion of over 5,000 psi are not uncommon. However, if the adhesive is compliant (modulus of 10,000 psi), the internal stress may be as low as several hundred psi.Another approach is to adjust the expansion coefficient of the adhesive to a value that is nearer to that of the substrates. This is generally accomplished by selection of a different adhesive or by formulating the adhesive with specific fillers to "tailor" the thermal expansion coefficient. Adhesives can be formulated with various fillers to modify their thermal-expansion characteristics and limit internal stresses. If the adhesive and adherends match in coefficient of thermal expansion, the resulting joint will generally be very reliable.A third possible solution is to coat one or both substrates with a primer or coupling agent. This substance can provide either resiliency or an intermediate thermal expansion coefficient that will help reduce the overall stress in the joint.Internal Stress Due to Non-Thermal Dimensional ChangesInternal stress in the bond line can also develop due to dimensional changes that are not related to temperature and differences in thermal expansion coefficient. There are two common sources for such dimensional change:∙Absorption or desorption of moisture or other fluids within the substrate or the adhesive∙Post-mold shrinkage of polymeric substrates due either to increased cosslinking, loss of low molecular weight constituents, or oxidation.The relative dimensional change between the adhesive and the substrate or between two different substrates can cause warpage of the joint (if the substrates are flexible and the adhesive is relatively strong) or bond failure if the internal stresses are sufficiently greaterthan the adhesive strength.Stresses Due to Shrinkage of the Adhesives or SealantNearly all polymeric materials (including adhesives and sealants) shrink during solidification. Sometimes they shrink because of escaping solvent, leaving less mass in the bond line. Even 100% reactive adhesives, such as epoxies and urethanes, experience some shrinkage because their solid polymerized mass occupies less volume than the liquid reactants. Table 1 shows typical percentage shrinkage for various adhesive systems. The result of such shrinkage is internal stresses at the interface and the possible formation of cracks and voids within the bond line itself.Table 1: Shrinkage of Common AdhesivesDepending on the base resin in the adhesive or sealant, the formulator may need to reduce the amount of shrinkage to minimize internal stress when the adhesive hardens. This can be accomplished in several ways.Fillers reduce the rate of shrinkage by bulk displacement of the resin in the adhesive formulation. Certain types of fillers can also add reinforcement to the adhesive resin. In these ways, fillers can improve operational bond strength by 50-100%.Another method for reducing shrinkage is blending the base resin with one that does not shrink as much on curing. In fact certain monomers have been developed (although expensive and not commercially available) that actually expand on curing. 8These monomers, when blended with more common resins, can provide a resulting adhesive system with either zero net shrinkage or actual volume expansion during cure. It is believed that when formulated into adhesive systems, these expanding monomers will provide exceptional bond strength and mechanical interlocking capability not realized with conventional adhesive technology.A possible solution to the internal stress arising from shrinkage may be to again flexibilize the adhesive. Elastic adhesives deform when exposed to such internal stress and are less affected by shrinkage. Formulators are often able to adjust the final hardness of the adhesive or sealant to minimize stress during shrinkage. It is also especially important that voids and gas bubbles be eliminated from adhesives that have a high degree of shrinkage. Small voids can grow due to the adhesive's shrinkage and significantly degrade the cohesive strength of the film. Thus, these adhesive systems should be mixed carefully and, preferably, vacuum degassed prior to application.References:1. Reinhart, F.W., "Survey of Adhesion and Types of Bonds Involved", in Adhesion and Adhesives Fundamentals and Practices, J.E. Rutzler and R.L. Savage, eds., London Society of Chemical Industry, 1954.2. Griffith, A.A., Phil. Trans. Roy. Soc. London, Series A, 221, 163, 1920.3. Mylonnas, C., Proc. Seventh Int. Congr. Appl. Mech., London, 1948.4. Petrie, E.M., "Trends in Adhesive Surface Treatments" , SpecialChem4Adhesives, October 20, 2004.5. Petrie, E.M. "Improving the Toughness of Structural Adhesives", SpecialChem4Adhesives, April 7, 2004.6. Petrie, E.M. "New Epoxy Adhesives are Flexible and Tough", SpecialChem4Adhesives, July 7, 2004.7. Yurek, D.A., "Adhesive Bonded Joints", Adhesives Age, December, 1965.8. Sadhir, R.K. and Luck, R.M., Expanding Monomers: Synthesis, Characterization, and Applications, CRC Press, Boca Raton, FL, 1992.。

金属腐蚀的原因及常用的防腐方法

东莞理工学院金属腐蚀原因及常用的防腐方法化学与环境工程学院08化工工艺2班200841511208王东贤2011-5-30金属腐蚀的原因及常用的防腐方法摘要：在当今工业生产中，金属腐蚀已变的越来越严重，造成的损失也越来越大，所以研究防腐的方法就显得尤为重要。

本文简单介绍了一些金属腐蚀的机理，在此基础上着重从改善金属本质、把金属和腐蚀介质分开、改善腐蚀环境、电化学保护这四方面介绍了防止金属腐蚀的措施及方法，为以后的研究和探索防腐方法打下基础。

关键词：腐蚀防腐防腐方法金属引言当金属和周围介质接触时，由于发生化学和电化学作用而引起的破坏叫做金属的腐蚀。

从热力学观点看，除少数贵金属（如Au、Pt）外，各种金属都有转变成离子的趋势，就是说金属腐蚀是自发的普遍存在的现象。

金属被腐蚀后，在外形、色泽以及机械性能方面都将发生变化，造成设备破坏、管道泄漏、产品污染，酿成燃烧或爆炸等恶性事故以及资源和能源的严重浪费，使国民经济受到巨大的损失。

据估计，世界各发达国家每年因金属腐蚀而造成的经济损失约占其国民生产总值3.5％～4.2％，超过每年各项大灾（火灾、风灾及地震等）损失的总和。

有人甚至估计每年全世界腐蚀报废和损耗的金属约为1亿吨！因此，研究腐蚀机理，采取防护措施，对经济建设有着十分重大的意义。

本文探讨化工生产中发生腐蚀的原因以及采取合适的防腐方法防止金属腐蚀。

1.引起金属表面腐蚀的多种原因1.1季节性腐蚀腐蚀可以发生在一年内的任何时候。

一般来说，7～9月的温度和相对湿度较高，在美国东部和中西部更容易发生腐蚀。

干旱地区，如克罗拉多州、新墨西哥州、亚利桑那州、犹他州及加州，这些地方的相对湿度较低，腐蚀情况就很少发生。

1.2手印腐蚀当工件接触人手后，就容易发生腐蚀。

搬运过程中新机床和金属工件表面留下的手印，会导致腐蚀。

这种情况普遍存在于皮肤呈酸性的人群，以及表面光洁度高的工件。

使用手印中和剂能防止类似的手印腐蚀。

随着温度上升，包括腐蚀在内的化学反应速度就会更快。

SIZE-DEPENDENT EFFECTS IN PROPERTIES OF

© 2009 Advanced Study Center Co. Ltd.Corresponding author: R.A. Andrievski, e-mail: ara@icp.ac.ruSIZE-DEPENDENT EFFECTS IN PROPERTIES OFNANOSTRUCTURED MATERIALSR.A. AndrievskiInstitute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region,142432, Russia Received: February 17, 2009Abstract. Size-dependent effects in nanostructured (nanocrystalline, nanophase or nanocomposite)materials are of great importance both for fundamental considerations and modern technology.The effect of the nanoparticle/nanocrystallite size on surface energy, melting point, phase transfor-mations, and phase equilibriums is considered as applied to nanostructured materials. The role of size-dependent effects in phonon, electronic, superconducting, magnetic, and partly mechanical properties is also analyzed in detail. Special attention is paid to the contribution of other factors such as the grain boundary segregations, interface structure, residual stresses and pores, non-uniform distribution of grain sizes, and so on. The little explored and unresolved problems are pointed and discussed.1. INTRODUCTIONSize-dependent effects (SDE, i.e. the characteris-tic size influence of grains, particles, phase inclu-sions, pores, etc ., on the properties of materials and substances) have been studied in physics,chemistry, and materials science for a long time. It is quite enough to list the following well-known equations of Laplace, Thomson (Kelvin), Gibbs-Ostwald, Tolman, J. Thomson, Hall-Petch,Nabarro-Herring, and Coble, which connect the capillary pressure (P ), saturated vapor pressure (p ), saturated solubility (C ), surface energy of flat surface (σ0), conductivity (λ), hardness (H ) and creep rate (′ε) correspondingly with the pore/in-clusion radius (r ), thickness film (h ) and grains/crys-tallites size (L ):P r =20σ/, (1)p r p rRT =B =B =002exp /,σΩ (2)C r C rRT =B =B=002exp /,σΩ (3)σσξ0012r r =B =B =+//,(4)λλh f =B =B =+0510./. (5)H L H AL =B =+−005., (6)~/,ε1L m (7)where p o is the equilibrium pressure of saturated vapor on flat surface, C o is the equilibrium solubil-ity of subject with flat surface, Ω is an atomic (mo-lar) volume, R is the gas constant, T is tempera-ture, ξ is the Tolman constant, λo is conductivity of grain-coarse material (thick film), f = h /l o , l o is the mean free pass of carriers (f < 1), H o is the friction stress in the absence of grain boundaries (GB) and A is a constant. The factors m =2 and 3 correspond to the Nabarro-Herring diffusion creep and to theCoble diffusion creep correspondingly.The development of modern advancednanostructured materials (NM) manifests some new problems such as the identification adaptabil-ity of these equations (1-7) and other those in na-108R.A. Andrievskinometer interval; the role of quantum effects as well as an influence of other factors in the NM prop-erties or their stability and reproducibility. All these things are very important and actual to consider the SDE features taking in mind the update high rate in this field and not only fundamental consid-erations, but the strategy optimal development for nanotechnology. These questions have been ana-lyzed early by the present author [1-5] and other investigators (see, e.g., [6-19]). It seems to be nec-essary to tell apart the SDE in the isolated nanosubjects (clusters, nanoparticles, nanowires,and nanotubes) and consolidated ones (nanobulks,nanocomposites, and nanofilms/nanocoatings).Analyses of SDE in consolidated NM can be found in reviews [1-6], but the most publications were devoted to nanoparticles and clusters. Naturally,the SDE topic as a whole seems not to be cov-ered, because there are many new results scat-tered throughout the literature.Taking into account the comprehensive books [9,10,13,15,16], this review is mainly devoted to the SDE recent analysis in consolidated NM (papers mainly from 2001-2002), although some results for isolated nanosubjects will be also considered with the exception of catalytic and biological properties.Moreover, the comprehensive problem on the SDE in mechanical properties will be also discussed in limited scale as applied only to brittle high-melting point compounds (see Section 4 below).It is important to point that there are at least five principal features of size effects in consolidated NM [1-5]:- the crystalline size reduction to the nanometer scale results in a significant increase of the role of the interface defects such as GB, triple junc-tions (TJ), and elastically distorted layers;- interfacial properties on a nanometer scale can be different from those of conventional grain-coarse materials;- the reduced crystallite size can be overlapped by characteristic physical lengths such as the mean free path of carriers or the Frank-Read loop size for dislocations and so on;- size effects in NM can have quantum nature if the crystallite size is commensurable with the De Broyle wavelength l B =D /(2m *E )1/2 where D is the Planck constant, m * is the electron effective mass, E is the electron energy. Based on known values of m * and E, it is possible to predict that the quantum size effects can be exhibited in met-als only when the crystallite size is lower than ~ 1nm. For semiconductors (especially with narrow gap-zone, e.g., InSb) and semimetals (e.g., Bi),the l B value is significantly higher and can be of about 100 nm;- unlike conventional grain-coarse materials, in NM there are many factors for masking SDE such as residual stresses, pores, TJ and the presence of other defects, progressive accumulation of inter-face segregations, non-equilibrium phase ap-pearance, and so on.All these peculiarities may reveal in the pres-ence of certain specific points in the size depen-dencies and in the non-monotonous change of the properties determined by decreasing of the grain size. As a rule, such non-monotonous change is especially characteristic for structure-sensitive properties. For example, such specific features, i.e.twist points, and non-monotonous change of prop-erties have been revealed in the known hardness and magnetic coercivity studies (see, e.g., [1,2,4]).Such changes can be connected with different fac-tors such as other mechanisms of SDE, progres-sive accumulation of segregations on interfaces,and so on.2. THERMODYNAMIC PROPERTIES 2.1. Surface energyThe problem concerning surface energy is impor-tant both for fundamental sense and for many materials science and engineering applications such as the prognosis of phase diagrams, the es-timations of the fracture, milling, dilution, wetting,nucleation, coagulation, recrystallization charac-teristics, and so on. In this connection, the reveal-ing of surface energy change in nanometer inter-val is of special interest.Tolman’s equation (4), i.e. the effect of the drop radius on surface energy, has been widely dis-cussed (see, e.g., [7,8,11,14,20-23]). Omitting the details of these calculations, which are based on different physical and chemical approaches, let us to consider these results as a whole. Being ap-plied to isolated nanocrystals under calculations [11,14], the amendment g (r ) to the conventional σ0value fixed on the capillary pressure (1) is describedby the following expressiong r r r rr rB=B =B =−+−−211422182ln /ln /For many nanocrystals this amendment is very small and comes into particular prominence (about 10%) only at r < 5 nm.The radius effect on surface energy can be also described by equations:109Size-dependent effects in properties of nanostructured materialsσσr Kr at r r at r r =B =<>456,,, (9)where K is a constant, r o is critical radius (of 2-10nm) [21]. There are other theoretical calculations that have revealed about the similar values of criti-cal radius lower of which surface energy is de-creased (see, e.g., [20,22]). The experimental re-sults in this field are very limited, ambiguous, and often mutually contradictory. From one side, elec-trochemical measurements have revealed the σr values about 0.2 J/m 2 and 0.7 J/m 2 for Ag nanoparticles of r ~ 50 nm and r ~ 150 nm accord-ingly to [24]. These values seem to be not so pre-cise but are reasonable (it is appropriate to com-pare them with the value of σo = 1.14 J/m 2 and with the GB energy of ~0.27 J/m 2). From the other side,the experimental study of size-dependent evapo-ration of free-spherical Ag and PbS nanoparticles using relationship (2) results in values of 7.2 J/m 2and 2.45 J/m 2 respectively, these values are sig-nificantly higher as compared to that of the flat bulks [25]. May be, this is an effect of the evaporation conditions (see Section 2.2) or there is a system-atic error in the experimental results [25].As applied to nanocrystalline solids the analy-sis of size- or curvature-dependent interface, free energy results to the following relationshipσσr t r =B =B≈−01/, (10)where t is an interfacial layer (the semi-width of GB in consolidated nanometals) [7,8]. It is easy to see that at the reasonable values of 2t ~ 1nm and r = 5 nm the σ decreasing is of 10% that is in close agreement with estimations under Eq. (8).In Debye approximation, the Tolman constant ξin Eq. (4) can be expressed asξα=′−151.,h =B(11)where h ’ is the height of atomic monolayer, α is the ratio of root-mean-square amplitude of thermal vi-brations of atoms on surface and in volume [23]. If α > 1 and ξ > 0, then σr < σo and in the opposite case α < 1 and ξ < 0 then σr > σo . As it will be seen from here on, these two cases are important as applied to the behavior analysis of nanoparticles in matrices.It is known that distinct feature of nanostructure in NM is that, with the grain size confinement, the part of TJ is increased and, accordingly, the part of GB is decreased (see, e.g., [4]). The computer modeling with account of GB and TJ contributions reveals that Ni grain size reducing is accompaniedby decrease of the total excess enthalpy (i.e. the total GB energy) [26]; this result quantitatively agrees with experimental data for nano Se [27].The calculated interface GB energy in Cu-Ni bilayered nanofilm changes from 0.9 J/m 2 to about 0.7 J/m 2 when bilayer thickness decreases from ~1 nm to ~0.4 nm [28].From the foregoing data it has been evident that in spite of different theoretical approaches in cal-culations, they are evidence of the σ decrease in the confinement of isolated nanosubjects and nanostructures in NM. It seems to be reasonable to introduce the amendments into grain/crystalline boundary energy values at L lower than near 10nm. However, it is also evident that experimental studies in this field are necessary for further de-tailed continuation.The comprehensive description of the SDE role in the other surface phenomena such as wetting,nucleation, adsorption, and capillarity can be found in book [16]. It is worth to note that the observation by high-resolution transmission electron micro-scope (HRTEM) methods is in common practice (see, e.g., [19,29,30]).2.2. Melting pointIt is well known for a long time that small particles and thin films are characterized by the lower melt-ing points (T m ) as compared with their counterparts in bulk form as a result of the atom thermal vibra-tion amplitude increase in the surface layers. There are many relationships contacting T m and r for free-standing (supporting) metal (Au, Ag, Cu, Sn, etc .)clusters/nanoparticles as well as h for thin films (see, e.g., [4,10,13,15,16,19]). Generally, all pro-posed equations have the form of T m ~ 1/r (h ) type.Recent theoretical and experimental works tend to obtain more precise specifications: the size,shape, and stress effects on the T m nanograins on a substrate [31]; the role of fractal structure [32];the comparison of SDE in the case of spherical nanoparticles, nanofilms, and nanowires [9,33]; the effect of transition to amorphous state [34], kinetic study of the Cu film melting-dispergation [35], etc .Thus the consideration of size-dependent cohesive energy results in the T m variation for spherical nanoparticle, nanowire, and nanofilm of a material in the same characteristic size as 3:2:1 that is con-firmed by experimental values for In [33]. The mo-lecular dynamics simulation of the melting behav-ior for “model ” nanocrystalline Ag has exhibited two characteristic regions on the grain size decrease [34]. The first is above about 4 nm where the T m110R.A. Andrievskivalues decrease with grain size decreasing. The second one (r < 4 nm) is a size-independent re-gion where the T m values almost keep a constant.The dominant factor in this situation is supposed to be the nanocrystal T m shifts from grain to GB.The amorphous phase (r < 1.3 nm), as indicated from the radial distribution function and common neighbor analysis, is different from the GB by the sharp enhancement of local fivefold symmetry and is characterized by a much lower solid-to-liquid transformation temperature than that of Ag nanocrystal and GB. Melting and non-melting of solid surfaces including partly behavior of nanosystems are discussed in review [12].When the nanosolids are entirely coated by a high-melting point substance or embedded in such matrix, the nanosolid T m values can not only de-crease but increase too; this interesting phenom-ena is named by superheating or overheating. TheSME detailed analysis at melting and superheat-Fig. 1. Melting point of In nanoparticles embedded in Al matrix for two methods of preparation as a function of particle diameter: ball milling (n ) and spinning (l ). HRTEM images illustrated the different In/Al interface structures, replotted from [19].ing of bulks and nanosolids can be found in review [19]. The crucial role of interface in superheating is clearly demonstrated by the measurement re-sults of the ball-milled and the melt-spun Al-In samples T m values as a function of particle size of In (Fig. 1) [19].Fig. 1 clearly demonstrates that samples pre-pared by the two methods undergo completely dif-ferent melting behaviors which were investigated using differential scanning calorimetry (DSC), in-situ HRTEM, and in-situ X-ray diffraction (XRD). In the case of ball-milling procedure, there are irregu-lar In particles and the incoherent random inter-faces were formed between particles and the ma-trix, then the nanoparticles exhibit the SDE T m de-pression, as described previously. In the case of melt-spun samples, the In particles were found to be distributed both in the Al GB and within the Al grains. The particles within Al grains are truncated by octahedral shapes bounded by {111}/(100) fac-111Size-dependent effects in properties of nanostructured materials Compound Usual bulk phase Observed(metal, alloy)at RT and P =106 Pa nanocrystalline phaseZrO 2 Monoclinic Tetragonal BaTiO 3 Cubic Tetragonal PbTiO 3 Cubic Tetragonal Al 2O 3 α-Al 2O 3 γ-Al 2O 3 TiO 2 RutileAnataseY 2O 3Cubic (α-Y 2O 3) Monoclinic (γ-Y 2O 3)CdSe, CdSWurtzite Rock salt Co hcp * (α-Co) fcc * (β-Co) T hcp (α-Ti) bcc * (β-Ti) Fe-NiMartensiteAustenite (fcc)*hcp is hexagonal-closed-packed structure; fcc is face-centered-cubic structure; bcc is body-centered-cubic structure.Table 1. Structure of unusual phases observed in some NM [37].ets and can be considered as epitaxial coherent interfaces revealing the T m increase with decreas-ing of r . It is interesting to know whether other prop-erties, not only melting point, are also changing under the ball-milled and melt-spun nanoparicles in matrices. The superheating has been also ob-served in the systems of Pb-Al and Ag-Ni both in the Al and Ni matrixes as well as partly in layered Pb/Al films [19].On phenomenological level, superheating is explained by change of root-mean-square ampli-tude of thermal vibrations of atoms on surface and in volume (Eq. (11) [23]) and by modification of in-terfacial energy [19] or the coherent interface pa-rameter between inclusions and matrix [36].2.3. Phase transformationsApart of melting point SDE make an impact on other phase transformations in NM. Table 1 summarizes some data in this field [37].Observed solid-state transformations are con-sidered to be connected with an increased effec-tive internal pressure due to high surface/interfa-cial curvature or with the whole and surface en-ergy difference between allotropic phases [37]. The tetragonal-to-monoclinic (T → M) phase transfor-mation in the zirconia-yttria system is the most ex-plored subject. Fig. 2 shows experimental data on the T → M transformation temperature (T tr ) for dif-ferent YSZ powders and sintered pellets with par-ticles/grains in the nanometer interval [38].In Fig. 2 each line demarcated the tetragonal phase stability region (defined as “T ”) and that toleft of the line (defined as “T+M ”) where the T-phase starts to transform into the M-phase which was fixed in both the DSC and the dilatometer studies. It is evident from these results that the T tr value is de-creased with a reduction of crystallite/grain size.The curve extrapolation provide the opportunity to predict the particle critical size values at room tem-perature of the T-phase stability: 15, 30, 51, and 71 nm for 0YSZ, 0.5YSZ, 1.0YSZ, and 1.5YSZ powders, respectively. In the case of the 0.5YSZ,1.0YSZ, and 1.5YSZ sintered pellets, the grain criti-cal size values are 70, 100, and 155 nm, respec-tively. The observed difference in crystalline/grain size (about 2 times) can be attributed to the strain energy term and difference in the surface and in-terfacial energies.In the thermodynamic approach frame, the fol-lowing relationships between the T tr value and criti-cal crystalline/grain size (D c , L c ) have been pro-posed116///for powders ,D H T T c b tr b =−∆∆σ=B =B =B (12)1166////for pellets ,L H T T U cbtrbd=−+∆∆Σ∆∆Σ=B =B =B (13)where ∆H b and T b are the enthalpy and transfor-mation temperature for bulk (coarse-grained) sol-ids, ∆σ and ∆Σ are the differences in the surface/interfacial energies for T/M phases in powders and pellets, ∆U d is the strain energy involved in the transformation (this additional strain-energy term estimates only for consolidated pellets) [37,38].112R.A. AndrievskiFig. 2. Inverse critical grain/crystalline size versus transformation temperature (T → M) for different yttria-doped zirconia (a) powders and (b) pellets: 0YSZ – pure ZrO2, 0.5YSZ – 0.5 mol.%Y2O3, 1.0YSZ – 1.0mol.%Y2O3, 1.5YSZ – 1.5 mol.%Y2O3, replotted from [38].113Size-dependent effects in properties of nanostructured materials Fig. 3. The phase stability diagram for Nb/Zr multilayers as a function of the Nb volume fraction (f NB ) and the inverse of bilayer thickness (λ-1): # 1 is the stability region of hcp Zr/bcc Nb; # 2 is the stability region of bcc Zr/bcc Nb; # 3 is the stability region of hcp Zr/hcp Nb. The circles indicate experimental results and the line boundary calculated from the thermodynamic model, replotted from [41].The possibility to observe also the high-tem-perature phase at low temperature is the situation when the elementary crystal (germ) size of this phase is lower than crystallite size. Such situation tends to the transformation blocking and the high-temperature phase is fixing. This example is typi-cal for some martensite transformations in the Fe-Ni and Ti-Ni-Co micro- and nanocrystalline alloys [39]. The martensite volume part (M ) depends on the high-temperature initial phase crystallite size under the equationM M K Lm =−−005., (14)where M o and K m are some constants. The rela-tionship (14) coincides with that of Hall-Petch one (6). This agreement could be connected with the analogous nature of elastic strain fields at the crack and germ propagation.The availability of non-equilibrium phases in thin film is observed for a long time. Under film thick-ness lower than some critical value (h c ), non-com-mon phases can be fixed; that is connected with the Gibbs free energy excess effect due to the sur-face effect. One of the first relationships describ-ing this effect was proposed more than 50 years agoh F F c =−−σσ1221=B =B/, (15)where indexes 1 and 2 correspond to equilibrium and non-equilibrium phases, respectively, σi and F i are the total surface energy and the Gibbs free energy of these phases [40]. The h c rough estima-tion by Eq. (15) resulted in the quite reasonable values (h c ~ 10 nm).Basically, the idea [40] based on a classical ther-modynamic approach with some modifications is used in many modern studies especially with the development of nanostructured thin film multilayers such as Ti/Al(Nb, Zr) and TiN/AlN(NbN, ZrN), Fe/Cr, etc ., which can exhibit metastable structures in one or both layers. Fig. 3 shows the phase stability diagram for Nb/Zr multilayers with varying volume fractions and bilayer (λNb + λZr ) thickness [41].The phase stability region boundaries were cal-culated using a classical thermodynamic model taking into account the structural energy assess-114R.A. AndrievskiFig. 4. The Bi-Pb phase diagram. The dashed lines are the equilibrium bulk phase diagram and the solid lines are experimental results for nanoparticles of (a) 10 nm radii and (b) 5 nm radii, replotted from [42].115Size-dependent effects in properties of nanostructured materials Fig. 5. Pseudobinary TiN-TiB 2 phase diagram for equilibrium state (the solid lines) and for nanostructured films (L ~ 10 nm), replotted from [44].ment in the interfacial energy value. The equilib-rium phases (hcp Zr and bcc Nb) were observed only in the region #1; at that, the effect of the Nb volume fraction is not monotonous. The presence of the non-equilibrium bcc Zr and hcp Nb phases in sputtered films (regions #2 and #3, respectively)was confirmed experimentally by XRD and elec-tron diffraction.2.4. Phase equilibriumsBy now there are several examples of theoretical calculations and experimental studies of the phase diagram SDE in nanointerval: ZrO 2-Y 2O 3 [37], Pb-Bi [42], In-Sn [30], Au-Sn [30], carbon phase dia-gram [43], Al-Pb [18], Bi-Cd [18], TiB 2-TiN [44], TiB 2-B 4C [45], hydrogen systems [46,47], etc . Fig. 2 data have been used for the T/T+M line design in the ZrO 2-Y 2O 3 diagram as a function of particle size [37].The most detailed study was undertaken in the Pb-Bi diagram observing in-situ the melting behav-ior of isolated alloyed nanoparticles by hot stage TEM. Fig. 4 compares this diagram for particles of 10 nm radii and 5 nm radii as well as for bulks [42].As shown in Fig. 4, T m is a size-depend decreas-ing from the bulk value. The progressive narrow-ing of two-phase fields and an increase of solubil-ity are also observed. The theoretical calculations developed from thermodynamic first principles were in agreement with experimental results.The significant increase of solubility for nanosized subjects was observed in many cases including the hydrogen-metal (intermetallic) sys-tems [46,47], Pb-Fe and Pb-Sn systems [48,49],and systems-based high-melting point compounds [44,45]. Fig. 5 shows the TiN- TiB 2 phase diagram both in equilibrium state and film one (the grain size about of 10 nm) [44].The significant increase in solubility was fixed by the experimental XRD test [50] and the eutectic temperature decrease that was calculated in the regular solution approximation using the phase equilibrium at the eutectic temperature. The con-116R.A. Andrievskitribution made by the surface energy excess for solid state was written in per mole terms as ∆F S = 6V σgb /L where V is the molar volume and σgb is the interfacial (grain boundary) energy (see also [51]). The same approach was used for the SDE analysis in the case of the TiB 2-B 4C phase diagram [45]. Unfortunately,the σgb value information is very limited. It was supposed in the TiN-TiB 2 phase diagram calculations (Fig.5) that σgb ~ 3 J/m 2; in the case of the TiB 2-B 4C phase diagram the more reasonable σgb interval from 1J/m 2 to 3 J/m 2 was used[45].The solubility features in nanosystems are theoretically discussed in papers [52,53]. In many cases,the great role of the grain boundary segregations is pointed (see, e.g., [48]). However, as a whole, the question on the oversaturated solution formation nature remains insufficiently explored as applied to mechanical alloying, ion plating, severe plastic deformation, electrodeposition, and other preparation methods of NM.Another interesting feature in the SDE on phase equilibriums is that the spinodal decomposition and the triple point coordinates. It was theoretically shown that the grain segregations (thickness of about 1nm) increase the solid solution decomposition degree when the grain size does not exceed 10 nm [54].The spinodal decomposition regularities of supersaturated TiN-AlN system with the thermal stable nanostructure formation are very interesting and important for the development of new advanced NM. Ab initio calculations revealed the contribution role of strain and surface energy on the energetic balance for decomposition process [55].The calculation of SDE on the carbon diagram results in the following data for the triple point coordi-nates defined regions for solid nanodiamond, liquid that and amorphous nanocarbon [43] Particle diameter, (nm) 1 1.2 1.5 2 3 4 6 Singlecrystal Pressure (GPa) 15.2 16.5 16.115.615.214.814.513.5 T, K2210316035503820409041904300 4470These results are in qualitative agreement with some experimental/theoretical information [56]. The movement of triple point, defined equilibrium between solid state, liquid one, and vapor one, to the tem-perature decrease and pressure increase with the particle decrease was also described in book [9].In the most cited works dedicated to the SDE in phase equilibriums, the conditional thermodynamic approaches were used and the interface structure influence was not analyzed. In mean time, as it was shown at the Fig. 1, the impact of external interfaces on T m can be very great and opposite, so that interface contributions to the thermodynamic functions become significant [18,19]. The analysis of two-phase equilibrium in alloy nanoparticles has revealed the possibility of the eutectic point degeneration into intervals of composition where the alloy melts discontinuously and of the phase diagram topology dra-matic changes [57]. These observations tended to conclusion that the concept of equilibrium in nanostructures yet remains to be understood and needs in further detailed study [18,51].3. PHYSICAL PROPERTIES3.1. Phonon and electronic properties. SuperconductivityMeasurements of electronic heat capacity (γe ) of Cu-Nb (Pb) nanocomposites and studies of their phonon spectra revealed the decrease of the electronic state density at the Fermi level N (E F ) and the increase of low-frequency oscillations as compared with their coarse-grained (cg ) counterparts [58,59]. The γe value for Nb inclusions (L ~20 nm) in Cu 90Nb 10 nanocomposite was of 3.0 mJ/mol K 2 that is about three times lower than that in conventional Nb. The Debye temperature (ΘD ) value is also reduced with the inclusion decrease. These changes were connected with the weakening of interatomic interactions at the GB and assisted by the superconducting transition temperature (T C ) decrease.The size dependence of T C , the residual resistance ratio (RRR), the upper critical magnetic field (H C2)and the Ginzburg-Landau coherence length (ξGL ) for the nanocrystalline Nb films are shown in Table 2[60,61].It is clear from Table 2 that while the T C and RRR values decrease with size monotonically, the H C2 and ξGL values increase with size but there is non-monotonous change. The first change is supposed to be connected with the N (E F ) decrease rather than by phonon softening, i.e. the effect of the electron-phonon。

SAEJ1121v001

SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.QUESTIONS REGARDING THIS DOCUMENT: (724) 772-8512 FAX: (724) 776-0243TO PLACE A DOCUMENT ORDER; (724) 776-4970 FAX: (724) 776-0790SAE WEB ADDRESS SAE J316—Oil-Tempered Carbon-Steel Spring Wire and SpringsSAE J351—Oil-Tempered Carbon-Steel Valve Spring Quality Wire and Springs SAE J461—Wrought and Cast Copper AlloysSAE HS J795—SAE Manual on Design and Application of Helical and Spiral Springs SAE J808—Manual on Shot PeeningSAE J916—Rules for SAE Use of SAE (Metric) Units SAE J1122—Helical Springs: Specification Check Lists3.Hot Coiled Springs3.1Materials and Heat Treatment—Round spring steel bars are available in carbon and alloy analyses. The bars are generally used in the "as rolled" condition (either commercial hot rolled or precision hot rolled), but they may be centerless ground before coiling.The heat treatment necessary to develop the required physical properties of the material may be accomplished by direct quench immediately after coiling, or by allowing the coiled spring to cool to a temperature below the critical, then reheating to the required temperature and quenching; the quench is followed by tempering to produce the specified hardness.Table 1 lists available materials. Their hardenability limitations dictate maximum bar size. For tensile and torsional properties, see MANUAL, SAE HS J795, Chapter 2, Table 2.21.TABLE 1—MATERIALS FOR HOT COILED COMPRESSION SPRINGSMaterialsSpecification Max. Bar (1)Dia., mm1.Based on a through hardened bar of 444 HB typicalhardness ranges are 444 - 495 HB and 461 - 514 HB.Carbon SteelsSAE 108510SAE 109510Carbon Boron Steel SAE 15B62H 25Alloy SteelsSAE 5150 H 10SAE 5160 H 20SAE 9260 H 10SAE 51B60H 30SAE 4161 H 60SAE 6150 H103.2Shot Peening—Shot peening is used to increase the fatigue life of springs. It consists of subjecting the springto a stream of metallic shot moving at high velocity. The peening action of the shot reduces the effect of surface defects and sets up beneficial stresses in a thin surface layer. It also results in cold working this layer.To be effective, the peening must reach the area of highest stress which for helical compression springs is the inside diameter of the coil.The fatigue life of hot coiled springs is greatly impaired when the bar surface is afflicted by such flaws as impurities, cracks, seams, or decarburization, but it can be increased by the peening operation in the order of 4 to 1. Even the much better fatigue life attainable in hot-coiled springs with nearly perfect bar surface will be improved by peening in the order of more than 2 to 1. For further details see MANUAL, SAE HS J795, Chapters 1 and 4, also SHOT PEENING MANUAL, SAE HS 84 J808.3.3Presetting—Presetting (also called scragging, cold setting, or bulldozing) is an operation during themanufacturing process in which the spring is compressed beyond the yield point of the heat treated material.In preparation for this, the spring is coiled to a free length in excess of the designated free length. The yielding in the surface layers of the bar which occurs during presetting produces beneficial residual stresses, thus increasing the elastic limit and thereby reducing the chances of settling in subsequent service. The yielding causes the spring to take a permanent set, thus bringing it down to the designated free length. See also Preset Length, 3.6.3.FIGURE 1—TYPICAL LOAD-DEFLECTION DIAGRAM OF HELICAL SPRING DURING PRESETTING3.3.1W ARM S ETTING—In order to reduce the "sag" of "settling" of helical suspension springs which occurs whenthey are subjected to vehicle loading over time, it has become common practice to warm set the spring at an elevated temperature (usually about 200 °C depending on the particular spring design). One theory holds that the major benefit of this operation results from an increase in the amount of strain hardening that occurs when the spring is stressed past the proportional limit (point "A" in Figure 1). Increasing the temperature lowers the proportional limit to some stress lower than point "A", and therefore if the spring is still stressed to point "B", the amount of strain hardening that occurs is greater. This increase in strain hardening will reduce the dynamic or static settling (load loss) that occurs over the useful life of the spring.A second theory is that a more effective beneficial residual stress pattern is set up over the bar cross section,when a spring is warm set at elevated temperature.It should be noted that a final (cold) presetting operation is still necessary.In general, warm setting will decrease the load loss by more than 50%, depending on the working stress level.3.4Bar Diameter and Length—Round bars are hot rolled to any desired diameter between 9 and 100 mm. Table 2 shows the cross section tolerances for commercial hot rolled bars. Bars may be precision hot rolled with 50%of the tolerances in Table 2, or they may be centerless ground with 25% of the tolerances in Table 2.Bars are commonly purchased in the exact length required to produce one spring. Tolerances for bar lengths are shown in Table 3.3.5Coil Diameter—The coil diameter can be expressed in terms of the mean coil diameter (D) which is used in the rate and stress formulae. However, coil diameter tolerances should be specified on either the inside diameter (ID) or the outside diameter (OD) of the coils, depending upon the importance of the respective dimensions to the user. Tolerances are shown in Table 4, based on coil diameter and spring length.For motor vehicle suspension springs, it is customary to specify the ID in order to facilitate the coiling of a family of springs on a single arbor.TABLE 2—CROSS SECTION TOLERANCES FOR HOT ROLLED CARBONAND ALLOY STEEL ROUND BARSSpecified Diameter, mmOverSpecified Diameter, mmThruTolerance,Plus and Minus,mmOut of Round,mm —100.150.2210150.180.2715200.200.3020250.230.3425300.250.3830350.300.4535400.350.5240600.400.6060800.600.90801000.801.20TABLE 3—LENGTH TOLERANCES FOR HOT ROLLED CARBONAND ALLOY ROUND STEEL BARSSpecified Diameter, mmOverSpecified Diameter, mmThruLength Tolerance,Plus Only, mm For Lengths, mmOver ThruLength Tolerance,Plus Only, mm For Lengths, mm15003000Length Tolerance,Plus Only, mm For Lengths, mm3000——251220255016255010025403.6Spring Lengths—Spring lengths are to be measured after preloading (see Preload Length, 3.6.4), as the distance parallel to the spring axis between the end surfaces, or else between two reference points specified on the spring drawing.3.6.1F REE L ENGTH —Free length is the length when no external load is applied. When load is specified, free length is used as a reference dimension only. When load is not specified, free length tolerance equals ±(1.5mm + 4% of free-to-solid deflection).3.6.2S OLID L ENGTH (SEE ALSO N UMBER OF C OILS , 3.7)—Solid length is the length when the spring is compressed with an applied load sufficient to bring all coils in contact; for practical purposes, this applied load is taken to equal approximately 150% of the load beyond which no appreciable deflection takes place.3.6.3P RESET L ENGTH —In the presetting operation (see Presetting, 3.3), the spring is usually compressed solid.However, if the stress at solid length is so high that the spring would be excessively distorted, the presetting operation may only be carried to a specified preset length. If more than one preset compression is desired,this must be specified on the drawing. See Also MANUAL, SAE HS J795, Chapters 1 and 4.3.6.4P RELOAD L ENGTH —Preloading is the operation of deflecting the spring to the preload length in order to remove temporary recovery of free length before the spring is checked for load and rate.If the spring was preset during the manufacturing process to the solid length, the preloading may also be carried to the solid length, but it may be restricted to a preload length slightly greater than the solid length,provided the maximum deflection during subsequent service will not go below the preload length.If the spring was preset to a specified preset length greater than the solid length, the preloading should be restricted to a preload length greater than the preset length.However, the preload length must not exceed the minimum spring length possible in the mechanism for which the spring is designed. In suspensions, this is called the "length at metal-to-metal position." The metal-to-metal contact will occur in the suspension mechanism when rubber bumpers are disregarded. The spring deflection from the specified loaded length to the metal-to-metal position is called "clearance."3.6.5L OADED L ENGTH —Loaded length is the length while the load is being measured; it is a fixed dimension, with the tolerance applied to the load.TABLE 4—COIL DIAMETER TOLERANCESFor Specified orComputer Outside Diameter, mmInside or Outside Diameter Tolerance,Plus and Minus, mm For Free Spring Length, mm Up to 250Inside or Outside Diameter Tolerance,Plus and Minus, mm For Free Spring Length, mm Over 250 thru 450Inside or Outside Diameter Tolerance,Plus and Minus, mm For Free Spring Length, mm Over 450 thru 650Inside or Outside Diameter Tolerance,Plus and Minus, mm For Free Spring Length, mm Over 650 thru 850Inside or OutsideDiameterTolerance,Plus and Minus, mm For Free Spring Length, mm Over850 thru 105075.0 thru 110.00.8 1.3 2.5 3.6 4.6Over 110.0 thru 150.0 1.3 2.5 3.6 4.6 5.6Over 150.0 thru 200.0 2.5 3.6 4.6 5.6 6.6Over 200.0 thru 300.03.64.65.66.66.63.7Number of Coils—Total number of coils (N t ) are counted tip to tip, active number of coils (N) are specified as the number of working coils at free length. With increasing load, N may progressively decrease due to the "bottoming out" effect. If no appreciable bottoming out occurs, the relationships between N and N t are as shown in Table 5 which also gives the formulae for nominal solid length.Since nominal solid length may be exceeded somewhat by actual solid length due to manufacturing variations,a frequent practice is to specify nominal solid length together with a maximum solid length, as shown in Table 6.whered = bar diametert = tip thickness of taper rolled bar1.01 = factor used to compensate for the cosine effect of the coil helix angleThe bracketed term in the solid length formula for springs with two pigtail ends may vary between (N t – 0.90)and (N t – 1.60), depending on the pigtail details.TABLE 5—FORMULAE FOR TOTAL COILS AND FOR NOMINAL SOLID LENGTHEnd ConfigurationTotal Coils (N t )NominalSolid Length (L s )Both ends taper rolled N + 2 1.01 d (N t − 1) + 2t Both ends with tangent tail N + 1.33 1.01 d (N t + 1)Both ends with pigtail N + 1.50 1.01 d (N t − 1.25)Taper rolled plus tangent tail N + 1.67 1.01 d N t + 1Taper rolled plus pigtail N + 1.75 1.01 d (N t − 1) + t Tangent tail plus pigtailN + 1.421.01 d N tTABLE 6—SPRING SOLID LENGTH TOLERANCESNominal Solid Length, mmOverNominal Solid Length, mmThruMaximum Deviation of Solid Length Above Nominal Solid Length, mm—175 1.5175250 2.5250325 3.0325400 4.0400475 4.8475550 5.55506256.53.8Spring Ends—Four types of ends are used (Figure 2):FIGURE 2—TYPICAL ENDS FOR HOT COILED COMPRESSION SPRINGS1. A flat end formed from a tapered bar end. The bar end is usually tapered for a length equal to 2/3 coiland to a tip thickness of approximately 1/3 of the bar diameter. When the spring is coiled, the tip shallbe in approximate contact with the adjacent coil and shall not protrude beyond the outside diameter bymore than 20% of the bar diameter.When stipulated, the bearing surface of the spring end shall be ground perpendicular to the axis of thespring helix in order to produce a firm bearing. The actual ground bearing surface shall not be shorterthan two-thirds of the mean coil circumference, nor narrower than half the width of the hot taperedsurface of the bar. However, this grinding is usually not required if the tapering and coiling operationsare performed adequately.2.An untapered end coil formed substantially smaller than the central coils of the spring and in such afashion as to have an outboard bearing surface perpendicular to the axis of the spring helix, the so-called "pigtail" end.3.An untapered end coil formed as a helix having a pitch substantially equal to the bar diameter. Tofacilitate coiling, a straight end portion about 25 mm long is permitted to project tangent to the helix ofthis end construction, the so-called "tangent tail" end. The use of this type of end requires a springseat formed at the same pitch of helix as that of the spring end.4.An untapered end coil formed perpendicular to the axis of the spring helix for a circumference of atleast 220 deg, the so-called "flat tangent tail" end. To facilitate coiling, a straight end portion about25mm long is permitted to project tangent to the outer circumference.Springs can be specified to have any combination of the four types of ends. The combination of two tangent tail ends may involve a complex arrangement for indexing the spring seats, unless the design of every spring is adjusted to an identical number of total coils. Springs for general automotive use generally have two flat tapered ends. Spring ends and seats are usually so formed as to render approximately two-thirds to one coil inactive at each end.3.9Squareness of Ends—Unless otherwise specified, the tapered ends of any spring having an outside diameterto bar diameter ratio of 4 or more, and a free length to outside diameter of 4 or less, shall not deviate more than3 deg from the perpendicular to the spring axis, as determined by standing the spring on its end and measuringthe angular deviation of the outer helix from a perpendicular to the plate on which the spring is standing. In the case of a tangent tail end, the spring must stand on a seat with matching helical ramp. Tolerances for springs outside these limits are subject to special agreement.3.10Load—Load is the force in newtons (N) measured on the load testing machine required to deflect the spring tothe specified loaded length. It is to be measured during compression of the spring (compression load) and not during release of the spring (release load), unless otherwise specified.With loaded length fixed, the usual tolerance for motor vehicle suspension springs is expressed in terms of load equivalent to a deflection of ±5 mm at the nominal rate. Where the demand for greater accuracy warrants the cost of additional presetting or other operations, the load tolerance may be specified as low as ±1.50 mm at the nominal rate.In the springs for general automotive use, the load tolerance (with loaded length fixed) typically equals ±(1.50mm + 3% of free-to-solid deflection) × nominal rate. This tolerance is limited to springs where the free length does not exceed 900 mm, does not exceed six times the free-to-solid deflection, and is not less than0.8times the OD.3.11Rate—Rate is the change of load per unit length of springs deflection (N/mm).In the springs for motor vehicle suspension, the rate is expressed in terms of the load increase per 25 mm deflection (N/25 mm). It is therefore determined as one-half the difference between the loads measured 25mm above and 25 mm below the specified loaded length. Tolerance is ±3% with centerless ground or with precision rolled bars, and ±4% when commercial hot rolled bars are used.In the springs for general automotive use, the rate is determined between 20 and 60% of the total deflection unless otherwise defined. T ypical tolerance is ±5%. In non-critical applications, this may be increased to ±10%.3.12Direction of Coiling—For most applications, the direction of coiling is unimportant; however, right hand coilingis preferred because most spring manufacturers are so equipped. When direction of coiling is important, as in the case of concentrically nested springs, it must be specified or each component spring, maintaining opposite directions for adjacent springs. For tangent tail springs, the direction of coiling must conform with the installation conditions.3.13Uniformity of Pitch—The pitch of coils in a compression spring must be sufficiently uniform so that when thespring is compressed, unsupported laterally, to a length representing a deflection of 80% of the nominal free-to-solid deflection, none of the coils must be in contact with one another, excluding the inactive end coils. This requirement does not apply when the design of the spring calls for variable pitch, or when it is such that the spring cannot be compressed to solid length without lateral support.3.14Shaped and Variable Rate Coils—Many newer motor vehicle applications require specially shapedsuspension coil springs, or springs with variable output characteristics. The coils which are specially shaped usually exhibit a partially conical or barrel form in order to satisfy restricted height, tire clearance, or other suspension requirements. In some cases, the ends of the spring may be offset in order to provide off center loading for suspension strut applications.With regard to variable output characteristics, some springs are designed to provide a variable rate and corresponding frequency change, for improved height control, ride and handling. The variable rate characteristic is achieved by designing and producing the spring with very specific oil spacing such that active coil segments "bottom out" against a spring seat or against each other as the spring is deflected, thereby decreasing the effective number of active coils and increasing the rate. This effect is achieved with the greatest material and space efficiency if the bar is conically tapered over the length of the coils which bottom out. It should be pointed out, however, that special equipment is required to conically taper the bars. Also, it is important to not that coil-to-coil or coil-to-seat contact can cause undesirable noise.3.15Concentricity of Coils—At free length, the center of all coils must be concentric with the spring axis within1.5mm. This axis is the straight line connecting the centers of the end coils.4.Cold Wound Springs4.1Material—Round wire sizes and tolerances may be found in the individual wire specifications, such as:Music Wire SAE J176Carbon Steel Spring Wire-Oil Tempered SAE J316-Hard Drawn SAE J113-Special Quality HighTensile Hard Drawn SAE J271-Valve Spring QualityOil Tempered SAE J351-Valve Spring QualityHard Drawn SAE J172Chromium Vanadium Wire - Valve Spring Quality SAE J132Chromium Silicon Alloy Steel Wire SAE J157Stainless Steel Wire, SAE 30302SAE J230Stainless Steel Wire, 17-7 PH SAE J217Phosphor-Bronze Wire,SAE CA510SAE J461Beryllium-Copper Wire, SAE CA172SAE J461Brass Wire,SAE CA260SAE J461Silicon-Bronze Wire,SAE CA655SAE J4614.2Shot Peening—Shot peening is used to increase the fatigue life of springs. It consists of subjecting the springto a stream of metallic shot moving at high velocity. The peening action of the shot reduces the effect of surface defects and sets up beneficial stresses in a thin surface layer. It also results in cold working this layer.To be effective, the peening must reach the area of highest stress which for helical compression and extension springs is the inside diameter of the coil.Even when the wire surface is virtually flawless, the fatigue life of the cold-wound spring can be increased by peening in the order of more than 2 to 1. See MANUAL, SAE HS J795, Chapter 1, also SHOT PEENING MANUAL, SAE HS 84 J808.4.3Presetting—The need for presetting depends upon the design stresses, the application and its conditions andrequirements. Then use of presetting is most beneficial when design stresses are at or near the yield point, and settling prevents the spring from performing as required.Presetting is an operation that is performed during the manufacturing of helical compression springs in which the spring is compressed beyond the yield point of the material. The yielding of the surface layers of the wire which occurs during the presetting produces beneficial residual stresses, thus increasing the elestic limit of the spring and thereby reducing the chances of settling in subsequent service. The spring is coiled to a free length in excess of the designated free length. The yielding causes the spring to take a permanent set, thus bringing it down to the required free length.The presetting operation may be performed at ambient temperature, called cold setting, or at some elevated temperature, called either heat setting or hot pressing. Heat setting consists of compressing the spring on a fixture, subjecting the compressed spring to a temperature higher than the desired operating temperature for a time suitable to insure complete penetration of the heat, and then cooling to room temperature before releasing.Hot pressing consists of heating the spring in its free or relaxed position to some temperature for sufficient time to insure complete penetration; then, while the spring is at the temperature, it is compressed to some height below the installed or operating position and released.4.4Coil Diameter—Coil diameter tolerances can be specified on either the inside diameter (ID) or the outsidediameter (OD) of the coils, depending upon the importance of the respective dimensions to the user.Tolerances are functions of the "Spring Index", which is the ratio of mean coil diameter (D) to wire diameter (d).They are to be considered as manufacturing tolerances and do not take into account the effects of changes in diameter due to applied loads. See Figure 3 and Figure 4.4.5Spring Lengths—Spring lengths of compression springs are overall dimensions measured parallel to the axisof the spring.Spring lengths of extension springs are measured inside to inside of the hooks (overall length minus two wire diameters).4.5.1F REE L ENGTH—Free length is the length under no load. When load is specified, free length is used as areference dimension only. When load is not specified, free length is specified for control and inspection purposes by using Figure 5 for compression springs and Figure 6 for extension springs.The tolerances in Figure 3 are based on the number of active coils (N), the free length (L o), and the spring index (D/d). With these parameters known, the N/L o value is established on the abscissa, and the tolerance is found by multiplying the corresponding ordinate value by L o. Round off the index to the nearest whole number and interpolate when this is an odd number. The tolerances shown in Figure 5 are for springs with ends closed and ground. For springs with the ends closed but not ground, multiply by 1.7.4.5.2S OLID L ENGTH (SEE ALSO N UMBER OF C OILS, 4.6)—In compression springs, this is the length with all activecoils closed, to be specified as a maximum dimension allowing the manufacturer any tolerance required by the variations in wire size, total coils, and the amount of grind at the ends; platings and coatings increase the wire diameter and must be considered.For springs with ground ends, the maximum solid length is the total number of coils times the wire diameter;for springs with ends not ground, the solid length is the total number of coils plus one, times the wire diameter.FIGURE 3—COIL DIAMETER TOLERANCE - COMPRESSION AND EXTENSION SPRINGS FOR WIRE SPRINGS FOR WIRE DIAMETERS 0.30 TO 9.50 mm. ROUND OFF INDEX TO NEAREST WHOLE NUMBER. INTERPOLATE WHEN THE ROUNDED-OFF VALUE IS AN ODD NUMBER.USE TOLERANCE FOR 0.30 mm WIRE DIAMETER WHEN WIRE DIAMETER IS LESS THAN 0.30 mm.FIGURE 4—COIL DIAMETER TOLERANCE - COMPRESSION AND EXTENSION SPRINGS FOR WIRE DIAMETERS 9.5 TO 16.0 mm. ROUND OFF INDEX TO NEAREST WHOLE NUMBER.INTERPOLATE WHEN ROUNDED-OFF VALUE IS ODD NUMBER.FIGURE 5—FREE LENGTH TOLERANCE - COMPRESSION SPRINGS. ROUND OFF INDEXTO NEAREST WHOLE NUMBER. INTERPOLATE WHEN ROUNDED-OFF VALUE IS ODD NUMBER.THESE ARE TOLERANCES FOR SPRINGS WITH ENDS CLOSED AND GROUND.FOR SPRINGS WITH ENDS CLOSED BUT NOT GROUND, MULTIPLY BY 1.7.FIGURE 6—FREE LENGTH TOLERANCE - EXTENSION SPRINGS4.5.3P RESET L ENGTH —After the compression spring has been coiled to a free length in excess of the designatedfree length, it is compressed solid or to a specified preset length; this produces yielding, which results in bringing the spring to the designated free length. If more than one preset compression is desired, it must be specified on the drawing. See also MANUAL, SAE HS J795, Chapters 1 and 4.4.5.4L OADED L ENGTH —This is the length while the load is being measured. It is a fixed reference dimension, with the tolerance applied to the load.4.5.5M AXIMUM E XTENDED L ENGTH —Extension springs normally do not have a definite stop to their deflection,therefore the drawing specifications should include a statement of the maximum extended length which must be attained without encountering permanent set.4.6Number of Coils—In compression springs, it is often necessary to vary the number of coils in order to meet the requirements on load, rate, free length, and solid length. Therefore, the number of coils should be specified as an approximate figure. For reference only, the tolerance for the number of coils is given in Table 7compression springs and in Table 8 for extension springs. It is expressed in degrees as a function of the number of active coils.In extension springs, either the number of coils in the body of the spring or the length over the coils may be specified, but only as an approximate figure. In computing the length over coils, it should be recognized that there is always one more wire diameter in the length than the number of coils in a close-wound spring.TABLE 7—NUMBER OF COILS TOLERANCE OF COMPRESSION SPRINGSActive CoilsTolerance, ± deg 3 - 1045For each additional 10 coils, add 30TABLE 8—NUMBER OF COILS TOLERANCE OF EXTENSION SPRINGSActive CoilsTolerance, ± deg Close Wound Tolerance, ± deg Open Wound 330904 - 104590For each additional 10 coils, add 15304.7Spring Ends—In compression springs, there are four typical end configurations (Figure 7):FIGURE 7—T YPICAL ENDS OF HELICAL COMPRESSION SPRINGS1.Plain end (with the end coil having the same pitch as all other coils);2.Plain end ground (the end surface being ground perpendicular to the spring axis);3.Closed end (with the tip of the wire contacting the adjacent coil);4.Closed and ground end (the closed end being ground perpendicular to the spring axis).The unground ends may be used for reasons of economy, but they give eccentric loading with some increase in maximum spring wire stress and space required. The plain ends similarly produce eccentric loading and additionally present a handling problem due to springs tangling together.In extension springs, many types of hooks, loops, eyes, etc. are used (see MANUAL, SAE HS J795, Figure3.3). Details such as hook opening restraint of the loop within the body diameter should be specified on thedrawing. The position of hooks relative to each other can be in line, at right angles, or at any other angular position as required. If this relative position is important, the spring drawing should emphasize the importance by a statement as well as by pictorial representation. Sharp bends in forming the end hooks should be avoided because they produce stress concentrations.。

ZGMn13喷丸强化有限元模拟

ZGMn13喷丸强化有限元模拟喷丸工艺是一种有效提高工件表面疲劳抗力的表面处理工艺，被广泛应用在航空、汽车、动力机械等重要领域。

喷丸数值模拟是制订喷丸工艺方案、评估喷丸后工件表面疲劳抗力的主要理论工具。

本文运用有限元仿真软件建立了ZGMn13喷丸强化的有限元模型，利用仿真结果预测了喷丸速度、喷丸时间、喷丸覆盖率对残余应力场分布的影响。

从计算结果可以看出，喷丸速度相同时，残余压应力层的深度和残余压应力的峰值随着喷丸时间的增加而增加，但是增加到一定程度后，会逐渐趨向于饱和，但残余压应力峰值深度位置并不随着喷丸时间的增加而增加，而是基本保持不变；随着喷丸速度的增加，残余压应力层的深度和残余压应力值的峰值随之增加。

标签：ZGMn13；喷丸强化；有限元分析1 绪论喷丸强化[1-4]是利用高速弹丸流对金属零件表面进行撞击，使零件表面产生残余应力场，改变零件的表面状态并提高零件的疲劳性能，与其他表面处理工艺相比，喷丸强化具有强化效果明显、消耗成本低、实施过程简便等特点，广泛应用于动力机械、汽车和航空等重要领域。

喷丸强化过程是高度非线性的动态冲击过程，喷丸工艺参数对喷丸效果的影响需要借助于数值仿真手段进行分析，近年相关学者开展了喷丸数值模拟[5-8]研究取得了较大进展。

但由于喷丸强化作用过程复杂且影响因素众多，至今仍有许多关键技术有待深化和解决。

本文针对工业常用耐磨材料ZGMn13[9-12]的喷丸表面强化展开研究，利用Abaqus建立了多丸粒喷丸强化模型，研究喷丸覆盖率、喷丸时间和喷丸速度对喷丸强化残余应力场的影响，建立了ZGMn13多丸粒喷丸模型，研究了喷丸覆盖率、喷丸时间和喷丸速度对于ZGMn13表面喷丸强化效果的影响，为ZGMn13喷丸强化效果预测和工艺参数的优化提供依据。

2 ZGMn13抛丸强化有限元模型由于在弹丸碰撞ZGMn13工件时，弹丸垂直于ZGMn13工件的表面撞击，弹丸接触ZGMn13工件的表面时的弹丸速度是瞬时不连续的，因此本文选择显式时间积分。

纳米压痕理论在残余应力检测方面的技术进展

纳米压痕理论在残余应力检测方面的技术进展李青;刘士峰【摘要】This paper described the nano-indentation theory and two typical indentation models for characterizing the residual stress. The two models both assume that there is equal-biaxial residual stress on the specimen surface, and the model proposed by Suresh and A. E. Giannakopoulos can determine the residual stress through the contact area ratio of stressed and unstressed materials. Later, Y. H. Lee and D. Kwon modified the model, and transferred the contact area into the function of load. Therefore, the residual stress is only related to load. This paper also summarized the application examples which used the nano-indentation theory to detect residual stress. However, further research has to be made on the nano-indentation technique for detecting residual stress.%介绍了纳米压痕理论以及2种典型的测量残余应力的理论模型,这2种模型都假设表面存在等双轴残余应力.其中Suresh和A.E.Giannakopoulos模型测量残余应力是由存在残余应力时和没有残余应力时的接触面积之比来确定；随后Y.H.Lee和D.Kwon对该模型进行了修正,根据载荷与硬度的对应关系,将接触面积转换成载荷的函数；最后的残余应力计算仅与载荷有关.本文还详细综述了用纳米压痕理论检测残余应力的应用实例,最后提出用纳米压痕技术检测残余应力的可能性还有待更深入的研究.【期刊名称】《新技术新工艺》【年(卷),期】2013(000)003【总页数】3页(P118-120)【关键词】纳米压痕;理论模型;残余应力;检测【作者】李青;刘士峰【作者单位】军械工程学院,河北石家庄 050003;邢台轧辊小冷辊有限责任公司,河北邢台 054000【正文语种】中文【中图分类】TG174.44纳米压痕(nano indentation)技术又被称为深度敏感压痕(depth sensing indentation)技术，是近年发展起来的一种新技术,它可以在不分离薄膜与基底材料的情况下，直接得到薄膜材料的许多力学性质，如弹性模量、硬度、屈服强度、加工硬化指数等[1-3]，其在微电子科学、表面喷涂、磁记录及薄膜等相关的材料科学领域得到越来越广泛的应用[4-6]。

GIWAXSA powerful tool for perovskite photovoltaics

GIWAXS: A powerful tool for perovskite photovoltaicsChenyue Wang 1, Chuantian Zuo 2, Qi Chen 1, †, and Liming Ding 2, †1MIIT Key Laboratory for Low-dimensional Quantum Structure and Devices, Experimental Center of Advanced Materials, School of MaterialsScience and Engineering, Beijing Institute of Technology, Beijing 100081, China2Center for Excellence in Nanoscience (CAS), Key Laboratory of Nanosystem and Hierarchical Fabrication (CAS), National Center forNanoscience and Technology, Beijing 100190, ChinaCitation: C Y Wang, C T Zuo, Q Chen, and L M Ding, GIWAXS: A powerful tool for perovskite photovoltaics[J]. J. Semicond., 2021,42(6), 060201. /10.1088/1674-4926/42/6/060201The power conversion efficiency (PCE) for perovskite sol-ar cells (PSCs) now reaches 25.2%[1]. However, the perovskite materials have complex compositions and variable phases,calling for suitable characterization techniques to investigate the underlying operation and degradation mechanism. Graz-ing-incidence wide-angle X-ray scattering (GIWAXS) plays an important role in studying perovskite materials. GIWAXS data are generally two-dimensional diffractograms containing dif-fraction rings of different crystal planes. Grazing-incidence small-angle X-ray scattering (GISAXS) is similar to GIWAXS,while it has a longer detection distance than that of GIWAXS (Fig. 1(a))[2]. GISAXS enlarges the observable spatial range up to 10–100 nm and reduces the measurement sensitivity of crys-tallization, and it is mainly used to determine the morpho-logy of bulk-heterojunction films in nanoscale [3, 4]. Compared to GISAXS, GIWAXS is more popular in perovskite study. This technique has several advantages as follows: (1) high signal-to-noise ratio (SNR) and sensitive structural resolution; (2) no-contact and nondestructive probing; (3) abundant structural in-formation; (4) depth resolution; (5) in-situ observation. Here,we discuss two applications of GIWAXS, i.e., the crystallograph-ic information at steady state, and the in-situ measurement to probe the temporal information. As an important structur-al parameter of perovskite films, crystallographic orientation affects the optoelectronic properties and materials stability.The 2D GIWAXS diffractogram presents the Debye-Scherrer ring for certain crystallographic plane, enabling characteriza-tion of structural orientation of perovskite films. The orienta-tion degree for crystal planes can be obtained quantitatively according to the diffraction rings along the azimuth by using Herman’s orientation function.Quasi-2D perovskites receive attention due to their vari-able structures, tunable composition, and relatively high stabil-ity. The insulating organic long-chain cations in quasi-2D per-ovskites can block carrier transport. Suitable crystal orienta-tion can enhance the carrier transport in 2D perovskites, thus improving device performance. GIWAXS measurements give in-formation about crystal orientation, it can also tell the stack-ing manner of grains at different depths, which is essential for understanding the crystallization mechanism. For ex-ample, by using GIWAXS, Choi et al. found that the nucle-ation and crystallization of BA 2MA 3Pb 4I 13 perovskite occurs at the gas-liquid interface during annealing, which results in the vertical alignment of 2D perovskite crystals (Fig. 1(b))[5]. They further regulated the solvent and cation to prepare highly ver-tically orientated 2D perovskite films [6]. Rafael et al. found that the intermediate solvent complexes provide building blocks in the formation of 2D perovskites according to GI-WAXS measurements [7].High-quality 3D perovskites tend to make strong orienta-tion at certain azimuth angle. GIWAXS results can be used to evaluate the crystallization quality of 3D perovskite thin films.The results can also be used to guide the process optimiza-tion, as well as to clarify the relationship between crystallo-graphic orientation and device performance. Zheng et al. regu-lated the preferential orientation of perovskite crystals and im-proved the interfacial carriers transport in the corresponding devices by substituting A-site alkali metal cations [8].Recently, residual strain was observed in perovskite films due to the mismatch of the expansion coefficients for the sub-strate and perovskites, which influences the operational stabil-ity and efficiency of perovskite solar cells. Microscopically, the residual stress within the film results from a biaxial stretch-ing of the perovskite lattice in in-plane direction. The shift of corresponding diffraction peaks at different azimuthal angles reveals the lattice tilting and stretching. By depth-resolved GI-WAXS, Zhu et al. observed a gradient strain in FA-MA per-ovskite films (Fig. 1(c)). The performance of PSCs was im-proved by reducing lattice mismatch of the crystals [9]. Wang et al. replaced A-site cations on the perovskite surface by us-ing OAI post-treatment, forming a “bone-joint” configuration,reducing surface residual stresses and thus improving humid-ity and thermal stability of PSCs [10].In-situ measurement is attractive in perovskite research.It provides a rapid approach to track microstructural changes in perovskite materials, including the crystallization and aging processes. It is the key to unravel the kinetics process of perovskite materials. The formation process of perovskite crystals is not fully understood yet. The film formation pro-cess includes liquid-film gelation stage and crystallization stage. Many studies have shown that the orientation and phase structure of perovskite are already established during gelation stage. The quality of the perovskite precursor film (gel) significantly affects the final perovskite film. In-situ GI-WAXS provides information for the composition evolution during spin-coating process. It also provides guidelines for pre-paration conditions, such as spin speed and time, dripping time of anti-solvent, etc. Amassian et al. have conducted a series of in-situ GIWAXS studies on perovskite. They ob-Correspondence to: Q Chen, ***********.cn ; L M Ding, ***************Received 22 MARCH 2021.RESEARCH HIGHLIGHTS Journal of Semiconductors(2021) 42, 060201doi: 10.1088/1674-4926/42/6/060201phase to sol–gel state, and investigated the effect of precurs-or spin-coating time on PSCs performance [11]. They revealed that Cs + and Rb + cations were able to stabilize the sol–gel state and suppress the phase separation during spin-coating (Fig. 1(d))[12, 13].GIWAXS can also be used to study the crystallization pro-cess during thermal annealing. Using the peak area integ-rated by the Debye-Scherrer ring of GIWAXS, all the phase con-tents of perovskites and their evolution during annealing can be deduced, which illustrates the phase transition from inter-mediate phase to perovskite phase. The activation energies for perovskite formation can be determined by using Arrheni-us equation.Perovskite degradation caused by humidity and heat lim-its the commercialization of PSCs. In conjunction with the mois-ture and temperature controller, the aging process of devices under different conditions can be monitored by GIWAXS.Through depth-resolved characterization, the physical and chemical reactions at different positions can be deduced by combining with other characterizations, which will reveal the degradation mechanisms. Kelly et al. performed systematic in-situ GIWAXS studies on perovskite degradation. They ob-served that MAPbI 3 films decomposed to a hydrated intermedi-ate phase with PbI 64– octahedra in a humid environment [14].To further investigate the performance and structure changes of PSCs under humidity, they developed a humidity control-ler in conjunction with I–V measurement system (Fig. 1(e)).The results revealed that the decrease of performance res-ults from the electrode corrosion, rather than perovskite de-composition (Fig. 1(f))[15].In summary, GIWAXS has been widely used to reveal the relationship between perovskite crystal structure and device performance. In-situ GIWAXS can be used to track the crystalliz-ation process and decomposition process of perovskites. This method can help us to develop stable and efficient per-ovskite solar cells.AcknowledgementsThis work was supported by National Natural Science Foundation of China (21975028, 22011540377), Beijing Muni-cipal Science and Technology Project (Z181100005118002),and Beijing Municipal Natural Science Foundation (JQ19008).L. Ding thanks the National Key Research and Development Program of China (2017YFA0206600) and the National Natur-(d)(f)1.61.20.80.400.5Max.Min.12111098T i m e (s )T i m e (s )q (nm −1)765412111098q (nm −1)7656H3C2H4300200100Solvate Disordered colloidsSolvate Disordered colloids30020010012111098q (nm −1)7654121110+ 5% Cs98q (nm −1)76541.0Q xy (Å−1)1.52.0GIWAXS GISAXSz xy k iq xzq xy≈0.1 m ≈ 2.0−5.0 mq zqαion mp-TiO 2 substrate interface—preferential orientationTensile-strain lm50 nm 200 nm 500 nm31.69531.68031.66531.6501.00.80.6N o r m a l i z e d p a r a m e t e r s0.40.2000.5 1.0 1.5 2.0 2.5 3.0Time (h)3.54.0 4.55.0 5.56.0(110)I sc V oc FF PCECarrier gasWater bubblersMass ow controllersSynchrotron X-ray beamSamplechamberKaptonwindowSource-measure unitCCD area detector0.250.50sin 2φ0.752θ (°)k fk fαfαfI−V dataψχψFig. 1. (Color online) (a) Schematic diagram of GIWAXS and GISAXS. Reproduced with permission [2], Copyright 2017, John Wiley & Sons Inc.(b) Schematic diagram of the formation of vertically orientated 2D perovskite. Reproduced with permission [5], Copyright 2018, Nature Publish-ing Group. (c) Gradient strain at different depths in perovskite layer. Reproduced with permission [9], Copyright 2019, Nature Publishing Group.(d) Time-resolved GIWAXS for precursor films with and without K + during spin-coating. Reproduced with permission [13], Copyright 2019, Elsevier Inc. (e) Humidity control set-up. (f) Time-dependence for MAPbI 3 (110) peak area and device performance parameters. (e) and (f), reproduced with permission [15], Copyright 2018, American Chemical Society.2Journal of Semiconductors doi: 10.1088/1674-4926/42/6/060201al Science Foundation of China (51773045, 21772030, 51922032, 21961160720) for financial support. ReferencesYoo J J, Seo G, Chua M R, et al. Efficient perovskite solar cells via im-proved carrier management. Nature, 2021, 590, 587[1]Schlipf J, Müller-Buschbaum P. Structure of organometal halide perovskite films as determined with grazing-incidence X-ray scat-tering methods. Adv Energy Mater, 2017, 7, 1700131[2]Rivnay J, Mannsfeld S C B, Miller C E, et al. Quantitative determina-tion of organic semiconductor microstructure from the molecu-lar to device scale. Chem Rev, 2012, 112, 5488[3]Richter L J, DeLongchamp D M, Amassian A. Morphology develop-ment in solution-processed functional organic blend films: An in situ viewpoint. Chem Rev, 2017, 117, 6332[4]Chen A Z, Shiu M, Ma J H, et al. Origin of vertical orientation in two-dimensional metal halide perovskites and its effect on photo-voltaic performance. Nat Commun, 2018, 9, 1336[5]Chen A Z, Shiu M, Deng X, et al. Understanding the formation of vertical orientation in two-dimensional metal halide perovskite thin films. Chem Mater, 2019, 31, 1336[6]Quintero-Bermudez R, Gold-Parker A, Proppe A H, et al. Composi-tional and orientational control in metal halide perovskites of re-duced dimensionality. Nat Mater, 2018, 17, 900[7]Zheng G, Zhu C, Ma J, et al. Manipulation of facet orientation in hy-brid perovskite polycrystalline films by cation cascade. Nat Com-mun, 2018, 9, 2793[8]Zhu C, Niu X, Fu Y, et al. Strain engineering in perovskite solar cells and its impacts on carrier dynamics. Nat Commun, 2019, 10, 815[9]Wang H, Zhu C, Liu L, et al. Interfacial residual stress relaxation in perovskite solar cells with improved stability. Adv Mater, 2019, 31, 1904408[10]Munir R, Sheikh A D, Abdelsamie M, et al. Hybrid perovskite thin-film photovoltaics: In situ diagnostics and importance of the pre-cursor solvate phases. Adv Mater, 2017, 29, 1604113[11]Wang K, Tang M C, Dang H X, et al. Kinetic stabilization of the sol–gel state in perovskites enables facile processing of high-effi-ciency solar cells. Adv Mater, 2019, 31, 1808357[12]Dang H X, Wang K, Ghasemi M, et al. Multi-cation synergy sup-presses phase segregation in mixed-halide perovskites. Joule, 2019, 3, 1746[13]Yang J, Siempelkamp B D, Liu D, et al. Investigation of CH3NH3PbI3 degradation rates and mechanisms in controlled hu-midity environments using in situ techniques. ACS Nano, 2015, 9, 1955[14]Fransishyn K M, Kundu S, Kelly T L. Elucidating the failure mechan-isms of perovskite solar cells in humid environments using in situ grazing-incidence wide-angle X-ray scattering. ACS Energy Lett, 2018, 3, 2127[15]Chenyue Wang got his BS from University ofScience and Technology Beijing in 2018. Nowhe is a MS student at Beijing Institute of Tech-nology under the supervision of Professor QiChen. His research focuses on perovskite sol-ar cells.Chuantian Zuo received his PhD in 2018 fromNational Center for Nanoscience and Techno-logy (CAS) under the supervision of ProfessorLiming Ding. Then he did postdoctoral re-search at CSIRO, Australia. Currently, he is an as-sistant professor in Liming Ding Group. His re-search focuses on innovative materials anddevices.Qi Chen holds BS and MS degrees of TsinghuaUniversity, and received his PhD degree fromUniversity of California, Los Angeles (UCLA). In2013–2016, he worked as a postdoc at Califor-nia Nanosystem Institute (CNSI), UCLA. Nowhe is a full professor at Beijing Institute of Tech-nology. His research focuses on hybrid materi-als design, processing and applications in opto-electronics.Liming Ding got his PhD from University of Sci-ence and Technology of China (was a joint stu-dent at Changchun Institute of Applied Chem-istry, CAS). He started his research on OSCsand PLEDs in Olle Inganäs Lab in 1998. Lateron, he worked at National Center for PolymerResearch, Wright-Patterson Air Force Base andArgonne National Lab (USA). He joined Kon-arka as a Senior Scientist in 2008. In 2010, hejoined National Center for Nanoscience andTechnology as a full professor. His research fo-cuses on functional materials and devices. Heis RSC Fellow, the nominator for Xplorer Prize,and the Associate Editors for Science Bulletinand Journal of Semiconductors.Journal of Semiconductors doi: 10.1088/1674-4926/42/6/0602013。

(整理)压电弹性体表面效应表面波

Surface effects on wave propagation in piezoelectric half-spaceWeijian Zhou, Weiqiu Chen*Department of Engineering Mechanics, Zhejiang University,Hangzhou 310027, P. R. ChinaAbstract：The surface waves in a piezoelectric half-space with material boundary are considered in this paper. The Stroh formalism and the modified Stroh formalism areutilized to discuss the existence of multiple modes of surface waves and wave number domain of each modein such body. The modified impedance tensor is introduced to investigate the wave propagation in electrically closed piezoelectric half-space, and the properties of such modified impedance tensor are discussed. Based on these theories, the surface waves in hexagonal piezoelectric material with material boundary are discussed in detail. The discussion tells that, the electrical boundary condition and the surface permittivity have no effect on the propagation of Rayleigh type surface waves but have significant effect on B-G waves. There are at most three modes in this material, i.e. fundamental Rayleigh wave modes, Sezawa wave modes and B-G wave modes. The existence criterions of each wave mode are established in detail, and the frequency domains are given for each mode when they exist. The numerical examples show the effect of material boundary on the wave propagation, and confirm the correctness of the discussions about the existence and frequency domain of each mode of the surface waves.Keywords：Surface waves, surface effects, piezoelectric, existence, multiple modes.*Author for correspondence. Tel.: +86 571 87951866; fax: +86 57187951866.E-mail address: chenwq@ (W.Q. Chen).1.InstructionThe surface effect, which is derived from the departure of homogeneity in the neighborhood of the surfacedue to the environment, plays an important role in determining the mechanical behaviors of a micro- and nano-sized structure[1, 2].A plenty of literatures can be found on this subject. Varieties of rigorous elasticity theories[3-8]have been established to describe the surface effect, among which the most widely used is the G-M theory[3]. This theory shows that the study of surface effect is relevant to the situation in which a body is coated by an extremely thin film. It has been pointed that[9] the G-M theory coincides with the lowest-order theory[4, 5] of a thin layer deposited on an elastic body, provided that the residual stress is absent in the material boundary and the surface constants in G-M theory are properly defined.The study of wave propagation in a body with material boundary may have great applications in the design of ultrasonic signal-processing devices. Various problems of wave propagation have been investigated, including the Love and Rayleigh waves[9], the Stoneley waves[10], the reflection of plane harmonic waves[11] and the B-G waves in a piezoelectric half-space with material boundary[8].The present paper develops a framework, based on the Stroh formalism[13, 14], which is a powerful and elegant mathematical method developed for the analysis of anisotropic elasticity, and the Barnett-Lothe theory [15-17]to study the subsonic velocity spectrum of surface waves along the material boundary of a general anisotropic piezoelectric body. The modified Stroh formalism [18]developed for generalized boundary conditions is utilized to investigate the wave propagation when the boundary is electrically closed. In addition, based on thesetheories, the existence problem and multiple modes phenomenon ofsurface waves are analyzed. It is pointed out that there are at most three wave modesalong the material boundary of a stress free and electrically open or closed piezoelectric body. In the case of hexagonal piezoelectric material with isotropic basal plane on12,x x-plane, the first mode is the fundamental Rayleigh wave (simplified by FRW hereafter) mode, whose dispersion curveevolves from the Rayleigh velocity; the second mode is the Sezawa wave (SW) mode, it always has higher frequency compared with FRW mode; the third mode is the B-G wave (BGW) mode, it is tremendously influenced by the electrical boundary of the body. The permissive frequency domainsof each wave mode in various cases are discussed in detail.In this paper, is divided into eight sections. In section 2, the basic equations of linear piezoelectricity is introduced; in section 3, the extended Stroh formalism for piezoelectricity is reviewed;in section 4, the impedance tensor ()vM and modified impedance ˆ()vM, important in analysis of mechanical response of piezoelectric body, is analyzed;in section 5, the surface effect of the piezoelectric body is modeled by an extremely thin conducting film; in section 6, we show the governing equations of surface waves; in section 7, the existence of surface waves in hexagonal piezoelectric body is analyzed, and the frequency domain of each wave mode is derived for various cases; section 8 is the numerical examples and discussions; the last part is the conclusion.2.Basic equationsConsider a piezoelectric half-space with isotropic plane parallel to its boundary surface. The Cartesian coordinate system (x1,x2, x3) is adopted, the x1o x3 is coincided with the half-space surface and the x2-axis is pointed tobulk V with a material boundary S occupying the half-space (20x ), inwhich the materials of bulk and boundary are both piezoelectric media. The constitute equations of the bulk can be written as [17],,,.ij ijkl k l kij k i ijk j k ij j C u h D E h u D σγ=+=+ (1)where ij σ, i u , i E and i D are the elastic stresses, mechanical displacements, electrical fields and electrical displacements, respectively; ij CThe comma denotes differentiation.The Latin indices ,,i j k range over 1, 2, 3, while the Greek indices ,αβ range over 1,3 throughout this paper. The Einstein'ssummationconvention is implied. For the static field, the potential F can be written in second order,,,1122ijkl i j k l kij i j k ij i j F C u u h u D D D γ=++(2)For a stable body, the free energy F is positive definite. Consider the integral F L.F L FdV =-⎰(3)We shall call F L the F Lagrange function for the moving field. According to Barnett and Lothe [17],,.|2Fkin L E v∂=-∂n σD n (4)here the subscripts ,.n σDn mean that ,.n σDn are constants on the boundary, kin E is the kineticenergyandn is the unit normal to the boundary.The equilibrium equations without body force and the Gauss equationare [17],,,,0.ij i j tt i i u D σρ== (5)The similarity of the upper equations indicates that it has some advantages to obtain treatment with σand D on equal footing. By setting the potentialF Φ=-⋅E D (6)the σ and D are now on equal footing, which indeed shows Φ no longer positive definite for a static field now. Consider the integral L ΦL dV Φ=-Φ⎰(7)We shall call L Φ the Φ Lagrange function for the moving field.Itsdifferential aboutv while keeping ,ϕu constants on surface is[17],|2kin L E vϕΦ∂=-∂u (8)The constitutive equations with σand D on equal footing are as follows,,,.ij ijkl k l kij k i ijk j k ij j u e E D e u E σλε=-=+ (9)where ijkl λ, kij e and ij εare the elastic stiffnesses, the piezoelectric constants and the permittivity constants, respectively, and they have the expressions of111(),(),()ijkl ijkl pij pq qkl ijk im mjk ij ijC h h e h λγγεγ---=-=-= (10)The tensors ijkl λ, kij e , ij ε obey the symmetries,,.ijkl klij jikl ijk ikj ij ji e e λλλεε====(11)andthe tensors ijkl λ, ij ε are positive definite.3. The Strohformalism for piezoelectricityWe consider the waves propagating in the 1x direction with speed v . All the state variables are independent of 3x , characterized by 3/0x ∂∂=. Leti iE x ϕ∂=-∂ (12)where ϕ is the electrical potential. The displacement function u and electric potentialϕ have the functions of[17]112212334exp[i ()],a u a u k x px vt a u a ϕ⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥==+-⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦U(13)here i =p is a complex constant to be determined, and 4,i a a (1,2,3i =) stand for the polarization of the displacement and electrical potential, respectively.From the equilibrium equations and Gauss equation(5), we know that there always exists a generalized stress potential f , which satisfies23,11,2,1ˆ,.v ρ-=-=τI U f τf (14)where2121123,1,2,3;,1,2,3;ˆ,,,4,4exp[i ()],diag[1,1,1,0]i i I I If I If I D If I D If I k x px vt σσττ==⎧⎧==⎨⎨==⎩⎩=+-=f b I (15)Throughout this paper, the capital Latin indices ,,,I J K L range over 1,2,3,4. From the constitute equations of the bulk, the four dimensional vector b satisfies1[][]T p p p=+=-+b R T a Q R a(16)where the superscript ‘T’ denotes the transposition, and the tensor ,,Q R T are formed in terms of the generalized elastic tensor,,1,2,3;,4,K 1,2,3;e ,1,2,3,4;,,4ijkl ikl iJKllijijIf J K e If J G If J K If J K λε'=⎧⎪==⎪=⎨==⎪⎪-=⎩ (17)by the prescription111222,,.JK JK JK JK JK JK Q G R G T G ===(18)Here ijklλ' are the dynamic elastic coefficients211.ijklijkl i l jk v λλρδδδ'=- (19)The physical interpretation of vector b is12341232i [b ,,,][,,,]k b b b J J J D =(20)where J is the force on a unit area parallel to the surface. With the upper definition of the generalized displacement vector U and the generalized force stress potential f , the constitutive equations, the equilibrium equations and Gauss equation can be stated asp =N ξξ(21)Here the eight-dimensional vector ξ is the state vector, denoted by [,]T T =ξU b . Thus p is the eigenvalue of N . The generalized fundamental elastic tensor N is defined by1231T ⎡⎤=⎢⎥⎣⎦N N N N N (22)where111123,,T T ---=-==-N T R N T N RT R Q(23)Now we rotate the coordinate system around 3x axis by an angle θ, then the vector1e and 2e in the old coordinate system turn to m and n in the new system, whichcan be defined by[cos ,sin ,0],[sin ,cos ,0]T T θθθθ==-m n(24)The generalized fundamental elastic tensor ()θN in the new system can be deduced by11121131()()()()()()()()()()()()()()T T T θθθθθθθθθθθθθθ----⎡⎤⎡⎤-==⎢⎥⎢⎥--⎣⎦⎣⎦N N T R T N N N R T R Q R T (25)where(),(),()JK iJKl i l JK iJKl i l JK iJKl i l Q G m m R G n m T G n n θθθ===(26)In the interval 0L v v ≤<,()θN has four pairs of conjugated complex eigenvalues, we assume that ()I p θ(1,2,3,4I =) are the fore eigenvalues with positive imaginary part, and the left four eigenvalues can be denoted by ()I p θ. Hereafter, the over bar stands for the conjugate operation. In this paper,L v is the so called ‘limiting velocity’[19] of the piezoelectric material.One of the most important properties the tensor ()θN has is1()d i ,πθθπ==±⎰N ξN ξξ (27)where i ±depends on whether ()p θ has positive or negative imaginary part.1()T d πθθπ⎡⎤==⎢⎥-⎣⎦⎰S H N N L S (28)The general solutions of U and f obtained from equation (21) by superposition ofthe eight vectors T T T [,]I I a b and T T T[,]I I a b associated with the eight eigenvalues I pand ()I p θ can be written as4411[exp(i )exp(i )],[exp(i )exp(i )]I I I I I I I I I I I I I I q kz q kz q kz q kz ===+=+∑∑U a a f b b(29)where I q (1,2,3,4I =) are arbitrary constants to be determined.The real form solution of U and f are**2Re{exp[i ]},2Re{exp[i ]},kz kz ==U A q f B q(30)where***2123412341234,[,,,],[,,,]exp[i ][exp(i ),exp(i ),exp(i ),exp(i )]I z x p x vt kz diag kz kz kz kz =+-===Αa a a a B b b b b (31)The introduction of impedance tensor [15]()v M is significant in the following analysis of surface waves when the boundary is mechanically free and electrically open, where()v M is a Hermitian matrix and111()i i v ---=-=+M BA H H S (32)However, when the boundary mechanically free and electrically closed, it is advantageous to introduce the modified Stroh Formalism [18] for such mixed boundary conditions. The modified generalized displacement and the modified generalized stress function are34*43*43443ˆˆˆˆ2Re{exp[i ]},2Re{exp[i ]},ˆˆdiag{0,0,0,1},,.kz kz φφ=+==+===+=+U I U I A q f I U I B q I A I A I B B I A I B (33)Similarly, the modified impedance tensor ˆ()v Mis introduced by111ˆˆˆˆˆˆ()i i v ---=-=+MBA H H S (34)ˆ()v Mremains to be Hermitian [18] and1114111441441444ˆˆ,.TS L ⎡⎤⎡⎤==⎢⎥⎢⎥--⎣⎦⎣⎦S H H S S H L S (35)where 11S is the 33⨯ upper left-hand block of S and 44S is the lower right-hand corner element; similarly for 11H and 44L . Likewise, S can be written as11144144,S ⎡⎤=⎢⎥⎣⎦SS S S (36)In addition, ˆ()v Mis related to ()v M by1111441441441411444144i ˆ()i M M v M M ----⎡⎤--=⎢⎥-⎣⎦M M M M M M (37)4. The properties of matrixes ()v M and ˆ()v M2.1 The M-Type matrixAs defined by Ting [20], a real 44⨯ symmetric matrix T is of T-type if its33⨯upper left-hand block E T is positive definite while its last element 44T isnegative and nonzero. A systematic study of a T-type matrix is accomplished byTing [20], and some important properties are listed as follows:(i). A matrix of T-type is not singular, and thus reversible.(ii). If ,T W are both of T-type , the matrix 12k k +T W is also of T-type , where12,k k are two arbitrary real constants.(iii).If T is of T-type , its inverse 1-T is also of T-type .(iv). A ssume that the three eigenvalues of its first 33⨯submatrix ET are123E E E λλλ≥≥ and the last element of T is 4422T ω=-. If T is of T-type , itsfour eigenvalues 1234λλλλ≥≥≥ are ranged as4223322110E E E λωλλλλλλ≤-<<≤≤≤≤≤(38)(v). If T is of T-type , it has three positive eigenvalues and one negativeeigenvalue.As an extension of T-type matrix, the M-type matrix is introduced here. A44⨯Hermitianmatrix M is of M-type if its 33⨯ upper left-hand blockEM ispositive definite and its last element 4422M w =- is negative. A matrix of M-type is not singular, the prove of which is similar to the prove of the first property of T-type matrix:1222222222222{w ()}EE TE Tw -==-+-M e M M e M e e (39)Hence, notice that 1()E -M is also positive definite, i.e. 12222()0TE ->e M e if 22e isnonzero. Therefore, 0<M , and M is not singular. Following the derivation of (39), we have1222222(){(w )(s )}E TE F s s s s -=-=--++-M I M I e M I e(40)Let 123E E E s s s ≤≤ be the three eigenvalues of E M , and 123,,ηηηbe the correspondingorthonormalized eigenvectors. This means that1122331111222233331111111122223333()()(),()()(),()()()().E E E EE E T E T E T E E T E T E T s s s s s s s s s s s s s s s s s s s s s -----=----=-+-+--=-+-+-M I M I ηηηηηηM I ηηηηηη(41)Substitution of (41) into (40) yields12322231113221233()()()()()()()()()()()E E E E E E E E E F s s s s s s s s w s s s s s x x s s s s x x s s s s x x =-=----+---------M I(42)where 22Tj j x =e η, (1,2,3j =). It is clear that,222130,,,()0,,,EE Eif s s F s if s w s s ⎧≥=-∞∞⎪⎨≤=-⎪⎩ (43)If (1,2,3,4)I s I = are the eigenvalues of M , 1234s s s s ≥≥≥, we can conclude from (43) that4223322110E EE s w s s s s s s ≤-<<≤≤≤≤≤(44)Thus, three eigenvalues of M-Type matrix are positive and nonzero, while the forth eigenvalue is negative and nonzero. With property that the M-type matrix is nonsingular, let1Tω-⎡⎤=⎢⎥-⎣⎦X y M y(45)It is easy to show that1112222222222221{M },[w ()]E T TE w ω---=+=+X e e e M e (46)Clearly, 0ω> and X is Hermitian and positive definite. Therefore, the inverse of M-type matrix is also of M-type . In addition, it is not difficult to prove that, if ,A B are of M-type , so are their linear combinations. Totally speaking, the properties of M-type matrix are similar to T-type matrix.2.2 The analysis of ()v M and ˆ()v MThe total averaged Φ Lagrange function L Φ is defined by2According to Lothe& Barnett [17], L Φ for a surface disturbance of amplitude a is14T L k Φ=-a Ma(48)where k is the wave number, and is positive. Consider a surface disturbance whose amplitude a is of the form[]123,,,0Ta a a =a(49)where 123,,a a a are arbitrary complex constants. Substitute (49)into (13), clearly we have =E 0. From equation (6)and (7), with (48) we have[][]12(kv)11231232011,,,0,,,0(2)42t T t L k a a a a a a kv dtdx ππ-∞+Φ-=-=-Φ⎰⎰M(50)When the wave speed 0v =,Φ is positive definite, which means that[][]123123,,,0(0),,,00Ta a a a a a >M (51)Assume that (0)E M is the ⨯３３ upper left-hand block of (0)M . Since 123,,a a a are arbitrary complex constants, we can conclude from (51) that (0)E M is positive definite.In addition, since (0)M is Hermitian, (0)E M is Hermitian.Let 22ω- be thelower right-hand corner elementof (0)M . Sincei -1-1M =H +H S(52)where H is of T-type and -1H S is skew-symmetric, we have 12244H ω--=＜０. Clearly,the Hermitian matrix (0)M is of M-type .()/v v ∂∂M is negative definite[17], i.e.M()0,,Tv nonzero complex vector v∂<∀∂a a a (53)Thus theeigenvalues of ()v M decrease monotonically with increasing v .The total averaged F Lagrange function F L is2It can be proved that112()2()11,1,2,2,1211ˆˆˆˆ(2)(2)()221ˆˆ(/)[M()]4t kv t kv K K K K t t T kv Fdt kv U U dt k d dx v ππππφφ--++--=-=⎰⎰U U (55)Since 2ˆlim 0x →∞=U, the total averaged Lagrange function F L is1ˆˆˆ[()]4F T L k v =-aM a (56)Because of the positive definiteness of F when 0v =, ˆ(0)Mis positive definite. From(8) and (56) it follows thatˆM()ˆˆˆ0,Tv nonzero complex vector v∂<∀∂a aa (57)Thus, the eigenvalues of ˆ(0)Mare monotonically decreasing functions of v . 5. The surface effectThe material boundary of surface is modeled as an extremely thin conducting film G deposited on piezoelectric body P . We assume that the film is stiff and highly conducting, which is one of the special cases of interfacial models deduced by Gu etc. [21]. Thepiezoelectric body G occupies the half-space 2{,0}x ≥x , while the film occupies the region 2{,0}h x -≤≤x . The direction vectors of the 1x ,2x and 3x axis are 1e ,2e and 3e , respectively. G and P are assumed to be homogenous and anisotropic. The effect of the material surface upon the mechanics response of the body can be represented by the efficient boundary condition. As the magnitude of the piezoelectric coefficients of the surface cannot be very high, the piezoelectric coupling in the stiff and highly conducting surface can be ignored [21]. For the staticdisturbance, the jump conditions governing such material surface is:002[[]]0;[[]];[[]]div (:),[[]]div ().s s s s D ϕϕ===-∇=⋅∇u 0t λu ε (58)where [[]]()()+-∙=∙-∙, and ()+∙stands for a quantity ∙ evaluated at P , and on the side of piezoelectric body, while ()-∙denotes the value of ∙ at P but on the side of vacuum. The operator ()()s ∇∙=∇∙⋅T is the plane gradient operator, div ()div():s ∙=∙T is the plane divergence operator anddiag[1,0,1]=T .Inequations(58),[]212223,,σσσ=t .The tensor 00,λεdetermined by 00,S S h h ==λλεε,are the surfaceelastic and permittivity tensors, respectively. The tensors ,S S λεare the referencequantities in the surface, of the same order as their bulk counterparts λandε, respectively. The surface elastic and permittivity tensors are symmetric andpositive definite, i.e.0000000,0,0ijkl klij jikl ij jiijkl i l j k ij i j v v w w nonzero vectors and v v nonzero vectors λλλεελε===>∀>∀v w v(59) If the vacuum side of the material surface is mechanically free and electrically open, then according to(58), the boundary conditions are0000211,1113,1331,3133,3322211,1112,1221,2122,220,0,0.k k k k k k k k u u u u D ααααασλλλλσεϕεϕεϕεϕ++++==----=(60)If the vacuum side of the material surface is mechanically free and electrically closed, the boundary conditionsare0000211,1113,1331,3133,33220,0,0.k k k k k k k k u u u u ααααασλλλλσϕ++++===(61)Similarly we can deduce the efficient boundary condition for the moving field. If thevacuum side of the material surface is mechanically free and electrically open, we have00000211,1113,1331,3133,33,0222,211,1112,1221,2122,22,,0.k k k k k k k k tt tt u u u u u u D αααααασλλλλρσρεϕεϕεϕεϕ++++==----=(62)If the vacuum side of the material surface is mechanically free and electrically closed, we have00000211,1113,1331,3133,33,0222,,,0.k k k k k k k k tt tt u u u u u u αααααασλλλλρσρϕ++++=== (63)In the upper equations, 0ρis the surface density, determined by 0S h ρρ=, in whichS ρis of the same order as its bulk counterpart ρ.6. The propagation of surface wavesFirst of all, the stress free and electrically open boundary conditions are considered. The substituting of the displacement and stress function(30) into the equivalent boundary condition (62) at 20x = leads to0023[()]k v ρ+-=M Q I Aq 0I I(64)where =diag[1,0,1,1]I and 0011IJ JK Q G =,00111111211131000012111221123100013111321133101100000λλλλλλλλλε⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥-⎢⎥⎣⎦Q (65)Secondly, the stress free and electrically closed boundary conditions are considered. Substitution of (33) into the boundary conditions (63) yields:0023ˆ[()],k v ρ+ΛΛ-=M Q I Aq 0 (66)where diag{1,0,1,0}.Λ=Define the tensors (),()F v v ΦZ Z as00230023()(),ˆ()()F v k v v k v ρρΦ=+-=+ΛΛ-Z M Q I Z MQ I I I(67)Thus, the dispersion equations of surface waves in mechanically free and electrically open piezoelectric half-space with material boundary is()0v Φ=Z(68)while the dispersion equations for stress free and electrical closed boundary is()0F v =Z(69)Subject to the positive definiteness of 0ijkl λand 0ij ε,(0)ΦZ is of M-type and (0)F Zis positive definite. Since0303()2,ˆ()2,F v k v v vv k v v vρρΦ∂∂=-∂∂∂∂=-∂∂Z MI Z MI (70)()/v v Φ∂∂Z and ()/F v v ∂∂Z are negative definite. Therefore, the eigenvaluesof ()v ΦZare monotonic decreasing functions of velocity v , andthree of them,()F i s v (1,2,3i =) for example,may decrease from positive to negativeif the velocity increases from 0toL v , while the forth eigenvalue stays negative.The eigenvaluesof ()F v Z are alsomonotonic decreasing functions of velocity v , and at most three of them may decrease from positive to negative with v increase from 0to L v , because14444440F F Z M L -==->, which means that ()FL v Z can’t be negative definite.Hence, wehave the following conclusions:Conclusion 1. If only one of ()I L s v Φ(1,2,3,4I =), say, 4()L s v Φ,is negative andnonzero, there is no wave speed corresponding tosuch wave number; if two of ()I L s v Φ,say 1()L s v Φ and 4()L s v Φ, are negative and nonzero, while 2()L s v Φ and 3()L s v Φarepositive or zero, there is a unique wave speed corresponding to such wave number; ifthree of ()I L s v Φ, say 12(),()L L s v s v ΦΦ and 4()L s v Φ, are negative and nonzero, while3()L s v Φ is positive or zero, there are at most two wave speeds 12,v v corresponding tosuch wave number; if 123(),(),()L L L s v s v s v ΦΦΦand 4()L s v Φ, are negative and nonzero,there are at most three wave speeds 123,,v v v corresponding to such wave number.Conclusion 2.If all of ()F I L s v (1,2,3,4I =) are positive or zero, there is no wave speed corresponding to such wave number; If only one of ()F I L s v , say, 1()F L s v is negative and nonzero, there is a unique wave speed corresponding to such wavenumber; If two of ()F I L s v , say 1()F L s v and 2()F L s v , are negative and nonzero, while3()F L s v and 4()F L s v are positive or zero, there are at most two wave speeds12,v v corresponding to such wave number; If three of ()F I L s v , say 12(),()F FL L s v s v and 3()F L s v , are negative and nonzero, while 4()FL s v is positive or zero, there are at mostthree wave speeds 123,,v v v corresponding to such wave number.7. The surface waves inhexagonal piezoelectric mediaWe consider the hexagonal piezoelectric material with isotropic basal plane on12,x x -plane.The constitutive relations are11111,1122,2133,331,323442,33,215,222121,1112,2133,331,313441,33,115,133131,1132,2333,333,323661,22,1;();;();;().u u u e u u e u u u e u u e u u u e u u σλλλϕσλϕσλλλϕσλϕσλλλϕσλ=+++=++=+++=++=+++=+ (71)And1151,33,111,12152,33,211,23311,1312,2333,333,3(u u ),(u u ),u e u e u .D e D e D e εϕεϕεϕ=+-=+-=++- (72)where 661112()/2λλλ=-, and contracted notations αβλ and i e α(,1,2,...,6αβ=) havebeen used here for ijkl λand ikl e . Respect to the positive definiteness of λ, we have1112λλ>and 66110λλ<<.The matrixes ,,Q R T defined in (18)are1166126611664415441515111511000000000000000000,,0000000000000e e e e λλλλλλλλεε⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥===⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥--⎣⎦⎣⎦⎣⎦Q R T (73) According to Soh etc. [22], the matrixes ,A B in (30) have the explicit expressions:2115112166266226626623315111i 00i 100,00100/12i (1)00(1)2i 0000i i 00i e V e ψψεψλψλψλψλρψε-⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎣⎦⎡⎤+⎢⎥-+⎢⎥=⎢⎥⎢⎥-⎢⎥⎣⎦A B (74)where123123V V V ψψψ======(75)Since 1166λλ>, we have 12ψψ>.The matrix 1-A is212121121215111i 10011i 10011001001/0e ψψψψψψψεψψψ-⎛⎫ ⎪--⎪ ⎪⎪-+- ⎪ ⎪ ⎪ ⎪-⎝⎭=A (76)The explicit expression of impedance matrix M is111121211222151133151511i 00i 0000/00e V e e κψκκκψερψε⎛⎫⎪⎪= ⎪-+⎪-⎝⎭-M (77)where 2111212122662622610(1)[2(1)]0,11ψκκλψλψψψψψψ=>=--+--<. It can be proved that 221112κκ>. From (37), ˆMhas the explicit expression 11112121122133111511111511i 00i 0000i 00ˆ()i V e e v κψκκκψρψεεε---⎛⎫⎪ ⎪ ⎪⎪-⎝⎭-=M(78)We assume that the surface is also transversely isotropic, with isotropic basalplane on 12,x x -plane. 0αβλand 0ij εare of the form0111213000012113311000000131333110044330440660********00,00000000000000000λλλλλλελλλελελλ⎡⎤⎢⎥⎢⎥⎡⎤⎢⎥⎢⎥==⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎢⎥⎢⎥⎢⎥⎣⎦λε (79)0Q in(65)is of the explicit form011066044011000000000λλλε⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥-⎢⎥⎣⎦Q (80)It is clear that ()v ΦZ and ()F v Z have the explicit expressions111121222331511152133110021102112002441511110021111112021211200244151111(i 0i 00,00/(00(00000(i 00i )()))())F k k V e k e k k v v v v e k V v i i v e v k e v λρκψρλρεεκψλρκκκψρλρκψκκρψερψεε--Φ⎡⎤+⎢⎥⎢⎥⎢⎥-⎢---=+------=+-⎥⎢⎥⎣⎦+-Z Z 1511.ε-⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦(81)The eigenvalues of ()v ΦZ are1234s s s s ΦΦΦΦ====(82)where 220023*******/()V e k v χρψελρ=-+-.Obviously, 40s Φ<. The eigenvaluesof ()F v Z are1234F FF F s s s s====(83)It can be proved that 40F s >, because21133111002441()20V k v ρψεελρ---+->(84)From (68), we have the dispersion equations of surface waves as2020221221111121200202002220244114002024111113131511113311()[()]0,()[()(/)]0.k v k or v k v V e k v V v ρψψψλκψψκλλρελρερρρκψεερψε++--+=-+--+-+= (85)formechanically free and electrical open boundary. From (69), we have202022122111112120002224433150202111111()[()]0,()/0.k v k o k V v rv e v λρρψψψλκψψκλρρψρεκ++-+--=-+-= (86)For the stress free and electrical closed boundary.Clearly,(85)1 and (86)1 are the dispersion equations of Rayleigh type waves, and they are the same, which means that the propagation of Rayleigh type waves is independent of the electrical boundary conditions.(85)2 and (86)2 are the dispersion equations of B-G type waves. When the surface effect is absent, (85) and (86) degenerate to。

以光伏晶硅废料构建三维骨架增强环氧树脂的导热性能

研究与开发CHINA SYNTHETIC RESIN AND PLASTICS合成树脂及塑料， 2023， 40（6）： 16以光伏晶硅废料构建三维骨架增强环氧树脂的导热性能姚健（海南大学材料科学与工程学院，海南海口 570228）摘要：以提纯的光伏晶硅废料为原料，添加高导热的片状BN粉末，采用冰模板法与真空浸渗环氧树脂（EP）相结合的方法制备了EP/Si 3N 4-SiC-BN复合材料，并研究了其性能。

结果表明：Si粉氮化反应产生的晶须在Si 3N 4-SiC-BN三维网络骨架中相互接触并分布在垂直定向的孔隙通道内；BN用量为晶硅废料质量的20%时，EP/Si 3N 4-SiC-BN复合材料的热导率最大，为1.08 W/（m ·K ）；随着BN含量的增加，复合材料的抗弯强度降低，BN用量为晶硅废料质量的5%时，抗弯强度最大，为133.6 MPa。

关键词：环氧树脂光伏晶硅废料氮化硅碳化硅氮化硼冰模板法热导率中图分类号： TQ 323.5 文献标志码： B 文章编号： 1002-1396（2023）06-0016-06Thermal conductivity of epoxy resin enhanced by constructing3D framework with photovoltaic crystalline silicon wasteYao Jian（School of Materials Science and Engineering ，Hainan University ，Haikou 570228，China ）Abstract ： The epoxy resin （EP ）/Si 3N 4-SiC-BN composites were prepared by the combination of ice-templating and vacuum impregnated EP，using purified photovoltaic silicon waste as raw material and adding high thermal conductivity flaky BN powder. The results showed that the crystal whiskers produced by the nitriding of silicon powder were interlinked in the Si 3N 4-SiC-BN skeletons and distributed in vertically orientedpore channels. The maximum thermal conductivity of 1.08 W/（m ·K ） was obtained for the EP/Si 3N 4-SiC-BN composites at the high 20% BN addition. The flexural strength of the composites decreased with the increase ofBN addition and the maximum flexural strength was 133.6 MPa at 5% BN addition.Keywords ： epoxy resin； photovoltaic silicon waste； silicon nitride； silicon carbide； boron nitride； ice-templating； thermal conductivityDOI：10.19825/j.issn.1002-1396.2023.06.04收稿日期： 2023-05-27；修回日期： 2023-08-26。

The effect of deep excavation-induced lateral soil movements

ORIGINAL ARTICLEThe eﬀect of deep excavation-induced lateral soil movements on the behavior of strip footing supported on reinforced sandMostafa El Sawwaf *,Ashraf K.NazirStructural Engineering Department,Faculty of Eng.,Tanta University,Tanta,Egypt Received 28August 2011;revised 13October 2011;accepted 2November 2011Available online 3December 2011KEYWORDSGranular soil reinforcement;Strip footing;Footing load level;Settlement;Deep excavationAbstract This paper presents the results of laboratory model tests on the inﬂuence of deep exca-vation-induced lateral soil movements on the behavior of a model strip footing adjacent to the exca-vation and supported on reinforced granular soil.Initially,the response of the strip footings supported on un-reinforced sand and subjected to vertical loads (which were constant during the test)due to adjacent deep excavation-induced lateral soil movement were obtained.Then,the effects of the inclusion of geosynthetic reinforcement in supporting soil on the model footing behavior under the same conditions were investigated.The studied factors include the value of the sustained footing loads,the location of footing relative to the excavation,the affected depth of soil due to deep excavation,and the relative density of sand.Test results indicate that the inclusion of soil rein-forcement in the supporting sand signiﬁcantly decreases both vertical settlements and the tilts of the footings due to the nearby excavation.However,the improvements in the footing behavior were found to be very dependent on the location of the footing relative to excavation.Based on the test results,the variation of the footing measured vertical settlements with different parameters are presented and discussed.ª2011Cairo University.Production and hosting by Elsevier B.V.All rights reserved.IntroductionIn urban areas,there are many situations where basement con-struction or underground facilities such as cut-and-cover tun-nels are proposed to be constructed adjacent to old buildings.Of greatest concern are buildings with shallow foun-dations that do not extend below the zone of inﬂuence of the adjacent excavation.Due to the greater depth of the founda-tion level of the new building below the existing foundation le-vel of the old building,the excavation needs to be braced during foundation construction.A major concern is to prevent or minimize damage to adjacent buildings and underground utilities using different types of retaining monly adopted wall types include contiguous piles,secant piles,sheet*Corresponding author.Tel./fax:+20403352070.E-mail address:Mos_sawaf@ (M.El Sawwaf).2090-1232ª2011Cairo University.Production and hosting by Elsevier B.V.All rights reserved.Peer review under responsibility of Cairo University.doi:10.1016/j.jare.2011.11.001pile wall or diaphragm walls.However,basement excavation works for the new building always cause ground movements in soil under foundations of adjacent building behind the retaining structure.These soil movements due to excavation in front of a retaining wall in turn can induce large deﬂection which may lead to structural distress and failure on the foun-dations supporting existing structures behind the wall.The magnitude and distribution of ground movements for a given excavation depend largely on soil properties,excavation geom-etry including depth,width,and length,and types of wall and support system,and construction procedures.Because of the great effects of deep excavation-induced ground movements on the nearby structures,the assessment of ground movements’effects of deep excavations has been the subject of interest of several studies.Most of these re-searches have been on the prediction of ground settlement and the lateral movement associated with deep excavation [1–8].Clough and O’Rourke[2]extended the work by Peck [1]and developed empirical settlement envelopes.Ou et al.[3]compiled and analyzedﬁeld data regarding wall movement associated with deep excavation and deﬁned the apparent inﬂuence range for damage assessment of adjacent structures. Yoo[5]collectedﬁeld data on lateral wall movement for walls constructed in soils overlying rock from more than60different excavation sites and analyzed the data with respect to wall and support types.Also,Leung and Ng[8]collected and analyzed ﬁeld monitored data on lateral wall deﬂection and ground sur-face settlement of the performance of14multi propped deep excavations in mixed ground conditions.Since many high-rise buildings are supported on pile foun-dations,there is a concern that lateral ground movements resulting from the soil excavation may adversely affect the nearby pile foundation systems.Several numerical and experi-mental studies were conducted to examine the behavior of piles subject to excavation-induced soil movement[9–15].These studies have demonstrated that lateral soil movements from excavation activities can be detrimental to nearby existing piles.Several studies have reported the successful use of soil rein-forcement as a cost-effective method to improve the load–set-tlement behavior of cohesionless soils under shallow foundations[16–23].This was achieved by the inclusion of multiple layers of geogrid at different depths and widths under the footing.These reinforcements resist the horizontal shear stresses built up in the soil mass under the footing and transfer them to the adjacent stable layers of soils and thereby improve the vertical behavior of the footing.The focus of the aforementioned previous studies were the estimation of maximum wall movement,the estimation of ground surface settlement,its effect on the exciting deep pile foundations and the potential of damage to occur to adjacent building due the differential settlement.However to the best knowledge of the author,the behavior of shallow footing sup-ported on either un-reinforced or reinforced soil adjacent to deep excavation has not been investigated.Hence,there is a lack of information in the literature about the effect of deep excava-tion-induced lateral soil movements on the behavior of reinforced soil loaded by strip loading.Therefore,the aim of this research was to model the retaining wall rotations and its effect on the behavior of a strip footing supported on either un-reinforced or reinforced sand.The object was to study the relationships between the lateral soil displacements due to deep excavation and the response of model footings and the variable parameters including initial relative density of sand,the foot-ing load level,and the location of the footing relative to the excavation.Model box and footingThe experimental model tests were conducted in a test box, having inside dimensions of 1.00m·0.50m in plan and 0.50m in depth.The test box is made from steel with the front wall made of20mm thickness glass and is supported directly on two steel columns.These columns areﬁrmlyﬁxed in two horizontal steel beams,which areﬁrmly clamped in the lab ground using4pins.The glass side allows the sample to be seen during preparation and sand particle deformations to be observed during testing.The tank box was built sufﬁciently ri-gid to maintain plane strain conditions by minimizing the out of plane displacement.To ensure the rigidity of the tank,the back wall of the tank was braced on the outer surface with two steel beamsﬁtted horizontally at equal spacing.The inside walls of the tank are polished smooth to reduce friction with the sand as much as possible by attachingﬁber glass onto the inside walls.In order to correctly simulate the deep excava-tion-induced ground movement characteristics on the adjacent footing,a498mm in length steel plate made with rotating hinge was used as shown in Fig.1.The steel plate was allowed to rotate anticlockwise direction around the hinge and the resulting settlements of the footing due to the lateral move-ments of soil under the footing were measured.A model strip footing made of steel with a hole at its top center to accommodate a bearing ball was used.The footing was498mm long,80mm in width and20mm in thickness. The footing was positioned on the sand bed with the length of the footing running the full width of the tank.The length of the footing was made almost equal to the width of the tank in order to maintain plane strain conditions.The two ends of the footing plate were polished smooth to minimize the end friction effects.A rough base condition was achieved byﬁxing a thin layer of sand onto the base of the model footing with epoxy glue.The load is transferred to the footing through a bearing ball.Such an arrangement produced a hinge,which al-lowed the footing to rotate freely as it approached failure and eliminated any potential moment transfer from the loading ﬁxture.The loading system consists of a horizontal lever mecha-nism with an arm ratio equal to4,pre-calibrated load cell, and incremental weights as shown in Fig.1.The load was applied by small incremental weights which were maintained constant until the footing vertical displacements had stabilized. The settlement of the footing was measured using two50mm travel dial gauges accurate to0.001mm placed on opposite sides of the footing at points A and B.Material and methodsTest materialThe sand used in this research is medium silica sand washed, dried and sorted by particle size.It is composed of rounded to sub-rounded particles.The speciﬁc gravity of the soil parti-cles was measured according to ASTM standards854.Three tests were carried out producing an average value of speciﬁc338M.El Sawwaf and A.K.Nazirgravity of2.66.The maximum and the minimum dry unit weights of the sand were found to be18.44and15.21kN/m3 and the corresponding values of the minimum and the maximum void ratios were0.44and0.75.The particle size dis-tribution was determined using the dry sieving method and the results are shown in Fig.2.The effective size(D10),the mean particle size(D50),uniformity coefﬁcient(C u),and coefﬁcient of curvature(C c)for the sand were0.12mm,0.38mm, 4.25and0.653respectively.In order to achieve reasonably homogeneous sand beds of reproducible packing,controlled pouring and tamping techniques were used to deposit sand in layers into the model box.In this method the quantity of sand for each layer,which was requiredrelative density,wasﬁrst weighed toand placed in the bin and eliminatedcompactor until achieving the requiredimental tests were conducted onaverage unit weights of16.37and17.50kN/m3representing loose and dense conditions,respectively.The relative densities of the samples(R d)were35%and75%,respectively.The esti-mated internal friction angle of the sand determined from direct shear tests using specimens prepared by dry tamping at the same relative densities were33.2°and39.4°,respectively.Geogrid reinforcementOne type of geogrid with peak tensile strength of13.5kN/m was used as reinforcing material for the model tests.Typical physical and technical properties of the grids were obtained from manufacturer’s data sheet and are given in Table1.Fig.1Schematic view of the experimental apparatus.size distribution of the used sand.Table1Engineering properties of geogrid. StructureAperture shapeAperture size,mm·mmPolymer typeWeight,g/m2Tensile strength at2%strain,kN/mTensile strength at5%strain,kN/mAt peak tensile strength kN/mThe experimental setup and test programThe experimental work aimed to study the effects of deep exca-vation-induced lateral soil movements on the behavior of a strip footing placed at different locations adjacent to the exca-vation and supported on either un-reinforced or reinforced sands.A425mm in height soil model samples were constructed in layers with the bed level and excavation ob-served through the front glass wall.Initially beds of either loose or dense sand were placed by pouring and tamping.In the reinforced tests,layers of geogrid were placed in the sand at predetermined depths during preparing the ground soil. The inner faces of the tank were marked at25mm intervals to facilitate accurate preparation of the sand bed in layers. On reaching the reinforcement level,a geogrid layer was placed and a layer of sand is poured and tamped and so on.The prep-aration of the sand bed and geogrid layers was continued in layers up to the level required for a particular depth of embed-ment.Great care was given to level the sand using special rulers so that the relative density of the top surface was not af-fected.The footing was placed at desired position andﬁnally the load was applied incrementally until it reached the required value and it was kept constant during the test.All tests were conducted with new sheets of geogrid used for each test.It should be mentioned that three series of tests were performed to study the effects of the depth of a single geogrid layer(u), the vertical spacing between layers(x)and the layer length (L)as shown in Fig.3.These series were performed on footings supported on dense sand using three layers of geogrid(N=3). The maximum improvement was obtained at depth ratio of u/ B=0.30,x/B=0.60and L/B=5.0.Theseﬁndings were consistent with the observed trends reported by Das and Omar [19],and El Sawwaf[22].Therefore,the test results andﬁgures are not given in the present manuscript for brevity and the val-ues of u/B=0.30and x/B=0.60and L/B=5.0were kept constant in the entire test program.A total of50tests in three main groups were carried out. Tests of group I(series1–3)were performed on model footing supported on sands with excavation at loose and dense condi-un-reinforced sand.In these tests,sand samples were set up at the required relative density.Then,the footing was placed in position and the load was applied incrementally until it reached the required value which was kept constant until the end of the test.Finally,the wall was forced to rotate and both lateral displacement of the wall and the vertical settlement of the footing were observed and measured.The studied param-eters include the value of footing load level(q m/q u),the loca-tions of the footing from the excavation(b/B),the relative density of sand(R d),and the different heights of rotation (H/B).Finally group III(series10–15)were carried out to study the effect of deep excavation-induced lateral soil move-ments on the behavior of strip model footing when placed on reinforced sand.The geometry of the soil,model footing, deep excavation and geogrid layers is shown in Fig.3.Table 2summaries all the tests programs with both the constant and varied parameters illustrated.Several tests were repeated at least twice to examine the performance of the apparatus, the repeatability of the system and also to verify the consis-tency of the test data.Very close patterns of load–settlement relationship with the maximum difference in the results of less than3.0%were obtained.The difference was considered to be small and negligible.It demonstrates that the used technique procedure and adopted loading systems can produce repeat-able and acceptable tests results.Results and discussionBearing capacity testsModel footing tests were carried out on un-reinforced loose and dense sands to measure the ultimate bearing capacity and the associated settlement of the model footing to establish the required values of the sustained constant load during the tests.Several values of monotonic loads applied prior to soil excavation were adopted to represent different values of factors of safety(FS=q u/q m).The footing settlement(S)is ex-pressed in non-dimensional form in terms of the footing width (B)as the ratio(S/B,%).The bearing capacity improvement of the footing on the reinforced sand is represented using a non-dimensional factor,called bearing capacity ratio(BCR).This factor is deﬁned as the ratio of the footing ultimate pressure reinforced sand(q u reinforced)to the footing ultimate pressure when supported on un-reinforced sand(q u).The ultimate bear-ing capacities for the model footing are determined from the load–displacement curves as the pronounced peaks,after which the footing collapses and the load decreases.In curves which did not exhibit a deﬁnite failure point,the ultimate load is taken as the point at which the slope of the load settlement curveﬁrst reach zero or steady minimum value[24].The mea-sured bearing load of model footing supported on un-rein-forced loose,and dense sands are147,and510N respectively.Typical variations of bearing capacity pressure(q)of foot-ing supported on dense sand with settlement ratio(S/B)for different number of geogrid layers are shown in Fig.4a.The behavior of the footing placed on un-reinforced sand is in-cluded in theﬁgure for comparison.Theﬁgure clearly shows that soil reinforcement greatly improves both the initial stiff-ness(initial slope of the load–settlement curves)and the bear-ing load at the same settlement level.Also,for the same footing load,the settlement ratio decrease signiﬁcantly by340M.El Sawwaf and A.K.Nazirincreasing the number of geogrid layers.The curves show thatthe inclusion of four geogrid layers resulted in the increase of the ultimate bearing load to294.01kN/m2relative to a value of125.28kN/m2for the case of un-reinforced sand.However, these improvements in bearing capacity were accompanied with an increase in both settlement ratio and footing tilt.This increase in footing ultimate load can be attributed to reinforcement mechanism,which limits the spreading and lat-eral deformations of sand particles.The mobilized tension in the reinforcement enables the geogrid to resist the imposed horizontal shear stresses built up in the soil mass beneath the loaded area.With increasing the number of geogrid layers, the contact area and interlocking between geogrid layers and soil increases.Consequently,larger soil displacements and hor-izontal shear stresses built up in the soil under the footing were resisted and transferred by geogrid layers to larger mass of soil. Therefore,the failure wedge becomes larger and the frictional resistance on failure planes becomes greater.The effect of number of geogrid layersTypical variations of BCR measured from model tests against number of layers are shown in Fig.4b.Two series of tests were carried out with all the variable parameters were kept constant except the number of layers was varied.It can be seen that the BCR much improves with the number of geogrid layers for both relative densities of sand.However,the effect of soil rein-forcement in dense sand is much greeter than that when placed in loose sand.The curves show that the increase in the BCR is signiﬁcant with increasing number of geogrid layers until N=3after which the rate of load improvement becomes much less.Similar conclusion that N=3is the optimum num-ber of layers were given by previous studies of centrally loaded strip or square plates over reinforced sands[16,19,22].How-ever,it should be mention that the optimum number of geogrid layers is much dependent on the vertical spacing be-tween geogrid layers and the embedment depth of theﬁrst layer.This is due to the fact that soil reinforcement is signiﬁ-cant when placed in the effective zone under the footing. Deep excavation-induced lateral displacements testsModel tests were carried out to model the rotation of retaining wall and the associated lateral soil displacements on the behav-ior of adjacent strip footing supported on either un-reinforcedBehavior of strip footings adjacent to deep excavation341or reinforced sand at different densities.In these tests,the model retaining walls were forced to rotate around a hinge. The settlements and tilts of the model footings due to the wall rotations were measured.The lateral wall displacement(D)at the wall top was measured as shown in Fig.3and the wall rotation is expressed in non-dimensional form as the ratio D/H,%).The improvements in deep excavation nearby-modelIn order to investigate the effect of footing load level on the deep excavation-nearby footing behavior,three different val-ues of q m/q u equal to0.30,0.45,and0.60were applied to the footing and were kept constant before allowing the retaining wall to rotate.In these tests,the depth of excavation(H/ B=3)along with the location of the footing(b/B=0)were kept constant.Fig.5shows typical variations of wall rotation (D/H)against settlement ratio(S/B)for model footings sup-ported on both un-reinforced and reinforced dense sand.The ﬁgure shows that the footing settlement increases signiﬁcantly with increasing the value of footing load q m/q u particularly when supported on un-reinforced sand.However,the inclusion of soil reinforcement not only much improves footing behavior and signiﬁcantly decreases the footing settlements but also provided more stability to the footing.For example,footing on un-reinforced sand loaded with q m/q u=0.45and0.60 and subjected to wall rotation failed with punching and tilted. However,the inclusion of soil reinforcement signiﬁcantly de-creased the deformations of supporting soil and no punching failure was observed.Fig.6a shows the variations of settlement ratio S/B with the footing load level q m/q u of footing supported on un-reinforced and reinforced sands set up at both loose and dense conditions. It can be seen that the footing settlement increases with increasing monotonic load level.Theﬁgure clearly indicates that geogrid reinforcement causes signiﬁcant reduction in the footing settlement in dense sand particularly at greater footing load level.However,the inclusion of soil reinforcement in loose sands causes little effect on the footing behavior.Effect of footing location relative to the excavationIn order to study the effect of the proximity of a footing to the excavation(b/B),four series of tests were carried out on model footings placed at different locations as shown in Table2.While theﬁrst two series were carried out on un-reinforced loose and dense sands,the other two series were performed on reinforced sands set up at the same relative densities.The variations of the settlement ratio S/B against the footing locations b/B are shown in Fig.6b.As the footing location moves away from the excava-tion,the effect of deep excavation-induced lateral soil move-ments decreases.However,the effect of deep excavation on the footing behavior is obvious until a value of about b/B=3 after which the effect can be considered constant.Also,it can be seen that the inclusion of soil reinforcement in dense sands causes greater effect on the footing behavior when the footing location was closer to the excavation.The effect of the height of rotationWhen approaching failure,a yield point is mobilized about which the retaining system may rotate.The depth of the af-fected depth of soil under the footing depends on the location of this point.However the location of this point depends in turn on several factors including type of soil,excavation depth, type of retaining system,the stiffness of retaining system and the support system.In order to study the effect of the depth of affected soil(H)under the footing due to the wall rotation, four series of tests were performed on model footing supportedFig.5Variations of S/B with D/H for different values of footing load level.on un-reinforced and reinforced dense sands.In these tests,the value of the footing load (q m /q u =0.30)was kept constant.Fig.6c shows the variations of the settlement ratio S /B against the ratio H /B for un-reinforced and reinforced dense sands.It is clear that the increase in the depth of excavation directly causes the footing settlement to increase.However the rate of increase is moderate until a value H /B =2.5after which the effect of H /B is signiﬁcant.However,the ﬁgure shows the beneﬁcial effect of soil reinforcement in decreasing footing settlement particularly at greater height of affected depth of soil for both locations of strip footing.Scale effectsThe present study indicated the beneﬁts that can be obtained when using geogrid to reinforce sandy soil on the behavior of an existing strip footing adjacent to deep excavation and provided encouragement for the application of geosynthetic reinforcement under footing placed at shallow depths.How-ever,the physical model used in this study is small scale while the problem encountered in the ﬁeld is a prototype footing-cell system.Although the use of small scale models to investigate the behavior of full scale foundation is a widely used tech-nique,it is well known that due to scale effects and the nature of soils especially granular soils,soils may not play the same role in the laboratory models as in the prototype [24].Also,the used reinforcement in this study are prototype geogrid while the used footing was reduced to a certain scale.Further-more,it should be noted that the experimental results were obtained for only one type of geogrid,one size of footing width,and one type of sand.Therefore,application of test results to predict the behavior of a particular prototype relying on these results cannot be made until the above limitations were considered.Despite this,test results provide a useful basis for further research using full-scale tests or centrifugal model tests and numerical studies leading to an increased understanding of the real behavior and accurate design in application of soil reinforcement.ConclusionsThe effect of deep excavation-induced lateral soil movements on the behavior of adjacent shallow strip footing resting on un-reinforced and reinforced sands were modeled and studied.The response of model footings due to the rotation of retaining wall and the associated lateral soil displacements wereare,the greater are footing settlements and tilts.Reinforce-ment is most effective when the footing is placed closer to the excavation and the inﬂuence of the excavation on the foot-ing behavior may be neglected once footing was placed a dis-tance of more than three footing width from the excavation.References[1]Peck RB.Deep excavations and tunneling in soft ground.State-of-the-art report.In:Proceedings of the 7th international conference on soil mechanics found engineering.Mexico;1969.p.225–90.[2]Clough GW,O’Rourke TD.Construction induced movements of in situ walls.In:Proceedings of the design and performance of earth retaining structures.Geotechnical Special Publication,vol.25,no.4.New York:ASCE;1990.p 390–470.[3]Ou CY,Hsieh PG,Chiou DC.Characteristics of ground surface settlement during excavation.Can Geotech J 1993;30:758–67.[4]Long M.Database for retaining wall and ground movements due to deep excavations.J Geotech Geoenviron Eng 2001;127(3):203–24.[5]Yoo C.Behavior of braced and anchored walls in soils overlying rock.J Geotech Geoenviron Eng 2001;127(3):225–33.[6]Wang ZW,Ng CW,Liu GB.Characteristics of wall deﬂections and ground surface settlements in Shanghai.Can Geotech J 2005;42(5):1243–54.[7]Liu GB,Ng CW,Wang ZW.Observed performance of a deep multi-strutted excavation in Shanghai soft clays.J Geotech Geoenviron Eng 2005;131(8):1004–13.[8]Leung HY,Ng CW.Wall and ground movements associated with deep excavations supported by cast in situ wall in mixed ground conditions.J Geotech Geoenviron Eng 2007;133(2):129–43.[9]Finno RJ,Lawence SA,Allawh NF.Analysis of performance of pile groups adjacent to deep excavation.J Geotech Eng ASCE 1991;117(6):934–55.[10]Poulos HG,Chen LT.Pile response due to unsupportedexcavation-induced lateral soil movement.Can Geotech J 1996;33:670–7.[11]Poulos HG,Chen LT.Pile response due to excavation-inducedlateral soil movement.J Geotech Geoenviron Eng 1997;123(2):94–9.[12]Chow YK,Yong KY.Analysis of piles subject to lateral soilmovements.J Inst Eng Singapore 1996;36(2):43–9.[13]Chen LT,Poulos HG.Piles subjected to lateral soil movements.J Geotech Geoenviron Eng 1997;123(9):802–11.[14]Leung CF,Chow YK,Shen RF.Behavior of pile subject toexcavation-induced soil movement.J Geotech Geoenviron Eng 2000;126(11):947–54.。

南京邮电大学硕士研究生学位论文第...

本文以具有球冠微结构的固体表面为研究模型，从本征亲水和本征疏水两个角度分析了表面微结构对固体表面浸润性的影响。对于本征亲水材料，基于吉布斯自由能最小化原理研究了具有球冠微结构材料上固液之间的接触状态，结果表明：液滴会与材料表面完全接触，并且当材料的本征接触角小于 58°时，固液接触角将达到 0°。由于固液接触角为 0°与常理不吻合，进一步分析表明，若材料本征接触角小于 74°，液滴将发生扩散，Wenzel 方程不再适用，并给出了液滴在扩散条件下的固液之间接触角的解析表达式。对于本征疏水材料，本文从粗糙表面固液接触角的 Wenzel 状态和 Cassie 状态出发，研究了球冠微结构表面的浸润性与结构参数之间的关系。结果表明，Cassie 状态下表观接触角随球冠直径与相邻球冠之间距离比的增大而增大，随相邻四个球冠构成的菱形单元内角的增大而增大，并以液滴的 Cassie 状态与 Wenzel 状态势能差越大越稳定为判据，给出了球冠微结构表面的稳定条件，即球冠直径与相邻球冠间的距离比为 1，相邻四个球冠构成的菱形单元锐角内角为 60°。本文最后还研究了与球冠微结构表面相对应的碗状微结构表面的浸润性，研究发现，在相同的结构参数下，对于提高本征弱疏水材料的疏水性而言，碗状微结构要优于球冠微结构。
Key words: wettability, contact angle , hemisphere microstructure, bowl microstr第一章绪论 ..............................................................................................................................................................1 1.1 背景 ..............................................................................................................................................................1 1.2 润湿性的研究现状及其应用 ......................................................................................................................2 1.3 本文的研究目的及研究方法 ......................................................................................................................6 1.4 本文的工作 ..................................................................................................................................................7

AFM作粘弹性材料力学性质的测试

AFM Nanoindentation of Viscoelastic Materials with Large End-Radius ProbesGUNTER MOELLERAnalytical &Systems Research,Arkema Inc.,King of Prussia,PennsylvaniaReceived 31March 2009;revised 26May 2009;accepted 29May 2009DOI:10.1002/polb.21758Published online in Wiley InterScience ().ABSTRACT:We used atomic force microscopy (AFM)nanoindentation to measure me-chanical properties of polymers.Although AFM is generally acknowledged as a high-resolution imaging tool,accurate quantiﬁcation of AFM nanoindentation results is challenging.Two main challenges are determination of the projected area for objects as small as AFM tips and use of appropriate analysis methods for viscoelastic mate-rials.We report signiﬁcant accuracy improvements for modulus measurements when large end-radius tips with appropriate cantilever stiffnesses are used for ing this approach,the instantaneous elastic modulus of four polymers we studied was measured within 30to 40%of Dynamic Mechanical Analysis (DMA)results.The probes can,despite their size and very high stiffnesses,be used for imaging of very small domains in heterogeneous materials.For viscoelastic materials,we developed an AFM creep test to determine the instantaneous elastic modulus.The AFM method allows application of a nearly perfect stepload that facilitates data analysis based on hereditary integrals.Results for three polymers suggest that the observed creep in the materials has a strong plastic ﬂow component even at small loads.In this respect,the spherical indenter tips behave like ‘‘sharp’’indenters used in indentationstudies with instrumented indenters.VC 2009Wiley Periodicals,Inc.J Polym Sci Part B:Polym Phys 47:1573–1587,2009Keywords:atomic force microscopy (AFM);creep;indentation;plastics;viscoelasticpropertiesINTRODUCTIONIndentation analysis is used to determine the me-chanical properties of an indented material from a plot of indentation force versus depth of inden-tation.The most common mechanical properties determined this way are the indentation modulus and hardness.Once the indentation modulus is known,the elastic modulus can be determined if the Poisson ratio of the indented material is known.1Methods and protocols for indentationanalysis using instrumented indenters like theHysitron or MTS systems are well established for homogeneous materials,ﬁlms,or heterogeneous materials with very large domains.1In many heterogeneous materials,domains are very small on the order of micrometers to nano-meters only.Accurate determination of local me-chanical properties in such materials through in-dentation analysis using conventional contact mechanics models requires minimizing matrix effects.Matrix effects can be minimized by lower-ing the size of the indenter and the contact load.For instrumented indenters,load limits are above 1l N and typical indenter dimensions are 1to 100micrometers.Journal of Polymer Science:Part B:Polymer Physics,Vol.47,1573–1587(2009)V C 2009Wiley Periodicals,Inc.Correspondence to:G.Moeller (E-mail:gunter.moeller@)1573To understand what that means in terms of matrix effects,consider the following:Using Hertz equations,the indentation depth at a load of1l N will be0.43l m when a material with an elastic modulus of2MPa and a Poisson ratio of0.5is indented using a spherical indenter with a radius of1l m.From thinﬁlm indentation analysis,it is known that matrix effects already have a signiﬁ-cant effect when the indentation depth is around 1/10of theﬁlm thickness.2Assuming the same size effects hold true for domains in heterogene-ous materials,the resolution limit for the1-micro-meter indenter is4.3l m or larger at an indenta-tion depth of0.43l m,which shows that the method is limited to fairly large domains.Lower-ing the diameter of the spherical indenter in our example and keeping the load constant will result in a higher indentation depth at the same load, which may minimize matrix effects from lateral conﬁnement of the domain but increase matrix effects caused by the matrix underneath the in-denter,unless the load can be further reduced. Besides load resolution and indenter size limita-tions,instrumented indenters have no or very limited imaging capabilities.Therefore,even if mechanical properties of individual domains could be measured accurately,visualization of these domains for position targeting of the indents may not be possible using traditional technology.Atomic force microscopy(AFM)can overcome most of these limitations.In AFM,very low loads of50nN or less can be applied with acceptable noise levels and feedback loop performance and standard AFM probes have an end-radius of only 10to30nm.AFM is also a high-resolution imag-ing tool for visualization of individual domains in nanostructured materials like polymers.Imaging resolution limits of less than1nm are reported, but the practical resolution limit using standard AFM probes is around10nm for most polymers.3 However,even though AFM has been used suc-cessfully to probe mechanical properties on the nanoscale,4–14it is generally seen as a semi-quan-titative method since accurate quantiﬁcation of AFM nanoindentation results is challenging.15–19 Poor accuracy and repeatability of AFM results is caused by convolution of cantilever deﬂection and movement of the piezoelectric ceramic used to displace the sample or scanner head,errors in cantilever spring constant determination,and inaccurate tip shape determination.Another im-portant source of error is use of purely elastic con-tact mechanics models to interpret results for viscoelastic materials like polymers.16,20–22Conse-quently,indentation studies with viscoelastic materials performed with both AFM and instru-mented indenters suggest that the Oliver Pharr method,23–25which is commonly used to extract the elastic modulus from force distance curves, does not produce accurate results for the instanta-neous elastic modulus of materials that exhibit signiﬁcant viscoelastic behavior.26–33Clifford and Seah addressed quantiﬁcation issues for elastic modulus measurements with AFM in much detail.On the basis of the results for nine different polymers,they recommend an indirect route for studying mechanical properties of nanodomains in heterogeneous materials, which includes measuring reference samples with a calibrated instrumented indenter and using the same materials to calibrate the AFM18before indenting nanodomains.Following this route, they found the elastic modulus of unknown poly-mers may be calculated within20%error using AFM.VanLandingham did detailed nanoindenta-tion studies of polymers using instrumented indenters and AFM.Although he acknowledges the value of AFM nanoindentation,he recom-mends using the technique for comparative stud-ies only and not absolute measurements of me-chanical properties especially when polymers are investigated.16Mogonov points out that quantiﬁ-cation issues with AFM nanoindentation will not be solved unless the true projected area of nano-meter sized objects can be measured with higher accuracy.17Tranchida is much more optimistic with regards to accuracy,but points out that the method only produces accurate results if the elas-tic limits are not exceeded and proper data analy-sis techniques and models are used.24This article is concerned with accuracy improvements in the mechanical analysis of poly-mers based on AFM nanoindentation.The goal is to improve accuracy of traditional AFM indenta-tion for viscoelastic materials without sacriﬁcing too much of the superb high resolution imaging capabilities of AFM,so that small domains in het-erogeneous materials can be imaged and targeted for local mechanical analysis.Weﬁrst demonstrate the accuracy levels that can be achieved when standard AFM probes are used and standard experimental protocols are followed for calibration and data analysis.We then show AFM indentation results for large end-radius probes and demonstrate how accuracy may improve when these probes are used.Four different polymers are indented,each of them with three independently calibrated large1574MOELLERJournal of Polymer Science:Part B:Polymer PhysicsDOI10.1002/polbend-radius probes.The elastic moduli of the poly-mers chosen vary from$20MPa to2.2GPa.AFM probes with cantilever stiffnesses from2.9N/m to 948N/m and end-radii from$30nm to761nm are used.AFM results are compared with DMA and instrumented indenter results,which are used as a reference.To assess the imaging capa-bilities of the large end-radius probes,we imaged an epoxy polymer blend with micrometer-sized rubbery particles dispersed in it.The sample was imaged in tapping mode with four different large end-radius probes and one standard tapping mode probe.Radii of the large end-radius probes varied from451nm to761nm.For viscoelastic materials,like polymers,we developed an AFM creep test.We show how accu-racy for instantaneous elastic modulus results may improve when the modulus is calculated from the unloading curve based on proper selec-tion of creep hold time and unloading time. Results from unloading are compared with elastic modulus results obtained directly from a creep curve analysis.Data analysis of the creep curves is based on3D linear viscoelastic theory for step-loading using equivalent circuit models.The method has been outlined by VanDamme34for a conical indenter.Application to a spherical in-denter is straightforward.In the AFM method,a nearly perfect stepload can be applied so that data analysis based on hereditary integrals is greatly facilitated.27,35,36A combination of unload-ing analysis and creep curve analysis can approxi-mately deconvolute the elastic,viscoelastic,plas-tic,and viscoplastic deformation components. EXPERIMENTALWe studied four different polymers with elastic moduli ranging from20MPa to2.2GPa.The poly-mers are Pebax V R3533,Kynar V R740,Kynar V R2800, and Kynar V R2750resins.They are commercially available from Arkema.Prior to any indentation experiment,the samples were embedded in epoxy cement(Ted Pella),trimmed,and cryomicrotomed to generate aﬂat surface.A MFP-3D instrument from Asylum research was used for all AFM inden-tation experiments.Standard force distance curves were acquired at indentation rates between 0.1and10l m/s using the MFP-3D software.Load-controlled creep tests were performed using cus-tomized software,which controls the piezoelectric ceramic and the cantilever deﬂection signal via feedback loops.The creep tests consisted of a 20ms stepload,a hold period,and unload.The hold period is varied between200ms and90s and the unloading time was varied between20ms and 60s.All results reported are based on average val-ues for several creep curves or force distance curves, which were usually acquired at three different areas on the microtomed sample surfaces.Details are given in the text.Loads between200nN and120 l N were applied.We used RTESP type AFM probes from Veeco instruments as well as four different types of LRCH probes from Team Nanotec.Cantile-ver stiffnesses of the probes vary from2.9N/m to 948N/m.End-radii of the RTESP probes vary from 10nm to50nm.The LRCH probes have much larger end-radii of530nm to761nm.The tempera-ture for all indentation experiments was kept at20 Æ1 Celsius.AFM images of a proprietary Arkema epoxy polymer were taken using a Veeco Dimension AFM in tapping mode.For comparison with AFM indentation data, the elastic moduli of the polymers were deter-mined using dynamic mechanical analysis(DMA) and an instrumented indenter.Pebax V R3533poly-mer was indented with a Hysitron TI900 Triboindenter V R at room temperature using a dia-mond60 conical probe with a5-l m radius.The elastic modulus was determined from the unload-ing part of the force distance curve using the Oliver Pharr method.DMA of Pebax V R3533and all three Kynar V R polymers was done using a RDA III instrument from Rheometric Scientiﬁc.Force distance curves and creep curves were analyzed using customized software to determine the instantaneous elastic modulus directly from the creep curve.34The tip shape and Poisson ratios of the indented materials are input parameters for the algorithms to determine the elastic modulus.The Poisson ratios were taken from the open literature.The tip shape was determined from Scanning Electron Microscopy(SEM)images.The cantilever deﬂec-tion calibration was done by acquiring force dis-tance curves on a silicon sample.Nine to20force distance curves at three different locations were acquired for calibration.The spring constant of the cantilever was determined with the thermal noise method using the standard software algorithm of the MFP-3D AFM,as well as the Sader method.37Accuracy Challenges for Elastic Modulus Determination via AFM NanoindentationIt is well known that accurate calculations of me-chanical properties based on AFM force distanceAFM NANOINDENTATION OF VISCOELASTIC MATERIALS1575Journal of Polymer Science:Part B:Polymer PhysicsDOI10.1002/polbcurves are a challenge.This is particularly true for the elastic modulus.15–19To demonstrate empirically what accuracy levels can be expected,we indented a Pebax V R3533elastomer with three independently calibrated standard tapping mode probes.Figure 1shows a typical force distance curve.The elastic modulus was determined from the unloading part of the curves using the Oliver Pharr method.23–25The Oliver Pharr method is widely used,even though it may produce in-accurate results for viscoelastic materials.16,21,31The material was indented with three independ-ently calibrated RTESP tapping mode probes with spring constants between 73.0N/m and 135.5N/m.In the commercial AFM used for this study,as well as most other AFM instruments,the cantile-ver is oriented at an angle of 11 relative to the sample plane.This may lead to signiﬁcant lateral movement when the sample is indented,and,unless the indenter is spherical,will result in deviations in the projected area from the case in which its main axis is exactly normal to the sam-ple surface.38Measurements of mechanical prop-erties,such as the elastic modulus,rely on accu-rate knowledge of the projected area.Therefore,these errors will directly impact accuracy of me-chanical properties calculations.We also note that only tractions normal to the surface of the in-denter are considered in common contact mechan-ics models used for indentation analysis.39Clearly ,this will add to the error.To approxi-mately compensate for the cantilever angle in our measurements,the AFM head was slightly tilted.Another source of error is the determination of the cantilever spring constant.Assuming linear elastic behavior,the spring constant error scales linearly with modulus.We used the ther-mal noise and Sader methods to determine springconstants.37,40–43According to Clifford,18typical errors for the thermal noise method,in spring constant determination are 15–20%.Proksch 44found that results for the thermal noise method are a strong function of the placement of the laser beam on the cantilever.He reports spring con-stant errors of up to 50%for this method when the laser is moved along the length of the cantile-ver.He also introduces a correction factor to mini-mize the placement error.The correction factor is 1.09for the case in which the laser is approxi-mated as a point at the end of the cantilever.We moved the laser beam from the center of the canti-lever towards the end until the reading of the photodiode dropped to around 80%of the value at the center.Assuming a laser spot size of 50l m,44this placement results in a correction factor of 1.04–1.07for our types of cantilevers.18We then determined the spring constant using the thermal noise method and compared results with those obtained from the Sader method.The Sader method requires knowledge of the dimensions of the cantilever,the resonance frequency,and the Q factor.The dimensions were obtained from SEM images,and the other parameters from the canti-lever frequency sweep and thermal tune results.We found agreement within 15%for the Sader and thermal noise methods following this approach.In the calculations we always used the value from the thermal noise method.For the Pebax V Rpolymer analysis,three sets of 5–10force distance curves per probe were obtained,each set at a different region of the sam-ple.To minimize surface roughness effects,the Pebax V R3533sample was cryomicrotomed before indentation to yield a ﬂat surface,and the inden-tation depth was always kept above 50nm but below 75nm to avoid nonlinearities in the photo-electrode detection signal.Surface roughness was determined from AFM measurements to be below 6nm after cryomicrotoming.We found that the RTESP probes wear signiﬁcantly during calibra-tion and,quite surprisingly,during polymer in-dentation experiments.This wear may result in large errors in the projected area.Clifford also observed probe wear during calibration.18For the modulus calculations,we calculated the area functions of the probes from SEM images obtained right after the polymer ing this approach,we measured average elastic modulus values between 16MPa and 44MPa for the three probes.Standard deviations for one probe are typically 10%for measurements in one area and $20%for measurements atdifferentFigure 1.AFM force distance curve of Pebax V R3533polymer,obtained with a RTESP tapping mode AFM probe.1576MOELLERJournal of Polymer Science:Part B:Polymer PhysicsDOI 10.1002/polbregions.The elastic modulus was also determined with a Hysitron TI-900Triboindenter and using DMA for comparison.The Triboindenter value is 20.1Æ2.42and the DMA value is 24.3Æ1.2.Two main factors limiting accuracy of AFM elastic modulus results are the size and shape of the indenter tip.The smaller the size of the in-denter,the less accurately the projected area can be determined.To minimize errors associated with the angled attack of the probe and cantilever bending,a spherical indenter should be used.To evaluate indenter size and shape effects on accuracy,we indented the same Pebax V R3533polymer with three independently calibrated large end-radius LRCH40probes.The LRCH40probes have a conical shape ending in a sphere.The vendor claims that the end-radius of the probes is 750nm.We determined the end-radii using our ﬁeld emission SEM and found that they actually vary from 530nm to 761nm.Figure 2shows an SEM image of LRCH40probe #1.As wekept the indentation depth below 85nm,the coni-cal part of the probe need not to be considered when calculating the area function.The LRCH40probes used have spring con-stants between 58.8N/m and 67.4N/m.The maxi-mum load applied was 1l N resulting in inden-tation depths of around 75nm.At this depth,the cantilever deﬂection is always below 75nm.Table 1summarizes the elastic modulus results for three independently calibrated LRCH40probes for the Pebax V R3533polymer.For refer-ence,elastic modulus results obtained with an instrumented indenter and DMA are shown as well.AFM results are based on three sets of 5to 10force distance curves for each LRCH40probe.Each set was obtained from a different region on the sample.A typical force distance curve is shown in Figure 3.Comparing the results from Table 1with the results for the RTESP probes,we see that the LRCH probes measure the elastic modulus with higher accuracy than the RTESP probes,as we expected.We also note that agreement with DMA is good,but that the instrumented indenter value is signiﬁcantly lower.We will discuss this last point later.To minimize matrix effects when analyzing het-erogeneous samples,the indentation depth needs to be minimized.Therefore,it is important to know the minimum indentation depth at which the elastic modulus can be measured with accept-able accuracy.At shallow indentation depths,the accuracy will be limited mainly by surface rough-ness.All samples in this study were cryomicro-tomed prior to indentation.This lowers the sur-face roughness to below 8nm.To evaluate the effects of surface roughness and shallow indenta-tion depths on elastic modulus results,we indented Pebax V R3533material with LRCH probes at depths of 20nm,40nm,and 65nm.ForTable 1.Elastic Modulus Results for Pebax V R3533Polymer Indented with Three Large End-Radius LRCH AFM Probes and Comparison with Instrumented Indenter and DMA ResultsElastic Modulus (MPa)AFM LRCH40Probe #324.6Æ2.9AFM LRCH40Probe #426.7Æ2.7AFM LRCH40Probe #530.3Æ3.5Average LRCH27.1Æ3.9Instrumented indenter 20.1Æ2.4DMA24.3Æ1.2Figure 2.SEM image of one of the large end-radius LRCH probes used.The probe is nearly perfectly spherical at indentation depths of less than 200nm.Figure 3.AFM force distance curve of Pebax V R3533polymer,obtained with a LRCH3AFM probe.AFM NANOINDENTATION OF VISCOELASTIC MATERIALS 1577Journal of Polymer Science:Part B:Polymer Physics DOI 10.1002/polbthe shallow depth experiments we used LRCH3 probes.These probes have spring constants between3N/m and6N/m compared to values of more than50N/m for the LRCH40probes.Origi-nally,the rationale behind this was to keep the deﬂection at comparable levels for very shallow and higher indentation depths.In experiments with LRCH3probes at higher depths we found, however,that these probes measure the elastic modulus at higher depths with no signiﬁcant loss in accuracy compared to the stiffer LRCH40 probes.We found that the average modulus value from multiple experiments does not signiﬁcantly change when the indentation depth is lowered from around80nm to20nm,but that the stand-ard deviation increases signiﬁcantly when the depth is lowered to20nm.Table2summarizes the results for65nm and20nm indentation depths.We note that,strictly speaking,changes in modulus with depth are not signiﬁcant,but the data suggest that the modulus is lower at lower indentation depths.Results in Table2are based on5to10indents at each of three different loca-tions on the cryomicrotomed sample.The increase in standard deviation is most likely a surface roughness effect.When the indentation depth is lowered to a value close to the root mean square of the surface roughness,the contact depth at asperities will signiﬁcantly deviate from the value for a perfectlyﬂat surface and cause a larger scat-ter in the values for the elastic modulus.Techni-cally,surface roughness should lower the pro-jected area at shallow depths when only asperities are in contact with the indenter.This will lower the true projected area and the modulus should increase.This concept,however,neglects that the asperities may provide less resistance to deforma-tion since they are not supported and may bend. If this is the correct picture,the modulus should actually drop.In Figures3and4,force distance curves obtained with LRCH3probes at maximum inden-tation depths of$40nm and65nm are shown.At a depth of40nm,the material behaves nearly perfectly elastically.At depths exceeding65nm, the trace and retrace curve do not overlap neatly anymore,which indicates onset of plastic defor-mation.It is important to note that a study of the elastic limits in a material like Pebax V R3533poly-mer using such small indenters cannot be done with an instrumented indenter,due to minimum load ing AFM,loads can be lowered to values much below1l N and this,in principle, allows the deconvolution of elastic deformation from plastic deformation,even when very small indenters are used.For the Pebax V R polymer we found that the unloading slope increases at indentation depths above70nm.This nosing effect is an indication of polymer creep.45Our results for different depths indicate that this creep is caused by viscoplastic-ity and not viscoelasticity.If viscoelasticity caused it,the curves wouldn’t overlay perfectly at shal-lower depths,unless the viscoelastic recovery is a very strong function of load and indentation depth.This is not what was observed for other polymers.46The nosing results in an overestima-tion of the contact stiffness and,therefore,higher elastic modulus values.For Pebax V R3533polymer this may result in$30%higher values for the elastic modulus for a maximum depth of80nm and at an indentation speed of1l m/s.As mentioned earlier,the instrumented in-denter value is signiﬁcantly smaller thanthe Figure4.AFM force distance curve of Pebax V R3533 polymer,obtained with a LRCH3AFM probe.Depth at maximum load is40nm.The material behaves nearly perfectly elastic.Table2.Elastic Modulus Results for Pebax V R3533 Polymer Indented with a Large End-Radius LRCH AFM probeAFM Probe IndentationDepth atMaximumLoadElasticModulus(MPa)AFM LRCH365nm24.4Æ1.8AFM LRCH320nm22.8Æ5.7The indentation depth at maximum load was varied from65nm to20nm.Elastic modulus changes are not signiﬁ-cant,but the standard deviation increases when the depth islowered.1578MOELLERJournal of Polymer Science:Part B:Polymer PhysicsDOI10.1002/polbAFM value at higher depths.The instrumented indenter value was obtained from an indentation experiment,which included a 20s hold period before unloading.At ﬁrst glance,our results indi-cate that time dependent processes,which are most likely viscoplastic effects,relaxed during the hold period and that the unloading was then mainly instantaneously elastic.This would explain why the AFM values for the elastic modu-lus at shallow depths are not signiﬁcantly differ-ent from the instrumented indenter values.This does not explain,however,why the DMA value is so high.Strains in the DMA measurements are very low to ensure that the elastic limits are not exceeded.It has been found by other investigators that the Oliver Pharr method may not produce accu-rate results for polymers.Indeed we found for Pebax V R3533that exponents for the Oliver Pharr unloading ﬁts deviate from the theoretical value of 1.5for a sphere.We determined exponents from 1.27to 1.5.Other investigators report higher exponents for polymeric materials.16,21From our analysis of the Pebax V Rpolymer,it is clear that the large end-radius probes can signiﬁ-cantly improve accuracy of results compared to standard AFM probes and that AFM results for the elastic modulus obtained from an Oliver Pharr ﬁt of the unloading curves are in good agreement with DMA results for this material as long as the indentation depths are not too large.At higher indentation depths,results may deviate due to plastic deformation.In the Oliver Pharr analysis it is assumed that the elastic recovery from a plastically deformed material is equivalent to the elastic recovery of a purely elastically deformed material;an assumption that may not be correct for materials like polymers.To evaluate the capabilities of the LRCH probes further,we performed an indentation study with three different ﬂuoropolymers.The polymers are Kynar V R740,Kynar V R2800,and Kynar V R2750res-ins.These polymers have elastic moduli between $500MPa (Kynar V R2750)and 2.2GPa (Kynar V R740).Three LRCH750probes with spring con-stants from 897.6N/m to 948N/m were used to indent the Kynar V R740polymer.The LRCH250probe used to indent the Kynar V R2800and Kynar V R2750polymers had a spring constant of 366.9N/m.Peak loads for the results in Table 3were 60to 70l N for the Kynar V R740,40to 50l N for the Kynar V R2800,and 25to 40l N for the Kynar V R2750materials.Table 3summarizes elas-tic modulus results.For comparison,DMA values for the elastic modulus for all three Kynar V Rgrades are also shown.Typical force distance curves for all three materials are shown in Fig-ures 5,6,and 7.The black line is the Oliver Pharr unloading ﬁt.Looking at the results from Table 3,we ﬁrst note that probe to probe variations in the meas-ured average elastic modulus for the three AFMTable 3.Elastic Modulus Results for Three Kynar V RMaterials and Comparison with DMA ResultsElastic Modulus (GPa)Kynar V R 740Elastic Modulus (GPa)Kynar V R 2800Elastic Modulus (MPa)Kynar V R2750AFM LRCH750Probe #2 2.59Æ0.35 2.19Æ0.190.97Æ0.16AFM LRCH750Probe #3 2.89Æ0.42 1.96Æ0.30 1.16Æ0.16AFM LRCH750Probe #4 3.30Æ0.44No data No data AFM LRCH250Probe #1No data 1.63Æ0.23 1.06Æ0.15Average AFM 2.95Æ0.49 1.96Æ0.33 1.07Æ0.17DMA (20 C)2.31Æ0.160.87Æ0.040.59Æ0.03The elastic modulus was calculated using the well-known Oliver Pharrmethod.Figure 5.AFM force distance curve of the Kynar V R740polymer,obtained with a LRCH750AFM probe.AFM NANOINDENTATION OF VISCOELASTIC MATERIALS 1579Journal of Polymer Science:Part B:Polymer Physics DOI 10.1002/polb。

一种控制硅深刻蚀损伤方法的研究

一种控制硅深刻蚀损伤方法的研究阮　勇1,叶双莉1,张大成2,任天令1,刘理天1(1.清华大学微电子所微/纳器件与系统实验室,北京　100084;2.北京大学微电子研究院,北京　100871)摘要:提出了提高硅深反应离子刻蚀的新方法。

该方法在硅的侧壁PECVD淀积SiO2,硅的底部采用热氧化的方法形成SiO2。

由于在刻蚀中硅与SiO2的刻蚀选择比为120∶1～125∶1,因此SiO2层可以抑制在硅2玻璃结构的刻蚀中出现的lag和footing效应,扫描电镜结果也证明,采用改进工艺后的硅结构在经过长时间的过刻蚀后仍然保持了完整性。

硅陀螺测试结果也证明了改进工艺的正确性。

关键词:微电子机械系统;硅2玻璃阳极键合;硅深刻蚀;刻蚀损伤中图分类号:TN405.983　文献标识码:A　文章编号:167124776(2007)07/0820037203Study on Methods to Protect Silicon Microstructures from the Dam ages in Deep R eactive Ion EtchingRUAN Y ong1,YE Shuang2li1,ZHAN G Da2cheng2,REN Tian2ling1,L IU Li2tian1(1.Micro/N ano Devices and S ystems Di vision,I nstit ute of Microelect ronics,Tsinghua Universit y,Bei j ing100084,China;2.I nstit ute of Microelect ronics,Peki ng Uni versit y,B ei j ing100871,Chi na)Abstract:New met hods for improving t he quality of t he silicon deep reactive ion etching(DRIE) procedure were investigated.It suggested t hat a PECVD o xide layer was deposited at t he silicon sidewall and a t hermal oxide layer was formed at t he silicon backside.Due to t he silicon to SiO2 etching selectivity(120∶1～125∶1),t hese oxide layers could protect t he silicon microst ruct ures from t he damages caused by t he lag and footing effect s usually occurred in t he basic silicon2on2 glass(SO G)p rocess.The SEM result confirms t hat t he silicon struct ure can endure a long time overetch and t he st ruct ure surface can remain intact by t he modified processes.The gyro scope de2 vice test result s are also in good agreement wit h new process met hods.K ey w ords:M EMS;silicon2glass anodic bonding;silicon DRIE;etching damage1　引　言在(M EMS)器件的制备中,硅反应离子刻蚀是一项重要的加工技术,特别在体硅与玻璃键合的M EMS结构上(SO G),硅反应离子深刻蚀更是被广泛使用。

抛丸的工艺流程

抛丸的工艺流程Shot blasting is a common surface finishing process used in manufacturing industries to clean, strengthen, or polish metal surfaces. 抛丸是一种常见的表面处理工艺，在制造业中用于清洁、强化或抛光金属表面。

By propelling small, hard pieces of material at high velocity, shot blasting can remove contaminants like rust, paint, or scale from metal surfaces, leaving them clean and ready for further processing. 通过以高速推动小而坚硬的材料，抛丸可以去除金属表面的锈、油漆或鳞片等杂质，使其干净并且可以进一步加工。

This process is essential for improving the surface finish and quality of metal parts, ensuring proper adhesion for coatings or preventing fatigue failure due to surface defects. 这一过程对于提高金属零件的表面光洁度和质量至关重要，确保涂层的正确附着或防止因表面缺陷而导致的疲劳破坏。

Furthermore, shot blasting is an environmentally friendly and cost-effective method compared to other surface treatment techniques, making it a preferred choice for many industries. 此外，与其他表面处理技术相比，抛丸是一种环保和具有成本效益的方法，因此成为许多行业的首选。

汽车弹簧的生产工艺流程

汽车弹簧的生产工艺流程英文回答：The production process of car springs involves several steps to ensure the quality and performance of the springs. Here, I will explain the process in detail.1. Material selection: The first step in the production process is selecting the appropriate material for the springs. Typically, car springs are made from high-quality steel, such as alloy steel or carbon steel. The material must have the necessary strength and durability towithstand the weight and pressure of the vehicle.2. Cutting and shaping: Once the material is selected,it is cut into the desired length and shape. This can be done using various cutting methods, such as shearing or sawing. The cut pieces are then shaped into the required form using specialized machinery, such as a coiling machine.3. Heat treatment: After shaping, the springs undergo a heat treatment process to improve their mechanical properties. This involves heating the springs to a specific temperature and then cooling them rapidly to achieve the desired hardness and strength. Heat treatment helps to enhance the resilience and durability of the springs.4. Shot peening: Shot peening is a process used to further enhance the strength and fatigue resistance of the springs. It involves bombarding the surface of the springs with small metallic shots at high velocity. This helps to create compressive stresses on the surface, which improves the resistance to cracking and fatigue failure.5. Surface finishing: The springs are then subjected to surface finishing processes to improve their appearance and protect them from corrosion. This can involve methods such as painting, powder coating, or electroplating. The choice of surface finishing method depends on the desired aesthetic and functional requirements of the springs.6. Quality control: Throughout the production process,quality control measures are implemented to ensure that the springs meet the required specifications. This can involve various inspections and tests, such as dimensional checks, load testing, and fatigue testing. Any defective springsare identified and rejected to maintain the overall quality of the production.7. Packaging and shipping: Once the springs pass the quality control checks, they are packaged and prepared for shipping. This involves proper packaging to protect the springs during transportation and storage. The packaged springs are then shipped to the customers or automotive manufacturers.中文回答：汽车弹簧的生产工艺流程包括多个步骤，以确保弹簧的质量和性能。

双曲面压电复合材料温度稳定性研究

感元件使用的核心功能材料，其性能决定了水声换能器的性能。然而，由于双曲面压电复合材料是由高分子聚合物（如环氧树脂、橡胶）和压电陶瓷复合而成的，其聚合物的热膨胀系数远大于压电陶瓷，当压电复合材料所处环境温度出现变化时，聚合物就会发生形变，从而引起复合材料产生形变，继而导致换能器出现振动频率漂移、波束开角波动等情况，影响声呐系统的稳定性。当环境温度较高时，聚合物将产生较大形变，甚至可能会使压电陶瓷与聚合物的界面剥离，直接导致复合材料失效，继而影响换能器的使用。而对于南极北极科考应用，要求换能器在－４０℃低温下稳定工作，这对压电复合材料低温稳定性提出了更高的要求。对于平面压电复合材料的温度形变已有一些研究，如白智奇等［６］应用光纤光栅法测试了平面压电复合材料长度、宽度和厚度方向的形变，并对介电常数和频率常数等数据进行了修正。然而，目前针对双曲面压电复合材料温度稳定性的研究较少，尤其是针对环境因素引起材料形变的检测及控制方法几乎未见，亟须就此开展研究。
Ｐ＝０．２２，则光纤光栅波长变化量与应变的关系为
Δλ ＝０．７８×ε λ
（３）
因此
ε＝０．Δ７λ８λ
（４）在实验中，本文采源自光纤光栅直接贴附压电复合材料表面的方法测量材料形变［１６］。当压电复合材料发
生应变时，将带动光纤光栅产生应变，通过计算光纤光
栅的反射波长，便可以得到所对应处的应变 ε。由于
环境因素（如温度、湿度、气压等）作用于光纤光栅，同
目前材料形变的测量方法有很多种，主要包括应变片测量法、数字散斑干涉法、光弹性法和三坐标测量法等［７－１１］。但这些方法存在接线方式单一、视场小、定性分析单一等缺点。相比较来说，光纤光栅（ｆｉｂｅｒｂｒａｇｇｇｒａｔｉｎｇ，ＦＢＧ）测量法具有较高精度，可实现测量数据的高速率、大容量传输［１２－１４］，不失为一种有效测量压电复合材料形变的方法。因此，本文以光纤光栅测量法为基础，在－４０～１００℃的温度范围内对双曲面压电复合材料的形变和机电性能进行系统测试与研究，测量不同方向的形变，并测试不同温度下压电复合材料的机电特性。

脉冲电流下纳米结构形成

Nanostructure formation in the surface layer of metals under inﬂuence of high-power electric current pulseA.Vinogradov ÆA.Mozgovoi Æzarev ÆS.Gornostai-Polskii ÆR.Okumura ÆS.HashimotoReceived:9April 2009/Accepted:15June 2009/Published online:1July 2009ÓSpringer Science+Business Media,LLC 2009Abstract The possibility to tailor the microstructure of metals is explored utilising a skin-effect for surface treat-ment.The theoretical simulation of the electric and mag-netic ﬁelds in a metallic cylinder shows that melting followed by rapid quenching can occur in a skin layer of 5–10-l m thickness if the amplitude of a single electric pulse of several nanoseconds duration is of the order of hundreds kiloamperes.The experiments using the SUS304stainless steel show that besides a thin amorphous layer,a speciﬁc nano-twin structure can form at the near-surface region.The appearance of nano-twins is explained considering the stress components arising at the surface layer and in the bulk of the specimen during shock wave propagation caused by temperature gradients and the Lorentz force.It is shown that the high stress amplitudes can arise locally,furnishing the required conditions for twin nucleation and resulting in intensive plastic deformation of the sub-surface layer.IntroductionMany physical and mechanical properties of materials depend strongly on the surface state.For instance,hard-ness,fatigue life and wear resistance beneﬁt from surfacestrengthening which can be achieved in a variety of tech-niques including severe plastic deformation,plating,ion implantation,laser irradiation,etc.The ultimate properties have been achieved in materials in their nano-and amor-phous states [1].Both nano-and amorphous structures are commonly obtained in metals from melts of very speciﬁc chemical compositions by utilising a variety of rapid quenching techniques where a rather high critical cooling rate of 105–107K/s is achieved as required for amorphi-sation.At lower quenching rates,ordinary crystallisation or formation of ultraﬁne grain or nano-structure is observed with characteristic grain dimensions from few nanometres to few hundred nanometres,respectively.Numerous rapid quenching techniques allow obtaining thin ﬁlms,ribbons,ﬂakes and powders of micrometre dimensions [2].In con-trast,severe plastic deformation is capable of producing bulk articles with the ultraﬁne grain and nano-structure [3].In this study,we explore the possibility to create novel microstructures by combining both rapid quenching and severe plastic deformation.We make use of a skin-effect in conductors,arising from the short electric current pulse ﬂowing through the conductor,for their surface heating up to melting followed by rapid cooling due to heat transfer the bulk.It was supposed that various ultraﬁne grain,nano-and even amorphous structures can be produced in the surface layer of metals in this way [4].The ﬁrst theoretical attempt has been made in ref.[4]to simulate the behaviour of the electric and magnetic ﬁelds in a metallic cylinder subject to a rapid discharge of a bank of capacitors as shown schematically in Fig.1.It was demonstrated that melting followed by rapid quenching can occur in a skin layer of 5–10-l m thickness if the amplitude of the passing electric pulse of several nano-seconds duration is high enough,i.e.of the order of 102kA.Furthermore,it appeared that since solidiﬁcation of the molten layer occurs within a microsecond or sub-microsecond timeA.Vinogradov (&)ÁS.HashimotoOsaka City University,Osaka 558-8585,Japan e-mail:alexei@imat.eng.osaka-cu.ac.jpA.Mozgovoi Ázarev ÁS.Gornostai-Polskii ÁR.Okumura Institute of Experimental Physics,Sarov 607190,Russia Present Address:R.OkumuraMaterials Engineering Department,Denso Corp.,Kariya 448-8661,JapanJ Mater Sci (2009)44:4546–4552DOI 10.1007/s10853-009-3689-zscale,very high quenching rates of108–109K/s are achiev-able,providing an appealing novel opportunity for amorphi-sation or signiﬁcant modiﬁcation and nano-structurisation of the surface layer in conductors.The possibility to obtain thickness of5–10l m amorphous layer in the commercial SUS304stainless steel was then successfully demonstrated by the same authors[5],which agrees with common estimates of the skin layer thickness[6].Theoretical calculations in this study show that the extremely high stresses may arise from the temperature gradients and Lorenz force action resulting in intensive plastic deformation of the sub-surface layer.The experiments under this study utilising an ultra-high power generator producing a short electric current pulseﬂowing through copper or SUS304stainless steel cylindrical speci-mens reveal that a speciﬁc nano-twin structure can be formed in the surface layer and in the bulk of the specimens depending on the electric pulse parameters.The appearance of nano-twins is explained from the theoretical consideration of the stress components arising at the surface vicinity and in the bulk of the specimen.Use of skin-effect for surface heating,melting and rapid quenchingLet us consider an endless conducting cylinder with the symmetry axis Z in a circuit shown in Fig.1.The proce-dure,which allows evaluating the parameters of the external circuit such as the resistance R,capacitance C, inductance L and the initial voltage U0,as well as the dimensions of the metallic cylinder l and r0,is given in[4] to ensure melting and rapid quenching in the surface layer.The initial system of differential equations describing a given problem can be written in a classic Maxwell’s form for the electric E and magnetic Hﬁelds together with a heat transfer equation:rÂH¼1 q E;rÂE¼Àl a o H o t;q m c V o To t¼rÁðk r TÞþ1qj E j2;ð1Þwhere the right-hand side of the last equation includes theJoule heating term proportional to j E j2as a heat source.Here,q m is the materials density,l a is the magneticpermeability,c V is the speciﬁc heat capacity and k is theheat conductivity of the material.Apparently,the system ofequations(1)should be completed with the ordinaryelectric equations for the external circuit given asLd Id tþRIÀUðtÞþlE zðt;r0Þ¼0;d Ud t¼ÀIðtÞC;ð2Þwith initial conditions setting the initial discharge voltageU0Uð0Þ¼U0;Ið0Þ¼0:ð3ÞIn order to model the dynamics of various processes inthe actual experimental installation utilising the electricalenergy of the bank of capacitors discharging on a low-inductance load,the system of equations(2)and(3)wassolved together.The details of the problem formulation andsolution have been reported in[4,5].For instance,for acopper cylinder having the length l=10mm and radiusr0=0.1–0.5mm at T0=300K,C=0.1l F,R=0.3Ohm,L=5nHn and U0=100kV,the peak currentmagnitude reaches180–250kA while the pulse duration isas short as40–50ns.The maximum thickness of the moltenlayer R m was found to be10l m,and the melting time was230ns.Cooling until complete solidiﬁcation occurredwithin approximately1l s.The maximum temperature onthe surface reached almost2,000K,which is between themelting point T m=1,356K and vaporization temperatureT v=2,868K.The maximum quenching rate,q T/q t,was of29108K s-1.This quenching rate is still not enoughfor amorphisation of pure metals;it is,however.within therange of typical quenching rates attained in melt-spinningtechniques used for production of a broad variety of amor-phous alloys[2].Using the model constituted by Eqs.1and3,one can show that the depth of the molten layer varies in arange of0.1–40l m,depending on the specimen dimensionsand initial voltage provided that the parameters of theexperiment have been the realistically chosen[4,5].Hence,utilising a high-power generator described brieﬂy in[7],which was modiﬁed toﬁt the cylindrical specimens of1-mmdiameter,the proposed scheme vas validated using Cu andSUS304stainless steel.It was demonstrated that formationof the amorphous(glassy-like)layer in the intimate prox-imity(from zero to about30l m depending on the initialvoltage U0)to a free surface of the SUS304steel(Fe–18Cr–8Ni)is possible after melting followed by rapid quenchingcaused by the short high power electric pulse.For this study,the most interestingﬁnding reported in ref.[4]is that aspeciﬁc twin structure is formed in the subsurfacelayer,extending up to 100l m inside the material from the surface as illustrated in Fig.2(the details of experimental procedure,specimen preparation and observation can be found in [5]).Transmission electron microscopy (TEM)with the selected area electron diffraction pattern (SAEDP)analysis reveals that this structure differs drastically from that is commonly found in the bulk of the as-received specimens.After the ‘skin’treatment,the structure near the surface consists primarily of regions which are multiply twinned along {111}planes with the nanometre scale twin spacing.The very ﬁne twin lamellae,parallel to each other can be readily found here and there in TEM foils.Apparently,the density of twin population reduces with depth from the surface,c.f.Fig.2a–d.Figure 2b shows that the twins in the bulk of the specimen are limited to the initial grain size which is of the order of 2–3l m.The appearance of such a very ﬁne nano-scaled twin structure,induced by the ‘skin’treatment,is difﬁcult to explain by annealing-type effects caused by the temperature rise at the specimen surface due to the skin electric current.Since the cooling rate has been proven very high [4,5],the time interval over which the surface layer is exposed to the high temperature inﬂuence is too short to facilitate diffusion processes controlling the annealing effects.Besides,the twin structure appearance does not resemble typical annealing twin patterns,for example [8].On the other hand,it is well known that the ﬁne twin lamellae with the nano-scale spacing can be produced mechanically at high stresses due to plastic deformation [9–11].Appearanceof mechanical twins assumes two factors of primary importance:(i)high stresses approaching a sizable fraction of the theoretical cohesive strength s /l =10with l —shear modulus of the material,(ii)impeded alternative accom-modative mechanisms such as dislocation motion.In the course of conventional plastic deformation,the dislocation motion can be blocked by high internal stresses arising from dislocation accumulation during strain hardening.In the experiments under this study,the dislocation motion is limited due to a very short inﬂuence from the electric pulse.The mechanical twins form very fast,with the velocity of sound [10]and can be highly possible candidates for alternative sources of plastic deformation.Therefore,the internal stresses arising from the inﬂuence of electric and magnetic ﬁelds during the ‘‘skin’’treatment of the metal surface should be evaluated to shed light on the feasibility of twin nucleation.This will be accomplished in the next section.Stress calculation Problem statementThe pressure caused by the electromagnetic ﬁeld acting on the specimen in the geometry shown in Fig.1is pro-portional to the Pointing vector,i.e.to the vectorproductFig.2Nano-scaled twinstructure below the surface of a ‘‘skin-’’treated SUS304stainless steel a 25l m below the surface;SEADP is indicative of the twinnedstructure;b 100l m below the surface;c and d 100l m below the surface.The initial discharge voltage is 70kV (a ,b )and 90kV (c ,d ),respectivelyE 9H .The displacement vector U ,will have both axial and radial components U ={U r ,0,U z }.In order to calculate the stresses which arise in the metallic specimen when the high power electric pulse is passing through,the equation for the vector U should be added to the system of Maxwell equations for electric and magnetic vectors.The equation describing the mechanical behaviour of an isotropic deforming media is written as q m o 2Uo t¼r Á½r þF ;ð4Þwhere the Lorentz force term and the linear isotropic expansion term are incorporated in the right hand side;[r ]is the stress tensor,F is the net bulk force vector.In the axially symmetrical case the stress tensor takes a form½r ¼r r 0r rz0r u 0r zr 0r z 0@1A ;ð5Þwith the components given as r rr u r z rrz0B B B @1C C C A ¼k 1Àm m 11011Àm m 10111Àm m00001À2mm0B B @1C C A e r Àa T ðT ÀT 0Þe u Àa T ðT ÀT 0Þe z Àa T ðT ÀT 0Þe rz 0B B @1C C A ð6ÞComponents of the strain tensor [e ]are given as:e r ¼o U r o r ;e u ¼U r r ;e z ¼o U z o z ;e rz ¼12o U r o z þo U z o r:ð7ÞHence,the initial system of equations takes a form:r ÂH ¼1q E ;r ÂE ¼Àl a o H o t;q m co T o t ¼r Áðk r T Þþ1qj E j 2;q m o 2Uo t2¼ðk þ2l Þrðr ÁU ÞÀl r Âðr ÂU ÞÀa T K r T þl a 1ÁE ÂH ;l ¼E u 2ð1þm Þ;k ¼E u m ð1þm Þð1À2m Þ;K ¼E u3ð1À2m Þ:ð8ÞHere,E u ,l and K are the Young’s,shear and bulk moduluses,respectively,m is the Poisson ratio,e ij are the strain tensor components,U r ,U z are the displacement vector components,a T is the linear heat expansion coefﬁcient and k is the Lame constant.The right-hand side of the third equation includes the Joule heating termproportional to j E j 2as a heat source.The system is said tobe thermally isolated because the energy losses due to irradiation have been proven negligible [4].Using Raleigh damping,which is commonly used to provide a source of energy dissipation in analyses of structures responding to dynamic loads and having H ={0,H ,0},E ={E r ,0,E z }and U ={U r ,0,U z },the equations (8)in cylindrical coordinates {r,z }take a ﬁnal form:l a 1q o H u o t ¼1r r o 2H u o r 2þo H u o r ÀH u rþo 2H uo z 2;E z ¼q r o o r rH u ÀÁ;E r ¼Àq o H u o z;q m c o T o t ¼k o 2T o r þo 2T o zþk r o T o r þ1q E 2rþE 2z ÀÁ;q m o 2U r ¼ðk þ2l Þo 2V r þo V rþl o 2V r o z 2þðk þl Þo 2V zo r o z Àl a q E z H u Àa T K o T o r þa R q mo U ro t ;q m o 2U z o t 2¼ðk þ2l Þo 2V z o z 2þl o 2V z o r 2þ1r o V z o rþðk þl Þo 2V r o r o z þ1r o V ro zþl a q E r H u Àa T K o T o z þa R q mo U zo t;V r ¼U r þb R o U r o t ;V z ¼U z þb R o U zo t:ð9Þwhere,U r and U z are the radial and axial components of thedisplacement vector U ,respectively,and a R and b R are the coefﬁcients of Raleigh damping,which are commonly expressed as a R ¼4pnf min f maxmin max;b R ¼nmin max ;ð10Þwhere n is the damping efﬁciency ranging between 0and 1,f min and f max stand for the lower and upper frequency in the working frequency range,respectively.For numeric cal-culations,f min and f max are chosen as 0.5an 90MHz,respectively.Initial and boundary conditions are set as H u ð0;r ;z Þ¼0;U z ð0;r ;z Þ¼0;U r ð0;r ;z Þ¼0;H u ðt ;r 0Þ¼I ðt Þ2p r 0;T ð0;r ;z Þ¼T 0;o T o r r ¼0¼0;o T o r r ¼r 0¼0;o E z o rr ¼0¼0ð11ÞThe free surface state determines boundary conditions for U z and U r in the Lame equation on the surface of the specimen:r r j y ¼r 0¼ð2l þk Þo U r o r þk o U z o z þU rr¼0;r u y ¼r 0¼ð2l þk ÞU r r þko U z o z þo U ro r¼0;r z j y ¼r 0¼ð2l þk Þo U z o z þk o U r o r þU rr¼0:ð12ÞThe boundary conditions on the Z axis in the centre ofthe specimen (r =0)take a form (due to the axial symmetry):U r ðt ;0;z Þ¼0;o U z o rt ;r ¼0;z¼0:ð13ÞThus,together with Eqs.2and 3,the problem is fully deﬁned and can be solved numerically.Numerical estimates and discussionEquations 6,7,9and10were solved together with electric equations (2)and initial and boundary conditions (3,11–13).Numeric solutions were obtained using ﬁnite element method within a mesh constructed in r -z space having 1440elements and 794nodes.The Lagrange polynomial func-tions of the second order were taken for approximations.For illustrative purposes,the calculations of internal stresses caused by high-power short electric pulse passing through a conductive material have been performed for Cu cylinder of r 0=0.5-mm initial radius and 5-mm length (regretfully,for the SUS304steel,only few required material constants are known,which makes it impossible to perform quantitative modelling).All the other conditions were set the same as in [4],i.e.T 0=300K,C =0.1l F,R =0.3ohm,L =5nH and U 0=100kV.Figures 3and 4show the cumulative von Mises stresses arising from the linear thermal expansion and Lorentz force componentsr Von ÀMises ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃr 2r þr 2h þr 2z Àr r r h Àr r r z Àr h r z þ3r 2rzq ð14Þand its components calculated in cylindrical coordinates(r ,h ,z)for r =0(specimen axis)and r =0.5mm (specimen surface)in the middle of the specimen z =2.5mm.The shock-wave character of the stress tem-poral and spatial distribution is evident,particularly in Fig.5,where the snapshots of the axial component of von Mises stresses distribution over the specimen are shown in subsequent instants of time.The shock wave propagates from the surface to the bulk and back in an oscillating manner with attenuation caused by Raleigh damping introduced in Eqs.9.The duration of wave propagation depends on materials’properties and may vary from sev-eral microseconds to several milliseconds which is quite enough to activate subsonic or even trasonic dislocation motion and mechanical twinning,which can be viewed as a cooperative motion of several partial dislocations.While the r rz component is negligible both at the surface and in the bulk,the radial r r and axial r z and r u components may attain very high peak magnitudes of several gigapascals,which is not unexpected for shock wave loading.The average magnitude of stress components near the surface is notably higher than that in the bulk which accounts for the higher possibility to ﬁnd the twinned domains in the sur-face proximity,i.e.decreasing twin density with the depth from the surface.Gerland et al.[12]used a surface treatment with shock waves caused by explosion in a thin layer applied to a 316L stainless steel.Similar to the results in this study,the near surface structure was found to be composed ofmechanicalFig.3Cumulative von Mises stress on the axis r =0and on the surface r =0.5mm of Cu cylinder subjected to theinﬂuence of the ultrahigh power short electric current pulse.The electric current magnitude I and surface temperature T areplotted for comparison and time scaling.T m —melting temperaturetwins,the density of which decreased with increasing depth.Firrao et al.[13]have also shown that mechanical twins are readily formed in the 304stainless steel subjected to stress impact caused by explosions of small charges in the surface vicinity.The beneﬁts for the mechanical properties of the nanostructured steels produced by explo-sion inﬂuence is argued in [12,13].Ample evidence exists in the literature showing twin formation due to severe plastic deformation caused by intense ultrasonic shot peening [14],mechanical attrition [15]or shock pulse loading [16].The minute mechanisms of twin formation under shock wave loading have yet to be explored,possibly with the help of atomistic molecular dynamic simulations in a way similar to those performed in [17].The results of this study may serve as a starting point for further quan-titative modelling.They suggest that the high local stress conditions required for twin nucleation in the surface layer are fulﬁlled.Indeed,assuming the shear stress required for twin nucleation given as [18]s %c SFE b 1;ð15Þwhere c SFE is the stacking fault energy and b 1is the Burgers vector of the twinning dislocation b 1¼a 6121h i for an f.c.c.crystal with a —lattice parameter,and taking c SFE for the 304Fe–Cr–Ni steel of 17mJ/m 2[19],one estimates s &0.12GPa,which is notably smaller than the possible peak values of stress components in elastic waves arising in the body due to the ‘skin’treatment by a high-power electric pulse.Furthermore,twinning can be plausibly expected in the materials with much higher stacking fault energy under the same treatment conditions.Signiﬁcant changes in the microstructure of skin-treated specimens and the formation of twin colonies in the sub-surface layer suggest that macrocharacteristics of treated metals may alter considerably.The Vickers microhardness HV was measured using a Shmiadzu dynamic Ultra-hard-ness tester DUH-1at 20-g load and 20-s exposure time.Ten to twenty measurements along the specimen gauge part were averaged.The depth of indentation did not exceed 2–3l m.The HV values in the specimens subjected to ‘skin’treatment with the capacitor discharge from 70,75and 80kV are found to be of 200±23HV,161±25HV and 140±27,respectively.All these values are notably higher than that for the reference of the ‘‘as-received’’SUS304sample—124±6HV,which is consistent with formation of the hardened twin nano-structure in thesurfaceFig.4Stress–tensor components (normal and shear)on the axis (a )and on the surface (b )of Cu cylinder subjected to the inﬂuence of the ultrahigh power short electric currentpulseFig.5Snapshots showing the von Mises stress distribution over the cylindrical specimen of 0.5-mm radius and 5-mm length in subsequent instants of timelayer.Interestingly,that discharging capacitors from smal-ler voltage (70kV)results in the highest hardness of the surface layer which agrees with microstructural observa-tions:populations of twins are easier to see in the 70-kV-treated specimens while the density of twins reduces with increasing voltage (this has been noticed earlier in ref.[5]).Furthermore,this is also consistent with numeric evaluation of the temperature proﬁle in the subsurface layer,Fig.6:the thickness of the heated layer is found to be typically of the order of 100l m almost independently of the discharge voltage,which is considerably wider than the skin layer (50–10l m).However,the maximum temperature reached in the proximate vicinity of surface reduces sharply with voltage reduction.Even though this temperature reduces very quickly as we have discussed above (see [5]for details),this can be another argument why the nano-twin structure is more clearly seen after discharge from 70kV.One can notice in Fig.5that maximum von Mises stresses are obtained in the shock-wave within the 100-l m sub-surface layer,being in accordance with TEM obser-vations showing that twin colonies are readily observed in the subsurface region up to about a 100-l m thickness,whereas they are rarely or not at all observed in the bulk of the specimen.Although,the only qualitative comparison between the results of calculations and structural observa-tions are still possible,a fair agreement is seen between the numeric estimates,microstructural observations and microhardness assessment.References1.Gleiter H (1989)Progr Mater Sci 33:2232.Beck H,Guntherodt H-J (eds)(1981)Glassy metals (topics in applied physics),vol 46.Springer,Germany3.Valiev RZ,Islamgaliev RK,Alexandrov IV (2000)Progr Mater Sci 45:1034.Vinogradov A,Lazarev SG,Mozgovoi AL,Hashimoto S (2005)Philos Mag Lett 85:5755.Vinogradov A,Lazarev SG,Mozgovoi AL,Gornostai-Polskii SA,Okumura R,Hashimoto S (2007)J Appl Phys 101:033510–033510-7ndau LD,Lifshitz EM (1984)Electrodynamics of continuous media,vol 8.Pergamon,Oxford,UK7.Voronin VV,Tananakin VA,Pavlov SS,Tsiberev VP,Voronov SL (1977)In:Proceedings 11th IEEE international pulsed power conference,Baltimore,Maryland,USA,p 15668.Jones AR (1981)J Mater Sci 16:1374.doi:10.1007/BF010338549.Nartia N,Takamura J (1992)In:Nabarro FRN (ed)Dislocations in solids,vol 9.Elsevier,Amsterdam10.Rigsbee JM,Benson RB (1977)J Mater Sci 12:406–409.doi:10.1007/BF0056628411.Friedel J (1964)Dislocations.Pergamon Press,Oxford,UK 12.Gerland M,Presles HN,Mendez J,Dufour JP (1993)J Mater Sci28:1551.doi:10.1007/BF0036334813.Firrao D,Matteis P,Scavino G,Ubertalli G,Ienco MG,Pellati G,Piccardo P,Pinasco MR,Stagno E,Montanari R,Tata ME,Brandimarte G,Petralia S (2006)Mat Sci Eng A 424:2314.Liu G,Wang SC,Lou XF,Lu J,Lu K (2001)Scripta Mater44:179115.Zhang HW,Hei ZK,Liu G,Lu J,Lu K (2003)Acta Mater51:187116.Bakalinskaya ND,Zubov VI,Nadezhdin GN,Petrov YuN,Svechnikov VI,Stepanov GV (1988)J Strength Mater 20:120517.Gumbsch P,Gao H (1999)Science 283:96518.Hirth JP,Lotte J (1982)Theory of dislocations.Wiley,New York 19.Murr LE (1975)In:Herndan VA (ed)Interfacial phenomena inmetals and alloys.Techbooks,HerndanFig.6Solutions of Eqs.8and 2showing temperature proﬁles in the subsurface layer of Cu cylinder of 0.5-mm radius and 10-mm length after 0.4l s since the capacitor discharge from different initial voltages.T m —melting temperature。

纳米薄膜尺度依赖的杨氏模量及表面应力导致的弯曲

米器件制造技术的迅速发展 , 薄膜的厚度越来越小 , 这使得纳米薄膜的表面效应 (如表面弹性、表面应力等效应 ) 对器件的影响越来越明显 . 因此在制备纳米器件时 , 表面效应成为不可忽略的重要因素 [2,6,7]. 由于纳米薄膜的厚度很小 , 这使得纳米薄膜与厚度较大 ( 量级为微米或者更大 ) 的薄膜有着完全不同的力学性质, 进入 21 世纪以来, 人们利用薄膜内部的剩余应变使得纳米薄膜发生卷曲现象 , 从而制作出了由纳米薄膜卷曲而成的纳米管[8–10]. 纳米薄膜卷曲为管状结构使得材料内部具有较大的剩余应变, X 射线衍射实验显示 , 卷曲薄膜内部剩余应变随着纳米管半径方向 (即薄膜的厚度方向 )呈线性变化 [11,12]. 这种
S Ys z dz ,
ts
将式(7)代入式(6)可得到用表面弹性系数 S 表示的杨氏模量
Yf Y 6t 3 Sts Sbs 2s Sts 面弹性系数 (2)
式 (1) 将纳米薄膜表面层内部的表面杨氏模量进行了平均化, 其中 Ys(z)为随 z 坐标变化的表面杨氏模量, 而 Ys 则是在表面层内对 Ys(z)所求得的平均值. 表面弹性系数 S 的单位为 N/m, 这个物理量与体杨氏模量有着不同的量纲 , 而表面杨氏模量 Ys 的单位为 Pa, 与体材料的杨氏模量有着相同的量纲 . 在纳米薄膜表面层内部, 其有效杨氏模量应由体杨氏模量 Y 和表
引用格式: 李建刚, 白那日苏, 云国宏. 纳米薄膜尺度依赖的杨氏模量及表面应力导致的弯曲. 中国科学: 物理学力学天文学, 2015, 45: 086801
Li J G, Bai N R S, Yun G H. Size-dependent Young’s modulus and surface stress-induced bending of nanofilms (in Chinese). Sci Sin-Phys Mech Astron, 2015, 45: 086801, doi: 10.1360/SSPMA2015-00074

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This article appeared in a journal published by Elsevier.The attached copy is furnished to the author for internal non-commercial research and education use,including for instruction at the authors institutionand sharing with colleagues.Other uses,including reproduction and distribution,or selling or licensing copies,or posting to personal,institutional or third partywebsites are prohibited.In most cases authors are permitted to post their version of thearticle(e.g.in Word or Tex form)to their personal website orinstitutional repository.Authors requiring further informationregarding Elsevier’s archiving and manuscript policies areencouraged to visit:/copyrightEffect of surface stresses on CuO nanowire growth in the thermal oxidation of copperRediola Mema a ,Lu Yuan a ,Qingtian Du b ,Yiqian Wang b ,Guangwen Zhou a ,⇑a Department of Mechanical Engineering &Multidisciplinary Program in Materials Science and Engineering,State University of New York,Binghamton,NY 13902,USA bThe Cultivation Base for State Key Laboratory,Qingdao University,No.308Ningxia Road,Qingdao 266071,Chinaa r t i c l e i n f o Article history:Received 16May 2011In ﬁnal form 5July 2011Available online 13July 2011a b s t r a c tBy exerting bending stresses on a metal surface,we show that in-plane tensile stresses can effectively promote CuO nanowire (NW)formation by signiﬁcantly increasing the NW growth density during the oxidation of copper.It is found that the improved NW growth is associated with decreased size of oxide grains and increased number of grain boundaries in the underlying Cu 2O and CuO layers.These results are attributed to the effect of in-plane tensile stresses that result in ﬁne grain structures in the underlying oxide layers,which facilitates the outward diffusion of Cu ions for enhanced oxide NW growth.Ó2011Elsevier B.V.All rights reserved.1.IntroductionNanostructured semiconductor materials such as Si,Ge etc.and oxides such as CuO,ZnO,SnO 2,etc.have been the focus of intensive studies due to their emerging and increasing use in nanodevices and integrated nanosystems [1].Nanowires (NWs)are one-dimen-sional nanocrystals with large aspect ratio (length/diameter)and have shown unique properties that are tunable by varying size.Most of the ways used to generate oxide nanowires are physical and chemical routes such as precursor methods [2],hydrothermal reaction [3],anodization [4],electrospinning [5],and seed-medi-ated growth solution [6].Compared to their relatively complex and multi-step synthesis procedures,the formation of CuO NWs by direct thermal oxidation of metals has been recently given con-siderable attention due to its simplicity and large-scale growth capability [1,7–22].Also,oxide NWs prepared by thermal oxida-tion exhibit higher crystallinity and longer aspect ratios compared to those prepared via solution-based routes [23].Oxide whisker generation from thermal oxidation dates back to the 1950’s [24,25],but the growth mechanism has widely been de-bated and lacks cohesive understanding [8–10].With powerful microscopy techniques widely available today,a general consensus established is that the oxidation of metals to form oxide NWs typ-ically requires the sequent growth of multiple and parallel oxide layers (with different oxide phases)followed by the subsequent growth of oxide NWs on the top oxide layer [8,26–31].While oxide layering can be understood from thermodynamic equilibrium anal-ysis,the growth of oxide NWs is usually attributed to kinetic ori-gins,largely because oxide NWs and the top oxide layer have the same oxide phase and crystal structure [8,27,28].Due to the large differences in molar volumes between the var-ious oxide phases and the metal substrate,it has been inferred that the presence of interfacial stresses has a substantial effect on the oxide NW formation by promoting grain boundary diffusion for initiating the nucleation and uniaxial growth of oxide NWs on the outmost surface.To date,however,there has been no straight-forward experimental veriﬁcation of this hypothesis.In this Letter we provide such veriﬁcation in form of results of simple experi-ments in which in-plane stresses are imposed upon oxidizing metal surfaces.Our results demonstrate unequivocal effects of applied tensile stress on both,the microstructures of the oxide ﬁlms and the resulting oxide NW growth.This work also provides a simple approach for efﬁciently promoting oxide nanowire forma-tion by thermal oxidation of metals.To observe the effects of surface stress,bending is commonly used to apply stress.A schematic of the scenario is shown in Figure 1.As bending occurs,the upper surface is no longer parallel to the bottom surface as the upper face shortens by d L while the bottom face is elongated by d L ,causing the generation of compres-sive stress in the upper face and tension stress in the bottom face.It follows that there is a line or region of zero stress between the two surfaces,called the neutral axis.The amount of bending stress existent at the surfaces can be calculated using the ﬂexure formulaof r ¼ÆEcq ,where E is the elastic modulus of the material,c is theposition along the vertical direction where the stress is being mea-sured,and q is the radius of curvature.An advantage of using bend-ing metals is that the effects of both compressive and tensile stresses can be studied simultaneously by examining oxide NW formation on the upper and bottom face of the bent metal oxidized under the same oxidation conditions.Our hypothesis is that these exerted surface stresses would modify the microstructures of the multilayered oxide ﬁlms,whereby inﬂuencing the mass transport process leading to the nucleation and growth of oxide NWs.0009-2614/$-see front matter Ó2011Elsevier B.V.All rights reserved.doi:10.1016/j.cplett.2011.07.012⇑Corresponding author.Fax:+16077774620.E-mail address:gzhou@ (G.Zhou).2.Experimental procedureThe test specimens were Cu foils (99.99%purity)with a thick-ness of 0.25mm.The foils were cut into strips 5mmin width and 25mm in length,following which they were uniformly bent at a radius of 10mm.The sample was then cleaned with 0.1M HCl,thoroughly rinsed with deionized water and then put in ace-tone for an ultrasound bath for 5min to remove impurities and na-tive oxide from the surface of the metal.The sample was dried in N 2and then put into an oxidation chamber.The chamber was sub-sequently pumped to $10À6Torr,oxygen gas was then admitted into the chamber to the pressure of 200Torr.The samples were then heated up to a temperature of 450°C at the rate of 10°C/min in oxygen and then oxidized for 30min in static oxygen.The oxygen pressure in the chamber increased to at $210Torr after the sample was heated to the oxidation temperature of 450°C.The sample temperature is monitored via a K-type thermocouple in contact with the heater.The sample was then cooled down to room temperature (23°C)at the same rate in oxygen.The oxida-tion loading apparatus was large enough so that both bent and ﬂat specimens could be loaded simultaneously and then oxidized under the same oxidation conditions.Surface morphology is exam-ined using a ﬁeld emission scanning electron microscope (FEG-SEM)FEI Supra 55VP.Density of nanowires on the inner and outer surface of the sample was compared to the density of nanowires on the ﬂat sample.The thickness of the oxide layers,size and shape of the oxide grains for the samples was investigated by SEM.The morphology and microstructure of individual CuO NWs are ana-lyzed by transmission electron microscopy (TEM)using a JEOL JEM2100F operated at 200kV.images of the growth morphology of CuO NWs on the upper and bottom surfaces,respectively.For comparison,an SEM image from the oxidation of unbent (i.e.,ﬂat)Cu surface is also given.It can be seen that the bottom surface is covered by dense CuO NWs with a much higher number density than the other two surfaces.The average density of NWs on the bottom surface of the bent Cu is about 5.15/l m 2,while the densities for the upper surface of the bent Cu and ﬂat Cu are 1.23/l m 2and 1.08/l m 2,respectively.The diameters of CuO NWs grown on these surfaces show no noticeable difference and are all in the range of 40–100nm.The observations reveal evidently that in-plane tensile stresses (the bottom surface of the bent Cu)result in signiﬁcantly increased number density of CuO NWs as compared to the compressed or ﬂat Cu.The lengths of CuO NWs do not show signiﬁcant dependence on the tensile stresses.Figure 3shows SEM images from the different surfaces.The lengths of NWs in all images are on average around 4l m and NWs on the upper and bottom surfaces of the bent Cu and the ﬂat Cu show no obvious difference.TEM analysis of CuO NWs formed on these different surfaces reveals the existence of a bi-crystalline structure in the NWs.The bi-crystalline structure is observed to run along the entire axial direction.As shown in Figure 4a,the NW is divided by a twin boundary,where the different crys-tal orientations cause visible contrast in the bright-ﬁeld TEM im-age.Figure 4b shows a typical selected area electron diffraction (SAED)pattern taken along [110]zone axis of a single CuO NW.The diffraction pattern can be identiﬁed as consisting of two sets of diffraction spots with mirror symmetry,consistent with the nat-ure of the bicrystalline structure within the nanowire.Figure 4c is a high-resolution TEM image conﬁrming the bicrystalline structure of the NW.It can be seen that each side of the twin boundary shows well-developed crystal lattice planes.In line with previous studies [8,26,27],the formation of CuO NWs on all these Cu surfaces involves Cu 2O/CuO double layer growth with Cu 2O being the bottom layer and CuO being the top layer.However,the microstructure of the underlying oxide layers is observed to show dependence on the type of applied stresses.Figure 5shows representative cross-sectional SEM images of CuO/Cu 2O layers on the bent and unbent Cu.For all the cases,the Cu 2O bottom layers contain column like grains while the CuO intermediate layer consists of ﬁner grains.Several features can be noted from their comparison.In the case of tensile stress the average sizes of Cu 2O and CuO grains are smaller than that of oxide grains affected by compressive stress or ﬂat sample.In addition,both the Cu 2O and CuO layers have larger thickness for the tensile stress case than that of compressive stresses or ﬂat Cu.Their quan-titative comparison is listed in Table 1,where the oxide grain sizes are estimated from cross-sectional SEM images by measuring the lateral sizes of individual grains.Measurements performed on Letters 512(2011)87–91Similar to the effect of CuO NW density,the effect of tensile stress on the oxide growth is noticeable,i.e.,decreasing the average sizes of Cu2O and CuO grains and increasing the average thickness of the Cu2O and CuO layers.However,the case of compressive stress does not show obvious difference in comparison to theﬂat Cu sample.4.DiscussionTable1summarizes the results of the experimental measure-ments on the different samples.The differences in the NW densi-ties,grain size and thickness of Cu2O and CuO layer between the upper surface(under compressive stress)of the bent sample and ﬂat Cu(stress-free surface)is small and at variance,and no deﬁnite conclusion can be drawn.However,one clear trend is evident:in-plane tensile stresses(i.e.,the bottom surface of the bent Cu)result in signiﬁcantly increased number density of CuO NWs.Moreover, there is an apparent trend for the tensile stress to result in thicker Cu2O layer and smaller sizes of grains in both Cu2O and CuO layers. Such trends suggest that the formation of NWs is intimately re-lated to the growth behavior and microstructures of the underlying CuO and Cu2O layers.Since both Cu2O and CuO are cation-deﬁcient p-type oxides,it has been shown that the oxide growth is controlled via outward diffusion of cations during the oxidation of Cu[30,32–37].CuO NW growth requires continuous supply of Cu ions from the sub-strate(i.e.,Cu2O/Cu interface)to the growth tip.For the intermedi-ate range of the oxidation temperature($300–550°C)under which oxide NW formation occurs,the atomicﬂux is dominated by grain boundary diffusion of Cu ions across the Cu2O and CuO layers.A higher density of grain boundaries within the oxide layers leads to more efﬁcient outward diffusion of Cu ions for CuO NW growth.The promoted CuO NW formation by the in-plane tensile stress can be understood from its effect of the microstructure char-acteristics of the oxideﬁlms formed,which can be strongly inﬂu-enced by the oxide nucleation and early-stage growth behavior.Early-stage oxidation of copper has been investigated by in situ TEM and the study has revealed that the oxidation typically in-volves nucleation,growth and coalescence of oxide islands[38–44].The nucleation of an oxide island on a metal substrate needs to overcome a nucleation barrier E N,and the number of critical nu-clei per unit area is N rÃ¼N0expÀE NkTÀÁ,where N0is the number of nucleation sites per unit area of the substrate,k and T are Boltz-mann constant and oxidation temperature,respectively.The main contributions to E N are volume free energy,surface/interfacial freeTable1Tabulated data for each of the cases studied:ﬂat surface,bent Cu(upper and bottom).Nanowire density(1/l m2)(±0.1)Cu2O layer(l m)CuO layer(l m)Thickness(±0.2)Grain Size(±0.05)Thickness(±0.05)Grain Size(±0.02)Flat Cu 1.0830.450.20.1Bent CuUpper surface(Compressive stress) 1.23 2.70.40.20.12 Bottom surface(Tensile stress) 5.15 3.70.10.40.05showing the effect of surface stresses on the microstructure of the oxide layers and the subsequent oxide NW growth,(a)tensile90R.Mema et al./Chemical Physics Letters512(2011)87–91since only Cu2O is formed initially,i.e.,Cu2O forms as the inner layer in direct contact with the Cu substrate.The strain energy D G S in oxide island due to the lattice mismatch is proportional toE 1Àm e2and D G S>0,where E and m is the Young’s modulus and Pois-son ratio of Cu2O,respectively,e is the lattice mismatch between Cu2O and the substrate(the lattice constants for Cu and Cu2O are 3.61Åand4.26Å,respectively).The lattice of the Cu substrate ex-pands under the in-plane tensile stress.Although our samples are polycrystalline Cu,the overall lattice mismatch e between the oxide and substrate should be reduced by the applied tensile stress.This results in a smaller nucleation activation barrier E N. Therefore,nucleation of oxide islands is facilitated by the loaded in-plane tensile stress,resulting in a high density of oxide islands on the surface.The lattice mismatch for unbent Cu is large and for in-plane compressive stress becomes even larger,therefore, oxide nuclei on these surfaces have lower densities.Based on our experimental observations and the early-stage oxidation behaviors described above,the effects of surface bending stresses on the oxide NW growth are schematically shown in Fig-ure6.Because of the higher density of oxide nuclei enhanced by the tensile stress,as oxidation continues,oxide islands may im-pinge while still quite small in their lateral size.As a result,the fraction of merged interfaces(i.e.,grain boundaries)is effectively increased,which results in a corresponding increase in the effec-tive diffusion rate and total oxide thickness.In addition,the smal-ler Cu2O grains leads toﬁner CuO grains in the top layer,whereby providing more surface sites available for CuO NW nucleation. Since the growth of CuO NWs occurs via the grain boundary diffu-sion of Cu ions across the Cu2O and CuO layers,the promoted NW density is a consequence of this enhanced grain boundary diffusion as well as the reduced grain sizes in the CuO layer.For unbent Cu or Cu surface under compression,the average sizes of grains are lar-ger and the fraction of grain boundaries is reduced in comparison to the tensile stress situation.Correspondingly,the total oxide growth including the thickness of the oxide layers and the density of CuO NWs is relatively slow due to the less efﬁcient grain bound-ary diffusion.The mechanism shown in Figure6stipulates a clear correspon-dence of the density of CuO NWs with that of the underlying CuO grains.Our preliminary results on Cu foils with different bending curvatures indicate that the NW density increases with increasing the tensile stress by enhancing the oxide nucleation.However,our experimental results show no clear dependence of the diameter and length of CuO NWs with the applied stresses.This is because the diameter of CuO NWs is not deﬁned by the lateral size of the underlying CuO grains.As revealed by our SEM observations,CuO NWs are grown from the top portion of CuO grains[28].Therefore, the diameter of CuO NWs is smaller than the lateral size of under-lying CuO grains,irrespective of the type of surface stresses applied.5.ConclusionWe have reported the oxidation of bent Cu foils for examining the effect of bending surface stresses on the formation of CuO NWs.In-plane tensile stresses are shown to lead to enhanced oxide NW growth(such as the NW densities)in comparison to in-plane compressive stresses or unbent Cu.These effects are attributed to the effect of tensile stresses on the reduction of lattice mismatch strain between the inner layer of Cu2O and the Cu substrate,which promotes the nucleation rate of Cu2O islands and therefore in-creases the number of grain boundaries formed by impinged small Cu2O grains.The efﬁcient outward diffusion of Cu ions via an in-creased number of grain boundaries signiﬁcantly enhances the CuO NW formation.Our results may have broader impact for fun-damental understanding of the mechanisms of metal oxidation and manipulating the gas-surface reaction for effectively promoting oxide NW formation.AcknowledgmentsThis work was supported by the National Science Foundation through a Graduate Research Supplement grant of CMMI-0825737.Y.Q.Wang would like to thank theﬁnancial support from the Natural Science Foundation for Outstanding Young Scientists in Shandong Province,China(Grant no.JQ201002),and the Taishan Outstanding Overseas Scholar Program of Shandong Province, 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