Effect of elastic anisotropy on the dissociation widths of superdislocations in TiAl
高熵合金PPT课件
Definition of high entropy alloys
Still in 2004, the concept of high entropy alloy was firstly introduced by Yeh JW
.
5
Yeh JW et al. Adv Eng Mater, 2004, 6: 299-303.
properties are not as simple as expected
17
Phase formation in the as-cast FeCoNiCrMn
➢Basically the alloy has a single fcc phase
but with a small fraction of unidentified phase (Cr2Mn oxide ?)
In 2004, Multicomponent FeCoNiCrMn alloy firstly reported by
Cantor B. with a simple fcc solid-solution structure.
.
4
Cantor B et al. MSE A, 2004, 375-377: 213-218.
feconicrmn吕昭平教授北京科技大学新金属材料国家重点实验室nationalsciencefoundationchinanos
FeCoNiCrMn高熵合金的组织稳定性及 变形行为
吕昭平 教授
北京科技大学 新金属材料国家重点实验室
.
1
Acknowledgements
➢ Students: W. H. Liu, S. Y. Li, H. L. Huang and Z. F. Lei
各向异性对软土力学特性影响的离散元模拟
DOI ：10.16030/ki.issn.1000-3665.202006027各向异性对软土力学特性影响的离散元模拟赵 洲1，宋 晶1,2,3，刘锐鸿1 ，杨守颖1 ，李志杰1（1. 中山大学地球科学与工程学院，广东 广州 510275；2. 广东省地球动力作用与地质灾害重点实验室，广东 广州 510275；3. 广东省地质过程与矿产资源探查重点实验室，广东 广州 510275）摘要：软土预压工程中，初始和诱发各向异性对软土力学性质的影响十分显著，而现有研究缺乏对初始和诱发各向异性的统一研究方法。
采用离散单元法，以颗粒长宽比作为定量评价指标，构建真实形态的颗粒模型，生成5组不同沉积角的初始各向异性试样，并进行竖直和水平两方向加载的双轴模拟实验，研究了初始各向异性和诱发各向异性对软土力学特性影响；在细观层面，以颗粒为对象研究了颗粒接触形式和转动角度的变化规律，以接触为对象研究了配位数和接触法向各向异性的发展趋势，在此基础上探究抗剪强度指标与各向异性关系。
结果表明：初始和诱发各向异性共同影响试样力学性质，当加载方向和软土沉积方向垂直时，土体有最大的峰值强度。
颗粒接触形式中面面接触的比例随加载的进行逐渐增大，并影响着试样初始模量和抗剪强度，配位数和接触法向各向异性受颗粒接触形式的影响有不同的演化规律，并在加载后期趋于稳定；同时，初始各向异性试样相较各向同性试样有更大的黏聚力，诱发各向异性主要影响试样内摩擦角，进而影响试样抗剪强度。
关键词：软土；各向异性；峰值应力；抗剪强度指标；细宏观性质中图分类号：TU411.3 文献标志码：A 文章编号：1000-3665（2021）02-0070-08Discrete element simulation of the influence of anisotropy on themechanical properties of soft soilZHAO Zhou 1，SONG Jing1,2,3，LIU Ruihong 1 ，YANG Shouying 1 ，LI Zhijie1（1. School of Earth Sciences and Engineering , Sun Yat-Sen University , Guangzhou , Guangdong 510275, China ；2. Guangdong Provincial Key Lab of Geodynamics and Geohazards , Guangzhou , Guangdong 510275, China ；3. Guangdong Provincial Key Laboratory of Geological Processes and Mineral Resource Exploration ,Guangzhou , Guangdong 510275, China ）Abstract ：The initial and induced anisotropy has a significant effect on the mechanical properties of soft soil in preloading engineering. However, there is a lack of unified research methods for the initial and induced anisotropy. Discrete element method is adopted in this study, and the length-width ratio of particles is used as the quantitative evaluation index. Five types of initial anisotropy samples with different deposition angles are generated. The effects of initial anisotropy and induced anisotropy on the mechanical properties of soft soil are studied by vertical and horizontal loading. At the micro level, the contact form and rotation angle of particles are examined from the point of view of particles, and the development trend of coordination number and contact normal to anisotropy is studied from the point of view of contact. The relationship between shear strength index收稿日期：2020-06-12；修订日期：2020-08-04基金项目：国家自然科学基金项目（41877228；41402239；41877229）；广东省自然科学基金项目（2019A1515010554）；广州市科技计划项目（201904010136）第一作者：赵洲（1995-），男，硕士研究生，主要从事软土微观结构及数值模拟。
基于双屈服条件准则的横观各向同性本构模型研究及其数值模拟
基于双屈服条件准则的横观各向同性本构模型研究及其数值模拟QU Guangxiu;REN Peng【摘要】为研究层状岩体的力学特性,提出基于双屈服条件强度准则的本构模型.基于双屈服条件强度准则,联合横观各向同性的广义虎克定律刚度矩阵建立考虑横观各向同性的本构模型,并结合岩石单轴压缩试验数据,通过最小二乘法拟合该模型的参数;实现该模型的单轴压缩试验数值模拟,并通过室内单轴压缩试验结果对数值模拟结果进行验证,分析模型的可靠性.研究结果表明:本文提出的本构模型在层状岩体的力学分析方面具有适用性,为层状岩体力学特性研究及层状岩质边坡的稳定性分析奠定了基础.【期刊名称】《铁道科学与工程学报》【年(卷),期】2019(016)006【总页数】6页(P1448-1453)【关键词】横观各向同性;本构模型;双屈服条件强度准则;数值模拟【作者】QU Guangxiu;REN Peng【作者单位】【正文语种】中文【中图分类】TU458层状岩质边坡广泛分布于我国西南地区，其明显的横观各向同性力学特性对边坡的稳定性有着显著影响，因此如何建立适用的本构模型以探究其力学行为具有重要的工程实践意义。
关于横观各向同性岩石的本构模型研究，国内外学者进行了大量研究。
刘运思等[1]通过室内试验对横观各向同性岩体的弹性参数进行了研究。
Gonzaga等[2]通过三轴压缩试验研究了如何确定横观各向同性岩石的力学参数。
ZHANG等[3−5, 11]通过不同试验手段研究了横观各向同性岩石的破坏机理，探讨了加载速率对破坏过程的影响。
熊良宵等[6−8]采用数值模拟方法，探讨了横观各向同性岩体的力学特性。
Colak等[9−10]对横观各向同性岩体的破坏强度准则进行了研究。
上述研究成果大都基于Hoek-Brown准则，描述横观各向同性岩体的强度和变形特征，并提出不同的强度准则和弹塑性本构模型，但大多研究成果仅从强度或者变形特征这种单一因素考虑横观各向同性岩体的本构模型，如何科学地描述层状岩石的强度和变形特征仍值得商榷。
x射线衍射,取向分布函数
158.10 -158Fra bibliotek03x o
x
LLI I ('4
157.95
•
157.88
157.80
o11o
o12o
o13o
o14o
s~n a
o15o
(PSI)
Fig. I - - N o n h n e a n t y of 2(0 v s sln2at~ for an equlbiaxial expanded steel sheet, {211} planes.
M. BARRAL, formerly Asmstant with the ENSAM, Paris, is Engineer with the FRAMATOME Company, Paris J.L. LEBRUN, MMtre Assistant, J.M. SPRAUEL, Research Engineer, and G MAEDER, Professor, are with Lab. Microstructure et M&anique des Mat~riaux (UA-CNRS1219), Ecole Nauonale Sup~neure d'Artset M&lers, 151 Bd. de l'Hrpital, 75640 Paris Cedex 13, France. Manuscript submitted August 4, 1986. METALLURGICAL TRANSACTIONS A
I.
INTRODUCTION
for residual stresses determination at the surface of a material by X-ray diffractometry is now well established when the hypothesis leading to the sin20 law is verified. One of its limitations is the presence of a texture in the material, which induces a nonlinear distribution of the d spacing with the incidence angle ~0 (Figure 1). Several authors have proposed theoretical explanations and experimental procedures to determine stresses on a textured material: 1. Description of the material by two regions (with, respectively, high and low dislocation densities) whose mechanical behavior induces a plastic anisotropy responsible for the nonlinear distribution of d vs sin2O, on textured material, conducting to a weighting of the d spacings by an intensity function f(0, ~).
第八章 本构-修正剑桥模型
7.5.1 Elastic properties
常用对数
自然对数
The elastic stiffness is nonlinear and depends on the current stress level.
剑桥模型
7.5.2 Yield criterion
Cam Clay Model Modified Cam Clay Model
(i) Influence of intermediate principal stress on deformation and strength (1)
Stress ratio – strain increment ratio relation Direction of strain increments on octahedral plane
(i) Influence of intermediate principal stress (ii) Stress path dependency of plastic flow (iii) Positive dilatancy during strain hardening (iv) Anisotropy and non-coaxiality (v) Behavior under cyclic loading (vi) Influence of density and confining pressure (vii) Structured soil (viii) Time effect and age effect
' po
pf
qf
M
破坏时
1 p / p 2
' f ' 0
1 k
f
食用碱添加对不同冷冻杂粮面团品质特性的影响
杜文凯，苏同超，胡向华，等. 食用碱添加对不同冷冻杂粮面团品质特性的影响[J]. 食品工业科技，2023，44（24）：54−62. doi:10.13386/j.issn1002-0306.2023010143DU Wenkai, SU Tongchao, HU Xianghua, et al. Effect of Edible Alkali Addition on the Quality Characteristics of Different Frozen Multigrain Doughs[J]. Science and Technology of Food Industry, 2023, 44(24): 54−62. (in Chinese with English abstract). doi:10.13386/j.issn1002-0306.2023010143· 研究与探讨 ·食用碱添加对不同冷冻杂粮面团品质特性的影响杜文凯，苏同超*，胡向华，曾 洁，高海燕，王洋洋，田佳楠，马明君，周海旭（河南科技学院食品学院，河南新乡 453003）摘 要：为了研究食用碱添加量对不同冷冻杂粮（小麦、荞麦、玉米、绿豆）面团品质的影响，本文设计了0%、1%、2%、3%、4%、5%（以100 g 冷冻杂粮面团为基准）食用碱添加量分别加入到小麦面团、荞麦面团、玉米面团、绿豆面团中，在−30 ℃条件下冷冻8 h ，在−18 ℃的条件下冷冻1 d ，然后在25 ℃下解冻30 min 。
然后分别测定冷冻面团的失水率、持水率、pH 、质构特性、水分分布以及利用扫描电子显微镜（SEM ）对冷冻面团表面网络结构和蛋白质结构的变化进行研究。
结果表明，食用碱添加量与冷冻面团的失水率呈负相关，可以显著（P <0.05）影响冷冻面团的pH ；在食用碱添加量为4%时，各个冷冻杂粮面团的弹性达到最大值，小麦面团、荞麦杂粮面团、玉米杂粮面团、绿豆杂粮面团的A 21分别达到48.189±1.509、45.652±2.202、43.585±2.472、43.743±1.155，说明食用碱可以抑制水分迁移，进而保持良好的持水性，且能有效改善冷冻杂粮面团面筋蛋白网络结构和品质，进一步提高冷冻杂粮面团品质。
显微组织对AA2050-T84铝锂合金拉伸性能的影响
Trans.Nonferrous Met.Soc.China31(2021)1189−1204Effects of microstructure on tensile properties of AA2050-T84Al−Li alloyDing-ding LU1,Jin-feng LI1,Hong NING1,Peng-cheng MA2,Yong-lai CHEN2,Xu-hu ZHANG2,Kai ZHANG3,Jian-mei LI4,Rui-feng ZHANG11.School of Materials Science and Engineering,Central South University,Changsha410083,China;2.Aerospace Research Institute of Materials and Processing Technology,Beijing100076,China;3.Monash Centre for Additive Manufacturing,Monash University,Clayton3800,Australia;4.School of Chemistry and Chemical Engineering,Ningxia University,Yinchuan750021,ChinaReceived27May2020;accepted8February2021Abstract:The effect of microstructure evolution on the tensile properties of2050Al−Li alloy thick plate aged at 150°C with80mm in thickness(t)was studied from a microstructural perspective.Scanning electron microscope, optical microscope,transmission electron microscope and X-ray diffractometer were used to explore the surface(t/6), interlayer(t/3)and center(t/2)thickness layer of this alloy.Results show that the secondary phases on grain boundaries, precipitates and textures vary depending on the thickness location.The precipitation strengthening has a stronger influence on the alloy along the rolling direction than the transverse direction from the under-aged to the peak-aging condition;however,its effect on the anisotropy is insignificant.The higher Taylor factor(M)value caused by strongerβfiber rolling textures and the intergranular phases is the main reason that leads to the highest strength at the t/2position along the rolling direction.The M-value has a limited change at different thickness layers along the transverse direction, which causes the same tensile strength.Key words:2050Al−Li alloy;tensile properties;anisotropy;precipitate;texture1IntroductionAluminum lithium alloys have been widely used in aerospace,transportation and other industries because of the low density,high strength and heat resistance stability[1].As a typical third-generation Al−Li alloy,the2050Al−Li alloy has a low Li content,increasing the damage resistance and strength by reducing the coplanar slip caused byθ′phase precipitation and the hydrogen embrittlement from excessive hydrogen absorption[2].The2050Al−Li alloy thick plate combines the flaw resistance performance of2xxx alloys and the ultra-high strength of7xxx alloys. Compared with the7xxx alloy thick plate,the2050 Al−Li alloy thick plate has higher elastic modulus,better damage resistance and higher specific strength[1,3,4].LEQUEU et al[5]suggested that an Al−Cu−Li thick plate has a better damage tolerance than a7050-T7451thick plate.WU et al[6]also found that the yield strength and ultimate tensile strength gradually increased from the surface layer to the center layer of an Al−Cu−Li plate with a final thickness of90mm.These uneven mechanical properties at different regions within thick plate dramatically restrict the application of 2050Al−Li alloys.The properties of2050Al−Li alloy can be affected by many factors like segregation in casting ingots,dissolution of secondary phases, recrystallization,hardenability and textures during plastic deformation[5,7].Previous reports[8] indicated that the coarse secondary phases wereCorresponding author:Rui-feng ZHANG,Tel:+86-186********,E-mail:*********************.cn DOI:10.1016/S1003-6326(21)65571-11003-6326/©2021The Nonferrous Metals Society of China.Published by Elsevier Ltd&Science PressDing-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−1204 1190observed in casting ingots and retained in subsequent heat treatment.It will result in stress concentration or crack,which reduces the plasticity, fracture toughness,fatigue properties and stress corrosion resistance[9].Coarse precipitates and dispersoids significantly affect the microstructure refinement and corresponding strengthening in the particle-containing materials[10].As a heat-treatable aluminum alloy,the2050 Al−Li alloy achieves a high yield strength from precipitation strengthening.However,it is also the main factor that leads to the inhomogeneous properties of the material.This hypothesis has been verified from tremendous works by characterizing the number density,size and types of precipitates under various aging environments[11]. LIU et al[7]reported that the Zn and Mg concentration of grain boundary precipitates led to the disparity of corrosion resistance under different quenching rates.Additionally,SHU et al[12]found that the Mg/Zn ratio difference can alter the growth kinetics of theη′phase distributed at the surface layer and central layer.Such a microstructure difference will cause distinct mechanical properties along the normal direction (ND)of7055thick plates.ZHAO et al[13] reported that the pitting corrosion behavior of 95mm-thick2297Al−Li alloy was mainly ascribed to the distribution of the inhomogeneous precipitates.Textures can also contribute to the inhomogeneous strength of thick plates.In contrast to the weak texture of the surface layer in an Al−Li−Cu−Zr alloy with a thickness(t)of12mm, the central part of this alloy presents a strong rolling texture[14].It was also proposed that the texture disparity contributed to the discrepancy of tensile strength.Similarly,WU et al[6]reported that an Al−Li−Cu alloy had a random texture at the surface layer,originating from the greater recrystallization degree with cold deformation during the rolling process.The typical shear texture of R-Cube and strongβfiber rolling textures were found at the t/8and t/2(center)layers due to the weaker recrystallization driving force.From the above mentioned results,it can be found that a strong anisotropy at different thickness layers on the mechanical properties is inevitable. SHE et al[12]investigated the influence of microstructure(center and edge)on the tensile properties along ND in aged7055aluminum alloy plate.They hypothesized that the anisotropy of tensile strength through ND could be mainly attributed to a strongβfiber rolling texture at the center layer.Most Al−Li alloy thin plates were extensively studied by researchers[3,11].However,few works have explored the inhomogeneity along ND of Al−Li thick plates.Further,the understanding of the inhomogeneous mechanical properties from a microstructural perspective is not completely clear. The2050Al−Li alloy thick plates may find potential applications for the aircraft industry for their excellent performance.Nevertheless,the inhomogeneous tensile properties along ND of 2050Al−Li alloy thick plates may hinder their further application.This work aims to investigate the microstructure inhomogeneities and their effect on tensile properties of2050Al−Li alloy plates with a thickness of80mm.We focus on the factors such as secondary phases at grain boundaries, precipitates and rolling texture and their influences on the strength and ductility.The effects of the anisotropy on different layers will also be discussed in this work.2Experimental2.1Materials and proceduresAs-received2050Al−Li alloy plate with a thickness of~80mm in T3condition was provided by Southwest Aluminum(Group)Co.,Ltd.The detailed chemical composition is listed in Table1. The samples were firstly solution heat-treated for60min at~520°C then water quenched to ~25°C.After quenching,the samples were pre-deformed to a plastic strain of4%and aged at 150°C for different durations.Table1Chemical composition of2050Al−Li alloy(wt.%)Composition range Cu Li Mg Ag Mn Zr Ti Zn Fe Si Al Maximum 3.9 1.30.60.70.50.140.10.25<0.1<0.08Bal.Minimum 3.20.70.20.20.20.060.10.25<0.1<0.08Bal.Ding-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−120411912.2Tensile testThe plate was cut into three equal layers from the surface to the center.The layers were spaced ~13mm apart.The samples cut from these equal layers(the surface,the interlayer,the center)were designated as t/6,t/3and t/2positions,respectively. The tensile samples with a diameter of8mm and a length gauge of48mm were prepared from the aged plate with different thickness layers along the rolling direction(RD)and the transverse direction (TD).A schematic about sampling is shown in Fig.1.Tensile testing was conducted on the MTS−810machine at ambient temperature with a strain rate of0.01s−1.Fig.1Schematic diagram showing sample orientations and three thickness positions(t/6,t/3and t/2positions) 2.3Microstructure characterizationThe microstructures were characterized by optical microscope(OM,Leica Microsystems Wetzlar GmbH,Germany)and transmission electron microscope(TEM,FEI Tecnai G220) operated at200kV.The chemical composition of secondary particles was defined by scanning electron microscopy(SEM,Quanta200)with energy-dispersive spectroscopy(EDS,GENE SIS60E).The SEM specimens along ND were ground,polished then etched in the Keller’s reagent for10s.The TEM specimens were prepared by cutting pieces with a thickness of500μm and carefully grinding them to a80μm-thick sheet. These thin pieces were subsequently punched into 3mm-diameter disks.The disks were finally thinned by electro polisher in a solution containing 75%methanol and25%nitric acid(volume fraction) at−40to−25°C.X-ray diffraction(XRD,BruckerD8Discovery) was carried out at40kV and40mA with Cu Kαradiation to determine the textures at different positions along ND.The samples with12mm(RD)×12mm(TD)×3mm(ND)taken from different layers along ND were prepared by electrical polishing.The incomplete pole figures in the three directions of{111},{200}and{220}were measured.The three-dimensional orientation distribution functions(ODFs)were calculated by analysis software to obtain the relative volume fraction of texture components.3Results3.1Tensile propertiesTypical engineering stress−strain curves of 2050Al−Li alloy thick plate aged at150°C along RD and TD are shown in Fig.2.Little serration is observed from the tensile curves.As shown in Figs.2(a,c,e),the curves of specimens along RD demonstrate a stress decrease at high strains,which indicates the occurrence of nonuniform deformation and necking.The ultimate tensile strength(UTS),yield strength(YS)and elongation(El)of2050Al−Li alloy aged plate at the three regions(along TD and RD)are shown in Fig. 3.Significantly inhomogeneous tensile properties appear at different thickness positions of the aged plate.The UTS and YS at the t/2position along RD are 50MPa higher than those at the other positions in all pared to the t/3position,the difference between the UTS and the YS at the t/6 position is slightly over10MPa.The El at the t/2 position is lower than that at the t/6and t/3 positions during all aging time.Meanwhile,El has a stable value of around 10%after30h at different thickness positions.The UTS,YS and El at all regions along TD decrease. The YS at the t/6and t/2positions is similar after 30h and that is10MPa higher than the t/3position. The UTS at different thickness positions has a similar situation as the YS.The YS and UTS at the t/6and t/3positions along TD and RD have nearly the same values in all aging conditions.However, the strength at the t/2position along TD is about 90%of that along RD.Notably,the alloy at the t/2 position exhibits severer anisotropy in strength than the other positions.The YS at the t/2position alongDing-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−12041192Fig.2Engineering stress−strain curves of2050Al−Li alloy thick plate aged at150°C along RD(a,c,e)and TD(b,d,f) at t/6position(a,b),t/3position(c,d),and t/2position(e,f)RD increases by about8%from under-aged to peak-aging condition,while the YS at other positions increases by10%.The YS at the t/3 position along TD has the highest increase(7.3%).3.2Microstructural inhomogeneitiesFigure4shows the fractions of secondary phases at the grain boundaries(GBs)in2050Al−Li alloy thick plate at the three thickness positions.The main chemical compositions of coarse phases are Cu,Fe and Mn basing on EDS point analysis.Li is too light to be detected by EDS.The area fraction (f A),minimum diameter(D min),maximum diameter (D max)of these phases are quantitatively analyzed, as shown in Table2.The area fraction of these coarse phases at the t/2position(1.18%)is higher than that at the t/6and t/3position(0.76%and 0.87%).Ding-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−12041193 Fig.3YS(a,b),UTS(c,d)and El(e,f)of2050Al−Li alloy thick plate aged at150°C from three thickness positions along RD(a,c,e),and along TD(b,d,f)Meanwhile,the D max of the secondary phases at the GBs at the t/2position is the maximum. Secondary phases within grains at the t/2position dissolve into the matrix after the solid-solution treatment,while some intergranular phases remain, as shown in Fig.4(d).Figure4indicates that the phase number around GBs increases from surface to center,where the morphology of these phases turns from particle to lump.Figure5depicts the selected area diffraction patterns(SADPs)along the[112]α(Al)zone axis at t/6position and the[001]α(Al)zone axis at t/3 position for2050Al−Li alloy aged at150°C for30h. The main strong diffraction spots come from theDing-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−12041194Fig.4SEM images of secondary phases in2050Al−Li alloy thick plate after hot rolling at t/6position(a),t/3position (b)and t/2position(c),after solution treatment at t/2position(d),and corresponding EDS analysis(e)Table2Microstructural parameters of coarse phases at GBs in2050Al−Li alloyPosition f A/%D max/μm D min/μmt/60.768.3 1.5t/30.87 6.5 1.6t/2 1.1810.5 1.9α(Al)matrix.The weak sharp diffraction spots at 1/3{220}α(Al)and2/3{220}α(Al)in the[112]α(Al) SADPs,marked with a red circle in Fig.5,are sheet-like T1(Al2CuLi)precipitates with a hexagonal close-packed lattice.Besides,the discontinuous lines passing through the{200}α(Al)and{110}α(Al)spots in the[001]α(Al)SADPs,marked with a white circle in Fig.5,are sheet-like θ′(Al2Cu)precipitates with the tetragonal system. There are no strong diffraction spots of other phases in the SADPs,indicating that T1andθ′precipitates are the dominant precipitates within the grains. Figure6illustrates the bright field TEM image (BFs)of the2050Al−Li alloy thick plate aged at 150°C for15h.Rod-like(A marked with red arrows)and equiaxed(B marked with black arrows) particles are observed at the t/2position.T1 precipitates are found at the t/3position,while the rod-like or equiaxed coarse particles are not observed,as shown in Fig.6(b).Ding-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−12041195 Fig.5Typical SADPs of2050Al−Li alloy aged at150°C for30h corresponding to[112]α(Al)(t/6position)(a)and [001]α(Al)zone axis(t/3position)(b)Fig.6TEM images of2050Al−Li alloy thick plate aged at150°C for15h from t/2position(a)and t/3position(b)in [112]α(Al)zone axisFigure7shows the SADPs and dark field images(DFs)at the t/6,t/3and t/2positions along [112]α(Al)and[001]α(Al)zone axes inside the grains, where both T1andθ′precipitates are observed.It is known that the strength of heat-treated alloys is mainly determined by the types,size and number density of precipitates[10,15].The sizes of T1and θ′precipitates were counted by the Image-Pro Plus software in the present work.Three photos were selected for statistics to ensure the accuracy of the data.The average diameters of T1andθ′precipitates at different regions were quantitatively measured.The average diameter of T1precipitates at the t/6position(70.1μm)is slightly less than that at the t/3and t/2positions(77.4and82.2μm, respectively).There is a competitive relationship for the Cu atoms between T1andθ′precipitates in the Al−Li alloy during aging treatment[16].The average diameter ofθ′precipitates at the t/3 position(99.6μm)is higher than that at the t/6and t/2positions(75.6and77.5μm,respectively).The result is supported by the histograms of diameter in precipitate from different thickness positions,as shown in Fig.8.3.3TextureThe ODF figures illustrate that textures of 2050Al−Li alloy thick plate aged at150°C for 30h are mainly the recrystallized texture(Goss {011}〈001〉,Cube{001}〈100〉),shear textures (Rotate-Cube{001}〈110〉),andβfiber rolling texture which aligns the three main texture components:Brass{011}〈112〉,S{123}〈634〉and Cu{112}〈111〉,as shown in Fig.9.Their volume fractions at the three thickness positions are summarized in Table3.Typical textures at the t/6 and t/2positions are similar,including Brass,S,Cu, Cube and Goss.Cube(30.77%)and Cu(22.66%)at the t/6position are greater than that in the t/2 position with13.46%and8.64%.The Cube,Goss and R-Cube dominate textures at the t/3position, and the volume fraction of R-Cube has the maximum fraction16.89%.The proportions of the recrystallized texture andβfiber rolling texture at the t/6position are36.2%and41.3%,respectively, like the t/2position(34.3%and40.2%).Ding-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−12041196Fig.7TEM images of2050Al−Li alloy thick plate aged at150°C for30h along[112]α(Al)zone axis(a,c,e)and [001]α(Al)zone axis(b,d,f)at t/6position(a,b),t/3position(c,d),and t/2position(e,f)4Discussion4.1Tensile properties and microstructuresPrecipitation is the main parameter that affects the mechanical properties of aged2050 Al−Li alloy.Equation(1)illustrates that the critical shear stress is primarily derived from the precipitates strengthening effect in the aging-hardening aluminum alloys.THOMAS et al[17] analyzed the equilibrium configurations of a dislocation interacting with random distributed unshearable fine-sized obstacles under applied stress.According to Eqs.(1)−(4),both T1andθ′precipitates can hinder the dislocation slip and improve the strength by the Orowan mechanism.Ding-ding LU,et al/Trans.Nonferrous Met.Soc.China 31(2021)1189−12041197Fig.8Histograms of diameter in typical precipitates of 2050Al−Li alloy thick plate aged at 150°C for 30h at t /6position (a,b),t /3position (c,d),and t /2position (e,f)1/2p 0p 0[/2(1)](1/)ln(1.061/)Gb L T R τυ=π-(1)p p p0p 0.2560.9310.9198D T D L T f ππ⎛⎫=⨯-⎪⎝⎭(2)1/2p 0p 0[/2(1)](1/)ln(1.225/)Gb L T R τυ=π-(3)p p p0p 0.3060.931 1.0618D T D L T f ππ⎛⎫=⨯-⎪⎝⎭(4)where τp is the critical resolved shear stress withinthe grain,G is the shear modulus,b is the Burgers vector component of the slip dislocation,υis the poisson ratio,D p is the average particle radius,T p is the average particle thickness,f is the particle volume fraction,R 0is the radius of the dislocation nucleation zone and L 0is the mean distance between particles.The habit plane of T 1precipitatesDing-ding LU,et al/Trans.Nonferrous Met.Soc.China31(2021)1189−12041198Fig.9ODFs of2050Al−Li alloy thick plate aged at150°C for30h at t/6position(a),t/3position(b),and t/2 position(c)Table3Texture content at different thickness positions of2050Al−Li alloy aged at150°C for30h(vol.%) Position Cube R-Cube Goss Brass S Copper t/630.77 5.38 6.0612.5922.66 t/310.4916.89 6.47t/213.4620.7915.6415.888.64 is{111}and that ofθ′precipitates is{100},while the slip system of2050Al−Li alloys is{111}〈110〉.τp of precipitates at the habit plane of{111}is greater than that of{100}.The above equations indicate that the shear strain gradually increased with the average diameter and number density of precipitates.The interaction between dislocation and T1precipitates consists of shearing and by-passing controlled by the thickness of T1 precipitates[17−20].Meanwhile,a similar thickening evolution(an average T1precipitate thickness less than2nm)in AA2050alloy aged at 155°C was reported[21].The shearing mechanism is another strengthening method of T1precipitates. The density and size of T1precipitates have a significant effect on the strengthening of this alloy.The temperature distribution at different thicknesses will not be uniform during the hot rolling,which affects the solute diffusion rate,strain, dynamic recrystallization and precipitations[13,22]. It has been well acknowledged that solute atoms have low free energy at the GBs,enabling the segregation of solute atoms and then reducing the formation energies of GBs[23].The strengthening effect of Cu solutes on GBs is forming new Cu−Al bonds that contribute to the grain boundary cohesion,thereby increasing GBs resistance against crack propagation[24].Segregation of solute(Cu and Fe)around GBs was observed in Al−Li-alloy systems[25].The Cu segregation at the t/2position at the GBs is higher than that at other positions due to the higher diffusion rate.The entropy difference of Cu in the Al-matrix adjacent to GBs during hot rolling will affect the feature of subsequent precipitates during aging treatment.Most alloying elements in specimens,like Cu and Mn,dissolve into the Al matrix due to the high solidification rate[1].This phenomenon explains the solute elements retained around GBs by forming the Cu-rich and Fe-rich phases(as shown in Fig.4). The strengthening effect of GBs at the t/2position is remarkable as the segregation of Cu/Fe and can significantly increase the fracture energy.The enrichment in Cu is not associated with an appreciable enrichment in Li[26].In an Al−Cu−Li alloy,the rapid segregation of Li around GBs was reported in underaged conditions[27].Hence,the segregation of Li around GBs can not be ignored in this alloy.LI et al[1]reported that the2050Al−Li alloyhas a“hardenability”which is different from the classical definition for steel.The Cu-rich secondary phases at GBs and lenticular-shaped Cu-containing secondary phases have more significant differences due to the distance away from the quenching end[1].The Cu-enriched secondary phases around GBs are formed during the quenching process by taking Cu atoms away from the matrix,which results in a restricted growth of T1precipitates within grains during the aging treatment.Two particles(A and B in Fig.6(a))at the t/2position have similar morphologies of those secondary phases reported by LI et al[1].This result implies that the concentration of Cu in the Al-matrix of this alloy from the t/2position is lower than that of the location near the quenching end due to the formation of those Cu-rich phases.The solid solubility of solute atoms in the Al-matrix from the t/6position is remarkable due to the higher quenching rate,contributing to the precipitation during aging.The slip system can activate easily with a higher Schmid factor(SF)that causes decreasing dislocation density by cross-slip and lower deformation within grains under a given load[28,29].SFs of the tested alloy along RD and TD in{111}〈110〉were calculated by the Orientation software,as shown in Tables4and5. According to Tables3−5,the weighted average SFs at the t/6,t/3and t/2positions along RD in {111}〈110〉are0.237,0.285and0.246respectively, which are higher than those along TD(0.227,0.276 and0.210).The average SF at the t/6and t/2 positions along RD in{111}〈110〉is almost the same.The dislocation density is supposed to have a minimal difference between the t/6and t/2positions after4%pre-deformation along RD.During the pre-deformation at the t/3position,the dislocation density yielded is lower due to the lowest SF value. Many works indicated that the stress field around the dislocation promotes the diffusion of Cu and also reduces the energy required for the T1 precipitates nucleation[30].The dislocations caused by the plastic deformation before aging can be treated as the ideal position for the T1 precipitates nucleation[19].The difference in the dislocation density and the concentration of Cu atoms from different thicknesses can dramatically alter microstructures.As a result,the number density of T1precipitates at t/6and t/2positions is Table4Schmid factors of typical texture in{111}〈110〉along RD of2050Al−Li alloy thick plate aged at150°C for30hTexture Cube R-Cube Goss Brass S Copper (111)[110]0.40800.4080.4100.1010 (111)[110]0.40800.4080.0040.2670 (111)[110]0.40800.4080.1380.0570.271 (111)[110]0.40800.4080.2750.4250.271 (111)[101]0.40800.4080.1380.2290.275 (111)[101]0.40800.4080.0040.0950.004 (111)[101]0.4080.4080.4080.4100.0070.001 (111)[101]0.4080.4080.4080.2750.3310.270 (111)[011]0000.2710.3310.275 (111)[011]00000.1720.004 (111)[011]00.40800.2710.0640.270 (111)[011]00.408000.0940.001Table5Schmid factors of typical texture in{111}〈110〉along TD of2050Al−Li alloy thick plate aged at150°C for30hTexture Cube R-Cube Goss Brass S Copper (111)[110]0.408000.0010.0710 (111)[110]0.40800.4080.0040.2660 (111)[110]0.408000.2700.1200 (111)[110]0.40800.4080.2750.0750 (111)[101]00.40800.2700.0570 (111)[101]00.4080.4080.0040.0890 (111)[101]0000.0010.2990.408 (111)[101]000.4080.2750.4450.408 (111)[011]0.4080.40800.2710.0140 (111)[011]0.4080.408000.1770 (111)[011]0.408000.2710.1790.408 (111)[011]0.4080000.3700.408higher than that at the t/3position.A higher diameter of T1precipitates at the t/2position was also observed.Minor lattice misfits between precipitate and matrix exist along other directions perpendicular to the elongation direction,making the corresponding interfaces around the precipitates[19,31].The strain field provides an effective impediment against dislocation movement, thus helps to strengthen the rger precipitates have a better effect on the strength dueto the increasing strain field caused by the lattice misfit between the precipitate and matrix.The number density of T1precipitates may cause the precipitation strengthening at the t/2position along RD is less than that at the t/6position.Previous reports[32]suggested that the strength anisotropy may be controlled by the volume fraction of T1 precipitates related to the{111}fiber texture intensity.The interaction between dislocations and precipitates is different at different grain orientations when loaded in a confirmed direction, which causes that the precipitation strengthening in specimens along RD is higher than that along TD. Nonetheless,the effect of precipitation in anisotropy is not significant,as shown in Fig.3.The secondary phases around GBs hinder the occurrence of slip transfer,which contributes to the higher tensile strength of alloys[1].However,these phases around GBs are brittle and incoherent, resulting in the formation and growth of cracks under the critical stress[33].The failure of macrocracks extended into the soft matrix results in decreasing ductility[12].The residual phases around GBs with a decreasing cooling rate on solidification and hot rolling process result in the strength increase.However,the ductility decreases from the t/6position to the t/2position.The segregation of Li and Cu contributes to the precipitation of T1andθ′during the aging treatment,which also causes the increase of strength and the decrease of ductility.The higher grain boundary density is the reason causing the greater strength along TD than that along RD.It suggests that the grain boundary strengthening is one of the factors that influence the anisotropy in strength.A schematic provides the crack propagation path of2050Al−Li alloy,as shown in Fig.10. When loaded along TD,the crack gathers and expands along GBs,and its propagation direction is difficult to change.Besides,the grains are easy to be elongated along RD by plastic deformation, which results in the necking and the deteriorated mechanical properties later.As shown in Fig.11, the fracture morphologies of2050Al−Li alloy thick plate artificially aged at150°C for30h after the tensile test support this result.At the same time, many rough dimples are found within grains.The dimples number and the GBs density in the alloy along RD are higher than those along TD, which means that the elongation at three different Fig.10Crack propagation path of2050Al−Li alloy thick plate under loading along RD(a)and TD(b)positions along TD is lower than that along RD.4.2Texture analysisIt should be noticed that the textures have minimal differences during the various aging conditions[34],which means that the textures of this alloy formed in the hot rolling and solution treatment.The deformation parameters of temperature and strain in hot rolling affect the microstructures of Al−Li alloy at different thickness positions[35,36].The interface between the alloy plate and the roller during the hot rolling process resulted in a remarkable temperature drop at the t/6position(the surface vicinity).While the temperature increases because of the heat generated by the plastic deformations at the t/2position[37]. Each variable leads to the temperature gradually decreasing in this alloy from the t/6position to。
声学双曲构型超材料的负折射特性研究
第53卷第2期2024年2月人㊀工㊀晶㊀体㊀学㊀报JOURNAL OF SYNTHETIC CRYSTALS Vol.53㊀No.2February,2024声学双曲构型超材料的负折射特性研究刘㊀松1,赵仁洁1,杜一帆1,吴㊀芳2,宋和滨3,高㊀鹏3(1.大连理工大学工业装备结构分析优化与CAE 软件全国重点实验室,大连㊀116024;2.大连船舶重工集团有限公司,大连㊀116011;3.中国船级社(CCS)大连分社,大连㊀116013)摘要:声学双曲超材料是具有双曲色散特性的人工材料,具有极强的各向异性,其负折射特性是研究实现高分辨率聚焦型超透镜的理论依据㊂针对远场噪声源识别受制于0.5倍波长声波瑞利衍射识别分辨率问题,结合声学超材料对声波的优异调控效果,引进可以实现亚波长超分辨率成像的双曲超材料,利用其负折射特性设计了一种用于工作频率为2271.5Hz 的声学双曲结构㊂分析了该构型的双曲结构色散特性及负折射特性,结果表明声波在该双曲超材料中传播的群速度方向垂直于波矢,并沿着色散曲线的法线方向㊂本文的研究为实现对声波和弹性波的任意调控,以及噪声源的聚焦定位㊁识别放大等提供了一定的设计参考㊂关键词:声学超材料;声学透镜;弹性波带隙特性;负折射;双曲色散;声聚焦中图分类号:O735;TL375.2㊀㊀文献标志码:A ㊀㊀文章编号:1000-985X (2024)02-0246-06Negative Refraction Characteristics of Acoustic Hyperbolic Configuration MetamaterialsLIU Song 1,ZHAO Renjie 1,DU Yifan 1,WU Fang 2,SONG Hebin 3,GAO Peng 3(1.State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China;2.Dalian Shipbuilding Industry Company,Dalian 116011,China;3.China Classification Society (CCS)Dalian Branch,Dalian 116013,China)Abstract :Acoustic hyperbolic metamaterials are artificial materials with hyperbolic dispersion characteristics and strong anisotropy.Their negative refractive properties are the theoretical basis for studying the implementation of high-resolution focused superlenses.In response to the problem that the recognition of far-field noise sources is limited by the resolution of 0.5times wavelength acoustic Rayleigh diffraction recognition,combined with the excellent control effect of acoustic metamaterials on sound waves,a hyperbolic metamaterial that can achieve sub wavelength super-resolution imaging is introduced,and its negative refractive characteristics are used to design an acoustic hyperbolic structure for working at a frequency of 2271.5Hz.The dispersion and negative refraction characteristics of the hyperbolic structure of this configuration were analyzed,and the results show that,the group velocity direction of sound waves propagating in this hyperbolic metamaterial is perpendicular to the wave vector and follows the normal direction of the dispersion curve.The research in this paper provides some design references for realizing arbitrary regulation of sound wave and elastic wave,as well as focusing,locating,identifying and amplifying noise sources.Key words :acoustic metamaterial;acoustic lens;elastic wave bandgap characteristic;negative refraction;hyperbolic dispersion;acoustic focusing㊀㊀收稿日期:2023-08-21㊀㊀基金项目:国家自然科学基金(51609037)㊀㊀作者简介:刘㊀松(1982 ),男,吉林省人,博士,高级工程师㊂E-mail:liusong@0㊀引㊀㊀言负折射率材料是某一特定频段下折射率为负数的新型超材料,当入射波与折射波位于法线的同侧时被称作负折射㊂正常聚焦透镜只聚焦传输波的能量,但是负折射材料可以在聚焦传输波的基础上继续聚焦倏㊀第2期刘㊀松等:声学双曲构型超材料的负折射特性研究247㊀逝波的能量,可以突破衍射极限,形成完美透镜㊂该类材料最早在电磁波领域被提出,前苏联物理学家Veselago[1]通过大量的理论推导设想了一种介电常数和磁导率均为负数的材料,具有负的折射率,当电磁波通过具有该特性的材料后出现负折射效应和声聚焦特性㊂Pendry[2]根据负折射的理论制备出具有等效负介电常数的周期性特性的超材料㊂Smith等[3]与Shelby等[4]设计了一种棱镜,首次从实验角度证实了负折射现象的真实存在,并由此实验证明当光线入射到负折射率介质表面时,折射光线与入射光线分布在分界面一侧㊂声学超材料具有与电磁材料通过周期性结构来调控电磁波传播的相似性[5]㊂声学超材料的特殊属性,尤其是负折射特性研究可为声场聚焦和声源定位提供支撑[6]㊂声学双曲超材料是具有双曲色散特性的人工材料,具有极强的各向异性,通过改变双曲材料结构尺寸㊁分布规律能够完成对声波强度和传播方向的控制[7]㊂对于声场聚焦问题,需要根据声源特性或设定的带宽对超材料进行详细的拓扑优化设计㊂王涵[8]从声学超材料的波衰减特性和双负特性这两个重要性质入手,提出三种新型蜂窝声学超材料均具有双负特性,但并未证实其负折射线现象㊂宋刚永[9]设计了基于变换声学理论的浸没式声学放大透镜,通过实验验证该透镜可在5650~6350Hz实现声场聚焦㊂杨帅等[10]在空气中将工字钢排列为正方形实现了负折射率,但只有在特定的频率范围,如5000Hz左右,声波在Z型线性波导中才能够较好地传播㊂整体来讲,目前双曲超材料的带隙频段较高,随着声源特性频率的降低,需设计可用于中低频段的超材料㊂本文基于拓扑优化方法,设计了一种可用于中低频段声场调控的双曲构型,从平面波入射三角棱镜声场分布研究入手,通过数值模拟方法分析了该构型的双曲结构色散特性及负折射特性㊂1㊀声学双曲构型设计在能够保持晶格对称性的前提下,构成晶体的最小的周期性结构单元称为晶体的单胞㊂本文设计双曲构型单胞示意图如图1所示,晶格常数a=26mm,交错分布的结构臂长d为22.5mm,壁厚t为1mm,尺寸构型由两个对称分形组成,两部分间隔c为2mm㊂图1㊀双曲构型单胞示意图Fig.1㊀Schematic diagram of the acoustic hyperbolic configuration metamaterial 本文设计亮点在于声子晶体内部有交错分布的结构臂,当声波通过此结构后能够延长声波的传递路径,进而延长了声波总的传播时间,最终实现对声波的相位调控㊂2㊀能带图分析结合双曲构型单胞特点,采用正方形晶格计算其能带特性,正方形晶格不可约布里渊区示意如图2所示㊂数值模拟双曲构型能带结构时,边界条件选为Floquet周期,根据Bloch定理可知,将波矢k沿着倒格矢空间内不可约布里渊区边界进行扫掠,即可得到能带结构,同时得到各能带对应的结构振动模态㊂扫掠方向为M-Γ-X-M㊂材料参数为:泊松比σ=0.41㊁弹性模量E=2450MPa㊁波速c1=716m/s,密度ρ1=1300kg/m3㊂空气参数为:密度ρ2=1.21kg/m3,速度c2=343m/s㊂计算得到的能带结构如图3所示㊂图中横坐标为波矢k的扫掠方向,即形成一个完整的扫掠回路;纵坐标为扫掠所对应的频率,频率范围为0~6000Hz㊂通过对所设计构型的能带结构模拟研究,从能带结构图中可以发现,第二能带的带顶较平,并且关于Γ248㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷点附近对称性较好,共振频率为2271.5Hz㊂这表明声学超材料拥有更多的分支㊁更长的传播路径,且在此频率附近将出现负折射现象㊂图2㊀正方形晶格不可约布里渊区示意图[11]Fig.2㊀Schematic diagram of irreducible Brillouin region of a square lattice[11]图3㊀设计的双曲超材料的能带结构图Fig.3㊀Energy band structure diagram of designed hyperbolic metamaterials 3㊀色散特性在二维空间内,声学双曲超材料的等频线分布情况可以用声波色散方程描述:k 2x ρx +k 2y ρy =ω2B (1)式中:k x 为x 方向的波矢分量,k y 为y 方向的波矢分量,ρx 为x 方向的等效密度分量,ρy 为y 方向的等效密度分量,ω为声波波数,B 为等效模量㊂本文设计的双曲构型在2271.5Hz 时的等频线为双曲分布,双曲色散曲线如图4(a)所示,入射波由自由空间入射到双曲媒质,其入射波的传播方向为k i ㊁折射方向为k r 及双曲媒质中的群速度方向为v g ,其中群速度与频率关系式由v g =Δk ω可知其群速度的方向垂直于波矢,即沿着色散曲线的法线方向㊂尽管折射波的相速度为正,但入射波与折射波的能流都在法线同侧,因而此时出现负折射㊂图4(b)为通过COMSOL Multiphysics 软件提取的双曲构型的二维等频色散分布图㊂图4㊀双曲构型色散曲线示意图Fig.4㊀Diagram of hyperbolic configuration dispersion curve 4㊀折射率计算双曲构型超材料折射率计算示意图如图5所示,计算区域由五大部分组成:完美匹配层(perfectly matched layer,PML)-背景压力场-双曲构型-周期性边界-完美匹配层㊂背景压力场区域提供幅值为1Pa 的㊀第2期刘㊀松等:声学双曲构型超材料的负折射特性研究249㊀平面波,模拟声波入射环境;图中四个红点表示提取双曲构型前后声压值的位置点,在声波入射方向布置两个传声器1和2,分别在距离单胞左边界30和0mm 处,在构型右侧同样布置2个传声器3和4,提取四个位置点的声压值便于后续计算㊂在COMSOL Multiphysics 压力声学频域中进行计算㊂进行网格划分时,完美匹配层划分5层网格,其余部分按照四边形网格划分,单元尺寸选为1mm㊂在折射率图中横坐标为扫频频率,范围为2000~3000Hz,纵坐标为各个频率计算得到对应的折射率㊂计算的双曲构型单胞尺寸选为26mm ˑ26mm,背景压力场尺寸选为26mm ˑ150mm,周期性边界尺寸选为26mm ˑ150mm,完美匹配层尺寸选为26mm ˑ130mm,图5中可看到计算域的划分以及各区域的名称㊂为保证超材料出现中低频带隙特性,将构型在2000~3000Hz 的频率范围内在空气场中作扫频分析,计算声场的尺寸为510mm ˑ26mm,随后提取构型左边界的入射声压及左边界的出射声压随之得到该双曲材料的透射系数与反射系数,得到透射系数和反射系数后可以得到折射率的表达式n =-i lg x +2πm ka (2)式中:k =ωC 0为声波波数,ω为圆频率,C 0为声波声速,ω=2πf ,f 为频率;m 为反余弦函数分支,仅能取整数,由于实际声传播方向不存在周期性结构,故m =0;i 为虚数㊂x =1-R 2P +T 2P +r 2T P (3)r =ʃ(R 2P -T 2P -1)-4T 2P(4)式中:T P 为透射系数,R P 为反射系数,n 为折射率,a 为晶格常数,取值为26mm㊂计算得本双曲构型折射率如图6所示,可以清晰看到本构型在2271.5Hz 时的折射率为负数㊂图5㊀COMSOL 计算折射率示意图Fig.5㊀COMSOL calculation of refractive index diagram 图6㊀双曲构型折射率计算示意图Fig.6㊀Schematic diagram for calculating refractive index of hyperbolic configuration 5㊀负折射特性数值仿真验证通过有限元分析方法对双曲构型的负折射特性进行仿真验证㊂将双曲构型排列为边长尺寸为461mm 的三角棱镜(见图7),置于自由场中,四周采用完美匹配层营造良好的吸声效果,避免回波干扰;在棱镜左侧设置介质为空气的背景压力场平面波幅值为1Pa,三角棱镜右侧部分设为空气域,如图8所示㊂为对比双曲构型负折射特性仿真的效果,在保证计算域条件相同的情况下,分别探讨了有无三角棱镜的声场传播特性㊂首先给出平面波在空气域中的传播特性,可以看到平面波在声场中均匀传播,如图9所示㊂然后在声场中添加三角棱镜,在棱镜左侧施加平面波完成激励,平面波的入射方向沿棱镜左侧向右(如图250㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷10)㊂观察平面波穿过声学双曲介质排布而成三角棱镜后的声场分布可以清晰看出,当声波在经过声学双曲超材料三角棱镜的声波调控后,入射波与经过声学双曲超材料调控后的折射波位于法线同侧,即出现了负折射现象㊂为了使负折射效果更加明显,该部分放大了显示倍数,且在完美匹配层的声学边界中对声压进行计算,证明了声压呈现衰减状态,声波传播无反射㊂图7㊀双曲构型棱镜示意图Fig.7㊀Schematic diagram of a hyperbolic configurationprism图8㊀COMSOL负折射验证示意图Fig.8㊀Schematic diagram of negative refractionverification图9㊀平面波无棱镜声场分布示意图Fig.9㊀Schematic diagram of plane wave sound field withoutprism图10㊀平面波入射三角棱镜声场分布示意图Fig.10㊀Schematic diagram of plane wave incidentsound field of triangular prism 从平面波有无三角棱镜耦合的声场分布图对比来看,负折射率的双曲介质对平面波的传播起到了调控作用,当声波穿过透镜后声波的传播方向得到了改变,入射声波经声学双曲超材料调控后的折射波与入射波位于法线的同侧㊂由斯涅耳定律可知,棱镜的折射率为负数,该材料存在负折射现象,经过有限元仿真验证了所设计声学双曲超材料的负折射属性㊂这说明本文所设计的声学双曲超材料单元可以对相应声波进行调控,该双曲构型后续可以用于声学透镜的聚焦㊂6㊀结㊀㊀论本文提出一种声学双曲超材料构型,分析了该构型的负折射特性,基于有限元分析软件对该构型的折射率进行了计算,折射率为负数,该构型满足负折射的条件㊂从能带结构图中可以发现第二能带的带顶较平,并且关于Γ点附近对称性较好,共振频率为2271.5Hz㊂这表明本文设计的声学双曲超材料拥有较多分支,对声波的传播路径可以有效延长,且在此频率附近出现了负折射现象,可用于声波调控及声场聚焦㊂本文的研究为实现对声波和弹性波的任意调控,以及远场噪声源的聚焦定位㊁识别放大等方面提供了一定的设计参考㊂参考文献[1]㊀TANASHYAN M M,LAGODA O V,VESELAGO O V,et al.A pathogeneteic approach to the treatment of vestibular disorders in angioneurology[J].Zhurnal Nevrologii i Psikhiatrii Im S S Korsakova,2019,119(5):32.[2]㊀PENDRY J B.Transfer matrices and conductivity in two-and three-dimensional systems.I.Formalism[J].Journal of Physics:CondensedMatter,1990,2(14):3273-3286.㊀第2期刘㊀松等:声学双曲构型超材料的负折射特性研究251㊀[3]㊀SMITH D R,PADILLA W J,VIER D C,et posite medium with simultaneously negative permeability and permittivity[J].PhysicalReview Letters,2000,84(18):4184-4187.[4]㊀SHELBY R A,SMITH D R,SCHULTZ S.Experimental verification of a negative index of refraction[J].Science,2001,292(5514):77-79.[5]㊀李丽萍.分形声学超材料声学特性研究[D].长沙:湖南大学,2018.LI L P.Study on acoustic characteristics of fractal acoustic metamaterials[D].Changsha:Hunan University,2018(in Chinese).[6]㊀LI J,FOK L,YIN X B,et al.Experimental demonstration of an acoustic magnifying hyperlens[J].Nature Materials,2009,8(12):931-934.[7]㊀SHEN C,XIE Y B,SUI N,et al.Broadband acoustic hyperbolic metamaterial[J].Physical Review Letters,2015,115(25):254301.[8]㊀王㊀涵.蜂窝型声学超材料带隙特性与双负特性的数值模拟研究[D].秦皇岛:燕山大学,2022.WANG H.Numerical simulation study on bandgap and double negative characteristics of honeycomb acoustic metamaterials[D].Qinhuangdao: Yanshan University,2022(in Chinese).[9]㊀宋刚永.声学超材料对声波的调控理论与实验研究[D].南京:东南大学,2019.SONG G Y.Theoretical and experimental study on the regulation of acoustic metamaterials on sound waves[D].Nanjing:Southeast University, 2019(in Chinese).[10]㊀杨㊀帅,李昌清,赖虹君,等.流固混合声子晶体中负折射与导波特性研究[J].哈尔滨工程大学学报,2022,43(9):1370-1375.YANG S,LI C Q,LAI H J,et al.Study on negative refraction and guided wave characteristics in liquid-solid mixed phononic crystals[J].Journal of Harbin Engineering University,2022,43(9):1370-1375(in Chinese).[11]㊀LIU J,LI L P,XIA B Z,et al.Fractal labyrinthine acoustic metamaterial in planar lattices[J].International Journal of Solids and Structures,2018,132/133:20-30.。
物理专业英语词汇(E)
物理专业英语词汇(E)e layer e 层e process e 过程eagle mounting 伊格尔光栅装置early type stars 早型星earnshaw theorem 厄钉定理earphone 耳机earth 地球earth bar 接地棒earth capacity 大地电容earth currents 大地电流earth ellipsoid 地球椭球earth magnetic field 地磁场earth magnetic pole 地磁极earth observation satellite 地球观测卫星earth plate 接地导板earth potential 大地电位earth satellite 地球卫星earth science 地球科学earth spheroid 地球偏球体earth's atmosphere 地球大气earth's magnetic field 地磁场earth's magnetic pole 地磁极earth's magnetism 地磁earth's mantle 地幔earth's oblateness 地球偏率earth's surface 地表earthing 接地earthquake 地震earthshine 地照earthtremors 地震east longitude 东经ebert fastie mounting 埃贝特法斯铁装置ebonite 硬橡胶ebullition 沸腾eccentric anomaly 偏近点角echelette 红外光栅echelette grating 红外光栅echelle 中阶梯光栅echelle spectroscope 中阶梯光栅分光镜echo 回声echo ranging 回波测距echo sounder 回声探测器echo sounding 回声探测echo suppressor 回声抑制器eclipse 食eclipsing binary 食双星eclipsing variable 食双星ecliptic 黄道ecliptic coordinates 黄道坐标ecliptic plane 黄道面economizer 节能器eddington limit 埃丁顿极限eddy 涡流eddy current 涡流eddy current loss 涡琉耗eddy currents 涡电流eddy diffusion 涡俩散eddy field 旋涡场eddy flow 涡流eddy friction 涡动摩擦eddy motion 涡旋运动eddy viscosity 涡动粘性edge dislocation 边缘位错edge effect 边缘效应edge focusing 边缘聚焦edge tone 边棱音edison effect 爱迪生效应effective area 有效面积effective atomic number 有效原子序数effective charge 有效电荷effective cross section 有效截面effective current 有效电流effective differential cross section 有效微分截面effective dose equivalent 有效剂量当量effective g value 有效 g 值effective head 有效落差effective height 有效高度effective impedance 有效阻抗effective inductance 有效电感effective interaction 有效相互酌effective magnetic field 有效磁场effective mass 有效质量effective multiplication factor 有效倍增因数effective power 有效功率effective pressure 有效压力effective pyranometer 地面辐射表effective quantum number 有效量子数effective radiation 有效辐射effective range 有效射程effective resistance 有效电阻effective temperature 有效温度effective value 有效值effective voltage 有效电压effective wavelength 有效波长efficiency 效率efflux velocity 喷气速度effusion 泻流ehrenfest theorem 厄伦费斯脱定理eia standard eia 标准eigenfrequency 本盏率eigenfunction 特寨数eigenmode 固有模式eigenrotation 固有转动eigenstate 本宅eigenvalue 本盏eigenvector 本崭量eigenvlaue problem 本盏问题eight vertex model 八顶点模型eightfold way 八维法eikonal 程函eikonal approximation 程函近似einstein 爱因斯坦einstein de broglie formula 爱因斯坦德布罗意公式einstein de haas effect 爱因斯坦德哈斯效应einstein de sitter universe 爱因斯坦德呜宇宙einstein equation 爱因斯坦方程einstein shift 爱因斯坦位移einstein tower 爱因斯坦塔einstein universe 爱因斯坦宇宙einstein's formula for specific heat 爱因斯坦比热公式einstein's relation 爱因斯坦关系einstein's transition probability 爱因斯坦跃迁概率einsteinium 锿ejection 放射ejector 喷射器ejector vacuum pump 喷射真空泵ekman layer 埃克曼层elastance 倒电容elastic 弹性的elastic after effect 弹性后效elastic anisotropy 弹性蛤异性elastic body 弹性体elastic coefficient 弹性常数elastic collision 弹性碰撞elastic compliance 弹性柔量elastic constant 弹性常数elastic deformation 弹性形变elastic energy 弹性能elastic equilibrium 弹性平衡elastic fatigue 弹性疲劳elastic force 弹力elastic hysteresis 弹性滞后elastic limit 弹性极限elastic manometer 弹性压力计elastic modulus 弹性模数elastic plastic deformation 弹塑性畸变elastic relaxation 弹性弛豫elastic scattering 弹性散射elastic scattering cross section 弹性散射截面elastic stability 弹性稳定性elastic surface wave device 弹性表面波设备elastic vibration 弹性振动elastic wave 弹性波elasticity 弹性elasto plastic deformation 弹塑性变形elastodynamics 弹性力学elastomer 弹性体elastoplastic wave 弹塑性波elastoviscoplasticity 粘弹可塑性electret 永电体electric 电的electric arc 电弧electric balance 电力秤electric bell 电铃electric calorimeter 电量热器electric capacity 电容electric charge 电荷electric circuit 电路electric clock 电钟electric conduction 电导electric conductor 导电体electric convection current 对羚流运羚流electric current 电流electric dipole 电偶极子electric dipole moment 电偶极矩electric dipole radiation 电偶极辐射electric discharge 放电electric discharge lamp 放电灯electric displacement 电移electric double layer 双电荷层electric field 电场electric field strength 电场强度electric force 电力electric furnace 电炉electric heater 电热器electric image 电象electric lamp 电灯electric lighting 电气照明电照electric line of force 电力线electric machine 电机electric micrometer 电测微计electric moment 电矩electric motor 电动机electric multipole radiation 电多极辐射electric musical instrument 电乐器electric noise 电噪声electric oscillation 电振荡electric potential 电势electric power 电功率electric quadrupole moment 电四极矩electric refrigerating element 电致冷元件electric resistance 电阻electric spark 电火花electric susceptibility 电极化率electric vector 电矢electric wave 电波electric welding 电焊electric wind 电风electric wire 电线electrical 电的electrical double layer 双电荷层electrical engineering 电工学electrical measuring instrument 电测量仪表electrical neutral axis 电中性线electrical pulse 电脉冲electrical resonance 电共振electrical thermometer 电温度表electricity 电electrification 电气化;带电electro discharge machining 放电加工electro rheological fluid 电龄学铃electroacoustic transducer 电声转换器electroacoustics 电声学electrocapillarity 电毛细酌electrochemical 电化学的electrochemical constant 电化学常数electrochemical equivalent 电化当量electrochemical polarization 电化学极化electrochemical potential 电化电势electrochemistry 电化学electrode 电极electrode potential 电极电位electrodynamic 电动力学的electrodynamics 电动力学electroendosmosis 电内渗electrography 电子照相法electrohydrodynamics 电铃动力学electrokinetic phenomenon 电动学现象electrokinetic potential 电动学电位electrokinetics 电动学electroluminescence 电发光electrolysis 电解electrolyte 电解质electrolytic condenser 电解电容器electrolytic conduction 电解导电electrolytic corrosion 电化腐蚀electrolytic polarization 电解极化electrolytic polishing 电解抛光electrolytic semiconductor 电解半导体electrolytic solution 电解液electromagnet 电磁铁electromagnetic 电磁的electromagnetic constant 电磁常数electromagnetic coupling 电磁耦合electromagnetic effect 电磁效应electromagnetic energy 电磁能electromagnetic field 电磁场electromagnetic flowmeter 电磁量计electromagnetic force 电磁力electromagnetic horn 电磁喇叭electromagnetic induction 电磁感应electromagnetic interaction 电磁相互酌electromagnetic lens 电磁透镜electromagnetic mass 电磁质量electromagnetic mass separator 电磁质量分离器electromagnetic momentum 电磁动量electromagnetic oscillations 电磁振荡electromagnetic oscillograph 电磁式示波器electromagnetic pump 电磁泵electromagnetic radiation 电磁辐射electromagnetic scattering 电磁散射electromagnetic shielding 电磁屏蔽electromagnetic system of units 电磁单位制electromagnetic unit 电磁单位electromagnetic wave 电磁波electromagnetics 电磁学electromagnetism 电磁electromechanical analogy 机电模拟electromechanical transducer 机电转换器electrometer 静电计electrometer tube 表用管electromotive force 电动势electron 电子electron accelerator 电子加速器electron affinity 电子亲和力electron attachment 电子附着electron avalanche 电子雪崩electron beam 电子束electron beam machining 电子束加工electron beam pumped laser 电子束激励激光器electron capture 电子俘获electron channeling 电子沟道效应electron cloud 电子云electron concentration 电子浓度electron correlation 电子关联electron current 电子流electron cyclotron resonance heating 电子回旋共振加热electron density 电子密度electron diffraction 电子衍射electron diffraction camera 电子衍射摄象机electron diffraction pattern 电子衍射图样electron donor acceptor complex 电子施周昼合物electron emission 电子发射electron energy loss spectroscopy 电子能量损失能谱法electron gas 电子气electron hole 电子空穴electron hole pair 电子空穴对electron holography 电子线全息学electron impact 电子撞击electron impact spectroscopy 电子撞烩谱学electron interferometer 电子干涉仪electron isomerism 电子同质异能性electron lens 电子透镜electron linac 电子直线加速器electron linear accelerator 电子直线加速器electron mass 电子质量electron microscope 电子显微镜electron migration 电子移动electron mirror 电子镜electron multiplier 电子倍增器electron neutrino 电子中微子electron nuclear double resonance 电子核双共振electron optical 电子光学的electron optics 电子光学electron orbit 电子轨道electron pair 电子对electron pair bond 电子对键electron phonon interaction 电子声子相互酌electron physics 电子物理学electron plasma 电子等离子体electron plasma wave 电子等离子波electron positron collision 电子正电子碰撞electron positron field 电子正电子场electron positron pair 电子正电子对electron rays 电子射线electron ring accelerator 电子环加速器electron scattering 电子散射electron shell 电子壳electron shell structure 电子壳层结构electron source 电子源electron spectroscopy 电子光谱学electron spectrum 电子能谱electron spin 电子自旋electron spin double resonance 电子自旋双共振electron spin resonance 电子自旋共振electron synchrotron 电子同步加速器electron telescope 电子望远镜electron temperature 电子温度electron theory 电子论electron theory of metals 金属电子论electron transit time 电子转移时间electron trap method 电子陷阱法electron traps 电子陷阱electron tube 电子管electron volt 电子伏特electron wave 电子波electronegative 阴电性的electronegative element 阴电性元素electronegative gas 阴电性气体electronegativity 负电性electronic 电子的electronic band spectrum 电子带谱electronic charge 电子电荷electronic configuration 电子组态electronic impact 电子撞击electronic lens 电子透镜electronic mail 电子邮政electronic musical instrument 电子乐器electronic polarization 电子极化electronic relay 电子继电器electronic state 电子态electronic structure 电子结构electronic switch 电子开关electronic transition laser 电子跃迁激光器electronics 电子学electrooptic crystal 电光晶体electroosmosis 电内渗electrophoresis 电泳现象electrophoretic currents 电泳电流electrophoretic mobility 电泳迁移率electrophoretic potential 电泳电位electrophorus 起电盘electrophotography 电子照相法electroplating 电镀electropositive 阳电性的electropositive element 阳电性元素electroscope 验电器electrostatic 静电的electrostatic accelerator 静电加速器electrostatic attraction 静电引力electrostatic capacity 静电容量electrostatic deflection 静电偏转electrostatic energy 静电能electrostatic field 静电场electrostatic focusing 静电聚焦electrostatic force 静电力electrostatic generator 范德格拉夫发电机electrostatic induction 静电感应electrostatic ion microscope 静电离子显微镜electrostatic lens 静电透镜electrostatic oscillograph 静电示波器electrostatic potential 静电势electrostatic precipitation 静电吸尘electrostatic repulsion 静电斥力electrostatic septum 静电隔极electrostatic spectrometer 静电能谱仪electrostatic type 静电型electrostatic unit 静电单位electrostatic wave 静电波electrostatics 静电学electrostriction 电致伸缩electrostrictive vibrator 电致伸缩振动器electrothermal rocket 电热火箭electrothermic type 热电型electrovalence 电价electroweak interaction 弱电相互酌element 元素element semiconductor 元素半导体elementary cell 单位晶胞elementary charge 元电荷elementary colors 原色elementary excitation 元激发elementary function 基本机能elementary particle 基本粒子elementary particle physics 基本粒子物理学elementary particle reaction 基本粒子反应elementary process 基本过程elementary quantity 基本量elements of orbit 轨道要素ellipsoid for dielectric constants 介电常数椭球ellipsoid of inertia 惯量椭球ellipsoid of revolution 转动椭球ellipsoid of rotation 转动椭球ellipsoid of wave normals 光学指标ellipsoidal coordinates 椭球坐标ellipsometer 椭圆偏振计elliptic coordinates 椭圆坐标elliptic function 椭圆函数elliptic oscillation 椭圆振荡elliptic polarization 椭圆偏振elliptical galaxy 椭圆星云elliptical nebula 椭圆星云elliptically polarized light 椭圆偏振光elliptically polarized wave 椭圆偏振波elongation 伸长embrittlement 脆化emergency core cooling system 堆芯事故冷却系统emergency shut down 紧急停堆emission 发射emission band 发射带emission current 发射电流emission efficiency 发射效率emission line 发射谱线emission measure 发射量emission nebula 发射星云emission of light 光发射emission probability 发射概率emission spectroscopy 发射光谱学emission spectrum 发射谱emissivity 发射率emittance 发射率emitter 发射体;发射极emitter follower 发射极跟随器emmetropic eye 正常眼empirical formula 实验式empirical mass formula 经验质量公式empirical temperature 经验温度empirical temperature scale 经验温标empty band 空带empty level 空能级emulsion 乳胶emulsion chamber 乳胶室enamel 瓷漆enantiomorphism 对形性enantiotropes 互变性晶体enantiotropy 互变性encke's comet 端彗星encoder 编码器编码机encounter hypothesis 偶迂假说end 端end correction 端部校正end product 最终产物endlessness 无穷endosmosis 内渗endothermic reaction 吸热反应endurance limit 疲劳极限endurance test 疲劳试验energetics 能量学energy 能energy balance 能量平衡energy band 能带energy band structure 能带结构energy barrier 能量势垒energy carrier 能量载体energy conservation law 能量守恒律energy density 能量密度energy distribution 能量分布energy equivalent 能量当量energy exchange 能量交换energy flow 能量流能通量energy flow of electromagnetic field 电磁场的能量流energy flux 能通量energy flux vector 坡印廷矢量energy gap 能隙energy level 能级energy level diagram 能级图energy liberation 能量释放energy loss spectrum 能量损失谱energy momentum tensor 能量动量张量energy of absolute zero 绝对零点能energy of light 光能energy of thermal motion 热运动能量energy principle 能量原理energy quantum 能量量子energy release 能量释放energy source 能源energy source of star 星能源energy spectrum 能谱energy surface 能面energy transfer 能量传递energy transformation coefficient 能量变换系数energy unit 能单位energy yield 能量产额engine 发动机engineering acoustics 应用声学enriched reactor 浓缩燃料堆enriched uranium 浓缩铀enrichment 浓缩ensemble 系综ensemble average 系综平均entanglement 缠结enthalpy 焓entrance angle 入射角entrance pupil 入射光瞳entropy 熵entropy diagram 熵图entropy elasticity 熵弹性entropy flow 熵流entropy of activation 激活熵entropy of mixing 混合熵entropy production 熵产生entropy wave 熵波environmental radiation 环境辐射enzyme 酶ephemeris 历表ephemeris time 历书时epitaxial growth 外延生长epitaxial layer 外延层epitaxial planar transistor 外延平面晶体管epitaxial transistor 外延型晶体管epitaxy 外延epithermal energy 超热能epithermal neutron 超热中子epoch 历元epoxy resin 环氧尸epsilon expansion 展开equal temperament 平均乐律equation of continuity 连续性方程equation of light 光差equation of motion 运动方程equation of state 状态方程equation of time 时差equation of transfer 传递方程equatorial 赤道仪equatorial acceleration 赤道加速度equatorial coordinates 赤道坐标equatorial parallax 赤道视差equilibrium 平衡equilibrium constant 平衡常数equilibrium diagram 平衡图equilibrium process 平衡过程equilibrium state 平衡态equinox 分点equipartition 均分equipartition of energy 能量均分equiphase surface 等相面equipotential 等势的equipotential line 等位线equipotential surface 等势面equivalence of mass and energy 质能相当性equivalence principle 等价原理equivalent 当量equivalent circuit 等效电路equivalent electrons 等价电子equivalent mass 等效质量equivalent network 等效网络equivalent orbital 等效轨函数equivalent resistance 等效电阻equuleus 小马座erbium 铒erect image 正象erect lens 正象透镜erect system 正象系erecting eyepiece 正象目镜erg 尔格ergodic hypothesis 脯历经假说ergodic problem 脯历经问题ergodic property 脯历经性ergodic theorem 脯历经定理ergodic theory 脯历经理论eridanus 波江座ernst equation 厄伦斯特方程error 误差error equation 误差方程error function 误差函数error law 误差律error of measurement 测量误差eruptive prominence 爆发日珥es layer es 层esaki diode 江崎二极管estimate 估计estimation 估计etalon 标准具etch figures 蚀象etching 蚀刻ether 以太ettingshausen effect 厄廷好森效应euclidean field theory 欧几里得场论euclidean geometry 欧几里得几何euclidean space 欧几里得空间euler angle 欧拉角euler lagrange equation 欧拉拉格朗日方程europium 铕eutectic 共晶eutectic alloy 低共熔合金eutectic mixture 低共熔混合物eutectic point 低共熔点eutectoid 共析evacuation 抽空evaluation of crystal 晶体评价evaporated film 蒸镀薄膜evaporating black hole 蒸发黑洞evaporation 蒸发evection 出差even even nucleus 偶偶核even odd nucleus 偶奇核even parity 偶宇称性event 事件evolution 演化evolution of stars 恒星演化ewald construction 埃瓦得造图ewald method 埃瓦得法ewald sphere 埃瓦得球ex nova 燃后新星exa 艾exact 正确的exactitude 精确度example 例exceptional lie group 例外李群excess 过剩excess electron 过剩电子excess entropy production 过剩熵产生excess force 过剩力exchange 交换exchange charge 交换电荷exchange coefficient 交换系数exchange current 交换流exchange degeneracy 交换简并exchange energy 交换能量exchange force 交换力exchange integral 交换积分exchange interaction 交换相互酌exchange inversion 交换反演exchange narrowing 交换窄化exchange operator 交换算符exchange polarization 交换极化exchange potential 交换势exchange reaction 交换反应excimer 受激二聚物excimer laser 准分子激光器excitation 激发excitation cross section 激发截面excitation curve 激发曲线excitation energy 激发能excitation function 激发函数excitation level 受激能级excitation potential 激发电压excitation state 受激态excitation transfer 激发转移excited 激发的excited atom 受激原子excited level 受激能级exciter 励磁机exciting field 激磁场exciting force 激发力exciton 激子exciton condensation 激子凝聚exciton laser 激子激光器exciton phonon interaction 激子声子相互酌excitonic luminescence 激子发光excitonic molecule 激子分子excitonic phase 激子相exclusion principle 泡利不相容原理exclusive reaction 排斥反应exergy 放射本领exit pupil 出射光瞳exoelectron 外电子exothermic nuclear reaction 放热核反应exothermic reaction 放热反应exotic atom 异原子exotic baryon 外来重子exotic meson 外来介子exotic metal 异金属expanding universe 膨胀宇宙expansion 膨胀expansion coefficient 膨胀系数expansion of the universe 宇宙膨胀expansion ratio 膨胀率expectation 期待值expected value 期待值experiment 实验experimental design 试验设计experimental error 实验误差experimental facilities 实验装置experimental physics 实验物理学experimental radio astronomy 实验射电天文学experimental reactor 实验反应堆explosion 爆炸explosive 炸药explosive material 炸药explosive reaction 爆炸反应explosive shower 宇宙线爆发exposure 曝光exposure meter 曝光计expression 表示extended dislocation 扩展位错extensive air shower 广延空气簇射extensive variable 示量变量exterior derivative 外微商external conversion 外部转换external dose 外照射剂量external forces 外力external friction 外摩擦external memory 外部存储器external mirror laser 外镜式激光器external noise 外噪声external photoelectric effect 外部光电效应external pressure 环境压力external quenching 外部猝灭external storage 外部存储器extinction 消光extinction angle 消光角extinction coefficient 消光系数extinction distance 消光距离extinction effect 消光效应extinction fringe 消光条纹extinction method 消光法extinction voltage 淬火电压extitation potential 激发电位extra current 额外电流extra high vacuum 特高真空extragalactic nebula 河外星云extragalactic radio astronomy 河外射电天文学extraneous current 外来流extranuclear 核外的extranuclear electron 核外电子extranuclear structure 核外结构extraordinary rays 非常光线extraordinary wave 非常波extratropical cyclone 温带气旋extrinsic conduction 杂质导电extrinsic conductivity 非本斋导率extrinsic semiconductor 含杂质半导体extrinsic stacking fault 非本昭垛层错eye 眼eye glass 单片眼镜eye piece 接目透镜eyepiece micrometer 目镜测微计。
机械工程学专业词汇英语翻译(E)
eagre 涌潮earth 土earth atmosphere 地面大气earth attraction 地球引力earth axis 地轴earth gravity 地球重力earth lateral pressure 土的侧压力earth orbit 地球轨道earth pressure 土压力earth pressure at rest 静土压力earth revolution 地球公转earth rotation 地球自转earth tides 地球潮汐earthquake force 地震烈度earthquake intensity 地震烈度earthquake proof 抗震earthquake proof wall 抗地震壁earthquake response 地震响应earthquake response spectrum 地震应谱earthquake shock 地震冲击earthquake wave 地震波easy glide region 易滑移区ebb tide 落潮ebullition 沸腾eccentric 偏心的eccentric anomaly 偏近点角eccentric collision 偏心碰撞eccentric compression 偏心压缩eccentric load 偏心荷载eccentric motion 偏心运动eccentric tension 偏心拉伸eccentricity orientation 偏心定向echo box 回波谐振盒echo pulse 回波脉冲echo wave 回波eddy 涡旋eddy conductivity 涡莲导率eddy current loss 涡琉耗eddy currents 涡流湍流eddy diffusion 涡动扩散eddy diffusivity 涡俩散率eddy energy 湍淋eddy energy flow 涡能通量eddy energy flux 涡能通量eddy field 涡场eddy flow 湍流涡流eddy freedom 无旋涡性eddy friction 涡动摩擦eddy generation 涡廖成eddy heat conduction 湍寥传导eddy invariant 涡旋不变量eddy loss 涡琉耗eddy motion 涡了动eddy resistance 涡凌力eddy source 涡源eddy space 涡琳间eddy spectrum 湍磷eddy stress 湍力力eddy transport 涡龄送eddy viscosity 涡脸性eddying whirl 涡流edge condition 边缘条件edge crack 边缘裂缝edge damping 边缘阻尼edge diffraction 边缘衍射edge dislocation 刃状位错edge effect 边缘效应edge fracture 边缘裂缝edge of crack 裂缝边缘edge point 边点edge wave 边缘波edgewise meter 边缘读数式仪表eerasive resistance 抗磨性effective area 有效面积effective coefficient 有效系数effective crack length 有效裂隙长度effective cross section 有效横截面effective energetic efficiency 有效能量效率effective head 有效水头effective horsepower 有效马力effective incidence 有效迎角effective length 有效长度effective load 有效负载effective mass 有效质量effective porosity 有效孔隙度effective pressure 有效压力effective radius 有效半径effective range of instrument 仪颇有效量程effective section 有效断面effective sound pressure 有效声压effective stress 有效应力effective surface energy 有效表面能量effective temperature 有效温度effective turbulent diffusivity 有效湍俩散系数effective value 有效值effective velocity 有效速度effective wake 有效伴流effective wavelength 有效波长effective work 有效功efficiency 效率effluence 瘤effluent 瘤水efflux 瘤efflux velocity 喷临度efflux viscometer 射脸度计effort 酌力effuser 喷管effusion 喷出eigen frequency 本盏率eigenfunction 本寨数eigenmoment 固有矩eigenperiod 固有周期eigenrotation 本正转eigentemperature 本章度eigentensor 本张量eigenvalue 本盏eigenvalue of energy 能量本盏eigenvector 本崭量einstein approximation 爱因斯坦近似einstein formula 爱因斯坦公式einstein frequency 爱因斯坦频率ejection seat 弹射座椅ejector 喷射器ekman flow 埃克曼流ekman helix 埃克曼螺线ekman layer 埃克曼层ekman number 埃克曼数elastic 弹性的elastic after effect 弹性后效elastic anisotropy 弹性蛤异性elastic axis 弹性轴elastic base 弹性基础elastic bending 弹性弯曲elastic buckling 弹性压曲elastic center 弹性中心elastic coefficient 弹性系数elastic coefficient matrix 弹性系数矩阵elastic collision 弹性碰撞elastic compliance 弹性顺度elastic constants 弹性常数elastic curve 弹性曲线elastic deformation 弹性形变elastic design 弹性设计elastic dipole 弹性偶极子elastic distortional potential 弹性形变势elastic elongation 弹性伸长elastic energy 弹性能elastic energy density 弹性能量密度elastic equilibrium 弹性平衡elastic failure 弹性破坏elastic fatigue 弹性疲劳elastic fiber 弹性纤维elastic fluid 弹性铃elastic force 弹力elastic foundation 弹性基底elastic ground 弹性地面elastic hardness 弹性硬度elastic heat wave 热弹性波elastic hysteresis 弹性滞后elastic hysteresis loop 弹性滞后曲线elastic impact 弹性碰撞elastic kernel 弹性核elastic lag 弹性滞后elastic limit 弹性极限elastic limit for compression 压缩弹性极限elastic limit for tension 拉伸弹性极限elastic line 弹性线elastic load 弹性负荷elastic membrane 弹性膜elastic modulus 弹性模数elastic oscillation 弹性振荡elastic plastic 弹塑性的elastic plastic body 弹塑性体elastic plastic deformation 弹塑性形变elastic plastic equilibrium 弹塑性平衡elastic plastic fracture 弹塑性断裂elastic plastic strain 弹塑性形变elastic porous flow 弹性渗流elastic potential 弹性势elastic potential energy 弹性势能elastic range 弹性区域elastic rebound 弹性复元elastic recovery 弹性复元elastic region 弹性区域elastic relaxation 弹性弛豫elastic ring 弹性环elastic scattering 弹性散射elastic scattering cross section 弹性散射截面elastic scattering submatrix 弹性散射子矩阵elastic shell 弹性壳elastic sol 弹性溶胶elastic state 弹性状态elastic strain 弹性形变elastic strain energy 弹性应变能elastic stress 弹性应力elastic support 弹性支承elastic surface 弹性曲面elastic vibration 弹性振动elastic viscoplastic 弹性粘塑性的elastic viscoplastic analogy 弹性粘塑性比拟elastic wave 弹性波elastic wave in bar 杆中弹性波elastica 弹性线elastically supported beam 弹性支承梁elasticity 弹性elasto osmometry 弹性渗压测定法elasto plastic bending 弹塑性弯曲elasto plastic interface 弹塑性分界面elasto viscosity 弹粘性elasto viscous solid 弹粘性固体elastodynamics 弹性动力学elastohydrodynamics 弹性铃动力学elastokinetics 弹性动力学elastomechanics 弹性力学elastomer 弹性体elastometry 弹性测量法elastoplastic material 弹塑性材料elastoplastic range 弹塑性范围elastoplastic wave 弹塑性波elastostatics 弹性静力学elbow 肘管electric displacement 介电移electric knudsen number 电气克努森数electric wind 电风electrical analogy 电比拟electrical fluid dynamics 电铃动力学electro conducting fluid 导电铃electro magnetic flow meter 电磁量计electrogasdynamics 电气体动力学electrohydraulics 电动水力学electrohydrodynamics 电铃力学electromagnetic continuum mechanics 电磁连续介质力学electromagnetic gun 电磁炮electromagnetic pump 电磁泵electromagnetic stirring 电磁搅拌electromagnetofluid dynamics 电磁铃动力学electromechanical pickup 机电传感器electromotive force 电动势electron cyclotron frequency 电子回旋频率electron diffusion coefficient 电子扩散系数electron sound velocity 电子声速electronic current 电子流electrostatically suspended gyroscope 静电支承陀螺仪element 元件element matrix 单元矩阵element of construction 建筑部件element of turbulence 湍联element of vortex 涡元elementary displacement 单元变位elementary wave 元波elementary work 元功elevation of pressure 增压elevator 升降机elevon 升降副翼ellipsoid of elasticity 弹性椭球ellipsoid of inertia 惯量椭球ellipsoid of stress 应力椭球ellipsoidal wave function 椭球面波函数elliptic coordinates 椭圆坐标elliptic function 椭圆函数elliptic pendulum 椭圆摆elliptic vortex of kirchhoff 基尔霍夫椭圆涡旋elliptical loading 椭圆加载elliptical orbit 椭圆轨道elliptical oscillation 椭圆振荡elliptical velocity 椭圆速度elongation 伸长elongation percentage 延伸率elongation quadric 伸长二次曲面elongational flow 伸长怜elutriation 淘析embrittlement 脆化emersion time 现出时间emersion wave 出现波emission 放射emissivity 辐射系数emollescence 软化empennage 尾翼empty state 空态empty weight 无载重量emulsified liquid 乳化液encounter 碰撞end effector 末端执行器end face flux 正面通量end face leakage flux 正面漏泄通量end on observation 轴向观察end on structure 端接结构end point energy 端点能量end rib 端肋end support 端点支承end thrust 轴向推力endothermic 吸热的endothermic reaction 吸热反应endurance 持久性endurance bending strength 抗弯疲劳强度endurance bending test 弯曲疲劳试验endurance failure 疲劳断裂endurance limit 疲劳极限endurance strength 疲劳强度endurance test 疲劳试验endurance testing machine 疲劳试验机energy 能energy absorption build up factor 能量吸收累积因子energy approximation 能量近似energy balance 能量平衡energy build up factor 能量累积因子energy carrier 能量载体energy conservation 能量守恒energy conservation law 能量守恒定律energy constant 能量常数energy content 能含量energy decrement 能量减量energy density 能量密度energy density spectrum 能量密度谱energy deposition 能量沉积energy dispersion formula 能量分散公式energy distribution 能量分布energy efficiency 能量效率energy equation 能量方程energy equivalent 能量当量energy exchange 能量交换energy exchange time 能量交换时间energy fault 能量缺陷energy flow 能通量energy flow density 能淋度energy fluence 能注量energy fluence build up factor 能注量累积因子energy flux 能通量energy flux density 能淋度energy flux of radiation 辐射能流energy function 能量函数energy generation 能量产生energy group 能量组energy head 能量头energy level density 能级密度energy line 能量线energy loss 能量损耗energy metabolism 能量代谢energy migration 能量迂移energy momentum flux 能量动量通量energy momentum tensor 能量动量张量energy of absorption 吸收能energy of attachment 附着能energy of combustion 燃烧能energy of interaction 相互酌能energy of thermal motion 热运动能量energy of turbulence 湍淋energy of vibration 振动能量energy operator 能量算符energy oscillation 能量振荡energy output 能量输出energy principle 能量原理energy relaxation 能量弛豫energy resolution 能量分辨率energy source 能源energy spectrum 能谱energy spectrum equation of turbulence 湍淋谱方程energy surface 能面energy transfer 能量传输energy unit 能单位engine power 发动机功率engine speed 发动机转速engineering fluid mechanics 工程铃力学engineering system of units 工程单位制engineering unit 工程单位engler degree 恶勒度engler viscosimeter 断粘度计enlargement 放大enlargement of pipe 管扩张enlargement scale 放大标度enrichment 浓缩entering 入射enthalpy 焓enthalpy of combustion 燃烧焓enthalpy of mixing 混合焓entrainment 卷入entrance loss 进口损失entrance pressure 进口压力entrance velocity 进口速度entropic efficiency 熵效率entropic wave 熵波entropy 熵entropy balance equation 熵平衡方程entropy elasticity 熵弹性entropy equation 熵方程entropy flow 熵流entropy increase 熵增加entropy inequality 熵不等式entropy layer 熵层entropy of evaporation 汽化熵entropy of formation 形成熵entropy of melting 熔融熵entropy of mixing 混合熵entropy wave 熵波envelope surface 包络面envelope velocity 包络速度environment 环境environment temperature 周围温度environmental aerodynamics 环境空气动力学environmental conditions 环境条件epicenter 震中epicycloidal motion 外摆线运动equal armed lever 等臂杠杆equal energy source 等能源equalization 均衡equalization of concentration 浓度均衡equalization of potential 位势均衡equally distributed 均匀分布的equating 均衡equation of compatibility 协到程equation of continuity 连续性原理equation of equilibrium 平衡方程equation of five moments 五力矩方程equation of heat balance 热平衡方程equation of hydrodynamics 铃动力学方程equation of hydrostatics 铃静力学方程equation of motion 运动方程equation of radiative transfer 辐射传递方程equation of the vibrating string 弦振动方程equations of gravitational field 引力场方程equations of gyroscopic motion 陀螺仪运动方程equatorial moment of inertia 轴惯性矩equiangular 等角的equiangular spiral 等角螺线equidensity 等密度equidimensional 等量纲的equidistribution 等分布equilbrium state 平衡态equilibrant force 补偿力equilibrating force system 平衡力系equilibrium 平衡equilibrium conditions 平衡条件equilibrium constant 平衡常数equilibrium criterion 平衡判据equilibrium diagram 平衡状态图equilibrium flow 平衡流equilibrium form 平衡形式equilibrium gradient 平衡梯度equilibrium momentum 平衡动量equilibrium of couples 力偶平衡equilibrium of forces 力平衡equilibrium partial pressure 平衡分压力equilibrium point 平衡点equilibrium process 平衡过程equilibrium state 平衡态equilibrium structure 平衡结构equilibrium surface 平衡面equilibrium surface tension 平衡表面张力equilibrium system 平衡系equilibrium tide 平衡潮equilibrium time 平衡时间equilibrium value 平衡值equilibrium vapor pressure 平衡蒸气压equipartition law 均分定律equipartition of energy 能量均分equiphase surface 等相面equipollent vectors 等效矢量equipotential line 等位线equipotential surface 等位面equivalence of mass and energy 质能等效equivalence principle 等效原理equivalence relation 等价关系equivalent bonds 等效结合equivalent couple 等值力偶equivalent damping 等价阻尼equivalent diameter 等效直径equivalent force systems 等效力系equivalent load 等效负载equivalent mass 等效质量equivalent permeability 当量渗透性equivalent roughness 等效粗度equivalent stopping power 等效阻止本领equivalent stress 等效应力equivalent system 等效系统equivalent thickness 等效厚度equivalent turbulence 等效湍寥equivalent twisting moment 等量扭矩equivoluminal wave 等容波erection load 装配负载erection stress 架设应力erg 尔格ergodic hypothesis 脯历经假说ergodic property 脯历经性ergodic random process 脯历经随机过程ergodic theorem 脯历经定理ergodic theory 脯历经理论erosion corrosion 侵蚀性腐蚀error function 误差函数error limit 误差限度error of division 分度误差error of graduation 分度误差error of mean square 均方误差error of measurement 测量误差escape velocity 脱离速度escape velocity from galaxy 脱离银河系的速度escape velocity from solar system 脱离太阳系的速度essential boundary condition 本质边界条件estimation 估计etalon 标准euler angle 欧拉角euler d'alembert principle 欧拉达朗伯原理euler dynamical equations 欧拉动力学方程euler equation 欧拉方程euler equation for turbomachine 欧拉涡轮机方程euler equations of hydrokinetics 欧拉铃运动方程euler gas dynamical equations 欧拉气体动力学方程euler lagrange equation 欧拉拉格朗日方程euler number 欧拉数euler static balance equation 欧拉静平衡方程euler stress tensor 欧拉应力张量euler stretching tensor 欧拉伸长张量euler theorem 欧拉定理euler turbine formula 欧拉涡轮机公式euler variable 欧拉变量eulerian coordinates 欧拉坐标eulerian correlation 欧拉相关eulerian derivative 欧拉导数eulerian difference method 欧拉差分法eulerian free period 欧拉自由周期evacuation 抽真空evanescent mode 衰减模式evanescent wave 衰减波evaporation 汽化evaporation coefficient 蒸发系数evaporation heat 蒸发热evaporation loss 蒸发损失evaporative cooling 蒸发冷却evection 出差evection tide 出差潮汐even fracture 平坦断口evolute 渐开线exact solution 精确解exactitude 精确exceptional plane 特战面excess air 过剩空气excess entropy 过剩熵excess head 超压水头excess heat 过剩热excess load 过负荷excess noise factor 过量噪声因数excess pressure of sound 声超压excess velocity 超速excessive pressure 超压exchange 交换exchange coefficient 交换系数exchange collision 交换碰撞exchange deformation 交换形变exchange diffusion 交换扩散exchange energy 交换能exchange energy density 交换能密度exchange force 交换力exchange frequency 交换频率exchange potential 交换势exchange rate 交换速率exchange resonance 交换共振exchange tensor 交换张量excitation 激发excitation energy 激发能量excitation level 激发级excitation of boundary layer 边界层激发excitation spectrum 激发谱excitation state 激发态excitation wave 激发波excited atom 受激原子excited state 激发态exciter 激振器exciting force 激发力executive device 执行机构exhaust nozzle 排气喷嘴exhaust pipe 排气管exhaust port 排出口exhaust pressure 排气压力exhaustion 排气exit 出口exit angle 出口角exit boundary point 出口边界点exit flow 出射流exit loss 出口损失exit momentum 出口动量exit pressure 出口压力exit temperature 出口温度exit track 出口轨道exit turn 出口转弯exit velocity 出口速度exosphere 外大气层exothermic 发热的expand 展开expansibility 膨胀性expansion 膨胀expansion coefficient 膨胀系数expansion crack 膨胀裂缝expansion curve 膨胀曲线expansion mach wave 膨胀马赫波expansion orbit 扩展轨道expansion parameter 展开参数expansion ratio 膨胀比expansion tank 膨胀水箱expansion vessel 膨胀水箱expansion wave 膨胀波expansion work 膨胀功expansive force 膨胀力expectation 期望值expected life 预期寿命expected value 期望值expected wind speed 期望风速experiment 实验experimental aerodynamics 实验空气动力学experimental check 实验检验experimental condition 实验条件experimental data 实验数据experimental error 实验误差experimental facility 实验装置experimental material 检验材料experimental method 实验法experimental point 实验点experimental result 实验结果experimental section 实验段experimental set up 实验装置experimental tests 实验检验experimental value 实验值explosion 爆炸explosion center 爆炸中心explosion chamber 燃烧室explosion equivalent 爆炸当量explosion forming 爆炸成形explosion heat 爆炸热explosion index 爆炸指数explosion limit 爆炸极限explosion line 爆破线explosion pressure 爆发压力explosion product 爆炸产物explosion theory 爆炸理论explosion wave 爆炸波explosion work 爆发功explosive 炸药explosive compaction 爆炸压实explosive force 爆炸力explosive gas 爆炸气explosive material 爆炸材料explosive power 爆炸力explosive reaction 爆炸反应explosive sintering 爆炸烧结explosive theory 爆炸理论explosive welding 爆炸焊接explosive working 爆炸加工explosiveness 爆炸性exponential curve 指数曲线expulsion 排出expulsive force 斥力extended tip 伸展翼梢extensibility 可延展性extension 延伸extension fissure 膨胀裂缝extensional oscillation 纵向振荡extensional vibration 纵向振荡extensional wave 膨胀波extensometer 伸长计exterior 外部exterior ballistics 膛外弹道学exterior pressure 外压力external constraint 外部约束external crack 外表裂纹external damping 外阻尼external effect 外效应external energy 外能external excitation 外加激发external force 外力external gravitational field 外引力场external heat of evaporation 外蒸发热external load 外加载external potential energy 外势能external power 外功率external pressure 外部压力external radiation 外辐射external resistance 外阻力external rotation 外转动external virtual work 外虚功external work 外功extinction 消光extra high pressure 超高压extract 提出物extraction of gas 放气extraction turbine 抽汽式涡轮机extraordinary wave 异常波extrapolation method 外推法extreme 极值extreme fiber stress 最外纤维应力extremity 端extremum 极值extremum conditions 极值条件extrinsic load 外加载extrusion 挤压。
各向异性屈服准则及其在汽车覆盖件中的应用
III
独创性声明
本人声明所呈交的学位论文是我个人在导师指导下进行的研究工作及取得的研究成 果。尽我所知，除文中已经标明引用的内容外，本论文不包含任何其他个人或集体 已经发表或撰写过的研究成果。对本文的研究做出贡献的个人和集体，均已在文中 以明确方式标明。本人完全意识到本声明的法律结果由本人承担。
学位论文作者签名： 日期： 年 月 日
I
华 中 科 技 大 学 硕 士 学 位 论 文 Abstract
The properties of the materials can be described by the anisotropy because most materials are rolled or heat treatment. In the stamping processes, anisotropy affects plastic deformation of the sheet metal, which ear mould and fracture of straight walls are revealed on, so the material property、dimension accuracy and utilization ratio are decreased. If those effects can be indicated, the quality of the sheet metal forming will be improved. This research is supported by NSF and named as: “The Independent Research of High-speed Simulation and Optimal Process Design aiming at the Formability of Automobile Panel” (NO.50575080). Based on the simulation software of FASTAMP with updated finite element inverse approach and dynamic explicit algorithm, which is developed by State Key Laboratory of Plastic Forming Simulation and Die & Mould Technology of HUST, three yield criteria like Hill48, three-parameter Barlat-Lian and Barlat91 have been studied. In the present paper, the strain-displacement relationship of BT element and BWC element are derived. A three-dimension finite-element analysis model of BWC element with Hill48 anisotropic criterion is developed based on the elastic-plastic large deformation finite element formulation of virtual power principle, and a total finite element program is written. Through simulating the forming of the box-shaped work piece, the superiority and inferiority of BT element and BWC element is compared and analyzed. In this paper, an updated five-parameter Barlat-Lian yield criterion based on the three-parameter Barlat-Lian planar anisotropic yield criterion was presented. The new yield criterion in which two transverse shear stresses are added can be combined with BT or BWC shell elements to simulate the anisotropic characters of the sheet in the stamping. We also introduce the Barlat91 yield criterion, and then deduce the relationship between r and the coefficients in the function. The program about these yield criteria are written which are integrated into the software FASTAMP. In the numerical simulation part, we study the influences on the distribution of thickness of elements by the degree of the criterion、anisotropy parameter r and angle of drop. From the results of simulation, the higher the degree of the criterion is, the elements are easier to thinner, the anisotropy parameter r and the angle of drop also have great influence on the thickness. Through experiment of the cylindrical part, we simply compare the different influences on the ear model and distribution of thickness of the three yield criterions.
基于三维构造恢复的地应力预测技术
Journal of Oil and Gas Technology 石油天然气学报, 2023, 45(1), 85-95 Published Online March 2023 in Hans. https:///journal/jogt https:///10.12677/jogt.2023.451011基于三维构造恢复的地应力预测技术陈 琪，熊晨皓，左田昕中石化勘探分公司物探研究院，四川 成都收稿日期：2023年2月3日；录用日期：2023年3月6日；发布日期：2023年3月27日摘要组合弹簧理论模型是预测地应力的一种常用方法，但模型忽略了对岩层各向异性的考虑，无法反映由于局部断层、裂缝发育等各向异性造成的应力局部扰动变化；对构造应力项的求取基于薄板理论，简单利用地层形变开展地应力预测，忽略了地质力学参数的空间变化。
本文通过叠前弹性参数反演和精细构造解释对常规弹簧组合模型的构造应力项求取进行了优化，提出了基于三维构造恢复的地应力预测技术，从构造建模开展地质力学分析与构造恢复，求取现今地应力的古构造应力残余分量，提高了模型对地应力的预测精度，结果与实钻井具有较好的吻合性，并通过实际工区应用验证了该方法的有效性，对页岩气勘探选区评价、井位部署、钻后评价、水平井设计具有借鉴作用。
关键词地应力预测，弹簧组合理论模型，三维构造恢复，页岩气水平井设计The Stress Prediction Technique Based on 3D Structural RestorationQi Chen, Chenhao Xiong, Tianxin ZuoGeophysical Exploration Research Institute of Sinopec Exploration Company, Chengdu SichuanReceived: Feb. 3rd , 2023; accepted: Mar. 6th , 2023; published: Mar. 27th, 2023AbstractThe composite spring model is a commonly used method for predicting the in situ stress. However, the model ignores the consideration of the anisotropy of the rock mass, which cannot reflect the stress disturbance caused by the anisotropy due to local faults, fractures, and other factors. More-over, the calculation of the tectonic stress term is based on the thin plate theory, which simplifies the geological deformation and neglects the spatial variation of the geological mechanical para-陈琪等meters. In this paper, the construction stress term of the conventional spring combination model was optimized by using pre-stack elastic parameter inversion and refined tectonic interpretation.A 3D tectonic reconstruction-based in situ stress prediction technology was proposed, which ana-lyzed the geological mechanics and tectonic reconstruction from the perspective of structural mod-eling. The residual tectonic stress component of the present-day stress was obtained, improving the prediction accuracy of the model for in-situ stress. The results have good consistency with ac-tual drilling, and the effectiveness of the proposed method was verified by application in a prac-tical working area. This method has reference significance for shale gas exploration zone evalua-tion, well deployment, post-drilling evaluation, and horizontal well design.KeywordsGround Stress Prediction, Spring Combination Model, Three-Dimensional Structure Restoration, Shale Gas Horizontal Well DesignThis work is licensed under the Creative Commons Attribution International License (CC BY 4.0)./licenses/by/4.0/1. 引言页岩储层较常规油气储层具有“低孔低渗”的特点，压裂改造是实现页岩储层商业开发的必须条件。
Sheet-MetalFormingProcessesandEquipment
FIGURE 16.13 (a) A cupping test (the Erichsen test) to determine the formability of sheet metals. (b) Bulge-test results on steel sheets of various widths. The specimen farthest left is subjected to, basically,
FIGURE 16.15 The deformation of the grid pattern and the tearing of sheet metal during forming. The major and minor axes of the circles are used to determine the coordinates on the forming-limit diagram in Fig.
TABLE 16.2 Important Metal Characteristics for Sheet-forming Op Yield-point elongation in a sheet-metal specimen. (b) Lüder’s bands in a low-carbon steel sheet. (c) Stretcher strains at the bottom of a steel can for household products. Source: (b) Courtesy
practice, clearances usually range between 2 and 10% of the thickness of the sheet. (b) Microhardness (HV) contours for a 6.4-mm (0.25-in.) thick AISI 1020 hot-rolled steel in the sheared region. Source: After
木材学双语教案-第8章
弹性模量E(modulus of elasticity)— 在弹性极限范围
内，物体抵抗外力改变其形状或体积的能力。它 是材料刚性的指标。
木材的拉伸、压缩和弯曲模量大致相等，但压缩 的弹性极限比拉伸的要低得多。
二、分类
（一）按力学性质分
1.强度(strength)— 是抵抗外部机械力破坏的能力。 2.硬度(hardness)— 是抵抗其它刚性物体压入的能力。 3.刚性(rigidity)— 是抵抗外部机械力造成尺寸和形状
（1） σbR ＞ σbT （2）①针叶材：uR ＞ uT ；②阔叶材通常关系不定。 4.剪切强度τ ：τ∥ /τ⊥=2.2~6.1 5.硬度H和磨损阻抗
①HRT ＞ HLT≥HLR，断面大于弦面，弦面大于或等于径面。同 时，硬度的异向性随密度增加而减少。
②木材磨损量A越大，表示磨损阻抗越小。ALR ≥ ALT ＞ ART 6.抗劈力S：径面和弦面的差异根据纹理通直性和射线组织的发
变化的能力。
4.韧性(toughness)— 是木材吸收能量和抵抗反复冲击 载荷，或抵抗超过比例极限的短期应力的能力。
（二）按载荷形式分
1.静力载荷（static test load） 是缓慢而均匀的施载 形式。木材强度测试除冲击外，都为静力载荷； 胶合板在热压机中的加载形式也属静力载荷。
2.冲击载荷（shock load） 集中全部载荷在瞬间猛击 的施载形式。如锻锤机下垫木所承受的载荷形式。
方泽（1947）给出木材松弛表达式如下：
时间 t 图9—3 应力松弛曲线
t
t 1 1 m lg t
式中： — 在t时间时的应力，随时间的延长而下降； 1 — 在单位时间内的应力；
m — 松弛系数，随树种和应力种类而不同。
钻井液对页岩力学特性及井壁稳定性的影响
文章编号：1000 − 7393(2022)06 − 0693 − 08 DOI: 10.13639/j.odpt.2022.06.005钻井液对页岩力学特性及井壁稳定性的影响罗鸣1,2 高德利1 黄洪林1 李军1,3 杨宏伟1 张更1 刘楷21. 中国石油大学(北京)；2. 中海石油(中国)有限公司海南分公司；3. 中国石油大学(北京)克拉玛依校区引用格式：罗鸣，高德利，黄洪林，李军，杨宏伟，张更，刘楷. 钻井液对页岩力学特性及井壁稳定性的影响［J ］. 石油钻采工艺，2022，44（6）：693-700.摘要：钻井液长期浸泡会对层理性页岩产生影响，进而影响到页岩地层的井壁稳定性。
利用川南地区龙马溪组页岩开展了不同钻井液浸泡后页岩单、三轴力学实验，分析了其力学特性及破坏形式的变化特征，并探讨了井壁失稳机理。
结果表明：受层理影响，页岩力学特性具有明显的各向异性特征，且具有围压效应；油基钻井液对层理面的润滑作用增强了各向异性，页岩沿层理面发生剪切破坏，破坏形式受层理面控制；水基钻井液对页岩造成水化损伤，微裂缝扩展沟通层理，降低了各向异性，易发生复合破坏，破坏形式受基质体和层理面双重控制，井壁更易失稳；黏土矿物水化作用和孔缝毛细管效应是页岩地层井壁失稳的根本原因。
该研究可为层理性页岩井壁稳定分析提供参考。
关键词：页岩；层理面；钻井液浸泡；各向异性；钻井液润湿特性；尺度效应；井壁稳定中图分类号：TE254 文献标识码： AEffects of drilling fluids on shale mechanical properties and wellbore stabilityLUO Ming 1,2, GAO Deli 1, HUANG Honglin 1, LI Jun 1,3, YANG Hongwei 1, ZHANG Geng 1, LIU Kai 21. College of Petroleum Engineering , China University of Petroleum (Beijing ), Changping 102249, Beijing , China ;2. CNOOC Limited Hainan Branch ,Haikou 524000, Hainan , China ; 3. China University of Petroleum-Beijing at Karamay , Karamay 934000, Xinjiang , ChinaCitation: LUO Ming, GAO Deli, HUANG Honglin, LI Jun, YANG Hongwei, ZHANG Geng, LIU Kai. Effects of drilling fluids on shale mechanical properties and wellbore stability ［J ］. Oil Drilling & Production Technology, 2022, 44(6): 693-700.Abstract: Long-term soaking in drilling fluids has vital effects on shale with well-developed bedding and subsequently wellbore stability in shale. The uni- and tri- axial compression tests were performed using the Longmaxi Formation shale samples from South Sichuan that have been immersed in different drilling fluids, to investigate the variation of mechanical characteristics and failure modes and also the mechanisms of wellbore instability. The results showed that due to the bedding development, the shale presents considerable mechanical anisotropy and dependency on confining pressure. The lubrication effect of oil-based drilling fluids on bedding planes strengthens the anisotropy, shale is found with the shear failure along bedding planes, and the failure mode is controlled by bedding planes. In the case of water-based drilling fluids, hydration damage is caused to shale, and the anisotropy is reduced due to the propagation and bedding connection of micro fractures. The failure is often composite, and the failure mode is controlled jointly by the matrix and bedding plane, which leads to high proneness to wellbore instability. The root causes of wellbore基金项目: 中国石油天然气集团有限公司-中国石油大学(北京)战略合作科技专项“准噶尔盆地玛湖中下组合和吉木萨尔陆相页岩油高效勘探开发理论及关键技术研究” (编号：ZLZX2020-01)。
各向异性对页岩地层钻井液安全密度窗口的影响
２０２３年１１月第３８卷第６期西安石油大学学报（自然科学版）ＪｏｕｒｎａｌｏｆＸｉ’ａｎＳｈｉｙｏｕＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅＥｄｉｔｉｏｎ）Ｎｏｖ．２０２３Ｖｏｌ．３８Ｎｏ．６收稿日期：２０２２ ０８ ０５第一作者：吴德胜（１９９１ ），男，硕士，工程师，研究方向：方案设计、钻井提速、井身结构等。
Ｅ ｍａｉｌ：ｗｕｄｅｓｈｅｎｇ２０１９＠ｐｅｔｒｏｃｈｉｎａ．ｃｏｍ．ｃｎＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１６７３ ０６４Ｘ．２０２３．０６．００３中图分类号：ＴＥ３２８文章编号：１６７３ ０６４Ｘ（２０２３）０６ ００２４ ０９文献标识码：Ａ各向异性对页岩地层钻井液安全密度窗口的影响吴德胜，李渊，武兴勇，胡开利，甘一风（中国石油新疆油田分公司，新疆克拉玛依８３４０００）摘要：为揭示页岩储层井壁失稳机理，开展了不同层理倾角页岩的抗压强度实验，采用Ｊａｅｇｅｒ弱面准则拟合页岩强度实验数据，为井壁稳定分析模型提供输入参数；评估了各向异性对井周应力集中的影响，并基于横观各向同性介质井周应力模型，建立了钻井液安全密度窗口分析模型，研究安全密度窗口对各向异性的敏感性。
结果表明：随着原地应力异性的增加，破裂压力与坍塌压力的差值减小，即钻井液安全密度窗口变窄，与地应力各向同性时的情况相比，地应力异性导致井筒失稳风险增大；随着页岩弹性模量异性度的增加，井壁破裂压力和坍塌均逐渐减小，因此维持井壁稳定的钻井液安全密度窗口迅速变窄。
泊松比异性度对井壁破裂压力和坍塌压力的敏感性分析表明，泊松比各向异性对维持井壁稳定的安全密度窗口的影响十分有限；而弹性模量是引起钻井液安全密度窗口变化的关键因素。
关键词：横观各向同性；钻井液；安全密度窗口；各向异性；页岩储层；敏感性分析ＥｆｆｅｃｔｏｆＡｎｉｓｏｔｒｏｐｙｏｎＳａｆｅＤｅｎｓｉｔｙＷｉｎｄｏｗｏｆＤｒｉｌｌｉｎｇＦｌｕｉｄｉｎＳｈａｌｅＦｏｒｍａｔｉｏｎＷＵＤｅｓｈｅｎｇ，ＬＩＹｕａｎ，ＷＵＸｉｎｇｙｏｎｇ，ＨＵＫａｉｌｉ，ＧＡＮＹｉｆｅｎｇ（ＰｅｔｒｏＣｈｉｎａＸｉｎｊｉａｎｇＯｉｌｆｉｅｌｄＣｏｍｐａｎｙ，Ｋａｒａｍａｙ，Ｘｉｎｊｉａｎｇ８３４０００，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｔｏｒｅｖｅａｌｔｈｅｍｅｃｈａｎｉｓｍｏｆｗｅｌｌｂｏｒｅｉｎｓｔａｂｉｌｉｔｙｉｎｓｈａｌｅｒｅｓｅｒｖｏｉｒｓ，ｃｏｍｐｒｅｓｓｉｖｅｓｔｒｅｎｇｔｈｅｘｐｅｒｉｍｅｎｔｓｗｅｒｅｃｏｎｄｕｃｔｅｄｏｎｓｈａｌｅｗｉｔｈｄｉｆｆｅｒｅｎｔｂｅｄｄｉｎｇａｎｇｌｅｓ．ＴｈｅｓｈａｌｅｓｔｒｅｎｇｔｈｅｘｐｅｒｉｍｅｎｔａｌｄａｔａｗｅｒｅｆｉｔｔｅｄｕｓｉｎｇＪａｅｇｅｒｗｅａｋｓｕｒｆａｃｅｃｒｉｔｅｒｉｏｎ，ｐｒｏｖｉｄｉｎｇｉｎｐｕｔｐａ ｒａｍｅｔｅｒｓｆｏｒｔｈｅｗｅｌｌｂｏｒｅｓｔａｂｉｌｉｔｙａｎａｌｙｓｉｓｍｏｄｅｌ；Ｔｈｅｉｍｐａｃｔｏｆａｎｉｓｏｔｒｏｐｙｏｎｗｅｌｌｂｏｒｅｓｔｒｅｓｓｃｏｎｃｅｎｔｒａｔｉｏｎｗａｓｅｖａｌｕａｔｅｄａｎｄａｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗａｎａｌｙｓｉｓｍｏｄｅｌｏｆｄｒｉｌｌｉｎｇｆｌｕｉｄｗａｓｅｓｔａｂｌｉｓｈｅｄｂａｓｅｄｏｎａｔｒａｎｓｖｅｒｓｅｉｓｏｔｒｏｐｉｃｍｅｄｉｕｍｗｅｌｌｂｏｒｅｓｔｒｅｓｓｍｏｄｅｌｔｏｓｔｕｄｙｔｈｅｓｅｎｓｉｔｉｖｉｔｙｏｆｔｈｅｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗｔｏａｎｉｓｏｔｒｏｐｙ．Ｔｈｅｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｗｉｔｈｔｈｅｉｎｃｒｅａｓｅｏｆｉｎ ｓｉｔｕｓｔｒｅｓｓａｎｉｓｏｔｒｏｐｙ，ｔｈｅｄｉｆｆｅｒｅｎｃｅｂｅ ｔｗｅｅｎｆｒａｃｔｕｒｅｐｒｅｓｓｕｒｅａｎｄｃｏｌｌａｐｓｅｐｒｅｓｓｕｒｅｄｅｃｒｅａｓｅｓ，ｗｈｉｃｈｍｅａｎｓｔｈａｔｔｈｅｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗｏｆｄｒｉｌｌｉｎｇｆｌｕｉｄｎａｒｒｏｗｓ．Ｃｏｍｐａｒｅｄｗｉｔｈｔｈｅｓｉｔｕａｔｉｏｎｗｈｅｎｔｈｅｉｎ ｓｉｔｕｓｔｒｅｓｓｉｓｉｓｏｔｒｏｐｉｃ，ｔｈｅｉｎ ｓｉｔｕｓｔｒｅｓｓａｎｉｓｏｔｒｏｐｙｉｎｃｒｅａｓｅｓｔｈｅｒｉｓｋｏｆｗｅｌｌｂｏｒｅｉｎｓｔａｂｉｌｉｔｙ．Ａｓｔｈｅａｎｉｓｏｔ ｒｏｐｙｏｆｔｈｅｅｌａｓｔｉｃｍｏｄｕｌｕｓｏｆｓｈａｌｅｉｎｃｒｅａｓｅｓ，ｂｏｔｈｔｈｅｗｅｌｌｂｏｒｅｆｒａｃｔｕｒｅｐｒｅｓｓｕｒｅａｎｄｃｏｌｌａｐｓｅｐｒｅｓｓｕｒｅｇｒａｄｕａｌｌｙｄｅｃｒｅａｓｅ，ｔｈｕｓｔｈｅｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗｏｆｄｒｉｌｌｉｎｇｆｌｕｉｄｔｈａｔｍａｉｎｔａｉｎｓｗｅｌｌｂｏｒｅｓｔａｂｉｌｉｔｙｒａｐｉｄｌｙｎａｒｒｏｗｓ．ＴｈｅｉｎｆｌｕｅｎｃｅｏｆＰｏｉｓｓｏｎ＇ｓｒａｔｉｏａｎｉｓｏｔｒｏｐｙｏｎｔｈｅｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗｏｆｄｒｉｌｌｉｎｇｆｌｕｉｄｉｓｖｅｒｙｌｉｍｉｔｅｄ．Ｔｈｅｅｌａｓｔｉｃｍｏｄｕｌｕｓｏｆｓｈａｌｅｉｓａｋｅｙｆａｃｔｏｒｃａｕｓｉｎｇｃｈａｎｇｅｓｉｎｔｈｅｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗｏｆｄｒｉｌｌｉｎｇｆｌｕｉｄ．Ｋｅｙｗｏｒｄｓ：ｔｒａｎｓｖｅｒｓｅｌｙｉｓｏｔｒｏｐｙ；ｄｒｉｌｌｉｎｇｆｌｕｉｄ；ｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗ；ａｎｉｓｏｔｒｏｐｙ；ｓｈａｌｅｒｅｓｅｒｖｏｉｒ；ｓｅｎｓｉｔｉｖｉｔｙａｎａｌｙｓｉｓ［Ｃｉｔａｔｉｏｎ］吴德胜，李渊，武兴勇，等．各向异性对页岩地层钻井液安全密度窗口的影响［Ｊ］．西安石油大学学报（自然科学版），２０２３，３８（６）：２４ ３２．ＷＵＤｅｓｈｅｎｇ，ＬＩＹｕａｎ，ＷＵＸｉｎｇｙｏｎｇ，ｅｔａｌ．Ｅｆｆｅｃｔｏｆａｎｉｓｏｔｒｏｐｙｏｎｓａｆｅｄｅｎｓｉｔｙｗｉｎｄｏｗｏｆｄｒｉｌｌｉｎｇｆｌｕｉｄｉｎｓｈａｌｅｆｏｒｍａｔｉｏｎ［Ｊ］．ＪｏｕｒｎａｌｏｆＸｉ’ａｎＳｈｉｙｏｕＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅＥｄｉｔｉｏｎ），２０２３，３８（６）：２４ ３２．吴德胜等：各向异性对页岩地层钻井液安全密度窗口的影响引 言水平井和水力压裂是开发页岩气的两大关键技术，受页岩结构、力学特征的影响，水平井钻井过程中极易发生垮塌、掉块等问题，井壁失稳成为制约页岩气水平井安全、高效钻井的主要技术难题［１ ４］。
考虑多重流动机制各向异性的页岩气运移数值模拟
第３８卷 第１期 ２０２３年３月 西 南 科 技 大 学 学 报 ＪｏｕｒｎａｌｏｆＳｏｕｔｈｗｅｓｔＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ Ｖｏｌ．３８Ｎｏ．１ Ｍａｒ．２０２３ＤＯＩ：１０．２００３６／ｊ．ｃｎｋｉ．１６７１ ８７５５．２０２３．０１．００６收稿日期：２０２２－０３－０４；修回日期：２０２２－０３－２４基金项目：国家自然科学基金面上项目（１１８７２３２４）作者简介：第一作者，赵静（１９９３—），女，硕士研究生，Ｅ ｍａｉｌ：６１０１３１５３１＠ｑｑ．ｃｏｍ；通信作者，古斌（１９７５—），男，博士，教授，研究方向为固体力学、多场耦合材料的动力学分析、非常规天然气开发中的力学问题，Ｅ ｍａｉｌ：ｇｕｂｉｎ＠ｓｗｕｓｔ．ｅｄｕ．ｃｎ考虑多重流动机制各向异性的页岩气运移数值模拟赵 静１，２ 古 斌１，２（１．西南科技大学制造科学与工程学院 四川绵阳 ６２１０１０；２．西南科技大学制造过程测试技术教育部重点实验室 四川绵阳 ６２１０１０）摘要：为研究多重流动机制各向异性对页岩气运移的影响，基于Ｂｉｏｔ线弹性孔隙介质模型，考虑黏性流动、气体流动动态效应和表面吸附扩散等流动机制的各向异性，采用各向同性应力依赖模型，建立流－固耦合的视渗透率模型，对应力约束边界条件下的页岩气运移过程进行数值模拟，定量分析流动各向异性对页岩气运移的影响。
结果表明各种流动机制的各向异性均对页岩气运移有显著影响：固有渗透率各向异性可明显改变页岩气运移开始时间和流通量大小，其影响随页岩储层渗透率增加而放大；当固有渗透率较小时，动态效应各向异性会削弱气体流动的动态效应，对页岩气运移开始时间和流通量的影响十分显著，但在固有渗透率较大时其影响可以忽略；表面吸附扩散各向异性的影响与固有渗透率各向异性相似。
准确评估页岩气的运移能力和产能应考虑运移过程中的流动各向异性。
关键词：页岩气运移 多重流动机制 流动各向异性 视渗透率模型 数值模拟中图分类号：ＴＥ３ 文献标志码：Ａ 文章编号：１６７１－８７５５（２０２３）０１－００４０－０７ＮｕｍｅｒｉｃａｌＳｉｍｕｌａｔｉｏｎｏｆＳｈａｌｅＧａｓＴｒａｎｓｐｏｒｔＣｏｎｓｉｄｅｒｉｎｇＡｎｉｓｏｔｒｏｐｙｏｆＭｕｌｔｉｐｌｅＦｌｏｗＭｅｃｈａｎｉｓｍｓＺＨＡＯＪｉｎｇ１，２，ＧＵＢｉｎ１，２（１．ＳｃｈｏｏｌｏｆＭａｎｕｆａｃｔｕｒｉｎｇＳｃｉｅｎｃｅａｎｄＥｎｇｉｎｅｅｒｉｎｇ，ＳｏｕｔｈｗｅｓｔＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ，Ｍｉａｎｙａｎｇ６２１０１０，Ｓｉｃｈｕａｎ，Ｃｈｉｎａ；２．ＫｅｙＬａｂｏｒａｔｏｒｙｏｆＴｅｓｔｉｎｇＴｅｃｈｎｏｌｏｇｙｆｏｒＭａｎｕｆａｃｔｕｒｉｎｇＰｒｏｃｅｓｓ，ＭｉｎｉｓｔｒｙｏｆＥｄｕｃａｔｉｏｎ，ＳｏｕｔｈｗｅｓｔＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ，Ｍｉａｎｙａｎｇ６２１０１０，Ｓｉｃｈｕａｎ，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＢａｓｅｄｏｎＢｉｏｔ’ｓｍｏｄｅｌｏｆｌｉｎｅａｒｅｌａｓｔｉｃｐｏｒｏｕｓｍｅｄｉｕｍ，ｔａｋｉｎｇｉｎｔｏａｃｃｏｕｎｔｆｏｒｔｈｅａｎｉｓｏｔｒｏｐｙｏｆｆｌｏｗｍｅｃｈａｎｉｓｍｓｓｕｃｈａｓｖｉｓｃｏｕｓｆｌｏｗ，ｄｙｎａｍｉｃｅｆｆｅｃｔｓｏｆｇａｓｆｌｏｗａｎｄｓｕｒｆａｃｅａｄｓｏｒｐｔｉｖｅｄｉｆｆｕｓｉｏｎ，ａｎｄａｄｏｐｔｉｎｇｔｈｅｉｓｏｔｒｏｐｉｃｓｔｒｅｓｓｄｅｐｅｎｄｅｎｃｅｍｏｄｅｌ，ａｆｌｕｉｄ－ｓｏｌｉｄｃｏｕｐｌｉｎｇａｐｐａｒｅｎｔｐｅｒｍｅａｂｉｌｉｔｙｍｏｄｅｌｗａｓｅｓｔａｂｌｉｓｈｅｄｔｏｉｎｖｅｓｔｉｇａｔｅｔｈｅｅｆｆｅｃｔｏｆａｎｉｓｏｔｒｏｐｙｏｆｍｕｌｔｉｐｌｅｆｌｏｗｍｅｃｈａｎｉｓｍｓｏｎｓｈａｌｅｇａｓｔｒａｎｓｐｏｒｔ．Ｎｕ ｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｏｎｔｈｅｓｈａｌｅｇａｓｍｉｇｒａｔｉｏｎｐｒｏｃｅｓｓｕｎｄｅｒｔｈｅｓｔｒｅｓｓｃｏｎｓｔｒａｉｎｔｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓｗａｓｔｈｅｎｃｏｎｄｕｃｔｅｄｔｏｑｕａｎｔｉｔａｔｉｖｅｌｙａｎａｌｙｚｅｔｈｅｉｎｆｌｕｅｎｃｅｏｆｆｌｏｗａｎｉｓｏｔｒｏｐｙｏｎｓｈａｌｅｇａｓｔｒａｎｓｆｅｒ．Ｔｈｅｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅａｎｉｓｏｔｒｏｐｙｏｆｅａｃｈｆｌｏｗｍｅｃｈａｎｉｓｍｈａｓｓｉｇｎｉｆｉｃａｎｔｉｍｐａｃｔｏｎｓｈａｌｅｇａｓｔｒａｎｓｐｏｒｔ．Ｔｈｅａｎｉｓｏｔ ｒｏｐｙｏｆｉｎｔｒｉｎｓｉｃｐｅｒｍｅａｂｉｌｉｔｙｃａｎｇｉｖｅｒｉｓｅｔｏｒｅｍａｒｋａｂｌｅｃｈａｎｇｅｓｏｎｔｈｅｂｅｇｉｎｎｉｎｇｏｆｓｈａｌｅｇａｓｔｒａｎｓｆｅｒａｎｄｔｈｅｇａｓｆｌｕｘ，ａｎｄｓｕｃｈｉｎｆｌｕｅｎｃｅｉｓｅｎｈａｎｃｅｄｂｙｉｎｃｒｅａｓｉｎｇｔｈｅｓｈａｌｅｐｅｒｍｅａｂｉｌｉｔｙ．Ｔｈｅａｎｉｓｏｔｒｏｐｙｏｆｄｙｎａｍｉｃｅｆｆｅｃｔｓｃａｎｄｉｍｉｎｉｓｈｔｈｅｄｙｎａｍｉｃｅｆｆｅｃｔｓｏｆｇａｓｆｌｏｗａｎｄｈａｓａｓｉｇｎｉｆｉｃａｎｔｉｎｆｌｕｅｎｃｅｏｎｔｈｅｂｅｇｉｎ ｎｉｎｇｏｆｓｈａｌｅｇａｓｔｒａｎｓｆｅｒａｎｄｔｈｅｇａｓｆｌｕｘｗｈｅｎｔｈｅｉｎｔｒｉｎｓｉｃｐｅｒｍｅａｂｉｌｉｔｙｉｓｌｏｗ．Ｗｈｉｌｅｔｈｅｉｎｆｌｕｅｎｃｅｃａｎｂｅｎｅｇｌｅｃｔｅｄｉｎｔｈｅｃａｓｅｏｆｌａｒｇｅｉｎｔｒｉｎｓｉｃｐｅｒｍｅａｂｉｌｉｔｙ．Ｔｈｅｅｆｆｅｃｔｏｆａｎｉｓｏｔｒｏｐｙｏｆｓｕｒｆａｃｅａｄｓｏｒｐｔｉｖｅｄｉｆｆｕ ｓｉｏｎｉｓｓｉｍｉｌａｒｔｏｔｈａｔｏｆｉｎｔｒｉｎｓｉｃｐｅｒｍｅａｂｉｌｉｔｙａｎｉｓｏｔｒｏｐｙ．Ｔｈｅｒｅｆｏｒｅ，ｉｔｉｓｎｅｃｅｓｓａｒｙｔｏｃｏｎｓｉｄｅｒｔｈｅｆｌｏｗａｎｉｓｏｔｒｏｐｙｉｎｔｈｅｍｉｇｒａｔｉｏｎｐｒｏｃｅｓｓｗｈｅｎａｃｃｕｒａｔｅｌｙｅｖａｌｕａｔｉｎｇｔｈｅｍｉｇｒａｔｉｏｎａｂｉｌｉｔｙａｎｄｐｒｏｄｕｃｔｉｖｉｔｙｏｆｓｈａｌｅｇａｓ．Ｋｅｙｗｏｒｄｓ：Ｓｈａｌｅｇａｓｍｉｇｒａｔｉｏｎ；Ｍｕｌｔｉｐｌｅｆｌｏｗｍｅｃｈａｎｉｓｍｓ；Ｆｌｏｗａｎｉｓｏｔｒｏｐｙ；Ａｐｐａｒｅｎｔｐｅｒｍｅａｂｉｌｉｔｙｍｏｄｅｌ；Ｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎ 页岩储层构造复杂、孔隙类型和大小多样、承受的地应力高、呈现超低孔隙率和渗透率、各向异性和非均质等特性。
gpa4dm
2010/11/25 GPA for DigitalMicrograph Geometric Phase AnalysisGPA Phase Manual 3.0HREM Research IncConventionsThe typographic conventions used in this help are described below.Convention DescriptionBold Used to denote components of the user interface such asbuttons, field names, menus, and menu options.For example, the New button.Menu...MenuOption Select the menu from the menu bar then select the menu optionfrom the menu.For example, File...Open would mean to select the File menuand then the Open option.CAPS Used to denote the name of a key on the keyboard.For example, the ENTER key.Italics Used to denote emphasis, captions and the result of an action ina procedure.Contact UsGeneral enquiries on the GPA for DigitalMicropraph should be sent to:HREM Research Inc.14-48 MatsukazedaiHigashimatsuyamaSaitama 355-0055JapanPhone: Fax: email: Website: +81 493 35 3913+81 493 35 3919support@ /Enquiries on GPA of a technical nature should be directed to: Dr. Martin HytchCEMES-CNRS, Toulouse, Franceemail: hytch@cemes.frCopyright Statements© Copyright 2008-2010 HREM Research Inc. and CEMES-CNRSAll rights reserved. This manual is protected by international copyright laws and treaties. Unauthorized reproduction and distribution of this manual, or any portion of it, will be prosecuted to the maximum extent possible and may result in severe civil and criminal penalties.Portions of this document were prepared by HREM Research Inc. by editing the materials supplied by Dr. Martin Hytch.DigitalMicrograph is a trade mark of Gatan Inc.Introduction to GPAWelcome to GPA Phase the DigitalMicrograph plug-in for strain mapping from high-resolution electron microscope images, or indeed any type of lattice image. The main reference for the theory is:M. J. Hÿtch, E. Snoeck and R. Kilaas, Ultramicroscopy 74 (1998) 131–146.Quantitative measurement of displacement and strain fields from HREM micrographs and additionally:F. Hüe, C.L. Johnson, S. Lartigue-Korinek,G. Wang, P.R. Buseck, M.J. Hÿtch,J. Electron Microscopy 54 (2005) 181-190. Calibration of projector lens distortions.doi:10.1093/jmicro/dfi042.M. J. Hÿtch and T. Plamann, Ultramicroscopy 87 (2001) 199–212. Imaging conditions for reliable measurement of displacement and strain from high-resolution electronmicroscope images.Applications of GPA can be found in the following:[1] F. Hüe, M.J. Hÿtch, H. Bender, F. Houdellier, and A. Claverie, Phys. Rev. Lett. 100(2008) 156602. Direct mapping of strain in a strained-silicon transistor by high-resolution electron microscopy. doi:10.1103/PhysRevLett.100.156602.[2] C.L. Johnson, E. Snoeck, M. Ezcurdia, B. Rodríguez-González, I. Pastoriza-Santos,L.M. Liz-Marzán, and M.J. Hÿtch, Nature Materials 7 (2008) 120-124. Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles.doi:10.1038/nmat2083.[3]M.J. Hÿtch, J.-L. Putaux, J. Thibault, Phil. Mag. 86 (2006) 4641–4656. Stress andstrain around grain-boundary dislocations measured by high-resolution electronmicroscopy. doi:10.1080/14786430600743876.[4]J.L. Taraci, M.J. Hÿtch, T. Clement, P. Peralta, M.R. McCartney, J. Drucker andS.T. Picraux, Nanotechnology 16 (2005) 2365-2371. Strain mapping in nanowires.doi:10.1088/0957-44/16/10/062.[5]M. J. Hÿtch, J-L. Putaux, J-M. Pénisson, Nature 423 (2003) 270-273. Measurement ofthe displacement field around dislocations to 0.03Å by electron microscopy.doi:10.1038/nature01638.Software requirementsThe following is a list of the software requirements necessary to run the GPA plug-in:-DigitalMicrograph (GATAN TM )-USB Key Driver-HREM Mouse Tool Plug-in (Free-ware downloadable from ) -GPA Plug-in (Free-ware downloadable from )Software InstallationInstalling USB Key DriverThe user key driver should be installed by following the instructions given by the key driver installer. The key driver installer comes with GPA, or you can find it on our web site.Installing GPA Plug-inThe plug-in can be installed by drag-and-drop copy to the folder “PlugIns” (The PlugIns folder should exist under a normal installation of the DigitalMicrograph.)When the DigitalMicrograph is launched after placing the plug-ins into the PlugIns folder, GPA menu commands will appear under “GPA Phase” menu.Installing Mouse ToolsAll the files relating Mouse tool plug-in can be installed by drag-and-drop copy to the folder “PlugIns.” (The PlugIns folder should exist under a normal installation of the DigitalMicrograph.)When the DigitalMicrograph is launched after placing the plug-ins into the PlugIns folder, the Mouse tool will appear as an addition to the standard tools.Installing IPU Plug-inGPA uses some functions based on the Intel’ MKL (Math Kernel Library) provided by the IPU plug-in. All the files relating the IPU plug-in can be installed by drag-and-drop copy. Please consult the ReadMe file that comes with the IPU plug-in.In this manual, we will dive straight into the use of the GPA Phase package with some worked examples. There is also a quick reference guide at the end of this document.But before starting, there are a few important points to remember:1.GPA Phase is a plug-in for DigitalMicrograph (Gatan). This means that results arefully compatible with the other functions present in DM. For example, the phaseimages produced, or strain maps, can be analysed or manipulated with functions likeAnalysis…Statistics or Process…Simple Math. However, if new images areproduced by these operations, internal GPA variables will not be transferred.2.All the commands related to GPA Phase are located in the menu GPA Phase:3.The only other additional feature to DigitalMicrograph is located in the StandardTools Window:This mouse tool is a regular feature of other HREM Research plug-ins and is only used in GPA Phase for the selection of spots in the Power Spectrum, as we will see.New features of version 3GPA Phase 3.0 can handle the complex image, which will be obtained by using electron hologram or an exit wave reconstruction procedure. Other additional features include: •Polynomial fit to Lens distortion correction. Lens distortion is normally changes slowly, and can be expressed by polynomial function. Thus, a polynomial fitting willreduce random noise in the lens distortion pattern.•Rotatable RIO. In some case you may want to use the reference rectangle area that is not parallel to horizontal or vertical direction. Now, after placing a regular rectangle ROI to show the size you want, you can rotate the rectangle RIO as well as change the size.•Color marker. The intensity scale can be added to images (for example, deformation maps) in the form of a color bar, including minimum and maximum values.New features of version 2GPA Phase 2.0 is faster and more user friendly than GPA Phase 1.0. In addition, there are a number of new features, such as:•Calibrated images. If the analysed image has a calibrated scale (in nm, for example), all phase results will be calibrated accordingly (even when binned, see below). More importantly, the spatial resolution of the results will be indicated when defining themask size in GPA Phase...Calculate Phase.•Image binning. The resulting phase image can be chosen to have a reduced size (in pixels) with respect to the original image, using the binning option in GPAPhase...Calculate Phase. Analysing a 2048 by 2048 pixel image at binning 4 willproduce results 512 square. This speeds calculations and liberates space. Noinformation is lost, as the mask used in Fourier space is always much smaller than the original picture size.•Automatic distortion correction. Previously, a reference image had to be analysed manually each time the phase images were to be corrected. Now, this is doneautomatically. The reference image just needs to be analysed once and saved using the new menu GPA Phase...Reference Images. All subsequent phase analyses can then call up and automatic correction using the Distortion tab in GPA Phase...CalculatePhase.•Repeat phase project. All the operations carried out during a phase project can be repeated on a new image with just one click using GPA Phase...Repeat phaseproject, including strain fields. This means of course that the reciprocal lattice vectors need to be roughly the same as before. This command is ideal for analysing a series of images of a specimen.GPA Phase TutorialGetting StartedOpen the image “GPA Test 0” using the DM command File…Open from the GPA PhaseManual folder:The first step in phase analysis is to calculate the Power Spectrumof the image:You will see an image similar to this:Now choose the mouse tool :, and click on one of the spots.Why not zoom in using the DM magnifying glass tool:For the moment we want only one spot marked, but GPA can deal with multiple selections, as we will see later. The chosen reciprocal lattice vector will be referred to as g .We are now ready to calculate our firstPhase Image :The following dialogue box will appear:The first choice “Project Name” gives the title prefix for all subsequent results e.g. phase images, strain maps etc. Choose a short name preferably. For the mask type, use the default value of “Cosine Mask” for the moment. The most important parameter is the mask size (radius) and can be modified using the menu “Size” from small (radius = g/4), medium (g/3) to large (g/2). As you do this, the result of your choice will be seen on the Power Spectrum:Now say OK and the phase image will appear:This phase image has values in radians from –! to +!. The next step is to define area which will correspond to the reference lattice. Use the DM ROI tool (region of interest tool) toselect and area:and choose the next GPA phase command Define Reference.The result will be the following:The phase image now has a well defined reference lattice and can be interpreted. The uniform area of phase shows that the lattice is identical to the reference (here in blue). The change in the relative phase shows that the central band (here in yellow) is displaced with respect to the reference. You can see this on the original image. This is the basis of the geometric phase technique: the measurement of displacement of lattice fringes.By choosing the DM profiling tool, the phase shift can be visualised:In the reference area the phase is zero and in the central band takes a value of 2.2 radians. This value can be verified in the original script used to create the image “GPA Test image 0”. From the theory, this represents a displacement of -2.2/2! of the lattice spacing. Now choose the reference area in the central band, and you will see that the displacement is reversed. This illustrates the overall principle:Only relativephase shifts are important and all measurements refer to the particular referencelattice used.Fringe deformation mappingMost people are interested in measuring deformation and strain, so let us move quickly on from the phase images and displacement. Open the image “GPA Test 1”:A cunning distortion of the fringes is hidden in this image. To measure this distortion the routine as ever is to produce a phase image with a well defined reference. Here is a typical result:The abrupt change in gradient of the phase from one side to the other is witness to the deformation. Let GPA calculate this deformation from the phase image using Fringe Deformation:The first image shows the change in lattice spacing relative to the reference lattice in fractional units (i.e. 0.02 means 2% expansion). The paired image shows the rotation of the lattice fringes with respect to the reference in degrees (in-plane rotation of course) and positive anticlockwise. By default the minimum and maximum values are (±5% deformation and ±5° rotation). Now the deformation and rotation can be visualised by taking profiles or measured in ROI boxes using DM Analysis…Statistics…Mean and Std. Dev. Precision and Spatial ResolutionGPA allows the visualisation of lattice deformation. In the previous example, we can clearly see that the image is divided neatly into two regions. On the left, lattice fringes with a particular lattice spacing and orientation, and on the right, lattice fringes expanded and rotated with respect to this lattice (or vice-versa, if the reference lattice was chosen on the right). GPA is much more than this, however, it is a tool for measuring deformation. Deformation can be measured using the profile tools and statistical tools in specified areas, as has been seen. Each pixel in the image is also a measure of the local deformation and lattice orientation. The question is how local and how precise ?It is not possible to give a general theoretical answer to this question. An experimental way of estimating will be given here: the standard deviation of the fluctuations in a uniform part of the lattice gives the precision, and the length scale of these fluctuations gives thespatialresolution . The fluctuations are assumed to be due to noise, of course. The standard deviation is easily measured using the DM command Analysis…Statistics…Mean and Std. Dev . The spatial resolution depends on the mask size used in the analysis. Did you spot the newfeature of GPA 2.0 when creating the phase image for GPA test 1 ?In this case, the spatial resolution of the results will be 0.2 nm. We also provide the radius of the FFT mask, " in pixels -1, which gives a spatial resolution of 1/" in pixels. Changing the mask size will change the spatial resolution (updated automatically).The precision is a direct function of the noise in the image. Double the amount of noise by modifying the original script “GPA Test image 1” and see the results. Similarly, the spatial resolution is a direct function of the Mask size used in the GPA analysis. Repeat the experiment with a smaller mask. Notice that the precision has increased but the spatial resolution has decreased. This is an essential feature of local measurements, precision is inversely related to spatial resolution.When quoting results from GPA, always quote the precisionat a certain spatial resolution.Determining strain tensorsIn order to measure 2-D strain tensors, two sets of lattice fringes are necessary in the image, as in the image “GPA Test 2”:Two phase images are needed to calculate strain, and to do this two spots in the Power Spectrumcan be selected at once.Carry out Phase Calculation and notice that a mask is placed around both spots in the Power. Choose a project name of “Test 2” and the results will look like the following:Spectrumon one of the phase images exactly like the previous examples:the DM ROI toolWhen the Define Reference command is used, GPA will automatically redefine the referencearea on all of the phase images in the group (here, two phase images):The strain tensor can now be determined with the command Strain . When asked, select the above two images “Test 2 P1” and “Test 2 P2” for the calculation (default values are the two most recent images). In the next dialogue, the angle requested corresponds to the direction of the x-axis with respect to the horizontal (angles anticlockwise positive):Choosing the x-axis parallel to the picture horizontal axis (i.e. angle zero) and selectingsymmetric strain matrix, dilatation and rotation, the following image group will be obtained:This is the final results of GPA strain analysis: the complete 2-D strain tensor.Now it is your job to enjoy and interpret the results!Additional functionsGeometric distortion correctionAll optical systems distort the images they form. CCD cameras and scanners (for digitising negatives for example) introduce additional distortions. Fortunately, these geometric distortions are usually fixed for a given system. It is therefore possible to eliminate these distortions by measuring them (usually only once) and then correcting subsequent images. The procedure is described in Hüe et al. J. Electron Microscopy 54 (2005) 181. The paper concerns projector lens distortions but is general for all geometrical distortions. All that is necessary is an image of a perfect crystal (or any other perfectly regular lattice).Open the image “GPA Test distortion” which is a simulation of a translation boundary:Calculate the two phase images as usual after selecting the spots in the power spectrum:The information contained in the image is dominated by the geometrical distortions.Distortion correctionIn order to correct for distortions, you need to set up a reference image. Open the reference image “GPA Test reference” image and calculate the Power Spectrum.Select two spots and calculate two phase images. In principle, any two non-colinear spotssuffice.With a phase image selected, use the new menu Reference Image and Save As… A standard Window's dialog will appear to save a file. By default, a folder is created in My Images folder but you can place your reference images anywhere. A good place, if you have administrator rights, is in the DigitalMicrograph folder in a folder called GPA reference images . Give the file a name, say “GPA Test reference”, and click OK. The program will save the GPA Test reference image with the necessary information for later use.Redo a Phase Calculation… for the GPA Test distortion image. At the menu stage, click on the Distortiontab. It should look something like this:Now you can choose the reference image you want using the scroll down menu Camera or Lens depending on the type of distortion. For example, you could have a list reference images for different cameras on different microscopes. The GPA Test reference corresponds to projector lens distortions so after selecting the reference in the Lens menu, tick Apply Correction and click OK.The phase images will automatically be corrected and, after using Define Reference, will have a nicely uniform appearance. Only the phase variation due to the crystal structure will be present:You only need to define the reference image once. From now on, it will be available in the Phase Calculation...Distortion tab. If you wish to delete it, just use Reference Image...Delete.Polynomial fittingYou will not always be so lucky with the reference image. Open the more realistic image GPA Test reference noisy:Repeat the procedure for defining a reference image for the distortions, and recalculate the phase image of GPA Test distortion using the new noisy reference. You will find thefollowing results for P1 and P2:The results are much noisier than the previous example, because the noise in the reference image is effectively added to the image. To alleviate this problem, we have included in GPA Phase 3.0 the possibility of applying a polynomial fit to the reference image phases before subtracting them from the experimental phase. Recalculate the GPA Test distortion phases by ticking the Polynomial fitoption:You should find the following result:The resulting phase images are much smoother, as no additional noise has been added to the experimental phases. Indeed it would be a pity to add noise to experiments which are already difficult to perform!AppendixesA: Important phase relationsPhase and displacement:2D displacement and phase:wherePhase gradient and reciprocal lattice deviation :Strain tensor for small deformations:i.e.i.e.i.e.Note: these relations are only valid for small deformations. However, GPAuses the full relations suitable for large deformations (see Appendix in Hytch, Snoeck, Kilaas.)B: Useful DigitalMicrograph commandsDM ROI tool:DM :C: Rotatable ROIThe edge length will be adjusted by one of theyellow edges, and the rotation angle will be adjusted by the yellow cross (+). (You can change the both edge lengths by dragging the yellow cross when pushing the SHIFT key.)Quick Reference GuideThe GPA Main MenuThe commands in the GPA menu are described below.Command DescriptionPower Spectrum First step in the GPA procedure. Calculates anddisplays the Fourier transform of the front mostimage. Spots are then selected in the image of theFourier transform (called Power Spectrum) using themouse tool.Phase calculation… Second step in the GPA procedure. Calculates phaseimages for the spots selected in the Power Spectrum.Results for each spot are displayed and managed aspart of a project (see options).Define Reference (see sub menus) Menu concerning the reference lattice and third step in the GPA procedure.Fringe deformation Calculates the deformation of lattice fringes from thefront most phase image. Displays variation in fringespacing (with respect to reference) and orientation (indegrees, anticlockwise positive).Strain field… Calculates the two dimensional deformation tensor.Asks for two phase images and options (see below).Repeat Project (see sub menus) Allows phase images and other output to be generated directly from the front most HREM image, exactly as for a previous project. Also allows to save details of the current project for later use (even in other sessions of DM).Phase Maths (see sub menus) Menu of different mathematical operations which can be performed on phase images.Phase Tools (see sub menus) Menu of useful operations, not necessarily restricted to phase images.Add Color Marker Adds a color bar and the low and high display ranges.You can move the whole color marker or change itssize. Since the display ranges are text annotations,you can move and edit them as you like. The colormarker can be placed outside of the image display.You can rotate and flip using Edit commands. (Theratio of the color bar is fixed.)Image Group (see sub menus) Menu to close or save groups of images within a particular project.Project(see sub menus)Menu to manage all the images in a particular project.Reference Images (see sub menus) Menu to define reference images for distortion correction due to CCD cameras or projector lenses.Phase Calculation MenuCreate Phase Image DialogThe components of the dialog are described below.Component DescriptionProject Name Name given to the group of images and results Mask Tab For information about the components of the Masktab, see Mask Tab below.Display Tab For information about the components of the Displaytab, see Display Tab below.Distortion Tab For information about the components of theDistortion tab, see Distortion Tab below.OK Closes the dialog and starts the image calculationaccording to the specified parameters.Cancel Closes the dialog without executing the command.Mask TabComponent DescriptionType Defines the shape of mask used to isolate theselected spots in the Fourier transform.Cosine Mask Half-cosine-shaped mask. Size corresponds to radiusof hard cut-off and cosine quarter period (i.e. firstzero).Hard Circular Mask Top-hat function. Size corresponds to radius of hardcut-off.Size Defines mask radius of hard cut-off (beyond whichvalues are set to zero).Selection Default values of large (g/2), medium (g/3) and small(g/4). Custom allows any value.Text Field In units of pixels in the FFT.Apply Button Displays mask size as circles on Power Spectrumaround selected spots (this is just for displaypurposes and is not necessary for the calculation). Spatial Resolution Displays the equivalent averaging in real space (butwill appear only if the original image is calibrated). Binning Defines if the resulting phase images are to be binnedwith respect to the original image thus reducing theirsize and speeding the calculation.Display TabComponent DescriptionDisplay Choice of images to be calculated and displayed. Geometric Phase Image Geometric phase image.Amplitude Image Amplitude of lattice fringes.Bragg Filtered Image Bragg filtered image i.e. image of selected latticefringes.Distortion TabOption DescriptionCamera Selection of the reference images used for correctingcamera distortions (these need preparing with theReference Image menu).Lens Selection of the reference images used for correctinglens distortions (these need preparing with theReference Image menu).Apply Correction Activates the use of the camera and/or lens referenceimages to correct distortions. If both are activated, thecorrections will be applied successively.Polynomial fit Activates the use of polynomial fit to the lensdistortion (not for camera distortion).Order Specifies the order of polynomial fit.Exclude border pixels Specifies the width of border pixels to be excludedwhen estimating polynomial fit parameters. (Most ofthe cases the border pixels are affected bydiscontinuity at the borders. Thus, it is a good idea toexclude some border pixels.)Show fittings Tick to display the polynomial fit in a new window.Define Reference MenuOption DescriptionRefine Third step in the GPA procedure. Before running thecommand, an area needs to be selected by the DMrectangular ROI tool. The command defines thisregion as the reference lattice and adjusts phaseimages accordingly (see options).Setup… Opens Setup dialog.Setup TabOption DescriptionUse Same Area Reference area is automatically applied to all phaseimages in the project when using the Refinecommand or Automatic Update option.Automatic Update Moving the reference area automatically updates thephase images and reference values.Show gx,gy Displays the values of the reference lattice gx and gyin the DM Results window each time the referencearea is updated.Rotatable Tick to make the rectangular ROI rotatable. The edgelength will be adjusted by one of the yellow edges,and the rotation angle will be adjusted by the yellowcross (+). (You can change the both edge lengths bydragging the yellow cross when pushing the SHIFTkey.)Strain Field menuCalculate Strain Dialog(Option Tab)Component DescriptionAngle of x-axis to horizontal Defines the orientation of the x-axis used for thestrain calculation. Angle defined in degrees fromthe horizontal plane of the image to the x-axis(anticlockwise positive). The values used for theprevious calculation will be shown.Note: You can specify the orientation of the x-axisby placing a Line ROI on the HREM image. In thiscase, the angle of the Line ROI appears hereautomatically.Show the following Images Choice of results to be displayed.Symmetric Strain Matrix Images of !xx, !yy and !xy to be displayed.Mean Dilatation Image of "xy to be displayed (average of !xx and!yy).Rotation Angle Image of #xy to be displayed. Values in degreesand anticlockwise positive.Repeat Project menuOption DescriptionRepeat Current Project Repeats the same operations as carried out in thecurrent project on the front most HREM image. Note:the current references of the phase images in therepeated project are used to calculate the new phaseimages. See dialog box for options.Repeat Saved Project Repeats the same operations as carried out in asaved project on the front most HREM image.Save Current Project As Saves the details of the current project for later use. Clean up Project List Removes project details.Repeat Current ProjectdialogOption DescriptionNew Project Defines the name of the new project.OutputPower Spectrum Tick for the power spectrum to be displayed.Phase calculation Tick for the phase image to be displayed (includingamplitude and Bragg filtered images if calculated inthe repeated project).Fringe deformation Tick for the fringe deformation to be displayed (ifcalculated in the repeated project).Strain field Tick for the strain field to be displayed (if calculated inthe repeated project).OptionsDefine reference Tick to Define reference in the same area as for therepeated project.Distortion correction Tick to apply the distortion correction as for therepeated project.。
物理专业常用英语词汇
物理：absolute acceleration 绝对加速度absolute error 绝对误差absolute motion 绝对运动absolute temperature 绝对温度absolute velocity 绝对速度absolute zero 绝对零度absorption 吸收absorptivity 吸收率accelerated motion 加速运动acceleration of gravity 重力加速度acceleration 加速度accidental error 偶然误差acoustics 声学acting force 作用力adjustment 调节aether 以太air pump 抽气机air table 气垫桌air track 气垫导轨alternating current circuit 交流电路alternating current generator 交流发电机alternating current 交流电altimeter 测高仪ammeter 安培计amperemeter 电流计ampere 安培Ampere's experiment 安培实验Ampere's force 安培力Ampere's law 安培定律amperemeter 安培计amplitude 振幅angle of rotation 自转角，转动角angular acceleration 角加速度angular displacement 角位移angular velocity 角速度anion 负离子anisotropy 各向异性annihilation 湮没anode 阳极antenna 天线applied physics 应用物理学Archimedes principle 阿基米德area 面积argumentation 论证argument 辐角astigmatoscope 散光镜atomic nucleus 原子核atomic physics 原子物理学atomic spectrum 原子光谱atomic structure 原子结构atom 原子Atwood ' s machine 阿特伍德机average power 平均功率average velocity 平均速度Avogadro constant 阿伏加德罗常数Avogadro law 阿伏加德罗定律balance 天平ballistic galvanometer 冲击电流计band spectrum 带状谱barometer 气压计basic quantity 基本量basic units 基本单位battery charger 电池充电器battery,accumulator 蓄电池battery 电池组beam 光束betatron 电子感应加速器Bohr atom model 玻尔原子模型boiling point 沸点boiling 沸腾bounce 反弹bound charge 束缚电荷bound electron 束缚电子branch circuit 支路breakdown 击穿brightness 亮度buoyancy force 浮力calorifics 热学camera 照相机capacitance 电容capacitor 电容器capillarity 毛细现象cathode ray 阴极射线cathode-ray tube 阴极射线管cathode 阴极cation 正离子cell 电池Celsius scale 摄氏温标centre of mass 质心centrifugal force 离心力centripetal acceleration 向心加速度centripetal force 向心力chain reaction 链式反应chaos 混沌characteristic spectrum 特征光谱charged body 带电体charged particle 带电粒子charge 充电circular hole diffraction 圆孔衍射circular motion 圆周运动classical mechanics 经典力学classical physics 经典物理学cloud chamber 云室coefficient of maximum staticfriction 最大静摩摩系数coefficient of restitution 恢复系数coefficient of sliding friction 滑动摩擦系数coefficient 系数coherent light 相干光源coil 线圈collision 碰撞component force 分力component velocity 分速度composition of forces 力的合成composition of velocities 速度的合成compression 压缩concave lens 凹透镜concave mirror 凹面镜concurrent force 共点力condensation 凝结condenser 电容器conducting medium 导电介质conductor 导体conservative force field 保守力场conservative force 保守力constant force 恒力constant 常量continuous spectrum 连续谱convergent lens 会聚透镜convex mirror 凸面镜coordinate system 坐标系coplanar force 共面力Corolis force 科里奥利力corpuscular property 粒子性corpuscular theory 微粒说Coulomb force 库仑力coulomb 库仑Coulomb's law 库仑定律counter 计数器creation 产生creepage 漏电crest 波峰critical angle 临界角critical resistance 临界电阻critical temperature 临界温度crystal 晶体current density 电流密度current element 电流元current source 电流源current strength 电流强度curvilinear motion 曲线运动cyclotron 回旋加速器damped vibration 阻尼振动damping 阻尼Daniell cell 丹聂耳电池data processing 数据处理data 数据decay 衰变definition of ampere 安培的定义defocusing 散集density 密度derived quantity 导出量derived unit 导出单位dielectric 电介质diffraction pattern 衍射图样diffraction 衍射diffuse reflection 漫反射digital timer 数字计时器dimensional exponent 量纲指数dimension 量纲diode 二级管diopter 屈光度direct current, DC 直流direct impact 正碰direct measurement 直接测量-disorder 无序dispersion 色散displacement 位移divergent lens 发散透镜Doppler effect 多普勒效应double slit diffraction 双缝衍射driving force 驱动力dry cell 干电池echo 回声eddy current 涡流effective value 有效值elastic body 弹性体elastic force 弹［性］力elasticity 弹性electric charge 电荷electric circuit 电路electric corona 电晕electric energy 电能electric field 电场electric field intensity 电场强度electric field line 电场线electric flux 电通量electric leakage 漏电electric neutrality 电中性electric potential 电位，电势electric potential difference 电位差，电势差electric potential energy 电位能electric power 电功率electric quantity 电量electrification 起电electrification by friction 摩擦起电electrified body 带电体electrode 电极electrolysis 电解electrolyte 电解质electromagnetic damping 电磁阻尼electromagnetic induction 电磁感应electromagnetic radiation 电磁辐射electromagnetic wave 电磁波electromagnetic wave spectrum 电磁波谱electromagnetism inductionphenomenon 电磁感应现象electromagnet 电磁体electrometer 静电计electromotive force 电动势electron 电子electron beam 电子束electron cloud 电子云electron microscope 电子显微镜electron volt 电子伏特electroscope 验电器electrostatic equilibrium 静电平衡electrostatic induction 静电感应electrostatic screening 静电屏蔽elementary charge 基本电荷，元电荷energy 能量energy level 能级equilibrium 平衡equilibrium condition 平衡条件equilibrium of forces 力的平衡equilibrium position 平衡位置equilibrium state 平衡态equivalent source theorem 等效电源定理erect image 正像error 误差ether 以太evaporation 蒸发excitation 激发excitation state 激发态experiment 实验experimental physics 实验物理学external force 外力eyepiece 目镜far sight 远视Faraday cylinder 法拉第圆筒Faraday law ofelectromagnetic induction 法拉第电磁感应定律Faraday's law ofelectromagnetic induct 法拉第电磁感应定律farad 法拉(电容的单位)film interference 薄膜干涉final velocity 末速度first cosmic velocity 第一宇宙速度fission 裂变fixed-axis rotation 定轴转动flotation balance 浮力秤fluid 流体focal length 焦距focusing 调焦，聚焦focus 焦点force 力forced vibration 受迫振动fractal 分形free charge 自由电荷free electron 自由电子free period 自由周期freezing point 凝固点frequency 频率friction force 摩擦力fusion 聚变galvanometer 电流计gas 气体general physics 普通物理学generator 发电机good conductor 良导体gravitation 引力gravity 重力gravitational potential energy重力势能gravity field 重力场ground earth 接地ground state 基态ground wire 地线hadron 强子half life period 半衰期heat 热heat transfer 传热henry 亨利hertz 赫兹(频率的单位)Hooke law 胡克定律humidity 湿度hydrogen 氢原子hypothesis 假设ice point 冰点ideal gas 理想气体image 像image distance 像距image height 像高imaging 成像imperfect inelastic collision 非完全弹性碰撞impulse 冲量incident angle 入射角incident ray 入射线indirect measurement 间接测量induced electric current 感应电流induced electric field 感应电场induction current 感应电流induction electromotive force感应电动势induction motor 感应电动机inertia 惯性inertial force 惯性力inertial system 惯性系infrared ray 红外线infrasonic wave 次声波initial phase 初位相initial velocity 初速度input 输入instantaneous power 瞬时功率instantaneous velocity 瞬时速度instrument 仪器insulated conductor 绝缘导体insulating medium 绝缘介质insulator 绝缘体intensity of sound 声强interference 干涉interference fringe 干涉条纹interference pattern 干涉图样interferometer 干涉仪internal energy 内能internal force 内力internal resistance 内阻intonation 声调-inverted image 倒像invisible light 不可见光ion beam 离子束ionization 电离irreversible process 不可逆过程isobaric process 等压过程isobar 等压线isochoric process 等体积过程isothermal 等温线isothermal process 等温过程isotope 同位素isotropy 各向同性joule 焦耳（功的单位）Joule heat 焦耳热Joule law 焦耳定律Joule' law 焦耳定律Kepler law 开普勒定律kinematics 运动学kinetic energy 动能Laplace's equation 拉普拉斯方程laser 激光，激光器law 定律law of conservation of angular momentum 角动量守恒定律law of conservation of energy 能量守恒定律law of conservation of mass 质量守恒定律law of conservation of mechanical energy 机械能守恒定律law of conservation of momentum 动量守恒定律law of electric charge conservation 电荷守恒定律Le Système International d ` Unit è s 国际单位制(SI)lead 导线length 长度lens 透镜lens formula 透镜公式Lenz's law 楞次定律lepton 轻子Light ray 光线light source 光源light wave 光波lightning rod 避雷针light 光line spectrum 线状谱lines of current 电流线lines of force of electric field 电力线liquefaction 液化liquefaction point 液化点liquid 液体longitudinal wave 纵波loop 回路Lorentz force 洛仑兹力luminous intensity 发光强度magnetic field 磁场magnetic field intensity 磁场强度magnetic field line 磁场线magnetic induction flux 磁感应通量magnetic induction 磁感应强度magnetic induction line 磁感应线magnetic material 磁性材料magnetic needle 磁针magnetic pole 磁极magnetics 磁学magnetism 磁学magnetization 磁化magnet 磁体magnification 放大率magnifier 放大镜，放大器manometer 流体压强计mass 质量mass defect 质量亏损mass-energy equation 质能方程matter 物质matter wave 物质波Maxwell's equations 麦克斯韦方程组mean speed 平均速率mean velocity 平均速度measurement 测量mechanical energy 机械能mechanical motion 机械运动mechanical vibration 机械振动mechanics 力学medium 介质melting fusion 熔化melting point 熔点metre rule 米尺microdetector 灵敏电流计micrometer caliper 螺旋测微器microscope 显微镜microscopic particle 微观粒子mirror reflection 镜面反射mirror 镜mixed unit system 混合单位制modern physics 现代物理学molar volume 摩尔体积molecular spectrum 分子光谱molecular structure 分子结构moment of force 力矩momentum of electromagneticfield 电磁场的动量momentum 动量motor 电动机multimeter 多用［电］表musical quality 音色N pole 北极natural frequency 固有频率natural light 自然光negative charge 负电荷negative crystal 负晶体negative ion 负离子negative plate 负极板network 网络neutralization 中和neutron 中子newton 牛顿（力的单位）Newton first law 牛顿第一定律Newton second law 牛顿第二定律Newton third law 牛顿第三定律nonequilibrium state 非平衡态north pole 北极nucleus force 核力nucleus of condensation 凝结核object 物object distance 物距object height 物高objective 物镜observation 观察Oersted's experiment 奥斯特实验ohm 欧姆Ohm law 欧姆定律ohmmeter 欧姆计Ohm's law 欧姆定律open circuit 开路optical bench 光具座optical centre of lens 透镜光心optical fiber 光导纤维optical glass 光学玻璃optical instrument 光学仪器optical lever 光杠杆optical path difference 光程差optical path 光程(路)optically denser medium 光密介质optically thinner medium 光疏介质optics 光学orbit 轨道order 有序oscillograph 示波器output 输出overweight 超重parallel connection ofcondensers 电容器的并联parallelogram rule 平行四边形定律parallel-resonance circuit 并联谐振电路parameter 参量particle 质点，粒子Pascal law 帕斯卡定律path 路程peak 峰值pendulum 摆penumbra 半影perfect conductor 理想导体perfect elastic collision 完全弹性碰撞perfect inelastic collision 完全非弹性碰撞-periodicity 周期性period 周期periscope 潜望镜permanent magnet 永磁体permittivity of vacuum 真空介电常数permittivity 电容率phase 位相phenomenon 现象photocurrent 光电流photoelectric cell 光电管photoelectric effect 光电效应photoelectron 光电子photography 照相术photon 光子physical balance 物理天平physical quantity 物理量physics 物理学piezometer 压强计pitch 音调Planck constant 普朗克常量plasma 等离子体point charge 点电荷polarization 偏振polarized light 偏振光polycrystal 多晶体poor conductor 不良导体positive charge 正电荷positive crystal 正晶体positive ion 正离子positive plate 正极板positron 正电子potential energy 势能potentiometer 电位差计power 功率pressure 压强，压力primary coil 原线圈principle of constancy of light velocity 光速不变原理prism 棱镜projectile 抛体projectile motion 抛体运动projector 投影仪proton 质子pulley 滑轮pulley block 滑轮组quantity of heat 热量quantization 量子化quantum 量子quantum mechanics 量子力学quantum number 量子数radar 雷达radioactive source 放射源radius of gyration 回旋半径random motion 无规则运动range 量程rated voltage 额定电压reacting force 反作用力real image 实像real object 实物reasoning 推理recoil 反冲rectilinear motion 直线运动reference frame 参考系，坐标系reference system 参考系reflected angle 反射角reflected ray 反射线reflection coefficient 反射系数reflection law 反射定律reflectivity 反射率refracted angle 折射角refracted ray 折射线refraction law 折射定律refraction coefficient 折射系数refractive index 折射率relative acceleration 相对加速度relative error 相对误差relative motion 相对运动relative velocity 相对速度relativity 相对论resistance 电阻resistance box 电阻箱resistivity 电阻率resistor 电阻［器］resolution of force 力的分解resolution of velocity 速度的分解resonance 共振，共鸣resonant frequency 共振频率resultant force 合力resultant velocity 合速度reversibility of optical path 光路可逆性reversible process 可逆过程rheostat 变阻器right-hand screw rule 右手螺旋定则rocker 火箭rotating magnetic field 旋转磁场rotation 自转，转动Rutherford scattering 卢瑟福散射Rutherford ［α-particlescattering］experiment 卢瑟福［α散射］实验S pole 南极saturation 饱和scalar 标量scalar field 标量场scanner 扫描器second cosmic velocity 第二宇宙速度selective absorption 选择吸收self-induced electromotiveforce 自感电动势self-inductance 自感self-induction phenomenon 自感系数semiconductor 半导体semi-transparent film 半透膜sensitive galvanometer 灵敏电流计sensitivity 灵敏度sensitometer 感光计sensor 传感器series connection ofcondensers 电容器的串联series-resonance circuit 串联谐振电路short circuit 短路short sight 近视shunt resistor 分流电阻significant figure 有效数字simple harmonic motion (SHM)简谐运动simple harmonic wave 简谐波simple pendulum 单摆single crystal（monocrystal）单晶体single slit diffraction 单缝衍射sinusoidal alternating current简谐交流电sinusoidal current 正弦式电流sliding friction 滑动摩擦slit 狭缝solar cell 太阳能电池solenoid 螺线管solidification 凝固solidifying point 凝固点solid 固体solution 溶液solvation 溶解sonar 声纳sound source 声源sound velocity 声速sound wave 声波sound 声［音］source 电源south pole 南极space 空间spark discharge 火花放电special relativity 狭义相对论specific heat capacity 比热容spectacles 眼镜spectral analysis 光谱分析spectral line ［光］谱线spectrograph 摄谱仪spectrography 摄谱学spectroscopy 光谱学spectrum 光谱speed 速率spherical mirror 球面镜spontaneous radiation 自发辐射spring balance 弹簧秤stability 稳定性stabilized current supply 稳流电源stabilized voltage supply 稳压电源standard atmosphericpressure 标准大气压-standard cell 标准电池standing wave 驻波static friction 静摩擦stationary state 定态steady current 恒定电流steady current source 恒流源steady voltage source 恒压源steam point 汽点stiffness 劲度［系数］stimulated radiation 受激辐射stop watch 停表sublimation 升华superconductivity 超导［电］性superconductor 超导体superposition principle of electric field 电场强度叠加原理superposition theorem 叠加定律supersaturation 过度饱和supersonic speed 超声速supersonic wave 超声波supply transformer 电源变压器surface resistance 表面电阻switch 开关system of concurrent forces 共点力系system of particles 质点系system of units 单位制systematic error 系统误差telescope 望远镜temperature 温度tension 张力the law of gravity 万有引力定律theorem 原理theorem of kinetic energy 动能定理theorem of momentum 动量定理theoretical physics 理论物理学theory 理论thermal capacity 热容［量］thermal equilibrium 热平衡thermal motion 热运动thermal transmission 传热thermodynamic scale ［of temperature］热力学温标thermodynamic temperature热力学温度thermometer 温度计thermometric scale 温标thermonuclear reaction 热核反应thick lens 厚透镜thin lens 薄透镜third cosmic velocity 第三宇宙速度three-phase alternatingcurrent 三相［交变］电流time 时间timer 定时器，计时器torsion balance 扭秤total reflection 全反射trajectory 轨道transformer 变压器transistor 晶体管transition 跃迁translation 平移transmission line 传输线transmissivity 透射率transverse wave 横波triboelectrification 摩擦起电triode 三极管trough 波谷tuning fork 音叉turbulent flow 湍流ultrasound wave 超声波ultraviolet ray 紫外线umbra 本影undulatory property 波动性uniform dielectric 均匀电介质uniform motion 匀速运动unit 单位unit system 单位制universal constant 普适常量universal gravitation 万有引力universal meter 多用［电］表vacuum tube 真空管vacuum 真空value of amplitude 幅值vaporization 汽化variable 变量vector 矢量velocity of light 光速velocity 速度verification 验证vernier 游标vernier caliper 游标卡尺vibration 振动viewing angle 视角viewing field 视场virtual image 虚像virtual object 虚物virtual value 有效值visibility 可见度visible light 可见光voltage 电压voltage division circuit 分压电路voltaic cell 伏打电池voltmeter 伏特计voltmeter-ammeter method伏安法volt 伏特volume 体积vortex electric field 涡旋电场watt 瓦特wave equation 波动方程wave theory 波动说wavelength 波长wave-particle dualism 波粒二象性wave 波weight 重量weightlessness 失重white light 白光work 功work function 逸出功X-ray X射线Young experiment 杨氏实验zero line 零线α -decay α衰变α -particle α粒子α -ray α射线β -decay β衰变β -ray β射线γ -decay γ衰变γ -ray γ射线。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
April2001Ž.Materials Letters482001273–280 r locate r matlet Effect of elastic anisotropy on the dissociation widths ofsuperdislocations in TiAlX.P.Song),G.L.ChenState Key Laboratory for AdÕanced Metals and Materials,UniÕersity of Science and Technology Beijing,Beijing,100083,People’s Republic of ChinaReceived20July2000;accepted10September2000Abstract²x²xThe dissociation widths of the and1r2superdislocations in TiAl have been calculated by the elasticity theory that the elastic interaction energies and stacking fault energies acting on the partial dislocations are equal.The results show²x²xthat the dissociation widths of the screw and1r2superdislocations in anisotropic condition are smaller than that²x²of isotropic condition,but the dissociation widths of the edge101and1r2112superdislocations in anisotropic condition are larger than or equal to that of isotropic condition.The equilibrium separations of the superlattice intrinsic stacking fault Ž.²x²xSISF formed by the two-fold101and1r2112superdislocation dissociations are nearly the same with each other in the elastic isotropy condition but are different in the elastic anisotropy condition.The stacking fault energy of SISF in a high-Nb2²xTiAl alloy,which was evaluated to be about45–55mJ r m from the101superdislocation dissociation and to be about 2²x62–69mJ r m from the1r2112superdislocation dissociation using the isotropic calculation,is determined to be about 2²x²x80"5mJ r m from both the and1r2superdislocation dissociations using the anisotropic calculation.q2001 Elsevier Science B.V.All rights reserved.Keywords:Elastic anisotropy;Superdislocations;Dissociation width;TiAl1.IntroductionIn recent years,a number of papers have studied the dislocation core configurations in TiAl alloys in an attempt to explain the mobility of dislocations atw xroom and elevated temperatures1–4.It was claimed that in the single-phase TiAl alloys the ordinary ²x1r2110dislocations are immobile because of strong directional Ti–Ti bonding and high intrinsicw x²x²x lattice friction5,while the101and1r2112 )Corresponding author.Tel.:q86-10-623-32806;fax:q86-10-623-32508.Ž.E-mail address:xpsong@ X.P.Song.superdislocations are usually disturbed by their dis-sociation configurations of splitting into non-coplanar configurations such as A roof B type barriers,A K–W Bw xlocks and so on6.It was also found that both the ²xedge101dislocations that have a planar core are²xglissile,while the screw101dislocations that havew xa non-coplanar A cross-shaped B core are sessile7.In²xthe case of planar dissociation of the101superdis-locations,the equilibrium dissociation widths havew xbeen calculated by some papers7–10,but unfortu-nately,these results disagreed with each other due to the different calculation methods and had a greater gap with the experimental results.This situation makes the evaluation of the mobility of superdisloca-00167-577X r01r$-see front matter q2001Elsevier Science B.V.All rights reserved.Ž.PII:S0167-577X0000315-3()X.P.Song,G.L.Chen r Materials Letters482001273–280 274Table1Ž2.Ž. Theoretical estimates of planar fault energies mJ r m in111 plane of TiAlPlane faults APB SISF CSF SESF APB ReferenceŽ100.w xEMA32260308602687,10w xLKKR6701102801103509,10w x FLAPW56090410804308,10 tions with different dissociation widths more com-plex and also brings about some differences in cal-culating the stacking fault energies from the dis-sociation widths determined by the weak-beamŽ. transmission electron microscopy WBTEM.Mean-time,the difference between the equilibrium widths²xof the planar stacking faults formed by the and ²x1r2superdislocation dissociations does not re-ceived much attention in distinguishing the mobility of these two superdislocations and in determining the stacking fault energies from different dissociation configurations.Thus,it is very necessary to carry out a more detailed study on the superdislocation disso-ciation widths.One of the reasons for the difference in superdis-location splitting widths between the calculated and experimental results is probably due to the elastic anisotropy in TiAl.As we know,the elastic shearmoduli and Young’s moduli existing in L1TiAl are0 different in directions and will bring about unequal elastic interaction energies between splitting partial dislocations and the different superdislocation line orientations.Therefore,adopting different shear moduli and Poisson rates with orientations will re-duce the difference.Another reason is probably due to the different dissociation configurations of the superdislocations in TiAl.It has been reported that ²x²both the and1r2superdislocations can occur in two-fold,three-fold or four-fold dissocia-tions,and at some cases,can also occur in coplanar or non-coplanar dissociation,but the relationship of the dissociation widths between these two superdis-locations does not get much attention.Thus,in this paper,the effect of elastic anisotropy on the dissocia-tion widths of different superdislocation configura-tions is evaluated and some interesting results are obtained.2.Calculation methodIn principle,when the splitting partial dislocations can move freely on the glide plane,the equilibrium separation widths of perfect superdislocations can be determined by the condition that the total radial interaction force acting on the partial dislocations is balanced by the fault surface tension acting in the opposite direction.The value of the fault surface tension is equal to the planar fault energy.The planarŽ.fault energies g that have been calculated by dif-ferent methods are summarized in Table1.These values will be regarded as the known and tempera-ture independent parameters to evaluate the dissocia-tion widths of the superdislocations in this study.The elastic interaction energy f between two12™™straight and parallel partial dislocations b and b12w xwhen expressed as slip plane is11:™™<<<<G b b12f s cos F y a cos F q bŽ.Ž.122p d12sin F y a sin F q bŽ.Ž.q1Ž.1y nwhere G is the shear modulus,n is the Poisson rate,d is the distance between partials,F,a,b are the 12Table2²xŽ.Ž.Elastic moduli and Poisson rates in the uÕw direction of111plane in TiAl at300and1273K unit of GPa²x²x²x²x²x²x²x 300K E200.52192.62200.52189.94173.67189.94200.52XG61.9060.4461.9065.1066.8465.1061.90XÕ0.6200.5930.6200.4590.2990.4590.620X1273K E156.96155.36156.96147.87138.35147.87156.96XG44.8044.6144.8045.2345.4245.2344.80XÕ0.750.740.750.630.520.630.75()X.P.Song,G.L.Chen r Materials Letters 482001273–280275²x Fig.1.The dissociation widths of SISF under the two-fold dissociation of the 101superdislocations at 300K.angles of Burger’s vectors of the perfect dislocation ™™™b ,partial dislocations b and b with the dislocation 12line direction,respectively.Under the elastic isotropic condition,the G and n are constants,but when thinking of the elastic anisot-ropy,the G and n should be transformed to the G X X ²x and n ,which will vary with the u Õw direction in Ž.the hkl slip plane.These values can be calculated w x using the following equations 12for both room and elevated temperatures:y 1X X G s s 2Ž.Ž.66y 1X X E s s 3Ž.Ž.11E X XG s4Ž.X 21q n s X s 4s a 2a 2q b 2b 2Ž.66111212q 4s g 2g 2q 8s a a b b 3312121212q 8s b b g g q a a g g Ž.131212121222q s b g q b g q a g q a g Ž.Ž.44122112212q s a b q a b 5Ž.Ž.661221s X s s a 4q b 4q s g 4q 2s a 2b 2Ž.1111113311211q 2s b 2g 2q a 2g 2Ž.131111q s b 2g 2q a 2g 2q s a 2b 26Ž.Ž.4411116611Ž.where are the elastic compliances,s s 1r 211w X Ž.x X =c r c q 1r c y c ,s s y c r c ,s s 331112131344Ž.w X Ž.x 1r c ,s s 1r 2c r c y 1r c y c ,s s 441233111233Ž.X X Ž.c q c r c ,s s 1r c ,c s c c q c y 111266663311122c 2,and c are elastic stiffnesses,their values are 12i j w x taken from the references 10,13for room and ele-vated temperatures,respectively.a ,b g ,a ,b ,11122²x g are the direction cosines of the u Õw direction 2Ž.and hkl slip plane in the tetragonal system,respec-Ž.tively.For the directions within 111slip plane,the shear moduli and Poisson rate are calculated for both the 300and 1273K,respectively and the results are listed in Table 2.()X.P.Song,G.L.Chen r Materials Letters 482001273–280276²x Fig.2.The dissociation widths of SISF under the four-fold dissociation of the 101superdislocations at 300K.In TiAl,the perfect superdislocations usually split into two-fold,three-fold or four-fold configurations w x 14–16.The following dissociations will be consid-ered in this study:Two-fold:11²²²x x x ™112q SISF q 7Ž.111²²²x x x112™112q SISF q 1128Ž.263Three-fold :Žcoplanar .11²²²x x x101™112q SISF q 2111²xq APB q 9Ž.2111²²²x x x112™112q SISF q 1121²x q SESF q 10Ž.6Four-fold :Žcoplanar .11²²²x x x 101™112q SISF q 211q APB11²²x xq 112q CSF q 21111Ž.For the multiple dissociation configurations,the equilibrium dissociation widths of the superdisloca-tions can be calculated by a set of equilibrium equations,which concerns each of the stacking fault energies.For instance,the dissociation widths corre-sponding to the different planar fault energies in Ž.equality 11can be obtained respectively by resolv-ing the following set of equations:gs f q f q f °SISF 121314~g s f q f q f 12Ž.CSF 434241¢gs f q f y f APB 231334()X.P.Song,G.L.Chen r Materials Letters482001273–280277where f implies the elastic interaction between thei jpartial dislocation i and j,and can be calculated by Ž.Eq.1,respectively.3.Calculation results and discussion²]3.1.Dissociation widths of the101superdisloca-tionsFig.1shows the dissociation widths of the two-²xfold superdislocations in the conditions of isotropic and anisotropic elastic fields.It can be seen that,under the isotropic condition,the splitting widths decrease with the increase of the planar fault energyŽ.and with the angle F from the edge orientation to screw orientation.However,under the anisotropic condition,the case is a little different.The splitting widths in the screw orientation become smaller than that of isotropy and the splitting widths in the edgeorientation become larger than that of isotropy.The²x dissociation widths of SISF under the four-fold101 superdislocations also show the same variable trendŽ. with that of the two-fold dissociation see Fig.2., although splitting widths still appear which is causedŽ.by complex stacking fault CSF and anti-phase Ž.boundary APB.It can also be seen from Fig.2thatwhen using the E s90mJ r m2,E s560SISF APBmJ r m2,E s410mJ r m2,the splitting width of CSFSISF in a screw orientation is calculated to be6.19 nm in isotropy and to be4.44nm in anisotropy.The isotropic splitting width is very close to the splittingw x width of5.9nm calculated by Yoo and Fu10for the screw orientation.Meantime,when using the E s110mJ r m2,E s670mJ r m2,E s SISF APB CSF 280mJ r m2,the splitting width of SISF in an edge superdislocation is calculated to be 6.75nm in isotropy and to be8.63nm in anisotropy.The²xFig.3.The dissociation widths of the SISF r SESF under the different dissociation configurations of the112superdislocations at300K.()X.P.Song,G.L.Chen r Materials Letters482001273–280 278anisotropic splitting width is very near the splittingwidth of8.7nm that was calculated by Woodward et w xal.9for the edge superdislocations.However,whenE s60mJ r m2,E s322mJ r m2,E s308 SISF APB CSFmJ r m2,the splitting width of SISF in an edge orientation is calculated to be12.84nm in isotropy and16.46nm in anisotropy.These calculations havea greater difference with the SISF splitting widths of5.7and4.5nm which was calculated by Panova andw xFarkas7by the elasticity theory and atomistic simulation of dislocation core configurations for the edge orientation.²]3.2.Dissociation widths of the superdisloca-tions²xThe splitting widths of the superdisloca-tions at different dissociation configurations are ex-²x amined in much the same way as that for the101 superdislocations.The effect of anisotropic elasticity on the splitting widths of SISF is almost the same²xwith that of the superdislocations,except thatthe edge orientation of the splitting width in the anisotropic condition is decreased to the level of the isotropic condition,as shown in Fig.3.The decreas-²xing Poisson rate in the110direction within the Ž.111plane is responsible for this exception.It can also be seen from Fig.3that the splitting widths of SISF in the three-fold dissociation are below the two-fold dissociation,the difference in the screw orientation is about2nm,and about3nm in theedge orientation when using E s90mJ r m2.SISFThe difference of the dissociation widths of SISF ²x²xbetween the and superdislocations in the two-fold dissociation is shown in Fig.4.It can be²xseen that the splitting widths of the superdislo-cations exhibit symmetrical distribution along the center line of about908,while the splitting widths of ²xthe superdislocations are asymmetrical.In the case of the isotropic condition,the splitting widthsof²x²xFig.4.The comparison of the dissociation widths of the SISF under the two-fold dissociation between the101and112superdislocations at300K.()X.P.Song,G.L.Chen r Materials Letters 482001273–280279²x the 112superdislocations are nearly equivalent to ²x that of the 101superdislocations.However,in the case of the anisotropic condition,the splitting width ²x of a screw 112superdislocation is about 1nm ²x larger than that of a screw 101superdislocation,²x while the splitting width of an edge 112superdis-location is about 3nm smaller than that of an edge ²x 101superdislocation when using E s 90SISF mJ r m 2.These will bring about the different defor-²x ²x mation characteristics between the and superdislocations.More research work is needed in this respect.3.3.Determination of the stacking fault energy by the isotropy and anisotropyThe experimentally measured splitting widths be-tween the partial dislocations usually vary with the imaging condition.At the diffraction condition,wherein the fault plane is normal to the electron beam direction,the splitting width will reach its maximum value and will be used to evaluate the stacking fault energy.Affected by the anisotropy,the actual splitting widths of superdislocations will be-come larger or smaller compared with that of isotropy,thus will bring about some difference in determining the stacking fault energy from the disso-ciation widths.For instance,in order to determine the stacking fault energy of SISF in a high Nb–TiAl alloy,which had experienced forging and annealing at 1273K,the dissociation widths of the two-fold ²x superdislocations were examined thoroughly;Ž.it was found that their splitting widths on the 111plane were to be 11–14nm at different angles.The stacking fault energy of SISF was then deduced to be 2w x about 45–55mJ r m by isotropic calculation 17.Meanwhile,the dissociation widths ofthe three-fold ²x superdislocations were also examined and it²x Fig.5.The determination of the stacking fault energy of SISF from the dissociation widths of the two-fold 101superdislocations and the ²x three-fold 112superdislocations by isotropic and anisotropic methods respectively at 1273K.()X.P.Song,G.L.Chen r Materials Letters482001273–280 280was found that the splitting widths of SISF were to be about6.2and6.8nm at the angles of308and908 with the dislocation line.The stacking fault energy of SISF was then deduced to be about62–69mJ r m2w xusing isotropic calculation18.Obviously,the mea-sured results are not acceptable due to the same TiAl alloy.On the contrary,when using anisotropic calcu-lation the stacking fault energy of SISF is deduced to be about80"5mJ r m2from both the splitting²x²xwidths of the and superdislocations,Ž.respectively see Fig.5.This result is acceptable because the stacking fault energy of SISF should be independent of the superdislocation dissociation con-figurations.4.SummaryThe present study has examined the splitting²x²xwidths of the101and112superdislocations on behalf of the elastic anisotropy.The orientation de-pendence of elastic constants makes the splitting²xwidths of the101superdislocations smaller in the screw orientation and larger in the edge orientation compared with the elastic isotropy.This trend is also²xthe same with the superdislocations except in the edge orientation wherein the splitting widths of ²xthe superdislocations under the isotropic and anisotropic conditions are nearly equal to each other. Meantime,the elastic anisotropy brings about the²x splitting width of SISF in a two-fold screw superdislocation to be larger than that of a two-fold ²xscrew superdislocation,and the splitting width²xof SISF in a two-fold edge112superdislocation to²xbe smaller than that of a edge101superdislocation. These results offer a new method to evaluate the stacking fault energies from the measured widths of the superdislocation dissociations.AcknowledgementsThe authors would like to thank the financial support from the National Nature Science Founda-tion of China.Referencesw x1K.J.Hemker,B.Viguier,ls,Mater.Sci.Eng.A164Ž.1993391.w x2J.P.Simmons,S.I.Rao, D.M.Dimiduk,in:I.Baker,R.Ž.Darolia,J.D.Whittenberger,M.H.Yoo Eds.,High-Temper-ature Ordered Intermetallic Alloys V,Materials Research Society,Pittsburgh,PA,1993,335.w x3S.Rao,C.Woodward,J.Simmons,D.Dimiduk,in:J.A.Ž.Horton Ed.,High-Temperature Ordered Intermetallic Al-loys VI,Materials Research Society,Pittsburgh,PA,1995, 129.w x4V.Paidar,H.Inui,K.Kishida,M.Yamaguchi et al.,Mater.Ž.Sci.Eng.A2331997111.w x5 B.F.Greenberg,V.I.Anisimov,Yu.N.Gornostirev,G.G.Ž.Taluts,Scr.Metall.221988859.w xŽ.6 B.A.Greenberg et al.,Acta Metall.Mater.391991233.w xŽ.7J.Panova,D.Farkas,Philos.Mag.A781998389.w xŽ.8J.Ehmann,M.Fahnle,Philos.Mag.A771998701.w x9 C.Woodward,J.M.MacLaren,S.Rao,J.Mater.Res.7Ž.19921735.w xŽ.10M.H.Yoo,C.L.Fu,Metall.Mater.Trans.A29199849. w x11J.P.Hirth,J.Lothe,Theory of Dislocations,2nd edn.,Wiley, 1982.w xŽ. 12Y.He,R.B.Schwarz,A.Migliori,J.Mater.Res.101995 1187.w xŽ.13Y.He et al.,Mater.Sci.Eng.A239–2401997157.w x14 D.Shechtman,M.J.Blackburn,H.A.Lipsitt,Metall.Trans.5Ž.19741373.w x15G.Hug, A.Loiseau, salmonie,Philos.Mag.A54Ž.198647.w x16S.A.Court,V.K.Vasudevan,H.L.Fraser,Philos.Mag.A61Ž.1990141.w x17L.C.Zhang,PhD Dissertation,University of Science andŽ.Technology Beijing P.R.China,1999.w x18W.J.Zhang,F.Appel,Acta Mater,submitted for publication.。