清华大学航天航空学院学术报告

1、1清华大学航天航空学院清华大学航天航空学院概况概况2发展历史发展历史/history Late 1930s: von Karman 1938: 1938: 航空工程系航空工程系, , Department of Aeronautics 中国第一位飞机设计中国第一位飞机设计大师徐舜寿大师徐舜寿 人才培养：人才培养：“两弹一两弹一星星”和载人航天的元和载人航天的元勋王永志院士等勋王永志院士等单翼教练机单翼教练机 3历史沿革历史沿革1936年航空工程组全体师生，左四为庄前鼎教授年航空工程组全体师生，左四为庄前鼎教授 在旧电机馆东面的航空馆在旧电机馆东面的航空馆 1936年摄年摄 飞机机架实验室飞机机

2、架实验室 1936年摄年摄 风洞实验室，风洞实验室，1936年年4里程碑里程碑/landmarks52004年年5月月18日日6Micro- Satellite50kg, (2000) Nano-satellite 30kg (2004)7学院构架学院构架n工程力学系工程力学系固体力学研究所固体力学研究所流体力学研究所流体力学研究所工程振动研究所工程振动研究所工程热物理研究所工程热物理研究所生物力学与医学工程生物力学与医学工程研究所研究所(2006.01)(2006.01)n 宇航中心宇航中心n 航空技术中心航空技术中心n 国防战略研究中心国防战略研究中心n航天航空系航天航空系飞行器设计研究所

3、飞行器设计研究所动力与推进研究所动力与推进研究所人机环境研究所人机环境研究所空天信息研究所空天信息研究所(宇航中心宇航中心)航空制造研究所航空制造研究所(机械系机械系)8n 120 120 名教职工名教职工 4 4 位院士：黄克智、过增元、杨卫、王永志位院士：黄克智、过增元、杨卫、王永志 35 35 位教授（含位教授（含4 4位院士，位院士，1 1位名师，位名师，4 42 2位长江特聘教授）位长江特聘教授） 35 35 位副教授，位副教授，1010位讲师位讲师n 20 20 位博士后位博士后n 360 360 名本科生：其中名本科生：其中7070普通生，普通生，3030定向生和国防生定向生和国

4、防生n 400 400 名研究生：其中博士生和硕士生各名研究生：其中博士生和硕士生各5050外国留学生外国留学生1010名法国、巴基斯坦、朝鲜、韩国名法国、巴基斯坦、朝鲜、韩国此外：此外： 航天工程硕士班航天工程硕士班航空工程硕士班航空工程硕士班(31(31人人) )师资和学生师资和学生9航天工程硕士班开班仪式航天工程硕士班开班仪式20052005年年1111月月师资和学生师资和学生10理念和目标理念和目标发展理念为：发展理念为：发展力学与热科学学科的优势，发展力学与热科学学科的优势，创建航空宇航科学与技术学科。创建航空宇航科学与技术学科。发展目标为：发展目标为：入主流、有特色、上水平。入主流

5、、有特色、上水平。建设清华大学国防（航天、航空、航海）建设清华大学国防（航天、航空、航海）科研和工程的平台。科研和工程的平台。11发展材料塑性行为发展材料塑性行为的多尺度计算框架的多尺度计算框架 北航大学北航大学-1-1 12Outlinen 尺度效应尺度效应n 应变梯度塑性理论应变梯度塑性理论n 单单晶铜动态变形的应变率效应晶铜动态变形的应变率效应-位错动位错动力学力学(DD)(DD)与连续介质有限元耦合与连续介质有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金属塑性行为的尺度和金属塑性行为的尺度和应变率效应应变率效应n 总结总结13nMotivationThe hard

6、er for the thinner material;Atomic scale experiment tool development: AFM, SEM;MEMS/NEMS are playing an important role in modern engineering;Chemical mechanical polishing process;Nano-machine development.Motivation14Nano-tweezerA nano-mirror/optical switchMulti-wall nano-tube BearingsNano-gearMotiva

7、tion15n With the development of material science, especially as MEMS/NEMS are playing a more important role in modern engineering, some mechanical behaviors, e.g., fracture, shear instability, need to be investigated from a different and multi-disciplinary perspective. MotivationMEMSNEMSBio-NEMSBio-

8、MEMS16n Molecular dynamics (MD) simulation is restricted by its length-scale and time-scale, as well as the loading rate is often very high.n Continuum mechanics (FE) cant capture the physical process occurring at meso-scale, where there doesnt exist a proper constitutive form currently.n It is nece

9、ssary to establish a multi-scale framework to investigate the behavior of materials.Motivation17Motivationn Recent researches focus onSize/strain rate/thermal effects on plastic behavior of metalsDislocation dynamics (DD) with continuum FE resulting in plasticity Energy dissipation on nano-scale con

10、tact and scratchn 研究目标是材料失效行为的多尺度机制研究目标是材料失效行为的多尺度机制18赵慧娟，庄茁，郑泉水，大变形扭转塑性硬化的实验和仿真研究，赵慧娟，庄茁，郑泉水，大变形扭转塑性硬化的实验和仿真研究，力学学报，力学学报，34(5), 2002, 804-811 Size effect宏观尺度的低碳钢扭转和拉伸试验宏观尺度的低碳钢扭转和拉伸试验 19细铜丝试验细铜丝试验(Fleck, 1994); (a) 扭转扭转; (b) 拉伸拉伸Q- torsion, k-torsion angle per unit length When diameter of copper wi

11、re reduced to d=12 m, torsion strength increased 3 times than it d=170 m. During thin beams bending test, Stolken and Evans found when the thickness from h=100 m reduced to h=12.5 m, the bending strength was also increased significantly. Size effect20When indentation deepness reduced from 10 m to 1

12、m, metal stiffness increased to twice; In SiC particle-reinforced Al matrix composite, Lloyd (1994) found that the strength increased as the particle diameter reduced from 16 m to 7.5 m, and kept volume fraction at 15%.Classical plasticity theory Size effect21Nix and Gao (1998) calculated micro inde

13、ntation for single crystal copper, which is agreed with the experiment data. While the classical plasticity is not size effect. Size effectH材料硬度材料硬度h压痕深度压痕深度22The thinner is, the harder is. According to classical plastic theory, they should be the same value for different diameters. What is the rela

14、tionship across the size from nano-, meso- to macro-scales.GSbMMThe tensile flow stress is related shear flow stress based on Taylor dislocation model, developed by Nix and Gao:lNref2For uniaxial tensile, there is no strain gradient and statistic dislocation can be decided. SoSize effect23n 尺度效应尺度效应

15、n 应变梯度塑性理论应变梯度塑性理论n 单单晶铜动态变形的应变率效应晶铜动态变形的应变率效应-位错动位错动力学力学(DD)(DD)与连续介质有限元耦合与连续介质有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金属塑性行为的尺度和金属塑性行为的尺度和应变率效应应变率效应n 总结总结Outline24plasticity.Taylor-based non-local theory of plasticity CMSG - conventional theory of plasticity25kjiijkijkijkjjkiikccc32126kijijkjikijkijku,ij

16、jiijuu,210,41, 0321cccijkijk2127cellijkijkijijijVijVVcelldVVcellVijcellijd1cellVjikijkcellijkVxxVd2128290.010.111010010000.1110IIIIIIKI=20Yl1/2 TNT Deformation Theory Classical Plasticity Theorye/Yr/lGuo Y, Huang Y, Gao H, Zhuang Z, Hwang KC, Taylor-based nonlocal theory of plasticity: numerical stu

17、dies of micro-indentation experiments and crack tip fields, Int. J. of Solids and Structures, 38(42-43), 2001, 7447-7460 distribution in 30H. Jiang, Y. Huang, Z. Zhuang, K.C. Hwang, Fracture in mechanism-based strain gradient plasticity, J. Mech. Phys. Solids, 2001, 49(5) 979-993 0123456780.00.51.01

18、.52.02.53.03.54.04.55.0 MSG Deformation Theory Experimental Data(H/H0)21/h (m-1)Indentation by MSG theory results and test data, which is shown size effect31Experiment data and theoretical results of strain gradient plasticity based on meso-mechanics to demonstrate the size effect at meso-scale.Stra

19、in gradient plasticity theories are based on continuum mechanics with a limitation at meso-scale. To bridge the micro- to meso-scales, strain gradient relates with geometrically necessary dislocation density.Conclusions-132Outlinen 尺度效应尺度效应n 应变梯度塑性理论应变梯度塑性理论n 单单晶铜动态变形的应变率效应晶铜动态变形的应变率效应-位错动位错动力学力学(DD

20、)(DD)与连续介质有限元耦合与连续介质有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金属塑性行为的尺度和金属塑性行为的尺度和应变率效应应变率效应n 总结总结33n Used continuum based dislocation nucleation criterion (DNC), discrete dislocation dynamics (DD) is combined with finite element (FE) simulation.n DD code yields the plastic strain based on the slip of disloc

21、ations.n FE code computes the displacement and stress fields during deformation. Multi-scale framework 34Multi-scale simulationContinuum basedDislocation Nucleation Criterion (DNC)input parameterDislocation Dynamics(mesoscale)FEM(macroscale)MDSimulationValidationMulti-scale framework 35FE (108 s)DD

22、(109 s)Interpolation:Stress defined at the element of FE mesh is estimated on dislocation lines A substitute of constitutive:the plastic strain produced by dislocation is returned to FE meshDevelop an interface with FE code位错动力学位错动力学(DD)(DD)计算模型计算模型36n 宏观问题宏观问题FEFE的临界时间尺度为的临界时间尺度为n 一般的值为一般的值为 n 所以所以

23、在时间尺度上在时间尺度上可以将可以将细观与宏观细观与宏观联系起来。而联系起来。而在空间尺度上在空间尺度上，随着单元的细划，也建立了，随着单元的细划，也建立了跨尺度跨尺度的联系，满足了研究材料力学行为的需要。的联系，满足了研究材料力学行为的需要。EccLt,s1085位错动力学位错动力学(DD)(DD)计算模型计算模型37n DD code developed serves as a substitute for the constitutive form used in a usual FE computation.n 3D model is implemented in a user-def

24、ined subroutine of explicit or implicit code, respectively, for example, UMAT in ABAQUS/Standard or VUMAT in ABAQUS/Explicit.位错动力学位错动力学(DD)(DD)计算模型计算模型38ePppC :(DD )(I:D) ep = C :(- ) The plasticity quantities are obtained by DD code:Small strain:p()2iiiiDnbbnp()2iiiinbbn1NigiilbvbvVConstitutive rel

25、ationshipFinite strain is based on Cauchy stress with Jaumann rate: 位错动力学位错动力学(DD)(DD)计算模型计算模型39Multi-scale simulationContinuum basedDislocation Nucleation Criterion (DNC)input parameterDislocation Dynamics(mesoscale)FEM(macroscale)MDSimulationValidationMulti-scale framework 40位错形核准则位错形核准则(DNC)(DNC)

26、n 均匀变形下，位错形核的准则：均匀变形下，位错形核的准则：Rice (1979 JMPS)Yip (2002 Nature)，Zhu T (2004 JMPS)n 基于晶体稳定性理论基于晶体稳定性理论 (Born and Huang 1959)41nConstitutive law based on EAM molecular potentialnFCC Crystal位错形核准则位错形核准则(DNC)(DNC),(XFWW XCXXFFXXFXFxxxTddddddddd2 iCVCFCW2110EEWCEWS2*42nDislocation nucleation criterion ba

27、sed on crystal stability 界面上变形梯度率的变化为：界面上变形梯度率的变化为： 根据平衡方程，要求在界面处：根据平衡方程，要求在界面处：位错形核准则位错形核准则(DNC)(DNC)43n Is this dislocation nucleation criterion right?位错形核准则位错形核准则(DNC)(DNC)n Validation DNC by Molecular simulation. MD can provide detail information of dislocations44Multi-scale simulationContinuum

28、basedDislocation Nucleation Criterion (DNC)input parameterDislocation Dynamics(mesoscale)FEM(macroscale)MDSimulationValidation分子动力学分子动力学(MD)(MD)模拟验证模拟验证45分子动力学分子动力学(MD)(MD)模拟验证模拟验证n 分子动力学中表征材料失效的量为：分子动力学中表征材料失效的量为：n 连续介质判断材料失稳的准则为：连续介质判断材料失稳的准则为： n n取取FCCFCC晶体的密排面晶体的密排面4 4个（个（111111）滑移面族的法向。）滑移面族的法向

29、。46n 验证模型验证模型通过简单剪切验证通过简单剪切验证分子动力学分子动力学(MD)(MD)模拟验证模拟验证47n 简单剪切结果简单剪切结果 n 取取FCC单单晶铜晶体的晶铜晶体的密排面密排面4个个(111)滑移面滑移面族的法向。族的法向。分子动力学分子动力学(MD)(MD)模拟验证模拟验证48n 简单剪切结果简单剪切结果分子动力学分子动力学(MD)(MD)模拟验证模拟验证连续介质与连续介质与MDMD具有相同的稳定性准则，在曲线相交处具有相同的稳定性准则，在曲线相交处为界面稳定性临界状态。为界面稳定性临界状态。49n Conclusion: The crystal stability cri

30、terion can be used as dislocation nucleation rule. The other MD results (tension etc.) show the same results.分子动力学分子动力学(MD)(MD)模拟验证模拟验证n 材料自下而上的设计材料自下而上的设计（from bottom to up）50Nucleation site计算框图计算框图51Result 1. IndentationThe dense dislocation under the indenter.Cu single crystal 151510 mthe radius

31、of indenter is 3.2 m 52Result 1. IndentationMD simulation of indentation at nano-scalePlastic strain distribution during indentation by DD and FE simulation 53Result 1. IndentationMD simulation54Result 2. Simple tensionCu single crystal 5510 m 2 Frank-read sourceBoundary condition:Upper surface is a

32、pplied tension loading along z axis The bottom is fixed.The other surfaces are free.1000/s (a) Initial dislocation line distribution in the single crystal copper; (b) Dimension of simulation cell and the FE mesh. 55Strain rate effect on yield stressStress-strain curves at different strain rates 56St

33、ress-strain curve under strain rate , and the corresponding dislocation states illustrating activation and motion of dislocation lines at different strain.5110 sStrain rate effect on yield stress57The dislocation microstructure at the yield point under strain rate (a) (b) (c) More Frank-Read sources

34、 are operating to accommodate the high-strain-rate deformation with increasing strain rate when yielding occurs.3110 s4110 s5110 sStrain rate effect on yield stress58Normalized resolved yield stresses versus four different strain rates. The linear regression line has a correlation coefficient . 20.9

35、9r Strain rate effect on yield stress59Strain rate effect on deformation patterning Distribution of strain in the crystal and corresponding dislocation microstructure after yielding3360Distribution of strain in the crystal and corresponding dislocation microstructure after yield33Deformation is most

36、ly localized in the shear bands along the most active slip plane, and with strain rate increasing, the width of the band is also increasing.Strain rate effect on deformation patterning 61The dislocation density evolution in different slip systems under different strain rate Strain rate effect on yie

37、ld stress62Distribution of Tresca stress in the crystal after yielding under different strain rate Strain rate effect on yield stress63Result 3. Shock waveCu single crystal: 2.52.520 mBoundary and loading condition: Shock loading on the upper surface (velocity); Infinite elements are placed on the b

38、ottom to avoid the reflection of the stress wave. The other surfaces are free to get uniaxial compression.64Plastic strain distribution after shock loadingResult 3. Shock wave65Dislocation micro-structure shocked by different velocitiesResult 3. Shock wave66The dislocation density evolution at diffe

39、rent shock velocities Result 3. Shock wave67Conclusions-2n A combined FE and DD approach is developed to investigate the dynamic deformation of single crystal copper at meso-scale.n With the increasing of strain rate, the yield stress of single crystal copper increases rapidly. A critical strain rat

40、e exists in each block for the given size and dislocation sources, below which the yield stress is relatively insensitive to the strain rate. n The crystal stability criterion can be used as dislocation nucleation rule (DNC). The other MD results (tension etc.) show the same results.68Z.L. Liu, Z. Z

41、huang, X.C.You, A Mesoscale investigation of strain rate effect on dynamic response of single crystal copper, Int. J. of Solids and Structures, 2007 (accepted)n The shear band width increases with the strain rate, which often takes place where the damage occurs. n Shear stresses in the shear bands a

42、re higher than that in the neighboring regions, which are resulted in shear flow in the crystals. n Many important failure forms, such as shear instability, fracture, take place on the meso-scale (Needleman, 1999)Conclusions-269 MotivationA combined FE and DD approach is used to investigate the dyna

43、mic deformation of single crystal copper at meso-scale to link with macro-scale.How to bridge the micro-, meso- and macro-scales？70Outlinen 尺度效应尺度效应n 应变梯度塑性理论应变梯度塑性理论n 单单晶铜动态变形的应变率效应晶铜动态变形的应变率效应-位错动位错动力学力学(DD)(DD)与连续介质有限元耦合与连续介质有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金属塑性行为的尺度和应金属塑性行为的尺度和应变率效应变率效应n 总结总结71u

44、 Size effectu Strain rate responseu Stress/Size/Strain rate hyper-surfaceOutline72Road mapFCC metalPlastic behavior at microns and nanometersMD SimulationsAvailable ExperimentsSize effectRate responseThermal effect73Computational modelBoundary and Loading Condition:1. Free surfaces in x- direction.2

45、. Periodic boundary in z-direction. 3. The atoms wrapped in the white boxes are assigned a fixed rigid velocity, and the central part of model is loaded by simple shear.Orientation :( 100, 011, 011)xyzA single crystal copper model under simple shearvvxyz74MD simulationsn EAM potential developed by M

46、ishin et al.(2001) is used.n 1fs is used as the time step size, Gear predictor-corrector algorithm is used to integrate the equations of motion. n A Nose-Hoover thermostat is employed to maintain a constant temperature of 300 K.n The averaged stress of the atoms in the central part of model is used

47、to determine the stress-strain response and yield stress of the copper block.75Size effectThree shear stress-strain curves with different atomistic model. The lengths of models in x-direction are 3.43 nm, 10.66 nm and 32.35 nm, respectively.vvxyz76Dislocation statesvvxyz(a) Start(b) After proportion

48、al limit(c) Peak stress(d) 15% strainShear stress-strain response of a copper model, and corresponding dislocation states illustrating nucleation and motion of dislocations.77Theory of dislocation nucleation222GrWr brHirth and Lothe ever gave an evaluation of the free energy of formation for a dislo

49、cation loop and applied shear stress:2024ln22 14brWr(2) (1)01 24ln214cbrrrb Let ，the critical shear stress can be derived as:0G(3)78Michalske and Houston (1998) observed in their Interfacial Force Microscopy (IFM) experiment that The formed dislocation loop r generally increases with the increasing

50、contact radius R. The asymptotic value of critical shear stress is NOT controlled only by the stacking fault energy. The radius of dislocation loop will also approach an asymptotic limit with the increasing contact radius. Given the information above, we assume that the like factor in Eq. (3) can be

51、 written in the power law form of the inverse of the contact radius as follows:004ln2NrbrrrR(4)1 rTheory of dislocation nucleation79Power relationThe power the yield stress and the characteristic length:relation betweenwhere(5)00NyykrxcyRx*241k0241yb809106103101310510410210110560.5410410yxNix-Gao Mo

52、del50.383.210yxModified power lawYield stress normalized by the elastic modulus and resolved on a (111) slip plane (NRYS) versus the ratio of volume to surface area for copper, nickel and gold with various experiments and atomistic simulations. 81Strain rate response for yield stressNormalized resolved yield stress versus strain rate for different fcc metals and model sizes.82Rate response modelTo describe the dependence of yield stress on the str