1、1清華大學航天航空學院清華大學航天航空學院概況概況2發(fā)展歷史發(fā)展歷史/history Late 1930s: von Karman 1938: 1938: 航空工程系航空工程系, , Department of Aeronautics 中國第一位飛機設計中國第一位飛機設計大師徐舜壽大師徐舜壽 人才培養(yǎng)：人才培養(yǎng)：“兩彈一兩彈一星星”和載人航天的元和載人航天的元勛王永志院士等勛王永志院士等單翼教練機單翼教練機 3歷史沿革歷史沿革1936年航空工程組全體師生，左四為莊前鼎教授年航空工程組全體師生，左四為莊前鼎教授 在舊電機館東面的航空館在舊電機館東面的航空館 1936年攝年攝 飛機機架實驗室飛機機

2、架實驗室 1936年攝年攝 風洞實驗室，風洞實驗室，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學院構架學院構架n工程力學系工程力學系固體力學研究所固體力學研究所流體力學研究所流體力學研究所工程振動研究所工程振動研究所工程熱物理研究所工程熱物理研究所生物力學與醫(yī)學工程生物力學與醫(yī)學工程研究所研究所(2006.01)(2006.01)n 宇航中心宇航中心n 航空技術中心航空技術中心n 國防戰(zhàn)略研究中心國防戰(zhàn)略研究中心n航天航空系航天航空系飛行器設計研究所

3、飛行器設計研究所動力與推進研究所動力與推進研究所人機環(huán)境研究所人機環(huán)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(機械系機械系)8n 120 120 名教職工名教職工 4 4 位院士：黃克智、過增元、楊衛(wèi)、王永志位院士：黃克智、過增元、楊衛(wèi)、王永志 35 35 位教授（含位教授（含4 4位院士，位院士，1 1位名師，位名師，4 42 2位長江特聘教授）位長江特聘教授） 35 35 位副教授，位副教授，1010位講師位講師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定向生和國防生定向生和國

4、防生n 400 400 名研究生：其中博士生和碩士生各名研究生：其中博士生和碩士生各5050外國留學生外國留學生1010名法國、巴基斯坦、朝鮮、韓國名法國、巴基斯坦、朝鮮、韓國此外：此外： 航天工程碩士班航天工程碩士班航空工程碩士班航空工程碩士班(31(31人人) )師資和學生師資和學生9航天工程碩士班開班儀式航天工程碩士班開班儀式20052005年年1111月月師資和學生師資和學生10理念和目標理念和目標發(fā)展理念為：發(fā)展理念為：發(fā)展力學與熱科學學科的優(yōu)勢，發(fā)展力學與熱科學學科的優(yōu)勢，創(chuàng)建航空宇航科學與技術學科。創(chuàng)建航空宇航科學與技術學科。發(fā)展目標為：發(fā)展目標為：入主流、有特色、上水平。入主流

5、、有特色、上水平。建設清華大學國防（航天、航空、航海）建設清華大學國防（航天、航空、航海）科研和工程的平臺。科研和工程的平臺。11發(fā)展材料塑性行為發(fā)展材料塑性行為的多尺度計算框架的多尺度計算框架 北航大學北航大學-1-1 12Outlinen 尺度效應尺度效應n 應變梯度塑性理論應變梯度塑性理論n 單單晶銅動態(tài)變形的應變率效應晶銅動態(tài)變形的應變率效應-位錯動位錯動力學力學(DD)(DD)與連續(xù)介質有限元耦合與連續(xù)介質有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金屬塑性行為的尺度和金屬塑性行為的尺度和應變率效應應變率效應n 總結總結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 研究目標是材料失效行為的多尺度機制研究目標是材料失效行為的多尺度機制18趙慧娟，莊茁，鄭泉水，大變形扭轉塑性硬化的實驗和仿真研究，趙慧娟，莊茁，鄭泉水，大變形扭轉塑性硬化的實驗和仿真研究，力學學報，力學學報，34(5), 2002, 804-811 Size effect宏觀尺度的低碳鋼扭轉和拉伸試驗宏觀尺度的低碳鋼扭轉和拉伸試驗 19細銅絲試驗細銅絲試驗(Fleck, 1994); (a) 扭轉扭轉; (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壓痕深度壓痕深度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 尺度效應尺度效應

15、n 應變梯度塑性理論應變梯度塑性理論n 單單晶銅動態(tài)變形的應變率效應晶銅動態(tài)變形的應變率效應-位錯動位錯動力學力學(DD)(DD)與連續(xù)介質有限元耦合與連續(xù)介質有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金屬塑性行為的尺度和金屬塑性行為的尺度和應變率效應應變率效應n 總結總結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 尺度效應尺度效應n 應變梯度塑性理論應變梯度塑性理論n 單單晶銅動態(tài)變形的應變率效應晶銅動態(tài)變形的應變率效應-位錯動位錯動力學力學(DD

20、)(DD)與連續(xù)介質有限元耦合與連續(xù)介質有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金屬塑性行為的尺度和金屬塑性行為的尺度和應變率效應應變率效應n 總結總結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位錯動力學位錯動力學(DD)(DD)計算模型計算模型36n 宏觀問題宏觀問題FEFE的臨界時間尺度為的臨界時間尺度為n 一般的值為一般的值為 n 所以所以

23、在時間尺度上在時間尺度上可以將可以將細觀與宏觀細觀與宏觀聯(lián)系起來。而聯(lián)系起來。而在空間尺度上在空間尺度上，隨著單元的細劃，也建立了，隨著單元的細劃，也建立了跨尺度跨尺度的聯(lián)系，滿足了研究材料力學行為的需要。的聯(lián)系，滿足了研究材料力學行為的需要。EccLt,s1085位錯動力學位錯動力學(DD)(DD)計算模型計算模型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.位錯動力學位錯動力學(DD)(DD)計算模型計算模型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: 位錯動力學位錯動力學(DD)(DD)計算模型計算模型39Multi-scale simulationContinuum basedDislocation Nucleation Criterion (DNC)input parameterDislocation Dynamics(mesoscale)FEM(macroscale)MDSimulationValidationMulti-scale framework 40位錯形核準則位錯形核準則(DNC)(DNC)

26、n 均勻變形下，位錯形核的準則：均勻變形下，位錯形核的準則：Rice (1979 JMPS)Yip (2002 Nature)，Zhu T (2004 JMPS)n 基于晶體穩(wěn)定性理論基于晶體穩(wěn)定性理論 (Born and Huang 1959)41nConstitutive law based on EAM molecular potentialnFCC Crystal位錯形核準則位錯形核準則(DNC)(DNC),(XFWW XCXXFFXXFXFxxxTddddddddd2 iCVCFCW2110EEWCEWS2*42nDislocation nucleation criterion ba

27、sed on crystal stability 界面上變形梯度率的變化為：界面上變形梯度率的變化為： 根據(jù)平衡方程，要求在界面處：根據(jù)平衡方程，要求在界面處：位錯形核準則位錯形核準則(DNC)(DNC)43n Is this dislocation nucleation criterion right?位錯形核準則位錯形核準則(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分子動力學分子動力學(MD)(MD)模擬驗證模擬驗證45分子動力學分子動力學(MD)(MD)模擬驗證模擬驗證n 分子動力學中表征材料失效的量為：分子動力學中表征材料失效的量為：n 連續(xù)介質判斷材料失穩(wěn)的準則為：連續(xù)介質判斷材料失穩(wěn)的準則為： n n取取FCCFCC晶體的密排面晶體的密排面4 4個（個（111111）滑移面族的法向。）滑移面族的法向

29、。46n 驗證模型驗證模型通過簡單剪切驗證通過簡單剪切驗證分子動力學分子動力學(MD)(MD)模擬驗證模擬驗證47n 簡單剪切結果簡單剪切結果 n 取取FCC單單晶銅晶體的晶銅晶體的密排面密排面4個個(111)滑移面滑移面族的法向。族的法向。分子動力學分子動力學(MD)(MD)模擬驗證模擬驗證48n 簡單剪切結果簡單剪切結果分子動力學分子動力學(MD)(MD)模擬驗證模擬驗證連續(xù)介質與連續(xù)介質與MDMD具有相同的穩(wěn)定性準則，在曲線相交處具有相同的穩(wěn)定性準則，在曲線相交處為界面穩(wěn)定性臨界狀態(tài)。為界面穩(wěn)定性臨界狀態(tài)。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.分子動力學分子動力學(MD)(MD)模擬驗證模擬驗證n 材料自下而上的設計材料自下而上的設計（from bottom to up）50Nucleation site計算框圖計算框圖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 尺度效應尺度效應n 應變梯度塑性理論應變梯度塑性理論n 單單晶銅動態(tài)變形的應變率效應晶銅動態(tài)變形的應變率效應-位錯動位錯動力學力學(DD)(DD)與連續(xù)介質有限元耦合與連續(xù)介質有限元耦合(FE)(FE)n 面心立方面心立方(FCC)(FCC)金屬塑性行為的尺度和應金屬塑性行為的尺度和應變率效應變率效應n 總結總結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