基于能量变化的微尺度金属应变突变准则研究
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摘要
微尺度金属在塑性变形过程中呈现出显著的应变突变特性.论文以力加载条件下单晶Ni微米柱体和位移加载下Au纳米柱体为对象,探讨应变突变的判定准则与不同特征阶段的判别条件.首先从经典塑性理论Hill稳定性条件出发,分析微柱体变形过程中的动能变化,提出了应变突变发生与结束的判定准则.进一步分析柱体变形过程中的内能变化,结合动能变化的分析结果,给出了微尺度金属不同变形阶段的判别条件.通过与文献中实验与理论结果对比发现,基于动能变化的应变突变判定准则能够判断应变突变的发生与结束,基于能量变化的判别条件可以有效区分微柱体的不同变形阶段.最后对新理论准则的可靠性与适用性进行了讨论.
Significant strain burst phenomenon is observed during the plastic deformation of microscale metal.This work aims to develop the strain burst criteria and judging conditions for different deformation stages of microscale metal,taking single-crystal Ni micro-pillar under force loading and Au nano-pillar under displacement loading as examples.Based on the classical Hill's stability condition in continuum plasticity theory,the criteria for the occurrence and termination of the strain burst are proposed according to the variations of kinetic energy during the deformation process of small pillars.Furthermore,the internal energy evolution of pillars during the deformation process is analyzed.Based on the simultaneous changes of kinetic energy and internal energy,the judging conditions for different deformation stages of pillars are established.Then,these theoretical developments are verified by comparing their finite element outputs with the experimental and theoretical results in literature.It is found that the proposed strain burst criteria using kinetic energy increment can effectively identify the occurrence and termination of the strain burst events,and the judging conditions based on energy changes are capable of distinguishing different deformation stages of micro-and nano-pillars.The applicability and merits of the newly proposed criteria are discussed at the end of the paper.
Significant strain burst phenomenon is observed during the plastic deformation of microscale metal.This work aims to develop the strain burst criteria and judging conditions for different deformation stages of microscale metal,taking single-crystal Ni micro-pillar under force loading and Au nano-pillar under displacement loading as examples.Based on the classical Hill's stability condition in continuum plasticity theory,the criteria for the occurrence and termination of the strain burst are proposed according to the variations of kinetic energy during the deformation process of small pillars.Furthermore,the internal energy evolution of pillars during the deformation process is analyzed.Based on the simultaneous changes of kinetic energy and internal energy,the judging conditions for different deformation stages of pillars are established.Then,these theoretical developments are verified by comparing their finite element outputs with the experimental and theoretical results in literature.It is found that the proposed strain burst criteria using kinetic energy increment can effectively identify the occurrence and termination of the strain burst events,and the judging conditions based on energy changes are capable of distinguishing different deformation stages of micro-and nano-pillars.The applicability and merits of the newly proposed criteria are discussed at the end of the paper.
引文
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[17]Zhang X,Shang F.A continuum model for intermittent deformation of single crystalmicropillars[J].International Journal of Solids and Structures,2014,51(10):1859-1871.
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[2]Greer J R,Weinberger C R,Cai W.Comparing the strength of f.c.c.and b.c.c.sub-micrometer pillars:Compression experiments and dislocation dynamics simulations[J].Materials Science&Engineering A,2008,493(1):21-25.
[3]Greer J R,De Hosson J T M.Plasticity in smallsized metallic systems:Intrinsic versus extrinsic size effect[J].Progress in Materials Science,2011,56(6):654-724.
[4]Dimiduk D M,Uchic M D,Parthasarathy T A.Sizeaffected single-slip behavior of pure nickel microcrystals[J].Acta Materialia,2005,53(15):4065-4077.
[5]MaaR,Derlet P M,Greer J R.Small-scale plasticity:Insights into dislocation avalanche velocities[J].Scripta Materialia,2013,69(8):586-589.
[6]Dimiduk D M,Woodward C,Lesar R,et al.Scalefree intermittent flow in crystal plasticity.[J].Science,2006,312(5777):1188-1190.
[7]Zaiser M,Schwerdtfeger J,Schneider A S,et al.Strain bursts in plastically deforming molybdenum micro-and nanopillars[J].Philosophical Magazine,2008,88(30-32):3861-3874.
[8]Zhou C,Biner S B,Lesar R.Discrete dislocation dynamics simulations of plasticity at small scales[J].Acta Materialia,2010,58(5):1565-1577.
[9]Rao S I,Dimiduk D M,Parthasarathy T A,et al.Athermal mechanisms of size-dependent crystal flow gleaned from three-dimensional discrete dislocation simulations[J].Acta Materialia,2008,56(13):3245-3259.
[10]MaaR,Derlet P M,Greer J R.Independence of slip velocities on applied stress in small crystals[J].Small,2015,11(3):341-351.
[11]Zhang X,Zhang X,Shang F,et al.Second-order work and strain burst in single-crystallinemicropillar plasticity[J].International Journal of Plasticity,2016,77:192-213.
[12]罗静,张旭,郭惠丽,尚福林.位移加载条件下微小尺寸单晶金属的应变突变模型及其间歇性塑性变形行为研究[J].固体力学学报,2018,39(5):482-491.(Luo J,Zhang X,Guo H L.Shang F L.Strain burst model and intermittent plastic flow of single crystal nanopillar under displacement loading mode[J].Chinese Journal of Solid Mechanics,2018,39(5):482-491.(in Chinese))
[13]Csikor F F,Motz C,Weygand D,et al.Dislocation avalanches,strain bursts,and the problem of plastic forming at the micrometer scale[J].Science,2007,318(5848):251-254.
[14]Argon A S.Strain avalanches inplasticity[J].Philosophical Magazine,2013,93(28-30):3795-3808.
[15]Hill R.On uniqueness and stability in the theory of finite elasticstrain[J].Journal of the Mechanics&Physics of Solids,1957,5(4):229-241.
[16]Hill R.A general theory of uniqueness and stability in elastic-plasticsolids[J].Journal of the Mechanics&Physics of Solids,1958,6(3):236-249.
[17]Zhang X,Shang F.A continuum model for intermittent deformation of single crystalmicropillars[J].International Journal of Solids and Structures,2014,51(10):1859-1871.
[18]Freund L B,Suresh S.Thin Film Materials:Stress,Defect Formation,and Surface Evolution[M].Cambridge University Press,2004.
[19]Zhang X,Pan B,Shang F.Scale-free behavior of displacement bursts:Lower limit and scalingexponent[J].EPL(Europhysics Letters),2012,100(1):16005.
[20]Zhang X,Shang F L.Theburst time duration in micropillar deformation[J].Chinese Physics Letters,2014,31(2):026401.
[21]El-Awady J A,Wen M,Ghoniem N M.The role of the weakest-link mechanism in controlling the plasticity of micropillars[J].Journal of the Mechanics and Physics of Solids,2009,57(1):32-50.