晶粒度对多晶铜纳米压痕表面变形机理影响
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摘要
为研究晶粒度在多晶材料纳米压痕过程中对其塑性变形机制及位错演生过程影响.采用Poisson-Voronoi和Monte Carlo方法建立大规模多晶铜分子动力学模型,针对多晶铜Hall-Petch效应曲线建立具有不同晶粒度的多晶铜模型,并与单晶铜纳米压痕模型对比,采用分子动力学方法模拟计算金刚石探针压入模型的纳米压痕过程,计算4种模型的缺陷结构的配位数、内应力、原子势能等参数.采用中心对称参数法研究压痕过程中位错等缺陷结构的演化机制.结果表明:具有不同晶粒度的多晶铜纳米压痕过程存在显著的规律性,单晶铜压痕力高于多晶铜,多晶铜压痕力随着晶粒度降低而下降;多晶铜的晶界结构能够限制压痕缺陷、内应力与原子势能向材料内部传递,而单晶铜难以限制此传递过程;压痕过程中,具有较小晶粒度的多晶铜具有更高的静水压力、范式等效应力与原子势能,单晶铜内应力与原子势能低于多晶铜.表层及亚表层为较低晶粒度而材料内部为较大晶粒度的梯度晶粒度材料具有极大的研究价值.
To study the effect of grain size on the mechanical properties and deformation mechanism of polycrystalline copper during the nanoindentation process, a large-scale molecular dynamics simulation model of polycrystalline copper is structured by Poisson-Voronoi method and Monte Carlo method. Based on the Hall-Petch relationship of the nanocrystalline copper, the single-crystalline and polycrystalline copper nanoindentation simulation models with different grain size are established. The nanoindentation process with different grain size are simulated by molecular dynamics method, and the nanoindentation force, internal stress and atomic potential energy of the atoms are calculated. Centrally symmetric parameter method is used to analyze the dislocation nucleation and propagation process in the surface and subsurface of the polycrystalline copper. The results show that the indentation force of single-crystalline copper is higher than that of polycrystalline copper, with the decrease of grain size, that of polycrystalline copper continuously decreases due to softening phenomenon. The high internal stress and atomic potential energy under the indenter leads to the defect evolution region under the indenter. The range of horizontal distribution of defects is larger than that of the vertical distribution, and such defects are limited in the grains around the indenter due to grain boundary network. The internal stress and atomic potential energy in polycrystalline copper with smaller grain size is larger than that with higher grain size, and the stress and potential energy in single-crystalline copper are lowest. Hence, during the nanoindentation process of polycrystalline copper, to improve the mechanical properties and deformation mechanism of nanocrystalline materials, it is suggests to adopt the nanocrystalline materials with grain size gradient.
To study the effect of grain size on the mechanical properties and deformation mechanism of polycrystalline copper during the nanoindentation process, a large-scale molecular dynamics simulation model of polycrystalline copper is structured by Poisson-Voronoi method and Monte Carlo method. Based on the Hall-Petch relationship of the nanocrystalline copper, the single-crystalline and polycrystalline copper nanoindentation simulation models with different grain size are established. The nanoindentation process with different grain size are simulated by molecular dynamics method, and the nanoindentation force, internal stress and atomic potential energy of the atoms are calculated. Centrally symmetric parameter method is used to analyze the dislocation nucleation and propagation process in the surface and subsurface of the polycrystalline copper. The results show that the indentation force of single-crystalline copper is higher than that of polycrystalline copper, with the decrease of grain size, that of polycrystalline copper continuously decreases due to softening phenomenon. The high internal stress and atomic potential energy under the indenter leads to the defect evolution region under the indenter. The range of horizontal distribution of defects is larger than that of the vertical distribution, and such defects are limited in the grains around the indenter due to grain boundary network. The internal stress and atomic potential energy in polycrystalline copper with smaller grain size is larger than that with higher grain size, and the stress and potential energy in single-crystalline copper are lowest. Hence, during the nanoindentation process of polycrystalline copper, to improve the mechanical properties and deformation mechanism of nanocrystalline materials, it is suggests to adopt the nanocrystalline materials with grain size gradient.
引文
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[30]赵鹏越,郭永博,白清顺,等.压痕位置对多晶铜纳米压痕变形机理的影响[J].哈尔滨工业大学学报,2018,50(7) :13.DOI:10.11918/j.issn.0367-6234.201711061 ZHAO Pengyue,GUO Yongbo,BAI Qingshun,et al.Influence of indentation position on the nanoindentation deformation mechanicsm of polycrystalline copper[J].Journal of Harbin Institute of Technology,2018,50(7):13.
[31]WANG T H,FANG T H,KANG S H,et al.Creep characteristics of clamped Cu membranes subjected to indentation [J].Japanese Journal of Applied Physics,2008,47(2R) :1019
[32]ZHAO M,SLAUGHTER W S,LI M,et al.Material-length-scalecontrolled nanoindentation size effects due to strain-gradient plasticity [J].Acta Materialia,2003,51(15) :4461.DOI:10.1016/S1359-6454(03)00281-7
[33]LI X,WEI Y,LU L,et al.Dislocation nucleation governed softening and maximum strength in nano-twinned metals [J].Nature,2010,464 :877
[34]VO N Q,AVERBACK R S,BELLON P,et al.Yield strength in nanocrystalline Cu during high strain rate deformation [J].Scripta Materialia,2009,61(1) :76.DOI:10.1016/j.scriptamat.2009.03.003
[35]QU S,ZHOU H.Hardening by twin boundary during nanoindentation in nanocrystals [J].Nanotechnology,2010,21(33) :335704-1
[36]JIANG J,BRITTON T B,WILKINSON A J.Evolution of intragranular stresses and dislocation densities during cyclic deformation of polycrystalline copper [J].Acta Materialia,2015,94 :193.DOI:10.1016/j.actamat.2015.04.031
[37]KYSAR J W,GAN Y X,MORSE T L,et al.High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals:Geometrically necessary dislocation densities [J].Journal of the Mechanics and Physics of Solids,2007,55(7) :1554.DOI:10.1016/j.jmps.2006.09.009
[38]PAN Z,RUPERT T J.Damage nucleation from repeated dislocation absorption at a grain boundary [J].Computational Materials Science,2014,93:206.DOI:10.1016/j.commatsci.2014.07.008
[39]ZHANG J J,SUN T,HARTMAIER A,et al.Atomistic simulation of the influence of nanomachining-induced deformation on subsequent nanoindentation [J].Computational Materials Science,2012,59:14.DOI:10.1016/j.commatsci.2012.02.024
[40]ZHOU K,LIU B,SHAO S,et al.Molecular dynamics simulations of tension-compression asymmetry in nanocrystalline copper [J].Physics Letters A,2017,381(13) :1163.DOI:10.1016/j.physleta.2017.01.027
[41]YEAP K B,ZSCHECH E,HANGEN U D,et al.Elastic anisotropy of Cu and its impact on stress management for 3D IC:Nanoindentation and TCAD simulation study [J].Journal of Materials Research,2012,27(1) :339.DOI:10.1557/jmr.2011.323
[42]REUBER C,EISENLOHR P,ROTERS F,et al.Dislocation density distribution around an indent in single-crystalline nickel:Comparing nonlocal crystal plasticity finite-element predictions with experiments [J].Acta Materialia,2014,71 :333.DOI:10.1016/j.actamat.2014.03.012
[43]LIU Y,VARGHESE S,MA J,et al.Orientation effects in nanoindentation of single crystal copper [J].International Journal of Plasticity,2008,24(11) :1990.DOI:0.1016/j.ijplas.2008.02.009
[2] LIN Y H,CHEN T C.A molecular dynamics study of phase transformations in mono-crystalline Si under nanoindentation [J].Applied Physics A,2008,92(3):571
[3] LUCCA D A,HERRMANN K,KLOPFSTEIN M J.Nanoindentation:Measuring methods and applications [J].CIRP Annals,2010,59(2):803.DOI:10.1016/j.cirp.2010.05.009
[4] MICIC M,KLYMYSHYN N,SUH Y D,et al.Finite element method simulation of the field distribution for AFM tip-enhanced surface-enhanced Raman scanning microscopy [J].The Journal of Physical Chemistry B,2003,107(7) :1574.DOI:10.1021/jp022060s
[5] FANG F,LIU B,XU Z.Nanometric cutting in a scanning electron microscope [J].Precision Engineering,2015,41 :145.DOI:10.1016/j.precisioneng.2015.01.009
[6] YAN J,ASAMI T,HARADA H,et al.Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining [J].Precision Engineering,2009,33(4) :378.DOI:10.1016/j.precisioneng.2008.10.008
[7] VOLKERT C A.Focused ion beam microscopy and micromaching [J].MRS Bulletin,2007,32(5) :389.DOI:10.1557/mrs2007.62
[8] PELLICER E,VAREA A,PANE S,et al.Nanocrystalline electroplated Cu-Ni:Metallic thin films with enhanced mechanical properties and tunable magnetic behavior [J].Advanced Functional Materials,2010,20(6) :983.DOI:10.1002/adfm.200901732
[9] LINDAN P J D.First-principles simulation:Ideas,illustrations and the CASTEP code [J].Journal of Physics:Condensed Matter,2002,14(11) :2717
[10]ROTERS F,EISENLOHR P,HANTCHERLI L,et al.Overview of constitutive laws,kinematics,homogenization and multiscale methods in crystal plasticity finite-element modeling:Theory,experiments,applications [J].Acta Materialia,2010,58(4) :1152.DOI:10.1016/j.actamat.2009.10.058
[11]GUNZBURGER M,ZHANG Y.A quadrature-rule type approximation to the quasi-continuum method [J].Multiscale Modeling & Simulation,2009,8(2) :571.DOI:10.1137/080722151
[12]CASALS O,OCENASEK J,ALCALA J.Crystal plasticity finite element simulations of pyramidal indentation in copper single crystals [J].Acta materialia,2007,55(1) :55.DOI:10.1016/j.actamat.2006.07.018
[13]ZHANG K,WEERTMAN J R,EASTMAN J A.The influence of time,temperature,and grain size on indentation creep in high-purity nanocrystalline and ultrafine grain copper [J].Applied Physics Letters,2004,85(22) :5197.DOI:10.1063/1.1828213
[14]SANSOZ F,STEVENSON K D.Relationship between hardness and dislocation processes in a nanocrystalline metal at the atomic scale [J].Physical Review B,2011,83(22) :224101-1.DOI:10.1103/PhysRevB.83.224101
[15]WANG F,HUANG P,XU K.Strain rate sensitivity of nanoindentation creep in polycrystalline Al film on silicon substrate [J].Surface and Coatings Technology,2007,201 :5216.DOI:10.1016/j.surfcoat.2006.07.114
[16]ZHANG F,LIU Z,ZHOU J Q.Molecular dynamics simulation of micromechanical deformations in polycrystalline copper with bimodal structures [J].Materials Letters,2016,183 :261.DOI:10.1016/j.matlet.2016.07.122
[17]HUANG C C,CHIANG T C,FANG T H.Grain size effect on indentation of nanocrystalline copper [J].Applied Surface Science,2015,353 :494
[18]LI J,GUO J W,LUO H,et al.Study of nanoindentation mechanical response of nanocrystalline structures using molecular dynamics simulations [J].Applied Surface Science,2016,364 :190.DOI:10.1016/j.apsusc.2015.12.145
[19]GAO Y,RUESTES C J,TRAMONTINA D R,et al.Comparative simulation study of the structure of the plastic zone produced by nanoindentation [J].Journal of the Mechanics and Physics of Solids,2015,75 :58.DOI:10.1016/j.jmps.2014.11.005
[20]GOEL S,FAISAL N H,LUO X,et al.Nanoindentation of polysilicon and single crystal silicon:Molecular dynamics simulation and experimental validation [J].Journal of Applied Physics,2014,47 :275304-1
[21]YAGHOOBI M,VOYIADJIS G Z.Effect of boundary conditions on the md simulation of nanoindentation [J].Computational Materials Science,2014,95 :626.DOI:10.1016/j.commatsci.2014.08.013
[22]YAGHOOBI M,VOYIADJIS G Z.Atomistic simulation of size effects in singlecrystalline metals of confined volumes during nanoindentation [J].Computational Materials Science,2016,111:64.DOI:10.1016/j.commatsci.2015.09.004
[23]SICHANI M M,SPEAROT D E.A molecular dynamics study of the role of grain size and orientation on compression of nanocrystalline Cu during shock [J].Computational Materials Science,2015,108 :226.DOI:10.1016/j.commatsci.2015.07.021
[24]VOYIADJIS G Z,PETERS R.Size effects in nanoindentation:An experimental and analytical study [J].Acta Mechanica,2010,211 :131
[25]ZHANG L,ZHAO H,DAI L,et al.Molecular dynamics simulation of deformation accumulation in repeated nanometric cutting on single-crystal copper [J].RSC Advances,2015,5(17) :12678.DOI:10.1039/C4RA12317D
[26]GUO Y B,XU T,LI M.Generalized type Ⅲ internal stress from interfaces,triple junctions and other microstructural components in nanocrystalline materials [J].Acta Materialia,2013,61 :4976.DOI:10.1016/j.actamat.2013.04.048
[27]GUO Y B,XU T,LI M.Hierarchical dislocation nucleation controlled by internal stress in nanocrystalline copper [J].Applied Physics Letters,2013,102(24) :241910-2.DOI:10.1063/1.4811791
[28]GUO Y B,XU T,LI M,Atomistic calculation of internal stress in nanoscale polycrystalline materials [J].Philosophical Magazine A,2012,92(24) :3064.DOI:10.1080/14786435.2012.685963
[29]赵鹏越,郭永博,白清顺,等.基于微观结构的多晶Cu纳米压痕表面缺陷研究[J].金属学报,2018,54(7) :1053.DOI:10.11900/0412.1961.2017.00411 ZHAO Pengyue,GUO Yongbo,BAI Qingshun,et al.Research of surface defects of polycrystalline copper nanoindentation based on microstructures[J].Acta Metallurgica Sinica,2018,54(7):1053.
[30]赵鹏越,郭永博,白清顺,等.压痕位置对多晶铜纳米压痕变形机理的影响[J].哈尔滨工业大学学报,2018,50(7) :13.DOI:10.11918/j.issn.0367-6234.201711061 ZHAO Pengyue,GUO Yongbo,BAI Qingshun,et al.Influence of indentation position on the nanoindentation deformation mechanicsm of polycrystalline copper[J].Journal of Harbin Institute of Technology,2018,50(7):13.
[31]WANG T H,FANG T H,KANG S H,et al.Creep characteristics of clamped Cu membranes subjected to indentation [J].Japanese Journal of Applied Physics,2008,47(2R) :1019
[32]ZHAO M,SLAUGHTER W S,LI M,et al.Material-length-scalecontrolled nanoindentation size effects due to strain-gradient plasticity [J].Acta Materialia,2003,51(15) :4461.DOI:10.1016/S1359-6454(03)00281-7
[33]LI X,WEI Y,LU L,et al.Dislocation nucleation governed softening and maximum strength in nano-twinned metals [J].Nature,2010,464 :877
[34]VO N Q,AVERBACK R S,BELLON P,et al.Yield strength in nanocrystalline Cu during high strain rate deformation [J].Scripta Materialia,2009,61(1) :76.DOI:10.1016/j.scriptamat.2009.03.003
[35]QU S,ZHOU H.Hardening by twin boundary during nanoindentation in nanocrystals [J].Nanotechnology,2010,21(33) :335704-1
[36]JIANG J,BRITTON T B,WILKINSON A J.Evolution of intragranular stresses and dislocation densities during cyclic deformation of polycrystalline copper [J].Acta Materialia,2015,94 :193.DOI:10.1016/j.actamat.2015.04.031
[37]KYSAR J W,GAN Y X,MORSE T L,et al.High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals:Geometrically necessary dislocation densities [J].Journal of the Mechanics and Physics of Solids,2007,55(7) :1554.DOI:10.1016/j.jmps.2006.09.009
[38]PAN Z,RUPERT T J.Damage nucleation from repeated dislocation absorption at a grain boundary [J].Computational Materials Science,2014,93:206.DOI:10.1016/j.commatsci.2014.07.008
[39]ZHANG J J,SUN T,HARTMAIER A,et al.Atomistic simulation of the influence of nanomachining-induced deformation on subsequent nanoindentation [J].Computational Materials Science,2012,59:14.DOI:10.1016/j.commatsci.2012.02.024
[40]ZHOU K,LIU B,SHAO S,et al.Molecular dynamics simulations of tension-compression asymmetry in nanocrystalline copper [J].Physics Letters A,2017,381(13) :1163.DOI:10.1016/j.physleta.2017.01.027
[41]YEAP K B,ZSCHECH E,HANGEN U D,et al.Elastic anisotropy of Cu and its impact on stress management for 3D IC:Nanoindentation and TCAD simulation study [J].Journal of Materials Research,2012,27(1) :339.DOI:10.1557/jmr.2011.323
[42]REUBER C,EISENLOHR P,ROTERS F,et al.Dislocation density distribution around an indent in single-crystalline nickel:Comparing nonlocal crystal plasticity finite-element predictions with experiments [J].Acta Materialia,2014,71 :333.DOI:10.1016/j.actamat.2014.03.012
[43]LIU Y,VARGHESE S,MA J,et al.Orientation effects in nanoindentation of single crystal copper [J].International Journal of Plasticity,2008,24(11) :1990.DOI:0.1016/j.ijplas.2008.02.009
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