准连续介质方法在晶体微观变形多尺度模拟中的应用
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摘要
随着微电子技术和微系统研究的发展,材料的微观力学性能越来越引起人们的关注。在载荷的作用下,微小构件常常会表现出与宏观条件下所不同的特性,例如高的强度、硬度、耐磨性、延展性、以及低温超塑性等。材料变形的微观机理研究也越来越受到人们的重视,近年来在理论和实验上的研究也取得不少进展。建立在连续介质理论基础上的传统宏观力学分析方法不再适用于微观尺度下材料变形的研究,而分子动力学、蒙特卡罗方法等微观尺度的模拟方法由于自由度过多导致计算量太大,无法在普通的计算机上实现较大模型的模拟。于是结合连续介质尺度和原子尺度的多尺度方法在计算机模拟中得到了广泛应用。
准连续介质方法(Quasi-continuum Method,QC)是多尺度方法的一种。其核心思想是在变形梯度变化比较小的区域采用有限元方法以“代表原子”(Representative Atoms)进行粗化描述,通过适当的权重处理求出整个系统的能量,而不是求出所有原子的能量。在缺陷密度较高、变形梯度变化较剧烈的区域对每个原子采用分子动力学来描述。这样就可以在不失精确的情况下极大地减少问题的自由度和计算量,以实现较大尺寸试件的原子尺度模拟。
本文采用QC方法对材料变形中产生的位错形核(Dislocation Nucleation)及孪生变形(Deformation Twinning,DT)的微观机理进行了分析,并讨论了该过程中呈现的尺寸效应,晶体取向效应和晶界效应及裂纹尖端扩展的变形过程,主要做了以下四个方面的工作:
1)模拟了四种金属薄膜——铝(Al)、银(Ag)、镍(Ni)、钯(Pd)——在四种压头宽度下的纳米压痕过程,得到了载荷—位移曲线和应变能—位移曲线。同时计算出四种材料的纳米硬度,并对其硬度值和压头宽度的关系进行了讨论;结果表明材料对压痕响应的尺度效应很明显,模拟得到的临界载荷与采用能量理论估算的临界载荷基本一致,四种金属薄膜扩展位错宽度大小模拟值与理论值相一致:最后,从微观角度讨论了材料载荷—位移曲线突降和材料中位错形核之间的关系,并画出了位错形核的原子图,进一步揭示材料变形机理。
2)模拟了单晶Al薄膜在三种不同晶体取向(分别为x[111],y[(?)10],z[(?)2]:x[(?)2],y[111],z[(?)10]:x[1(?)0],y[001],z[(?)0])条件下的纳米压痕响应,以此来探讨纳米压痕的晶体取向效应。得到了不同晶体取向下的载荷—位移曲线和微观原子图,同时观察到位错形核、孪生变形等一些独特的微观构造,模拟所得结果与相关实验现象一致。最后采用位错理论对不同晶体取向下纳米压痕响应的差异进行了讨论,并从微观变形机理的角度分析了产生这种差异的原因。
3)模拟了存在晶界的Al薄膜的纳米压痕过程,探讨了纳米压痕的晶界效应。在加载过程中,对薄膜内部变形比较剧烈的部分画出原子图,并从微观角度分析产生剧烈变形的原因,同时对纳米压痕过程中的载荷—位移曲线和压头下方微结构的变化在有晶界与无晶界两种情况下的区别进行了分析;最后,讨论了位错在滑移过程中与晶界的相互作用。
4)模拟了单晶Cu在拉伸(Ⅰ型加载)和剪切(Ⅱ型加载)两种加载模式,三种晶体取向条件下裂纹尖端的变形过程。观察到位错滑移和孪生变形现象,并对三种晶体取向下该现象的变形机制进行了分析。结果表明,不同的加载模式和不同晶体取向对模拟的结果影响很大。当位错滑移能力枯竭时,会产生{111}<112>孪生变形或位错形核。
As the development of Micro-electronics and Microsystems, researchers pay much attention on the micro-mechanical properties of materials. Because micro-components always show different characteristics from components in macro-scale (such as higher intensity, hardness, abrasion resistance, ductibility and low temperature super plasticity, etc), the microcosmic mechanism of deformation is important to study the properties of material in micro-scale. However, traditional methods based on continuum theories do not work in investigating the mechanism of micro-deformation, and microcosmic methods such as Molecular Dynamics and Monte Carlo method can not be used to simulate the deformation of a large region in common personal computers for its large computation memory caused by large degrees of freedom. In this situation, the multi-scale methods coupling atomistic scale and continuum scale are widely applied in computer simulations.
The Quasi-continuum Method is developed as a typical multi-scale method. The key idea is that of selective representation of atomic degrees of freedom. Instead of treating all atoms making up the system, a small relevant subset of atoms is selected to represent, by appropriate weighting, the energetics of the system as a whole. Based on their kinematic environment, the energies of individual "representative atoms" are computed either in nonlocal fashion in correspondence with straightforward atomistic methodology or within a local approximation as befitting a continuum model. The representation is of varying density with more atoms sampled in highly deformed regions (such as near defect cores) and correspondingly fewer in the less deformed regions further away, and is adaptively updated as the deformation evolves.
In this thesis, the effect of size, crystal direction, and grain boundary in micro-deformation are investigated using Quasi-continuum Method. The mechanisms of the dislocation nucleation and the deformation twinning are also have been analyzed. Based on the Quasi-continuum Method, the works of this thesis are as follows:
1) The processes of nano-indention of four FCC metals (Al, Ag, Ni, and Pd) under four different indenters with various widths are simulated. Load-displacement curves, strain energy vs displacement curves, as well as nano hardness are obtained. The values of the critical load are in good agreement with theoretical values. The relation between rigidity and indenter width is discussed. The widths of extended dislocation are in agreement with theoretical values. To study the deformation mechanism, the dislocation pictures are plotted and the relation between load-displacement curves and dislocations are discussed.
2) The nano-indention of Al film in three crystal orientations(x[111], y[-110], z[11-2]; x[-1-12], y[111], z[-110]; x[1-10], y[001], z[-1-10]) are simulated. Load-displacement curves and atomistic arrangements pictures are obtained. The results are in good agreement with experiments. Dislocations and deformation twining are observed in the simulation. The differences between different crystal orientations are analyzed by dislocation theory.
3) The nano-indentation on an Al film with a grain boundary is simulated. The load-displacement curve and micro-structures under the indenter are compared with the situation with no grain boundary. The interaction between dislocations and grain boundary is analyzed.
4) The deformation of crack tips in FCC Cu under modeⅠandⅡload in three crystal orientations are simulated. Dislocations and deformation twining are observed in the simulation. The deformation mechanisms in three crystal orientations arediscussed. From the results of the simulation, we can find that the {111}<112>deformation twinning and dislocation nucleation present itself when the slippage of the dislocation dried up.
准连续介质方法(Quasi-continuum Method,QC)是多尺度方法的一种。其核心思想是在变形梯度变化比较小的区域采用有限元方法以“代表原子”(Representative Atoms)进行粗化描述,通过适当的权重处理求出整个系统的能量,而不是求出所有原子的能量。在缺陷密度较高、变形梯度变化较剧烈的区域对每个原子采用分子动力学来描述。这样就可以在不失精确的情况下极大地减少问题的自由度和计算量,以实现较大尺寸试件的原子尺度模拟。
本文采用QC方法对材料变形中产生的位错形核(Dislocation Nucleation)及孪生变形(Deformation Twinning,DT)的微观机理进行了分析,并讨论了该过程中呈现的尺寸效应,晶体取向效应和晶界效应及裂纹尖端扩展的变形过程,主要做了以下四个方面的工作:
1)模拟了四种金属薄膜——铝(Al)、银(Ag)、镍(Ni)、钯(Pd)——在四种压头宽度下的纳米压痕过程,得到了载荷—位移曲线和应变能—位移曲线。同时计算出四种材料的纳米硬度,并对其硬度值和压头宽度的关系进行了讨论;结果表明材料对压痕响应的尺度效应很明显,模拟得到的临界载荷与采用能量理论估算的临界载荷基本一致,四种金属薄膜扩展位错宽度大小模拟值与理论值相一致:最后,从微观角度讨论了材料载荷—位移曲线突降和材料中位错形核之间的关系,并画出了位错形核的原子图,进一步揭示材料变形机理。
2)模拟了单晶Al薄膜在三种不同晶体取向(分别为x[111],y[(?)10],z[(?)2]:x[(?)2],y[111],z[(?)10]:x[1(?)0],y[001],z[(?)0])条件下的纳米压痕响应,以此来探讨纳米压痕的晶体取向效应。得到了不同晶体取向下的载荷—位移曲线和微观原子图,同时观察到位错形核、孪生变形等一些独特的微观构造,模拟所得结果与相关实验现象一致。最后采用位错理论对不同晶体取向下纳米压痕响应的差异进行了讨论,并从微观变形机理的角度分析了产生这种差异的原因。
3)模拟了存在晶界的Al薄膜的纳米压痕过程,探讨了纳米压痕的晶界效应。在加载过程中,对薄膜内部变形比较剧烈的部分画出原子图,并从微观角度分析产生剧烈变形的原因,同时对纳米压痕过程中的载荷—位移曲线和压头下方微结构的变化在有晶界与无晶界两种情况下的区别进行了分析;最后,讨论了位错在滑移过程中与晶界的相互作用。
4)模拟了单晶Cu在拉伸(Ⅰ型加载)和剪切(Ⅱ型加载)两种加载模式,三种晶体取向条件下裂纹尖端的变形过程。观察到位错滑移和孪生变形现象,并对三种晶体取向下该现象的变形机制进行了分析。结果表明,不同的加载模式和不同晶体取向对模拟的结果影响很大。当位错滑移能力枯竭时,会产生{111}<112>孪生变形或位错形核。
As the development of Micro-electronics and Microsystems, researchers pay much attention on the micro-mechanical properties of materials. Because micro-components always show different characteristics from components in macro-scale (such as higher intensity, hardness, abrasion resistance, ductibility and low temperature super plasticity, etc), the microcosmic mechanism of deformation is important to study the properties of material in micro-scale. However, traditional methods based on continuum theories do not work in investigating the mechanism of micro-deformation, and microcosmic methods such as Molecular Dynamics and Monte Carlo method can not be used to simulate the deformation of a large region in common personal computers for its large computation memory caused by large degrees of freedom. In this situation, the multi-scale methods coupling atomistic scale and continuum scale are widely applied in computer simulations.
The Quasi-continuum Method is developed as a typical multi-scale method. The key idea is that of selective representation of atomic degrees of freedom. Instead of treating all atoms making up the system, a small relevant subset of atoms is selected to represent, by appropriate weighting, the energetics of the system as a whole. Based on their kinematic environment, the energies of individual "representative atoms" are computed either in nonlocal fashion in correspondence with straightforward atomistic methodology or within a local approximation as befitting a continuum model. The representation is of varying density with more atoms sampled in highly deformed regions (such as near defect cores) and correspondingly fewer in the less deformed regions further away, and is adaptively updated as the deformation evolves.
In this thesis, the effect of size, crystal direction, and grain boundary in micro-deformation are investigated using Quasi-continuum Method. The mechanisms of the dislocation nucleation and the deformation twinning are also have been analyzed. Based on the Quasi-continuum Method, the works of this thesis are as follows:
1) The processes of nano-indention of four FCC metals (Al, Ag, Ni, and Pd) under four different indenters with various widths are simulated. Load-displacement curves, strain energy vs displacement curves, as well as nano hardness are obtained. The values of the critical load are in good agreement with theoretical values. The relation between rigidity and indenter width is discussed. The widths of extended dislocation are in agreement with theoretical values. To study the deformation mechanism, the dislocation pictures are plotted and the relation between load-displacement curves and dislocations are discussed.
2) The nano-indention of Al film in three crystal orientations(x[111], y[-110], z[11-2]; x[-1-12], y[111], z[-110]; x[1-10], y[001], z[-1-10]) are simulated. Load-displacement curves and atomistic arrangements pictures are obtained. The results are in good agreement with experiments. Dislocations and deformation twining are observed in the simulation. The differences between different crystal orientations are analyzed by dislocation theory.
3) The nano-indentation on an Al film with a grain boundary is simulated. The load-displacement curve and micro-structures under the indenter are compared with the situation with no grain boundary. The interaction between dislocations and grain boundary is analyzed.
4) The deformation of crack tips in FCC Cu under modeⅠandⅡload in three crystal orientations are simulated. Dislocations and deformation twining are observed in the simulation. The deformation mechanisms in three crystal orientations arediscussed. From the results of the simulation, we can find that the {111}<112>deformation twinning and dislocation nucleation present itself when the slippage of the dislocation dried up.
引文
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