扭转中尺寸依赖塑性的离散位错分析
A discrete dislocation analysis of size-dependent plasticity in torsion
AI总结：
本文提出单极子离散位错塑性框架求解三维边界值问题，揭示线材扭转中尺寸与初始位错密度对塑性变形的三种响应机制。
摘要：
本文提出了一种使用位错单极子表示法求解三维离散位错塑性边界值问题的方法。在每个时间步，有限体中的位移、应变和应力场通过无限体位错场与施加边界条件的镜像场叠加获得。三维无限体场通过将位错表示为由携带位错线和Burgers矢量信息的点（称为单极子）组成来获得。镜像场通过三维线弹性有限元计算获得。由于单极子表示与有限元法的耦合实现，包括弯曲位错与自由表面的相互作用，与基于位错线的表示实现存在显著差异，本文对此进行了详细阐述。研究探讨了大尺度计算中的数值收敛性和位错环形核的建模。单极子离散位错塑性框架用于研究尺寸和初始位错密度对直径变化跨越三个数量级的线材扭转的影响。根据初始位错源密度和线材直径，获得了三种扭转-扭转响应机制：(i) 对于直径足够小的线材，塑性变形由形核控制且具有强尺寸依赖性；(ii) 对于直径较大的线材，位错塑性由位错相互作用控制，几何必需位错和位错堆积的出现起关键作用，且具有强尺寸依赖性；(iii) 对于直径足够大的线材，塑性变形变得不那么异质，对尺寸的依赖性大幅减弱。
英文摘要：
A method for solving three dimensional discrete dislocation plasticity boundary-value problems using a monopole representation of the dislocations is presented. At each time step, the displacement, strain and stress fields in a finite body are obtained by superposition of infinite body dislocation fields and an image field that enforces the boundary conditions. The three dimensional infinite body fields are obtained by representing dislocations as being comprised of points, termed monopoles, that carry dislocation line and Burgers vector information. The image fields are obtained from a three dimensional linear elastic finite element calculation. The implementation of the coupling of the monopole representation with the finite element method, including the interaction of curved dislocations with free surfaces, is presented in some detail because it differs significantly from an implementation with a line based dislocation representation. Numerical convergence and the modeling of dislocation loop nucleation for large scale computations are investigated. The monopole discrete dislocation plasticity framework is used to investigate the effect of size and initial dislocation density on the torsion of wires with diameters varying over three orders of magnitude. Depending on the initial dislocation source density and the wire diameter, three regimes of torsion-twist response are obtained: (i) for wires with a sufficiently small diameter, plastic deformation is nucleation controlled and is strongly size dependent; (ii) for wires with larger diameters dislocation plasticity is dislocation interaction controlled, with the emergence of geometrically necessary dislocations and dislocation pile-ups playing a key role, and is strongly size dependent; and (iii) for wires with sufficiently large diameters plastic deformation becomes less heterogeneous and the dependence on size is greatly diminished.
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