基于能量极值原理的单晶体塑性滑移的有限变形分析

对FCC单晶体的率无关弹塑性力学响应的本构关系进行了数值模拟.用一个基于能量极值原理的数值计算方法来处理复杂的多面塑性问题.这种算法可以有效地模拟单晶体多滑移系的启动.在这一理论框架下,增量的应力应变关系可以从所构造的能量函数中推导出来.对于滑移系激活情况的判定则可转化为求解活动约束的非线性数学规划问题.通过对时间的离散,此问题又可细化为逐步二次规划问题,并采用有效集法来搜索启动滑移系,进而求得弹塑性本构关系.数值结果表明该方法具有稳定、收敛、可行的特点.在数值计算的基础上研究了单轴拉伸下晶体的不同取向对单晶体硬化程度和滑移系激活情况的影响.

ON ANALYSIS OF FINITE DEFORMATION FOR SINGLE CRYSTAL PLASTIC SLIP BASED ON THE MINIMUM PRINCIPLE

This paper deals with simulation of the mechanical response of FCC single crystals for a rate-independent elastic-plastic constitutive law. An algorithm based on the minimum principle is presented to cope with the complex multi-surface plasticity. This method effectively simulates multi-slip in single crystals. Under this framework, the stress-strain relations are derived from a pseudo-elastic strain-energy density. The determination of active slip system is reduced to a nonlinear optimization problem. By time discretization this problem is equal to a sequential quadratic programming problem. Active set method is used to search active constraint. Simulation results show that this algorithm is stable, convergent and efficient. The influence of crystal orientation on crystal hardening and activity of slip system under uniaxial tension is studied according to the numerical results.