线搜索增强的率相关晶体塑性本构积分算法及数值实现

Numerical Implementation of Line Search Enhanced Integration Method of Rate-Dependent Crystal Plasticity Constitutive Law

关键词:  材料  力学性能  微观结构  晶体  塑性本构  积分算法

Key words:  Material  Mechanical performance  Microstructure  Crystal  Plasticity constitutive  Integration method

摘要:

建立在晶体微观变形机制上的晶体塑性本构理论提供了研究细观尺度上晶体材料力学行为的理论与方法。在率相关晶体塑性本构积分方法中，Newton-Raphson（N-R）迭代方法往往是迭代求解剪切应变增量的核心算法。为了提高采用N-R迭代算法的晶体塑性本构积分方法的效率，在理论上采用线搜索方法对N-R迭代方法的迭代步长进行再规划并编写了采用传统N-R迭代方法和采用线搜索增强N-R迭代方法的晶体塑性本构积分方法子程序，采用不同子程序对镍基高温合金多晶体的高温单调拉伸力学行为进行有限元模拟，比较了采用不同子程序的模拟结果与计算效率。结果表明，采用传统N-R迭代方法与线搜索增强N-R迭代方法的晶体塑性本构子程序均能有效地模拟镍基高温合金的单轴拉伸行为且计算结果一致，并且采用线搜索增强N-R迭代方法的总有效增量步数目和计算耗时分别为前者的1/5和1/6。

Abstract:

The theory of crystal plasticity constitutive law， which is based on the micromechanics of crystal deformation， has been applied in studying the deformation of crystal materials on meso-scale. In integration methods of rate-dependent crystal plasticity constitutive equations， Newton-Raphson （N-R） iteration is always adopted as the core algorithm in solving increments of shear strain. In order to improve the efficiency， line search method was utilized to modify the step length of N-R iteration in the theory； then， the integration methods of crystal plasticity constitutive law with normal and line search enhanced N-R iteration were programmed into subroutines. The simulations of monotonic tensile mechanical behavior of Ni-based polycrystal superalloy were conducted with different subroutines. And the simulated results and computation efficiency were compared and analyzed. The results show that the tensile mechanical behavior is simulated by both subroutines and the results are identical. Furthermore， the consumed total number of increments and the time cost of the simulation with line search enhanced subroutine are 1/5， 1/6 respectively of that without line search method.