A fast Fourier transform (FFT) based modular solver for crystal plasticity is presented in this work. In the framework, balance of momentum is solved in a global iterative loop and single crystal plasticity is solved in an inner loop. For the latter, a fully implicit time integration scheme is used in which the correct solution is found using a residual established based on plastic velocity gradient. The elastic–viscoplastic response of single crystals is modeled by coupling slip system based constitutive equations to crystal kinematics. The single crystal response is validated using experimentally observed behavior of fcc and hcp single crystals for uniaxial and cyclic deformation, respectively. The single crystal plasticity module provides solution to the global FFT solver. An FFT scheme based on deformation gradient is derived to address the full-field micromechanical response for finite deformation. Adaptive time increment is used for ensuring convergence. OpenMP based multi–threading is employed for ensuring faster simulations. The current FFT model is validated for an fcc polycrystal by comparing the results against those from an open–source crystal plasticity code, and shows an excellent agreement. In the second study, the FFT solver is used for analyzing the deformation behavior of an $\alpha -\beta$ Ti polycrystal. In this dual phase polycrystal, plastic deformations of $\alpha$ and $\beta$ phases are modeled using a dislocation density based and a power law based constitutive framework, respectively. The model is able to capture the expected salient features of deformation of both phases. Simulations for fcc polycrystal and $\alpha -\beta$ Ti polycrystal also show excellent agreement against an open–source finite element crystal plasticity solver and FFT solver, respectively.

本文提出了一种基于快速傅里叶变换 (FFT) 的晶体塑性模块化求解器。在该框架中，动量平衡在全局迭代循环中解决，单晶塑性在内部循环中解决。对于后者，使用完全隐式时间积分方案，其中使用基于塑性速度梯度建立的残差找到正确的解决方案。通过将基于滑移系统的本构方程与晶体运动学耦合来模拟单晶的弹粘塑性响应。使用实验观察到的 fcc 和 hcp 单晶分别用于单轴和循环变形的行为来验证单晶响应。单晶可塑性模块为全球 FFT 求解器提供了解决方案。推导出基于变形梯度的 FFT 方案来解决有限变形的全场微机械响应问题。自适应时间增量用于确保收敛。采用基于 OpenMP 的多线程来确保更快的仿真。通过将结果与来自开源晶体可塑性代码的结果进行比较，验证了当前 FFT 模型对于 fcc 多晶的验证，并显示出极好的一致性。在第二项研究中，FFT 求解器用于分析一个变形行为 并表现出极好的协议。在第二项研究中，FFT 求解器用于分析一个变形行为 并表现出极好的协议。在第二项研究中，FFT 求解器用于分析一个变形行为$\alpha -\beta$钛多晶。在这种双相多晶中，塑性变形$\alpha$和$\beta$相分别使用基于位错密度和基于幂律的本构框架进行建模。该模型能够捕获两个阶段变形的预期显着特征。fcc 多晶的模拟和$\alpha -\beta$Ti 多晶也分别与开源有限元晶体塑性求解器和 FFT 求解器表现出极好的一致性。