A modular spectral solver for crystal plasticity. (September 2022) - Dadhich, Ritesh; Alankar, Alankar
Abstract: 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 α − β Ti polycrystal. In this dual phase polycrystal, plastic deformations of α and β 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 α − β Ti polycrystal also show excellent agreement against an open-source finite element crystal plasticity solver and FFT solver, respectively. Highlights: Any new material point model can be added as a module with ease. The framework is validated against open–source crystal plasticity FFT and FE frameworks. Uniaxial behavior of single crystal aluminum is modeled using a dislocation density based model. Cyclic behavior of Ti–5Al is modeled considering backstress and non-Schmid effect. Different crystal plasticity frameworks for different phases can be simultaneously used.