Time efficient crystal plasticity modeling

Abstract

In this study, it is proposed stress integration algorithm based on Finite Difference Method (FDM) for Crystal Plasticity Finite Element Method (CPFEM). Nonlinear equations should be solved in the Euler backward stress integration algorithm, thus the Newton-Raphson method where the first derivative of the resolved shear stress is required has been widely used. However, calculations of the derivatives are time consuming when the tensor exponential function is included in the integration algorithm. To effectively solve this complexity, the analytical first derivatives of the resolved shear stress were approximated by FDM. Also, finite element simulations were performed for numerical verification of the proposed algorithm. Considering the results, the proposed numerical algorithm could be the substitute of the Euler backward method based on analytical derivatives in view of accuracy, convergence, computational efficiency, and easy implementation. Meanwhile, there are numerous grains in metals so that consideration of all the grains in CPFEM demands high computational cost. Therefore, Reduced Texture Methodology (RTM) was adopted with the proposed method to reduce the computational time. For the RTM, specific material parameters were calibrated to characterize anisotropic hardening. The predicted results from one element simulation showed a good agreement with the experimental data for the stress-strain curves including 0, 45 and 90 degrees from the rolling direction. Finally, circular cup drawing simulations were performed to validate the applicability of the RTM for macroscale finite element analysis. The predicted profiles of earing, which happens due to anisotropy, were compared with the experimental data, and the accuracy was evaluated. In addition, the results from the RTM with the proposed algorithm were compared with those with the Euler backward method based on analytical derivatives in terms of computational time and accuracy. The results showed that the RTM with the developed algorithm could be an alternative approach for continuum level advanced yield function such as Yld2004-18p.