An implicit staggered algorithm for CPFEM-based analysis of aluminum

Abstract

In this paper, we propose an implicit staggered algorithm for crystal plasticity finite element method (CPFEM) which makes use of dynamic relaxation at the constitutive integration level. An uncoupled version of the constitutive system consists of a multi-surface flow law complemented by an evolution law for the hardening variables. Since a saturation law is adopted for hardening, a sequence of nonlinear iteration followed by a linear system is feasible. To tie the constitutive unknowns, the dynamic relaxation method is adopted. A Green-Naghdi plasticity model is adopted based on the Hencky strain calculated using a $[2/2]$ Padé approximation. For the incompressible case, the approximation error is calculated exactly. A enhanced-assumed strain (EAS) element technology is adopted, which was found to be especially suited to localization problems such as the ones resulting from crystal plasticity plane slipping. Analysis of the results shows significant reduction of drift and well defined localization without spurious modes or hourglassing.

Figures (13)

• Figure 1: Dominant slip systems for a FCC crystal.
• Figure 2: Rotation of the FCC cell in the space $x,y,z$.
• Figure 3: Upper bound on the error $E_{[2/2]\log}^{\max}$ compared with the error in closed form $E_{[2/2]\log}^{1D}$.
• Figure 4: Relative error for an incompressible $2D$ problem, $E_{[2,2]\log}=\left\Vert 1/2[2/2]_{\log}(-2\boldsymbol{E})-\boldsymbol{\varepsilon}\right\Vert$.
• Figure 5: Verification test: geometry and boundary conditions for the single crystal cylinder under tension.