Finite element implementation of non-unified visco-plasticity model considering static recovery

Abstract

In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in time-dependent plasticity model. Implicit integration algorithm for non-unified visco-plasticity model is derived. Plastic strain is divided into two parts: the visco-plastic strain, which is calculated based on the viscosity function, and the steady strain which only depends on the equivalent deviatoric backstress. Using the Newton iterative strategy, two sets of equations for deviatoric stress and relative stress tensors are solved. Additionally, the return mapping method is applied in numerical method, and consistent tangent stiffness modulus is progressed for convergence in finite element analysis. The model is implemented into commercial software ABAQUS as user subroutine UMAT. Dwell experiments of nickel-based superalloy under strain-controlled cyclic loading with holding periods for relaxation at high temperature are selected to verify the method. The results indicate that the user subroutine attains convergence with good speed even at large increment, and the additional static recovery terms can improve the simulation for relaxation behaviors.