Numerical implementation of a phase mixture model for rate-dependent inelasticity of tempered martensitic steels

Tempered martensitic steels with a high chromium content are used for power plant components at elevated temperatures under creep–fatigue conditions. In order to model the complex mechanical behavior of the alloy X20CrMoV12-1, a phase mixture model is used. This model is based on the distinction of hard and soft constituents, which are connected via an iso-strain approach. Nonlinear kinematic hardening and softening effects are taken into account by introducing a backstress and a softening variable. This paper focuses on the numerical implementation of the phase mixture model, i.e., the stress update algorithm and the consistent tangent operator. For implicit time integration of the governing equations, the backward EULER method in combination with NEWTON–RAPHSON iterations is applied. The model is implemented as user material subroutine into the commercial finite element code ABAQUS. For verification, several benchmarks considering uniaxial and multi-axial stress states are presented and analyzed. Furthermore, a thermo-mechanical fatigue test based on a typical sequence of start-ups and shutdowns of power plants is simulated.