A multi-scale crystal plasticity model for cyclic plasticity and low-cycle fatigue in a precipitate-strengthened steel at elevated temperature

In this paper, a multi-scale crystal plasticity model is presented for cyclic plasticity and low-cycle fatigue in a tempered martensite ferritic steel at elevated temperature. The model explicitly represents the geometry of grains, sub-grains and precipitates in the material, with strain gradient effects and kinematic hardening included in the crystal plasticity formulation. With the multiscale model, the cyclic behaviour at the sub-grain level is predicted with the effect of lath and precipitate sizes examined. A crystallographic, accumulated slip (strain) parameter, modulated by triaxiality, is implemented at the micro-scale, to predict crack initiation in precipitate-strengthened laths. The predicted numbers of cycles to crack initiation agree well with experimental data. A strong dependence on the precipitate size is demonstrated, indicating a detrimental effect of coarsening of precipitates on fatigue at elevated temperature.