A multi-scale model combining martensitic transformations with multi-phase crystallographic slip

Abstract

Mechanically induced martensitic transformations are an essential mechanism influencing the constitutive behaviour of many advanced steel grades, such as austenitic stainless steels and Transformation Induced Plasticity (TRIP) alloys. In this work, a single-crystal constitutive model is developed to predict their complex microstructural behaviour during mechanical loading. The model is based on the work of Vieira de Carvalho et al. [16] and crucially proposes crystallographic slip in the martensitic phase after transformation from retained austenite. Austenite and martensite plasticity are incorporated following a standard finite strain single crystal plasticity approach and are fully coupled with the martensite formation kinematics, enabling the simultaneous evolution of the three mechanisms. The numerical treatment of the coupled constitutive equations is described in detail. In particular, the solution of the monolithic system of equations with the Newton-Raphson methodology, including the exact linearisation of both the local and global problems. An algorithmic strategy for handling the martensite volume fraction constraints is proposed for return-mappings in the restarted step. The model is validated using macroscopic experimental results for an austenitic stainless steel where an efficient calibration procedure for the micro-constitutive parameters is devised using derivative-free optimisation methods.