Modeling strain-induced martensitic transformation in austenitic stainless steels subjected to cryogenic temperatures using incremental mean-field homogenization schemes

Austenitic stainless steels are commonly used as structural materials in high-field superconducting magnet\nsystems because they retain high strength, ductility, and toughness at very low temperatures, and they\nare paramagnetic or antiferromagnetic under the Néel temperature in their fully austenitic state. However,\nthey are susceptible to strain-induced martensitic transformation, especially at cryogenic temperatures, which\nmodifies the material properties, induces volume changes and additional strain hardening, and leads to\nferromagnetic behavior. Thus, accurate predictions of the structural performance of these materials at very low\ntemperatures are of great interest for the conception and design of these cryo-magnetic systems. In this paper,\nwe propose an adequate constitutive model for the evolving bi-phase material—austenite and martensite—\nbased on a Hill-type incremental formulation. Two different versions of the model are proposed based on\nthe linear mean-field homogenization scheme: Mori-Tanaka and Self-Consistent. Moreover, a rate-independent\nnonlinear mixed kinematic-isotropic hardening law is used for each phase, and the martensitic transformation\nis described by the nonlinear kinetic law proposed by Olson and Cohen (1975). The constitutive model is\nimplemented in ABAQUS/Standard through a UMAT user subroutine, for which a return mapping algorithm\nbased on the implicit backward Euler integration scheme is used and a closed-form expression of the consistent\nJacobian tensor is provided. The Mori-Tanaka and Self-Consistent approaches are evaluated in terms of their\nability to describe the mechanical behavior of the bi-phase aggregate by comparing the predictions of the\nhomogenization schemes with unit-cell finite element calculations with an explicit description of the martensite\ninclusions and the austenite matrix. The comparison is carried out for different stress states with controlled\ntriaxiality and Lode parameter under monotonic and cycling loading, paying special attention to the evolution\nof the mechanical fields in each phase. The unit-cell calculations are performed for both constant and evolving\nmartensite volume fractions. In addition, numerical simulations of tensile tests on samples subjected to different\ninitial temperatures are carried out for the transforming bi-phase material and the results are compared to\nexperimental data for AISI 304L and AISI 316LN steels.