A numerical investigation on the heterogeneous and anisotropic mechanical behaviour of AISI H11 steel using various stress-strain formulations : a multi-scale approach

In this paper, a numerical investigation is carried out on the heterogeneous and anisotropic mechanical behaviour of AISI H11 martensitic steel with a multi-scale approach. For this purpose, an elasto-viscoplastic model that considers nonlinear isotropic and kinematic hardenings is implemented in a finite element code using three stress-strain formulations: the small strain assumption where rotation is neglected; and two formulations based on finite strain theory in Eulerian framework which are respectively defined by the Jaumann-Zaremba and the Olroyd objective rates of Kirchhoff stress. The parameters of the constitutive equations are identified using macroscopic quasi-static and cyclic material responses and small strains assumption by the mean of a localization rule. By using particular Voronoi tessellations, a virtual realistic microstructure, consisting of laths and grains, is generated considering the specific crystallographic orientations alpha'/gamma (martensitic/austenitic phases) relation (i.e. Kurdjumov-Sachs relation). Finite element computations are then performed on this virtual microstructure and exhibit that; besides laths orientations, morphologies and interactions; the full-field local mechanical fields are dependant on the used stress-strain formulation.