Prediction of tension–compression cycles in multiphase steel using a modified incremental mean-field model

A micromechanical model is proposed for multiphase metals consisting of a ductile matrix reinforced by hard, equiaxed inclusions. The model belongs to a class of incremental mean-field theories of the first order and is suitable for general, non-monotonic loading paths. This paper specifically addresses the definition of the effective, instantaneous shear modulus of the isotropic comparison materials which intervene in the solution of the linearized, homogenisation problem. Time integration of the composite response is calculated using a Newton–Raphson scheme and a consistent tangent operator is derived. Predictions of the phase stresses developed under various loading modes and for a wide range of volume fractions of inclusions are assessed by a comparison with finite element simulations of periodic unit cells. It is argued that the latter predictions depend dramatically on the topological arrangement of the inclusions. Considering a cubic ordering of inclusions, it is possible to reproduce FE predictions with the mean-field model on the condition that the comparison materials are stiffer than the real phases during the first few percent of plastic strain. The mean-field model provides an accurate prediction of the average stress developed within individual phases.