A multi-scale computational model using Generalized Method of Cells (GMC) homogenization for multi-phase single crystal metals

A multi-scale computational model for determining the elastic-plastic behavior of a multi-phase metal is developed on a finite element analysis (FEA) framework. A single crystal plasticity constitutive model that can capture the shear deformation and the associated stress field on the slip planes is employed at the microstructural (grain) length scale. The Generalized Method of Cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, the ability of GMC for homogenization is evaluated by analyzing simple problems using GMC as a stand-alone tool. A repeating unit cell (RUC) of a two-phase CMSX-4 Ni-based superalloy with 72.9% volume fraction of gamma' inclusion in the c matrix phase is used for the evaluation. The evaluation is performed by comparing the results with those predicted by a FEA model incorporating the same crystal plasticity constitutive model. The average global stress-strain behavior predicted by GMC demonstrated excellent agreement with FEA. The agreement between the local distribution of the field quantities predicted by GMC and FEA was satisfactory, especially when considering the substantial savings in the computational cost due to homogenization. Finally, the capability of the developed multi-scale model, linking FEA and GMC, to solve real life sized structures is demonstrated by analyzing an engine disk component and determining the microstructural scale details of the field quantities of the two-phase CMSX-4 Ni-based superalloy. (C) 2014 Elsevier B. V. All rights reserved.