Forming Simulations of MMC Components by a Micromechanics Based Hierarchical FEM Approach

The present work deals with computational simulations of an elastoplastic particulate metal matrix composite undergoing finite strains. Two different approaches are utilized for homogenization and localization; an analytical constitutive material law based on a mean field approach, and a periodic unit cell method. Investigations are performed on different length scales. The Finite Element Method is employed to predict the macroscopic response of a component made from a metal matrix composite. Its constitutive material law, based on the incremental Mori Tanaka approach, has been implemented into an Finite Element Method package, and is extended to the finite strain regime. This approach gives access to the mesoscale fields as well as to approximations for the microscale fields in the individual phases of the composite. Selected locations within the macroscopic model are chosen and their entire mesoscopic deformation history is applied to unit cells using the periodic microfield approach. As a result, mesoscopic responses as well as highly resolved microfields are available. A Gleeble-type experiment employing a metal matrix composite with 20vol% of particles is investigated as an example. Comparison of the composite's effective response exhibits excellent agreement in the deformation as well as stress and strain fields, which qualifies the incremental Mori Tanaka approach as appropriate constitutive law for the studied application. For detailed predictions of the fluctuating fields in the matrix and the particles the unit cell approach is employed