A general method to obtain the homogenized response of metal-matrix composites is developed. It is assumed that the microscopic scale is sufficiently small compared to the macroscopic scale such that the macro response does not affect the micromechanical model. Therefore, the microscopic scale is analyzed using a Representative Volume Element (RVE), while the homogenized data are saved and used as an input to the macro scale. The dependence of fiber size is analyzed using a higher order plasticity theory, where the free energy is stored due to plastic strain gradients at the micron scale. Hill-Mandel’s energy principle is used to find macroscopic operators based on micro-mechanical analyses using the finite element method under generalized plane strain condition. A phenomenologically macroscopic model for metal matrix composites is developed based on constitutive operators describing the elastic behavior and the trapped free energy in the material, in addition to the plastic behavior in terms of the anisotropic development of the yield surface. It is shown that a generalization of Hill’s anisotropic yield criterion can be used to model the Bauschinger effect, in addition to the pressure and size dependence. The development of the macroscopic yield surface upon deformation is investigated in terms of the anisotropic hardening (expansion of the yield surface) and kinematic hardening (translation of the yield surface). The kinematic hardening law is based on trapped free energy in the material due to plastic deformation. The macroscopic operators found, can be used to model metal matrix composites on the macroscopic scale using a hierarchical multi-scale approach. Finally, decohesion under tension and shear loading is studied using a cohesive law for the interface between matrix and fiber.
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Dcamm Special Report
Tvergaard, Viggo, Legarth, Brian Nyvang, Niordson, Christian Frithiof