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Abstract
A general method to obtain the homogenized response of metalmatrix 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. HillMandel’s energy principle is used to find macroscopic operators based on micromechanical 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 multiscale approach. Finally, decohesion under tension and shear loading is studied using a cohesive law for the interface between matrix
and fiber.
Original language  English 

Place of Publication  Kgs. Lyngby, Denmark 

Publisher  Technical University of Denmark 
Publication status  Published  2011 
Series  DCAMM Special Report 

Number  S135 
ISSN  09031685 
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 1 Finished

Multiscale Modeling of Composites
Azizi, R., Niordson, C. F., Legarth, B. N., Richelsen, A. B., Fleck, N. A., Jensen, H. M. & Tvergaard, V.
15/09/2008 → 21/12/2011
Project: PhD