Particle size effects in ductile composites: An FFT homogenization study

We present a computational homogenization study on the particle size effect in ductile composites. The micromechanical formulation is based on non-local models through (i) the incorporation of a lower-order strain gradient plasticity model and (ii) the application of an implicit gradient regularization technique to the Gurson–Tvergaard–Needleman ductile damage model for metals. In this way, the extended model is equipped with two length-scale parameters, one for each non-local extension, which modulate the size dependent character of the formulation. The problem consists of a system of partial differential equations in which two Helmholtz-type equations for the damage regularization are coupled with the balance of linear momentum through the stress, which depends on the non-local variables and on the plastic strain gradient. A series of numerical simulations are conducted to investigate the behavior of three-dimensional microstructures representative of particle reinforced metal matrix composites. The change in strengthening and ductility, as a function of the particle size, is first analyzed by means of a parametric study in which the considered non-local extensions act both independently and together. Finally a comparative study with experimental results demonstrates that the particle size induced strengthening in metal matrix composites can be quantitatively captured by the considered model.