Modeling Interparticle Size Effect on Deformation Behavior of Metal Matrix Composites by a Gradient Enhanced Plasticity Model

Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, besides volume fraction, have a considerable effect on the macroscopic mechanical response of metal matrix microreinforced composites. Classical (local) plasticity models unlike nonlocal gradient enhanced plasticity models cannot capture this size dependency due to the absence of a material length scale. In this paper, one form of higher-order gradient plasticity enhanced model, which is derived based on principle of virtual power and laws of thermodynamic, is employed to investigate the size effect of elliptical inclusions with different aspect ratios based on unit cell simulations. It is shown that by decreasing the particle size or equivalently the interparticle spacing (i.e., the spacing between the centers of inclusions), while keeping the volume fraction constant, the average stress–strain response is stronger and more sensitive to the inclusion’s aspect ratio. However, unexpectedly, decreasing the free-path interparticle spacing (i.e., the spacing between the edges of inclusions perpendicular to the principal loading direction) does not necessarily lead to largest strengthening. This is completely dependent on the plastic strain gradient hardening due to distribution and evolution of geometrically necessary dislocations that depend on the particle size and shape. Gradient-hardening significantly alter the stress and plastic strain distributions near the particle-matrix interface.