An enhanced continuum model for size-dependent strengthening and failure of particle-reinforced composites

We present an enhanced continuum model for the size-dependent strengthening and failure of particle-reinforced composites. The model accounts explicitly for the enhanced strength in a discretely defined “punched zone” around the particle in a metal matrix composite as a result of geometrically necessary dislocations developed through a mismatch in the coefficients of thermal expansion. We incorporate the punched zone explicitly through a unit-cell model within this work, but the approach can be used more generally to account for discrete particle distributions and particle shapes. Smaller particles lead to greater strengthening, and this size effect is larger for larger volume fractions. An equation for the coupling of the size-dependent increase of yield strength of metal matrix composites with the particle volume fraction is obtained. The results indicate that the punched zone effect may amplify the occurrence of a variety of failure modes such as matrix localization, particle fracture and/or particle–matrix interface failure; smaller particles perceive higher stresses. We account for interface failure through a cohesive approach, and show that the interface damage mechanism is also particle-size-dependent. Some implications are presented for microstructural design of metal matrix composites.