A new constitutive model of micro-particle reinforced metal matrix composites with damage effects

It is well known that the mechanical behavior of micro-particle-reinforced metal matrix composites (MPMMCs) in service is significantly influenced by the particle size, matrix damage and interface debonding. In order to characterize the mechanical property of such a two-phased elasto-plastic material with the three kinds of effects, a new theoretical model is developed based on the secant modulus method, a low-order strain gradient theory with damage and an effective reduced moduli approach, in which both the size effect of reinforcing particles and the effects of matrix damage and interface debonding are included. As a result, a non-linear elasto-plastic constitutive relation is achieved, with which the stress-strain response of MPMMCs in both uniaxial tension and uniaxial compression tests can be reproduced very well, in contrast to the predictions by the existing strain gradient theories without considering damage. An interesting phenomenon is further found that the dominant role of damage in MPMMCs changes from the interface debonding to the matrix damage with the increase of load in tension test, while the matrix damage always dominates in compression test. The present study provides not only a more comprehensive understanding of the in-service performance of MPMMCs but also a useful theoretical tool for mechanical prediction and optimizing design of other advanced composite materials.