Modeling the Particle Size and Interfacial Hardening Effects in Metal Matrix Composites with Dispersed Particles at Decreasing Microstructural Length Scales

The focus of this paper is on incorporating the particle size effect and the effect of particle-matrix interfacial properties on the average onset of plasticity and strain hardening rates of metal matrix composites reinforced with hard, stiff, or soft particles. In order to achieve this objective, a higher-order gradient plasticity theory that explicitly includes the effect of interfacial energy at particle-matrix interfaces is formulated within the frameworks of virtual power and thermodynamic laws. The derived higher-order gradient plasticity theory also takes into account large variations in plastic strain tensor and effective plastic strain; namely, the gradient of plastic strain, the gradient of the effective plastic strain, and the accumulation of plastic strain gradients. Moreover, unlike the majority of the existing gradient plasticity theories in the literature, it is shown that the matrix nonlocal yield condition as well as a yield-like condition for the particle-matrix interface can be directly derived front the principle of virtual power without any further constitutive assumptions. Also, in this work the interfaces dissipate energy similar to the bulk material during plastic deformation. The interfacial yield condition takes into consideration the particle type (soft, stiff, hard) through the incorporation of the particle-matrix interfacial yield strength and interfacial hardening in case of dislocation transmission across the interface (i.e. shearing of particles). The proposed higher-order gradient plasticity theory is shown to be qualitatively successful in predicting the increase in the average yield strength, strain hardening rates, and flow stress as the particle size decreases and the particle interfacial strength increases.