A Theory of Particle-Reinforced Plasticity

A simple, albeit approximate, theory is developed to determine the elastoplastic behavior of particle-reinforced materials. The elastic, spherical particles are uniformly dispersed in the ductile, work-hardening matrix. The method proposed combines Mori-Tanaka’s concept of average stress in elasticity and Hill’s discovery of a decreasing constraint power of the matrix in polycrystal plasticity. Under a monotonic, proportional loading the latter was characterized, approximately, by the secant moduli of the matrix. The theory is established for both traction and displacement-prescribed boundary conditions, under which, the average stress and strain of the constituents and the effective secant moduli of the composite are explicitly given in terms of the secant moduli of the matrix and the volume fraction of particles. In particular, the yield stress and work-hardening modulus of the composite are shown to be inversely proportional to the deviatoric part of average stress concentration factors of the matrix, and therefore will increase (or decrease) with increasing hard (or soft) particle concentration. It is also found that, even if the matrix is plastically incompressible, the composite as a whole is not. Comparison between the theory and the experiment for a silica/epoxy system shows a reasonable agreement. The theory is also compared with a recently developed one by Arsenault and Taya; while both give the same initial yield stress for the composite, the work-hardening modulus predicted by their theory is found to be higher.