A Theory of Particle-Reinforced Plasticity

Abstract

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.

Influence of porosity on cavitation instability predictions for elastic–plastic solids

“…For an elastic solid containing the volume fraction f of spherical holes, Tandon and Weng [25] have derived the following relations for the macroscopic E and n, expressed in terms of the matrix values E 0 and n 0…”

Simplified prediction of the monotonic uniaxial stress–strain curve of non-linear particulate composites

“…This approach has in particular been formulated for metal matrix composites, i.e., structures containing elastic reinforcements within a softer isotropic elastoplastic power-law hardening matrix [4,19,[25][26][27]35]. Given its equivalence with the secant method using the quadratic average (second-order moment) of the strain over each phase [21,28] (as opposed to using the average phase strain, which generally gives overly stiff predictions and suffers important limitations [3,4,16,37]), formulations of this model also exist in the form of secant modulus estimates [14,15,18,20,28,37,38].…”

“…Approximations that have most often been used to this end for non-dilute two-phase linear elastic composites include (i) the Mori-Tanaka model, corresponding to the lower Hashin-Shtrikman bound for isotropic composites with a spherical reinforcement (e.g., Refs. [3,4,12,[14][15][16]), (ii) the two-phase self-consistent model (e.g., Refs. [15,17,18]), (iii) the generalized self-consistent scheme (e.g., Refs.…”

An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals

“…He noticed that, for power-law creep, Hill's formulation may be integrated into a`total' one making use of`secant' creep compliances. Other secant moduli or compliances have also been de®ned (Berveiller and Zaoui, 1979;Tandon and Weng, 1988) leading to a (classical)`secant formulation', closely related to Hill's incremental formulation.…”