A Theory of Inclusion Debonding and its Influence on the Stress-Strain Relations of a Ductile Matrix Composite

Abstract

The progressive debonding process and its influence on the overall elastoplastic response of a two-phase, ductile composite containing aligned oblate inclusions are examined as a function of inclusion shape and concentration, and the interfacial strength. The theory developed is based upon a Weibull statistical function to describe the probability of debonding, and Qiu and Weng's (1992) energy approach to determine the internal stress state of the inclusions and the homogenized plastic state of the ductile matrix. The axisymmetric loading condition-in the form of U22 = a₃₃ = (3a -is studied in detail, including the dependence of 0 on the aspect ratio of inclusions and their concentration to produce a purely hydrostatic tensile state in the inclusions. It is shown that the stress-strain curve of the debonding system always starts out with that of a perfectly bonded composite, then deviates from it, and finally approaches that of a porous material containing similarly aligned voids. It is also found that complete debonding is faster with spherical inclusions, and is more difficult with thin circular discs. Debonding is also faster at a lower particle concentration and, as expected, faster when the interfacial strength is weaker. The evolution of volume concentration of the debonded particles (or voids) is also determined for each case to reflect the damage process in the two-phase system.