Nonlinear Analysis of Particle Cavitation and Matrix Yielding Under Equitriaxial Stress

Abstract

Cavitation of a rubber particle is a possible microscopic mechanism for toughness improvement of polymer materials, as it reduces the stress triaxiality and promotes shear yielding in the matrix. This phenomenon is presently studied theoretically by examining the radial deformation of a particle-matrix composite sphere. The rubber particle is modeled as a nonlinear elastic sphere and the surrounding matrix as a concentric elastoplastic shell. Two possible modes of deformation are identified: One represents the pure expansion of the particle and the other corresponds to particle cavitation. The analysis accounts for finite bulk stiffness of the particle and possibility of plastic yielding in the matrix. Based on the analytical expressions for the finite deformation and the stress fields derived, numerical solutions are demonstrated to illustrate the effect of cavitation to suppress the increase of triaxial stress and enhance the plastic yielding in the matrix.