POLYMERS TOUGHENED WITH RUBBER MICROSPHERES - AN ANALYTICAL SOLUTION FOR STRESSES AND STRAINS IN THE RUBBER PARTICLES AT EQUILIBRIUM AND RUPTURE

Large strains in rubber toughened polymers cause void formation and gr owth in the rubber particles and yielding in the matrix. Void formatio n usually precedes plasticity in the matrix around the particle and pr evious papers have proposed models for the relationship between rubber surface energy, volume strain energy and void growth. In this paper, it is shown that another volume criterion must also be satisfied arisi ng from the fact that in all these models, no decohesion is allowed at the particle-matrix interface. A fracture mechanics approach, where l inear and nonlinear elasticity are assumed for the matrix and the rubb er particle, respectively, is used to define a void formation criterio n depending on the rubber fracture surface energy. After formation, th e stability of the void is examined, taking into account the volume co nservation between matrix and particle and the stress due to surface t ension when the void size is very small. A size effect is observed, in dicating that voids cannot grow in small particles. The required value of fracture energy in a particle on a microscopic scale is discussed.