Contribution of matrix yielding energy to the crack resistance of particle reinforced composites

The incorporation of particles into polymer matrix causes local stresses in their neighbourhood when the composite is loaded. High multiaxial stress fields are created in front of a crack which leads to various fracture processes in a region close to the crack tip. These processes contribute to the energy dissipation of the moving crack, increasing the crack resistance of the material. One of these processes is matrix yielding around particles after debonding of the particles and that is considered in this paper. At first the crack resistance for this mechanism was obtained by integration over the stress field within the dissipation zone. At second the mechanical problem of a spherical particle within a spherical elastic/perfectly plastic matrix under uniform radial tensile stress was solved. After particle debonding, the yielding energy of the matrix shell was calculated. Finally an analytical equation for the composite crack resistance for this mechanism was obtained, which is a function of mechanical properties of the components, particle volume fraction in the composite and local particle fraction. Debonding energy, matrix yield stress and particle size come only into play if the debonding stress is larger than the minimum uniform stress for yielding initiation.