Plastic yielding contribution to fracture toughness of polymers modified with rubber and inorganic fillers

High-multiaxial stresses 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 which may happen before debonding of the particles and the calculation of that mechanism is the subject of this paper. At first, the mechanical problem of a spherical particle within a spherical elastic–plastic rubber filled matrix under hydrostatic tensile stress was solved. With the knowledge of the stresses and displacements of such a composite element, the yielding energy around one particle was calculated. Finally, an analytical equation for the composite fracture toughness for this mechanism was obtained by integration of the yielding energy density over the normalized hydrostatic stress within the yielding zone, which provides an increase with increasing particle fraction towards a maximum.