PLASTIC YIELDING CONTRIBUTION TO FRACTURE TOUGHNESS OF POLYMERS MODIFIED WITH RUBBER AND INORGANIC FILLERS

High multiaxial stress fields are created in front of a crack which lead to various fracture processes in a region close to the crack tip. One of these is matrix yielding around particles which may happen before debonding of the particles and that is the subject of this contribution. A hybrid composite consisting of a brittle polymer matrix and two filler components which are very different in size are considered. The larger particles are enclosed in a material consisting of matrix and nano-size rubber particles which form an effective material. At first the mechanical problem of a local composite element consisting of a stiff spherical particle within a spherical elastic-plastic rubber filled matrix under uniform tensile stress was solved. This implies the approximation of the triaxial stress state by a hydrostatic one. Because the stiff larger particles are not allowed to debond from the matrix it was assumed that the volume increase during loading of the local composite element is caused by elastic volume change and plastic dilatation of the voided effective matrix material. With the knowledge of the stresses and displacements of such a local 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 over the stress field of the crack within the dissipation zone. Fracture toughness increases with increasing volume fraction of inorganic micro-size particles towards a maximum.