Geometrical factors related to composite microcracking

Abstract With the addition of second-phase reinforcements to a monolithic matrix it is possible to create structural systems from materials that are normally considered unsuitably weak or brittle. For example, the addition of a soft, ductile phase to a hard, brittle matrix can significantly increase the toughness and possibly the failure strain of the brittle component. However, due to the variation of processing techniques, the second-phase reinforcements can be formed into either elongated strands or more equiaxed dispersoids resulting in a range of fracture properties for a given material combination. The finite element analysis is presented here quantifies the plane-strain elastic interaction between a crack under pure mode I loading and a particle in terms of crack length, particle size, particle shape and crack-particle separation. Findings suggest that the influence of a particle on a crack tip decrease rapidly as the crack-particle distance increases so that an effective zone can be defined around the particles in which the particles directly affect crack propagation. Outside of this zone, cracks do not interact elastically with particles to any significant extent. The size of the zone is a function of crack length and particle size. In the specific case of NiAl reinforced with Nb, the zone width is approximated to be on the order of the grain size. For all reasonable values of Dundurs' parameters, α and β, shape-specific relations are given for a wide range of specimen geometries in order to provide simple, yet accurate estimates of the stress intensity factors of cracks in the composite. For the case of plastically deforming inclusions, the analysis becomes more complicated due to the introduction of the non-linear relationship between stress and strain, as well as the variable yield stress and strain hardening exponent.