CRACK TIP REINFORCEMENT BY BRIDGING ELEMENTS - MODELING THE FRACTURE OF THE MATRIX MATERIAL

There is a wide range of physical situations where the faces of a crack in a matrix material with limited ductility are restrained from opening, a phenomenon known as crack reinforcement. In quantifying this phenomenon, the simplest way of modelling the behaviour of the matrix material ahead of a crack tip is to assume that it deforms in accord with the laws of linear elasticity with the crack extending when the stress intensity at the crack tip (the leading edge of the restraining region) attains a critical value, KIC, the fracture toughness of the matrix material; i.e. the details of the matrix deformation and fracture behaviour are ignored. The viability of this K-matrix assumption is examined for the case of a semi-infinite crack in a remotely loaded infinite solid, for which the restraining stress between the crack faces increases linearly with crack opening until the attainment of a critical opening when the restraining stress falls to zero. The analysis defines the range of material parameters for which the K-matrix assumption is adequate with regard to the determination of (a) the "applied" value of K required for the crack tip and restraining zone to propagate through the solid, and (b) the size of the restraining zone when propagation occurs. The K-matrix assumption always gives an overestimate of the applied K, but the overestimation is small when the matrix toughness contribution is small or is dominant. However, when the contributions from the matrix toughness and the toughness provided by the restraining material are roughly equivalent, the K-matrix assumption leads to a significant overestimate of the applied K, and in this situation the matrix material behaviour should be modelled more precisely. © 1990 Chapman and Hall Ltd.