Plastic extension of a shear crack at a circular inclusion

The plastic relaxation of a shear crack situated normal to the interface of a second phase particle of circular cross-section is quantitatively analyzed. The ratio of applied stress to yield stress and the relative displacement of the crack faces at the tips of the crack in the matrix and the interface in the second phase are related to the crack parameters namely the length of the crack, the width of the plastic zone in the matrix and the second phase. The effect of the shear modulus and size of the second phase particle on the behaviour of the plastic zones is determined. A critical value of the relative displacement of the crack faces at the tip of the crack is used as the criterion to determine the tendency to brittle crack extension into the matrix and the second phase.