Elastic–plastic stress investigation for an arc-shaped interface crack in composite material

Abstract

Abstract The plastic zone size and crack tip opening displacement have been investigated for a curved interface crack between a circular inclusion and an infinite matrix. The mixed-mode Dugdale model is used to study the plastic deformation where the stresses in the plastic zones satisfy the Von Mises yield criterion. The plastic zone size at the crack tip is calculated by satisfying the condition that the complex stress intensity factors induced by external load and those induced by closure stress cancel off. With the distributed dislocation method, the physical problem is formulated into a set of singular integral equations which are numerically solved by using Jacobi polynomials. The influence of the material properties and other geometric parameters on the stress intensity factors (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) is discussed in detail. The numerical examples show that both the crack debonding angle and the inclusion/matrix shear modulus ratio have significant influence on the normalized values of SIF, PZS and CTOD. The normalized PZS reaches its maximum value when the crack debonding angle is 90°. The effect of shear modulus ratio is very significant when the inclusion is “softer” than the matrix. When the inclusion is much “stiffer” than the matrix, the inclusion plays a dominant role. Changing the shear modulus ratio does not have great influence on the plastic deformation ahead the crack tips.