Global and local approaches to fracture normal to interfaces

Abstract

The problem of a crack perpendicularly approaching a bimaterial interface is examined using both global and localapproaches to fracture. The global approach is based on the J-integral with a second parameter, Q, which scales the stress triaxiality ahead of the crack. The local approach is based on either brittle fracture(Beremin model ) or ductile fracture (Rice and Tracey model ). In the first case, the Weibull stress over the plasticzone is calculated. In the second case, the void growth rate is calculated at the tip of the crack over a representativevolume (generally associated with a characteristic length of the material ). After a brief summary of each approach,the results for a crack near an elastically homogeneous, plastically mismatched interface are presented. Thebehaviour of the bimaterial is expressed in relation to the behavior of the homogeneous material. It is shown thatthere is an effect on the crack behavior which depends on the direction of crack propagation, i.e. from the hardermaterial to the softer material or vice versa. This effect is examined as a function of change in yield strength ratioand hardening exponent, n. For the case of brittle fracture, the effect of changing the Weibull modulus, m, is also examined. The models based on the local approach show that both stress- and strain-controlledfracture mechanisms must be accounted for. This implies the necessity of using the two parameters J and Q in the global approach. This is due to the fact that the stress–strain fields ahead of the crack tip areaffected by the nature of the second material.