When do corners behave like cracks in lap-shear geometries?

Abstract

A cohesive-zone analysis is used to explore the question of whether a crack is needed to determine the toughness of an interface using a lap-shear geometry. The analysis shows that, if the cohesive-length scale is large enough, the work done against tractions at the corner of a bonded ligament is identical to what would be given by the J-integral for the same geometry with a crack at the interface. This means that the lap-shear strength is insensitive to the details of the corner under the appropriate conditions. From a practical perspective, this means that one may not have to introduce a flaw into the interface when using a lap-shear geometry to measure the toughness of an interface. Furthermore, it has been shown that, for the special case of a symmetrical lap-shear geometry and a large cohesive-length scale, the partition of the work done against the corner tractions into shear and normal components is independent of geometry. This is probably a general result, although the large-scale phase angle for a crack is different from the LEFM value.If the cohesive-length scale is small, the details of the corner become very important. The corner work depends on both the corner angle and the cohesive-length scale. A dimensional argument suggests that the relationship between the corner work and the cohesive length depends on the singularity of the elastic stress field. The concept of a critical stress-intensity factor modified for corners, Kc, is valid, but it must incorporate the cohesive length of the interface to relate it to the material property of toughness. However, Kc cannot be considered to be an interface property in itself, because it is linked to the toughness by the geometry of the corner. In the special case of a crack, Kc is independent of the cohesive-length scale. Conversely, in the continuum limit, where the cohesive length goes to zero, Kc→∞ for all geometries other than a crack.