When do corners behave like cracks in lap-shear geometries?. (15th October 2022) - Gorman, J.M.; Thouless, M.D.
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, K c, is valid, but it must incorporate the cohesive length of the interface to relate it to the material property of toughness. However, K c 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, K c is independent of the cohesive-length scale. Conversely, in the continuum limit, where the cohesive length goes to zero, K c → ∞ for all geometries other than a crack.