On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface

Abstract

The plane problem of a crack that terminates at the interface of a bimaterial composite and is loaded on its faces is treated within the two-dimensional theory of elastostatics. The emphasis is placed on determining how the order of the singularity in the stress field at the crack tip depends on the material constants and the angle at which the crack meets the interface. Numerical results are presented through figures showing this dependence on the material parameters for several fixed angles. It is then shown by way of examples how to use these figures to obtain the dependence on the angle for any desired composite. For the two examples chosen, it is found that when the crack is in the weaker constituent the stress singularity is most severe if the crack is tangent to (lies in) the interface; whereas, when the crack is in the stronger constituent a particular angle is associated with the most severe stress singularity for each composite.