Stress Distribution in Bonded Dissimilar Materials With Cracks

The problem of two bonded dissimilar semi-infinite planes containing cracks along the bond is reconsidered. The external loads considered include the tractions on the crack surfaces, in-plane moments, residual stresses due to temperature changes, concentrated load and couple acting at an arbitrary location in the plane, and one-sided wedge loading of the crack. The stresses along the bonds are calculated and shown in graphs. In the example of wedge loading, the stress state and displacements in the vicinity of the crack tip are more closely studied; and the bonding stress σ and the relative displacement v1 − v2 along the crack are plotted as functions of log(r/a). It was found that, even though the stresses and displacements oscillate as r approaches zero, for the example of glass-steel bond the first zero of σ occurs around (r/a) = 10−10.63, and at a distance (r/a) = 10−10 the stress-concentration factor has already exceeded 104. Similarly, the region within which relative displacements oscillate is 0 < (r/a) < 10−7, and the maximum value of interference becomes v2 − v1 = P10−9.7, P (lb/in.) being the wedge load. It was concluded that, considering the magnitudes of distances and stresses involved, in practical applications the phenomenon of stress oscillation, which seems to be a peculiar characteristic of mixed-boundary-value problems of linear infinitesimal elastostatics, may be ignored.