The exact form of caustics in mixed-mode fracture: A comparison with approximate solutions

Summary The form of caustics created by stress singularities in elastic problems was up-to-now derived from the Sneddon expressions for the components of stresses at the point of singularity, which are based on the first and singular term of the series expansion of the Muskhelishvili complex stress function. In this paper the closed from expression for the Muskhelishvili complex stress function (z) was used to define the exact form of the caustic. Moreover, the forms of the caustics were constructed for several terms, besides the first one, in the Taylor expansion of (z).The approximate forms with the singular term of (z) and several terms of the Taylor expansion of (z) were compared with the form derived from the exact solution. The discrepancies between exact and approximate solutions were evaluated for the case of a slant crack in an infinite plate under in-plane biaxial loading where theK_I andK_II-mode stress intensity factors were compared as derived from the various solutions. It was concluded that, although the method of caustics yields superior results than any other experimental method, it is possible to improve these results by using either the exact solution for the particular problem, or higher order approximations.With 11 Figures