CRACK-TIP INTERPOLATION, REVISITED

It is well known that the near tip displacement field on a crack surfa ce can be represented in a power series in the variable root r, where r is the distance to the tip. It is shown herein that the coefficients of the linear terms on the two sides of the crack are equal. Equivale ntly, the linear term in the crack opening displacement vanishes. The proof is a completely general argument, valid for an arbitrary (e.g., multiple, nonplanar) crack configuration and applied boundary conditio ns. Moreover, the argument holds for other equations, such as Laplace. A limit procedure for calculating the surface stress in the form of a hypersingular boundary integral equation is employed to enforce the b oundary conditions along the crack faces. Evaluation of the finite sur face stress and examination of potentially singular terms lead to the result. Inclusion of this constraint in numerical calculations should result in a more accurate approximation of the displacement and stress fields in the tip region, and thus a more accurate evaluation of stre ss intensity factors.