Method for efficient computation of stress intensity factors from weight functions by singular point elimination

Mode I stress intensity factor KI can be computed by integration of a function representing a stress profile (e.g., variation of stress with depth), modified by an appropriate weight function. Usually, numerical integration is required. However, widely used weight functions cause the end (s) of integration intervals to be singular points, complicating numerical integration. Approaches for computing KI that deal with singularities by approximating stress profiles by a linear function near a singular point, or transforming a weight function to a form that enables Gauss–Chebyshev integration, are reviewed. As an alternative to those approaches, this study presents a different method for numerical integration involving weight functions. First, a general, variable transformation method to eliminate singularities is introduced. Elimination of singular point enables elementary integration approaches such as Simpson’s rule, as well more involved methods, such as adaptive-Lobatto integration, to be applied. Benchmark tests using a variety of numerical integration formulas show the singular point elimination method to provide accurate, robust and computationally efficient integrations.