The Weight Function Method for Determining Stress Intensity Factors

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Abstract
An alternate method to those of Bueckner and Rice is presented for the derivation of the two-dimensional weight function for determining crack tip stress intensity factors. The weight function has r−1|2 type displacement singularity at the crack tip. It is shown that this singular field can be formulated using Westergaard stress functions in a manner similar to the method used for r1⊢2 type fields in crack tip displacements. A straight-forward approach for obtaining weight functions for cracked finite bodies is presented. This technique can be combined in a simple fashion with the finite element method. As an example, a weight function for the SEN strip is obtained in this manner. Moreover, closed form infinite body weight functions are also developed and used to derive some well-known stress intensity factor formulas.

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