Evaluation of various analytical weight function methods base on exact K-solutions of an edge-cracked circular disc

Weight function method is a powerful tool for the determination of key parameters such as stress intensity factors and crack opening displacements for cracks in complicated stress fields. Accurate determination of the weight functions is of primary importance for successful applications of the method. This paper makes detailed accuracy evaluation of two kinds of widely used approximate (2D) weight function approaches, one being based on crack opening displacement for one reference stress, the other on two reference stresses coupled with a geometric condition. To eliminate possible sources of error, the edge-cracked circular disc with exact K-solutions is used for deriving the two kinds of weight functions and for benchmarking against the two weight function approaches. A highly accurate numerical weight function method using the complex Taylor series expansion and complex finite element computation is also used for assessing the related Green's functions. Results from the evaluation will be instructive for accurate determination of weight functions for other finite edge-crack geometries.