Customized weight function for cracks initiated from semi-circular notches

A new weight function is analytically derived for calculating the stress intensity factor of a crack initiated from a semi-circular notch root. This function is dependent on crack size and notch radius and independent from loading condition. The employed method is based on the solution of the weight function for an edge crack. A proper modification factor is applied to considering the effect of the notch and crack geometry on the weight function of the edge crack. It is initially assumed that the notch is a part of the crack. This assumption is used in an analytical method to obtain accurate solution for the weight function. The modification factor is obtained in terms of dimensionless parameters for the ease of application. The provided weight function is examined for different geometries under different loading conditions, and the results are compared with finite element solutions. The weight function is found accurate and reliable. Accuracy is not altered by crack size, notch geometry, and loading conditions. Therefore, the weight function can be used to study the different stages of the initiation and growth of short and large cracks with suitable accuracy.