Weibull stress solutions for 2-D cracks in elastic and elastic-plastic materials

The Weibull stress is widely used as a measure of the probability of cleavage failure. In this work analytical and semi-analytical expressions for the Weibull stress are developed in terms of the remote loading parameters, J or K, and material properties. Results are presented for sharp cracks and notches in elastic and elastic-plastic materials under plane stress and plane strain conditions. The proposed relations enable Weibull stress estimates to be obtained without the need for costly finite element analyses and provide insight into the use of the Weibull stress as a parameter for the prediction of cleavage failure of cracked bodies. The expressions have been verified using finite element techniques and good agreement has been found throughout. The results of the analyses have been used to interpret the mesh size dependence of Weibull stress values obtained from finite element calculations.