Fracture load prediction under mixed mode I + II using a stress based method for brittle materials tested with the asymmetric four-point bend specimen

Abstract Fracture load prediction for brittle cracked components under mixed mode tensile-shear loading is an essential task for integrity assessments and reliability analysis of structures containing flaws or cracks. Most of the available fracture criteria are usually derived based on the crack tip stress /strain fields that consider a limited terms of William’s infinite series expansion that are related to singular stress term ( K I and K II ), first non-singular stress term ( T -stress) and sometimes other higher order terms. However, an approach is proposed in this research for mixed mode fracture prediction that does not need direct determining the crack tip fracture parameters (i.e. the coefficients of the William’s series expansion) and instead takes into account the total tangential stress component in predicting the corresponding fracture load under any desired mode I/II mixity. For employing this simple model which is called “Tangential stress contour-TSC”, it is only required to obtain the contour of tangential stress component ahead of the crack tip via performing a numerical finite element analysis. Based on this model at the onset of fracture which corresponds to the critical fracture load of the cracked specimen the maximum tangential stress ( σ θθ ) at a critical distance r c from the crack tip becomes identical with the tensile strength ( σ t ) of the material. The TSC criterion was utilized for predicting the mixed mode I/II fracture loads of two rock materials (granite and marble) tested with the edge cracked asymmetric four-point bend (AFPB) specimen. It was demonstrated that the suggested TSC model can predict very well the fracture loads of tested materials for the whole mode mixities ranging from pure mode I to pure mode II.