A Semi-analytical Model of Maximal First Principal Stress at Mode I Crack Tip

Abstract

The first principal stress plays a key role in ductile fracture processes. Investigation of the distribution and evolution of the first principal stress at the crack tip is essential for exploring elastoplastic fracture behaviors. A semi-analytical model was developed in this study to determine the maximal first principal stress at the mode I crack tip with 3D constraints for materials following the Ramberg–Osgood law. The model, based on energy density equivalence and dimensional analysis, was validated through finite element analysis (FEA) of various materials and geometric dimensions of specimens with mode I cracks, under over 100 different types of working conditions. The dimensionless curves of maximal first principal stress versus load, as predicted by the model, agreed well with the FEA results, demonstrating the accuracy and applicability of the model. This research can provide a basis for future theoretical predictions of crack initiation and propagation.