Prediction of Crack Initiation Direction for Surface Flaws Under Biaxial Loading

This paper presents a simple method based on the strain energy density factor $ΔS$ to study the fatigue characteristics of rhombic plates with induced angled flaws under biaxial stress field. The paper discusses in detail the procedures followed to predict the fracture crack initiation angle, $θo,$ as a function of induced crack angle, β, the path of the crack trajectory at the initial stage of fracture and develop an expression for the crack growth rate. This method assumes that the crack extends in a radial direction and that the initial fracture crack angle, $θo,$ is obtained by maximizing the hoop stress along a circumference of a radius r. Expressions for the stress-state near the crack tip were developed for computing the crack trajectory and the strain energy density factor. The crack trajectory path was estimated by computing the new values of the crack angle and a fictitious crack length. These computed values were in turn used to determine the strain energy density factor. The developed method revealed two important observations: i) The crack trajectory was in close agreement with the experimental data for the first 20% of the lifetime to failure, ii) the crack propagation rate is dependent on the crack angle using the stress intensity factor and exhibited no variation with respect to the crack angle when the strain energy density factor is used.