Rapid and accurate semi-analytical method for the fatigue assessment with critical plane methods under non-proportional loading and material plasticity

Despite the substantial progress made over recent decades, fatigue assessment of structural components remains a challenge for designers, often culminating in unforeseen failures. Among the well established methods for evaluating fatigue, critical plane models have the capability of identifying the critical location and the direction of early crack propagation within a component. However, the use of the critical plane concept with the standard plane scanning method results extremely demanding when dealing with real-world scenarios, since, due to complex geometries, loading conditions and constraints, a comprehensive analysis of the part is required. In such situations, a more efficient computational method can be the discriminant to finalize a fatigue assessment. This study introduces a novel semi-analytical algorithm, which efficiently calculates critical plane factors. The algorithm was designed to be implemented alongside finite element analysis which may include elastic–plastic material behavior and non-proportional loading conditions. The method was tested on a notched component subjected to proportional and non-proportional loading conditions. As compared to the plane scanning method, the proposed method offers a time-efficient tool for evaluating critical plane factors and their associated plane orientations, with almost identical results.