Analytical approach and numerical simulation to investigate the stress field and the dynamic stress intensity factors of a cracked tooth subjected to a periodic loading

Abstract

A new analytical approach was developed in this paper to study the dynamic analysis of a cracked gear tooth subjected to a periodic loading. The finite elements method (FEM) based on the contour integral technique was used in order to validate the effectiveness and reliability of the analytical formulation. A three-dimensional (3D) model of a cracked tooth was designed where a refined mesh was applied in the crack region to better simulate the stress concentration. The main objective of this study was to investigate the influence of the crack depth and the external load on the variation of the stress intensity factors (SIF) KI and KII associated with the opening crack modes I and II, respectively, and on the stress field near the crack tip. The obtained results show a significant agreement between the analytical results and the FEM findings.