An analytical stress field for bi-material V-notches with end hole: New solution and effects of higher order terms

Abstract

Current manuscript develops an analytical stress solution for the bi-material V-notches with an end hole (VO). To do so, based on the Kolosov-Muskhelishvili’s approach, while appropriate potential functions are employed, the boundary conditions of the problem are imposed to the solution to reduce the number of unknown parameters. Subsequently, the analytical stress field is derived as an asymptotic series solution, where each term possessing a constant coefficient and an order of singularity. The order of singularity for each term is obtained from the characteristic equations of the problem which is dependent on the notch geometry and material combinations. The so-called least square method (LSM) is then used to compute the constant coefficients of the asymptotic series for several case studies. Special attention is given to the bi-material notch stress intensity factors (BNSIFs) and the coefficients of the higher order terms (HOTs) in the stress series expansion. The accuracy of the presented stress solution is verified by benchmarking the results with numerical values obtained from finite element (FE) method. In this process, several notch opening angles and notch radii are simulated using the three-point bend (3PB) specimen. The developed asymptotic stress solution is demonstrated to be capable of accurately evaluating the stress field around bi-material VO-notched structures.