Three‐dimensional stress fields due to notches in plates under linear elastic and elastic–plastic conditions

Abstract

AbstractThe paper deals with a 3D multi‐parametric stress field representation ahead of notches in plates of finite thickness under different loading conditions. Under certain hypotheses, the 3D governing equations of elasticity can be reduced to a system where a bi‐harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out‐of‐plane shear notch problem. The solution is valid close the notch edge, through the plate thickness, with exclusion of a very limited zone close to the free surface of the plates. Also, under elastic–plastic conditions there are circumstances where it is possible to separate the in‐plane problem from the out‐of‐plane problem. A new analytical frame is proposed, and the results are compared with those obtained from 3D finite element models of a plate with a square notch. In the presence of remote applied tensile stress, the slope of the induced, out‐of‐plane, shear stress component matches that of the mode III plastic problem.