Stress intensity factors in elastic plates with re-entrant corners asymmetrically loaded

Abstract

The method of reflected caustics was extended to evaluate the complex stress intensity factors at the roots of re-entrant corners in elastic plates under generalized plane-stress conditions. The plates were considered loaded under a general mode of loading creating asymmetric stress states at the corners and, thus, engendering complex stress intensity factors at these zones.

For the evaluation of the complex stress intensity factors the coordinates of at least two points on the caustics are necessary whose polar coordinates on the respective initial curves on the specimen are defined in advance. These experimental data must be introduced into a system of six equations, four of which are linear and the remaining two non-linear. The solution of this system yields the components of the complex stress intensity factors with a high accuracy, independently of the form and shape of the caustics developed around the roots of the corners. This high accuracy was achieved among others by the fact that two terms in the asymptotic expansion of Muskhelishvili's complex stress function Φ(z) are taken into consideration for the evaluation of stress intensity factors.

The method was applied first to a symmetric notch whose theoretical solution is known, so that the accuracy of the method could be checked, and afterwards to an asymmetrically loaded notch whose theoretical solution does not exist. For this case a recurrent procedure was applied for checking the accuracy of the experimental results.