Combining Thermoelastic and Stress Function Data to Evaluate Individual Stresses Around a Near-Edge Hole

Abstract

The individual stresses are determined on and near the edge of a hole immediately beneath but close to a concentrated edge load in an approximate half-plane. Experimental thermoelastic data is combined with Airy’s stress functions to achieve this. Two approaches are utilized, both involving a series representation of the stress function. Coefficients of the respective stress functions are evaluated from measured temperature information. One of the stress functions utilizes real variables and the traction-free conditions on the hole boundary are satisfied by imposing σr = τrθ = 0 on the edge of the hole for all values of the angle θ, see Lin et. al. [1,2]. This advantageously enables one to reduce the number of coefficients in the stress function series. The second concept, which employs a complex variable representation of the stress function and mapping techniques, satisfies the traction-free conditions on the edge of the hole by analytic continuation. Although the second approach is very effective it tends to be most convenient for evaluating stresses on, and reasonably close to, the edge of a geometric discontinuity. Moreover, since it also only provides stresses throughout a finite region and along only a portion of the entire edge of the hole, the scheme has to be repeated to determine stresses around the entire hole. On the other hand, the real variable representation of the stress function enables the individual components on and near the entire hole boundary to be evaluated in a single operation. Both methods simultaneously smooth the measured input data, satisfy the traction-free boundary conditions, and evaluate individual stresses on, and in the neighborhood of, the edge of the hole.