Regularization of Hole-Drilling Residual Stress Measurements with Eccentric Holes: An Approach with Influence Functions

The hole-drilling method is one of the most widespread techniques to measure residual stresses. Since the introduction of the Integral Method to evaluate non-uniform stress distributions, there has been a considerable improvement in the instrumentation technology, as step increments of about 10 microns are now achievable. However, that spatial resolution makes the ill-posedness of the problem stand out among other sources of uncertainty. As the solution becomes totally dominated by noise, an additional regularization of the problem is needed to obtain meaningful results. Tikhonov regularization is the most common option, as it is also prescribed by the hole-drilling ASTM E837 standard, but it has only been studied in the reference case of a hole with no eccentricity with respect to the strain rosette. A recent work by Schajer addresses the eccentricity problem by defining a correction strategy that transforms strain measurements, allowing one to obtain the solution with the usual decoupled equations. In this work, Tikhonov regularization is applied to the eccentric hole case through the influence functions approach, in order to avoid the introduction of new error-compensating functions and bias-prone interpolations. Some useful general considerations for a practical implementation of the procedure and an experimental test case on an aluminum specimen are presented.