Abandoning the Notion of Measured Stress as a Point Quantity to Remove "Unknowable" Bias in Residual Stress Inverse Solutions

Although it is not always recognized, almost all residuals stress measurement methods require an inverse solution to analyze the data, and inverse solutions suffer from a bias-variance tradeoff. The bias is mathematically “unknowable” and often at least the same magnitude as the variance. Therefore, and unfortunately, just the variance is often reported as the total uncertainty, but it significantly underestimates the true total uncertainty. Beghini and Grossi recently proposed an ingenious method to spatially average a low-bias high-variance inverse solution to get an accurate uncertainty without noisy results. In this talk, their method is checked on the incremental slitting method using various data sets to show that, indeed, the bias is avoided and the uncertainty is accurate. The implications of stress measurements being averaged over some volume, rather than defined at a point, are examined. In most cases, the effects of residual stress are an integral effect over some volume anyways, so the implications are minimal. The payoff of an accurate uncertainty is extremely beneficial.