Merging Data with Modeling: An Example from Fatigue

It is well known that errors are inevitable in experimental observations, but it is equally unavoidable to eliminate errors in modeling the process leading to the experimental observations. If estimation and prediction are to be done with reasonable accuracy, the accumulated errors must be adequately managed. Research in fatigue is challenging because modeling can be quite complex. Furthermore, experimentation is time-consuming, which frequently yields limited data. Both of these exacerbate the magnitude of the potential error. The purpose of this paper is to demonstrate a procedure that combines modeling with independent experimental data to improve the estimation of the cumulative distribution function (cdf) for fatigue life. Subsequently, the effect of intrinsic error will be minimized. Herein, a simplified fatigue crack growth modeling is used. The data considered are a well-known collection of fatigue lives for an aluminum alloy. For lower applied stresses, the fatigue lives can range over an order of magnitude and up to 107 cycles. For larger applied stresses, the scatter in the lives is considerably reduced. Consequently, modeling must encompass a variety of conditions. The primary conclusion of the effort is that merging independent experimental data with a reasonably acceptable model vastly improves the accuracy of the calibrated cdfs for fatigue life, given the loading conditions. This allows for improved life estimation and prediction. For the aluminum data, the calibrated cdfs are shown to be quite good by using statistical goodness-of-fit tests, stress-life (S-N) analysis, and confidence bounds estimated using the mean square error (MSE) method. A short investigation into the effect of sample size is also included. Thus, the proposed methodology is warranted.