Multi-scale Curvature Analysis and Correlations with the Fatigue Limit on Steel Surfaces after Milling

A strong correlation (R2 >0.96) is found between machined surfaces and their fatigue limits. In a larger study, the four- point bending fatigue limit was determined on steel specimens milled with two different conditions, in two directions, with and without residual stresses relieved. Curvature analysis is shown here, based on Heron's formula, as a function of scale and position, on profiles extracted parallel to the direction of maximum tensile stress, from areal texture measurements. Several combinations of parameters are regressed linearly with the fatigue limits over a range of scales. The strongest correlations are found with the mean curvature plus two standard deviations, at a scale of 610 μm. The correlation varies smoothly, although not monotonously, with respect to decreasing scale, with R2 falling to zero at 100 μm.