New method for evaluation of the Manson–Coffin–Basquin and Ramberg–Osgood equations with respect to compatibility

Abstract In the modern description of the fatigue behaviour of materials the stress–strain curve, described with Ramberg–Osgood equation, and the strain–life curve, described with Manson–Coffin–Basquin equation, are typically used. It is known that the assumption of equality of the plastic and elastic components in both equations leads to the so-called compatibility condition and connect the equations theoretically. The conventional method for evaluation of the fatigue parameters use one set of experimental data from strain-controlled uni-axial fatigue tests but they not ensure the compatibility conditions. The presented new method for determining the stress–strain and strain–life curves retains the mathematical and physical relationships between the considered curves. The method involves fitting the curve to experimental data points in a three-dimensional strain–stress–life space. With the plastic part of strain, stress and fatigue life as coordinates, a straight line is used for fitting the experimental data points. The material parameters are calculated directly from projections of the three-dimensional straight line on suitable planes. The results obtained from this new method using high-strength aluminium alloys subjected to different manufacturing conditions and different test temperatures are presented. These results are then compared to results obtained with a conventional method for determining the fatigue parameters.