Evaluation of distribution of fatigue lives of the extruded magnesium alloy AZ61

In this study, fatigue tests were carried out to study the distribution of fatigue lives of the extruded Mg alloy AZ61 under constant stress amplitudes. The scattering in the distribution of fatigue lives becomes larger at lower stress amplitudes compared to higher stress amplitudes. During the fatigue process of the alloy, it was observed that cracks initiated from inclusions existing on the specimen surface, then propagated, and finally led to the final failure of the specimen. Statistical distributions of both densities and areas (sizes) of the inclusions were experimentally investigated in detail and were approximated by Weibull distributions. In addition, the distribution of ${{A}_{\rm max}^{1/2}}$ , the square root of the maximum inclusion areas within a division of 0.75 mm², was also investigated. The experimental data were approximated well by the extreme-value distribution. The distributions of the fatigue lives of the extruded Mg alloy were evaluated using both Monte-Carlo simulation and surface fatigue crack propagation behaviour. In the simulation, the random numbers corresponding to the above statistical distributions of the inclusions, i.e., densities, areas, and square root of the maximum inclusion areas were utilized. The evaluated distribution of the fatigue lives corresponded well with the experimental one. It was concluded that for the evaluation of the distribution of fatigue lives, employing the extreme-value distribution of the inclusions is recommended because of convenience and accuracy of the method.