Biaxial Fatigue Life Predicted by Crack Growth Analysis in Various Material Microstructures Modeled by Voronoi-Polygons

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Fatigue life is affected by the crack growth behavior that depends on the material microstructure as well as the stress biaxiality. By considering such effects on crack growth, a numerical procedure for predicting failure life in biaxial fatigue of materials with different microstructures was proposed in this study. Such a procedure will be helpful in the material design for higher performance of fatigue resistance in a material. The microstructure of a material was first modeled using Voronoi-polygons, and the crack initiation was analyzed as the result of slip-band formation in individual grains in the modeled microstructure. In the analysis, stress states in individual grains were randomized so that the average stress state should be equivalent to the bulk stress state. An algorithm for the crack growth analysis was established as a competition between the crack-coalescence growth and the propagation as a single crack. The failure life was statistically predicted based on the crack growth behavior simulated for 40 distinct microstructural configurations, which were generated by randomizing shapes of Voronoi-polygons for the same material. By applying the proposed procedure, simulations were conducted for experimental conditions of fatigue tests, which had been conducted under axial, torsional, and combined loading modes using circumferentially notched specimens of pure copper, medium carbon steel, and (α + β) and β titanium alloys. In this case, 40 different failure-lives were obtained for each combination of material and loading mode. It was revealed that the failure lives observed in experiments were almost covered by the life-ranges between the minimum and the maximum lives given in simulation. Statistical characteristics in simulated life-distributions were investigated using Weibull distribution function and its related statistical parameters.