Simulated extreme value fatigue sensitivity to inclusions and pores in martensitic gear steels

The objective of this work is to model the sensitivity of high cycle fatigue resistance of secondary hardening martensitic gear steels to variability in extrinsic inhomogeneities such as primary inclusions, and pores, coupled with intrinsic microstructure variability. A simplified approach is presented to quantify the variability in the driving force for fatigue crack formation in the matrix at non-metallic inclusions and pores in lath martensitic gear steels using a three-dimensional crystal plasticity constitutive model. The utility of a simulation-based strategy for exploring sensitivity of minimum fatigue lifetime (low probability of failure) to microstructure lies in its inherent capability to consider parametric simulations of hundreds of inclusions and microstructures in contrast to limited numbers of physical experiments. Experiments are used to calibrate the polycrystalline cyclic stress–strain response and mean (50% probability) fatigue crack formation life. Several remote loading conditions are considered in the high cycle fatigue (HCF) regime relevant to typical gear applications. Idealized inhomogenieties (spherical) in the form of hard (Al2O3), soft inclusions (La2O2S), and pores are systematically investigated in this parametric computational study. Relations between remote loading conditions and local plasticity are discussed as a function of stress amplitude and microstructure. The maximum plastic shear strain range is used in the modified form of Fatemi–Socie parameter evaluated at the grain scale as a measure of the driving force for fatigue crack formation (nucleation and early growth to lengths on the order of several times the average grain size). Multiple realizations of the polycrystal microstructure are considered to obtain a statistical distribution of this fatigue indicator parameter (FIP). The results are used to construct an extreme value Gumbel distribution of the FIPs for the selected microstructures. Subsequently, a computational micromechanics based minimum life estimate that corresponds to 1% fatigue crack formation probability is calculated.