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This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding the effects of stress amplitude, R -ratio, and microstructure on fatigue crack formation and early growth at notches, including pores and non-metallic inclusions for Ti alloys and Ni-base superalloys. The simulations employ fatigue indicator parameters (FIPs) computed over finite volumes that relate to processes of fatigue crack formation and early growth at the scale of individual grains. It is argued that both coarse scale (uncracked, mesoscale) and fine scale FIPs (computed in the vicinity of cracks in single grains or crystals) serve as a driving force for crystallographic fatigue crack growth, and correlate directly with the cyclic crack tip displacement (CTD). Furthermore, variability in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) responses is computationally assessed using multiple statistical volume elements and the distribution of FIPs of extreme value character. The concepts of marked correlation functions and weighted probability density functions are reviewed as a means to quantify the role of multiple microstructure attributes that couple to enhance the extreme value FIPs in the HCF regime. An algorithm for estimation of the cumulative probability distribution of cycles for crack formation and growth from notches in HCF and VHCF is also described.

Strategies are described for microstructure-sensitive computational methods for estimating variability of high cycle fatigue (HCF) crack formation and early growth in metallic polycrystals to support design of fatigue resistant alloys. We outline a philosophy of employing computational simulation to establish relations between remote loading conditions and microstructure-scale slip behavior in terms of Fatigue Indicator Parameters (FIPs) as a function of stress amplitude, stress state and microstructure, featuring calibration of mean experimental responses for known microstructures. Effects of process history (carburization and shot peening) and resulting residual stresses are considered in the case of subsurface crack formation at primary inclusions in martensitic gear steel. The need to characterize extreme value correlations of microstructure attributes coupled to the local driving force (i.e., features) for HCF crack formation is outlined, along with a strategy involving a set of FIPs relevant to different mechanisms of crack formation. Surface to subsurface transitions are considered in terms of competing mechanisms in the transition from HCF to very high cycle fatigue (VHCF) regimes.