Microstructure-sensitive HCF and VHCF simulations

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.