Microstructure-Sensitive HCF and VHCF Simulations (Preprint)

This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding 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. Fatigue indicator parameters (FIPs) are 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) can be related to the cyclic crack tip displacement that serves as a driving force for crystallographic fatigue crack growth, and that the fine scale FIPs correlate directly with cyclic crack tip displacement. Scatter in HCF and VHCF 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...