Modeling the statistical distribution of fatigue crack formation lifetime in large volumes of polycrystalline microstructures

Microstructure-scale interactions involving crystallographic texture (orientation and disorientation distributions), distributions of grain shape and size, nearest neighbor grains/phases, etc. in polycrystals can be simulated using the Crystal Plasticity Finite Element Method (CPFEM). Digital statistical volume element (SVE) instantiations that comprise a significant number of grains are analyzed by CPFEM to compute fatigue indicator parameters (FIPs) which are used as surrogate measures of the driving force for fatigue crack formation within the first grain or nucleant phase. The computed maximum FIPs usually increase in magnitude with larger numbers of realistic microstructure instantiations or SVEs analyzed. This work predicts the extreme value distribution (EVD) of the maximum FIPs associated with large engineering components comprised of up to 10 ⁸ SVEs using a recently developed upscaling scheme, based on statistical information identified from simulations involving only hundreds of SVEs, with each SVE containing nominally 264 grains. This scheme is numerically validated by extensive simulations for samples of duplex Ti-6Al-4V microstructure models with sharp transverse texture strained in two characteristic directions. The size of the training dataset for a reliable prediction is determined for different textures and loading directions based on uncertainty analysis. Finally, the statistical distribution of fatigue crack formation lifetime (FCFL) is correlated with the EVD of the maximum FIPs, facilitating quantitative exploration of the effect of crystallographic texture and sample size on the FCFL.