Homogenized constitutive and fatigue nucleation models from crystal plasticity FE simulations of Ti alloys, Part 2: Macroscopic probabilistic crack nucleation model

This is the second of a two-part paper aimed at the developing macroscopic models of fatigue deformation and failure in polycrystalline Ti alloys. In this part, a probabilistic crack nucleation model is developed for predicting damage nucleation in macroscopic computations of the structural components from rigorous microscopic analyzes. Inputs to this model include morphological characteristics of the microstructure at any material point along with the local stress/strain state. This stress-state, needed to trigger this model, can be obtained from finite element analysis using the homogenized, anisotropic plasticity constitutive (HAPC) model developed in part 1 (). A deterministic functional form, relating time for macroscopic crack nucleation to the macroscopic stress state and microstructural characteristic parameters, is derived from rigorous crystal plasticity FE simulations of representative volume element of a bi-crystal system that implements a physics-based grain level crack nucleation model. Subsequently, a probabilistic model for expected crack nucleation in the macroscopic (structural) scale is generated from this functional form. The probabilistic model has a direct connection to the mechanisms of microstructural crack nucleation and can be obtained from macroscopic FE analysis with knowledge of statistics of the local microstructure.