Two-way multi-scaling for predicting fatigue crack nucleation in titanium alloys using parametrically homogenized constitutive models

Abstract

This paper develops a two-way (bottom-up or hierarchical and top-down) multi-scale modeling framework for predicting fatigue crack nucleation in structural components of Titanium alloys, e.g. Ti-7Al. Pure micromechanical analyses are deficient in this regard. A parametrically homogenized constitutive model (PHCM) and a parametrically homogenized crack nucleation model (PHCNM) are developed from computational homogenization of crystal plasticity finite element (CPFE) simulation results performed on microstructural statistically equivalent RVEs or M-SERVEs. Image-based CPFE of the M-SERVEs predict time-dependent plastic deformation, as well as location and time-dependent fatigue crack nucleation in the microstructure. Micromechanical analysis data is utilized by a machine learning code to derive functional forms of PHCM and PHCNM coefficients. Macroscopic FE models for Ti-7Al test specimens are created next, by matching correlation functions of the micro-texture and other microstructural variabilities in EBSD scans. Macroscopic simulations of dwell and cyclic loading are performed and nucleation hotspots are identified by PHCNM. Top-down simulations of the local M-SERVEs are then used to probe microstructural fatigue crack nucleation sites and cycles. The multi-scale simulations predict sub-surface nucleation for a majority of dwell cracks, which is corroborated by fractography images. The computed nucleation cycles and spatial distributions across a range of loading conditions follow experimentally observed characteristics of dwell effect in Ti alloys.