Uncertainty Quantification for Microstructure-Sensitive Fatigue Nucleation and Application to Titanium Alloy, Ti6242

Abstract

Microstructure of polycrystalline materials has profound effects on fatigue crack initiation, and the inherent randomness in the material microstructure results in significant variability in fatigue life. This study investigates the effect of microstructural features on fatigue nucleation life of a polycrystalline material using an uncertainty quantification framework. Statistical volume elements (SVE) are constructed, where features are described as probability distributions and sampled using the Monte Carlo method. The concept of SVE serves as the tool for capturing the variability of microstructural features and consequent uncertainty in fatigue behavior. The response of each SVE under fatigue loading is predicted by the sparse dislocation density informed eigenstrain based reduced order homogenization model with high computational efficiency, and is further linked to the fatigue nucleation life through a fatigue indicator parameter (FIP). The aggregated FIP and its evolution are captured using a probabilistic description, and evolve as a function of time. The probability of fatigue nucleation is measured as the probability that the predicted FIP exceeds the local critical value which represents the ability of material to resist the fatigue load. The proposed framework is implemented and validated using the fatigue response of titanium alloy, Ti-6Al-2Sn-4Zr-2Mo (Ti-6242).