A Nonconformal Nonlocal Approach to Calculating Statistical Spread in Fatigue Indicator Parameters for Polycrystals

Abstract

In the study of fatigue fracture in metals, fatigue indicator parameters (FIPs) are nonlocal quantities that are used to model and predict the driving force needed to incubate fatigue cracks. These FIP values can be used to design materials with microstructural features less prone to fatigue failure. However, the nonlocal nature of fatigue indicator parameters introduces another unknown variable that must be determined for accurate predictions: the volume over which nonlocal averages are performed. Many studies use nonlocal volumes that enclose a predetermined number of finite elements in a polygranular crystal plasticity simulation. To encapsulate the entire microstructure, these nonlocal volumes must be conformal to the microstructure (i.e., they do not overlap or have gaps between them). Some studies base the length scale of these nonlocal volumes on constant values or on the size of relevant microstructural features. It has been shown that if the length scale is too small, the nonlocal FIP predictions are mesh dependent. But, if the length scale is too large, the experimentally observed statistical spread in fatigue life is not captured. This work introduces a nonconformal nonlocal volume (i.e., a volume that surrounds each element and overlaps nonlocal volumes). Averaging FIP over this nonlocal volume both captures the spread in fatigue data and is mesh independent. It also allows for weighted nonlocal averages that would have excluded some of the microstructure using the conformal approach. While this approach is more accurate than the previous approaches, it does require a large amount of computational resources to determine each nonlocal volume, so a parallelized algorithm that is scalable across multiple computing nodes is employed. The example polycrystalline material for this work is Ti-6Al-4V, a common titanium alloy with a hexagonal closed-packed crystal structure.