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.