Microstructure-sensitive extreme-value probabilities of high-cycle fatigue for surface vs. subsurface crack formation in duplex Ti–6Al–4V

The distributions of the extreme-value driving force(s) for surface vs. subsurface fatigue crack formation (nucleation and early growth) in high-cycle fatigue are evaluated for a microstructure variant of duplex Ti–6Al–4V. In polycrystalline metals, previous work has explored estimation of the driving force(s) for fatigue crack formation at the scale of the grains by computing non-local fatigue indicator parameters (FIPs) based on the cyclic plastic strain averaged over domains on the length scale of the grains. Instantiated statistical volume elements (SVEs), which sample the distributed microstructure attributes of interest for a given material system, can be simulated via the finite element method with embedded polycrystalline plasticity models to estimate the distributed plasticity and resulting FIPs. This strategy of simulating multiple SVEs is in contrast to the simulation of a single representative volume element which is typically untenably large for extreme-value distributions of microstructure attributes or response variables. In this work, multiple SVEs are instantiated with both traction-free (i.e. surface) boundary conditions and fully periodic (i.e. subsurface) boundary conditions. In addition to estimating the extreme-value distributions of the FIPs, newly introduced extreme-value marked correlation functions are applied to characterize the coupled crystallographic microstructure attributes (e.g. grain size, grain orientation, grain misorientation) that most influence the extreme-value distributions of the FIPs. It is shown that there is overlap in the distributions of the driving forces for surface vs. subsurface crack formation in the low to moderate range of failure probability based on FIPs; however, at higher failure probability levels, the driving forces are highest for surface crack formation. The overlap in the distributions of the driving forces for fatigue crack formation in the low to moderate probability range may assist in describing the competing surface vs. subsurface failure modes that are observed experimentally.