Mechanistic cohesive zone laws for fatigue cracks: Nonlinear field projection and in situ synchrotron X-ray diffraction (S-XRD) measurements

A weak interface model with a predefined traction-separation relationship (denoted as the cohesive zone law), when embedded in a bulk solid, is oftentimes adopted to simulate the crack advancement and thus determine the crack resistance under either monotonic or cyclic loading conditions. To-date, various types of loading-unloading irreversibility and hysteresis are only presumed in the cohesive zone law for fatigue crack growth, but without any direct determination from experimental measurements. Using a fine-grained Mg alloy and synchrotron X-ray diffraction (S-XRD) measurements with a sub-millimeter beam, in situ lattice strain mapping can be obtained with the needed resolution to cover both the “messy” process zone as modeled by the cohesive zone law and the “clean” process zone caused by plastic deformation. We extend our previously developed nonlinear field projection method, and create trial elastic fields from the S-XRD-measured elastic strain fields at different loading levels when choosing the fully unloaded state as the new reference. From the Maxwell-Betti's reciprocal theorem, we reconstruct a mechanistic cohesive zone law for fatigue cracks, where the reciprocity gap is governed by the residual stress field at the fully unloaded state. Combining our inverse approach with S-XRD measurements, it is discovered that the fatigue-crack cohesive zone exhibits a bilinear unloading and reloading behavior that is distinctively different than all prior works. This particular form suggests the origin of irreversibility be primarily from crack-surface oxidation and the hysteresis from dislocation plasticity in surrounding grains.