Resolving the fundamentals of the -integral concept by multi-method in situ nanoscale stress-strain mapping.

The integrity of structural materials is oftentimes defined by their resistance against catastrophic failure through dissipative plastic processes at the crack tip, commonly quantified by the -integral concept. However, to date the experimental stress and strain fields necessary to quantify the -integral associated with local crack propagation in its original integral form were inaccessible. Here, we present a multi-method nanoscale strain- and stress-mapping surrounding a growing crack tip in two identical miniaturized fracture specimens made from a nanocrystalline FeCrMnNiCo high-entropy alloy. The respective samples were tested in situ in a scanning electron microscope and a synchrotron X-ray nanodiffraction setup, with detailed analyzes of loading states during elastic loading, crack tip blunting and general yielding, corroborated by a detailed elastic-plastic finite element model. This complementary in situ methodology uniquely enabled a detailed quantification of the -integral along different integration paths from experimental nanoscale stress and strain fields. We find that conventional linear-elastic and elastic-plastic models, typically used to interpret fracture phenomena, have limited applicability at micron to nanoscale distances from propagating cracks. This for the first time unravels a limit to the path-independence of the -integral, which has significant implications in the development and assessment of modern damage-tolerant materials and microstructures.