This is in-line with already published work in the literature. The tendency is that the plastic zone is smeared out (seen as less distinct features) when increasing the material rate sensitivity. In this way, the chosen benchmark problem for the new modeling framework serves as an extension to the conventional study of the corresponding problem without size effects presented in Juul et al. The focus is on the plastic zone shape and size, as well as its influence on the macroscopic fracture toughness. Subsequently, the modeling framework is demonstrated on Mode I steady-state crack growth in HCP single crystals, where the impact of size effects on the active plastic zone that surrounds the crack tip is investigated.
Details on the modeling framework are laid out, and the numerical challenges and stability issues are discussed. The model takes as offset the higher-order gradient plasticity theory by Kuroda and Tvergaard (J Mech Phys Solids 54:1789–1810 2006), and it is strongly inspired by an existing steady-state framework for conventional elastic–viscoplastic materials. Computational models and experiments to ascertain the range of validity of this theory are proposed.Ī new modeling framework for analyzing steady-state elastic–viscoplastic single crystal problems at micron scale is presented. Consequences of this theory are explored in the context of slow cleavage cracking, stress-assisted corrosion, fast running crack, fatigue crack growth, constraint effects, and mixed mode fracture along metal/ceramic interfaces. This near-tip elasticity accomodates a large stress gradient, matching the nanoscopic, high cohesive strength to the macroscopic, low yield strength.
An elastic cell, of size comparable to dislocation spacing or dislocation cell size, is postulated to surround the crack tip.
The fracture process therefore consists of two elements: atomic decohesion and background dislocation motion. It is argued that the pre-existing dislocations, except for occasional interceptions with the crack front, are unlikely to blunt the major portion of the crack front, so that the crack front remains nanoscopically sharp, advancing by atomic decohesion. Dislocations are assumed not to emit from the crack front. A theory is proposed for cleavage cracking surrounded by pre-existing dislocations.
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