Effects of Characteristic Material Lengths on Ductile Crack Propagation

Abstract

Classical plasticity theories fail in characterizing the constitutive behavior of ductile materials at the micron scale, which is necessary to define in order to investigate the stress and strain fields near a propagating crack tip. Experimental observation on the macroscopic fracture toughness and atomic work of separation of an interface between a ductile crystal of niobium and a sapphire single crystal performed by Elssner et al. [1] found that the interface between the two materials remained sharp and not blunted up to the atomic scale. Moreover, the stress level required to produce atomic decohesion of the lattice turns out to be about 10 times the tensile yield stress, whereas fracture mechanics analyses based on classical plasticity theories (Drugan et al., [2]) provide a maximum stress level near a crack tip not larger than 4–5 times the tensile yield stress. Classical continuum theories are also unable to predict the size effect arising at small scales, due to the lack of a length scale. Therefore, in order to describe the stress and deformation fields very near the crack-tip during its propagation, it become necessary to adopt enhanced incremental constitutive models, which account for the non linear behaviour of the material as well as for the microstructure and the presence of dislocations, by incorporating one or more characteristic lengths, typically of the order of few microns for ductile metals.KeywordsCouple StressStress SingularityCouple Stress TheoryTensile Yield StressSapphire Single CrystalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.