3D effects on Fracture Mechanics

Simplified mathematical models are extremely useful for understanding and characterizing physical phenomena; this is the case of plane (stress/strain) elasticity, which has been the main analytical framework of Fracture Mechanics since its origins. Bowed crack fronts in thin sheets and plates, unpredicted fatigue crack paths, and crack initiation as well as brittle fracture location are only examples of fracture mechanisms not completely explained by the classical closed form 2D solutions, e.g. Westergaard's solution. This paper aims to provide a brief review on 3D effects on the brittle fracture behavior of linear, elastic, homogeneous and isotropic solids in presence of cracks or notches, under the hypothesis of small scale plasticity (LEFM). We overview the main theoretical and numerical results on coupled modes of fracture, i.e. coupling of shear (Mode II) and out-of-plane (Mode III) modes, due to three-dimensional effects and on 3D vertex singularities close to a corner point generated by the intersection of a crack/notch front with free surfaces. We also address recent theoretical-numerical studies and inconsistencies on the relation of crack (notch) tip stress singularities, usually characterized by local (notch) stress intensity factors, in the vicinity of a corner point and far away from it. Despite numerous works have attempted to interpret finite element and analytical results, no consensus exists on the behavior of the 3D stress field near a vertex of cracked/notched solids; a unifying theory, able to guarantee the extension of the results of experimental tests prescribed by standards, based on the 2D theory of elasticity, to real cases, is still required. (C) 2020 The Authors. Published by Elsevier B.V.