3D finite fracture mechanics under mode I loading: the flat elliptical crack

The determination of the remote stress causing crack propagation in an infinite 3D domain with an embedded flat elliptical crack is here revisited in the framework of the Coupled Criterion of Finite Fracture Mechanics. We started reviewing Linear Elastic Fracture Mechanics approaches, which differ by accounting for different infinitesimal crack growths. Then, we provide the solution based on Finite Fracture Mechanics: if the elliptical flaw is sufficiently small, the crack grows along iso-stress lines. For larger sizes, other crack growths may take place. Thus, the present investigation shows that assuming an iso-stress crack front may effectively provide the exact Finite Fracture Mechanics solution, particularly for small defects; on the other hand, it can be wrong for larger size, providing moreover un-conservative predictions. However, for the geometry at hand, it yields failure stress estimates differing from the actual one by a few percents. Thus, the iso-stress assumption, conjectured by Leguillon [D. Leguillon, “An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case”, Theor. Appl. Fract. Mech. 74 (2014), pp. 7–17]—implying strong simplifications in the numerical implementation of the coupled criterion in 3D problems—seems to be largely justified by the present results. Moreover, regardless of the initial crack size, the finite growth predicted by the model results in a new elliptical crack shape closer to the circular one, meaning the eccentricity consistently decreases as the crack propagates.