3D effects around notch and crack tips

Notches and cracks are usually treated as two-dimensional problems in most structural design and analysis applications, employing 2D limit solutions from plane elasticity theories to evaluate highly localized stress/strain concentration effects around their tips. However, such effects are also associated to high stress gradients, which cause three-dimensional stress/strain fields around those tips that can severely restrict local Poisson-induced transversal strains. Modeling of fatigue crack initiation and propagation, estimation of plastic zone sizes and shapes, and localized constraint effects are typical problems affected by such 3D effects, which may lead to non-conservative damage and life predictions if neglected. To quantify how important they can be in practical applications, first traditional finite element techniques are used to simulate effects of component thickness and notch tip radius in the stress and strain fields along and around such tips, and to evaluate their importance from the structural design point of view. Then, versatile sub-modeling techniques are used to study similar effects along the fronts of short and long cracks. Finally, a stepwise remeshing routine is used to show how an initially straight crack must slightly curve its front during its propagation by fatigue, due to the unavoidable 3D effects that always surround real crack tips.