Issue 33

R.C.O. Góes et alii, Frattura ed Integrità Strutturale, 33 (2015) 89-96; DOI: 10.3221/IGF-ESIS.33.12 89 Focussed on characterization of crack tip fields 3D thickness effects around notch and crack tip stress/strain fields R.C.O. Góes, J.T.P. Castro, M.A. Meggiolaro Pontifical Catholic University of Rio de Janeiro cesarafael@gmail.com , jtcastro@puc-rio.br, meggi@puc-rio.br A BSTRACT . Notches and cracks are usually approximately modeled as two-dimensional problems using solutions from plane elasticity to quantify localized stress/strain concentration effects around their tips. However, they may be associated with high gradients that can severely restrict local Poisson-induced transversal strains and cause important 3D stress fields around those tips. Fatigue crack initiation and growth, plastic zone sizes and shapes, and localized constraint effects that affect toughness are typical problems associated with such 3D effects, which may lead to non-conservative damage and life predictions if neglected. To quantify how important they can be, first finite element techniques are used to simulate thickness and notch-tip radius effects in the fields 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, and a stepwise re-meshing 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. K EYWORDS . 3D notch and crack tip fields, 3D stress concentration, fatigue crack front curvature, stress gradient effects. I NTRODUCTION or design purposes, the maximum stresses  max that act at notch tips are usually calculated using a linear elastic (LE) stress concentration factor (SCF) K t to multiply the nominal stress  n that would act there if the notch had no effect on the stress and strain fields that surround it:  max  K t  n (1) Since Kirsch and Inglis studied circular and elliptical notches in infinite plates, a few analytical and many numerical and experimental SCF have been obtained for many other notch geometries from their 2D approximations, assuming idealized plane stress ( pl-σ ), plane strain ( pl-ε ), or axisymmetric conditions [1-2]. Creager and Paris [3] estimated SCF from stress intensity factors (SIF) of similar cracks, but most SIF assume planar geometries as well [4]. However, 2D models of notched components have limitations, even in simple cases like a notched plate loaded by a uniform nominal stress. Indeed, in such cases the material works under pl-  far from the notch tips, but the stress/strain fields that surround the tips are in fact 3D, due to the Poisson restriction induced by the stress/strain gradients that act there. If  is the Poisson ratio, a transversal constraint factor T z can be defined to quantify this transversal restriction at any point by 0, , z z x y pl T pl               (2) Since very few analytical solutions are available for 3D fields around notches [5-6], numerical tools are needed to study most 3D SCF problems. Using finite element (FE) to model many notches, Guo et al. [7-10] and Yang et al. [11] F