13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Fracture initiation and size effect in V-notched structures under mixed mode loading Pietro Cornetti1,*, Alberto Sapora1, Alberto Carpinteri1 1 Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino, Torino, 10124, Italy * Corresponding author: pietro.cornetti@polito.it Abstract In asserting structural safety it is of paramount importance to be able to evaluate the loading capacity of notched components, where stresses concentrate and can trigger cracks leading to a catastrophic failure or to a shortening of the assessed life of the structure. Restricting the analysis to brittle materials, we apply the Finite Fracture Mechanics criterion to address the problem of a V-notched structure subjected to a mixed-mode loading, i.e. we provide a way to determine the direction and the load at which a crack propagates from the notch tip and express the critical conditions in terms of the generalized stress intensity factors plus a suitable definition of the notch mode mixity. Weight functions of the stress intensity factors for V-notch emanated cracks available in the literature allow us to implement the fracture criterion proposed in an almost completely analytical manner: the determination of the critical load and the direction of crack growth is reduced to a minimization-under-constraint problem. We then highlight the size effect for a V-notched structure under mixed-mode loading and the differences between the structural behaviours of cracked and notched geometries. Keywords sharp notches, mode mixity, size effect, finite fracture mechanics 1. Introduction The development of suitable fracture criteria for brittle (isotropic or orthotropic) materials containing V-notches or multi-material interfaces is a problem of primary concern in order to control fracture onset phenomena taking place in mechanical components, composite materials and electronic devices. As well-known, the singularity of the stress field in the vicinity of the notch tip makes the problem non-trivial. Concerning re-entrant corners in homogeneous media subjected to mode I loadings, since the pioneering paper by Carpinteri [1] a good correlation has been found between the critical value of the generalized stress intensity factor (i.e. the generalized fracture toughness) and the failure loads. Theoretical models to relate the generalized fracture toughness to material tensile strength, fracture toughness and re-entrant corner amplitude have been set by a number of researchers, e.g. [2-5]. Fewer contributions are available for what concerns mixed mode loading conditions [6-8]. Here we provide the generalization of the results obtained by Carpinteri et al. [5] to mixed mode problems. The proposed approach (as well as the ones previously cited) is based on the assumption that the region around the corner dominated by the singular stress field is large compared to intrinsic flaw sizes, inelastic zones or fracture process zone sizes. This hypothesis is the analogous of small-scale yielding in Linear Elastic Fracture Mechanics (LEFM). While in LEFM there is a direct connection between the Stress Intensity Factors (SIFs) and the strain energy release rate (i.e. Irwin’s relationship), this relation is missing in the case of notches, so that correlating fracture initiations with critical values of the stress intensity [1] could appear questionable. However, the recently introduced Finite Fracture Mechanics (FFM) criterion has shown this is not the case [4,5]. In fact, under the assumption of a finite crack extension at fracture initiation, it is possible to prove a relation between the Generalized Stress Intensity Factors (GSIFs) and the energy released when a crack appears at the V-notch tip.
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