13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A fracture-mechanics-based non-local damage model for crack prediction in brittle materials Zhang Xiao-Bing1, Li Jia2* 1LAMI, Université Blaise Pascal de Clermont, Montluçon, France; 2LSPM, CNRS UPR 3407, Université Paris XIII, Villetaneuse, France; * Corresponding author: jia.li@univ-paris13.fr Abstract: Description of crack initiation and crack growth is a principal aim of numerical simulations in fracture mechanics. In this work, we have established a non-local damage model based on the fracture mechanics for brittle materials. This non-local model associates the classical failure criteria for non-cracked materials and the Griffith criterion for cracked materials throughout a non-local approach. Consequently, this model can be used to predict the crack initiation as well as the crack growth. The maximal principal stress criterion was considered in the proposed non-local framework. It was shown that after the non-local treatment, the classical failure criteria can be used in the prediction of crack initiation and crack growth with different failure mechanisms. By using the proposed model, we carried out several numerical simulations on different specimens in order to assess the fracture process in brittle materials. From these studies, we can conclude that the present model can be used to deal with crack initiation and crack growth in brittle materials with high accuracy and efficiency. Keywords: fracture, crack, damage, non-local model 1. Introduction The fracture prediction of structures made of brittle materials is an important issue in engineering designs. In real structures, the failures are often initiated from a few geometrical weaknesses near which stress concentrations are formed. The stress concentrations are of many types and different levels. The failure prediction for all these stress concentrations is an essential research topic for scientists and engineers. However, it seems that fractures can be accurately predicted only for few types of stress states as so far. For brittle materials, failure criteria for two simple situations are commonly accepted: 1: Under uniform uniaxial tension, fracture occurs when the maximum tensile stress reaches the ultimate stress of the material: c σ σ≥ (1) 2: For solids including a macrocrack, the crack grows when the Griffith criterion is fulfilled: c G G≥ (2) where G and Gc are respectively the energy release rate and its critical fracture value. Unfortunately, these criteria have to be used separately: one for damage initiation and another for crack growth. In the cases when the stress distribution is not uniform but does not present a crack singularity, these criteria are no longer sufficient to describe accurate fracture conditions. Many factors such like stress gradient, multi-axial stress state or structure size may influence the material strength. With the aim of unifying these criteria in a single damage model and extending them to
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