13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A constitutive approach to fracture simulation based on augmented virtual internal bond method Zhennan Zhang*, Shaofeng Yao School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China ∗ Corresponding author: zhennanzhang@sjtu.edu.cn Abstract The K-dominant zone, which is a small area surrounding the fracture tip, has been the interesting focus of the fracture mechanics. In the traditional linear elastic fracture mechanics(LEFM), a stress intensity factor is used to characterize the stress field of the K-dominant zone and a separate fracture criterion is used to predict the fracture behaviors. However, when using LEFM to simulate fracture propagation, the computation of stress intensity factor is a tough problem. The LEFM is actually a phenomenological methodology. The fracture behaviors are determined by material microstructure. The augmented virtual internal bond(AVIB) is a constitutive model based on microstructure. Its constitutive relation is derived from the micro bond potential, which contains the micro fracture mechanism. Hence, the so-called fracture criterion is implicitly built in the constitutive relation. In this paper, the AVIB constitutive model is used in the K-dominant zone while the usual linear elastic constitutive model is used in the rest zone to simulate fracture propagation. By this method, the computation of stress intensity factor is avoided. When and how fracture propagation is completely governed by the AVIB constitutive relation. It provides an efficient approach to fracture simulation. Keywords Fracture simulation, Augmented virtual internal bond, Constitutive model，Microstructure 1. Introduction In the methodology of linear elastic fracture mechanics(LEFM), the singular mechanical field of crack tip is characterized by the so-called stress intensity factors (SIFs). Whether fracture propagates is governed by SIF and material fracture toughness. So, many fracture criteria in terms of SIFs have been proposed. When using FEM to simulate fracture behaviors, the SIF is a key factor that has to be calculated. However, the computation of SIF is a tough problem in computational mechanics, which requires very fine mesh scheme at vicinity of crack tip or special treatment on mesh scheme. The cohesive surface methodology pioneered by Barenblatt[1] and Dugdale[2] take a different philosophy to deal with the fracture tip problem. It is assumed that there is a cohesive zone ahead of crack tip, which is governed by a cohesive law. The cohesive law is characterized by the cohesive strength and the fracture energy. When using this method, the stress intensity problem, therefore the SIF problem, is avoided. However, in FEM simulation, a cohesive zone is usually inserted into the bulk material, which brings inconvenience to numerical procedure. In the present paper, the cohesive properties of microstructure at vicinity of crack tip are directly built in the constitutive relation through augmented virtual internal bond(AVIB)[3] model. Hence, in the present simulation strategy, only at the K-dominant zone is the AVIB constitutive model used while at the rest zone, the linear elastic constitutive model is used. The present method is suggested highly efficient, avoiding the SIF computation and fracture criteria problem. 2. Constitutive relation of material at vicinity of crack tip Before the deformation of material reaches its linear elastic limit, the linear elastic continuum constitutive relation can well describe the behaviors of material. However, once the deformation exceeds this limit, the conventional continuum constitutive model couldn’t well describe it. In such situation, the augmented virtual internal bond(AVIB)[3] is an effective approach to address this
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