13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Finite Element Simulation of Crack Propagation for α-Ti Based on Cohesive Zone Law Deriving from Molecular Dynamics Yi Liao1, Xiangguo Zeng1, Jun Chen2, Rongpeng Xu1,3*, Huayan Chen1 1 College of Architecture and Environment, Sichuan University, Chengdu, 610065, PR China 2 Institute of Applied Physics and Computational Mathematics, Beijing, 100094, PR China 3 School of Engineering, Alfred University, Alfred, NY, USA 14802 Corresponding author: xuyun14567@163.com Abstract In order to parameterize and obtain a traction-separation (T-S) law, molecular dynamics (MD) simulations via Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) are used at atomic scale for the deformation and fracture for models with dimension of 200Å×204Å×8.82Å with crack for alpha titanium (α-Ti) with HCP crystal structure under tensile loadings at different loading directions. Visualization of the atomistic configurations during deformation is realized by use of ATOMEYE. It can be concluded that crack extension are correlate with the α-Ti crystal structure and crystal orientation intrinsically. We also found that HCP→BCC phase transition and twin deformation occur in the vicinity of the crack tip for HCP α-Ti under different loading directions via the common neighbor analysis (CNA). The complex mechanisms of deformation, i.e., phase transition, twin deformation, and failure, i.e., crack blunting and extension, were contained in the traction-separation (T-S) law. Then, the generated parameterized traction-separation law is implemented in the finite element model with the behavior of the CZM governed by traction-separation (T-S) law. Finally, the ABAQUS finite element commercial software is employed to simulate the crack propagation behavior for α-Ti CT specimen. Keywords Alpha Titanium, Molecular dynamics, Cohesive zone model, Crack propagation, Finite element 1. Introduction Titanium has two kinds of superior properties: high specific strength and corrosion resistant. Titanium has long had appeal to metal designers and material scientists[1]. Commercially, pure titanium is, of course, alpha titanium (α-Ti). Its elemental crystal structure is closed-packed hexagonal, as illustrated in Fig.1[2]. Alpha titanium is anisotropic material. The mechanical properties in its different crystal orientations have significant difference. In this paper, the micro-deformed mechanisms of α-Ti on different conditions of loading are obtained by means of open source MD code LAMMPS[3] developed by Sandia. Visualization of the atomistic configurations during deformation is realized via ATOMEYE software[4]. Xu and Needleman[5,6] first related the cohesive zone model (CZM) with finite element analysis, and they successfully applied it to simulate crack propagation problems. Cohesive elements that possess zero volume in an undeformed state are inserted between bulk elements. They are particularly appropriate when the crack propagation path can be determined. Cohesive zone law defines the relation between traction and crack opening displacement. Because it is difficult to direct experimentally quantify the relation, construction of such a law has been a challenging task in the past decade[7,8]. The traction-separation (T-S) relationship in a CZM is generally parameterized through empirical data. Our approach to studying crack propagation has included the use of MD simulation for obtaining the functional form of parameterized T-S relations in cohesive elements[9,10]. This paper simulated a compact tension fracture mechanics specimen through cohesive elements whose T-S relation was derived from MD simulations. These results enable us to make several recommendations to improve the methodology to obtain cohesive laws and better comprehend the crack propagation behavior of
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