PSI - Issue 25

A.M. Al-Mukhtar / Procedia Structural Integrity 25 (2020) 8–12 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2. Crack Simulation using LEFM The teeth splitting occur in vertical direction (Rosen 1982)(Yoldas et al. 2012). Horizontal and vertical flaws combination may also appear. Traditionally, the cracked tooth refers to the vertical defects that may extended longitudinally reaching the root (Rosen 1982)(Yoldas et al. 2012). Any dentin procedure can create crack and in turn fracture (Yoldas et al. 2012). Previous studies mentioned that little literature on cracked tooth are existed (Rosen 1982). Moreover, little studies trying to simulate the crack growth in teeth (Ramezani et al. 2018). Like in bone, most studies evaluate the fracture toughness of dentin using LEFM, hence, ignoring the plastic deformation (Yan et al. 2008). LEFM as in metal, its assumed that the crack tip behavior and the propagation under elastic properties (Yan et al. 2008). Elastic analysis obtained from ABAQUS is used in Ref. (Ramezani et al. 2018). However, the plasticity effect was estimated due to the collagen content in dentin (about 30% by volume) (Yan et al. 2008). The plasticity enhances the fracture toughness. Therefore, significant differences have been found between the using LEFM, and elastic-plastic fracture mechanics (EPFM) to calculate fracture toughness (K JC ). Therefore, it was emphasized to consider EPFM to evaluate the fracture toughness in human dentin. Nevertheless, linear elastic analysis was proposed also in other studies (Ramezani et al. 2018). LEFM based on the fracture mechanics assumptions is used in this work. 2.1. FE Model In this work, Fracture Analysis Code (Franc2D) from Cornell University Fracture Group was used, see Ref. (Cornell Fracture Group 2010). LEFM approach is based on the linear relation between the peak load, and the crack length. Therefore, the accurate crack path has been presented using Franc2D. The series of the crack path simulation and the fracture behavior of different materials have been presented in Refs. (A.M. Al-Mukhtar 2011; A. Al-Mukhtar 2013; A. Al-Mukhtar et al. 2009; Al-Mukhtar 2016, 2017; Al-Mukhtar et al. 2011; A. Al-Mukhtar et al. 2010; A. M. Al-Mukhtar 2013b, 2013a; A. M. Al-Mukhtar et al. 2009, 2010; Al-Mukhtar 2010, 2014; Al-Mukhtar and Merkel 2015). Franc2D is a FE based simulator for curvilinear crack propagation in planer structures (plane stress, plane strain, and axisymmetric). CASCA which is used for the creation the meshes (see Fig. 2a), is a pre-processor for generating the initial input files for Franc2D (Cornell Fracture Group 2010). This program has the ability to analyze a cracked body using special isoparametric crack tip elements. In addition, it describes the singularity a head of the crack tip. The materials have been assumed to be isotropic and linear elastic. The effects of mesh density and crack increment have been evaluated previously, see Refs. (A.M. Al-Mukhtar 2011; A. Al-Mukhtar 2013; A. Al-Mukhtar et al. 2009; Al-Mukhtar 2016, 2017; Al-Mukhtar et al. 2011; A. Al-Mukhtar et al. 2010; A. M. Al-Mukhtar 2013b, 2013a; A. M. Al-Mukhtar et al. 2009, 2010; Al-Mukhtar 2010, 2014; Al-Mukhtar and Merkel 2015). Figure 2a shows the FE model of virtual deformed and stress concentration in the teeth. The model that compromise of triangle and bilinear 4-sided meshes is shown in Fig. 2(a). The distributed constant load was used on the crown of the teeth. The step by step or the automatic crack propagation is available. The crack grows according to the maximum stress criteria where the plane of the crack is perpendicular to the applied load. The comparison with the experiment work Ref. (Xie et al. 2017) have been presented in Fig. 2b-d. 3. Conclusions The crack is a common phenomenon for human teeth. The crack resistance decreases at the aged teeth. Nevertheless, the crack starts from the high stress notches due to the distributed load over the crown. The understanding of the crack path will prevent the splitting and teeth failure. In this work, a 2D model is proposed to simulate the crack path. LEFM approach as based on linear elastic and an isotropic material property was used. Franc2D shows the ability for this simulation. The crack path was compared with literature. The comparison is well defined.