PSI - Issue 61

236 Bahman Paygozar et al. / Procedia Structural Integrity 61 (2024) 232–240 Paygozar et al./ Structural Integrity Procedia 00 (2019) 000 – 000 5 the crack (i.e., jump discontinuity). ( ) and are respectively referred to as crack tip asymptotic function and crack tip enriched nodal degree of freedom (Giner et al. 2009). In this method, the processes of crack initiation and consequent propagation can be modeled through a triangular damage law defined by a cohesive zone model (CZM) (Sadigh et al. 2018). In this study, the commercial FE software ABAQUS 2020 was used to simulate the Mode-I fracture using the XFEM. The maximum principal stress (MaxPS) criterion was selected in this study in order to model the crack initiation (Campilho et al. 2011). According to this criterion, failure in that element starts when an element's maximum principal stress ( ) reaches the material's ultimate strength ( ). The failure equation is given by =1 (6) To model crack propagation through damage evolution, fracture energy power-law criteria in 2D and 3D versions can be utilized (Paygozar et al. 2020a). { }+{ }+{ }=1 (7) Here , , and are strain energy release rates (i.ee., fracture energies) in normal, first, and second shear directions concerning the interface, respectively. Superscript C added to the previous parameters reflects the critical values or the PLA material properties. Taking account of the nature of the numerical analyses (i.e., Mode-I SENB model) in this study, only the first term in Eq. (7) was set equivalent to 1. In other words, only the normal direction was considered, and the first and second shear components were ignored because the Mode-I fracture was investigated in this study. Then, the fracture toughness of the PLA calculated based on the experiments from Eq. (3) is assigned to be in Eq. (7). 3.2. Simulation of SENB specimen The FE model of the SENB specimen was employed in a commercial package ABAQUS/Standard. Two dimensional plane strain elements (CPE4) were utilized in the numerical model with a boundary condition as displacement-controlled in order to economize on the computational cost. A pre-crack (notch) with a length of 10 mm was inserted into the mid-bottom edge of the specimen. Three rigid pins of 5 mm in radius were touched the specimen to impose the 3P bending loading. To avoid stress concentrations and singularities, point loading was avoided, and loading through rigid rollers was provided. A displacement of 2 mm was exerted onto the specimen through the rigid roller at the top for the purpose of loading (Akhavan-Safar et al. 2020). The SENB specimen model is shown in Fig.3. 4. Results and discussion The load-displacement responses were extracted from the 3P bending tests of SENB specimens. The peak loads were obtained and utilized to find the fracture toughness and fracture energy values. Numerical analyses were conducted using XFEM based on the calculated data. Crack propagation in both experimental and numerical levels was interpreted.