PSI - Issue 61

Bahman Paygozar et al. / Procedia Structural Integrity 61 (2024) 232–240 Paygozar et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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The dimensions of the specimen used in this study, as well as the configuration of the rollers in the 3P bending test, are shown in Fig.2(a). The loading was fulfilled in a universal tensile testing machine (Instron 600 LX, USA) under a constant crosshead speed of 5 mm/min (Stoia et al. 2020). Fig.2(b) illustrates a SENB specimen under three-point bending tests. 2.2. Formulation After the 3P bending tests, the load-displacement response of each specimen was plotted. The maximum amount of the experienced load was drawn as the critical load ( ). By using the dimensions of the samples in Fig. 2(a), the mode I fracture toughness ( ) values were calculated by = 0.5 ( ⁄ ) [ . √ ] (1) where is the critical load in [N], determined according to (Stoia et al. 2020), and are the thickness and width of the SENB specimens in [mm]. The dimensionless geometrical function, ( ⁄ ) , is given in terms of the initial crack length ( a ) and specimen width by ( ) =6 √ 1.99−( )(1− )[2.15−3.93( )+2.7( ) 2 ] (1+2 )(1− ) 1.5 (2) The fracture energy can be calculated by = 2 ′ (3) where ′ represents the Young’s Modulus defined for plane stress or plane strain cases as follows: ′ ={ 1 − 2 (4) where is the Poisson’s ratio of the material. The XFEM permits the crack to propagate through the element interior due to its enrichment functions added to the conventional FE method. Various studies have already utilized it to predict crack propagation without locating any initial crack definition (Mubashar et al. 2014). It also predicts crack propagation in additively manufactured parts (Akhavan-Safar et al. 2020). The enrichment functions in XFEM facilitate displacement jump through the crack faces and model the crack tip’s singularity by ( ℎ ) =∑ ( ) [ + ( ) +∑ ( ) 4 =1 ] (5) where ( ) indicates a Heaviside enrichment, and ∑ ( ) 4 =1 shows crack tip enrichment. Also, ( ) demonstrates the Heaviside distribution, reflects the enriched nodal degree of freedoms for the elements cut through 3. Numerical work 3.1. Theory of XFEM