PSI - Issue 61

Toros Arda Akşen et al. / Procedia Structural Integrity 61 (2024) 268 – 276 4 Toros Arda Akşen, Bora Şener, Emre Esener, Ümit Kocabıçak, Mehmet Fırat / Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Ductile fracture Models This section explains the fundamentals of ductile fracture models. A reasonable fracture strain prediction is ensured by incorporating the hydrostatic pressure and the maximum normalized shear stress effects. These effects are evaluated by the triaxiality effect and Lode angle parameter, respectively. The stress triaxiality ( η ) is a function of the average stress (σ m ), while the Lode angle parameter (L) is associated with the angle of Lode ( θ ) that defines the loading path in stress space. These parameters are expressed in Eq. (11). Within the scope of this research, two ductile fracture models, VGM and MMC, are implemented to predict the fracture locus and fracture FLC of AA6016-T4 alloy. The VGM model involves only the triaxiality effect (Rice and Tracey (1969)), while the MMC criterion includes simultaneously the triaxiality effect and the Lode angle parameter’s effect (Bai and Wierzbicki (2010)). Hence, this research elucidates the difference in prediction performance as well for triaxiality-based fracture models and both the Lode parameter and triaxiality-based models. The VGM model is a widely adopted model in literature (Barnwal et al. (2020), Kong et al. (2020)) and the generalized form of VGM is given in Eq. (12). 2 ( ) , 1 ( ) c p f ce    − = (12) Here, the parameters c 1 and c 2 are to be adjusted. Besides, ̅ , denotes the plastic equivalent fracture strain. The plastic equivalent fracture strain for the MMC criterion in terms of η and L is as follows (Habibi et al. (2018)). 1 2 2 1 , 3 3 1 2 2 2 1 3 3 1 ( , ) [ ( (1 )( 1))( ( ( )))] 3 3 3 3 2 3 n p f b K L L L b b b b L L    − + + − = + − − + + + + − (13) Here, b 1-3 are the adjustable parameters. Moreover, this model has two hardening parameters which are K and n. These two parameters are relevant to the Hollomon hardening law (Park et al. (2019), Luo and Wierzbicki (2010)). These parameters were computed by equalizing the Hollomon parameters to Swift hardening parameters adopted in this work using Eq. (14). 0 ( ) n p p p C K    + = (14) Where, the C and p are the Swift law parameters relevant to the hardening response, whereas K and n correspond to the Hollomon law’s reciprocal parameters. 3. Test Procedure Inducing different loading paths on uniaxial tensile test specimens necessitates creating varying geometrical discontinuities. These different loading paths yield different equivalent fracture strains for each test specimen. In the present research, the test specimen’s geometries and the test outcomes were procured from the study of Zhang et al. (2019). These specimens are standard uniaxial tensile test (STT), centered hole (CH), and shear (SH) specimens, along with the notched tensile test specimens with 5 mm radius (NT5), 10 mm radius (NT10), and 20 mm radius (NT20). All these specimens are 1,5 mm thick, and they are demonstrated in Fig. 1. 1 2  + + 3 3 m = = eqv eqv       ; 2 1   − − − 3 1 3 2 3tan L     = = (11)