PSI - Issue 35

İbrahim Yelek et al. / Procedia Structural Integrity 35 (2022) 51 – 58 Yelek et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Therefore, the upper limit of the true stress-strain curves was determined by extending them by linear extrapolation. The correlation of the experiments and FEA results was done by using the curves created iteratively at these intervals. This iterative extension study was done for both materials. In order to determine the onset of fracture for the tensile tests, the b parameter values of two fracture curves in the literature were modified as seen in the equivalent strain on stress triaxiality graph in Fig. 3. As a result of this work, both the flow curves were found and the b parameter for the Hosford-Coulomb ductile fracture model was determined according to the results of the tensile tests. After these processes, hemming analyzes were performed with the new modified fracture curves. /FAIL/EMC failure card definition in Radioss was used to model the Hosford-Coulomb ductile fracture initiation. For comparison of two different mechanical properties for DX51D material, the Hosford-Coulomb fracture parameters were taken from the literature as stated in the introduction. S235JR grade material’s fracture parameters were supposed as the equivalent of normal-level DX51D mechanics because of its similar tensile test values such as yield and tensile stress and elongation. The similarity of tensile test values in between high-level DX51D grade material and S275JR grade material, S275JR grade’s fracture parameters were chosen to represent high-level mechanics of DX51D. These fracture curve parameters are given in Table 2. As recommended by Roth and Mohr (2016), the transformation constant n equals 0.1. The analyzes were repeated iteratively by changing only the b parameter which is related to uniaxial tension. After modification of the b value for normal-level and high-level DX51D mechanics, the fracture initiation was represented in the most accurate way for tensile specimens. The triaxiality dependent strain to fracture paths of tensile specimens and the inverse proportion between the mechanics and ductility of the materials can be seen in Fig. 3. Stress triaxiality (3), lode angle (4) and strain to fracture (5) equations are given in below = ̅ (3) ̅ = 1 − 2 ̅ arc cos (− 2 2 7 ( 2 − 1 3 )) − 2/3 ≤ ≤ 2/3 (4) ̅ = ̅ [ , ̅, , , ] (5) The damage is calculated as expressed in = ∫ ̅ 1 ( , ̅ ) ̅ ̅ 0 (6) The Hosford-Coulomb failure criteria is given Mohr and Marcadet (2015) calculated as ̅ [ , ̅ ] = (1 + ) {[ 1 2 (( 1 − 2 ) + ( 2 − 3 ) + ( 1 − 3 ) )] 1 + (2 + 1 + 3 ) } −1 ⁄ (7) where, 1 , 2 and 3 are functions of the lode angle and they are stated as 1 [ ̅ ] = 2 3 cos [ 6 (1 − ̅ ) ] (8) 2 [ ̅ ] = 2 3 cos [ 6 (3 + ̅ ) ] (9) 3 [ ̅ ] = − 2 3 cos [ 6 ( 1 + ̅ )] (10) Table 2. Calibrated Hosford-Coulomb fracture parameters for materials Fracture Model a b c n Pantousa and Karavasilis (2021) for S275JR 1,1 0,82 0,06 0,1 Kõrgesaar et al. (2018) for S235JR 1,31 1,55 0,01 0,1 Modified S275JR for high-level DX51D mechanics 1,1 1,40 0,06 0,1 Modified S235JR for normal-level DX51D mechanics 1,31 1,45 0,01 0,1