PSI - Issue 61

Toros Arda Akşen et al. / Procedia Structural Integrity 61 (2024) 260 – 267 Toros Arda Akşen, Bora Şener, Emre Esener, Mehmet Firat / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Tearing is the primary failure mode that occurred in the metal forming processes and it causes significant material loss in the manufacturing and the accurate prediction of the tearing is important in terms of the increasing of the productivity. Sheet metals are exposed to large plastic deformation, therefore ductile fracture is the main research topic in the industry. Ductile fracture models are divided into two approaches: coupled and uncoupled models. Coupled models are based on the void initiation, expansion and coalescence within the material and several models have been developed in the literature (Gurson (1977), Tvergaard (1982), Needleman and Tvergaard (1984)). Uncoupled models are empirical and compute the ductile damage explicitly (Mu et al. 2018). These models involve a threshold value and consider that fracture take place when it reaches to a critical value (Freudenthal (1950), Cockroft and Latham (1986), Clift et al. (1990), Oyane et al. (1980), Atkins (1981)). The calibration of the fracture models is performed with different mechanical tests, and they affect the value of the critical damage indicator in an uncoupled model. The literature survey showed that an appropriate mechanical test decision for fracture model calibration enhances the predictability of fracture initiation. Yoon et al. (2017) conducted research to predict the edge cracking performance of different advanced high-strength steels. They took the fracture toughness in the uniaxial test as the critical damage factor and obtained satisfactory results for a hole expansion process. Apart from the study of Yoon et al. (2017), the fracture prediction was concentrated on the equivalent plastic fracture strain calibration (Park et al. (2020); Lou et al. (2017)). Chung et al. (2011) employed a uniaxial test for crack initiation in the hole extrusion test of TRIP590 and TWIP940 steel. They provide accurate results, especially for the TWIP940 steel. Further, they extended their theory to enhance the prediction performance of the adopted model for the TRIP590 steel. In the hole expansion process, uniaxial tension is prominent near the hole; however, in the cup drawing process, biaxial tension is dominant for the punch radius region of the blank where the fracture initiates in general (Singh et al. (2018)). Therefore, the mechanical tests exhibiting equi-biaxial tension stress state were picked out, such as the bulge test, equi-biaxial tensile test, or Nakajima test with fully square circular specimens, etc. are extensively utilized to improve the prediction capability of the fracture models for corresponding stress state (Gu et al. (2020); Qin and Beese (2020)). In this study, the influence of the fracture model calibration test on the initiation of the fracture prediction was studied. A numerical tool based on the anisotropic polynomial yield function and a ductile fracture model was developed and it was applied to predict tearing in the rectangular cup drawing. Damage indicator was calibrated with uniaxial and bulge tests and its effect on the prediction performance was studied. 2. Material and method Determination of the material properties in the different directions with respect to the rolling direction and performing of the different mechanical tests are required to model anisotropic behavior and investigate the influence of the calibration test on the failure prediction. 2.1. Description of the anisotropic behavior Anisotropic behavior of the sheet was described with the fourth-order polynomial yield function which its formulation is given below (Soare et al. (2008)): (1) where, a 1-9 are anisotropy parameters of the function, and they can be determined with yield stress ratios and Lankford coefficients (r values) in the different orientations. The experimental yield stresses and r-values (r θ ) were determined from the uniaxial tension tests conducted for different material’s orientation in line with the ASTM -E8 specifications (ASTM, 2016). The stress ratios and r-values at % 0.2 plastic strain value were taken into consideration in the determination of the yield function coefficients. The r-values were determined based on the ratio of the width strain to thickness strain for each interested direction. The yield stresses for each orientation were acquired based on the stresses corresponding to the %0.2 plastic strain (Sener et al. (2021)). The biaxial yield stress (σ b ) is obtained from 4 a a   + + + + + + + = + 3 2 2 yy xx 3 4 4 1 2 3 4 1 6 7 2 8 9 2 4 2 a a ( ) eqv xx xx yy xx yy xy xx xx yy y x yy y y a a a a a 