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Prediction of the bending and out-of-plane loading effects on formability response of the steel sheets

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Abstract

Failure in sheet metal forming can occur by necking, fracture or wrinkling. By using a forming limit diagram (FLD) as a powerful tool to prevent sheets metal failures in the forming process, provides parameters controlling throughout forming. There are different developed methods for predicting FLDs, which estimate sheet metal forming strains limits. Assessment of FLD estimation reveals that there is a dependency between the effect of several factors containing normal stress, shear stress, sheet thickness, mechanical properties, metallurgical properties, yield function, strain path, and bending with formability. In this research, the effects of bending via two finite element models are investigated. In the first method, the out-of-plane deformation is applied by increasing punch displacement to study the effects of bending. In the second method, the effect of bending is investigated via changing punch diameter (25, 50, 70 and, 100 mm). The Marciniak–Kuczynski (M–K) theory is used to predict the time of localized necking in finite element simulations. Furthermore, a novel method for the determination of the inhomogeneity coefficient is presented in M–K model to simulate the groove width for M–K model. To verify finite element simulation results, Nakazima tests with 50 and 100 mm punch diameters were done as experimental studies. The comparison of experimental results and finite element analysis illustrates that the increasing bending or the out-of-plane loading can improve formability. At the end, the effect of bending on FLD is reported as an equation based on minor and major strains.

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Abbreviations

E :

Modulus of elasticity (MPa)

f :

M–K model defect coefficient

K :

Hardness coefficient (MPa)

n :

Hardness index

\({r}_{0}\) :

Anisotropy in the rolling direction

\({r}_{45}\) :

Anisotropy in 45-degree direction

\({r}_{90}\) :

The anisotropy in a perpendicular direction

\({\varepsilon }_{1}\) :

Major strain

\({\varepsilon }_{2}\) :

Minor strain

\({\varepsilon }_{e}\) :

Equivalent strain

\({\sigma }_{e}\) :

Equivalent stress

\({\sigma }_{y}\) :

Yield stress

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Authors and Affiliations

  1. National-Local Joint Engineering Laboratory of Marine Mineral Resources Exploration Equipment and Safety Technology, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Deping Peng

  2. School of Mechanical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Deping Peng

  3. CNPC Bohai Equipment Julong Steel Pipe Co., Ltd., Qingxian, 062658, Hebei, China

    Shun Chen

  4. Department of Mechanical Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Roya Darabi

  5. INEGI, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Roya Darabi

  6. Department of Civil, Environmental and Construction Engineering, Texas Tech University, Lubbock, TX, 79409, USA

    Aria Ghabussi

  7. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Mostafa Habibi

  8. Faculty of Electrical–Electronic Engineering, Duy Tan University, Da Nang, 550000, Vietnam

    Mostafa Habibi

  9. Center of Excellence in Design, Robotics, and Automation, Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9567, Tehran, Iran

    Mostafa Habibi

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  1. Deping Peng
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Peng, D., Chen, S., Darabi, R. et al. Prediction of the bending and out-of-plane loading effects on formability response of the steel sheets. Archiv.Civ.Mech.Eng 21, 74 (2021). https://doi.org/10.1007/s43452-021-00227-1

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