Abstract
Servo press forming machines are advanced forming systems that are capable of imparting interrupted punch motion, resulting in enhanced room temperature formability. The exact mechanism of the formability improvement is not yet established. The contribution of interrupted motion in the ductility improvement has been studied through stress relaxation phenomena in uniaxial tensile (UT) tests. However, the reason for improved formability observed when employing servo press is complicated due to the additional contribution from frictional effects. In the present work, an attempt is made to decouple the friction effect on formability improvement numerically. The improved formability is studied using a hole expansion test (HET). The limit of forming during hole expansion is modeled using the Hosford-Coulomb (HC) damage criteria, which is implemented as a user subroutine in a commercial explicit finite element (FE) software. Only the contribution of stress relaxation is accounted for in the evolution of the damage variable during interrupted loading. Therefore, the difference between simulation and experimental hole expansion ratio (HER) can be used to decouple the friction effect from the overall formability improvement during hole expansion. The improvement in HER due to stress relaxation and friction effect is different. The study showed that the model effectively captures the hole expansion deformation process in both monotonic and interrupted loading conditions. Compared to stress relaxation, friction effect played a major role during interrupted HET.
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Abbreviations
- a m, b m, c m :
-
Monotonic fracture parameters
- a r, b r, c r :
-
Relaxation fracture parameters
- d f :
-
Average final hole diameter
- d i :
-
Average initial hole diameter
- d outer :
-
Outer hole diameter at fracture
- d inner :
-
Inner hole diameter at fracture
- D c :
-
Damage variable
- ΔD c :
-
Evolution of damage variable
- J 2 :
-
Second invariant of deviatoric stress tensor
- J 3 :
-
Third invariant of deviatoric stress tensor
- k :
-
Hardening law
- t :
-
Relaxation time
- t i :
-
Initial sheet thickness
- t edge :
-
Sheet thickness around circumference at failure
- ε :
-
Strain at the beginning of relaxation
- ε 1 :
-
Major strain
- ε 2 :
-
Minor strain
- ε c :
-
Circumferential strain
- ε p :
-
Plastic strain
- ε r :
-
Strain ratio
- ε t :
-
Thickness strain
- ε eq :
-
Equivalent strain
- \({\dot \varepsilon }\) :
-
Strain rate
- \(\overline \varepsilon \) :
-
Equivaent plastic strain
- \({\overline \varepsilon _{\rm{f}}}\) :
-
Equivalent plastic strain at fracture
- \({\overline \varepsilon _{\rm{r}}}\) :
-
Equivalent plastic strain at relaxation
- η :
-
Stress triaxiality
- μ :
-
Friction coefficient
- \(\overline \theta \) :
-
Lode angle parameter
- σ 0 :
-
Initial yield stress (YS)
- σ 1, σ 2, σ 3 :
-
Principal stresses
- σ vM :
-
Equivalent stress
- \({{\bar \sigma }_f}\) :
-
Equivalent stress at fracture
- SDV1:
-
Damage state variable: equivalent plastic strain
- SDV3:
-
Damage state variable: stress triaxiality
- SDV4:
-
Damage state variable: Lode angle parameter
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Acknowledgements
The authors would like to express their gratitude to ArcelorMittal for providing the steel utilized in this study. Authors affiliated to Indian Institute of Technology Madras gratefully acknowledge the funding received from the Institute of Eminence Research Initiative project on materials and manufacturing for futuristic mobility.
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Kali PRASAD. He is currently a Ph.D. student in the Department of Mechanical Engineering at Indian Institute of Technology Madras, India. He received his master’s degree in the Department of Metallurgical and Materials Engineering, Indian Institute of Technology Madras, India. His research interests mainly focus on the sheet metal forming and mechanical behaviour of materials.
Aishwary GUPTA. He is currently a Ph.D. student in the Department of Materials Science and Engineering, Seoul National University, Republic of Korea. He received his bachelor’s and master’s degrees in the Department of Mechanical Engineering, Indian Institute of Technology Madras, India. His research interests mainly focus on the ductile fracture modelling of metallic materials.
Hariharan KRISHNASWAMY. He is an associate professor in the Department of Mechanical Engineering at Indian Institute of Technology (IIT) Madras, India. Previously, he worked as an assistant professor at IIT Madras during 2016–2021. Prior to joining IIT Madras, he was an assistant professor in the Department of Mechanical Engineering at IIT Delhi. He received his Ph.D. from IIT Madras in 2012 and B.E. from University of Madras. Earlier, he has worked as a post-doc researcher in Graduate Institute of Ferrous Technology (GIFT), Pohang University of Science and Technology (POSTECH), Republic of Korea (2012–2014), and in the Research Department of Ashok Leyland Ltd, India (2004–2012). His research interests mainly focus on sheet metal forming, plasticity, fatigue, and mechanical behaviour of materials.
Dilip K. BANERJEE. He is a research engineer in the Mechanical Performance Group of the Materials Science and Engineering Division (MSED) of the Material Measurement Laboratory (MML) at the National Institute of Standards and Technology (NIST), USA. He received his B.Tech. degree (honours) from the Indian Institute of Technology Kharagpur, India, and his M.S. and Ph.D. degrees from The University of Alabama, USA, in materials engineering (an interdisciplinary program among Materials Engineering, Mechanical Engineering, and Engineering Mechanics Departments). His current research efforts are focused on developing accurate computational models in support of the NIST Center of Automotive Lightweighting (NCAL)’s goals to develop the measurement methodology and analysis necessary for the automotive industry to transition to advanced lightweighing materials and adopt these emerging materials as sheet metal components.
Uday CHAKKINGAL. He is a professor in the Department of Metallurgical and Materials Engineering at Indian Institute of Technology Madras, India. He received his Ph.D. from Rensselaer Polytechnic Institute, USA, in 1994. His research interests mainly focus on metal forming processes, sheet metal forming, severe plastic deformation processes, and aluminium, magnesium, titanium alloys and metallic biomaterials.
Myoung-Gyu LEE. He is a professor in the Department of Materials Science and Engineering at Seoul National University, Republic of Korea. He received his Ph.D. from Seoul National University, Republic of Korea, in 2004. Prior to joining Seoul National University, he was an associate professor in the Department of Material Science Engineering at Korea University, Republic of Korea. His research interests mainly focus on computational materials science, mechanics of materials, mechanics of anisotropic structure materials, experimental mechanics, optimization of manufacturing process, and forming and shaping of automotive parts.
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Prasad, K., Gupta, A., Krishnaswamy, H. et al. Does friction contribute to formability improvement using servo press?. Friction 11, 820–835 (2023). https://doi.org/10.1007/s40544-022-0698-2
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DOI: https://doi.org/10.1007/s40544-022-0698-2