Research Papers

Forming Limit Differences in Hemispherical Dome and Biaxial Test During Equibiaxial Tension on Cruciform

[+] Author and Article Information
Chetan P. Nikhare

Department of Mechanical Engineering,
The Pennsylvania State University Erie,
Erie, PA 16563
e-mail: cpn10@psu.edu

Emmett Vorisek

Department of Mechanical Engineering,
The Pennsylvania State University Erie,
Erie, PA 16563
e-mail: ejv5072@psu.edu

John R. Nolan

Department of Mechanical Engineering,
The Pennsylvania State University Erie,
Erie, PA 16563
e-mail: jrn5231@psu.edu

John T. Roth

Department of Mechanical Engineering,
The Pennsylvania State University Erie,
Erie, PA 16563
e-mail: jtr11@psu.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received December 11, 2016; final manuscript received May 7, 2017; published online July 6, 2017. Assoc. Editor: Ashraf Bastawros.

J. Eng. Mater. Technol 139(4), 041011 (Jul 06, 2017) (9 pages) Paper No: MATS-16-1365; doi: 10.1115/1.4037020 History: Received December 11, 2016; Revised May 07, 2017

Traditionally, the mechanical properties of materials have been characterized using the uniaxial tension test. This test is considered adequate for simple forming operations where single axis loading is dominant. Previous studies, however, have noted that the data acquired from this type of testing are not enough and additional details in other axes under simultaneous deformation conditions are important. To analyze the biaxial strain, some studies have suggested using the limiting dome height test and bulge test. However, these tests limit the extent of using multi-axial loading and the resulting stress pattern due to contact surfaces. Therefore, researchers devised the biaxial machine which is designed specifically to provide biaxial stress components using multiple and varying loading conditions. The idea of this work is to evaluate the relationship between the dome test data and the biaxial test data. For this comparison, cruciform specimens with a diamond shaped thinner gage in the center were deformed with biaxial stretching on the biaxial testing machine. In addition, the cruciform specimens were biaxially stretched with a hemispherical punch in a conventional die-punch setting. Furthermore, in each case, the process was simulated using a three-dimensional (3D) model generated on abaqus. These models were then compared with the experimental results. The forces on each arm, strain path, forming, and formability were analyzed. The differences between the processes were detailed. It was found that biaxial tests eliminated the pressurization effect which could be found in hemispherical dome tests.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Pleta, A. D. , Krugh, M. C. , Nikhare, C. P. , and Roth, J. T. , 2013, “ Comparison of Electrical and Thermal Effects on AA 5083 Aluminum Alloy,” International Deep Drawing Research Group Conference (IDDRG), Zurich, Switzerland, June 2–5, pp. 299–304.
Hosford, W. F. , and Caddell, R. M. , 2007, Metal Forming: Mechanics and Metallurgy, 3rd ed., Cambridge University Press, Cambridge, UK, p. 207.
Abu-Farha, F. , Hector, L. G., Jr. , and Khraisheh, M. , 2009, “ Cruciform-Shaped Specimens for Elevated Temperature Biaxial Testing for Light Weight Materials,” J. Miner., Met. Mater. Soc. (TMS), 61(8), pp. 48–56. [CrossRef]
Chen, X. , Jiang, H. , Cui, Z. , and Lu, C. , 2014, “ Hole Expansion Characteristics of Ultra High Strength Steels,” Procedia Eng., 81, pp. 718–723. [CrossRef]
Nikhare, C. P. , and Nolan, J. R. , 2016, “ Hole Expansion and Strain Evolution During Biaxial Testing,” International Deep Drawing Research Group Conference (IDDRG), Linz, Austria, June 12–15, pp. 446–456.
Lester, S. R. , and Nikhare, C. P. , 2014, “ Investigation of Strain Development and Hole Expansion Ratio in Mild Steel and AA 5083,” International Deep Drawing Research Group Conference (IDDRG), Paris, France, June 1–5, pp. 210–215.
Kuwabara, T. , Hashimoto, K. , Iizuka, E. , and Yoon, J. W. , 2011, “ Effect of Anisotropic Yield Functions on the Accuracy of Hole Expansion Simulations,” J. Mater. Process. Technol., 211(3), pp. 475–484. [CrossRef]
Ram, S. M. , and Kang, H. T. , 2010, “ Investigation of Hole Expansion Characteristics of DP 600 With Testing and Modeling,” ASME Paper No. IMECE2010-39455.
Ko, Y. K. , Lee, J. S. , Huh, H. , Kim, H. K. , and Park, S. H. , 2007, “ Prediction of Fracture in Hub Hole Expanding Process Using a New Ductile Fracture Criterion,” J. Mater. Process. Technol., 187–188, pp. 358–362. [CrossRef]
Narayanasamy, R. , Narayanan, C. S. , Padmanabhan, P. , and Venugopalan, T. , 2010, “ Effect of Mechanical and Fractographic Properties on Hole Expandability of Various Automobile Steels During Hole Expansion Test,” Int. J. Adv. Manuf. Technol., 47(1), pp. 365–380. [CrossRef]
Naka, T. , Torikai, G. , Hino, R. , and Yoshida, F. , 2001, “ The Effects of Temperature and Forming Speed on the Forming Limit Diagram for Type 5083 Aluminum-Magnesium Alloy Sheet,” J. Mater. Process. Technol., 113(1–3), pp. 648–653. [CrossRef]
Wu, P. D. , Embury, J. D. , Lloyd, D. J. , Huang, Y. , and Neale, K. W. , 2009, “ Effects of Superimposed Hydrostatic Pressure on Sheet Metal Formability,” Int. J. Plast., 25(9), pp. 1711–1725. [CrossRef]
Padwal, S. B. , Chaturvedi, R. C. , and Rao, U. S. , 1992, “ Influence of Superimposed Hydrostatic Tension on Void Growth in the Neck of a Metal Sheet in Biaxial Stress Fields. Part-I—Modelling,” J. Mater. Process. Technol., 32(1–2), pp. 91–98. [CrossRef]
Banabic, D. , and Soare, S. , 2008, “ On the Effect of the Normal Pressure Upon the Forming Limit Strains,” P. Hora , ed., Seventh International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Interlaken, Switzerland, Sept. 1–5, pp. 199–204. https://www.researchgate.net/profile/Stefan_Soare/publication/274008204_On_the_effect_of_the_normal_pressure_upon_the_forming_limit_strains/links/55125bf20cf268a4aaea2ac2/On-the-effect-of-the-normal-pressure-upon-the-forming-limit-strains.pdf
Allwood, J. M. , and Shouler, D. R. , 2009, “ Generalised Forming Limit Diagrams Showing Increased Forming Limits With Non-Planar Stress States,” Int. J. Plast., 25(7), pp. 1207–1230. [CrossRef]
Zhang, F. , Chen, J. , Chen, J. , and Zhu, X. , 2014, “ Forming Limit Model Evaluation for Anisotropic Sheet Metals Under Through-Thickness Normal Stress,” Int. J. Mech. Sci., 89, pp. 40–46. [CrossRef]
Zhang, F. , Chen, J. , and Chen, J. , 2014, “ Effect of Through-Thickness Normal Stress on Forming Limits Under Yld2003 Yield Criterion and M-K Model,” Int. J. Mech. Sci., 89, pp. 92–100. [CrossRef]
Nurcheshmeh, M. , and Green, D. E. , 2014, “ The Effect of Normal Stress on the Formability of Sheet Metals Under Non-Proportional Loading,” Int. J. Mech. Sci., 82, pp. 131–139. [CrossRef]
Wang, H. , Wu, P. D. , Lee, S. Y. , Wang, J. , and Neale, K. W. , 2015, “ Numerical Study of the Effects of Shear Deformation and Super-Imposed Hydrostatic Pressure on the Formability of AZ31B Sheet at Room Temperature,” Int. J. Mech. Sci., 92, pp. 70–79. [CrossRef]
Banabic, D. , 2016, Multiscale Modelling in Sheet Metal Forming, Springer, Berlin.
Keeler, S. P. , and Backofen, W. A. , 1963, “ Plastic Instability and Fracture in Sheets Stretched Over Rigid Punches,” ASM Trans. Q., 56(1), pp. 25–48.
Goodwin, G. M. , 1968, “ Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop,” SAE Paper No. 680093.
Basak, S. , Panda, S. K. , and Zhou, Y. N. , 2015, “ Formability Assessment of Prestrained Automotive Grade Steel Sheets Using Stress Based and Polar Effective Plastic Strain-Forming Limit Diagram,” ASME J. Eng. Mater. Technol., 137(4), p. 041006. [CrossRef]
He, J. , Xia, Z. C. , Zeng, D. , and Li, S. , 2013, “ Forming Limits of a Sheet Metal After Continuous-Bending-Under-Tension Loading,” ASME J. Eng. Mater. Technol., 135(3), p. 031009. [CrossRef]
Parsa, M. H. , Ettehad, M. , and Matin, P. H. , 2013, “ Forming Limit Diagram Determination of Al 3105 Sheets and Al 3105/Polypropylene/Al 3105 Sandwich Sheets Using Numerical Calculations and Experimental Investigations,” ASME J. Eng. Mater. Technol., 135(3), p. 031003. [CrossRef]
Chow, C. L. , Yang, X. J. , and Chu, E. , 2002, “ Prediction of Forming Limit Diagram Based on Damage Coupled Kinematic-Isotropic Hardening Model Under Non Proportional Loading,” ASME J. Eng. Mater. Technol., 124(2), pp. 259–265. [CrossRef]
Chow, C. L. , Yu, L. G. , and Demeri, M. Y. , 1997, “ A Unified Damage Approach for Predicting Forming Limit Diagrams,” ASME J. Eng. Mater. Technol., 119(4), pp. 346–353. [CrossRef]
Nikhare, C. , Hodgson, P. D. , and Weiss, M. , 2011, “ Necking and Fracture of Advanced High Strength Steels,” Mater. Sci. Eng. A, 528(6), pp. 3010–3013. [CrossRef]
Trozzo, W. , and Nikhare, C. P. , 2014, “ Experimental Investigation of Annealed 5083 Aluminum Alloy,” International Deep-Drawing Research Group (IDDRG), Paris, France, June 1–5, pp. 451–456.
Khaleel, M. A. , Johnson, K. I. , Hamilton, C. H. , and Smith, M. T. , 1998, “ Deformation Modelling of Superplastic AA5083,” Int. J. Plast., 14(10–11), pp. 1133–1154. [CrossRef]
Zhalehfar, F. , Hashemi, R. , and Hossenipour, S. J. , 2015, “ Experimental and Theoretical Investigation of Strain Path Change Effect on Forming Limit Diagram of AA5083,” Int. J. Adv. Manuf. Technol., 76(5), pp. 1343–1352. [CrossRef]


Grahic Jump Location
Fig. 1

Tensile sample dimension and MTS tensile test machine [29]

Grahic Jump Location
Fig. 2

Cruciform specimen with diamond center

Grahic Jump Location
Fig. 3

Biaxial experiment setup with DIC

Grahic Jump Location
Fig. 4

Nakajima hemispherical dome test setup

Grahic Jump Location
Fig. 5

Biaxial model: (a) 3D model and (b) meshed samples

Grahic Jump Location
Fig. 6

Hemispherical dome test model

Grahic Jump Location
Fig. 7

Engineering stress–strain curve for three samples in rolling direction

Grahic Jump Location
Fig. 8

True stress–strain curve along with fitted power law

Grahic Jump Location
Fig. 9

Strain pattern through DIC on deformed biaxial specimen: (a) intermediate strain pattern representation with picked elements for analysis, (b) specimen at the start of deformation, and (c) specimen near to failure

Grahic Jump Location
Fig. 10

Equivalent plastic strain pattern on simulated biaxial specimen: (a) near to failure and (b) separation

Grahic Jump Location
Fig. 11

Engineering stress–strain curve for selected arm regions of cruciform

Grahic Jump Location
Fig. 12

Arm stress–strain curve in biaxial experiment and simulation

Grahic Jump Location
Fig. 13

Deformed specimen during hemispherical dome tests: (a) experiment, (b) simulated equivalent plastic strain patter near to failure, and (c) simulated separation

Grahic Jump Location
Fig. 14

Punch force–displacement comparison during experiment and simulation of hemispherical dome test

Grahic Jump Location
Fig. 15

Engineering stress–strain curve for arm location during biaxial and hemispherical dome simulation

Grahic Jump Location
Fig. 16

Engineering stress–strain curve for center location during biaxial and hemispherical dome simulation

Grahic Jump Location
Fig. 17

Biaxial strain path during biaxial and hemispherical dome simulation along with as received material forming limit diagram

Grahic Jump Location
Fig. 18

Stress–strain response under hydrostatic pressure (Reprinted with permission from Wu et al. [12]. Copyright 2009 by Elsevier.)

Grahic Jump Location
Fig. 19

Effective stress–strain response under hydrostatic pressure (Reprinted with permission from Wu et al. [12]. Copyright 2009 by Elsevier.)

Grahic Jump Location
Fig. 20

Forming limit diagram under hydrostatic pressure (Reprinted with permission from Wu et al. [12]. Copyright 2009 by Elsevier.)

Grahic Jump Location
Fig. 21

Biaxial strain path during biaxial and hemispherical dome simulation along with hypothetic annealed FLC and pressurized FLC




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In