Research Papers

Experimental and Numerical Investigation of Forming Limit Differences in Biaxial and Dome Test

[+] Author and Article Information
Chetan P. Nikhare

Department of Mechanical Engineering,
Penn State Erie—The Behrend College,
Erie, PA 16563
e-mail: cpn10@psu.edu

Manuscript received July 28, 2017; final manuscript received February 24, 2018; published online May 28, 2018. Assoc. Editor: Gracious Ngaile.

J. Manuf. Sci. Eng 140(8), 081005 (May 28, 2018) (12 pages) Paper No: MANU-17-1481; doi: 10.1115/1.4039587 History: Received July 28, 2017; Revised February 24, 2018

For centuries, metals and materials have been characterized using a traditional method called a uniaxial tension test. The data acquired from this test found to be adequate for operations of simple forming where one axis stretching is dominant. Currently, due to the demand of lightweight component production, multiple individual parts eliminated by stamping a single complex shape, which also further reduces many secondary operations. This change is driving by the new fuel-efficiency requirement by corporate average fuel economy of 55.8 miles per gallon by 2025.1 Due to complex part geometry, this forming method induces multiaxial stress states, which are difficult to predict using conventional tools. Thus, to analyze these multiaxial stress states limiting dome height tests and bulge tests were recommended in many research publications. However, these tests limit the possibilities of applying multiaxial loading and rather a sample geometry changes are required to imply multiaxial stresses. Even this capability is not an option in bulge test due to leakage issue. Thus, a test machine called a biaxial test was devised that would provide the capability to test the specimen in multiaxial stress states by varying the independent load or displacement on two independent axis. In this paper, two processes, limiting dome tests and biaxial tests were experimented, modeled, and compared. For the biaxial tests, a cruciform test specimen was utilized, and conventional forming limit specimens were used for the dome tests. Variation of sample geometry in limiting dome test and variation of loading in biaxial test were utilized to imply multiaxial stress states in order to capture the limit strain from uniaxial to equibiaxial strain mode. In addition, the strain path, forming, and formability investigated and the differences between the tests provided. From the results, it was noted that higher limit strains were acquired in dome tests than in biaxial tests due to contact pressure from the rigid punch. The literature shows that the contact pressure (which occurs when the rigid tool contacts the deformed body), increases the deformation and thus increases the limit strains to failure. This contact pressure parameter is unavailable in biaxial test, and thus, a pure material behavior can be obtained. However, limit strains from biaxial test cannot be considered for a process where rigid tool is processing the metal, and thus, calibration is necessary.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Mayyas, A. , Shen, Q. , Mayyas, A. , Shan, D. , Qattawi, A. , and Omar, M. , 2011, “ Using Quality Function Deployment and Analytical Hierarchy Process for Material Selection of Body-in-White,” Mater. Des., 32(5), pp. 2771–2782. [CrossRef]
Banabic, D. , 2016, “ Advances in Plastic Anisotropy and Forming Limits in Sheet Metal Forming,” ASME J. Manuf. Sci. Eng., 138(9), p. 090801. [CrossRef]
Abu-Farha, F. , Hector, L. G. , and Khraisheh, M. , 2009, “ Cruciform-Shaped Specimens for Elevated Temperature Biaxial Testing of Lightweight Materials,” JOM J. Miner. Met. Mater. Soc., 61(8), pp. 48–56. [CrossRef]
Woodthrope, J. , and Pearce, R. , 1970, “ Anomalous Behaviour of Aluminium Sheet Under Balanced Biaxial Tension,” Int. J. Mech. Sci., 12(4), pp. 341–347. [CrossRef]
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.
Nikhare, C. , Korkolis, Y. , and Kinsey, B. L. , 2012, “ Numerical Analysis of Restrike Process on Al-2008-T4 Aluminum Alloy Square Pan Drawing,” International Deep Drawing Research Group Conference, Mumbai, India, Nov. 25–29, pp. 581–686.
Keeler, S. , 1965, “ Determination of Forming Limits in Automotive Stampings,” SAE Paper No. 650535.
Goodwin, G. M. , 1968, “ Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop,” SAE Paper No. 680093.
Sowerby, R. , and Duncan, J. L. , 1971, “ Failure in Sheet Metal in Biaxial Tension,” Int. J. Mech. Sci., 13(3), pp. 217–229. [CrossRef]
Arrieux, R. , Boivin, M. , and Le Maître, F. , 1987, “ Determination of the Forming Limit Stress Curve for Anisotropic Sheets,” CIRP Ann. Manuf. Technol., 36(1), pp. 195–198. [CrossRef]
Arrieux, R. , Bedrin, C. , and Boivin, M. , 1982, “ Determination of an Intrinsic Forming Limit Stress Diagram for Isotropic Metals Sheets,” 12th Biennial Congress International Deep Drawing Research Group, Santa Margherita Ligure, Italy, May 24–28, pp. 61–72.
Da Rocha, A. B. , Barlat, F. , and Jalinier, J. M. , 1985, “ Prediction of the Forming Limit Diagrams of Anisotropic Sheets in Linear and Non-Linear Loading,” Mater. Sci. Eng., 68(2), pp. 151–164. [CrossRef]
Graf, A. F. , and Hosford, W. F. , 1993, “ Calculations of Forming Limit,” Metall. Mater. Trans. A, 24(11), pp. 2497–2501. [CrossRef]
Sheng, Z. Q. , and Mallick, P. K. , 2017, “ Predicting Sheet Forming Limit of Aluminum Alloys for Cold and Warm Forming by Developing a Ductile Failure Criterion,” ASME J. Manuf. Sci. Eng., 139(11), p. 111018. [CrossRef]
Ghosh, A. K. , 1974, “ Strain Localization in the Diffuse Neck in Sheet Metal,” Metall. Trans., 5(7), pp. 1607–1616. [CrossRef]
Stachowicz, F. , 1989, “ Effects of Microstructure on the Mechanical Properties and Limit Strains in Uniaxial and Biaxial Stretching,” J. Mech. Work. Technol., 19(3), pp. 305–317. [CrossRef]
Li, J. , Carsley, J. E. , Stoughton, T. B. , Hector, L. G. , and Hu, S. J. , 2013, “ Forming Limit Analysis for Two-Stage Forming of 5182-O Aluminum Sheet With Intermediate Annealing,” Int. J. Plast., 45, pp. 21–43. [CrossRef]
Korkolis, Y. P. , and Kyriakides, S. , 2009, “ Path-Dependent Failure of Inflated Aluminum Tubes,” Int. J. Plast., 25(11), pp. 2059–2080. [CrossRef]
Yoshida, K. , Kuwabara, T. , Narihara, K. , and Takahashi, S. , 2005, “ Experimental Verification of the Path-Independence of Forming Limit Stresses,” Int. J. Form. Process., 8, pp. 283–298. https://www.researchgate.net/publication/284544650_Experimental_verification_of_the_path-independence_of_forming_limit_stresses
Nikhare, C. P. , Korkolis, Y. P. , and Kinsey, B. L. , 2015, “ Formability Enhancement in Titanium Tube-Flaring by Manipulating the Deformation Path,” ASME J. Manuf. Sci. Eng., 137(5), p. 051006. [CrossRef]
Raghavan, K. S. , 1995, “ A Simple Technique to Generate In-Plane Forming Limit Curves and Selected Applications,” Metall. Mater. Trans. A, 26(8), pp. 2075–2084. [CrossRef]
Nikhare, C. , Filho, R. A. C. , Tigrinho, L. M. V. , and Marcondes, P. V. P. , 2012, “ Influence of Blank Holding Force on the Forming Limits of DP590 Steel,” International Deep Drawing Research Group Conference, Mumbai, India, Nov. 25–29, pp. 553–559.
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. 475–481. [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(1–4), 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 II: Plastic Instability,” J. Mater. Process. Technol., 32(1–2), pp. 99–107. [CrossRef]
Banabic, D. , and Soare, S. , 2008, “ On the Effect of the Normal Pressure Upon the Forming Limit Strains,” Seventh International Conference and Workshop on Numerical Simulation of 3D Metal Forming Process (Numisheet), Interlaken, Switzerland, Sept. 1–5, pp. 1–5. 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 MK 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 Superimposed Hydrostatic Pressure on the Formability of AZ31B Sheet at Room Temperature,” Int. J. Mech. Sci., 92, pp. 70–79. [CrossRef]
Banabic, D. ed., 2016, Multiscale Modelling in Sheet Metal Forming, Springer, Berlin. [CrossRef]
Nikhare, C. P. , Vorisek, E. , Nolan, J. , and Roth, J. T. , 2017, “ Forming Limit Differences in Hemispherical Dome and Biaxial Test During Equi-Biaixal Tension on Cruciform,” ASME J. Eng. Mater. Technol., 139(4), p. 041011. [CrossRef]
Nikhare, C. P. , 2018, “ Numerical Analysis on the Effect of Thickness on Biaxial Tension Limits,” Mater. Today: Proc., 5(1), pp. 37–43. [CrossRef]
ASTM, 2004, “ Standard Test Methods for Tension Testing of Metallic Materials,” ASTM International, West Conshohocken, PA, Standard No. ASTM E8-04. https://www.astm.org/DATABASE.CART/HISTORICAL/E8-04.htm
Nakazima, K. , Kikuma, T. , and Hasuka, K. , 1968, “ Study on the Formability of Steel Sheets,” Yawata Tech. Rep., 264, pp. 8517–8530.
Abu-Farha, F. , 2011, “ The Development of a Forming Limit Surface for 5083 Aluminum Alloy Sheet,” JOM, 63(11), pp. 72–78. [CrossRef]
Menezes, L. F. , and Teodosiu, C. , 2000, “ Three-Dimensional Numerical Simulation of the Deep-Drawing Process Using Solid Finite Elements,” J. Mater. Process. Technol., 97(1–3), pp. 100–106. [CrossRef]
Wagoner, R. H. , and Chenot, J. L. , 2001, Metal Forming Analysis, Cambridge University Press, Cambridge, UK, pp. 198–199. [CrossRef] [PubMed] [PubMed]
Hasan, R. , Kasikci, T. , Tsukrov, I. , and Kinsey, B. L. , 2014, “ Numerical and Experimental Investigations of Key Assumptions in Analytical Failure Models for Sheet Metal Forming,” ASME J. Manuf. Sci. Eng., 136(1), p. 011013. [CrossRef]
Kumar, S. , Date, P. P. , and Narasimhan, K. , 1994, “ A New Criterion to Predict Necking Failure Under Biaxial Stretching,” J. Mater. Process. Technol., 45(1–4), pp. 583–588. [CrossRef]
Nandedkar, V. M. , 2000, “ Formability Studies on a Deep Drawing Quality Steel,” Ph.D. thesis, IIT Bombay, Mumbai, India.
Marziniak, Z. , and Kuczynski, K. , 1967, “ Limit Strain in the Process of Stretch-Forming Sheet Metals,” Int. J. Mech. Sci., 9(9), pp. 609–620. [CrossRef]
He, J. , Xia, Z. C. , Li, S. , and Zeng, D. , 2013, “ M–K Analysis of Forming Limit Diagram Under Stretch-Bending,” ASME J. Manuf. Sci. Eng., 135(4), p. 041017. [CrossRef]
Hosford, W. F. , and Caddell, R. M. , 1993, Forming Limits. Metal Forming-Mechanics and Metallurgy, 2nd ed., Prentice Hall, Upper Saddle River, NJ.
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]


Grahic Jump Location
Fig. 2

Cruciform specimen with diamond center

Grahic Jump Location
Fig. 1

True stress–true strain curve along with fitted power law (Permission to reprint from ASME @ 2017 [37])

Grahic Jump Location
Fig. 9

Schematic illustration of a sheet with pre-existing groove (Reproduced from [49])

Grahic Jump Location
Fig. 7

Cruciform specimen with center diamond (a) with boundary condition and (b) mesh specimen

Grahic Jump Location
Fig. 6

Nakajima hemispherical dome test setup

Grahic Jump Location
Fig. 5

Electrochemically etched circles on samples

Grahic Jump Location
Fig. 4

Seven specimen geometries to provide strain from uniaxial to equibiaxial strain in hemispherical dome test (diameter = 101.6 mm, radius = 38.1 mm, x = 12.7, 25.4, 38.1, 50.8, 63.5, and 76.2 from specimen 1 to 6) [41]

Grahic Jump Location
Fig. 3

Biaxial experiment setup with DIC

Grahic Jump Location
Fig. 8

Nakajima hemispherical dome test (a) numerical model, (b) specimen general dimension, and (c) mesh specimen

Grahic Jump Location
Fig. 10

Deformed samples using biaxial test machine: (a) uniaxial strain, (b) plane–strain, (c) between plane–strain and equibiaxial strain, (d) equibiaxial strain deformation mode, and (e) deformed diamond shape comparison for (a)–(d) deformation modes

Grahic Jump Location
Fig. 11

All formed specimens using biaxial method captured at neck/fail frame: (a) uniaxial strain, (b) between uniaxial strain and plane–strain, (c) plane–strain, (d) between plane–strain and equibiaxial strain, and (e) equibiaxial strain deformation mode (legend shows engineering major strain, i.e., NE22 in abaqus)

Grahic Jump Location
Fig. 12

Forming limit diagram from specimen simulated in biaxial model

Grahic Jump Location
Fig. 13

Seven deformed specimens using dome test: (a) uniaxial strain, (b) and (c) between uniaxial strain and plane–strain, (d) plane–strain, (e) and (f) between plane–strain and equibiaxial strain, and (g) equibiaxial strain deformation mode

Grahic Jump Location
Fig. 14

All formed specimens using dome test method captured at neck/fail frame: (a) uniaxial strain, (b) between uniaxial strain and plane–strain, (c) plane–strain, (d) between plane–strain and equibiaxial strain, and (e) equibiaxial strain deformation mode (legend shows engineering major strain, i.e., NE22 in abaqus)

Grahic Jump Location
Fig. 15

Forming limit diagram from specimen simulated in dome test model

Grahic Jump Location
Fig. 16

Forming limit diagram for limit comparison between biaxial test and dome test



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