A Review of Cruciform Biaxial Tensile Testing of Sheet Metals



Biaxial testing technology enables the comprehensive study of sheet-forming performance and has great potential developmental and commercial value. This work is a review of cruciform biaxial tensile testing technology, as used in actual production, and provides evidence for sheet metal forming processes to describe problems that remain to be solved and to suggest new ideas for future study. The testing apparatus including cruciform biaxial tensile testing machines, heating devices, and optical strain measurement systems are discussed. Some typical descriptions of material tests to achieve stress and strain curves, the yield loci, and limit strains relating to both ambient and high temperatures are also presented. Moreover, finite element modeling as applied to specimen design, material deformation prediction, and material model determination is investigated. Furthermore, the sample design methods and a few examples are summarized in spite of the lack of geometry standard. Future prospects are mainly focused on the establishment of specimen geometry standard, reverse modeling technique for high temperature tests, and the actual applications of biaxial tensile tests.


Biaxial tensile Specimen design Testing apparatus Material testing 



The funding source of this work from the “Superplastic forming and diffusion bonding technology of light-weight material multilayer structure” research project are gratefully acknowledged. The funding number is G011801. The author thanks the Heat Processing Department, Beijing Hangxing Technology Development Company.


  1. 1.
    Zhou M, Clode MP (1997) A constitutive model and its identification for the deformation characterized by dynamic recovery. J Eng Mater Technol 119(2):138–142CrossRefGoogle Scholar
  2. 2.
    Meng B, Wan M, Wu X, Zhou Y, Chang C (2014) Constitutive modeling for high-temperature tensile deformation behavior of pure molybdenum considering strain effects. Int J Refract Met Hard Mater 45:41–47CrossRefGoogle Scholar
  3. 3.
    Nakazima K, Kikuma T, Hasuka K (1968) Study on the formability of steel sheets. Yawata Technical Report, No 264:8517–8530Google Scholar
  4. 4.
    Takuda H, Mori K, Fujimoto H, Hatta N (1996) Prediction of forming limit in deep drawing of Fe/Al laminated composite sheets using ductile fracture criterion. J Mater Process Technol 60(1):291–296CrossRefGoogle Scholar
  5. 5.
    Lang L-H, Du P-M, Liu B-S, Cai G-C, Liu K-N (2013) Pressure rate controlled unified constitutive equations based on microstructure evolution for warm hydroforming. J Alloys Compd 574:41–48CrossRefGoogle Scholar
  6. 6.
    Shiratori E, Ikegami K (1967) A new biaxial tensile testing machine with flat specimen. Bulletin of the Tokyo Institute of Technology 82:105–118Google Scholar
  7. 7.
    Nikhare CP, Vorisek E, Nolan JR, Roth JT (2017) Forming limit differences in hemispherical dome and biaxial test during Equibiaxial tension on cruciform. J Eng Mater Technol 139(4):041011CrossRefGoogle Scholar
  8. 8.
    Makinde A, Thibodeau L, Neale K (1992) Development of an apparatus for biaxial testing using cruciform specimens. Exp Mech 32(2):138–144CrossRefGoogle Scholar
  9. 9.
    Kuwabara T, Ikeda S, Kuroda K (1998) Measurement and analysis of differential work hardening in cold-rolled steel sheet under biaxial tension. J Mater Process Technol 80-81:517–523CrossRefGoogle Scholar
  10. 10.
    Deng N, Kuwabara T, Korkolis YP (2015) Cruciform specimen design and verification for constitutive identification of anisotropic sheets. Exp Mech 55(6):1005–1022CrossRefGoogle Scholar
  11. 11.
    Schmaltz S, Willner K (2014) Comparison of different biaxial tests for the inverse identification of sheet steel material parameters. Strain 50(5):389–403CrossRefGoogle Scholar
  12. 12.
    Boehler JP, Demmerle S, Koss S (2003) A new direct biaxial testing machine for anisotropic materials. Exp Mech 20(2):153–159Google Scholar
  13. 13.
    Lin SB, Ding JL (1995) Experimental study of the plastic yielding of rolled sheet metals with the cruciform plate specimen. Int J Plast 11(5):583–604CrossRefGoogle Scholar
  14. 14.
    Kulawinski D, Ackermann S, Seupel A, Lippmann T, Henkel S, Kuna M et al (2015) Deformation and strain hardening behavior of powder metallurgical TRIP steel under quasi-static biaxial-planar loading. Mater Sci Eng A 642:317–329CrossRefGoogle Scholar
  15. 15.
    Lamkanfi E, Van Paepegem W, Degrieck J (2015) Shape optimization of a cruciform geometry for biaxial testing of polymers. Polym Test 41: 7–16Google Scholar
  16. 16.
    Liu W, Guines D, Leotoing L, Ragneau E (2016) Identification of strain rate-dependent mechanical behaviour of DP600 under in-plane biaxial loadings. Mater Sci Eng A 676:366–376CrossRefGoogle Scholar
  17. 17.
    Wu X-D, Wan M, Zhou X-B (2005) Biaxial tensile testing of cruciform specimen under complex loading. J Mater Process Technol 168(1):181–183CrossRefGoogle Scholar
  18. 18.
    Zidane I, Guines D, Léotoing L, Ragneau E (2010) Development of an in-plane biaxial test for forming limit curve (FLC) characterization of metallic sheets. Meas Sci Technol 21(5):055701CrossRefGoogle Scholar
  19. 19.
    Pan B, Qian K, Xie H, Asundi A (2009) TOPICAL REVIEW: two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20(6):152–154CrossRefGoogle Scholar
  20. 20.
    Pan B, Yu L, Wu D (2015) Thermo-mechanical response of superalloy honeycomb sandwich panels subjected to non-steady thermal loading. Mater Des 88:528–536CrossRefGoogle Scholar
  21. 21.
    Kuwabara T (2014) 1.06 - biaxial stress testing methods for sheet metals. In: Hashmi S, Batalha GF, Van Tyne CJ, Yilbas B (eds) Comprehensive materials processing. Elsevier, Oxford, pp 95–111CrossRefGoogle Scholar
  22. 22.
    Güler B, Efe M (2018) Forming and fracture limits of sheet metals deforming without a local neck. J Mater Process Technol 252:477–484CrossRefGoogle Scholar
  23. 23.
    Abu-Farha F, Khraisheh M (2010) Uniaxially-driven controlled biaxial testing fixture US Patent No - US2009282929Google Scholar
  24. 24.
    Abu-Farha F, Hector LG, Khraisheh M (2009) Cruciform-shaped specimens for elevated temperature biaxial testing of lightweight materials. Jom J Miner Met Mater Soc 61(8):48–56CrossRefGoogle Scholar
  25. 25.
    Iizuka E, Hashimoto K, Kuwabara T (2014) Effects of anisotropic yield functions on the accuracy of forming simulations of hole expansion. Procedia Engineering 81:2433–2438CrossRefGoogle Scholar
  26. 26.
    Medellín LFP, De la Peña JÁD (2017) Design of a biaxial test module for uniaxial testing machine. Materials Today: Proceedings 4(8):7911–7920CrossRefGoogle Scholar
  27. 27.
    Iadicola MA, Creuziger AA, Foecke T (2014) Advanced biaxial cruciform testing at the NIST Center for automotive Lightweighting. In: Rossi M et al (eds) Residual stress, Thermomechanics & Infrared Imaging, hybrid techniques and inverse problems. Conference proceedings of the Society for Experimental Mechanics Series, vol 8. Springer, Cham, pp 277–285Google Scholar
  28. 28.
    Iadicola MA, Foecke T (2005) Effect of plastic deformation and strain history on X-ray elastic constants. In: Smith L M, Pourboghrat F, Yoon J W, Stoughton T B (eds) Numerical Simulation of 3D Sheet Metal Forming Process. AIP Conference Proceedings, Vol. 778, No. 1, pp. 240–240. American Institute of PhysicsGoogle Scholar
  29. 29.
    Terriault P, Settouane K, Brailovski V (2004) Biaxial Testing at Different Temperatures of Cruciform Ti-Ni Samples. In: SMST 2003: Proceedings of the International Conference on Shape Memory and Superelastic Technologies, Hong Kong, pp. 247–257. ASM InternationalGoogle Scholar
  30. 30.
    Geiger M, Hußnätter W, Merklein M (2005) Specimen for a novel concept of the biaxial tension test. J Mater Process Technol 167(2–3):177–183CrossRefGoogle Scholar
  31. 31.
    Bruschi S, Altan T, Banabic D, Bariani PF, Brosius A, Cao J et al (2014) Testing and modelling of material behaviour and formability in sheet metal forming. CIRP Ann 63(2):727–749CrossRefGoogle Scholar
  32. 32.
    Geiger M, van der Heyd G, Merklein M, Hussnätter W (2005) Novel concept of experimental setup for characterisation of plastic yielding of sheet metal at elevated temperatures. Adv Mater Res 6-8:657–664CrossRefGoogle Scholar
  33. 33.
    Chevalier L, Marco Y (2007) Identification of a strain induced crystallisation model for PET under uni- and bi-axial loading: influence of temperature dispersion. Mech Mater 39(6):596–609CrossRefGoogle Scholar
  34. 34.
    Kulawinski D, Henkel S, Holländer D, Thiele M, Gampe U, Biermann H (2014) Fatigue behavior of the nickel-base superalloy Waspaloy™ under proportional biaxial-planar loading at high temperature. Int J Fatigue 67:212–219CrossRefGoogle Scholar
  35. 35.
    Xiao R, Li X-X, Lang L-H, Chen Y-K, Yang Y-F (2016) Biaxial tensile testing of cruciform slim superalloy at elevated temperatures. Mater Des 94:286–294CrossRefGoogle Scholar
  36. 36.
    Shao Z, Li N, Lin J, Dean TA (2016) Development of a new biaxial testing system for generating forming limit diagrams for sheet metals under hot stamping conditions. Exp Mech 56(9):1489–1500CrossRefGoogle Scholar
  37. 37.
    Le Cam J-B, Robin E, Leotoing L, Guines D (2017) Calorimetric analysis of Portevin-Le Chatelier bands under equibiaxial loading conditions in Al–mg alloys: kinematics and mechanical dissipation. Mech Mater 105:80–88CrossRefGoogle Scholar
  38. 38.
    Kuwabara T, Kumano Y, Ziegelheim J, Kurosaki I (2009) Tension–compression asymmetry of phosphor bronze for electronic parts and its effect on bending behavior. Int J Plast 25(9):1759–1776CrossRefGoogle Scholar
  39. 39.
    Banerjee D, Iadicola M, Creuziger A, Foecke T (2016) An experimental and numerical study of deformation behavior of steels in biaxial tensile tests. In: The minerals, Metals & Materials Society (eds) TMS 2015 144th annual meeting & exhibition, Orlando. Springer, Cham, pp 279–288Google Scholar
  40. 40.
    Xiao R, Li X-X, Lang L-H, Song Q, Liu K-N (2017) Forming limit in thermal cruciform biaxial tensile testing of titanium alloy. J Mater Process Technol 240:354–361CrossRefGoogle Scholar
  41. 41.
    Shao Z, Li N, Lin J (2017) The optimisation of cruciform specimen for the formability evaluation of AA6082 under hot stamping conditions. Procedia Eng 207:735–740CrossRefGoogle Scholar
  42. 42.
    Shao Z, Li N, Lin J, Dean T (2017) Formability evaluation for sheet metals under hot stamping conditions by a novel biaxial testing system and a new materials model. Int J Mech Sci 120:149–158CrossRefGoogle Scholar
  43. 43.
    Kuwabara T (2007) Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations. Int J Plast 23(3):385–419CrossRefGoogle Scholar
  44. 44.
    Kuwabara T, Hashimoto K, Iizuka E, Yoon JW (2011) Effect of anisotropic yield functions on the accuracy of hole expansion simulations. J Mater Process Technol 211(3):475–481CrossRefGoogle Scholar
  45. 45.
    Kuwabara T, Van Bael A, Iizuka E (2002) Measurement and analysis of yield locus and work hardening characteristics of steel sheets wtih different r-values. Acta Mater 50(14):3717–3729CrossRefGoogle Scholar
  46. 46.
    Wu X-D, Wan M, Zhou X-B (2006) Theoretical and experimental study on constitutive modeling of sheet metal under proportional loading path. Chin J Mech Eng-En 17(19):1993–1996Google Scholar
  47. 47.
    Song X, Leotoing L, Guines D, Ragneau E (2017) Identification of forming limits at fracture of DP600 sheet metal under linear and unloaded non-linear strain paths. Procedia Eng 207:562–567CrossRefGoogle Scholar
  48. 48.
    Song X, Leotoing L, Guines D, Ragneau E (2017) Characterization of forming limits at fracture with an optimized cruciform specimen: application to DP600 steel sheets. Int J Mech Sci 126:35–43CrossRefGoogle Scholar
  49. 49.
    Seymen Y, Güler B, Efe M (2016) Large strain and small-scale biaxial testing of sheet metals. Exp Mech 56(9):1519–1530CrossRefGoogle Scholar
  50. 50.
    Leotoing L, Guines D (2015) Investigations of the effect of strain path changes on forming limit curves using an in-plane biaxial tensile test. Int J Mech Sci 99:21–28CrossRefGoogle Scholar
  51. 51.
    Han F, Wan M, Wu X-D, Wang H-B (2007) A new method for establishing forming limit stress diagram of sheet metals. J Plast Eng 14(4):1–5Google Scholar
  52. 52.
    Hußnätter W, Merklein M, Geiger M (2007) Characterization of yielding of sheet metal at elevated temperatures. J Mater Process Technol 191(1–3):20–23CrossRefGoogle Scholar
  53. 53.
    Merklein M, Hußnätter W, Geiger M (2008) Characterization of yielding behavior of sheet metal under biaxial stress condition at elevated temperatures. CIRP Ann Manuf Technol 57(1):269–274CrossRefGoogle Scholar
  54. 54.
    Geiger M, Merklein M, Hußnätter W, Grüner M (2008) Experimental determination of yield loci for magnesium alloy AZ31 under biaxial tensile stress conditions at elevated temperatures. Prod Eng 2(3):303–310CrossRefGoogle Scholar
  55. 55.
    Xiao R (2017) Research on the deformation behavior of materials under complex loading and its application in the hot hydroforming. PhD Thesis, Beihang UniversityGoogle Scholar
  56. 56.
    Dawicke DS, Pollock WD (1997) Biaxial testing of 2219-T87 aluminum alloy using cruciform specimens. Nasa Contractor Report 4782:1–46Google Scholar
  57. 57.
    Liu W, Guines D, Leotoing L, Ragneau E (2015) Identification of sheet metal hardening for large strains with an in-plane biaxial tensile test and a dedicated cross specimen. Int J Mech Sci 101-102:387–398CrossRefGoogle Scholar
  58. 58.
    Zhang S, Léotoing L, Guines D, Thuillier S (2015) Potential of the cross biaxial test for anisotropy characterization based on heterogeneous strain field. Exp Mech 55(5):817–835CrossRefGoogle Scholar
  59. 59.
    Tomičević Z, Kodvanj J, Hild F (2016) Characterization of the nonlinear behavior of nodular graphite cast iron via inverse identification: analysis of biaxial tests. Eur J Mech A Solids 59:195–209CrossRefGoogle Scholar
  60. 60.
    Green DE, Neale KW, MacEwen SR, Makinde A, Perrin R (2004) Experimental investigation of the biaxial behaviour of an aluminum sheet. Int J Plast 20(8–9):1677–1706CrossRefGoogle Scholar
  61. 61.
    Leotoing L, Guines D, Zidane I, Ragneau E (2013) Cruciform shape benefits for experimental and numerical evaluation of sheet metal formability. J Mater Process Technol 213(6):856–863CrossRefGoogle Scholar
  62. 62.
    Song X, Leotoing L, Guines D, Ragneau E (2016) Investigation of the forming limit strains at fracture of AA5086 sheets using an in-plane biaxial tensile test. Eng Fract Mech 163:130–140CrossRefGoogle Scholar
  63. 63.
    Hannon A, Tiernan P (2008) A review of planar biaxial tensile test systems for sheet metal. J Mater Process Technol 198(1–3):1–13CrossRefGoogle Scholar
  64. 64.
    Tiernan P, Hannon A (2012) Design optimisation of biaxial tensile test specimen using finite element analysis. Int J Mater Form 7(1):117–123CrossRefGoogle Scholar
  65. 65.
    Xiao R, Li X-X, Lang L-H, Chen Y-K, Ge Y-L (2016) Design of Biaxial Tensile Cruciform Specimen Based on Simulation Optimization. In: International Conference on Machinery, Materials Engineering, Chemical Engineering and Biotechnology, Chongqing, pp. 178–186. Atlantis PressGoogle Scholar
  66. 66.
    Creuziger A, Iadicola MA, Foecke T, Rust E, Banerjee D (2017) Insights into cruciform sample design. Jom J Miner Met Mater Soc 69(5):902–906CrossRefGoogle Scholar
  67. 67.
    Hu JJ, Chen GW, Liu YC, Hsu SS (2013) Influence of specimen geometry on the estimation of the planar biaxial mechanical properties of cruciform specimens. Exp Mech 54(4):615–631CrossRefGoogle Scholar
  68. 68.
    Upadhyay MV, Panzner T, Van Petegem S, Van Swygenhoven H (2017) Stresses and strains in cruciform samples deformed in tension. Exp Mech 57(6):905–920CrossRefGoogle Scholar
  69. 69.
    Li Z, Shi X, Chen X, Wang H (2013) Optimization of a Biaxial Loading for Cruciform Specimen of Composite Based on Modified ACO Mechanical Science and Technology for Aerospace Engineering 32(3): 462–468Google Scholar
  70. 70.
    Merklein M, Biasutti M (2013) Development of a biaxial tensile machine for characterization of sheet metals. J Mater Process Technol 213(6):939–946CrossRefGoogle Scholar
  71. 71.
    Mitukiewicz G, Głogowski M (2016) Cruciform specimen to obtain higher plastic deformation in a gauge region. J Mater Process Technol 227:11–15CrossRefGoogle Scholar
  72. 72.
    Hanabusa Y, Takizawa H, Kuwabara T (2013) Numerical verification of a biaxial tensile test method using a cruciform specimen. J Mater Process Technol 213(6):961–970CrossRefGoogle Scholar
  73. 73.
    Tasan CC, Hoefnagels JPM, Quaak G, Geers MGD (2008) In-plane biaxial loading of sheet metal until fracture. In: Proulx T (ed) 11th international congress and exhibition on experimental and applied mechanics 2008. Society for Experimental Mechanics, Orlando, pp 1729–1736Google Scholar
  74. 74.
    Ghiotti A, Bruschi S, Bariani PF (2007) Determination of yield locus of sheet metal at elevated temperatures: a novel concept for experimental set-up. Key Eng Mater 344:97–104CrossRefGoogle Scholar

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© The Society for Experimental Mechanics, Inc 2019

Authors and Affiliations

  1. 1.Thermal Processing Department, Beijing Hangxing Machinery Co., LtdBeijingChina

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