# Biaxial Testing of Sheet Materials at High Strain Rates Using Viscoelastic Bars

- 534 Downloads
- 25 Citations

## Abstract

A dynamic bulge testing technique is developed to perform biaxial tests on metals at high strain rates. The main component of the dynamic testing device is a movable bulge cell which is directly mounted on the measuring end of the input bar of a conventional split Hopkinson pressure bar system. The input bar is used to apply and measure the bulging pressure. The experimental system is analyzed in detail and the measurement accuracy is discussed. It is found that bars made of low impedance materials must be used to achieve a satisfactory pressure measurement accuracy. A series of dynamic experiments is performed on aluminum 6111-T4 sheets using viscoelastic nylon bars to demonstrate the capabilities of the proposed experimental technique. The parameters of the rate-dependent Hollomon–Cowper–Symonds J2 plasticity model of the aluminum are determined using an inverse analysis method in conjunction with finite element simulations.

## Keywords

Bulge test Biaxial experiments Rate-dependent plasticity Split Hopkinson pressure bar apparatus High strain rates## Notes

### Acknowledgement

The partial support by the program “De la mise en forme au comportement dynamique” of the Région Bretagne is gratefully acknowledged. The authors wish to thank Mr. R. Barre from LMS, Mr. H. Bellegou from LG2M and Mr. F. Portanguen from UBS University for their technical assistance.

## References

- 1.Atkinson M (1997) Accurate determination of biaxial stress–strain relationships from hydraulic bulging tests of sheet metals. Int J Mech Sci 39(7):761–769.CrossRefGoogle Scholar
- 2.Broomhead P, Grieve RJ (1982) Effect of strain rate on the strain to fracture of a sheet steel under biaxial tensile stress conditions. J Eng Mater Technol 104(2):102–106.CrossRefGoogle Scholar
- 3.Brown WF Jr., Thompson FC (1949) Strength and failure characteristics of metal in circular bulging. Trans Am Soc Mech Eng 71:575–585.Google Scholar
- 4.Chakrabarty J, Alexander JM (1970) Hydrostatic bulging of circular diaphragms. J Strain Anal 5(3):155–161.CrossRefGoogle Scholar
- 5.Gary G (2005) DAVID instruction manual, Palaiseau, France http://www.lms.polytechnique.fr/EQUIPE/dynamique/index.html.
- 6.Gleyzal A (1948) Plastic deformation of a circular diaphragm under pressure. J Appl Mech 70:288–296.MathSciNetGoogle Scholar
- 7.Gutscher G, Wu H-C, Ngaile G, Altan T (2004) Determination of flow stress for sheet metal forming using the viscous pressure bulge (VPB) test. J Mater Process Technol 146(1):1–7.CrossRefGoogle Scholar
- 8.Hill R (1950) A theory of the plastic bulging of a metal diaphragm by lateral pressure. Philos Mag 4(322):1133–1142.Google Scholar
- 9.Jones N (1997) Structural impact. Cambridge University Press.Google Scholar
- 10.Livermore Software Technology Corporation (2003) LS-DYNA 970 user's manuals. Livermore Software Technology Corporation, Livermore.Google Scholar
- 11.Mahmudi R (1993) Forming limits in biaxial stretching of aluminium sheets and foils. J Mater Process Technol 37(1–4):203–216.CrossRefGoogle Scholar
- 12.Nicholson ED, Field JE (1994) The mechanical and thermal properties of thin films. J Hard Mater 5:89–132.Google Scholar
- 13.NIST (1994) Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST Technical Note 1297. NIST, Gaithersburg.Google Scholar
- 14.Othman R, Blanc RH, Bussac M-N, Collet P, Gary G (2002) Identification of the dispersion relation in rods, C.R. Mecanique 330:849–855.CrossRefzbMATHGoogle Scholar
- 15.Pickett AK, Pyttel T, Payen F, Lauro F, Petrinic N, Werner H, Christlein J (2004) Failure prediction for advanced crashworthiness of transportation vehicles. Int J Impact Eng 30(7):853–872.CrossRefGoogle Scholar
- 16.Ranta-Eskola AJ (1979) Use of the hydraulic bulge test in biaxial tensile testing. Int J Mech Sci 21(8):457–465.CrossRefGoogle Scholar
- 17.Rees DWA (1995) Instability limits to the forming of sheet metals. J Mater Process Technol 55(3–4):146–153.CrossRefGoogle Scholar
- 18.Rees DWA (1995) Plastic flow in the elliptical bulge test. Int J Mech Sci 37(4):373–389.CrossRefMathSciNetGoogle Scholar
- 19.Rees DWA (2001) Bi-axial pole strain transducer device. Meas Sci Technol 12(1):97–102.CrossRefGoogle Scholar
- 20.Ross EW, Prager W (1954) On the theory of the bulge test. Q Appl Math 12(1):86–91.zbMATHMathSciNetGoogle Scholar
- 21.SiDoLo (2003) User’s manual (in French), Laboratoire Genie Mecanique et Materiaux, Universite de Bretagne Sud, Lorient, France.Google Scholar
- 22.Small MK, Nix WDF (1992) Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films. J Mater Res 7(6):1553–1563.CrossRefGoogle Scholar
- 23.Tsakalakos T (1981) The bulge test: a comparison of theory and experiment for isotropic and anisotropic films. Thin Solid Films 75:293–305.CrossRefGoogle Scholar
- 24.Yang D-Y, Oh SI, Huh H, Kim YH (2002) Proceedings of the 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes. Elsevier, Amsterdam, pp 861–870.Google Scholar
- 25.Zhao H, Gary G (1995) A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques. J Mech Phys Solids 43(8):1335–1348.zbMATHCrossRefMathSciNetGoogle Scholar