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Experimental Mechanics

, Volume 43, Issue 2, pp 173–182 | Cite as

A new method for the biaxial testing of cellular solids

  • D. Mohr
  • M. Doyoyo
Article

Abstract

Commercial cellular solids such as metal foams and honeycombs exhibit deformation and failure responses that are dependent on specimen size during testing. For foams, this size dependence originates from the fabrication-induced material and structural inhomogeneities, which cause the uncontrolled localization of deformation during the testing of foam cubes. Different peak loads and failure modes are observed in honeycomb specimens in the plate-shear configuration depending on specimen height. This size dependence causes difficulty in obtaining a more representative constitutive behavior of the material. It has recently been established that the size dependence under uniaxial compression can be eliminated with tapered cellular specimens, which enable controlled deformation at a given region of the specimen. This concept is extended in this paper to the biaxial testing of butterfly-shaped cellular specimens in the Arcan apparatus, which focuses deformation at the central section of the specimen. The Arcan apparatus has been modified such that all displacements at the boundaries of the specimen could be controlled during testing. As a consequence of this fully displacement controlled Arcan apparatus, a force perpendicular to that applied by the standard universal testing machine is generated and becomes significant. Thus, an additional load cell is integrated on the apparatus to measure this load. Example responses of butterfly-shaped specimens composed of aluminum alloy honeycomb, aluminum alloy foam and hybrid stainless-steel assembly are presented to illustrate the capabilities of this new testing method.

Key Words

Arcan test cellular solids biaxial testing sandwich core materials foam honeycomb hybrid stainless-steel assembly 

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References

  1. 1.
    Shaw, M.C. andSata, T., “The Plastic Behavior of Cellular Materials,”Int. J. Mech. Sci.,8,469–478 (1966).Google Scholar
  2. 2.
    Zaslawsky, M., “Multi-axial Stress Studies on Rigid Polyurethane Foam,” EXPERIMENTAL MECHANICS,13,70–76 (1973).CrossRefGoogle Scholar
  3. 3.
    Papka, S.D. andKyriakides, S., “Biaxial Crushing of Honeycombs—Part I: Experiments,”Int. J. Solids Struct.,36,4367–4396 (1999).Google Scholar
  4. 4.
    Wierzbicki, T., “Experimental, Numerical, and Analytical Study of Honeycomb Material,” Report No. 1, Joint MIT/Ultralight Consortium, Impact and Crashworthiness Laboratory, MIT (1997).Google Scholar
  5. 5.
    Chen, C. andFleck, N.A., “Size Effects in the Constrained Deformation of Metallic Foams,”J. Mech. Phys. Solids,50,955–977 (2002).Google Scholar
  6. 6.
    Triantafillou, T.C., Zhang, J., Shercliff, L.J., Gibson, L.J. andAshby, M.F., “Failure Surfaces for Cellular Materials Under Multi-axial Loads—II. Comparison of Models with Experiment,”Int. J. Mech. Sci.,31,665–678 (1989).Google Scholar
  7. 7.
    Hanssen, A.G., “Validation of Constitutive Models Applicable to Foams,”Ph.D. Thesis, Norwegian University of Science and Technology, Norway (2000).Google Scholar
  8. 8.
    Wierzbicki, T. and Doyoyo, M., “Determination of the Local Stress-strain Response of Foams,” J. Appl. Mech. in press (2003).Google Scholar
  9. 9.
    Arcan, M., Hashin, Z., andVoloshin, A., “A Method to Produce Uniform Plane-stress States with Applications to Fiber-reinforced Materials,” EXPERIMENTAL MECHANICS 18,141–146 (1978).CrossRefGoogle Scholar
  10. 10.
    Mohr, D. andDoyoyo, M., “Analysis of the Arcan Apparatus in the Clamped Configuration,”J. Compos. Mater.,36 (22),2583–2594 (2002).CrossRefGoogle Scholar
  11. 11.
    Petras, A. andSutcliffe, M.P.F., “Indentation Failure Analysis of Sandwich Beams,”Compos. Struct.,50,311–318 (1998).Google Scholar
  12. 12.
    Bastawros, A.F., Bart-Smith, H., andEvans, A.G., “Experimental Analysis of Deformation Mechanisms in a Closed-cell Aluminum Alloy Foam,”J. Mech. Phys. Solids,48,301–322 (2000).Google Scholar
  13. 13.
    Andrews, E.W., Gioux, G., Onck, P., andGibson, L.J., “Size Effects in Ductile Cellular Solids. Part II: Experimental Results,”Int. J. Mech. Sci.,43,701–713 (2001).CrossRefGoogle Scholar
  14. 14.
    Rice, J.R., “The Localization of Plastic Deformation,”Theoretical and Applied Mechanics, W.T. Koiter (ed),North-Holland, Amsterdam, 207–220 (1976).Google Scholar
  15. 15.
    Anand, L. andGu, C., “Granular Materials: Constitutive Equations and Strain Localization,”J. Mech. Phys. Solids,48,1701–1733 (2000).MathSciNetGoogle Scholar
  16. 16.
    Meguid, S.A., Cheon, S.S., andEl-Abbasi, N., “FE Modelling of Deformation Localization in Metallic Foams,”Finite Elements in Analysis and Design,38 (7),631–643 (2002).CrossRefGoogle Scholar
  17. 17.
    Hung, S.-C. andLiechti, K.M., “Finite Element Analysis of the Arcan Specimen for Fiber Reinforced Composites Under Pure Shear and Biaxial Loading,”J. Compos. Mater.,33,1288–1316 (1999).Google Scholar
  18. 18.
    Doyoyo, M. andWierzbicki, T., “Measurement of the Failure Surfaces for Ductile and Brittle Aluminum Foams,”Plasticity, Damage and Fracture at Macro, Micro and Nano Scales, A.S. Khan andO. Lopez-Pamies (eds),Neat Press, Fulton, MD, 114–116 (2002).Google Scholar
  19. 19.
    Doyoyo, M. andWierzbicki, T., “Experimental Studies on Yield Behavior of Ductile and Brittle Aluminum Foams Under a Biaxial State of Stress,”Int. J. Plasticity,19,1195–1214 (2003).CrossRefGoogle Scholar
  20. 20.
    Doyoyo, M. and Mohr, D., “Microstructural Response of Aluminum Honeycomb to Combined Out-of-plane Loading,” Mech. Mater., in press (2002).Google Scholar
  21. 21.
    Mohr, D. and Doyoyo, M., “Numerical and Theoretical Analysis of the Response of Out-of-plane Honeycomb Microstructure to a Biaxial State of Stress,” submitted (2002).Google Scholar
  22. 22.
    McFarland, R.K., “Hexagonal Cell Structure Under Post-buckling Axial Load,”AIAA Journal, 1, 1380–1385 (1963).Google Scholar
  23. 23.
    Wierzbicki, T., “A Crushing Analysis of Metal Honeycomb,”Int. J. Impact Eng.,1,157–174 (1983).Google Scholar
  24. 24.
    Gibson, L.J. andAshby, M.F., Cellular Solids: Structure and Properties, 2nd edition, Cambridge University Press, Cambridge (1997).Google Scholar

Copyright information

© Society for Experimental Mechanics 2003

Authors and Affiliations

  • D. Mohr
    • 1
  • M. Doyoyo
    • 1
  1. 1.Impact and Crashworthiness LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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