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.
Similar content being viewed by others
References
Shaw, M.C. andSata, T., “The Plastic Behavior of Cellular Materials,”Int. J. Mech. Sci.,8,469–478 (1966).
Zaslawsky, M., “Multi-axial Stress Studies on Rigid Polyurethane Foam,” EXPERIMENTAL MECHANICS,13,70–76 (1973).
Papka, S.D. andKyriakides, S., “Biaxial Crushing of Honeycombs—Part I: Experiments,”Int. J. Solids Struct.,36,4367–4396 (1999).
Wierzbicki, T., “Experimental, Numerical, and Analytical Study of Honeycomb Material,” Report No. 1, Joint MIT/Ultralight Consortium, Impact and Crashworthiness Laboratory, MIT (1997).
Chen, C. andFleck, N.A., “Size Effects in the Constrained Deformation of Metallic Foams,”J. Mech. Phys. Solids,50,955–977 (2002).
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).
Hanssen, A.G., “Validation of Constitutive Models Applicable to Foams,”Ph.D. Thesis, Norwegian University of Science and Technology, Norway (2000).
Wierzbicki, T. and Doyoyo, M., “Determination of the Local Stress-strain Response of Foams,” J. Appl. Mech. in press (2003).
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).
Mohr, D. andDoyoyo, M., “Analysis of the Arcan Apparatus in the Clamped Configuration,”J. Compos. Mater.,36 (22),2583–2594 (2002).
Petras, A. andSutcliffe, M.P.F., “Indentation Failure Analysis of Sandwich Beams,”Compos. Struct.,50,311–318 (1998).
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).
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).
Rice, J.R., “The Localization of Plastic Deformation,”Theoretical and Applied Mechanics, W.T. Koiter (ed),North-Holland, Amsterdam, 207–220 (1976).
Anand, L. andGu, C., “Granular Materials: Constitutive Equations and Strain Localization,”J. Mech. Phys. Solids,48,1701–1733 (2000).
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).
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).
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).
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).
Doyoyo, M. and Mohr, D., “Microstructural Response of Aluminum Honeycomb to Combined Out-of-plane Loading,” Mech. Mater., in press (2002).
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).
McFarland, R.K., “Hexagonal Cell Structure Under Post-buckling Axial Load,”AIAA Journal, 1, 1380–1385 (1963).
Wierzbicki, T., “A Crushing Analysis of Metal Honeycomb,”Int. J. Impact Eng.,1,157–174 (1983).
Gibson, L.J. andAshby, M.F., Cellular Solids: Structure and Properties, 2nd edition, Cambridge University Press, Cambridge (1997).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mohr, D., Doyoyo, M. A new method for the biaxial testing of cellular solids. Experimental Mechanics 43, 173–182 (2003). https://doi.org/10.1007/BF02410498
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02410498