Superelasticity and stability of a shape memory alloy hexagonal honeycomb under in-plane compression. (English) Zbl 1167.74425
Summary: Nitinol (NiTi) shape memory alloy honeycombs, fabricated in low densities using a new brazing method, recently demonstrated enhanced shape memory and superelastic properties by exploiting kinematic amplification of thin-walled deformations. The realization of such adaptive, light-weight cellular structures opens interesting possibilities for design and novel applications. This paper addresses the consequent need for design and simulation tools for engineers to make effective use of such structures by, as a first step, analyzing the multi-scale stability aspects of the superelastic behavior of a particular hexagonal, thin-walled, SMA honeycomb under in-plane compression. An in-depth parameter study is performed of the influence of different material laws on the behavior of honeycombs of finite and infinite extent with perfect and imperfect initial geometries. A finite element-based simulation is presented that credibly captures the behavior seen in experiments.
MSC:
| 74G60 | Bifurcation and buckling |
| 74M05 | Control, switches and devices (“smart materials”) in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
References:
| [1] | Ashby, M.; Evans, A.; Fleck, N.; Gibson, L.; Hutchinson, J.; Wadley, H.: Metals foams: A design guide, (2000) |
| [2] | FEAP, 2005. User Manual, seventh ed. University of California at Berkeley (Civil and Environmental Engineering) and the University of Michigan (Aerospace Engineering). |
| [3] | Freed, Y., Aboudi, J., Gilat, R., 2008. Investigation of shape memory alloy honeycombs by means of a micromechanical analysis. Modelling and Simulation in Materials Science and Engineering 16 (5), 055002 (22pp). http://stacks.iop.org/0965-0393/16/055002. |
| [4] | Gall, K.; Sehitoglu, H.; Chumlyakov, Y.; Kireeva, I.: Tension – compression asymmetry of the stress – strain response in aged single crystal and polycrystalline niti, Acta materialia 47, No. 4, 1203-1217 (1999) |
| [5] | Geymonat, G.; Mueller, S.; Triantafyllidis, N.: Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity, Archive of rational mechanics and analysis 122, 231-290 (1993) · Zbl 0801.73008 · doi:10.1007/BF00380256 |
| [6] | Gibson, L. J.; Ashby, M. F.: Cellular solids: structure and properties, Cambridge solid state series (1997) · Zbl 0723.73004 |
| [7] | Grummon, D.; Shaw, J.; Foltz, J.: Fabrication of cellular shape memory alloy materials by reactive eutectic brazing using niobium, Materials science and engineering A, 1113-1118 (2006) |
| [8] | Grummon, D. S.; Shaw, J. A.; Gremillet, A.: Low-density open-cell foams in the niti system, Applied physics letters 82, No. 16, 2727-2729 (2002) |
| [9] | Hassan, M.R., Scarpa, F.L., Mohamed, N.A., 2004. Shape memory alloys honeycomb: design and properties. In: Lagoudas, D.C. (Ed.), Proceedings of SPIE: Smart Structures and Materials 2004: Active Materials: Behavior and Mechanics. Vol. 5387. SPIE, pp. 557 – 564. http://link.aip.org/link/?PSI/5387/557/1. |
| [10] | Hill, R.: A general theory of uniqueness and stability in elastic – plastic solids, Journal of the mechanics and physics of solids 6, 236-249 (1958) · Zbl 0091.40301 · doi:10.1016/0022-5096(58)90029-2 |
| [11] | Iadicola, M. A.; Shaw, J. A.: Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy, International journal of plasticity 20, 577-605 (2004) · Zbl 1134.74345 · doi:10.1016/S0749-6419(03)00040-8 |
| [12] | Lagoudas, D. C.; Vandygriff, E. L.: Processing and characterization of niti porous sma by elevated pressure sintering, Journal of intelligent material systems and structures 13, 837-850 (2002) |
| [13] | Li, B. -Y.; Rong, L. -J.; Luo, X. -H.Y.-Y.L.: Transformation behavior of sintered porous niti alloys, Metallurgical and materials transactions 30A, 2753-2756 (1999) |
| [14] | Okabe, Y., Minakuchi, S., Shiraishi, N., Murakami, K., Takeda, N., March 2008. Smart honeycomb sandwich panels with damage detection and shape recovery functions. Advanced Composite Materials 17, 41 – 56. http://dx.doi.org/10.1163/156855108X295645. |
| [15] | Papka, S.; Kyriakides, S.: In-plane compressive response of crushing of honeycomb, Journal of the mechanics and physics of solids 42, 1499-1532 (1994) |
| [16] | Shaw, J.A., Churchill, C., Triantafyllidis, N., Michailidis, P., Grummon, D., Foltz, J., 2007a. Shape memory alloy honeycombs: Experiments and simulation. In: Proceedings of the AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Vol. 1. Waikiki, HI, United States, pp. 428 – 436. |
| [17] | Shaw, J. A.; Grummon, D. S.; Foltz, J.: Superelastic niti honeycombs: fabrication and experiments, Smart materials and structures 16, S170-S178 (2007) |
| [18] | Shaw, J. A.; Kyriakides, S.: Thermomechanical aspects of niti, Journal of the mechanics and physics of solids 43, No. 8, 1243-1281 (1995) |
| [19] | Shaw, J. A.; Kyriakides, S.: On the nucleation and propagation of phase transformation fronts in a niti alloy, Acta materialia 45, No. 2, 683-700 (1997) |
| [20] | Triantafyllidis, N.; Nestorović, M. D.; Schraad, M. W.: Failure surfaces for finitely strained two-phase periodic solids under arbitrary plane strains, Journal of applied mechanics 73, 505-515 (2006) · Zbl 1111.74666 · doi:10.1115/1.2126695 |
| [21] | Triantafyllidis, N., Samanta, S.K., 1986. Bending effects on flow localization in metallic sheets. Proceedings of the Royal Society of London A406, 205 – 226. · Zbl 0593.73039 · doi:10.1098/rspa.1986.0073 |
| [22] | Triantafyllidis, N.; Schnaidt, W. C.: Comparison of microscopic and macroscopic instabilities in a class of two-dimensional periodic composites, Journal of the mechanics and physics of solids 41, 1533-1565 (1993) · Zbl 0808.73051 · doi:10.1016/0022-5096(93)90039-I |
| [23] | Triantafyllidis, N.; Schraad, M. W.: Onset of failure in aluminum honeycombs under general in-plane loading, Journal of the mechanics and physics of solids 46, 1089-1124 (1998) · Zbl 0973.74072 · doi:10.1016/S0022-5096(97)00060-4 |
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