Plastic Hinging Collapse of Periodic Cellular Truss Cores
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CELLULAR metals are hybrids of metal and space, i.e., effective materials with their own sets of properties.[1] The lightweight benefits of conventional stochastic metal foams are well established, as in Reference 2, for example. Low relative densities (e.g., as low as less than 10 pct of the parent metal) are achieved through an internal void structure that can be either connected (open cell) or separated (closed cell). More recently, periodic cellular metals (PCMs) have been developed, which reduce the total material mass by retaining only that which has geometrically high load-bearing efficiency.[1,3] These microtruss structures are designed such that the internal struts are primarily loaded in compression or tension, rather than bending; the lightweight performance of these ‘‘stretch-dominated’’ PCM architectures is greater than that of ‘‘bending-dominated’’ conventional stochastic metal and polymer foams.[1] As a consequence, the PCM architectures have become an attractive option for weight-limited engineering applications such as panel stiffening in sandwich constructions, as in References 1 and 4, for example. When PCMs are loaded in compression, members (i.e., struts) having intermediate slenderness ratios generally fail by inelastic buckling, as in References 5 through 8, for example. For the case of an ideal homogeneous single column, the load-deflection diagram will have a well-defined B.A. BOUWHUIS and E. BELE, Doctoral Candidates, and G.D. HIBBARD, Assistant Professor, are with the Department of Materials Science and Engineering, University of Toronto, Toronto, ON, Canada M5S 3E4. Contact e-mail: [email protected] Manuscript submitted January 16, 2008. Article published online July 15, 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
elastic region up to the sharply defined buckling load, which can be determined using the tangent modulus theory.[9] Beyond the peak load, the fully inelastic collapse is resisted by a hinging mechanism at the nodes of the microtruss. The overall performance of ideal space frames is, therefore, a function of both axial buckling and bending stability, as in References 10 and 11, for example. However, if the support contains eccentricities, curvatures, or material inhomogeneities, the load-deflection diagram begins to deviate from linear elasticity prior to the peak buckling load, due to the local yielding and bending of the column.[12] Similarly, the peak strength due to the inelastic buckling failure in PCMs is influenced by imperfection sensitivity[3,7] and strut curvature.[3,6] In addition, significant bending of core members can occur even before the overall peak strength of the PCM has been reached, as in Reference 7, for example. These effects result in gradual failure rather than in the collective bifurcation of a lattice structure or PCM.[11,13] Strut rotation and plastic hinging is, therefore, not just an issue beyond the peak load, but can also play a significant role leading up to the peak buckling strength. Two recent examples illustrate the influence of strut
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