Abstract
Recent progress in advanced manufacturing enables fabrication of macro-scale hollow metallic lattices with unit cells in the millimeter range and sub-unit cell features at the submicron scale. If designed to minimize mass, these metallic microlattices can be manufactured with densities lower than 1 mg/cm3, making them the lightest metallic materials ever demonstrated. Measuring the compressive stiffness of these ultralight lattices with conventional contact techniques presents a major challenge, as the lattices buckle or locally fracture immediately after contact with the loading platens is established, with associated reduction in stiffness. Non-contact resonant approaches have been successfully used in the past for modulus measurements in solid materials, at both small and large scales. In this work we demonstrate that Laser Doppler Vibrometry coupled with Finite Elements Analysis is a suitable technique for the reliable extraction of the Young’s modulus in ultralight microlattices.
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Notes
A stubby geometry, with a very low L/D ratio, is heavily affected by the boundary conditions, as a significant fraction of the bar nodes are on the boundary. Fully constraining all the boundary nodes against rotations, and imposing a symmetric deformation, results in excessive stiffening, as in practice minor rotations between cells can occur. Furthermore, stubby geometries are more affected by the details of the nodal fillets, which are difficult to capture exactly.
References
Schaedler TA, Jacobsen AJ, Torrents A et al (2011) Ultralight metallic microlattices. Science 334:962–965
Maloney KJ, Roper CS, Jacobsen AJ, et al. (2013) Microlattices as architected thin films: Analysis of mechanical properties and high strain elastic recovery. APL Materials 1:022106–8
Torrents A, Schaedler TA, Jacobsen AJ et al (2012) Characterization of nickel-based microlattice materials with structural hierarchy from the nanometer to the millimeter scale. Acta Mater 60:3511–3523
Cleveland JP, Manne S, Bocek D, Hansma PK (1993) A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy. Rev Sci Instrum 64:403–405
Kiesewetter L, Zhang J-M, Houdeau D, Steckenborn A (1992) Determination of young’s moduli of micromechanical thin films using the resonance method. Sensors Actuators A Phys 35:153–159
Chopra NG, Zettl A (1998) Measurement of the elastic modulus of a multi-wall boron nitride nanotube. Solid State Commun 105:297–300
Qin Q, Xu F, Cao Y et al (2012) Measuring true young’s modulus of a cantilevered nanowire: effect of clamping on resonance frequency. Small 8:2571–2576
ASTM E1875 − 08 (2013) standard test method for dynamic young’s modulus, shear modulus, and poisson’s ratio by sonic resonance.
ASTM E1876 − 09 (2013) standard test method for dynamic young’s modulus, shear modulus, and poisson’s ratio by impulse excitation of vibration.
Ritchie IG (1973) Improved resonant bar techniques for the measurement of dynamic elastic moduli and a test of the timoshenko beam theory. J Sound Vib 31:453–468
Righini GC, Tajani A, Cutolo A (2009) An introduction to optoelectronic sensors. Hackensack, NJ
Castellini P, Martarelli M, Tomasini EP (2006) Laser Doppler Vibrometry: Development of advanced solutions answering to technology’s needs. Mech Syst Signal Process 20:1265–1285
Meirovitch L (1967) Analytical methods in vibrations. Macmillan, New York
Godfrey SW, Schaedler TA, Jacobsen AJ et al (2014) Optimal design of stiff and light hollow microlattices. Materials and Design, Submitted
Valdevit L, Godfrey SW, Schaedler TA et al (2013) Compressive strength of hollow microlattices: experimental characterization, modeling, and optimal design. J Mater Res 28(17):2462–2473
16. Godfrey SW, Valdevit L (2012) A novel modeling platform for characterization and optimal design of micro-architected materials. Proceedings AIAA SDM Conference, pp. 2003–2012
Acknowledgments
This work was financially supported by the Office of Naval Research under Grant No.N00014-11-1-0884 (program manager: D. Shifler). This support is gratefully acknowledged. The authors are also thankful to Tobias Schaedler, Alan J. Jacobsen, William B. Carter of HRL Laboratories for providing samples and for useful discussions.
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Salari-Sharif, L., Valdevit, L. Accurate Stiffness Measurement of Ultralight Hollow Metallic Microlattices by Laser Vibrometry. Exp Mech 54, 1491–1495 (2014). https://doi.org/10.1007/s11340-014-9917-8
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DOI: https://doi.org/10.1007/s11340-014-9917-8