Abstract
A model based on classical laminated plate theory reduced to one-dimension is proposed for analysis and data reduction of tensile testing of a bimaterial. The model is formulated in such a way that, through simple measurement of the bimaterial elastic response in a tensile test, it is possible to obtain the elastic modulus of one of the materials composing the bimaterial, if the dimensions and modulus of the other material are known. The sensitivity of the model to different material and geometric parameters is examined. The accuracy of the model is investigated comparing the model predictions to independent tensile testing and simple rule of mixtures. The proposed model can be used in cases where the properties of one of the materials in a bimaterial are difficult to obtain directly because of geometric constrains, like in the case thin films bonded to a thicker substrate. The model could also be extended to multilayers and/or bending loading cases.
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References
S.P. Timoshenko, Analysis of Bimetal Thermostats, J. Opt. Soc. Am., vol. 11, pp. 233–255, 1925.
E. Suhir, Stresses in Bi-Metal Thermostats, J. Appl. Mech., vol. 53, pp. 657–660, 1986.
M.L. Williams, The Stress Around a Fault or Crack in Dissimilar Media, Bull. Seism. Soc. Am., vol. 49, pp. 199–204, 1959.
Z. Suo, and J.W. Hutchinson, Interface Crack between Two Elastic Materials, Int. J. Fracture, vol. 43, pp. 1–18, 1990.
M.P. O’Day, and W.A Curtin, Bimaterial Interface Fracture: A Discrete Dislocation Model, J. Mech. Phys. Solids, vol. 53, pp. 359–382, 2005.
M. Ohring, The Material Science of Thin Films, Academic Press, NJ, 1995.
Y. Cao, S. Allameh, D. Nankivil, S. Sethiaraj, T. Otiti, and W. Soboyejo, Nanoindentation Measurements of the Mechanical Properties of Polycrystalline Au and Ag Thin Films on Silicon Substrates: Effects of Grain Size and Film Thickness, Mater. Sci. Eng. A, 2006, 427(1–2), p 232–240
M.M. De Lima, Jr., R.G. Lacerda, J. Vilcaromero, F.C. Marques, Coefficient of Thermal Expansion and Elastic Modulus of Thin Films, J. Appl. Phys., vol. 86, pp. 4936–4942, 1999.
J.H. Zhao, Y. Du, M. Morgen, and P.S. Ho, Simultaneous Measurements of Young’s Modulus, Poisson Ratio and Coefficient of Thermal Expansion of Thin Films on Substrates, J. Appl. Phys., vol. 87, pp. 1575–1577, 2000.
Y.Y. Hu, and W.M.Huang, Elastic and Elastic-Plastic Analysis of Multilayer Thin Films: Closed-form Solutions, J. Appl. Phys., vol. 96, pp. 4154–4160, 2004.
X. Chen, and J.J. Vlassak, Numerical Study on the Measurement of Thin Film Mechanical Properties by means of Nanoindentation, J. Mater. Res., vol. 16, pp. 2974–2982, 2001.
J.L. Bucaille, S. Stauss, P. Schwaller, and J. Michler, A New Technique to Determine the Elastoplastic Properties of Thin Metallic Films using Sharp Indenters, Thin Solid Films, vol. 447–448, pp. 239–245, 2004.
B. Oommen, and K.J. Van Vliet, Effects of Nanoscale Thickness and Elastic Nonlinearity on Measured Mechanical Properties of Polymeric Films, Thin Solid Films, vol. 513, pp. 235–242, 2006.
J.M. Whitney, Structural Analysis of Laminated Anisotropic Plates, Technomic, Lancaster, 1987.
M.W. Hyer, Stress Analysis of Fiber-Reinforced Composite Materials, McGraw-Hill, Massachusetts, 1998.
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The authors wish to acknowledge the assistance of Paulo Várguez in this work.
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Avilés, F., Oliva, A. & May-Pat, A. Determination of Elastic Modulus in a Bimaterial Through a One-dimensional Laminated Model. J. of Materi Eng and Perform 17, 482–488 (2008). https://doi.org/10.1007/s11665-007-9185-1
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DOI: https://doi.org/10.1007/s11665-007-9185-1