Determination of Elastic Modules in Dependence on Orientation by the Resonant Beam Technique


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A novel procedure, based on the Resonant Beam Technique, and its application to anisotropic composites is presented. The evaluation of the elastic modules of anisotropic materials from the measurement of the transverse eigenfrequency spectra of resonant beams is performed by a two step process: firstly the beams cut out from the test material in different directions are evaluated in-dependently of each other under the assumption, that they are isotropic, solving Timoshenko´s equations using an isotropic correction factor for shear. Secondly the beams are evaluated together as representatives of one anisotropic material, using an anisotropic correction factor for shear. The equipment, developed for such measurements is presented. Finally, the procedure is applied to a transversely isotropic carbon fibre-reinforced carbon composite and the relevance of the results is discussed.



Materials Science Forum (Volumes 514-516)

Edited by:

Paula Maria Vilarinho




S. Puchegger et al., "Determination of Elastic Modules in Dependence on Orientation by the Resonant Beam Technique", Materials Science Forum, Vols. 514-516, pp. 815-824, 2006

Online since:

May 2006




[1] W Lins, G. Kaindl, H. Peterlik, K. Kromp: A novel resonant beam technique to determine the elastic modulus in dependence on orientation and temperature up to 2000 °C; Rev. Sci. Instrum 70/7(1999)3052-3058.

DOI: 10.1063/1.1149867

[2] G. Kaindl, W. Lins, H. Peterlik, K. Kromp, R. Reetz, T. Reetz: The determination of the elastic modulus of anisotropic ceramics and ceramic composites at high temperatures by a novel resonant beam technique; Interceram 49/2(2000)92-101.

[3] D. Loidl, S. Puchegger, H. Peterlik, K. Kromp: On the determination of elastic moduli with brittle matrix composites; Brittle Matrix Composites 7, ed. by A. M. Brandt, V. C. Li and I. H. Marshall; ZTUREK RSI and Woodhead Publ., Cambridge and Warsaw; 389-400; (2003).

DOI: 10.1533/9780857093103.389

[4] D. Loidl, S. Puchegger, K. Kromp, J. Zeschky, P. Greil, M. Bourgeon, H. Peterlik: Elastic moduli of porous and anisotropic composites at high temperatures; Adv. Eng. Mater. 6/3(2004)138142.

DOI: 10.1002/adem.200300533

[5] European Prestandard: Advanced technical ceramics-Ceramic composites, Determination of elastic modules in dependence on orientation up to 2000 °C by the resonant beam technique; subm. to CEN TC 184, Subcommittee 1 (AFNOR, France), (2005).

[6] T.C. Huang, The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions, ASME Journal of Applied Mechanics 28(1961)579-584.

DOI: 10.1115/1.3641787

[7] R.E. Moore: Interval Arithmetic; Prentice-Hall, Englewood Cliffs, NJ, (1966).

[8] H. Ratschek, J. Rokne: New Computer Methods for Global Optimation; Ellis Horwood, Ltd., Chichester, England, (1988).

[9] E. Hansen: Global Optimisation using Interval Analysis; Marcel Dekker, Inc., New York, (1992).

[10] H. Ratschek, J. Rokne: Computer Methods for the Range of Functions; Ellis Horwood, Ltd., Chichester, England, (1988).

[11] M. Lerch, G. Tischler, J. Wolff von Gudenberg, W. Hofschuster, W. Krämer: The interval library filib++ 2. 0 - Design, features and sample programs; Preprint 2001/4, Universität Wuppertal, Wissenschaftliches Rechnen/Softwareentwicklung, Germany.

DOI: 10.1145/1141885.1141893

[12] J.R. Hutchinson: Shear coefficients for Timoshenko beam theory; ASME Journal of Applied Mechanics 68(2001)87-92.

[13] J. Bard: Nonlinear parameter estimation; Academic Press, (1974).

[14] S. Puchegger, D. Loidl, K. Kromp, H. Peterlik: Hutchinson's shear coefficient for anisotropic beams, Journal of Sound and Vibration 266(2003)207-216.

DOI: 10.1016/s0022-460x(02)01532-8

[15] S.D. Conte, Carl de Boor: Elementary Numerical Analysis, An Algorithmic Approach; McGraw-Hill, (1972).

[16] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery: Numerical Recipes in C; 2nd edition, Cambridge University Press, Cambridge, England, (1992).

DOI: 10.1017/s0263574700010675

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