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Experimental Mechanics

, Volume 45, Issue 5, pp 404–411 | Cite as

Identification of the four orthotropic plate stiffnesses using a single open-hole tensile test

  • J. Molimard
  • R. Le Riche
  • A. Vautrin
  • J. R. Lee
Article

Abstract

The identification of mechanical parameters for real structures is still a challenge. With the improvement of optical full-field measurement techniques, it has become easier, but in spite of many publications showing the feasibility of such methods, experimental results are still scarce. In this paper we present a first step towards a global approach of mechanical identification for composite materials. The chosen mechanical test is an open-hole tensile test according to standard recommendations. For the moment, experimental data are provided by a moiré interferometry setup. The global principle of the identification developed in this paper is to minimize a discrepancy between experimental and theoretical results, expressed as a cost function, using a Levenberg-Marquardt algorithm. This approach has the advantage of having high adaptability, largely because the optical system, the signal processing as well as the mechanical aspects, can be taken into consideration by the model. In this paper we consider different types of cost functions, which are tested using an identifiability criterion. Although mechanically based cost functions have been studied, a simpler mathematical form is finally more efficient. Two different models were tested. The first is an analytical model based on the Lekhnitskii approach. This approach has the advantage of being a meshless solution; however, the results appeared to be partially false due to boundary effects, leading to a second approach, a classical finite element analysis. The resulting identified values are similar to values from classical mechanical tests (within 6%). which, in practice, validates our approach.

Key words

Optical full-field method identification composite materials open-hole tensile test 

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References

  1. 1.
    Bulhak, J., Lu, J., Montay, G., Surrel, Y., and Vautrin, A., “Grating Shearography and Its Application to Residual Stresses Evaluation,” Interferometry in Speckle Light: Theory and Applications, Lausanne Switzerland, September 25–28, P. Jacquot and J.-M. Fournier, editors, 607–614 (2000).Google Scholar
  2. 2.
    Cárdenas-Garcia, J.F., Ekwaro-Osire, S., and Berg, J.M. “Nonlinear Least-squares Solution to the Moiré Hole-drilling Problem in Orthotropic Materials,” SEM Annual Conference on Experimental and Applied Mechanics, Milwaukee, WI, June 10–12 (2002).Google Scholar
  3. 3.
    Furgiuele, F.M., Muzzupappa, M., and Pagnotta, L., “A Full-field Procedure for Evaluating the Elastic Properties of Advanced Ceramics,” EXPERIMENTAL MECHANICS,37, 285–291 (1997).CrossRefGoogle Scholar
  4. 4.
    Bruno, L., Furgiuele, F.M., Pagnotta, L., and Poggialini, A., “A Fuilfield approach for the Elastic Characterization of Anisotropic Materials,” Optics and Lasers in Engineering,37, 417–431 (2002).CrossRefGoogle Scholar
  5. 5.
    Cárdenas-Garcia, J.F., Cho, S., and Chasiotis, I., “Determination of Elastic Properties from non-uniform MEMS Geometries,” Society for Experimental Mechanics Conference and Exposition on Experimental and Applied Mechanics, Charlotte, NC, June 2–4 (2003).Google Scholar
  6. 6.
    Grédiac, M., and Pierron F., “A T-shaped Specimen for the Direct Characterization of Orthotropic Materials,” International Journal for Numerical Methods in Engineering,41, 293–309 (1998).CrossRefzbMATHGoogle Scholar
  7. 7.
    Pierron, F., and Grédiac, M., “Identification of the Through-thickness Moduli of Thick Composites from Whole-field Measurements Using the losipescu Fixture: Theory and Simulations,” Composite Part A,31, 309–318 (2000).CrossRefGoogle Scholar
  8. 8.
    Pierron, F., Zhavoronok, S., and Grédiac, M., “Identification of the Through-thickness Properties of Thick Laminated Tubes Using the Virtual Field Method,” International Journal of Solids and Structures,37, 4437–4453 (2000).CrossRefzbMATHGoogle Scholar
  9. 9.
    Grédiac, M., Toussaint, E. and Pierron, F., “Special Virtual Fields for the Direct Determination of Material Parameters with the Virtual Fields Method. I — Principle and Definition,” International Journal of Solids and Structures,39, 2691–2705 (2002).CrossRefzbMATHGoogle Scholar
  10. 10.
    Grédiac, M., Toussaint, E., and Pierron, F., “Special Virtual Fields for the Direct Determination of Material Parameters with the Virtual Fields Method. 2 — Application to In-plane Properties,” International Journal of Solids and Structures.39, 2707–2730 (2002).CrossRefzbMATHGoogle Scholar
  11. 11.
    Grédiac, M., Toussaint, E., and Pierron, F., “Special Virtual Fields for the Direct Determination of Material Parameters with the Virtual Fields Method. 3 — Application to the Bending Rigidities of Anisotropic Plates,” International Journal of Solids and Structures,40, 2401–2419 (2003).CrossRefzbMATHGoogle Scholar
  12. 12.
    Cardenas-Garcia, J., “Determination of the Elastic Constants Using Moiré,” Mechanical Research Communications.27 (1), 69–77 (2000).zbMATHCrossRefGoogle Scholar
  13. 13.
    Post, D., Han, B., and Ifju, P., High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials, Springer-Verlag, New York (1994).Google Scholar
  14. 14.
    Kujawinska, M., “Use of Phase-stepping Automatic Fringe Analysis in Moiré Interferometry,” Applied Optics.26, 4712–4715 (1987).CrossRefGoogle Scholar
  15. 15.
    Surrel, Y. “Fringe Analysis,” Photomechanics, P.K. Rastogi, ed., Springer-Verlag, Berlin, 55–102 (1999).Google Scholar
  16. 16.
    Lekhnitskii, S.G., Tsai, S.W., and Cheron, T., Anisotropic Plates, Gordon and Breach, New York (1968).Google Scholar
  17. 17.
    Yuan, F.G., “Lecture on Anisotropic Elasticity — Application to Composite Fracture Mechanics,” NASA Langley Research Center, July (1998).Google Scholar
  18. 18.
    Guyon, F., and Le Riche, R., “Lesst-squares Parameter Estimation and the Levenberg-Marquardt Algorithm: Deterministic Analysis, Sensitivities and Numerical Experiments,” Technical Report INSA de Rouen, No. 041/99, November 20 (2000).Google Scholar
  19. 19.
    Molimard, J. and Le Riche, R., “Identification de Piézoviscosité en Lubrification,” Mécanique et Industries,4, 645–653 (2003).CrossRefGoogle Scholar
  20. 20.
    Bouh Bouha, S., “Evaluation des Performances de Divers Eléments Finis et des Effets d'anisotropie pour les Plaques Composites en Flexion,” Ph.D Thesis, No. 9492, ENSM-SE (1992).Google Scholar

Copyright information

© Society for Experimental Mechanics 2005

Authors and Affiliations

  • J. Molimard
    • 1
  • R. Le Riche
    • 1
  • A. Vautrin
    • 1
  • J. R. Lee
    • 2
  1. 1.SMS/MeM, GDR CNRS 2519, ENSM-SESaint EtienneFrance
  2. 2.Structural Health Monitoring GroupResearch Institute of Instrumentation Frontier, National Institute of Advanced Industrial Science and Technology, AIST Tsukuba Central 2TsukubaJapan

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