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Precracking and interfacial delamination in a bi-material structure: Static and dynamic loadings

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Abstract

The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper. Firstly, it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading. Secondly, the “shear-lag model” is applied to the structure under dynamic loading. To solve the problem for an interface delamination of the structure and to determine the debond length along the interface, our own 2D boundary element method (BEM) code is proposed in the case of static loading, and the shear-lag model together with the Laplace transforms and half-analytical calculations are used in the case of dynamic loading. The interface layer is assumed as a very thin plate compared with the other two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shear-lag model. In the dynamic case, the influence of loading characteristics, i.e., frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time, is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite, namely cermet, and depicted in figures.

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References

  1. Bensoussan, A., Lions, J.L., Papanicolau G.: Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978)

    MATH  Google Scholar 

  2. Sanchez-Palencia, E.: Nonhomogeneous Media and Vibration Theory. Lecture Notes in Physics 127. Springer Verlag, Berlin (1980)

    Google Scholar 

  3. Milton, G.: Theory of Composites. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  4. Telega, J.J., Lewiński, T.: Stiffness loss of cross-play laminates with interlaminar cracks. In: International Seminar on Micromechanics of Materials. 317–326. Editions Eyrolls, Paris (1993)

    Google Scholar 

  5. Gambin, B., Telega, J.J.: Effective properties of elastic solids with randomly distributed microcracks. Mech. Res. Comm. 27, 697–706 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gambin, B.: Stochastic homogenization. Control and Cybern. 23(4), 672–676 (1994)

    MathSciNet  Google Scholar 

  7. Leguillon, D., Laurencin, J., Dupeux, M.: Failure initiation in an epoxy joint between two steel plates. Eur. J.Mech. A Solids 22, 509–524 (2003)

    Article  MATH  Google Scholar 

  8. Andrianov, I.V., Bolshakov V.I., Danishevskyy V.V., et al.: Asymptotic simulation of imperfect bonding in periodic fibrereinforced compositematerials under axial shear. Int. J.Mech. Sci. 49, 1344–1354 (2007)

    Google Scholar 

  9. Cox, L.H.: The elasticity and strength of paper and other fibrous materials. Brit. J. Appl. Phys. 3, 72–79 (1952)

    Article  Google Scholar 

  10. Hedgepeth, J.M.: Stress concentrations in filamentary structures. In: NASA TN D-882 (1961)

  11. Nairn, J.A.: Fracture mechanics of unidirectional composites using the shear-lag model I: Theory. J. Comp. Mat. 22(6), 561–588 (1988a)

    Article  Google Scholar 

  12. Nairn, J.A.: Fracture mechanics of unidirectional composites using the shear-lag model II: Experiment. J.Comp. Mat. 22(6), 589–600 (1988b)

    Article  Google Scholar 

  13. Nikolova, G., Ivanova, J., Valeva, V., et al.: Mechanical and thermal loading of two-plate structure. Comptes Rendus De L Academie Bulgare Des Sciences 60(7), 735–745 (2007)

    Google Scholar 

  14. Ivanova, J., Valeva, V., Mroz, Z.: Mechanical modelling of the delamination of bi-material plate structure. Journal of Theoretical and Applied Mechanics (Bulgarian Academy of Sciences), 36(4), 39–54 (2006)

    Google Scholar 

  15. Varias, A.G., Mastorakos, I., Aifantis E.C.: Numerical simulation of interface cracks in thin films, Int. J. of Fract. 98, 195–207 (1999)

    Article  Google Scholar 

  16. Chen, B., Chou, T.W.: Local elastodynamic stresses in the unit cell of a woven fabric composite. Arch. of Appl. Mech. 70(6), 423–442 (2000)

    Article  MATH  Google Scholar 

  17. Chen, B., Chou, T.W.: The propagation of one-dimensional transient elastic waves in woven-fabric composites. Composites Science and Technology 58, 1385–1396 (1998)

    Article  Google Scholar 

  18. Valeva, V., Ivanova, J., Gambin, B.: BEM for interface problem of bi-material structure under static loading. In: Proc. 11-th National Congress on Theoretical and Applied Mechanics (September 2–5 2009) Borovets, Bulgaria, ISSN: 1313-9665, 93-116-2-PB (2009)

  19. Shridhar, N., Massabo, R., Cox, B.N., et al.: Delamination dynamic in through-thickness reinforced laminates with application to DCB specimen. Int. J. of Fract. 118, 119–144 (2002)

    Article  Google Scholar 

  20. Nikolova, G., Ivanova, J.: Cracked bi-material plates under thermomechanical loading, Key Engineering Materials 409, 406–413 (2009)

    Article  Google Scholar 

  21. Nikolova, G.: Thermo-mechanical behavior of thin graded layered structures. [PhD thesis]. Institute of Mechanics. Bulgarian Academy of Sciences (2008)

  22. Song, G.M., Sloof W.G., Pei, Y.T. et al.: Interface fracture behaviour of zinc coating on steel: Experiments and finite element calculations. Surface and Coating Technology 201, 4311–4316 (2006)

    Article  Google Scholar 

  23. Hutchinson, J.W., Suo Z.: Mixed mode cracking in layered materials,. Adv. Appl. Mech. 28, 63–189 (1991)

    Article  Google Scholar 

  24. Nikolova, G.: Thermo-mechanical behaviour of thin graded layered structures. [PhD thesis]. Institute of Mechanics. Bulgarian Academy of Sciences (2008)

  25. Manolis, G., Beskos, D.: Boundary Element Methods in Elastodynamics. Boston Allen and Unwinn Inc., London, Sydney (1987)

    Google Scholar 

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Gambin, B., Ivanova, J., Valeva, V. et al. Precracking and interfacial delamination in a bi-material structure: Static and dynamic loadings. Acta Mech Sin 27, 80–89 (2011). https://doi.org/10.1007/s10409-011-0414-3

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  • DOI: https://doi.org/10.1007/s10409-011-0414-3

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