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Investigation of a crack situated in a thin adhesive layer between two different isotropic materials

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Abstract

A plane strain problem for a crack in a thin adhesive elastic-perfectly plastic layer between two different isotropic elastic materials under the action of remote mechanical loading is considered. First, the problem is solved numerically using the finite element method. The stress distributions at the crack continuations and the J-integral values are found. Further, the analytical investigation of the formulated problem is performed. It is assumed that the pre-fracture zones arise at the crack continuations and the interlayer thickness is negligibly small in comparison with the crack length. Modeling the pre-fracture zones by the crack continuations with unknown constant normal and shear cohesive stresses applied to faces of the crack, the problem of linear relationship is formulated and solved analytically. The unknown pre-fracture zone lengths and cohesive stresses are derived from the condition of stress finiteness at the new crack tips and the yielding criterion of the interlayer material. The method of definition of the normal stress co-directed with the crack faces which is used in the mentioned yielding criterion is discussed. Expressions for the crack opening displacement and for the J-integral are obtained in an analytical form as well. The values of the J-integral obtained by means of the analytical method are in a good agreement with the results of the finite element solution.

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References

  1. Leonov, M.Y., Panasyuk, V.V.: Development of the smallest cracks in a rigid body. Appl. Mech. 5(4), 391–401 (1959) (in Russian)

  2. Dugdale D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)

    Article  Google Scholar 

  3. Barenblatt G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129 (1962)

    Article  MathSciNet  Google Scholar 

  4. Needleman A.: A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54, 525–531 (1987)

    Article  MATH  Google Scholar 

  5. Needleman A.: An analysis of tensile decohesion along an interface. J. Mech. Phys. Solids 38, 289–324 (1990)

    Article  Google Scholar 

  6. Tvergaard V., Hutchinson J.W.: The relation between crack growth resistance and fracture process parameters in elastic–plastic solids toughness. J. Mech. Phys. Solids 40, 1377–1397 (1992)

    Article  MATH  Google Scholar 

  7. Tvergaard V., Hutchinson J.W.: The influence of plasticity on mixed mode interface toughness. J. Mech. Phys. Solids 41, 1119–1135 (1993)

    Article  MATH  Google Scholar 

  8. Feraren P., Jensen H.M.: Cohesive zone modelling of interface fracture near flaws in adhesive joints. Eng. Fract. Mech. 71, 2125–2142 (2004)

    Article  Google Scholar 

  9. Freed Y., Banks-Sills L.: A new cohesive zone model for mixed mode interface fracture in bimaterial. Eng. Fract. Mech. 75, 4583–4593 (2008)

    Article  Google Scholar 

  10. Mohammed I., Liechti K.M.: Cohesive zone modeling of crack nucleation at bimaterial corners. J. Mech. Phys. Solids 48, 735–764 (2000)

    Article  MATH  Google Scholar 

  11. Yan Y., Shang F.: Cohesive zone modeling of interfacial delamination in PZT thin films. Int. J. Solids Struct. 46, 2739–2749 (2009)

    Article  Google Scholar 

  12. Kaminsky A.A., Kipnis L.A., Kolmakova V.A.: On the Dugdale model for an interface crack. Int. Appl. Mech. 72, 1805–1817 (1999)

    Google Scholar 

  13. Bakirov V.F., Gol’dshtein R.V.: The Leonov–Panasyuk–Dugdale model for a crack at the interface of the joint of materials. J. Appl. Maths. Mech. 68, 153–161 (2004)

    Article  Google Scholar 

  14. Varias A.G., Suo Z., Shih C.F.: Ductile failure of a constrained metal foil. J. Mech. Phys. Solids 39, 963–986 (1991)

    Article  Google Scholar 

  15. Turner M.R., Evans A.G.: An experimental study of the mechanisms of crack extension along an oxide/metal interface. Acta Mater. 44, 863–871 (1996)

    Article  Google Scholar 

  16. Tvergaard V., Hutchinson J.W.: On the toughness of ductile adhesive joints. J. Mech. Phys. Solids. 44, 789–800 (1996)

    Article  Google Scholar 

  17. He M.E., Evans A.G., Hutchinson J.W.: Interface cracking phenomena in constrained metal layer. Acta mater. 44, 2963–2971 (1996)

    Article  Google Scholar 

  18. Pickthall C., Wang C., Rose L.R.F.: Plasticity in constrained layer: model with point forces. Eng. Fract. Mech. 69, 647–658 (2002)

    Article  Google Scholar 

  19. Mello A.W., Liechti K.M.: The effect of self-assembled monolayers on interfacial fracture. J. Appl. Mech. 73, 860–870 (2006)

    Article  MATH  Google Scholar 

  20. Brunner A.J., Blackman B.R.K., Davies P.: A status report on delamination resistance testing of polymer-matrix composites. Eng. Fract. Mech. 75, 2779–2794 (2008)

    Article  Google Scholar 

  21. Choupani N.: Mixed-mode cohesive fracture of adhesive joints: experimental and numerical studies. Eng. Fract. Mech. 75, 4363–4382 (2008)

    Article  Google Scholar 

  22. Marannano G.V., Mistretta L., Cirello A., Pasta S.: Crack growth analysis at adhesive-adherent interface in bonded joint under mixed mode I/II. Eng. Fract. Mech. 75, 5122–5133 (2008)

    Article  Google Scholar 

  23. Hao S., Cornec A., Schwalbe K.-H.: Plastic stress-strain fields and limit loads of a plane strain cracked tensile panel with a mismatched welded joint. Int. J. Solids Struct. 34, 297–326 (1997)

    Article  MATH  Google Scholar 

  24. Loboda V., Lapusta Y., Sheveleva A.: Analysis of pre-fracture zone for an electrically permeable crack in an interlayer between piezoelectric materials. Int. J. Fract. 142, 307–313 (2006)

    Article  MATH  Google Scholar 

  25. Loboda V., Lapusta Y., Sheveleva A.: Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric bimaterial. Int. J. Solids Struct. 44, 5538–5553 (2007)

    Article  MATH  Google Scholar 

  26. Loboda V., Lapusta Y., Govorukha V.: Mechanical and electrical yielding for an electrically insulated crack in an interlayer between piezoelectric materials. Int. J. Eng. Sci. 46, 260–272 (2008)

    Article  MATH  Google Scholar 

  27. Lapusta Y., Loboda V.: Electro-mechanical yielding for a limited permeable crack in an interlayer between piezoelectric materials. Mech. Res. Commun. 36, 183–192 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Voloshko O., Lapusta Y., Loboda V.: Analytical and numerical study of cohesive zones for a crack in an adhesive layer between identical isotropic materials. Eng. Fract. Mech. 77, 2577–2592 (2010)

    Article  Google Scholar 

  29. Rice J.R., Sih G.C.: Plane problem of cracks in dissimilar media. Trans. ASME. J. Appl. Mech. 32, 418–423 (1965)

    Article  Google Scholar 

  30. Rice J.R.: A path independent integral and the approximated analyses of strain concentration by notches and cracks. J. Appl. Mech. 35, 379–386 (1968)

    Article  Google Scholar 

  31. Herrmann K.P., Loboda V.V., Kharun I.V.: Interface crack with a contact zone in an isotropic bimaterial under thermomechanical loading. Theor. Appl. Fract. Mech. 42, 335–348 (2004)

    Article  Google Scholar 

  32. Muskhelishvili N.I.: Some Basic Problems in the Mathematical Theory of Elasticity. Noordhoff, Groningen (1963)

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, Dniepropetrovsk National University, Gagarin Av., 72, Dniepropetrovsk, 49010, Ukraine

    O. Voloshko & V. Loboda

  2. UMR 6602/UBP/CNRS/IFMA, French Institute of Advanced Mechanics, Institut Pascal, Clermont Université, BP 265, 63175, Aubière Cedex, France

    Y. Lapusta

Authors
  1. O. Voloshko
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  2. V. Loboda
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  3. Y. Lapusta
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Correspondence to V. Loboda.

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Voloshko, O., Loboda, V. & Lapusta, Y. Investigation of a crack situated in a thin adhesive layer between two different isotropic materials. Acta Mech 226, 683–696 (2015). https://doi.org/10.1007/s00707-014-1196-z

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  • DOI: https://doi.org/10.1007/s00707-014-1196-z

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