Skip to main content
Log in

Model of Shear Elastic-Plastic Deformation of a Thin Adhesive Layer

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract—

The stress-strain state of a thin adhesion layer in a layered composite is investigated under shear loading taking into account its possible elastoplastic deformation. The layer thickness is treated as a linear parameter. Analyzed is the analytical solution obtained on the basis of a simplified formulation of the problem in differential form. For small layer thicknesses, a generalized criterion for the transition to the state of plasticity associated with a linear parameter is proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayer Structures (Mashinostroyenie, Moscow, 1980) [in Russian].

    Google Scholar 

  2. G. P. Cherepanov, Fracture Mechanics of Composite Materials (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  3. H. G. Allen and Z. Feng, “Classification of structural sandwich panel behavior,” in Mechanics of Sand-wich Structures (Springer, Dordrecht, 1998), pp. 1–12.

    Google Scholar 

  4. D. D. Ivlev, “A survey of quasi-brittle fracture crack theory,” J. Appl. Mech. Tech. Phys. 8 (6), 60–85 (1967).

    Article  ADS  Google Scholar 

  5. L.Yu. Frolenkova and V.S. Shorkin, “Surface energy and adhesion energy of elastic bodies,” Mech. Solids 52 (1), 62–74 (2017).

    Article  ADS  Google Scholar 

  6. I. S. Astapov, N. S. Astapov, and V. M. Kornev, “Lamination model of composite affected by lateral shift,” Mekh. Komp. Mater. Konstr. 21 (2), 149–161 (2015).

    Google Scholar 

  7. A. Baldan, “Adhesively-bonded joints in metallic alloys, polymers and composite materials: Mechanical and environmental durability performance,” J. Mater. Sci. 39 (15), 4729–4797 (2004).

    Article  ADS  Google Scholar 

  8. C. T. Sun and C. J. Jih, “On strain energy release rates for interfacial cracks in bi-material media,” Eng. Fract. Mech., No 1 (28), 13–20 (1987).

  9. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plate and Shells (Mc-Graw-Hill, New York, Toronto, London, 1959).

    MATH  Google Scholar 

  10. X. Fang and P. G. Charalambides, “The fracture mechanics of cantilever beams with an embedded sharp crack under end force loading,” Eng. Fract. Mech. 149, 1–17 (2015).

    Article  Google Scholar 

  11. O. Mattei and L. Bardella, “A structural model for plane sandwich beams including transverse core deformability and arbitrary boundary conditions,” Eur. J. Mech. A: Solids 58, 172–186 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  12. V. I. Andreyev, N. Yu. Tsybin, and R. A. Turusov, “Analysis of the edge effect of shear stresses of a two-console beam affected by shift,” Stroit. Mekh. Inzh. Konstr. Soor. 14 (3), 180–186 (2018).

    Google Scholar 

  13. V. I. Andreyev, N. Yu. Tsybin, and R. A. Turusov, “Determination of the stress-strain state of a three-layer beam using a contact layer,” Vestn. MGSU, No. 4, 17–26 (2016).

    Google Scholar 

  14. V. V. Glagolev, A. A. Markin, and A. A. Fursaev, “Separation process modeling of composite with adhesive layer,” Vestn. PNIPU Mekh., No. 2, 34–44 (2016).

  15. V. V. Glagolev, A. A. Markin, and S.V. Pashinov, “Bimetal plate in a uniform temperature field,” Mekh. Komp. Mater. Konstr. 23 (3), 331–343 (2017).

    Google Scholar 

  16. A. A. Abdurakhmanov, V. V. Glagolev, and A. A. Fursaev, “About the shear of adhesive layer in the composite plate,” Vestn. TulGU Ser. Differ. Uravn. Prikl. Zad., No. 1, 51–60 (2017).

  17. V. V. Glagolev and A. A. Markin, “Fracture models for solid bodies, based on a linear scale parameter,” Int. J. Solids Struct. 158, 141–149 (2019).

    Article  Google Scholar 

  18. A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity (Fizmatlit, Moscow, 2001) [in Russian].

    Google Scholar 

  19. O. Volkersen, “Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten,” Luftfahrtforschung, 15, 41–47 (1938).

    Google Scholar 

  20. V. V. Glagolev and A. A. Markin, “One formulation of the problem of elastoplastic separation,” J. Appl. Mech. Tech. Phys. 50 (4), 701–707 (2009).

    Article  ADS  Google Scholar 

  21. A. A. Abdurakhmanov, V. V. Glagolev, and O. V.Inchenko, “Elastoplastic shear adhesive deformation,” Vestn. Chuvash. Gos. Ped. Univ. Im. Yakovleva Ser.: Mekh. Pred. Sost., No. 4 (42), 34–45 (2019).

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, grant no. 19-41-710001 р_а.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to V. V. Glagolev or A. A. Markin.

Additional information

Translated by I. K. Katuev

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Glagolev, V.V., Markin, A.A. Model of Shear Elastic-Plastic Deformation of a Thin Adhesive Layer. Mech. Solids 55, 837–843 (2020). https://doi.org/10.3103/S0025654420060072

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654420060072

Keywords:

Navigation