Stressed State of the Axisymmetric Adhesive Joint of Two Cylindrical Shells under Axial Tension

Abstract:

The research of the deflected mode of the construction, composed of two coaxially-glued cylindrical pipes, is done. Pipes are considered as thin-walled axisymmetric shells, which are joined by adhesive layer of a certain thickness. The shearing stresses in the glue are considered to be constant over the thickness of the adhesive layer, and normal stresses are linearly dependent on the radial coordinate. The shearing stresses in the adhesive layer are considered to be proportional to the difference in the longitudinal displacements of the shell sides that are faced to the adhesive layer. Normal stresses are proportional to the difference in radial displacement of the shells. It is supposed that the change in the adhesive layer thickness under deformation does not affect the stress, that is, the linear model is considered. The problem of the joint deflected mode finding is reduced to the system of four ordinary differential equations relative to the radial and longitudinal displacements of the layers. The system is solved by the matrix method. Displacements of layers outside of the adherent area can be found by the classical theory of axisymmetric shells. Satisfaction of boundary conditions and conjugation conditions leads to a system of twenty two linear equations with twenty two unknown coefficients. The model problem is solved; the results are compared with the computation made by the finite element method. The tangential and normal stresses in the glue reach the maximum values at the edges of the adhesive line. It is shown that the proposed model describes the stressed state of the joint with high accuracy, and this joint has an influx of glue residues at the ends of the adhesive line but can not be applied in the absence of adhesive influxes. Because in this case, the tangential stresses due to the parity rule reach maximum values not on the edge, but at some distance from the edge of the line. As a result, the distribution of normal stresses at the edge of the line also substantially changes. Thus, the proposed model with certain restrictions has sufficient accuracy for engineering problems and can be used to solve design problems.

• Periodical: Materials Science Forum (Volume 968)
• Pages: 519-527
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.968.519
• Online since: August 2019
• Authors: S.S. Kurennov*, Konstantin P. Barakhov, A.G. Poliakov
• Keywords: Adhesive Joint, Analytical Solution, Cylindrical Axisymmetric Shells, Symmetric Matrices, System of Ordinary Differential Equations

References

[1] R.D. Adams, N.A. Peppiatt, Stress analysis of adhesive bonded tubular lap joints. The Journal of Adhesion, 9 (1977) 1-18.

DOI: 10.1080/00218467708075095

[2] E. Dragoni, L. Goglio, Adhesive stresses in axially-loaded tubular bonded joints - Part I: Critical review and finite element assessment of published models. Int. J. of Adhesion and Adhesives, 47 (2013) 35-45.

DOI: 10.1016/j.ijadhadh.2013.09.009

[3] J.L. Lubkin, E. Reissner, Stress distribution and design data for adhesive lap joints between circular tubes. Trans. ASME, 78 (1956) 1213-1221.

DOI: 10.1115/1.4013993

[4] I.A. Skoryi, L.P. Terekhova Stresses in adhesive joints in cylindrical shells and panels. Polymer Mechanics, 8(6) (1972) 964-972.

DOI: 10.1007/bf00858340

[5] O. Nemes, F. Lachaud, & A. Mojtabi, Contribution to the study of cylindrical adhesive joining. International Journal of Adhesion & Adhesives, 26 (2006) 474–480.

DOI: 10.1016/j.ijadhadh.2005.07.009

[6] N. Pugno, A. Carpinteri, Tubular Adhesive Joints Under Axial Load. Journal of Applied Mechanics, 70 (6) (2003) 832-836.

DOI: 10.1115/1.1604835

[7] O. Nemes, F. Lachaud, Modeling of Cylindrical Adhesively Bonded Joints. Journal of Adhesion Science and Technology, 23 (2009) 1383–1393.

DOI: 10.1163/156856109x432983

[8] R.A. Esmaeel, F. Taheri, Stress Analysis of Tubular Adhesive Joints with Delaminated Adherend. Journal of Adhesion Science and Technology, 23 (2009) 1827–1844.

DOI: 10.1163/016942409x12459095670511

[9] J.Y. Cognard, H. Devaux, & L. Sohier, Numerical analysis and optimisation of cylindrical adhesive joints under tensile loads. International Journal of Adhesion and Adhesives, 30(8) (2010) 706–719.

DOI: 10.1016/j.ijadhadh.2010.07.003

[10] D.R. Barbosa, R.D.S.G. Campilho, & R.J.B. Rocha, Experimental and numerical assessment of tensile loaded tubular adhesive joints. The Journal of Materials: Design and Applications, (2018) 1-13.

[11] Yu. P. Artyukhin, Modificzirovannaya teoriya Golanda–Rejssnera skleenny`kh plastin. Issled. po teor. plastin i obolochek. Izd-vo Kazanskogo un-ta, – Kazan, 11 (1975) 136–148.

[12] S. Amidi, J. Wang, An analytical model for interfacial stresses in double-lap bonded joints. The Journal of Adhesion, (2018) 1–25.

DOI: 10.1080/00218464.2018.1464917

[13] J. Wang, C. Zhang, Three-parameter elastic foundation model for analysis of adhesively bonded joints. International Journal of Adhesion and Adhesives, 29 (2009) 495–502.

DOI: 10.1016/j.ijadhadh.2008.10.002

[14] S.S. Kurennov, Longitudinal-Flexural Vibrations of a Three-Layer Rod. Аn Improved Model. Journal of Mathematical Sciences, 2 (2016) 159-169.

DOI: 10.1007/s10958-016-2829-7

[15] S.S. Kurennov, O raspredelenii napryazhenij po tolshhine kleevogo soedineniya. Voprosy proektirovaniya i proizvodstva konstrukczij letatelnykh apparatov, 4 (2016) 80-89.

[16] Y. Frostig, O.T. Thomsen, & F. Mortensen, Analysis of adhesive-bonded joints, square-end, and spewfillet-high-order theory approach. J of Engineering Mechanic. 125 (1999) 1298–1307.

DOI: 10.1061/(asce)0733-9399(1999)125:11(1298)