Viscoelastic analysis of stress distribution in balanced and unbalanced adhesively bonded single-lap joints with functionally graded adherends under the Reddy model

Document Type: Research Paper

Authors

Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

In this study, shear and peel stress distributions in the viscoelastic adhesive layer of a single-lap joint (SLJ) with functionally graded (FG) adherends are investigated. The study focuses on the effect of different adherend profiles and material composition on the time-dependent stress concentration/distribution in balanced and unbalanced SLJs. For this purpose, the Reddy model is applied to the FG adherends and a three-parameter solid viscoelastic model is used to simulate the adhesive layer behavior. Using the first-order shear deformation theory for the FG adherends, the governing differential equations are derived and then transformed into the Laplace domain. A finite element model of the joint was also developed to further backup the numerical solution. The numerical inverse Laplace transform method was used to extract the desired results that were then compared with those of finite element method (FEM) findings. Very good agreements were observed between the results of both methods. Results show that the geometric and mechanical properties of the FG adherends have an essential role in reducing the shear and peel stress concentrations as well as the uniformity of shear stress distribution in the overlap region. Results also show that either method (finite element or the proposed semi-analytical method) can be utilized with confidence for prediction of stress relaxation in the adhesively bonded SLJs with FG adherends.

Keywords


[1]           M. Banea, L. F. da Silva, Adhesively bonded joints in composite materials: an overview, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Vol. 223, No. 1, pp. 1-18, 2009.

[2]           L. F. da Silva, P. J. das Neves, R. Adams, J. Spelt, Analytical models of adhesively bonded joints—Part I: Literature survey, International Journal of Adhesion and Adhesives, Vol. 29, No. 3, pp. 319-330, 2009.

[3]           L. F. da Silva, P. J. das Neves, R. Adams, A. Wang, J. Spelt, Analytical models of adhesively bonded joints—Part II: Comparative study, International Journal of Adhesion and Adhesives, Vol. 29, No. 3, pp. 331-341, 2009.

[4]           X. He, A review of finite element analysis of adhesively bonded joints, International Journal of Adhesion and Adhesives, Vol. 31, No. 4, pp. 248-264, 2011.

[5]           S. Budhe, M. Banea, S. De Barros, L. Da Silva, An updated review of adhesively bonded joints in composite materials, International Journal of Adhesion and Adhesives, Vol. 72, pp. 30-42, 2017.

[6]           M. Shishesaz, M. Hosseini, Effects of joint geometry and material on stress distribution, strength and failure of bonded composite joints: an overview, The Journal of Adhesion, pp. 1-69, 2018.

[7]           O. Volkersen, Stress distribution of bonded joint under tensile stress with constant cross section of straps, Aerospace research, Vol. 15, pp. 41-68, 1938.

[8]           M. Goland, The stresses in cemented joints, J. appl. Mech., Vol. 17, pp. 66, 1944.

[9]           L. J. Hart-Smith, Adhesive bonded Double-lap joints, NASA Langley Contract Report, 1973.

[10]         Q. Luo, L. Tong, Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends, International Journal of Solids and Structures, Vol. 45, No. 22-23, pp. 5914-5935, 2008.

[11]         Q. Luo, L. Tong, Linear and higher order displacement theories for adhesively bonded lap joints, International journal of solids and structures, Vol. 41, No. 22-23, pp. 6351-6381, 2004.

[12]         Q. Luo, L. Tong, Analytical solutions for nonlinear analysis of composite single-lap adhesive joints, International Journal of Adhesion and Adhesives, Vol. 29, No. 2, pp. 144-154, 2009.

[13]         B. Zhao, Z.-H. Lu, Y.-N. Lu, Closed-form solutions for elastic stress–strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness, International Journal of Adhesion and Adhesives, Vol. 31, No. 6, pp. 434-445, 2011.

[14]         E. Selahi, M. Tahani, S. A. Yousefsani, Analytical solutions of stress field in adhesively bonded composite single-lap joints under mechanical loadings, Int J Eng, Vol. 27, No. 3, pp. 475-486, 2014.

[15]         Z. Liu, Y. Huang, Z. Yin, S. Bennati, P. S. Valvo, A general solution for the two-dimensional stress analysis of balanced and unbalanced adhesively bonded joints, International Journal of Adhesion and Adhesives, Vol. 54, pp. 112-123, 2014.

[16]         B. Zhao, Z.-H. Lu, Y.-N. Lu, Two-dimensional analytical solution of elastic stresses for balanced single-lap joints—Variational method, International Journal of Adhesion and Adhesives, Vol. 49, pp. 115-126, 2014.

[17]         M. Shishesaz, A. Reza, M. Daniali, Stress distribution in single lap joints with a cracked composite adherend—part I: single lamina adherends, The Journal of Adhesion, Vol. 90, No. 11, pp. 912-931, 2014.

[18]         M. Shishesaz, A. Reza, M. Daniali, Stress distribution in single lap joints with a cracked composite adherend—part II: laminated adherends, The Journal of Adhesion, Vol. 90, No. 12, pp. 933-954, 2014.

[19]         Z. Jiang, S. Wan, Z. Zhong, M. Li, Geometrically nonlinear analysis for unbalanced adhesively bonded single-lap joint based on flexible interface theory, Archive of Applied Mechanics, Vol. 86, No. 7, pp. 1273-1294, 2016.

[20]         Z. Jiang, S. Wan, T. Keller, A. P. Vassilopoulos, Two-dimensional analytical stress distribution model for unbalanced FRP composite single-lap joints, European Journal of Mechanics-A/Solids, Vol. 66, pp. 341-355, 2017.

[21]         E. Selahi, M. Kadivar, Non-linear Analysis of Adhesive Joints in Composite Structures, Composite Structures, Vol. 9, No. 1, pp. 83-92, 2016.

[22]         A. T. l’Armée, N. Stein, W. Becker, Bending moment calculation for single lap joints with composite laminate adherends including bending-extensional coupling, International Journal of Adhesion and Adhesives, Vol. 66, pp. 41-52, 2016.

[23]         F. Delale, F. Erdogan, Viscoelastic analysis of adhesively bonded joints, Journal of Applied Mechanics, Vol. 48, No. 2, pp. 331-338, 1981.

[24]         P. Pandey, H. Shankaragouda, A. K. Singh, Nonlinear analysis of adhesively bonded lap joints considering viscoplasticity in adhesives, Computers & structures, Vol. 70, No. 4, pp. 387-413, 1999.

[25]         Y. Nagaraja, R. Alwar, Viscoelastic analysis of an adhesive-bonded plane lap joint, Computers & Structures, Vol. 11, No. 6, pp. 621-627, 1980.

[26]         S. Yadagiri, C. P. Reddy, T. S. Reddy, Viscoelastic analysis of adhesively bonded joints, Computers & structures, Vol. 27, No. 4, pp. 445-454, 1987.

[27]         W. C. Carpenter, Viscoelastic analysis of bonded connections, Computers & Structures, Vol. 36, No. 6, pp. 1141-1152, 1990.

[28]         H. L. Groth, Viscoelastic and viscoplastic stress analysis of adhesive joints, International Journal of Adhesion and Adhesives, Vol. 10, No. 3, pp. 207-213, 1990.

[29]         C. Sato, Stress estimation of joints having adherends with different curvatures bonded with viscoelastic adhesives, International Journal of Adhesion and Adhesives, Vol. 31, No. 5, pp. 315-321, 2011.

[30]         M. Shishesaz, A. Reza, The effect of viscoelasticity of polymeric adhesives on shear stress distribution in a single-lap joint, The Journal of Adhesion, Vol. 89, No. 11, pp. 859-880, 2013.

[31]         A. Reza, M. Shishesaz, The effect of viscoelasticity on the stress distribution of adhesively single-lap joint with an internal break in the composite adherends, Mechanics of Time-Dependent Materials, Vol. 22, No. 3, pp. 373-399, 2018.

[32]         A. Reza, M. Shishesaz, K. Naderan-Tahan, The effect of viscoelasticity on creep behavior of double-lap adhesively bonded joints, Latin American Journal of Solids and Structures, Vol. 11, No. 1, pp. 35-50, 2014.

[33]         A. Reza, M. Shishesaz, Transient load concentration factor due to a sudden break of fibers in the viscoelastic PMC under tensile loading, International Journal of Solids and Structures, Vol. 88, pp. 1-10, 2016.

[34]         N. Stein, P. Weißgraeber, W. Becker, Stress solution for functionally graded adhesive joints, International Journal of Solids and Structures, Vol. 97, pp. 300-311, 2016.

[35]         N. Stein, H. Mardani, W. Becker, An efficient analysis model for functionally graded adhesive single lap joints, International Journal of Adhesion and Adhesives, Vol. 70, pp. 117-125, 2016.

[36]         N. Stein, J. Felger, W. Becker, Analytical models for functionally graded adhesive single lap joints: A comparative study, International journal of adhesion and adhesives, Vol. 76, pp. 70-82, 2017.

[37]         N. Stein, P. Rosendahl, W. Becker, Homogenization of mechanical and thermal stresses in functionally graded adhesive joints, Composites Part B: Engineering, Vol. 111, pp. 279-293, 2017.

[38]         M. K. Apalak, R. Gunes, Investigation of elastic stresses in an adhesively bonded single lap joint with functionally graded adherends in tension, Composite structures, Vol. 70, No. 4, pp. 444-467, 2005.

[39]         M. K. Apalak, R. Gunes, Elastic flexural behaviour of an adhesively bonded single lap joint with functionally graded adherends, Materials & design, Vol. 28, No. 5, pp. 1597-1617, 2007.

[40]         W. E. Guin, J. Wang, Theoretical model of adhesively bonded single lap joints with functionally graded adherends, Engineering Structures, Vol. 124, pp. 316-332, 2016.

[41]         S. Amidi, J. Wang, Three-parameter viscoelastic foundation model of adhesively bonded single-lap joints with functionally graded adherends, Engineering Structures, Vol. 170, pp. 118-134, 2018.

[42]         M. Khan, S. Kumar, J. Reddy, Material-tailored adhesively bonded multilayers: A theoretical analysis, International Journal of Mechanical Sciences, Vol. 148, pp. 246-262, 2018.

[43]         X. Zhao, R. Adams, L. F. da Silva, A new method for the determination of bending moments in single lap joints, International Journal of Adhesion and Adhesives, Vol. 30, No. 2, pp. 63-71, 2010.