Meshless analysis of substrate stiffness and its effect on metallic double-L joint strength and stress distributions. (English) Zbl 1464.74410

Summary: Aircraft, automotive, and wind turbine blade construction often require bonding of non-parallel substrates. T-joints are used for such purpose. However, reduced information about their mechanical behaviour is available in the literature, mostly reported with similar substrate thickness. When bonding a thin substrate on a thicker one, the thinner substrate could largely deform before the adhesive layer fails. Therefore, numerical techniques as the meshless methods (MM) are suitable to analyse this joint configuration. In this work, a MM was used to analyse T-joints with metallic substrates. The analyses were elastic-plastic and considered the Exponent Drucker-Prager (EDP), which is appropriate for ductile adhesives. Four substrate thicknesses (1–4 mm), and three different adhesive systems were considered, aiming to investigate the EDP suitability for the analysis of adhesive joints with non-parallel substrates and how substrate thickness and adhesive ductility influence joint strength \((P_{\max})\). Thus, \(P_{\max}\), stress and strains along the bond-line, and plastic hinges in the substrates were evaluated. Regardless of the adhesive system, the increase of substrate thickness \((t_{P 2})\) also increased \(P_{\max}\). For adhesives with failure strain \((\epsilon_f)\) below 10%, experimental and numerical results have a good agreement, showing that the proposed methodology is suitable to analyse this joint type.


74S99 Numerical and other methods in solid mechanics
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65D12 Numerical radial basis function approximation
74A10 Stress
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
Full Text: DOI


[1] Sutherland, L. S.; Amado, C.; Guedes Soares, C., Statistical analyses of the effects of bonding parameters and fabrication robustness on the strength of adhesive T-joints, Compos Part B Eng (2019)
[2] Stein, N.; Weißgraeber, P.; Becker, W., A model for brittle failure in adhesive lap joints of arbitrary joint configuration, Compos Struct, 133, 707-718 (2015)
[3] da Silva, L. F.M.; Adams, R. D., The strength of adhesively bonded T-joints, Int J Adhes Adhes, 22, 311-315 (2002)
[4] de Freitas, S. T.; Sinke, J., Failure analysis of adhesively-bonded skin-to-stiffener joints: metal-metal vs. composite-metal, Eng Fail Anal, 56, 2-13 (2015)
[5] Apalak, Z. G.; Apalak, M. K.; Davies, R., Analysis and design of tee joints with double support, Int J Adhes Adhes, 16, 3, 187-214 (1996)
[6] Akpinar, S.; Aydin, M. D.; Özel, A., A study on 3-D stress distributions in the bi-adhesively bonded T-joints, Appl Math Model, 37, 10220-10230 (2013)
[7] Carneiro, M. A.S.; Campilho, R. D.S. G., Analysis of adhesively-bonded T-joints by experimentation and cohesive zone models, J Adhes Sci Technol, 31, 18, 1998-2014 (2017)
[8] Moreira, F. J.P.; Campilho, R. D.S. G., Use of the XFEM for the design of adhesively-bonded T-joints, Frat ed Integrita Strutt, 13, 49, 435-449 (2019)
[9] Ma, X.; Liu, H.; Bian, K.; Lu, J.; Yang, Q.; Xiong, K., A numerical and experimental study on the multiple fracture progression of CFRP T-joints under pull-off load, Int J Mech Sci, 177, December 2019, 105541 (2020)
[10] Crocombe, A. D.; Kinloch, A. J., Review of adhesive bond failure criteria, Tech. Rep. (1994), AEA Technology INC: AEA Technology INC Didcot, Oxfordshire,UK
[11] Ramalho, L. D.C.; Campilho, R. D.S. G.; Belinha, J.; da Silva, L. F.M., Static strength prediction of adhesive joints: areview, Int J Adhes Adhes (2020)
[12] Raghava, R.; Caddell, R. M.; Yeh, G. S.Y., The macroscopic yield behaviour of polymers, J Mater Sci, 8, 225-232 (1973)
[13] Dean, G. D.; Crocker, L. E.; Read, B.; Wright, L., Prediction of deformation and failure of rubber-toughened adhesive joints, Int J Adhes Adhes, 24, 4, 295-306 (2004)
[14] Dean, G. D.; Crocker, L. E., The use of finite element methods for design with adhesives., Tech. Rep. (2001), National Physical Laboratory: National Physical Laboratory Teddington, Middlesex. UK
[15] Özer, H.; Öz, Ö., The use of the exponential Drucker-Prager material model for defining the failure loads of the mono and bi-adhesive joints, Int J Adhes Adhes, 76, 17-29 (2017)
[16] Sánchez-Arce, I. J.; Ramalho, L. D.C.; Campilho, R. D.S. G.; Belinha, J., Material non-linearity in the numerical analysis of SLJ bonded with ductile adhesives: a meshless approach, Int J Adhes Adhes, 104, 102716 (2021)
[17] Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P., Meshless methods: an overview and recent developments, Comput Methods Appl Mech Eng, 139, 1-4, 3-47 (1996) · Zbl 0891.73075
[18] Liu, G. R., An overview on meshfree methods: for computational solid mechanics, Int J Comput Methods, 13, 5 (2016) · Zbl 1359.74388
[19] Chen, J.-S.; Hillman, M.; Chi, S.-W., Meshfree methods: progress made after 20 years, J Eng Mech, 143, 4 (2017)
[20] Nguyen, V. P.; Rabczuk, T.; Bordas, S.; Duflot, M., Meshless methods: a review and computer implementation aspects, Math Comput Simul, 79, 3, 763-813 (2008) · Zbl 1152.74055
[21] Belinha, J., Meshless methods in biomechanics: bone tissue remodelling analysis (2015), Springer International Publishing · Zbl 1314.92001
[22] Wang, J. G.; Liu, G. R., A point interpolation meshless method based on radial basis functions, Int J Numer Methods Eng, 54, 11, 1623-1648 (2002) · Zbl 1098.74741
[23] Belinha, J.; Araújo, A. L.; Ferreira, A. J.M.; Dinis, L. M.J. S.; Natal Jorge, R. M., The analysis of laminated plates using distinct advanced discretization meshless techniques, Compos Struct, 143, 165-179 (2016)
[24] Dinis, L. M.J. S.; Natal Jorge, R. M.; Belinha, J., Analysis of 3D solids using the natural neighbour radial point interpolation method, Comput Methods Appl Mech Eng, 196, 13-16, 2009-2028 (2007) · Zbl 1173.74469
[25] Bodjona, K.; Lessard, L., Nonlinear static analysis of a composite bonded / bolted single-lap joint using the meshfree radial point interpolation method, Compos Struct, 134, 1024-1035 (2015)
[26] Mubashar, A.; Ashcroft, I. A., Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints, J Adhes, 93, 6, 444-460 (2017)
[27] Ramalho, L. D.C.; Campilho, R. D.S. G.; Belinha, J., Single lap joint strength prediction using the radial point interpolation method and the critical longitudinal strain criterion, Eng Anal Bound Elem, 113, 268-276 (2020) · Zbl 1464.74129
[28] Tsai, C. L.; Guan, Y. L.; Ohanehi, D. C.; Dillard, J. G.; Dillard, D. A.; Batra, R. C., Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method, Int J Adhes Adhes, 51, 67-80 (2014)
[29] Hart-Smith, L. J., Adhesive-bonded single-lap joints, Tech. Rep. (1973), NASA: NASA Hampton, Virginia. USA
[30] ISBN 0-906674-05-2. · Zbl 0482.73051
[31] Dinis, L.; Natal Jorge, R. M.; Belinha, J., The radial natural neighbours interpolators extended to elastoplasticity, 175-198 (2009), Springer Science & Business Media B.V. · Zbl 1157.74049
[32] Farahani, B. V.; Belinha, J.; Amaral, R.; Tavares, P. J.; Moreira, P. M.P. G., Extending radial point interpolating meshless methods to the elasto-plastic analysis of aluminium alloys, Eng Anal Bound Elem, 100, 101-117 (2019) · Zbl 1464.74390
[33] Simulia User Assistence. 2017.
[34] Campilho, R. D.S. G.; Pinto, A. M.G.; Banea, M. D.; Silva, R. F.; da Silva, L. F.M., Strength improvement of adhesively-bonded joints using a reverse-bent geometry, J Adhes Sci Technol, 25, 2351-2368 (2011)
[35] Faneco, T. M.S.; Campilho, R. D.S. G.; Silva, F. J.G.; Lopes, R. M., Strength and fracture characterization of a novel polyurethane adhesive for the automotive industry, J Test Eval, 45, 2, 398-407 (2017)
[36] Harris, J. A.; Adams, R. D., Strength prediction of bonded single lap joints by non-linear finite element methods, Int J Adhes Adhes, 4, 2, 65-78 (1984)
[37] Ramalho, L. D.C.; Campilho, R. D.S. G.; Belinha, J., Predicting single-lap joint strength using the natural neighbour radial point interpolation method, J Braz. Soc Mech Sci Eng, 41, 9, 1-11 (2019)
[38] Cordes, L. W.; Moran, B., Treatment of material discontinuity in the element-free Galerkin method, Comput Methods Appl Mech Eng, 139, 1-4, 75-89 (1996) · Zbl 0918.73331
[39] Broughton, W. R.; Crocker, L. E.; Urquhart, J. M., Strength of adhesive joints: a parametric study, Tech. Rep. (2001), National Physical Laboratory: National Physical Laboratory Teddington, Middlesex. UK
[40] ISBN 0072520361 9780072520361.
[41] Hu, P.; Shao, Q.; Li, W.; Han, X., Experimental and numerical analysis on load capacity and failure process of T-joint: effect produced by the bond-line length, Int J Adhes Adhes, 38, 17-24 (2012)
[42] da Silva, L. F.M.; Carbas, R. J.C.; Critchlow, G. W.; Figueiredo, M. A.V.; Brown, K., Effect of material, geometry, surface treatment and environment on the shear strength of single lap joints, Int J Adhes Adhes (2009)
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