Single lap joint strength prediction using the radial point interpolation method and the critical longitudinal strain criterion. (English) Zbl 1464.74129

Summary: Adhesive joining is currently a very popular joining method. This increases the necessity for better strength prediction tools to aid in the design of these joints. Currently, Cohesive Zone Modeling (CZM) is the most popular method to study joint strength. However, CZM requires traction-separation laws, which define the adhesive behavior, and these are dependent on the adhesive thickness \((t_A)\). This means that, when using CZM, the traction separation law parameters have to be measured multiple times to predict the strength of joints with different \(t_A\). The recently proposed Critical Longitudinal Strain (CLS) criterion is a criterion based on continuum mechanics, which was previously used with the Finite Element Method (FEM) to predict the strength of Single Lap Joints (SLJ). The use of meshless methods to predict the strength of adhesive joints is scarce and the CLS criterion has never been used with the Radial Point Interpolation Method (RPIM). In this work, the CLS criterion was used with the RPIM to determine the strength of SLJ bonded with three different adhesives. The strength predictions with this approach were accurate for the three adhesives, which ranged from brittle to highly ductile.


74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] Marques, G. P.; Campilho, R. D.S. G.; Da Silva, F. J.G.; Moreira, R. D.F., Adhesive selection for hybrid spot-welded/bonded single-lap joints: experimentation and numerical analysis, Compos Part B Eng, 84, 248-257 (2016)
[2] Teixeira, J. M.D.; Campilho, R. D.S. G.; da Silva, F. J.G., Numerical assessment of the double-cantilever beam and tapered double-cantilever beam tests for the gic determination of adhesive layers, J Adhes, 94, 11, 951-973 (2018)
[3] da Silva, L. F.M.; das Neves, P. J.C.; Adams, R. D.; Spelt, J. K., Analytical models of adhesively bonded joints-Part I: literature survey, Int J Adhes Adhes, 29, 3, 319-330 (2009)
[4] da Silva, L. F.M.; das Neves, P. J.C.; Adams, R. D.; Wang, A.; Spelt, J. K., Analytical models of adhesively bonded joints. Part II: comparative study, Int J Adhes Adhes, 29, 3, 331-341 (2009)
[5] Stein, N.; Felger, J.; Becker, W., Analytical models for functionally graded adhesive single lap joints: a comparative study, Int J Adhes Adhes, 76, February, 70-82 (2017)
[6] Le Pavic, J.; Stamoulis, G.; Bonnemains, T.; Da Silva, D.; Thévenet, D., Fast failure prediction of adhesively bonded structures using a coupled stress-energetic failure criterion, Fatigue Fract Eng Mater Struct, 42, 42, 627-639 (2019)
[7] Moreira, R. D.F. F.; Campilho, R. D.S. G., Strength improvement of adhesively-bonded scarf repairs in aluminium structures with external reinforcements, Eng Struct, 101, 99-110 (2015)
[8] Moreira, R. D.F.; Campilho, R. D.S. G., Parametric study of the reinforcement geometry on tensile loaded scarf adhesive repairs, J Adhes, 92, 7-9, 586-609 (2016)
[9] 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)
[10] Li, J.; Yan, Y.; Liang, Z.; Zhang, T., Experimental and numerical study of adhesively bonded cfrp scarf-lap joints subjected to tensile loads, J Adhes, 92, 1, 1-17 (2016)
[11] Ji, Y. M.; Han, K. S., Fracture mechanics approach for failure of adhesive joints in wind turbine blades, Renew Energy, 65, 23-28 (2014)
[12] Luo, H.; Yan, Y.; Zhang, T.; Liang, Z., Progressive failure and experimental study of adhesively bonded composite single-lap joints subjected to axial tensile loads, J Adhes Sci Technol, 30, 8, 894-914 (2016)
[13] Moya-Sanz, E. M.; Ivañez, I.; Garcia-Castillo, S. K., Effect of the geometry in the strength of single-lap adhesive joints of composite laminates under uniaxial tensile load, Int J Adhes Adhes, 72, 23-29 (2016), 2017
[14] Ji, G.; Ouyang, Z.; Li, G.; Ibekwe, S.; Pang, S. S., Effects of adhesive thickness on global and local mode-I interfacial fracture of bonded joints, Int J Solids Struct, 47, 18-19, 2445-2458 (2010) · Zbl 1196.74241
[15] da Silva, L. F.M.; de Magalhães, F. A.C. R.G.; Chaves, F. J.P.; De Moura, M. F.S. F., Mode ii fracture toughness of a brittle and a ductile adhesive as a function of the adhesive thickness, J Adhes, 86, 9, 889-903 (2010)
[16] Ji, G.; Ouyang, Z.; Li, G., Local interface shear fracture of bonded steel joints with various bondline thicknesses, Exp Mech, 52, 5, 481-491 (2012)
[17] Ji, G.; Ouyang, Z.; Li, G., On the interfacial constitutive laws of mixed mode fracture with various adhesive thicknesses, Mech Mater, 47, 24-32 (2012)
[18] da Silva, L. F.M.; Campilho, R. D.S. G., Advances in numerical modeling of adhesive joints (2012), Springer · Zbl 1284.74002
[19] Razavi, S. M.J.; Ayatollahi, M. R.; Majidi, H. R.; Berto, F., A strain-based criterion for failure load prediction of steel/CFRP double strap joints, Compos Struct, 206, April, 116-123 (2018)
[20] Zhao, X.; Adams, R. D.; Da Silva, L. F.M., Single lap joints with rounded adherend corners: stress and strain analysis, J Adhes Sci Technol, 25, 8, 819-836 (2011)
[21] Zhao, X.; Adams, R. D.; Da Silva, L. F.M., Single lap joints with rounded adherend corners: experimental results and strength prediction, J Adhes Sci Technol, 25, 8, 837-856 (2011)
[22] Reis, P. N.B.; Ferreira, J. A.M.; Antunes, F., Effect of adherends rigidity on the shear strength of single lap adhesive joints, Int J Adhes Adhes, 31, 4, 193-201 (2011)
[23] Ayatollahi, M. R.; Akhavan-Safar, A., Failure load prediction of single lap adhesive joints based on a new linear elastic criterion, Theor Appl Fract Mech, 80, 210-217 (2015)
[24] Akhavan-Safar, A.; da Silva, L. F.M.; Ayatollahi, M. R., An investigation on the strength of single lap adhesive joints with a wide range of materials and dimensions using a critical distance approach, Int J Adhes Adhes, 78, August, 248-255 (2017)
[25] Akhavan-Safar, A.; Ayatollahi, M. R.; da Silva, L. F.M., Strength prediction of adhesively bonded single lap joints with different bondline thicknesses: a critical longitudinal strain approach, Int J Solids Struct, 109, 189-198 (2017)
[26] Khoramishad, H.; Akhavan-Safar, A.; Ayatollahi, M. R.; Da Silva, L. F.M., Predicting static strength in adhesively bonded single lap joints using a critical distance based method: substrate thickness and overlap length effects, Proc Inst Mech Eng Part L J Mater Des Appl, 231, 1-2, 237-246 (2017)
[27] Hell, S.; Weißgraeber, P.; Felger, J.; Becker, W., A coupled stress and energy criterion for the assessment of crack initiation in single lap joints: a numerical approach, Eng Fract Mech, 117, 112-126 (2014)
[28] Sugiman, S.; Ahmad, H., Comparison of cohesive zone and continuum damage approach in predicting the static failure of adhesively bonded single lap joints, J Adhes Sci Technol, 31, 5, 552-570 (2017)
[29] Silva, J. O.S.; Campilho, R. D.S. G.; Rocha, R. J.B., Crack growth analysis of adhesively-bonded stepped joints in aluminium structures, J Braz Soc Mech Sci Eng, 40, 11, 540 (2018)
[30] Belinha, J., Meshless methods in biomechanics (2014), Springer · Zbl 1314.92001
[31] 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
[32] Liu, G. R.; Gu, Y. T., A point interpolation method for two-dimensional solids, Int J Numer Methods Eng, 50, 4, 937-951 (2001) · Zbl 1050.74057
[33] Liu, G. R., A point assembly method for stress analysis for two-dimensional solids, Int J Solids Struct, 39, 1, 261-276 (2002) · Zbl 1090.74699
[34] Lucy, L. B., A numerical approach to the testing of the fission hypothesis, Astron J, 82, December, 1013-1024 (1977)
[35] Gingold, R. A.; Monaghan, J. J., Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon Not R Astron Soc, 181, 3, 375-389 (1977) · Zbl 0421.76032
[36] Belytschko, T.; Lu, Y. Y.; Gu, L., Element-free galerkin methods, Int J Numer Methods Eng, 37, 2, 229-256 (1994) · Zbl 0796.73077
[37] Liu, W. K.; Jun, S.; Zhang, Y. F., Reproducing kernel particle methods, Int J Numer Methods Fluids, 20, 8-9, 1081-1106 (1995) · Zbl 0881.76072
[38] 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)
[39] 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)
[40] 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)
[41] Di Pisa, C.; Aliabadi, M. H., Boundary element analysis of stiffened panels with repair patches, Eng Anal Bound Elem, 56, 162-175 (2015) · Zbl 1403.74161
[42] ASTM International, “ASTM E8M-04, standard test methods for tension testing of metallic materials [Metric] (Withdrawn 2008), West Conshohocken, PA, 2008, www.astm.org”.
[43] 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, 18, 2351-2368 (2011)
[44] Neto, J. A.B. P.; Campilho, R. D.S. G.; Da Silva, L. F.M., Parametric study of adhesive joints with composites, Int J Adhes Adhes, 37, 96-101 (2012)
[45] Campilho, R. D.S. G.; Banea, M. D.; Neto, J. A.B. P.; Da Silva, L. F.M., Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer, Int J Adhes Adhes, 44, 4-6, 48-56 (2013)
[46] Campilho, R. D.S. G.; Moura, D. C.; Gonçalves, D. J.S.; Da Silva, J. F.M. G.; Banea, M. D.; Da Silva, L. F.M., Fracture toughness determination of adhesive and co-cured joints in natural fibre composites, Compos Part B Eng, 50, 120-126 (2013)
[47] Nunes, S. L.S., Comparative failure assessment of single and double lap joints with varying adhesive systems, J Adhes, 92, 7-9, 610-634 (2016)
[48] Adams, R. D., Adhesive bonding: science, technology and applications (2005), Woodhead Publishing Limited: Woodhead Publishing Limited Cambridge
[49] Adams, R. D.; Peppiatt, N. A., Stress analysis of adhesive-bonded lap joints, J Strain Anal, 9, 3, 185-196 (1974)
[50] Davis, M.; Bond, D., Principles and practices of adhesive bonded structural joints and repairs, Int J Adhes Adhes, 19, 2, 91-105 (1999)
[51] Liu, Z.; Huang, Y.; Yin, Z.; Bennati, S.; Valvo, P. S., A general solution for the two-dimensional stress analysis of balanced and unbalanced adhesively bonded joints, Int J Adhes Adhes, 54, 112-123 (2014)
[52] Wang, J. G.; Liu, G. R., On the optimal shape parameters of radial basis functions used for 2-D meshless methods, Comput Methods Appl Mech Eng, 191, 23-24, 2611-2630 (2002) · Zbl 1065.74074
[53] 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
[54] Taylor, D., The theory of critical distances, Eng Fract Mech, 75, 7, 1696-1705 (2008)
[55] Liu, G. R., Meshfree methods (2010), CRC Press: CRC Press Boca Raton · Zbl 1205.74003
[56] 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
[57] Campilho, R. D.S. G.; Banea, M. D.; Pinto, A. M.G.; Da Silva, L. F.M.; De Jesus, A. M.P., Strength prediction of single- and double-lap joints by standard and extended finite element modelling, Int J Adhes Adhes, 31, 5, 363-372 (2011)
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