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Analytical Approach

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Handbook of Adhesion Technology

Abstract

This chapter presents analytical approach for determining stress and strength of adhesively bonded joints. Selected applications of adhesively bonded joints are discussed first, and then mathematical models for stress analysis of these joints are outlined. Various closed-form solutions for adhesive stresses and edge bending moment for balanced single-lap joints are presented and compared. The method for finding analytical solutions for asymmetric and unbalanced adhesive joints is also discussed. Explicit expressions for mode I and mode II energy release rates for cohesive failure and interfacial debonding are presented for asymmetric joints with a semi-infinitive length subjected to general load combinations.

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References

  • Adams RD (1989) Strength predictions for lap joints, especially with composite adherends: a review. J Adhes 30(1–4):219–242

    Article  Google Scholar 

  • Adams RD, Mallick V (1992) A method for the stress analysis of lap joints. J Adhes 38(3–4):199–217

    Article  Google Scholar 

  • Adams RD, Comyn J, Wake WC (1997) Structural adhesive joints in engineering. Chapman and Hall, London

    Google Scholar 

  • Allman DJ (1977) A theory for the elastic stresses in adhesive bonded lap joints. Q J Mech Appl Math 30:415–436

    Article  MathSciNet  Google Scholar 

  • Bigwood DA, Crocombe AD (1989) Elastic analysis and engineering design formulae for bonded joints. Int J Adhes Adhes 9(4):229–242

    Article  Google Scholar 

  • Bigwood DA, Crocombe AD (1990) Nonlinear adhesive bonded joint design analyses. Int J Adhes Adhes 10(1):31–41

    Article  Google Scholar 

  • Blackman BRK, Hadavinia H, Kinloch AJ, Williams JG (2003) The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints. Int J Fract 119(1):25–46

    Article  Google Scholar 

  • Bruno D, Greco F, Lonetti P (2003) A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites. Int J Solids Struct 40(26):7245–7268

    Article  Google Scholar 

  • Carpenter W (1980) Stresses in bonded connections using finite elements. Int J Numer Methods Eng 15(11):1659–1680

    Article  Google Scholar 

  • Carpenter WC (1991) A comparison of numerous lap joint theories for adhesively bonded joints. J Adhes 35(1):55–73

    Article  Google Scholar 

  • Chen D, Cheng S (1983) An analysis of adhesive-bonded single lap joints. J Appl Mech 50(1):109–115

    Article  Google Scholar 

  • Delale F, Erdogan F, Aydinoglu MN (1981) Stresses in adhesively bonded joints-a closed form solution. J Compos Mater 15:249–271

    Article  Google Scholar 

  • Fernlund G, Spelt JK (1991) Failure load prediction of structural adhesive joints, part 1: analytical method. Int J Adhes Adhes 11(4):213–220

    Article  Google Scholar 

  • Fernlund G, Papini M, McCammond D, Spelt JK (1994) Fracture load predictions for adhesive joints. Compos Sci Technol 51(4):587–600

    Article  Google Scholar 

  • Gleich DM, Van Tooren MJL, Beukers A (2001) Analysis and evaluation of bondline thickness effects on failure load in adhesively bonded structures. J Adhes Sci Technol 15(9):1091–1101

    Article  Google Scholar 

  • Goland M, Reissner E (1944) The stresses in cemented joints. J Appl Mech 11:A17–A27

    Google Scholar 

  • Grant P, Teig IC (1976) Strength and stress analysis of bonded joints, British Aircraft Corporation Ltd. Military Aircraft Division, Report No SOR PJ 109

    Google Scholar 

  • Harris JA, Adams RD (1984) Strength prediction of bonded single lap joints by non-linear finite element methods. Int J Adhes Adhes 4(2):65–78

    Article  Google Scholar 

  • Hart-Smith LJ (1973) Adhesive-bonded single-lap joints, NASA Langley research Center, NASA CR-112235

    Google Scholar 

  • Harvey CM, Wood JD, Wang S, Watson A (2014) A novel method for the partition of mixed-mode fractures in 2D elastic laminated unidirectional composite beams. Compos Struct 116:589–594

    Article  Google Scholar 

  • Huang H, Yang CD, Tomblin JS, Harter P (2002) Stress and failure analyses of adhesive-bonded composite joints using ASTM D3165 specimens. J Compos Technol Res 24(2):93–104

    Article  Google Scholar 

  • Humi M, Miller W (1988) Second course in ordinary differential equations for scientists and engineers. Springer-Verlag, New York

    Book  Google Scholar 

  • Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. Adv Appl Mech 29:63–191

    Article  Google Scholar 

  • Jiang Z, Wan S, Zhong Z, Li M (2016) Geometrically nonlinear analysis for unbalanced adhesively bonded single-lap joint based on flexible interface theory. Arch Appl Mech 86(7):1273–1294

    Article  Google Scholar 

  • Johnson WS (1986) Stress analysis of the cracked lap shear specimen-an ASTM round robin, NASA Technical Memorandum 89006

    Google Scholar 

  • Lee J, Kim H (2007) Elasto-plastic analysis of adhesively bonded symmetric single lap joints under in-plane tension and edge moments. J Adhes 83(9):837–870

    Article  Google Scholar 

  • Li W, Cheng G, Wang D, Wu J (2015) A mixed mode partition method for delaminated beam structure. Eng Fract Mech 148:15–26

    Article  Google Scholar 

  • Liljedahl CDM, Crocombe AD, Wahab MA, Ashcroft IA (2006) Damage modelling of adhesively bonded joints. Int J Fract 141(1–2):147–161

    Article  Google Scholar 

  • Luo Q, Tong L (2002) Exact static solutions to piezoelectric smart beams including peel stresses–I: theoretical formulation. Int J Solids Struct 39(18):4677–4695

    Article  Google Scholar 

  • Luo Q, Tong L (2004) Linear and higher order displacement theories for adhesive bonded lap joints. Int J Solids Struct 41(22–23):6351–6381

    Article  Google Scholar 

  • Luo Q, Tong L (2007) Fully-coupled nonlinear analysis of single lap adhesive joints. Int J Solids Struct 44(7–8):2349–2370

    Article  Google Scholar 

  • Luo Q, Tong L (2008) Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends. Int J Solids Struct 45(22–23):5914–5935

    Article  Google Scholar 

  • Luo Q, Tong L (2009a) Calculation of energy release rates for cohesive and interlaminar delamination based on the classical beam-adhesive model. J Compos Mater 43(4):331–348

    Article  Google Scholar 

  • Luo Q, Tong L (2009b) Energy release rates for interlaminar delamination in laminates considering transverse shear effects. Compos Struct 89(2):235–244

    Article  MathSciNet  Google Scholar 

  • Luo Q, Tong L (2009c) Fracture prediction of adhesively bonded structures using energy release rates. J Adhes Sci Technol 23(10):1415–1440

    Article  Google Scholar 

  • Luo Q, Tong L (2012) Analytic formulas of energy release rates for delamination using a global–local method. Int J Solids Struct 49(23–24):3335–3344

    Article  Google Scholar 

  • Luo Q, Tong L (2016) Solutions for clamped adhesively bonded single lap joint with movement of support end and its application to a carbon nanotube junction in tension. J Adhes 92(5):349–379

    Article  Google Scholar 

  • Ojalvo IU, Eidinoff HL (1978) Bond thickness upon stresses in single-lap adhesive joints. AIAA J 16(3):204–211

    Article  Google Scholar 

  • Oplinger DW (1994) Effects of adherend deflection on single lap joints. Int J Solids Struct 31(18):2565–2587

    Article  Google Scholar 

  • Renton WJ, Vinson (1975) The efficient design of adhesive bonded joints. J Adhes 7(3):175–193

    Article  Google Scholar 

  • Shahin K, Kember G, Taheri F (2008) An asymptotic solution for evaluation of stresses in balanced and unbalanced adhesively bonded joints. Mech Adv Mater Struct 15(2):88–103

    Article  Google Scholar 

  • Sheppard A, Kelly D, Tong LY (1998) A damage zone model for the failure analysis of adhesively bonded joints. Int J Adhes Adhes 18(6):385–400

    Article  Google Scholar 

  • da Silva LFM, Rodrigues TNSS, Figueiredo MAV, de Moura MFSF, Chousal JAG (2006) Effect of adhesive type and thickness on the lap shear strength. J Adhes 82(11):1091–1115

    Article  Google Scholar 

  • da Silva LFM, das Neves PJC, Adams RD, Spelt JK (2009) Analytical models of adhesively bonded joints-part II: comparative study. Int J Adhes Adhes 29(3):331–341

    Article  Google Scholar 

  • Srinivas S (1975) Analysis of bonded joints, NASA TN D-7855, Apr 1975

    Google Scholar 

  • Tong L (1996) Bond strength for adhesive-bonded single-lap joints. Acta Mech 117(1–4):101–113

    Article  Google Scholar 

  • Tong L, Luo Q (2008) Chapter 2 Analysis of cracked lap shear (CLS) joints. In: da LFM S, Oechsner A (eds) Modelling of adhesively bonded joints. Springer, Heidelberg

    Google Scholar 

  • Tong L, Steven GP (1999) Analysis and design of structural bonded joints. Kluwer Academic, Boston. 1999

    Book  Google Scholar 

  • Van Tooren MJL (2004) Experimental verification of a stress singularity model to predict the effect of bondline thickness on joint strength. J Adhes Sci Technol., 2004 18(4):395–412

    Article  Google Scholar 

  • Volkersen O (1938) “Die Nietkraftverteilung in Zugbeanspruchten Nietverbindungen mit Konstanten Laschenquerschnitten” (The rivet load distribution in lap-joints with members of constant thickness subjected to tension). Luftfahrtforschung 15:41–47

    Google Scholar 

  • Wang S, Harvey C (2012) A theory of one-dimensional fracture. Compos Struct 94(2):758–767

    Article  Google Scholar 

  • Williams JG (1988) On the calculation of energy release rates for cracked laminates. Int J Fract 36(2):101–119

    Article  Google Scholar 

  • Yang C, Pang SS (1993) Stress–strain analysis of adhesive-bonded single-lap composite joints under cylindrical bending. Compos Eng 3(11):1051–1063

    Article  Google Scholar 

  • Yang CD, Huang H, Tomblin JS, Sun WJ (2004) Elastic-plastic model of adhesive-bonded single-lap composite joints. J Compos Mater 38(4):293–309

    Article  Google Scholar 

  • Yousefsani SA, Tahani M (2013) Analytical solutions for adhesively bonded composite single-lap joints under mechanical loadings using full layerwise theory. Int J Adhes Adhes 43:32–41

    Article  Google Scholar 

  • Zhao B, Lu ZH (2009) A two-dimensional approach of single-lap adhesive bonded joints. Mech Adv Mater Struct 16(2):130–159

    Article  Google Scholar 

  • Zhao X, Adams RD, da Silva LFM (2010) A new method for the determination of bending moments in single lap joints. Int J Adhes Adhes 30(2):63–71

    Article  Google Scholar 

Download references

Acknowledgment

The authors are grateful for the support of the Australian Research Council via a Discovery Projects grant (DP140104408).

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Correspondence to Liyong Tong .

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Tong, L., Luo, Q. (2018). Analytical Approach. In: da Silva, L., Öchsner, A., Adams, R. (eds) Handbook of Adhesion Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-55411-2_24

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