SpringerLink
Log in

Stress Analysis Map** for Mechanically Fastened Composite Bolted Lap Joints Using Cohesive Zone Model

  • Original Research Article
  • Published:
Journal of Failure Analysis and Prevention Aims and scope Submit manuscript

Abstract

Quasi-brittle materials such as composite laminates, concrete, and toughened ceramics are subject to size effects in which the nominal strength decreases with increasing specimen size. Analyzing the joining of such materials is very important. Mechanically bolted joints are a widely used and suitable method for joining composite laminates in aircraft materials. Two-parameter cohesive laws—linear, constant, and exponential—were implemented analytically to analyze tearing, bearing stress, and remotely applied stress. An extended 2-D finite element model was created to validate the remote applied stress. The model provides reasonably acceptable results that can be used as fast design data for the selection of such materials and optimization of composite bolted joints.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

\(\sigma_{{\text{b}}}\) :

Bearing stress

\(\sigma\) :

Tensile stress

\(\lambda\) :

Biaxiality ratio

\(\delta\) :

Crack opening displacement

\(\gamma\) :

Geometric parameter \(\gamma = \frac{R}{R + l}\)

\(\alpha\) :

Load pressure angle

w :

Width of the plate

t :

Thickness of the plate

r :

Crack tip radius

R :

Radius of the hole

P :

Contact pressure in loaded hole

K :

Stress intensity factor

F :

Applied force

e :

Eccentricity

d :

Half crack length with radius

D :

Hole diameter

a :

Crack length which is equal to hole radius

\(\sigma_{{\text{u}}}\) :

Unnotch tensile strength

\(\sigma_{i}\) :

Cohesive strength at point (i)

\(\sigma_{{\text{C}}}\) :

Cohesive stress

\(\rho_{{{\text{Cr}}}}\) :

The transformation function which relates the nominal strength by specimen size

\(\theta_{{\text{l}}}\) :

Normalized fracture process zone length

\(\delta_{i}\) :

Crack opening at pint (i) on crack face

\(\delta_{{\text{C}}}\) :

Critical crack opening displacement

\(\beta_{w}\) :

Aspect ratio which is equal to (R/w)

\(\beta_{i} \left( {\theta_{l} , \beta_{w} , P} \right),\overline{\beta }\left( {\theta_{L} , \beta_{w} , P} \right)_{i}\) :

Connecting function for remote stress and loaded hole

\(l_{{{\text{FPZ}}}}\) :

Length of fracture processing zone

\(k_{T}\) :

Stress concentration factor

\(f_{ij} \left( {\theta_{L} , \beta_{w} ,P} \right)\) :

Influence functions that are independent of the crack geometry and loading conditions

\(a_{i}\) :

Crack length at point (i)

\(S_{{\text{t}}}\) :

Tearing stress

\(S_{{\text{s}}}\) :

Shear strength

\(S_{{\text{r}}}\) :

Remote applied stress

\(S_{{\text{n}}}\) :

Nominal strength of composite structure or net tension strength

\(S_{{\text{b}}}\) :

Normalized bearing strength

\(K_{\sigma }\) :

Cohesive stress intensity factor

\(K_{{\text{s}}}\) :

Remote stress intensity factor

\(K_{b}\) :

Loaded hole stress intensity factor

\(K_{{{\text{sT}}}}\) :

Total stress intensity factor at crack tip

\(K_{{{\text{Ic}}}}\) :

Fracture toughness

\(G_{{{\text{IC}}}}\) :

Surface release energy or may called fracture toughness

\(F_{4}\) :

Partially loaded finite width correction factor

\(F_{3 }\) :

Partially loaded hole correction factor

\(F_{2}\) :

Geometric correction factor for finite width

\(F_{1}\) :

Geometric correction factor for circular hole

\(F_{o}\) :

The correction factor of loaded holes

\(\overline{{K_{i} }}\) :

The stress intensity of segment i

\(\overline{C}_{i} ,\overline{b}_{i}\) :

Dimension for partially loaded cracks, i, j = 1, 2

References

  1. M.K. Hassan, Y. Mohammed, T. Salem, A. Hashem, Prediction of nominal strength of composite structure open hole specimen through cohesive laws. Int. J. Mech. Mech. Eng. IJMME-IJENS. 12, 1–9 (2012)

    Google Scholar 

  2. N.G. Naguib, M.K. Hassan, Y.A. Mohammed , W.W. Marzouk, M.A. Abdel-Rahman, Evaluation of fracture toughness of epoxy/glass fiber and its nano composites via the essential work of fracture (EWF) Method. Minia J. Eng. Technol. 34(2), 91–104 (2015)

  3. A.M. Kabeel, P. Maimí, N. Gascons, E.V. González, Net-tension strength of double lap joints taking into account the material cohesive law. Compos. Struct. 112, 207–213 (2014)

    Article  Google Scholar 

  4. A. Riccio, S. Saputo, A. Sellitto, A. Russo, V. Acanfora, P. Iaccarino, M. Zarrelli, On the mechanical behavior of laminated composite plates subjected to compression after impact tests. Mater. Today Proc. 34, 53–56 (2021)

    Article  CAS  Google Scholar 

  5. A. Russo, A. Sellitto, S. Saputo, V. Acanfora, A. Riccio, A numerical-analytical approach for the preliminary design of thin-walled cylindrical shell structures with elliptical cut-outs. Aerospace. 6(5), 52 (2019)

    Article  Google Scholar 

  6. Y. Mohammed, M.K. Hassan, H. Abu El-Ainin, A. Hashem, Size effect analysis in laminated composite structure using general bilinear fit. Int. J. Nonlinear Sci. Numer. Simul. 14(3–4), 217–224 (2013)

    Article  Google Scholar 

  7. C. Soutis, P. Curtis, A method for predicting the fracture toughness of CFRP laminates failing by fibre microbuckling. Compos. A Appl. Sci. Manuf. 31(7), 733–740 (2000)

    Article  Google Scholar 

  8. C. Soutis, P. Curtis, N. Fleck, Compressive failure of notched carbon fibre composites. Proc. R. Soc. London A Math. Phys. Eng. Sci. 440, 241–256 (1993)

    CAS  Google Scholar 

  9. C. Soutis, N. Fleck, P. Smith, Failure prediction technique for compression loaded carbon fibre-epoxy laminate with open holes. J. Compos. Mater. 25(11), 1476–1498 (1991)

    Article  Google Scholar 

  10. B. Yang, Examination of free-edge crack nucleation around an open hole in composite laminates. Int. J. Fract. 115(2), 173–191 (2002)

    Article  Google Scholar 

  11. Q. Yang, B. Cox, Cohesive models for damage evolution in laminated composites. Int. J. Fract. 133(2), 107–137 (2005)

    Article  Google Scholar 

  12. B. Han, Y. Ju, C. Zhou, Simulation of crack propagation in HTPB propellant using cohesive zone model. Eng. Fail. Anal. 26, 304–317 (2012)

    Article  CAS  Google Scholar 

  13. J. **g, F. Gao, J. Johnson, F.Z. Liang, R.L. Williams, J. Qu, Simulation of dynamic fracture along solder-pad interfaces using a cohesive zone model. ASME Int. Mech. Eng. Congr. Expos. 48678, 171–176 (2008)

    Google Scholar 

  14. D. Cartwright, A. Parker, Opening mode stress intensity factors for cracks in pin-loads joints. Int. J. Fract. 18(1), 65–78 (1982)

    Article  Google Scholar 

  15. G. Catalanotti, P.P. Camanho, A semi-analytical method to predict net-tension failure of mechanically fastened joints in composite laminates. Compos. Sci. Technol. 76, 69–76 (2013)

    Article  CAS  Google Scholar 

  16. P.P. Camanho, M. Lambert, A design methodology for mechanically fastened joints in laminated composite materials. Compos. Sci. Technol. 66(15), 3004–3020 (2006)

    Article  Google Scholar 

  17. J.M. Whitney, R.J. Nuismer, Stress fracture criteria for laminated composites containing stress concentrations. J. Compos. Mater. 8(3), 253–265 (1974)

    Article  Google Scholar 

  18. H.A. Whitworth, O. Aluko, N.A. Tomlinson, Application of the point stress criterion to the failure of composite pinned joints. Eng. Fract. Mech. 75(7), 1829–1839 (2008)

    Article  Google Scholar 

  19. S. Yamada, C. Sun, Analysis of laminate strength and its distribution. J. Compos. Mater. 12(3), 275–284 (1978)

    Article  Google Scholar 

  20. S. Zhou, C. Yang, K. Tian, D. Wang, Y. Sun, L. Guo, J. Zhang, Progressive failure modelling of double-lap of composite bolted joints based on Puck’s criterion. Eng. Fract. Mech. 206, 233–249 (2019)

    Article  Google Scholar 

  21. B.M. İçten, R. Karakuzu, Progressive failure analysis of pin-loaded carbon–epoxy woven composite plates. Compos. Sci. Technol. 62(9), 1259–1271 (2002)

    Article  Google Scholar 

  22. Z. Hashin, Failure criteria for unidirectional fiber composites. J. Appl. Mech. 47, 329 (1980)

    Article  Google Scholar 

  23. A.A. Abd-Elhady, H.E.-D.M. Sallam, Crack sensitivity of bolted metallic and polymeric joints. Eng. Fract. Mech. 147, 55–71 (2015)

    Article  Google Scholar 

  24. C. Echavarría, P. Haller, A. Salenikovich, Analytical study of a pin–loaded hole in elastic orthotropic plates. Compos. Struct. 79(1), 107–112 (2007)

    Article  Google Scholar 

  25. P. Rozylo, Experimental-numerical study into the stability and failure of compressed thin-walled composite profiles using progressive failure analysis and cohesive zone model. Compos. Struct. 257, 113303 (2021)

    Article  Google Scholar 

  26. Z. Ma, J. Chen, Q. Yang, Z. Li, X. Su, Progressive fracture analysis of the open-hole composite laminates: experiment and simulation. Compos. Struct. 262, 113628 (2021)

    Article  CAS  Google Scholar 

  27. L. Jemblie, V. Olden, O.M. Akselsen, A review of cohesive zone modelling as an approach for numerically assessing hydrogen embrittlement of steel structures. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 375(2098), 20160411 (2017)

    Article  Google Scholar 

  28. K. Davey, R. Darvizeh, O. Akhigbe-Midu, H. Sadeghi, Scaled cohesive zone models for fatigue crack propagation. Int. J. Solids Struct. 256, 111956 (2022)

    Article  Google Scholar 

  29. J. Nordmann, K. Naumenko, H. Altenbach, Cohesive zone models—theory, numerics and usage in high-temperature applications to describe cracking and delamination, in Advances in Mechanics of High-Temperature Materials. ed. by K. Naumenko, M. Krüger (Springer International Publishing, Cham, 2020), p.131–168

    Chapter  Google Scholar 

  30. W. Wciślik, T. Pała, Selected aspects of cohesive zone modeling in fracture mechanics. Metals. 11(2), 302 (2021)

    Article  Google Scholar 

  31. A. Aktaş, H. İmrek, Y. Cunedioğlu, Experimental and numerical failure analysis of pinned-joints in composite materials. Compos. Struct. 89(3), 459–466 (2009)

    Article  Google Scholar 

  32. F. Sen, M. Pakdil, O. Sayman, S. Benli, Experimental failure analysis of mechanically fastened joints with clearance in composite laminates under preload. Mater. Des. 29(6), 1159–1169 (2008)

    Article  CAS  Google Scholar 

  33. M. Pakdil, Failure analysis of composite single bolted-joints subjected to bolt pretension. Indian J. Eng. Mater. Sci. 14, 79–85 (2009)

  34. H. Hammoud, A. Naaman, Ferrocement bolted shear joints: failure modes and strength prediction. Cement Concr. Compos. 20(1), 13–29 (1998)

    Article  CAS  Google Scholar 

  35. P.P. Camanho, F. Matthews, Stress analysis and strength prediction of mechanically fastened joints in FRP: a review. Compos. A Appl. Sci. Manuf. 28(6), 529–547 (1997)

    Article  Google Scholar 

  36. D. ASTM, 5961/D 5961 M-05 Standard test method for bearing response of polymer matrix composite laminates (ASTM International, West Conshohocken, PA, 2005).

  37. Uj**, Prediction of bearing failure in pin-loaded laminates, PhD Thesis, School of Mechanical and Manufacturing Engineering, University UNSW, Sydney, Australia, 2007. https://doi.org/10.26190/unsworks/17235

  38. A.S.f. Testing, Materials, Standard Test Method for Bearing Strength of Plastics, ASTM International (2002)

  39. J.C. Newman Jr, An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries, Technical Report TN D-6376, NASA (1971)

  40. C. Soutis, N. Fleck, Static compression failure of carbon fibre T800/924C composite plate with a single hole. J. Compos. Mater. 24(5), 536–558 (1990)

    Article  Google Scholar 

  41. M.Y. Abdellah, Comparative study on prediction of fracture toughness of CFRP laminates from size effect law of open hole specimen using cohesive zone model. Eng. Fract. Mech. 191, 277–285 (2018)

    Article  Google Scholar 

  42. R. Narayanan, F.-Y. Chow, Strength of biaxially compressed perforated plates. Thin-Walled Struct. 2, 241 (1984)

    Article  Google Scholar 

  43. M.Y. Abdellah, An approximate analytical model for modification of size effect law for open-hole composite structure under biaxial load. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 235(18), 3570–3583 (2020). https://doi.org/10.1177/0954406220959378

    Article  Google Scholar 

  44. M.K.H. Mohammed, Y. Abdellah, A.F. Mohamed, K.A. Khalil, A novel and highly effective natural vibration modal analysis to predict nominal strength of open hole glass fiber reinforced polymer composites structure. Polymers. 13(8), 1251 (2021)

    Article  Google Scholar 

  45. Z.P. Bazant, J. Planas, Fracture and Size Effect in Concrete and Other Quasi-Brittle Materials. (CRC Press, Boca Raton, 1998)

    Google Scholar 

  46. J. Newman Jr, A nonlinear fracture mechanics approach to the growth of small cracks. Proceedings of the AGARD Conference 328(6), 1–26 (1983)

  47. M. Y. Abdellah, Essential work of fracture assessment for thin aluminium strips using finite element analysis. Eng. Fract. Mech. 179, 190–202 (2017). https://doi.org/10.1016/j.engfracmech.2017.04.042

    Article  Google Scholar 

  48. C. Soutis, P. Curtis, Failure analysis of composite laminates with an open hole under bi-axial compression-tension loading (ICAS CONGRESS, 2000), pp. 4161–4166. https://www.icas.org/ICAS_ARCHIVE/ICAS2000/PAPERS/RESERVED/ICA0416.PDF

  49. G. Pluvinage, J. Capelle, On characteristic lengths used in notch fracture mechanics. Int. J. Fract. 187(1), 187–197 (2014)

    Article  Google Scholar 

  50. T. Belytschko, T. Black, Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Meth. Eng. 45(5), 601–620 (1999)

    Article  Google Scholar 

  51. J.M. Melenk, I. Babuška, The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Eng. 139(1–4), 289–314 (1996)

    Article  Google Scholar 

  52. M.Y. Abdellah, M.S. Alsoufi, M.K. Hassan, H.A. Ghulman, A.F. Mohamed, Extended finite element numerical analysis of scale effect in notched glass fiber reinforced epoxy composite. Arch. Mech. Eng. 62(2), 217 (2015)

    Article  Google Scholar 

  53. D. Datta, Introduction to extended finite element (XFEM) method, ar**v preprint ar**v:1308.5208, (2013)

  54. J. Yvonnet, H.L. Quang, Q.-C. He, An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites. Comput. Mech. 42, 119–131 (2008)

    Article  Google Scholar 

  55. M. Zaid, S. Mishra, K.S. Rao, Finite element analysis of static loading on urban tunnels. in Geotechnical Characterization and Modelling. Lecture Notes in Civil Engineering. ed. by M. P. Latha Gali, R.R., vol. 85 (Springer, Singapore). https://doi.org/10.1007/978-981-15-6086-6_64

  56. L. Wen, R. Tian, Improved XFEM: accurate and robust dynamic crack growth simulation. Comput. Methods Appl. Mech. Eng. 308, 256–285 (2016)

    Article  Google Scholar 

  57. Y. Wang, Extended Finite Element Methods for Brittle and Cohesive Fracture. (Columbia University, Columbia, 2017)

    Google Scholar 

  58. Z. Yang, Y. Lei, G. Li, Experimental and finite element analysis of shear behavior of prestressed high-strength concrete piles. Int. J. Civ. Eng. 21(2), 219–233 (2023)

    Article  Google Scholar 

  59. H. Ning, H. Zheng, X. Ma, X. Yuan, Finite analysis of carbon fiber–reinforced polymer delamination damage during multi-pass milling. Int. J. Adv. Manuf. Technol. 119(7), 4573–4585 (2022)

    Article  Google Scholar 

  60. N. Nguyen, T. Nguyen, D. Du, D. Nguyen, Finite-element analysis of RC beams strengthened with CFRP U-wraps. Mech. Compos. Mater. 58(4), 567–584 (2022)

    Article  Google Scholar 

  61. S. Huzni, M. Ilfan, T. Sulaiman, S. Fonna, M. Ridha, A. Arifin, Finite element modeling of delamination process on composite laminate using cohesive elements. Int. J. Autom. Mech. Eng. 7, 1023–1030 (2013)

    Article  Google Scholar 

  62. R. Pippan, A. Hohenwarter, Fatigue crack closure: a review of the physical phenomena. Fatigue Fract. Eng. Mater. Struct. 40(4), 471–495 (2017)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. P. Zhang, J. Li, Y. Zhao, J. Li, Crack propagation analysis and fatigue life assessment of high-strength bolts based on fracture mechanics. Sci. Rep. 13(1), 14567 (2023)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. F.F. Luiz, T.H. Ricardo, L.C. Topper, H. Ricardo, A.J. Carlos Miranda, Crack propagation in the threshold stress intensity region a short review, in Mechanical Fatigue of Metals: Experimental and Simulation Perspectives. ed. by J.A.F.O. Correia, A.M.P. De Jesus, A.A. Fernandes, Ri. Calçada (Springer International Publishing, Cham, 2019), p.175–180. https://doi.org/10.1007/978-3-030-13980-3_23

    Chapter  Google Scholar 

  65. K. Puchała, E. Szymczyk, J. Jachimowicz, P. Bogusz, M. Sałaciński, The influence of selected local phenomena in CFRP laminate on global characteristics of bolted joints. Materials. 12(24), 4139 (2019)

    Article  PubMed  PubMed Central  Google Scholar 

  66. J. Zhang, Q. **e, Y. **e, L. Zhou, Z. Wang, Investigation of mechanical performances of composite bolted joints with local reinforcements. Sci. Eng. Compos. Mater. 25(1), 75–83 (2018)

    Article  Google Scholar 

  67. M.Y. Abdellah, Delamination modeling of double cantilever beam of unidirectional composite laminates. J. Fail. Anal. Prev. 17, 1011–1018 (2017)

    Article  Google Scholar 

  68. Z.P. Bazant, Fracture and Size Effect in Concrete and Other Quasibrittle Materials. (Routledge, London, 2019)

    Book  Google Scholar 

  69. J. Ekh, J. Schön, Effect of secondary bending on strength prediction of composite, single shear lap joints. Compos. Sci. Technol. 65(6), 953–965 (2005)

    Article  Google Scholar 

  70. P. Maimí, E.V. González, N. Gascons, L. Ripoll, Size effect law and critical distance theories to predict the nominal strength of quasibrittle structures. Appl. Mech. Rev. 65(2), 020803 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, South Valley University, Qena, 83523, Egypt

    Mohammed Y. Abdellah, Nouby M. Ghazaly & A. A. Gomma

  2. Mechanical Engineering Department, College of Engineering and Architecture, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

    Mohammed Y. Abdellah, Dhia K. Suker, Hamzah Alharthi & Ahmed H. Backar

  3. Technical College, Imam Ja’afar Al-Sadiq University, Baghdad, Iraq

    Nouby M. Ghazaly

  4. Production Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, 21544, Egypt

    Ahmed H. Backar

Authors
  1. Mohammed Y. Abdellah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dhia K. Suker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hamzah Alharthi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nouby M. Ghazaly
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. A. Gomma
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ahmed H. Backar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Y. Abdellah.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdellah, M.Y., Suker, D.K., Alharthi, H. et al. Stress Analysis Map** for Mechanically Fastened Composite Bolted Lap Joints Using Cohesive Zone Model. J Fail. Anal. and Preven. (2024). https://doi.org/10.1007/s11668-024-01952-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11668-024-01952-4

Keywords

Search

Navigation