The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

Khaled Shahin, Farid Taheri

Research output: Contribution to journalArticlepeer-review


An analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin's crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory's expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.

Original languageEnglish (US)
Pages (from-to)6284-6300
Number of pages17
JournalInternational Journal of Solids and Structures
Issue number25-26
StatePublished - Dec 15 2008


  • Adhesive joints
  • Mixed-mode fracture
  • Strain energy release rate
  • Unbalanced joints

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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