General expressions for energy-release rates for delamination in composite laminates

Z. Zou, S. R. Reid, S. Li, P. D. Soden

Research output: Contribution to journalArticlepeer-review


When two-dimensional or three-dimensional elasticity theory is applied to interfacial cracks, individual components of the energy-release rate are not well defined in their classical crack closure integral form due to oscillatory stress and displacement fields around crack tips. These are associated with physically inadmissible interpenetration of crack surfaces. When dealing with composite laminates, it is generally preferable to use a laminate theory. However, when applied to delaminations most laminate models can only produce a total energy-release rate but not the individual components of it. In this paper, expressions for individual energy-release rates have been derived for delaminations based on a sublaminate model. By considering delamination growth as a variational problem with variable endpoints, the total energy-release rate can be expressed simply in terms of stress resultant jumps and the derivatives of relative displacements between the delamination surfaces at its tip. The mode I, mode II and mode III components of the energy-release rate are then determined according to their definitions. The use of laminate theory eliminates oscillatory behaviour along with the stress singularity encountered in two-dimensional or three-dimensional linear elastic fracture mechanics theory for this problem. Instead, the effect of the singular stress field is reflected in the stress resultant jumps across the delamination tip. The individual energy-release rates derived in this way are all well defined. The present approach shows significant advantages over the popular finite-element-based virtual crack closure technique used for delamination problems.
Original languageEnglish
Pages (from-to)645-667
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2019
Publication statusPublished - 8 Mar 2002


  • Delamination
  • Energy-release rates
  • Laminated composites
  • Mixed mode problems
  • Sublaminate theory


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