General J integral solution for specimens loaded by moments, axial forces and residual stresses – A unifying stiffness formulation

Helmuth Langmaack Toftegaard*, Bent F. Sørensen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

Abstract

An exact, general solution for the J integral is derived and applied to a cracked double cantilever beam specimen loaded with axial forces in combination with bending moments (including residual stresses). Apart from the loads and the specimen width, the solution depends only on the extensional stiffness and the bending stiffness of the specimen beams. The elastic properties and expansion coefficients may vary continuously in the height direction (functionally graded material) or be piecewise constant within a layered structure. The stiffness formulation unifies analytical fracture mechanics solutions in terms of stiffness referring to the elastic centre, of stiffness per width referring to the mid-height (laminate beam theory), and of deformations (strain and curvature approach). The derived J integral solution is particularly useful for the determination of mixed mode cohesive laws for large-scale crack bridging problems.
Original languageEnglish
Article number106500
JournalEngineering Fracture Mechanics
Volume217
Number of pages22
ISSN0013-7944
DOIs
Publication statusPublished - 2019

Keywords

  • J-integral
  • Delamination
  • Mixed mode fracture
  • Cohesive zone modelling
  • Residual stress
  • Laminate

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