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Concept of Equivalent Crack Length

Measurement of the crack length:

  • extremely difficult and time consuming
  • requires a travelling microscope or a high-resolution camera (with DIC)
  • can introduce a significant uncertainty in the determination of the fracture resistance

The concept of equivalent crack length: 

  • only the applied load, F, and the crack mouth opening displacement, v, are measured
  • the equivalent crack length a_eq, is used instead of the actual one to make simple beam-theory formulae based on LEFM valid for measured values of F and v

Applications:

  • because Gc is computed as the derivative of the total potential energy with respect to the actual crack length, when equivalent crack length is used Gc= dPi/da_eq da_eq/da
  • the derivative da_eq/da is very close to 1, even for cases of ductile adhesives
  • fracture resistance can be accurately computed assuming that Gc=dPi/da_eq (which does not require measurement of the crack length)

More details available here.

Suggested literature:

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