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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