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5 Variations of angular stress and strain functions for a Mode I crack under plane strain. e. σ   E =   y when σ < σy σ σy n when σ > σy 41 Here α = 1, and y and σy are used instead of and σ0 and have the interpretation of 0 yield strain and yield stress respectively. Close to the crack tip the plastic power law term will dominate so the HRR field applies. Thus J fulfills the role of K for a non-linear power law material, J characterises the intensity of the near tip field. The condition for fracture is simply J = JIC .

The collapse moment for the cracked plate is the same as that for a plate of width W − a. The additional subscript ‘C’ here emphasises that it is the solution for a cracked plate. Often the ‘C’ is left out. For a center cracked plate with crack length 2a and plate width 2W , in tension with a << W , subjected to a load 2P , the limit load under plane stress conditions, is given by PLC = σy (W − a)B. Limit load solutions are commonly used in fracture mechanics. The ratio between load and limit load is a measure of the extent of plasticity and provides a good means of compar2W ing two geometries.

1 Size requirements for small scale yielding The requirement for small scale yielding is that the plastic zone size at fracture should be much less than the crack length. 1 a. 2 KIC . 5(KIC /σy )2 . This implies that the specimen dimensions are about 25 times larger than the plastic zone size. The requirement that the plate thickness, B, is much greater than the plastic zone also ensures that plane strain rather than plane stress conditions prevail. Under these conditions, specimens with the same K value will have the same crack tip fields and fracture will occur when the K value reaches the plane strain fracture toughness value, KIC .