An upper-bound on J for a cracked infinite plate made of wholly non-linear material

An approximate solution is provided for an internally cracked plate, loaded biaxially at infinity, where the material exhibits a wholly non-linear constitutive relation. The solution may be applied to plasticity problems where the applied stress is substantially above the limit of proportionality, or to stationary creep problems through the elastic analogy. The analysis leads to an upper bound on the value of J or J, the path-independent line integral which is well-known in the field of fracture mechanics. Results are provided for a material following a simple n -power stress-strain or stress-strain-rate law and these are compared with another theoretical solution and experimental results taken from the literature.