The origin of similarity fields in steady elastoplastic crack propagation under K–T loading

Abstract

It has been inferred from computer simulations that the plastic-zone fields of a crack that propagates steadily under K–T loading are similarity fields. Here, we show theoretically that these similarity fields are but a manifestation of the existence of an invariant path integral. We also show that the attendant similarity variable involves an intrinsic length scale set by the specific fracture energy that flows into the crack tip. Finally, we show that where the crack is stationary there can be no similarity fields, even though there exists a (different) invariant path integral. Our results afford some new insights into the relation between similarity fields and invariant path integrals in mathematical physics.