ASYMPTOTIC FINITE DEFORMATION ANALYSIS OF GROWING CRACK FIELDS IN ELASTIC PERFECTLY PLASTIC MATERIALS

AsYMPTOTIC, finite deformation solutions for the stress and velocity fields near the tip of a quasi-statically propagating Mode I plane strain crack in an incompressible, elastic-perfectly plastic material are derived. An objective form of the Prandtl-Reuss constitutive relation is employed. The solutions obtained are represented by a singular perturbation series with the singularity described by integer powers of the quantity (mu In r) where mu, the perturbation parameter. is of the order (yield stress/elastic modulus) and r is the non-dimensional distance from the crack tip. Previously developed small-displacement-gradient solutions are shown to result to leading order. However, the extension of these solutions to higher order is not straightforward; the introduction of strained coordinates and asymptotic modifications of the interfaces joining different near-tip angular sectors are required. The resulting solutions contain an asymptotically indeterminate parameter that is equivalent to the free parameter m in DRUGAN and CHEN'S (1989, J. Mech. Phys. Solids 37, 1) small-displacement-gradient solution family. Indeed, a principal conclusion is that the present solution approaches that of Drugan and Chen outside an extremely small radius (of the order of the microstructural scale of the material), differing significantly only for radii below which the quantity (mu In r) becomes significant compared to unity. Thus, at least for the constitutive class analysed, the finite deformation solutions confirm and quantify the remarkable accuracy and range of validity of the previous small-displacement-gradient growing crack solutions.