Dilational plastic stress-strain relations and flow localisation

Holes may be produced in materials by many processes such as neutron irradiation, diffusional creep cavitation, or by the hole nucleation process which occurs in ductile failure. The presence of holes alters the overall stress-strain relationship of the material. The present work is concerned with effect of voids on the plastic stress-strain relations of a porous material, for example the neck of tensile specimen of Swedish Iron. The relevance of stress-strain relations to process such as ductile failure is discussed. In uni-axial tension the necking instability occurs when the axial load reaches a maximum. Similarly, in the plane strain expansion of a cylindrical hole, instability occurs when the radial loads reaches a maximum