Abstract
The Considère construction is applied to the compressive deformation of rate insensitive materials exhibiting flow softening, enabling the onset and termination of plastic instability to be determined. For rate sensitive materials, the tensile analysis of Hart is adapted to compressive loading, and indicates that the onset and termination of flow localization occurs earlier and later, respectively, than in rate sensitive materials. A new instability criterion based on the localization of strain, is introduced; this type of flow localization is shown to begin at the Considère strain, and to develop at a rate inversely proportional to the rate sensitivity. The effects of mechanical and geometric defects are distinguished and the Hart analysis is demonstrated to apply to specimens which have undergone mechanical damage. The influence of geometric defects is analyzed by the method of Campbell, and these are shown to begin to grow, unlike mechanical defects, as soon as flow is initiated. The unstable growth of geometric defects, however, does not take place until a further criterion is satisfied and even then, rapid growth only occurs if the rate sensitivity is less than about 0.2.
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