Abstract
Mathematical analysis of a simple, one-dimensional, canonical problem has yielded a number of scaling laws that relate various characteristic features of an adiabatic shear band to the physical properties of the material and the ambient conditions. Specific formulas have been obtained from solutions to linear and non-linear problems coupled with asymptotic representations of the results. Examples are shear band width, most sensitive strain rate and shear band spacing. Other results show the equivalence of initial fluctuations in strength or temperature, and still others show how to scale the defect in formulas for estimating the timing of localization. The paper summarizes previous results and presents some new formulas that show how strain rate sensitivity affects band spacing, number density and morphology as a function of strain rate.
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