Microdynamics of Plastic Flow at Constant Stress

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Abstract
Arguments are presented which conclude that the mean density of mobile dislocations in a crystalline solid increases linearly with plastic strain for small strains and decays exponentially for large strains, all at constant stress and low temperatures. The resulting analytic expression combined with the strain-rate equation can be integrated explicitly in terms of tabulated exponential integral functions. This creep equation has a general form that is consistent with many experiments and detailed comparison with a particularly well-documented experimental curve yields quantitative agreement. The large strain limit of the proposed creep equation is the familiar logarithmic creep law. A simple transformation of the creep equation yields the shape of a slowly propagating plastic front, and it is shown that the predicted shape corresponds to experimental observations for mild steel. The lengths of the incubation periods that precede fast flow, as predicted by the equation, have a stress dependence that agrees with experiment. Finally, the present arguments together with previous ones yield a strain-rate equation which generates both stress-strain and strain-time curves that are good reproductions of experimental observations.