Theory of plastic and viscous deformation
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I. INTRODUCTION AND EQUATIONS OF THE THEORY
RECENTstudies of the strain rate response of some materials to variations of stress and stress rate (in a soft tensile machine) have significantly extended our knowledge of inelastic deformation behavior. 1,2 Partly as a consequence of these studies, it is becoming increasingly evident that behavioral differences between soft metals and hard alloys may be observed in a variety of experiments, and that these differences may represent evidence for two limiting types of inelastic behavior, 3 termed plastic and viscous. 1 Some examples of these experimental differences, aside from hardness itself, include the length of the loading transient, 1,2 rate sensitivity of flow stress, 4 strain response to a high rate stress pulse ,3,5,6extent of low temperature creep, and degree of strain rate continuity. It is known that low temperature inelastic deformation of metals is a consequence of the glide of dislocations7 and that, except for some uncertainty about the soft metals, 4's the deformation rate is given by the Orowan equation: k = pmbv.
[1]
There is a need for additional information before this equation can be used to describe the result of a mechanical test or to predict the operating parameters of a deformation processing operation. Specifically, it is required that the mobile dislocation density, Pro, and the dislocation velocity, v, be known quantitatively in terms of appropriate external deformation variables and the physical constants and internal microstructural variables of the material. 4'7 Recently, significant features of the deformation of 304 stainless steel have been predicted by a new model 2 in which (1) the THOMAS H. ALDEN is Professor of Metallurgical Engineering, University of British Columbia, Vancouver, BC, Canada V6T IW5. Manuscript submitted March 21, 1986. METALLURGICALTRANSACTIONS A
mobile density is determined by a competition between injection and velocity-dependent trapping, and (2) the velocity is determined by an effective stress and by the frictional resistance to dislocation motion conferred by the short-range obstacles or lattice interactions. The most significant new concept in the theory ~'2 is that the injection rate of mobile dislocations is determined by the rate of increase of external stress. It is assumed that the total dislocation content Pt in single phase alloys is determined by the external stress according to cr = or* + ctGbp~ 12.
[2]
tr* is an elastic limit stress. Equation [2] is based on experimental observation of dislocation content as a function of stress in deformed metals. 9-12 If this function is taken to be time independent, as written, then if the stress is increased, the content of dislocations will also increase, and this rate of increase will be determined by the stress rate. It is not usually possible to distinguish, experimentally, between mobile and immobile (network) dislocations. Therefore a second assumption is required, namely that all newly injected dislocations are mobile. Consequently, 1.2 the rate of i
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