Load relaxation in aluminum: I. Theory of plastic deformation. II. Plastic equation of state
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According to the theory of thermally-activated deformation, the plastic strain rate equality ( 4 p ) t = - d t = (4~)t =dt will hold in a load relaxation experiment, where t = 0 is defined as the time at WhiCh the crosshead stops. In this theory, plastic flow is intrinsically time dependent and its rate is controlled by interaction of glide dislocations with thermal obstacles (e.g. forest dislocations). The strain rate equation is of the form ~p = 4p(e,S,T) and at t = 0 none of these variables changes instantaneously. Measurements reported here for [111] aluminum single crystals indicate that this prediction is wrong. The ratio (Ep)t =dt/(4p)t =-dt is near zero at low s t r e s s and approaches unity only at high s t r e s s . This result is predicted if plastic strain itself is time-independent (athermal), as in the author's recent theory. Time-dependent strain is then the result of thermal changes in structure, namely loss (recovery) and r e a r r a n g e m e n t of obstacle dislocations. Experiments were also done to test further the essential hypothesis of H a r t ' s recent formulation of an equation of state for plastic d e f o r m a t i o n - n a m e l y that each distinct or-4 curve derived from load relaxation data corresponds to a unique " h a r d n e s s " state and that r e covery does not occur. Significant differences were observed in the 77 K s t r s s s - s t r a i n curves for 295 K relaxed and unrelaxed samples which indicate that substantial loss and some r e a r r a n g e m e n t of dislocations has occurred during the relaxation. It is concluded f r o m both experiments that load relaxation in aluminum is a manifestation of r e c o v e r y creep and cannot be taken as evidence for a plastic equation of state. I. THEORY OF PLASTIC DEFORMATION A. Introduction T H E R E are two distinct formal theories of t e m p e r a ture-dependent plastic deformation. These are the theories of thermally-activated deformation, x-4 ( " r e action-rate theory") and time-independent d e f o r m a tion ~'6 ( " r e c o v e r y - r e a r r a n g e m e n t theory"). In P a r t I of this paper, it is argued that simple measurements taken from load relaxation experiments can distinguish which theory is appropriate for given conditions of temperature, s t r e s s , alloy type and so forth. The measurements are done for pure aluminum recently studied by other scientists 7 and chosen as an example of a strain-hardened fcc metal. For this case, it will be shown that the results clearly favor the theory of time-independent deformation. Considering the case of strain hardened metals alone, both theories in their general formsX,2, 4,5 contain the assumption of a thermally unstable microstructure, i.e. one that is altered and influenced not only by strain but also by time and temperature*. *In certain models, thermal instability of structure may be a feature only at high stress, e.g. Stage III of the low temperature strain hardening curve.
However in the thermally-activated deformation (TAD) theory, plastic .flow itself is also
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