Temperature and strain rate dependence of the portevin-le chatelier effect in a rapidly solidified Al alloy
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I.
INTRODUCTION
THE serrated flow phenomenon, characteristic of the plastic deformation in a large number of commercial alloys, has received extensive attention since the pioneering work t~l of Portevin and Le Chatelier after whom the phenomenon has been named (the Portevin-Le Chatelier effect or PL effect). The micromechanism is generally recognized to be associated with the dynamic strain aging (DSA) process, and a critical strain is required for its occurrence,t2] Besides this strain dependence, the occurrence of the PL effect depends strongly on temperature[3-14] and strain rate.ta ~6] For the temperature dependence, a "critical temperature" Tc is given,V7] at which the equilibrium point defect concentration is large enough to allow the serrated flow to occur at a zero plastic strainY 8~ The starting situation of the alloy for T > T~ is a population of aged mobile dislocations, while that for T < Tc is a population of free mobile ones. [171 With regard to the dependence of strain rate, it is demonstrated by both theoretical analysis[~Sl and experimental resultst3 5,7,14,161that a negative strain rate sensitivity of flow stress is a necessity for the PL effect to occur. Similarly, a "critical strain rate" k. was presented previously, which allows a dislocation to break away from its solute atmosphere and which increases with the diffusion coefficient and the dislocation density.[~9] While various theoretical models have been put forward to elucidate the thermodynamic aspects, those dealing with temperature (T) and strain rate (k) dependence of the critical strain (ec) have received better recognition. In the low-temperature/high strain rate" regime, an early treatment by Cot*"Low" or "high" has only relative implications when referring to temperature and/or strain rate in the present context.
trell t~gi correlates this dependence according to e m -=- A.k.exp (E,,/RT)
[1]
D.M. LI, formerly with the Department of Materials Science, Delft University of Technology, is with the College of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China. A. BAKKER, Professor, is with the Department of Materials Science, Delft University of Technology, 2628 AL Delft, The Netherlands. Manuscript submitted October 31, 1994. METALLURGICALAND MATERIALSTRANSACTIONS A
where Em is the migration energy of vacancies (for substitutional alloys) or of interstitial solutes, A and m are constants,** and R is the gas constant. Following van den **The sign of the constants is positive except otherwise noted.
Beukel's treatment,t2] this correlation becomes e7 +p = K.~.exp (E,,/RT)
[2]*
tHere, R replaces the Boltzmann constant k in the cited formulat2j to unify the units of energy parameters appearing in this article. The same notes apply to Eq. [3].
with K and fl as constants. For interstitial alloys, m = 0. Equation [2] improves on Eq. [1] in that it accounts for the effect of dislocation density Pm as a result of increased strain (by the relation Pm ----B " e~, where B is a const
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