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I.

s 5 sm 1 s *

INTRODUCTION

INTERSTITIAL atoms in solid solution are able to produce two very significant effects on the mechanical properties of metallic materials; at lower temperatures, where the interstitial atom diffusion rates are insignificant, they produce solid solution hardening, and at higher temperatures, where diffusion rates become appreciable, they cause dynamic strain aging (DSA). Both phenomena involve pinning of dislocations by interstitial atoms. In solid solution hardening, the pinning occurs by in situ interstitials that are effectively stationary. This is illustrated in Figure 1, which is based on a figure in Hirth and Lothe’s Theory of Dislocations.[1] These authors point out that at low temperatures, because the interaction force between a dislocation and a solute atom has a very short range, ‘‘a dislocation becomes wiggly, adjusting its configuration to conform to the internal stresses of the immobile solute atoms.’’ In Figure 1(a), the dislocation is assumed to be unstressed, while in Fig. 1(b), the dislocation is under stress. At DSA temperatures, the interstitials are mobile and thus able to increase the level of pinning by either forming solute atom atmospheres at the dislocations (Cottrell–Bilby aging[2]) or by jumping into lower energy interstitial sites lying within the stress fields of the dislocations (Snoek aging[3]).

where sm is the internal stress and s * the effective stress. (2) The thermally activated strain rate equation:

~

!

H εz 5 εz 0 exp 2 RT z z where ε is the strain rate, ε 0 a constant, H the activation enthalpy, R the gas constant, and T the Kelvin temperature. (3) The activation volume v:

~]]Hs *!

y52

T

(4) The Conrad–Wiedersich equation:[4] H 5 2Ty

~]]Ts *!

εz

where (]s */]T)εz is the slope of a s * vs T plot obtained at a constant strain rate. (5) The dimensionless strain rate sensitivity n: n5

d ln (s *) d ln (εz )

(6) The alternative strain rate sensitivity S: II.

OUTLINE OF THE ANALYSIS

The effects of these pinning phenomena on the mechanical properties are capable of being rationalized over an extensive temperature range, but it is first necessary to find an alloy whose interstitial solute concentrations and metallurgical structure are basically temperature independent within this range and whose internal stress can also be properly evaluated in this interval. The analysis for doing this uses the following universally accepted metallurgical relations. (1) The flow stress s: R.E. REED-HILL, Professor Emeritus, C.V. ISWARAN, Postdoctoral Associate, and M.J. KAUFMAN, Professor, are with the Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611. Manuscript submitted December 7, 1995. 3524—VOLUME 27A, NOVEMBER 1996

S5

III.

ds * d ln (εz )

THE YOKOBORI ACTIVATION ENTHALPY

The present procedure differs from the traditional technique of analyzing stress strain data because of its use of the Yokobori[5] activation enthalpy: H 5 H 0 ln

~ss**! 0

where H0 is a material constant, s *0 the effective stress at