Part VII – July 1969 – Communications - A Method for Producing Small Grain Size in Super-purity Aluminum

eralized strain equation appear quite different they are really identical. This identity can be shown in a simple mathematical rearrangement. Referring to Eq. [I], the substitution of ln(1 +?E) for ? (where ?E is the engineering strain) yields: a =s8- (s8?so)e?1/?c) ln(1 +s8??E) [4] or s =s8?(s8?so)(l +?E)-1 [5] Replacing (1 + cE) with its equivalent, (l/lo): s=s8?(s8?so)l/€c [6] Adding and subtracting the quantity (s8 - so) yields: s=s8?(s8?so)+ (s8-so) l-(^)l/£c [7] = s0+(s8?so)ri-(^0)1/^l [8] Letting n = 1/?c it follows that: This equation will be seen to be identical to the generalized strain expression in Eq. [3], the coefficients a and b being equal to so and (s8?so)/?c or n(s8?so), respectively. Confirmation of the relationship noted above was provided by fitting experimental stress-strain data5 for 304 stainless steel (total strain from 0.072 to 1.15) at room temperature at a true total strain rate of 4 x 10-3 sec-1 to Eqs. [I] and [3]. In this study nonlinear regression analyses were used to evaluate the equation constants. The results of this evaluation are presented in Table I. When these constants are used in Eqs. [I] and [3] the curves obtained are coincident. It will also be noted that the value of n is equal to YE,, the value of a is equal to so, and the value of b is equal to (s8 - so)/Ec. These equalities are illustrated in Table I where the Voce constants in parentheses were calculated from a, b, and n values. Excellent agreement is seen to exist. It is concluded, therefore, that the Voce equation is, indeed, identical to the linear expression involving generalized strain. In applying the generalized strain concept to stress-strain data, it has been noted3 that data within what was termed the transition region (first few points in the plastic flow region) must be excluded from the analysis in order to obtain the linearity in Eq. [3]. A similar exclusion applies in the use of the Voce equation since an expression which would describe the strain-hardening region would usually be found to be not too effective in the elastic-plastic fillet2 which connects the elastic line to the strain-hardening region. These considerations further substantiate that Eqs. [I] and [3] do indeed describe identical behavior. Note added in proof. Since this manuscript was submitted for publication, correspondence with Professor S. R. Davies, University of Edinburgh, (of Ref. 3) indicated that his associates have also confirmed the identity between the Voce equation and the generalized strain concept. It is sometimes desirable to obtain a small grain size in super-purity metals. Unfortunately, the absence of impurities, the low recrystallization temperatures, and the low activation energies for boundary motion result in rapid growth of relatively few grains when conventional recrystallization practices are used. For example, Arajs et al.1 were unable to obtain a mean grain diameter less than about 0.4 mm in iron containing 38 at. ppm of impurity. The <1 at. ppm purity range in many modern superpurity metals results in yet larger limiting grain sizes. It is the purpose of this communication to describe a technique by which mean grain diameters as small as 30 µ have been produced in aluminum having an impurity content < 0.5 at. ppm. The technique should be applicable to superpurity metals other than aluminum and has potential applications to grain refinement of commercial alloys. The necessary and sufficient requirements for production of a small grain size are as follows: a) a large number of potential nucleating sites must be created randomly within the cold worked material, b) sufficient thermal energy must be provided at a rate that will simultaneously activate a large fraction of the potential nuclei, and c) the grain growth must be stopped shortly after grain impingement.&apos; A high density of potential grain nuclei may be cre-