Abstract
(1) The flow data of f (stress) and ${\dot{s}$ (strain rate) for Fe and Ti alloys were plotted in the form of f vs. -ln ${\dot{s}$ by using the literature values. (2) The plot showed two distinct patterns A and B; Pattern A is a straight line with a negative slope, and Pattern B is a curve of concave upward. (3) According to Kim and Ree's generalized theory of plastic deformation, pattern A & B belong to Case 1 and 2, respectively; in Case 1, only one kind of flow units acts in the deformation, and in Case 2, two kinds flow units act, and stress is expressed by $f={X_1f_1}+{X_2f_2}$where $f_1\;and\;f_2$ are the stresses acting on the flow units of kind 1 and 2, respectively, and $X_1,\;X_2$ are the fractions of the surface area occupied by the two kinds of flow units; $f_j=(1/{\alpha}_j) sinh^{-1}\;{\beta}_j{{\dot{s}}\;(j=1\;or\;2)$, where $1/{\alpha}_j\;and\;{\beta}_j$ are proportional to the shear modulus and relaxation time, respectively. (4) We found that grain-boundary flow units only act in the deformation of Fe and Ti alloys whereas dislocation flow units do not show any appreciable contribution. (5) The deformations of Fe and Ti alloys belong generally to pattern A (Case 1) and B (Case 2), respectively. (6) By applying the equations, f=$(1/{\alpha}_{g1}) sinh^-1({\beta}_{g1}{\dot{s}}$) and $f=(X_{g1}/{\alpha}_{g1})sinh^{-1}({\beta}_{g1}{\dot{s}})+ (X_{g2}/{\alpha}_{g2})\;shih^{-1}({\beta}_{g2}{\dot{s}})$ to the flow data of Fe and Ti alloys, the parametric values of $x_{gj}/{\alpha}_{gj}\;and\;{\beta}_{gs}(j=1\;or\;2)$ were determined, here the subscript g signifies a grain-boundary flow unit. (7) From the values of ($({\beta}_gj)^{-1}$) at different temperatures, the activation enthalpy ${\Delta}H_{gj}^{\neq}$ of deformation due to flow unit gj was determined, ($({\beta}_gj)^{-1}$) being proportional to , the jumping frequency (the rate constant) of flow unit gj. The ${\Delta}H_{gj}\;^{\neq}$ agreed very well with ${\Delta}H_{gj}\;^{\neq}$ (self-diff) of the element j whose diffusion in the sample is a critical step for the deformation as proposed by Kim-Ree's theory (Refer to Tables 3 and 4). (8) The fact, ${\Delta}H_{gj}\;^{\neq}={\Delta}H_{j}\;^{\neq}$ (self-diff), justifies the Kim-Ree theory and their method for determining activation enthalpies for deformation. (9) A linear relation between ${\beta}^{-1}$ and carbon content [C] in hot-rolled steel was observed, i.e., In ${\beta}^{-1}$ = -50.2 [C] - 40.3. This equation explains very well the experimental facts observed with regard to the deformation of hot-rolled steel..