METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 29A, MAY 1998—1415 Kinetics of Strain Aging in Drawn Pearlitic Steels V.T.L. BUONO, M.S. ANDRADE, and B.M. GONZALEZ The kinetics of strain aging in a drawn pearlitic steel wire were analyzed based on measurements from three different experimental techniques: tensile testing, electrical resistivity, and internal friction. The progress of aging after a total reduction in area of 86 pct by drawing and heating between 60 °C and 200 °C was evaluated in terms of the changes in yield strength, electrical resistivity, and temperature-dependent background damping. The kinetic law and the apparent activation energies of the processes occurring in this temperature range were determined by the isothermal variation of the transformed fraction, obtained from the changes in properties with aging time. Under the conditions considered, static strain aging of drawn pearlitic steels seems to occur in two distinct stages, each associated with different atomic mechanisms. The first stage takes place between 60 °C and 100 °C and is characterized by a small increase in yield strength and a decrease in electrical resistivity and background damping. The second stage of aging occurs at higher temperatures or longer aging times and is marked by a sharp increase in yield strength and an increase in electrical resistivity, while the background damping reaches very small values. The probable mechanisms related to this behavior are discussed in terms of the empirical law and the apparent activation energy found. I. INTRODUCTION DURING the drawing of a steel wire rod, the combined effects of deformation and heat generated by metal die fric- tion can lead to strain aging of the wire, which is known to greatly influence drawability as well as the mechanical properties of the finished product. [1–4] In low-carbon steels, it seems well established that strain aging is associated with the segregation of C and N atoms to the dislocations, and its occurrence can be controlled by a number of different procedures such as microalloying [1,2] or the use of slow post–hot rolling cooling rates. [3] On the other hand, strain aging of high-carbon steels, which is an important subject concerning the development of high-strength steel wire components such as ropes and cables, is not yet fully un- derstood. Research work on this matter lacks uniformity in terms of steel composition, amount and type of prestrain, and initial microstructure. Nevertheless, it is reported that, in addition to the classical aging phenomena occurring in low-carbon steels related to dislocation pinning by C and N atoms interstitially dissolved in ferrite, high-carbon steels exhibit a second stage of aging, governing their behavior at higher aging temperatures, which is characterized by pro- nounced variations in mechanical properties. These changes have been associated with dislocation pinning by C atoms originating from the decomposition of cementite. [4–8] From the point of view of the kinetics of strain aging associated with the presence of interstitial solutes, as in the case of low-carbon steels, the model proposed by Cottrell and Bilby [9] is generally accepted as conceptually correct. [10] According to this model, the aging process starts with the formation of atmospheres of interstitial atoms around dis- V.T.L. BUONO and B.M. GONZALEZ, Associate Professors, are with the Department of Metallurgical and Materials Engineering, Universidade Federal de Minas Gerais-UFMG 30160-030 Belo Horizonte-MG, Brazil. M.S. ANDRADE, Research Associate, is with the Metallurgical Technology Division, Fundac ¸a ˜o Centro Tecnolo ´gico de Minas Gerais - CETEC, 31170-000 Belo Horizonte, MG, Brazil. Manuscript submitted March 17, 1997. locations. The migration of these atoms toward the dislo- cations takes place under the action of their elastic potential fields. During the initial stages of atmosphere formation, the number of atoms arriving at the dislocations per unit of time (t), by unitary length of dislocation, is proportional to t 2/3 . The model of Cottrell and Bilby does not take into account the effects of back-diffusion flow and saturation of the elastic potential, which should occur when a solute at- mosphere approaches saturation, and, thus, is expected to describe strain aging only for the initial stages of atmo- sphere formation. The equation proposed by Cottrell and Bilby was mod- ified by Harper, [11] in an attempt to extend its applicability, by making the assumption that the rate of solute migration is proportional to the fraction of atoms still in solution. This assumption takes care of the effect of solute depletion dur- ing the process and leads to Harper’s equation, 1/3 2/3  ADt W = 1 - exp - 3 L [1]     2 kT relating W, the amount of solute segregated to the dislo- cations at a time t, with the density of dislocations (L), the diffusion coefficient of the interstitial in the matrix (D), the aging time, and the aging temperature (T ), in degrees Kel- vin. The term k is the Boltzmann constant, and A is a con- stant defining the intensity of solute-dislocation interaction. Harper did not consider back diffusion and saturation of the elastic potential, and, thus, Eq. [1] should also describe only the initial stages of strain aging. The limitations and simplifications of the models previ- ously described have been pointed out by many au- thors [12,13,14] and discussed in detail in a review work by Baird, [15] in which it is emphasized that the deviations ob- served with respect to the models of Cottrell and Bilby and of Harper seem to be associated with the formation of pre- cipitates on the dislocations or in the matrix, especially in quenched Fe-C and Fe-N alloys. However, in slowly cooled and in some quenched alloys, even when precipitation takes place, if it occurs following atmosphere formation, Harper’s