Formation of the cottrell atmosphere during strain aging of bake-hardenable steels
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I. INTRODUCTION
BAKE hardening is essentially a strain-aging process caused by carbon diffusion, which affects the mechanical properties by three mechanisms: the stress-induced ordering of carbon atoms among the possible sets of interstitial sites,[1,2,3] the segregation of carbon to dislocations,[4] and the precipitation of carbides.[2,5–7] Each of these carbon redistributions can occur during the strain aging.[8–11] The Cottrell mechanism is of first importance in causing the return of the sharp yield point. This is especially true for ultra-lowcarbon steels, whose strain-aging behavior is receiving renewed attention due to the development of dent-resistant bake-hardening steels for automotive applications.[12] Cottrell’s theory was generally applied to describe the formation of the so-called Cottrell atmosphere surrounding dislocations.[4] But this theory, as pointed out by the authors themselves, is not applicable to the late stage of the atmosphere formation, due to the neglect of the variation of the free-carbon concentration and the saturation of dislocations. Harper tried to modify Cottrell’s theory by assuming that the segregation rate of carbon atoms was proportional to the fraction of carbon remaining in solution.[13] However, it has been found that his model is not really applicable to the investigation of the formation of the Cottrell atmosphere.[14] During the aging of a bake-hardenable steel, carbon atoms may also segregate to grain boundaries and pre-existing cementite particles. Some researchers reported that no correlation was found between the bake hardening and the grain size,[15] while others mentioned an increasing bake-hardening effect by refining the grain size of the ferrite.[16,17,18] It has also been reported that pre-existing cementite particles may affect the formation of the Cottrell atmosphere.[18] These effects have not yet been treated theoretically. A model that takes into account the concurrent segregation of carbon to dislocations, grain boundaries, and pre-existing cementite particles was, therefore, developed to describe the formation J.Z. ZHAO, Professor, is with Institute of Metals Research, Chinese Academy of Science, 72 Wenhua Road, Shenyang 110015, China, A.K. DE, Graduate Student, and B.C. De COOMAN, Professor, are with the Laboratory for Iron and Steelmaking, Ghent University, B-9052 Ghent, Belgium. Manuscript submitted March 7, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
of the Cottrell atmosphere during aging of a bake-hardening steel. Strain-aging experiments were carried out with a vacuum-degassed ultra-low-carbon bake-hardening steel, in order to verify experimentally the model predictions. II. THEORETICAL MODEL The elastic-strain field of a carbon atom dissolved in iron interacts with the elastic-strain field of a dislocation, and this causes the carbon atom to diffuse toward the dislocation. The total area (S) that can supply carbon atoms to a dislocation in the interval of time from t to t ⫹ ⌬t is[4] S ⫽ Vdis
⌬t t1/3
[1]
where Vdis ⫽ 2(/2)1/3 (AD/kT )2
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