Grain growth in capped steel
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I.
INTRODUCTION
IN order to control the mechanical properties of low carbon steel sheet, the grain size must be controlled through manipulation of process variables including chemical composition, cold reduction, annealing temperature, and time at temperature. Grain growth following recrystallization during coil annealing is an important factor in final grain size; however, there is little information on this process for low carbon steels. Experimental studies of grain growth are usually performed using either high purity metals or dilute solutions of specific impurities or precipitates in high purity metals. Knowledge gained from these studies has been used to establish relationships and models which are used to describe the grain growth process. In the classical model of grain growth proposed by Beck e t a l . , t the rate of grain growth is represented by the equation D 1in _ D~/n = ct
[1]
where D is average grain diameter, Do is the initial diameter before growth, t is time, and c and n are constants. The constant n is an indicator of the rate of grain growth. The higher the value of n, the more rapidly a given percentage grain growth will occur. When the value of D 1:, >> D~:,, Eq. [1] may be simplified to D
= kt"
[2]
where k = 1 / c . This latter equation has been suitable for most studies of steady state grain growth. The value of n for growth is limited to 0.5, but in practice this level is seldom approached and usually only at temperatures near the melting point. For most high purity metals and single phase alloys n is in the range from 0.2 to 0.4. Hu 2 reported that grain growth in zone refined iron obeyed Eq. [2]. Grain growth rates are a significant factor in establishing annealing procedures, so it is more useful to consider the differential of Eqs. [1] and [2] 1 dD/dt
= n k I:"D (1-1:.)
[3]
J. S. H. LAKE is Senior Research Officer, Research and Technology Centre, Coated Products Division, BHP Steel International Group, P.O. Box 77, Port Kembla, New South Wales 2505, Australia. Manuscript submitted January 2, 1986. METALLURGICALTRANSACTIONS A
The rate of grain growth is consequently a function of the instantaneous grain size if Eqs. [ 1] and [2] provide a complete description of grain growth. Developments of Beck's model have been used to describe grain growth in commercial materials. Normally the value of n is low when compared with high purity materials. Rhines et al. 3,4 have proposed that the rate of grain growth depends on the distribution of individual grain sizes. That is, a specimen with high proportions of very small and very large grains with respect to the average size will grow more rapidly than one in which there is less variation even though the average grain size is the same. Their results for aluminum and those of Conrad et al. for a titanium-oxygen alloy5 support the model. To determine whether these models represent the behavior of low carbon steels, grain growth measurements were made on typical commercial sheet steel samples, subjected to subcritical heat treatment.
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