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It also has an unknown factor because it is now well established that bainitic ferrite can be considerably supersaturated with carbon. The lengthening rate of acicular ferrite with various carbon contents predicted by the modified Zener—Hillert model. The dashed, solid, and dash-dotted lines represent the growth rates calculated by applying the diffusivities D 0 , D eff , and D max , respectively.

In addition to the preceding uncertainties, the method of calculating the effective diffusion coefficient will be different for different geometries, and Trivedi and Pound considered diffusion in one dimension, whereas for edgewise growth of a plate, it is two dimensional.

This difference will be more important at a stronger dependence of composition.

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Already in the recent work of Leach et al. The reason is that the carbon content in local equilibrium with ferrite will increase with lowering temperature and may partly balance the natural decrease of the diffusivity with decreasing temperature. It was now realized that this effect on the C-curve would be more pronounced if it is assumed that the effective diffusivity falls even closer to the maximum value in the diffusion field, i.

Comparison of experimental lengthening rates for the 0. Comparison of experimental lengthening rates for the three 0. When searching for the effect making the calculated nose much flatter, we decided to explore the possibility that there is an increased deviation from local equilibrium at the tip of acicular ferrite at decreasing temperature.

He suggested that lower bainite would finally form as a diffusionless product at low temperatures. With his model, Hillert[ 1 ] demonstrated that at constant temperature, there can be a critical carbon content of the alloy below which the growth of ferrite turns diffusionless. Prediction of critical rate for transition from diffusional to diffusionless with varying temperature. Three choices of carbon diffusivity were considered. Similarly, transition from diffusional to diffusionless is expected when the rate exceeds the 0. The experimentally determined growth rate and the T 0 are given for the 0.

For the 0. Note that the width of the carbon spike in front of an advancing tip of ferrite was here based on one-dimensional diffusion and a constant diffusion coefficient.

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Numerical simulation of more realistic situations would be most welcome. Since the present model is crude and the numerical values of various parameters are uncertain, the result may be taken only as an indication that the shapes of C-curves for low carbon steels may be affected by an increasing deviation from local equilibrium, as suggested by Zener.

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If there is such a deviation from local equilibrium, it should certainly result in an increasing supersaturation of the growing ferrite, although this simple model cannot make that kind of prediction. Such an effect would decrease the requirement for rejection of carbon and thus result in less carbon diffusion during growth. That would yield higher growth rates than predicted by Eq. However, the decisive factor would probably not be the low carbon content but the high growth rate.

Additions of alloying elements may decrease the growth rates even more. From this point of view, it seems impossible that deviation from local equilibrium for carbon at the growing tip of acicular ferrite could have a decisive effect on the growth of bainite in general. Accepting the results of the model, obtained with the effective diffusivity, as defined by Trivedi and Pound, it seems that the model will formally predict that diffusionless growth may occur beneath the last experimental point for the alloy with 0. On the other hand, this is difficult to test due to martensite formation.

As already mentioned, the problem connected to a solute spike has occurred for the transition to growth under paraequilibrium in Fe-C-X alloys, and it can be solved only with a more sophisticated model. It may not matter much if the phase change occurs by a displacive mechanism or by a partly reconstructive mechanism such as the one presented by Aaronson et al.

There have been many studies of the supersaturation of carbon in bainitic ferrite, initially performed by X-ray diffraction and later dominated by the atomic probe technique. This is an essential feature of the diffusionless model, which predicts that ferrite should inherit all the carbon of the parent austenite. Supersaturation has been repeatedly confirmed over the years, e. The experimental technique has gradually improved, and several such papers of admirable quality have appeared recently. For the diffusionless model, it is of interest whether all the carbon content has been trapped; however, that is difficult to test because supersaturated carbon in ferrite may immediately start to partition into austenite.

The growth rate predicted from the diffusional rate equation will be higher the smaller that fraction is. To a first approximation, it is inversely proportional to that fraction of carbon. In the present work, the growth rates were predicted under the assumption that all the carbon in the parent austenite must diffuse away. To increase the growth rate markedly, it is necessary that the fraction retained in the ferrite plate is large, i. Information on the low content of carbon in the defect-free ferrite is also of interest for the diffusional model but only if it is established already by the growth mechanism and is not the result of a later redistribution because the chemical potential of all the carbon trapped in the growing ferrite is controlled by that content.

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Even without a detailed model, it may be concluded that with a lower carbon content in the defect-free part of ferrite, a lower deviation from local equilibrium at the advancing interface has been required. It is an interesting question whether a future unified model will have more characteristics of the diffusionless or diffusional model.

It is suggested that the separation of kinetic information on acicular ferrite into two curves, which has often been reported for TTT diagrams, should not be accepted as an indication of different growth mechanisms but of complex kinetic factors governing the volume fractions. Using the effective diffusivity for carbon, as defined by Trivedi and Pound,[ 26 ] predictions from the growth rate equation for diffusional growth in an Fe Virtually, the temperature-independent lengthening rate of bainite at low temperatures was observed in an old study of low-alloyed, hypoeutectoid steels.

A simple model of the carbon spike in front of the advancing tip of acicular ferrite has been applied. It indicates when a deviation from local equilibrium can be expected, which is the case at the lowest experimental temperature for Fe It is proposed that this is the explanation as to why the growth rate has not decreased there.

In that case, the effect would be coupled to the high growth rate relative to the diffusivity of carbon and can only indirectly be an effect of the low carbon content. This simple model describes a rate-dependent deviation from local equilibrium under the conditions where this effect has been observed, but it does not describe the possible supersaturation due to the deviation.

Computer Calculation of Phase Diagrams

Two Fe-C alloys investigated in this work were kindly offered by Dr. Skip to main content Skip to sections. Advertisement Hide. Download PDF. Open Access. First Online: 10 July The choice of 0. It was thus possible to carry out measurements over a wide range of temperatures. The austenitization conditions were chosen such that large grain sizes were obtained to aid subsequent measurements. At all temperatures, acicular ferrite was often featherlike when nucleated on a grain boundary.

Critical Driving Forces for Formation of Bainite

Close inspection by SEM showed that, by proper sectioning, individual ferrite plates within a feather could be traced from grain boundary to growing tip without any interruption. For each specimen, the length of the longest plate or the largest width of a feather was measured. However, due to rapid transformation and insufficient cooling rate, the transformation may have started before isothermal conditions had been established in some specimens.

The result was a coarser layer of the feather, in a region close to the grain boundary. This effect is most pronounced for low holding temperatures.

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Instead, in specimens from high temperatures, a ferrite plate may continue to grow during the final quench and sometimes form an extremely thin tip. Efforts were made to exclude such parts when measuring the length. Open image in new window.