Análisis de la Simulación 5

It is noted that the quantity of carbon consumed at the 𝛾/𝛼 interphase boundary is not known to any degree of certainty. It is therefore, at this opportunity, expedient to explore the role this parameter has upon the 𝛾 → 𝛼 transformation kinetics and inter-sheet spacing of interphase precipitates. Further, modelling has been undertaken.

Through considering a threshold velocity at which the 𝛾/𝛼 interphase boundary can be said to have become impinged and the transformation completed of

𝑣 = 1 × 10−10 _𝑚𝑠−1_{= 0.1 𝑛𝑚𝑠}−1 _{an analogue of Figure 6.5-3 can be}

calculated. Through computing Equations ( 4.3-8 ), ( 6.5-14 ) and ( 6.5-16 ) with the fixed threshold velocity over the range 𝑆 = 0 → 𝐿0₂ (i.e. over the range of ferrite fraction 0 → 1) ∆𝐺_𝑚𝛾→𝛼 can be calculated. As before, through post- processing the computed data, an intersect between the intersect between the

∆𝐺_𝑚𝛾→𝛼 against 𝑆 curve and Δ𝐺_{𝐷𝑖𝑠𝑠}𝑇𝑜𝑡𝑎𝑙 against 𝑆 curve can be found as shown in Figure 6.7-1. The intersect corresponds to the distance from the prior austenite boundary at which the interphase boundary becomes impinged. The process is repeated considering varying degrees of carbon consumption at the interphase boundary according to the normalised parameter 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶

𝑋_𝐶0 in the range of no

carbon consumption by interphase precipitates to the entire bulk nominal carbon concentration, 𝑋𝐶0, being accounted for in the forming ferrite and

interphase precipitates, i.e. 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶 𝑋_𝐶0 =

𝑋_𝐶𝛼𝛾 𝑋_𝐶0 → 1.

Figure 6.7-1 Extemporary dissipation and driving force curves determining the

final ferrite fraction for Alloy 1 at a temperature of 700 ℃ for with varying

degree of carbon consumption.

Figure 6.7-2 Final ferrite fraction for Alloy 1 at a temperature of 700 ℃ for with

varying degree of carbon consumption.

Figure 6.7-2 shows that the final 𝛼 fraction is directly proportional to the degree of carbon consumption at the 𝛾/𝛼 interphase boundary by interphase carbide

precipitates. Now that the role of carbon consumption by interphase carbide precipitates at the interphase boundary has been established the role of this parameter on the 𝛾 → 𝛼 should be established. This is accomplished through sequentially computing the model as cast in Section 6.5 with variable carbon consumption at the interphase boundary according to the normalised parameter

𝑋_𝐶𝛼𝛾+𝑋𝐶𝑀𝐶

𝑋_𝐶0 in the range of no carbon consumption by interphase precipitates to the

entire bulk nominal carbon concentration, 𝑋_𝐶0, being accounted for in the forming ferrite and interphase precipitates, i.e. 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶 𝑋_𝐶0 =

𝑋_𝐶𝛼𝛾 𝑋_𝐶0 → 1.

Figure 6.7-3 Contour plot showing the effect of consumption at the 𝛾/𝛼

interphase boundary by interphase carbide precipitates upon the 𝛾 → 𝛼

transformation kinetics for for Alloy 1 at a temperature of 700 ℃.

Figure 6.7-3 shows a contour plot elucidating the effect of consumption at the

𝛾/𝛼 interphase boundary by interphase carbide precipitates upon the 𝛾 → 𝛼 transformation kinetics for Alloy 1 at a temperature of 700 ℃. It is evident that increasing the degree of carbon consumption not only increases the final fraction

with increasing 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶

𝑋_𝐶0 , the location of the ‘kink’ is marked on Figure 6.7-3 by

the red dashed line. This ‘kink’ is also evident in the transformation curves shown

in Figure 6.6-1 and corresponds to the transition between quasi-parequilibrium where, the dissipation of Gibbs energy is dominated by ∆𝐺_𝑚𝑓𝑟𝑖𝑐𝑡 and quasi- negligible partitioning local equilibrium where, the dissipation of Gibbs energy is dominated by Δ𝐺_𝑚𝑑𝑖𝑓𝑓.

Finally, the role of carbon consumption at the 𝛾/𝛼 interphase boundary on the inter-sheet spacing (using Equation 6.7-1) can be revealed considering an 𝛾/𝛼 interfacial energy of 𝜎 = 0.55 𝐽𝑚−2. Figure 6.7-4 shows a contour plot elucidating the effect of consumption at the 𝛾/𝛼 interphase boundary by interphase carbide precipitates upon the inter-sheet spacing of interphase precipitates in nm for Alloy 1 at a temperature of 700 ℃. A characteristic

‘boomerang’ in the inter-sheet spacing can be seen in the results. Generally, at a given 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶

𝑋_𝐶0 the inter-sheet spacing initially increases with ferrite half

thickness to a peak value then falls down to a roughly constant value as shown in Figure 6.6-2 and Figure 6.6-3. However, the ferrite half thickness distances at which these transitions occur are increasingly delayed with increasing carbon consumption by interphase carbide precipitates, 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶 𝑋_𝐶0 .

Figure 6.7-4 shows that as 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶

𝑋_𝐶0 → 1 the inter-sheet spacing goes to a

constant small value. 𝑋𝐶

𝛼𝛾_+𝑋 𝐶𝑀𝐶

𝑋_𝐶0 → 1 corresponds to a partitionless massive

transformation where the velocity of the interphase boundary moves at a constant and large velocity until the 𝛾 → 𝛼 transformation is fully completed. Although, this uniform fine array of interphase carbide precipitates would yield the optimised exploitation of the interphase precipitation mechanism at a given

transformation temperature for a given temperature, it remains to be revealed if interphase precipitation can occur during a rapid massive transformation.

Figure 6.7-4 Contour plot showing the effect of consumption at the 𝛾/𝛼

interphase boundary by interphase carbide precipitates upon the inter-sheet

spacing of interphase precipitates in nm for Alloy 1 at a temperature of 700 ℃.

In order to develop this study further an improved understanding of the following is prerequisite:

An accurate means of determination and prediction of the interfacial energy of the 𝛾/𝛼 interphase boundary is required.

Further theoretical work is required towards understanding the formation of nano-clusters and their composition.

Additional experimental studies are required where both the crystallography and transformation kinetics are extracted simultaneously coupled with site-specific a posteriori and site-specific TEM analysis, using