Dilatometric analysis of austenite decomposition considering the effect of non-isotropic volume change

doi:10.1016/j.actamat.2006.12.007

Acta Materialia

Volume 55, Issue 8, May 2007, Pages 2659-2669

https://doi.org/10.1016/j.actamat.2006.12.007 Get rights and content

Abstract

One of the important assumptions underlying conventional dilatometric analysis is that volume changes isotropically during phase transformations. However, the volume change does not in fact occur isotropically and thus dilatation data contain non-isotropic contributions. In the present study, we expand the conventional analysis model to take into account the effect of non-isotropic volume change. The contribution of the non-isotropic effect to the dilatation data is quantified and is implemented in the analysis model. Dilatometric analysis is conducted on measured dilatation data of low-carbon steels to validate the suggested model. The phase fractions evaluated with the model show a good agreement with those obtained by metallographic analysis. It can be shown that considering the effect of non-isotropic volume change is critical for quantitative dilatometric analysis.

Introduction

Dilatometric analysis is a useful technique for the study of solid-state phase transformations in ferrous alloys [1], [2], [3], [4], [5], [6]. When a phase transformation occurs with an accompanying volume change, the dilatometric curve provides information on the change in atomic volume due to the transformation as well as on the thermal expansion characteristics. Therefore, by extracting the transformation-induced atomic volume change from the dilatometric curve and interpreting it with an analysis model, the fraction of individual phases involved in the transformation can be determined as a function of time or temperature.

The conventional method of calculating the phase fraction from the dilatometric curve is the so-called “lever rule” [1]. The dilatometric curve shows linear thermal expansion characteristics in the temperature range where no transformation occurs. In the lever rule, two linear segments of a dilatometric curve are extrapolated as shown in Fig. 1, and the fraction of the transformed phase at a given temperature is evaluated by the relative position of the measured dilatometric curve between the extrapolated lines. In principle, the lever rule is only valid for the case in which partitioning of alloy elements does not occur during the phase transformation.

During the austenite decomposition into ferrite in low-carbon steels, carbon is ejected from the ferrite due to its solubility limit and enriched in the untransformed austenite. The carbon enrichment increases the atomic volume of austenite by stretching the austenite lattice, which makes the dilatometric curve of austenite deviate from linearity as illustrated in Fig. 1. However, the lever rule cannot consider such non-linear dilatation of austenite caused by carbon enrichment.

Several authors have independently suggested dilatometric analysis models that consider the carbon redistribution during the austenite to ferrite transformation [3], [4], [5], [6]. They converted the measured dilatation data into the average atomic volume of the specimen, and then calculated the phase fraction by analyzing the average atomic volume with the lattice parameters of austenite, ferrite and cementite formulated as functions of temperature and solute carbon content.

One of the most important assumptions in the previously suggested analysis models is that the volume changes isotropically during the transformation. This means that the measured dilatation data is assumed to reflect a one-dimensional change originating from the isotropic volume change associated with the transformation. In general, however, the volume change does not occur isotropically in dilatometric specimens during phase transformation [7], [8], [9], [10]. Fig. 2 shows the dilatometric curve of low-carbon steel undergoing a thermal cycle consisting of continuous heating and cooling. The change of specimen length would not be found after the thermal cycle if the volume change associated with the phase transformation were isotropic. But the permanent strain appearing in dilatometric curve indicates that the specimen length is changed by the thermal cycle, which implies that the volume change with the transformation has non-isotropic characteristics.

When the volume change originating from the transformation occurs non-isotropically, the measured dilatation data include the effect of non-isotropic volume change. The observed dilatation during the transformation consists of the contribution of both isotropic and non-isotropic volume change as shown in Fig. 3. In view of the fact that dilatometry monitors only the length change, the implementation of the non-isotropic contribution into the dilatometric analysis model is important for quantitative evaluation of the phase fraction from the measured dilatation data.

In the present study, we expand the previous dilatometric analysis model to take into account the effect of non-isotropic volume change. The contribution of non-isotropic volume change to the dilatation data is quantified and implemented in the analysis model. To validate the suggested analysis model, we apply the model to the analysis of the measured dilatometric curves of low-carbon steels. The analysis results are compared with those from metallographic measurement, and the importance of considering the non-isotropic contribution is discussed.

Section snippets

Previous dilatometric analysis scheme [5,6]

The average atomic volume of a specimen is represented by a linear combination of the atomic volumes of the constituent phases as follows: $V = \sum_{i} f^{i} \cdot V^{i}$ where V is the average atomic volume of the specimen, Vⁱ is the atomic volume of phase i, and fⁱ is the volume fraction of phase i. Assuming that austenite decomposes into ferrite and pearlite successively on cooling, the volume fractions of ferrite (f^α) and pearlite (f^p) during the transformation are derived from Eq. (1): $f^{α} = \frac{V - V^{γ}}{V^{α} - V^{γ}}$ $f^{p} = V - V^{γ} + f^{α} \cdot (V^{γ} - V^{α}$

Experimental procedure

Table 2 shows the chemical composition of the alloys used here for dilatometric measurement. The ingots of steel A and B were prepared by vacuum induction melting and hot-rolled into plates of 30 and 20 mm thick, respectively. For homogenization of initial microstructure, the plates were heat-treated at 1300 °C for 2 h followed by air-cooling to room temperature and then reheated to 950 °C followed by furnace cooling. Cylindrical dilatometric specimens (3 mm (diameter) × 10 mm (length, L)) were

Dilatometric curves

Fig. 6 shows the measured dilatometric curves of the investigated low-carbon steels. Note that the dilatometric curves are shifted along y-axis to coincide with each other in the austenite region. Fig. 6a shows the dilatometric curves of steel A measured during repeated thermal cycling. The dilatometric curves show similar behavior on each thermal cycle, but they exhibit some deviation along both the temperature and the length scales. The shift of the dilatometric curve along the length scale

Conclusion

In the present study, the previous dilatometric analysis model is expanded to consider the effect of non-isotropic volume change. Dilatometric curves of low-carbon steels are measured and analyzed with the suggested model. The phase fractions evaluated by the dilatometric analysis are compared with those from the metallographic analysis, and the following conclusions can be drawn.

(1)
The contribution of the non-isotropic volume change to the measured dilatation data, designated as non-isotropic

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Dilatometric analysis of austenite decomposition considering the effect of non-isotropic volume change

Abstract

Introduction

Section snippets

Previous dilatometric analysis scheme [5,6]

Experimental procedure

Dilatometric curves

Conclusion

Scripta Mater

Mater Sci Eng

Mater Sci Eng

Acta Mater

Acta Mater

Scripta Metall Mater

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Acta Metall Mater

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