Papers by Keyword: Rodrigues-Frank Space

Abstract: The orientation relationships that apply to the fcc (γ) – bcc (α) phase transformation in high-performance hot-rolled TRIP-aided steels were characterised by EBSD techniques. A statistical treatment of the experimental data allows the mean orientation relationship to be determined. This mean orientation relationship was compared to the models commonly proposed in the literature and confronted qualitatively to the predictions of the phenomenological theory of martensite crystallography (PTMC). The variant selection phenomenon was also characterized quantitatively at the level of individual austenite grains. The reconstruction of the EBSD maps evidences that bainite grows by packets in which the bainite laths share a common {111}γ plane in the austenite. This growth mechanism is not influenced by the prior hot deformation of the austenite. The hot deformation has a critical influence on the number of packets that forms. The analysis of the crystallographic features of the bainite packets reveals that all possible variants are formed in a packet, though in different proportions.

Abstract: The orientation relationships that apply to phase transformations in high-performance TRIP and TWIP steels were characterised by orientation imaging and EBSD techniques. The results are presented in the fundamental zones of Rodrigues-Frank space that correspond to the specific phase transformation under consideration (cubic to cubic or cubic to hexagonal). The use of Rodrigues-Frank space enables straightforward comparison to be made with orientation relationships proposed in the literature. The observations indicate that the active slip systems in the parent phase play important roles in variant selection.

Abstract: Orientations of both the α and γ phases in a multi-phase commercial steel were measured by means of electron backscatter diffraction (EBSD) techniques. Using the average orientation of each austenite grain as the reference frame, the orientation relationships between the two lattices were compared with the common orientation relationships (i.e. the Kurdjumov-Sachs and Nishiyama-Wassermann) in Rodrigues-Frank space. The occurrence of variant selection in individual austenite grains was examined using a recent dislocation-based model. This model considers the role of the slip systems that were active during prior deformation, as well as those of in-plane reactions, cross-slip and the partial dislocations that are linked to specific variants. It also unites the competing K-S and N-W relationships through the dissociation of perfect dislocations. Reasonably good agreement was observed between the predictions and the observations. Possible explanations for some of the discrepancies are also presented.

Abstract: The orientation relationships operating during the austenite (FCC) to BCC phase transformation were investigated in a high performance steel using X-ray and electron diffraction techniques and employing several length scales. These steels contain some retained austenite that permits the direct comparison of the textures of the parent (austenite) and product (ferrite, bainite, martensite) phases. X-ray diffraction allowed the global texture of the rolled parent austenite phase to be determined as well as that of its transformation product. EBSD techniques permitted study of the orientation relationships on a local scale. The observed correspondence relations are expressed in Rodrigues-Frank space. The exact Kurdjumov-Sachs relation was never found. The local spread of orientation in the parent austenite (due to deformation) is seen to be inherited by the bainite. This is attributed to the displacive mode of transformation to bainite. The influence of prior deformation of the austenite on the occurrence of variant selection was also studied. It appears that a critical strain is necessary to produce a significant amount of variant selection.

Abstract: It is often assumed that the texture formation during solid state transformations in low carbon steels critically depends on the local crystallographic misorientation at the interface between transformed and not yet transformed material volume. In some cases, a theoretical crystallographic orientation relation can be presumed as a necessary prerequisite for the transformation to occur. Classical examples of such misorientation conditions in steel metallurgy are the orientation relations between parent and product grains of the allotropic phase transformation from austenite to ferrite (or martensite) or the hypothetical <110>26.5º misorientation between growing nuclei and disappearing grains in a recrystallization process. One way to verify the validity of such misorientation conditions is to carry out an experiment in which the transformation is partially completed and then observe locally, at the transformation interface, whether or not the presumed crystallographic condition is complied with. Such an experiment will produce a large set of misorientation data. As each observed misorientation Dg is represented by a single point in the Rodrigues-Frank (RF) space, a distribution of discrete misorientation points is obtained. This distribution is compared with the reference misorientation Dgr, corresponding to a specific physical condition, by determining the number fraction dn of misorientations that are confined within a narrow misorientation volume element dw around the given reference misorientation Dgr. In order to evaluate whether or not the proposed misorientation condition is obeyed, the number fraction dn of the experimentally measured distribution must be compared with the number fractions dr obtained for a random misorientation distribution. The ratio dn/dr can be interpreted as the number intensity fi of the given reference misorientation Dgr. This method was applied on the observed local misorientations between the recrystallizing grains growing into the single crystal matrix of a Fe-2.8%Si alloy. It was found that the number intensity of the <110>26.5º misorientation increased with a factor 10 when the misorientation distribution was evaluated before and after the growth stage. In another example the method was applied to the misorientations measured at the local interface between parent austenite and product martensite grains of a partially transformed Fe-28%Ni alloy. It could be established that the Nishiyama- Wasserman relations ({111}g//{110}a <112>g//<110>a) prevail over the Kurdjumov-Sachs relations ({111}g//{110}a and <110>g//<111>a) although a considerable scatter was observed around either of the theoretical correspondences. A full parametric misorientation description was also applied to evaluate the relative grain boundary energies associated with a set of crystallographic misorientations observed near triple junctions in Fe-2%Si. In this instance it was found that the boundaries carrying a misorientation of the type <110>w carry a lower interfacial energy than the <100> or <111> type boundaries.

Abstract: The mechanisms governing the formation of transformation textures during the austenite-to-ferrite transformation are the subject of major debate. In this study, two extreme cases were examined: those of undeformed and deformed austenite. The first involves the transformation of austenite into Widmanstätten ferrite under "equilibrium" conditions in the Gibeon iron-nickel meteorite. This meteorite passed through the transformation at the rate of a few degrees per million years. Such cooling rates cannot of course be reached under laboratory conditions. The second concerns the transformation of hot rolled austenite after a quench into the bainite temperature range. These two behaviors were investigated by means of optical microscopy and electron backscatter diffraction (EBSD) techniques. The orientations of both the parent and product phases were measured and the orientation relationships are represented in Rodrigues-Frank (R-F) space. From the orientation of a particular FCC crystal, the crystallographic orientations of the product BCC crystals can be predicted according to the Bain, Kurdjumov-Sachs (K-S) and Nishiyama- Wassermann (N-W) correspondence relationships. Comparison of the predicted and measured orientations reveals that the Bain rotation is never observed; the K-S and N-W relationships are both observed and there is a continuous distribution of orientations between the exact K-S and N-W positions. The formation of preferred orientations under non-equilibrium conditions is scrutinized. These results are compared to recent models accounting for variant selection.

Abstract: A Fe-2.8%Si single crystal was scratched in order to randomise the texture in the neighbourhood of the notch. Annealing resulted in recrystallization and grain growth starting from the deformed zone. Misorientations between the single crystal matrix and the grown grains were gathered and were studied in order to investigate the possibility for selective growth based on a specific misorientation. However, instead of studying the misorientation angle or axis profiles separately in a 1D or 2D projection a full misorientation analysis was carried out in the 3-dimensional Rodrigues-Frank misorientation space, which offers an unambiguous interpretation of the data because no features are hidden or masked by a projection. It is concluded that the selective growth phenomenon following the <110>26.5deg misorientation relationship is strongly supported by the gathered orientation data, after appropriately normalizing these data with respect to a random misorientation distribution.