Youliang He

Observations of the Gibeon meteorite and the inverse Greninger–Troiano orientation relationship

All the possible parallelism conditions associated with low-index crystallographic planes and directions in face- and body-centred cubic crystals are enumerated in terms of their minimum angle–axis misorientations. These include the Kurdjumov–Sachs (K-S), Nishiyama–Wassermann (N-W) and Pitsch orientation relationships, which are expressed in terms of close-packed (and near-close-packed) planes, close-packed directions, or both in the two crystal systems. By classifying these into either coplanar or codirectional relationships, it is possible to specify intermediate relations with either high-index directions or planes. In such a way, the Greninger–Troiano (G-T) relationship is approximated as a coplanar relation lying between the K-S and N-W relations. Based on geometric symmetry, a further correspondence relationship, which falls into the codirectional category and is located between the K-S and Pitsch relations, is represented both in pole-figure form and in Rodrigues–Frank space. It is referred to here as the inverse G-T, or G-T′. Experimental evidence from the plessite regions of the Gibeon meteorite is presented to support the validity of this relationship. It is shown that, in plessite, all the well known models, as well as their intermediates, are applicable to the γ-to-α transformation. By contrast, in the Widmanstatten portions, the misorientations are largely limited to the K-S, G-T and N-W relations.

Crystallographic features of the gamma-to-alpha transformation in a Nb-added transformation-induced plasticity steel

A Nb-bearing transformation-induced plasticity (TRIP) steel was control rolled and a certain amount of austenite was retained through appropriate heat treatment. Electron backscatter diffraction (EBSD) measurements were conducted on specimens deformed to various reductions, and the orientations of theα grains formed within individual prior-austenite grains were compared to those expected from the common correspondence relationships. While most of the bainite orientations cluster around the Bain circles formed by these relations, the polygonal (allotriomorphic) ferrite formed at the austenite grain boundaries does not obey any of these relations with respect to the neighboring austenite orientations. Grain-scale variant selection was observed in both the deformed and undeformed austenite grains. The crystallographic features of the deformation-induced ferrite transformation are also discussed.

Representation of orientation relationships in Rodrigues–Frank space for any two classes of lattice

The fundamental zones of Rodrigues–Frank (R-F) space applicable to misorientations between crystals of any two Laue groups are constructed by using a unified formulation in terms of quaternion algebra. Some of these regions are fully bounded by planes that are determined solely by the symmetries of the groups, while others have at least one unbounded direction. Each of the bounded fundamental zones falls into one of nine geometrically distinct configurations. The maximum symmetry-reduced angles and the corresponding Rodrigues–Frank vectors for these fundamental zones are evaluated. The use of Rodrigues–Frank space for the representation of orientation relationships between crystals of any two symmetry groups is also addressed. Examples concerning the transition of phases of the same symmetry group, i.e. from face-centered cubic to body-centered cubic, and of different groups, i.e. from body-centered cubic to hexagonal close-packed, are given to illustrate the usefulness of this space for representing orientation relationships during phase transformation or precipitation.

Representation of Misorientations in Rodrigues-Frank Space: Application to the Bain, Kurdjumov-Sachs, Nishiyama-Wassermann, Pitsch and Greninger-Troiano Orientation Relationships

Orientation relationships between individual crystals can be readily represented in Rodrigues-Frank space because of the one-to-one correspondence between each misorientation and a vector in the fundamental zone of this space. This is done by integrating the rotation angle and axis into a three-component vector. In this study, the three classical orientation relationships describing the γ-to-α transformation, namely the Bain, Kurdjumov-Sachs and Nishiyama- Wassermann, are represented in Rodrigues-Frank space. Also considered are the somewhat less common Pitsch and Greninger-Troiano relationships. The misorientations between these types of transformation variants are displayed in R-F space based on alternative reference systems to highlight the differences. Examples of the various crystallographic relationships between fcc and bcc crystals during the γ-to-α transformation are given to demonstrate the advantages of the use of this space.

Multiscale characterisation of the transformation texture in a high performance steel

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.

A Study of the γ-to-α Transformation Using EBSD Techniques

The crystallographic relationship between the g and a phases in samples of the Gibeon meteorite and a TRIP steel was investigated by means of EBSD techniques. The orientations of the two phases were measured and are represented in pole figures. The results are compared to predictions made on the basis of the Bain, Kurdjumov-Sachs (K-S), Nishiyama-Wassermann (NW), Greninger-Troiano (G-T) and Pitsch orientation relationships. The local misorientation between individual fcc and bcc crystals along their common interface was measured to demonstrate the way in which the exact orientation relationship varies along the boundary. The local orientations within lamellae and laths of kamacite and bainite are compared to that in recrystallised ferrite polygons. The occurrence of variant selection during the transformation of deformed austenite is analyzed using a recent dislocation-based model.

An EBSD study of orientation relationships during phase transformations in ultra high performance steels

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.

Grain Scale Assessment of Variant Selection in a Thermomechanically Processed TRIP Steel

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.