Theory Of Martensite Crystallography Research Articles

The crystallography of bainite in a medium-carbon steel containing Si, Mn, and Mo

A composite microstructure consisting of upper bainite laths and lower bainite plates, both carbide-free, plate (twinned) martensite, and carbon-enriched retained austenite, was produced by air-cooling a medium-carbon alloy steel (0.55 pct C, 1.35 pct Si, 0.78 pct Mn, 0.45 pct Mo) from 900 °C. Well-defined midribs and subunits were found to be associated with both the upper bainite laths and lower bainite plates, clearly showing that the two kinds of bainite growvia a sympathetic nucleation and growth process. The orientation relationship between the bainite and austenite, as determined by electron diffraction, showed that the close-packed planes in the two phases were separated by 0.5 deg and the close-packed directions were 1.9 apart. The habit plane determined from the midrib was (5 127)f, about 20 deg away from the nearly parallel close-packed planes (111)f/(011)b. The experimentally determined orientation relation-ship and habit plane (as defined by the midrib) were in good agreement with the predictions of the phenomenological theory of martensite crystallography.

Wedge-like microstructure in martensites

The wedge-like microstructure commonly seen in martensites, especially in shape-memory alloys, is an important mechanism for thermoelastic austenite-martensite transformation. This microstructure is analyzed using a suitable energy minimization principle. The Hadamard jump condition is used to characterize coherent interfaces. The crystallographic theory of martensite follows as a consequence of this. It is shown that only very special materials whose lattice parameters satisfy certain highly restrictive conditions can form the wedge-like microstructure. The lattice parameters of common shape-memory alloys satisfy these relations and their morphology shows good agreement with the predictions. This suggests that the microstructure and consequently the macroscopic behavior of martensites may depend very delicately on the lattice parameters.

Deformation of Shape-Memory Materials

AbstractWe present an overview of a theory of martensitic transformations developed by J. M. Ball and the author, and additional related results by Bhattacharya, Chu and Collins and Luskin and Kinderlehrer. This theory is in a form that is amenable to detailed numerical computations of microstructure. We describe the energy minimizing microstructures of a single crystal under applied displacements and under detailed dead loading. The relation of the theory to the crystallographic theory of martensite is presented.A consequence of the theory is the sensitivity of the patterns of microstructure to the precise lattice parameters. In the case of the wedge-like microstructure studied by Bhattacharya, it is found that this microstructure is only possible as a coherent, energy minimizing microstructure if very restrictive conditions on the lattice parameters are satisfied. Materials that exhibit the wedge satisfy this relation closely. The analysis suggests that optimal shape-memory behavior may be related to relations of this type.The theory has a relation to the work of Khachaturyan, Roitburd and Shatalov. We compare and contrast the two approaches. We present results that suggest that any approach based on the kinematics of linear elasticity will make serious quantitative errors in the prediction of microstructure.

Application of the double-shear theory of martensite crystallography to the β → α′ transformation in an U(Ga) alloy

The phenomenological double-shear theory of martensite crystallography has been applied to the β → α′ martensitic transformation in the U-1.6 at. pct Ga alloy. A correspondence matrix for the β → α′ transformation was derived from the experimentally determined β/α′ orientation relationship, and the double lattice invariant shear was considered as a combination of the principal slip (010) [100]a with one of the minor slips in the α-uranium structure. The theoretical predictions of the habit plane are in good agreement with the experimental observations.

An investigation of the γ → α martensitic transformation in uranium alloys

A detailed study of the γ → α martensitic transformation in uranium alloys is presented. Five binary uranium-base alloys containing 0.77Ti, 1.2 Mo, 2.2 Mo, 4.3 Mo and 5.0 Mo, respectively, were examined. As quenched, the U-0.77 Ti and U-1.2 Mo alloys consisted of an orthorhombic a/ a , martensite phase with an acicular morphology. The acicular martensite plates contain deformation twins which result from transformation stresses. The U-2.2 Mo and U-4.3 Mo alloys transformed during quenching to orthorhombic α/ b and monoclinic α/ b , martensite phases, respectively. The banded morphology observed in these two alloys consists of long, parallel martensite plates containing fine arrays of transformation twins. The type I transformation twinning modes were identified as {021},{130} and {131}. There was also evidence for a type II 〈512〉 {111} mode. It was found that adjacent bands could contain different kinds of transformation twins. In the U-5.0 Mo alloy, some of the cubic parent phase was retained during water quenching, and the α γ orientation relationship was determined. The γ phase was completely retained in this alloy by slow cooling from the solution treatment temperature of 800°C, and it was found that a martensitic reaction could be induced by deformation. The strain-induced martensite plates contained {021} transformation twins. The α γ orientation relationship was found to be different than the one determined in the quenched condition, and both orientation relationships are irrational. The invariant plane strain theory of martensite crystallography was applied to the twinned martensites, and a number of different parent/product lattice correspondences were considered for the γ → α transformations. It was concluded that more than one correspondence may be operative during these transformations. The single-shear theory was not able to explain the occurrence of all of the observed transformation twinning modes, although the theory was quite successful in predicting the observed crystallography for the strain-induced transformation.

Crystallography of Stress‐Induced Martensitic Transformations in Partially Stabilized Zirconia

The phenomenological theory of martensite crystallography was applied to the tetragonal‐monoclinic transformation in zirconia. Operation of variants of the lattice deformation can lead to a near‐twin orientation relation between different regions of a transformed particle, and if these regions are in the form of plates, as observed, they will fit together with very small contact stresses. Misfit stresses with the matrix are also minimized, and the overall misfit strain of a transformed particle is a very close approximation to a plane strain.

The crystallography of the δ to α martensitic transformation in plutonium alloys

The CRAB formulation of the theory of martensite crystallography has been applied to the δ to α phase transformation in plutonium alloys. The low symmetry of the monoclinic α-phase results in 41 lattice invariant transformation shear modes being considered possible. The predictions, when these shears are used with the three available correspondences have been analysed and the 20 most likely mechanisms selected for presentation. Because of the lack of experimental information with which to compare the results it is difficult to select the best mechanism. However twinning of the product phase on (001) using the third correspondence is suggested. This has a habit plane near {258} δ which is the crucial piece of information which needs to be checked experimentally. Further theoretical work on the atomic shuffles associated with the correspondence also needs to be carried out.

On a martensitic phase transformation in zirconia (ZrO 2)—II. Crystallographic aspects

Crystallographic aspects of the martensitic tetragonal → monoclinic phase transformation in zirconia single crystals have been studied experimentally and compared with predictions of the phenomenological theory of martensite crystallography. Two different orientation relationships have been observed between the high and low temperature phases. Above 1000°C, the transformation occurs according to the orientation relations (100) m∥~(100) t and [010] m∥~[001] t, while below 1000°C, (100) m~(100) t and [001] m∥~[001] t were observed. These results indicate that the habit planes of the plate-like martensite products reported in the first paper of this series [ Acta Met. 20, 1281 (1972)] had been incorrectly indexed; this occurred because of an incorrect assumption that a single crystal undergoing a monoclinie → tetragonal → monoclinic cycle would return to its original orientation at the end of the cycle. Application of the phenomenological theory of martensite crystallography indicates that the observed habit planes can be predicted using a single Bain correspondence, implied by the lower temperature orientation relations, combined with different lattice invariant deformation modes.

The crystallography of the bainite transformation in beta brass

The crystallography of low-temperature (plate) bainite formation in beta brass was studied in alloys containing 40–45 wt.% zinc. Habit plane of the bainite plates were determined using single surface trace analysis for plates formed between 200 and 400°C in these alloys. It was found that the mean position of the habit plane pole scatter region varied with temperature of formation and composition of the alloy. Except for the habit plane near (123)β, most of the variation is in a region near the sub-zero martensite habit plane, (2 11 12)β. The former is observed for the first time in plate bainite formation in beta brass. Application of the phenomenological theory of martensite crystallography to the bainite formation using stacking fault shear as the lattice invariant shear shows that the variation of the habit plane could be due to the variation in tetragonality, c α a α and relative volume, ν of bainite produced at different temperatures in these alloys. The habit plane scatter near (2 11 12)β falls within the ranges 0.90 < c α a α < 1.00 and 1.00 < ν < 1.02. These ranges are consistent with the structure proposed for lowtemperature bainite by previous workers. The habit plane near (123)β is consistent with an axial ratio ~0.96 and relative volume ~0.935. The latter corresponds to a dilatation parameter, δ ~0.975 relative to the undistorted martensite habit interface.

An assessment of the double shear theory as applied to ferrous martensitic transformations

The recently proposed double shear theory of martensite crystallography is analyzed in detail with particular reference to the {252} transformation in ferrous alloys and new experimental results. For the available experimental information on the orientation relationship and shape strain an eigenvalue analysis is used to assess the consistency of the data with the theory. It is shown that by perturbations of the data within the range of experimental error it is possible to obtain sets of data which are consistent with the basic assumption of the theory that the lattice invariant deformation is an invariant line strain consisting of two shears. For such cases possible shear combinations have been calculated, and although the analysis indicates that a major component of the lattice invariant deformation is a shear approximately in the [1̄01] F direction (consistent with observations of (112)[1̄1̄1] B twinning) the remaining shear is not rational and cannot be expressed in terms of rational shears. It is shown that in certain cases the number of lattice invariant shears of the theory can be extended from two to four and that in these cases the theory can account for a two-dimensional spread in habit plane normal. It is concluded that the double shear theory results in improved predictions relative to the original single shear theory, but does not provide a complete description of the crystallography of {252} martensite. However the improved predictions of the double shear theory and recent transmission electron microscopy results both suggest a martensite substructure which is more complex than purely (112) B transformation twinning as the habit plane deviates from (3, 15, 10) towards (252) F , and in this sense both theory and experiment are in agreement.

A generalized theory of martensite crystallography and its application to transformations in steels

In view of recent experimental observations of martensitic structures exhibiting two independent transformation shears, a new theory of martensite crystallography has been developed which enables the features of transformations involving mechanisms of this kind to be predicted. Like earlier treatments, the generalized theory is based on an invariant plane strain criterion, the total shape deformation being resolved into a lattice deformation and two independent lattice invariant shears. The new theory is first described in terms of geometrical models followed by a formal algebraic version, and then used to investigate the effects on predictions of the crystallographic features of the martensite reaction in steels of various double shear mechanisms. Some general features of the results, such as the effect of reversing the order of the two shears and the influence of algebraic restrictions are first examined. Mechanisms giving rise to predictions of practical interest are then discussed. In particular, two mechanisms giving habit planes near {225}γ and other crystallographic features consistent with experimental results are analysed in detail. These involve small lattice invariant shears on the (011̄)[11̄1̄]α and (1̄12)[11̄1)α systems preceding the observed (112)[1̄1̄1]α twinning shear. Finally, the relation of the new theory to other theories, particularly those attempting to describe the {225}γ transformation in steels, is discussed, special mention being made of an equivalent theory developed concurrently by Acton and Bevis.

Twinned martensite

In view of the recent thin film work which has shown that at least some plates of martensite are twinned on a fine scale, the possible twinning modes of the martensite structure are examined in detail. These reduce to fourteen different shear modes, which are used as initial data for a current theory of martensite crystallography. It is shown that only six of these modes can in fact result in twinned martensite plates and a comparison of the corresponding predictions and the observed crystallographic features indicates that only one type of twinned martensite is likely to occur in practice. This type has been observed in several steels. Further developments of the theory which appear to be necessary in order to explain all the observed features are also discussed.

On the theory of martensite crystallography

The restrictions on the initial data which are necessary for the existence of solutions in the analysis of martensite crystallography are presented in their most general form. Relations restricting the habit plane solutions themselves are also given and other further developments of the general theory discussed.