Theory Of Martensite Crystallography Research Articles

Transformation potential predictions for the stress-induced austenite to martensite transformation in steel

The stress-induced transformation behavior of retained austenite is considered in this work. With the development of transformation-induced plasticity (TRIP) steels this deformation mode is of growing importance. Twinned martensite structures were calculated using the crystallographic theory of martensite. An available work criterion was used to predict the transformation potentials for 16 different in-plane stress states for sheet sample geometry. By rotating the twinned martensite structures over all crystallographic orientations using Euler angles, the magnitude of the transformation potential was plotted as an orientation distribution plot for comparison with typical texture components. From these data, the Brass and Copper orientation components that are typical in retained austenite such as in TRIP steels were found to have low transformation potential values. Grains aligned with these orientations would require higher stresses to transform than other orientations, and may therefore never transform. This correlates to experimental observations that heavily deformed TRIP steel contains residual retained austenite.

Prediction of transformation texture under complex rolling condition

This paper deals with the prediction of transformation textures under different complex rolling conditions. With the help of mathematical models, it has been shown that the texture prediction can be done when martensite forms from a high Ni austenitic steel, which has undergone heavy deformation above M d . It has also been shown that the texture prediction can be done quite accurately when the steel is deformed under M d and transformation takes place simultaneously with deformation. This work also clearly proves that the Patel and Cohen’s theory can be utilised to predict the variant selection in complex rolling conditions, if it is used correctly along with the phenomenological theory of martensite crystallography (PTMC). It is quite clear from the set of results that no simplification, in terms of martensite transformation theory, is required to obtain the correct texture prediction as previously done by some researchers in which only the Bain variants are considered to be operative for martensite transformation.

Precise measurement of strain accommodation in austenite matrix surrounding martensite in ferrous alloys by electron backscatter diffraction analysis

Local strain distributions in austenite matrix that is deformed to accommodate shape strain associated with formation of martensite were investigated by means of electron backscatter diffraction (EBSD) analysis for various morphologies of lath, lenticular and thin plate martensite in ferrous alloys. By detecting small changes in EBSD patterns through image analysis of the patterns, components of both strain and rotation tensors in austenite matrix adjacent to martensite were measured quantitatively. In the austenite matrix surrounding thin plate martensite, the magnitude of components of strain tensor is nearly as large as those of rotation tensor, implying that shape strain of thin plate martensite is accommodated by elastic deformation of austenite. On the other hand, in the austenite matrices surrounding lenticular and lath martensite, components of strain tensor are found to be much smaller than those of rotation tensor even near the austenite/martensite interface. This indicates that most of the shape strain associated with the formation of lenticular and lath martensite is accommodated by plastic deformation in the austenite matrix. The misorientation axis of austenite adjacent to lenticular and lath martensite coincides well with that predicted from the phenomenological theory of martensite crystallography.

Mesoscale kinetics produces martensitic microstructure

We present molecular dynamics (MD) simulations of a martensitic phase transformation studying post-transformation microstructure and moving austenite–martensite interfaces. Unlike in energy-minimisation theories, the transformation dynamics dominate the martensite morphology. We use a binary Lennard-Jones potential to describe a square-to-hexagonal transformation by shear-and-shuffle. The high-T stable square lattice and low-T hexagonal lattice represent austenite and martensite, giving four martensitic variants. Compatible twin variants have no lattice misfit and zero interfacial energies which makes our model directly comparable with the crystallographic theory of martensite. Although our dynamical interpretation is different to previous work, our MD simulations exhibit very similar martensitic morphologies to real materials. We observe the nucleation of wedge-shaped, twinned martensite plates, plate growth at narrow, travelling transformation zones, subsonic transformation waves, elastic precursors inducing secondary nucleations and the formation of martensitic domains. Martensite is produced within narrow transformation zones where atoms change their lattice sites in a co-operative manner so as to form crystallographic layers. These motions produce inertia forces on the mesoscopic length-scale which induce the formation of twin variants in the subsequent layers to transform.

Observation and prediction of out-of-plane deformation in CuAlNi

This paper discusses the out-of-plane deformation caused by stress-induced shape memory phase transformations in CuAlNi. Using three-dimensional optical profilometry, the step-like phase transformation is measured and compared to predictions from the crystallographic theory of martensite. By examining the deformation around a notch in mode I loading, it is observed that the martensite plates formed cause the area near the notch tip to displace into the sample. This behavior is an additional constraint on deformation in shape memory alloys.

Self-accommodation in the bainitic microstructure of ultra-high-strength steel

In this study, the bainitic microstructure of a furnace-cooled electro-slag-refined 5% Cr steel was studied by the electron backscattered diffraction (EBSD) technique. The pole figures suggest a strong orientation relationship close to the Nishiyama–Wassermann type, i.e. there are 12 variants of the bainite sheaf that emerge from the three Bain correspondences. The microstructure consists of the bainite variants arranged in four sheaf colonies or morphological groups. Each sheaf colony, in turn, is made of one crystallographic group composed of 3 variants of bainite – one from each of the three Bain correspondences. Computations based on the phenomenological theory of martensitic crystallography (PTMC) show that the observed morphology is a product of stress-coupled autocatalytic nucleation. The 〈111〉Austenite 3-variant tension-coupled sheaf group predicted by the computations is the one that is experimentally observed.

Composition dependent crystallography of α″-martensite in Ti–Nb-based β-titanium alloy

Composition dependence of crystallographic features of α″-martensite in Ti–Nb-based alloy was systematically examined in Ti–Xmol%Nb–3mol%Al alloy, where X is 10–30. One of the lattice deformation strains, η3, became 0 at the critical Nb concentration of 23 mol% and the sign of η3 changed across the composition. The phenomenological theory of martensite crystallography (PTMC) predicted that the lattice invariant shear (LIS) would vanish at the critical composition. Transmission electron microscopy revealed that non-twinned martensite was formed with a habit plane of {755}b when η3 = 0, and that martensite with an internal twin of {111}o type I was formed with a {443}b habit plane for η3 = +0.008. Subscript b and o indicate β and α″ lattice, respectively. The crystallography of these two α″-martensites were well explained by the PTMC. On the other hand, non-twinned martensite with {111}b–{775}b habit plane was formed even when η3 was not zero. It was found that there is a critical value of |η3| for the formation of twinned martensite and that class B transformation, in which LIS is a {011}o compound twin, hardly occurs in β-titanium alloys.

Two ways for predicting the hysteresis minimisation for shape memory alloys

In a recent communication, James and Zhang proposed four criteria for hysteresis width minimization for alloys exhibiting a first order solid–solid phase transformation. In the present work, four different phase transformations are investigated through four different alloys: cubic → trigonal R-phase for NiTi, cubic → monoclinic II for Cu–Zn–Al, cubic → monoclinic I for NiTi and cubic → tetragonal for Ni–Mn–Ga. The first aim of this paper is to validate the efficiency of these four criteria of reversibility. The second aim of the paper is to show how the crystallographic theory of martensite, built to predict microstructure under stress free state or dead loads, can be used for continuous loadings. Except for Ni–Mn–Ga, the criteria predictions are in good agreement with the experimental observations and with the choice of the Helmholtz free energy function expression.

On the determination of shear angle in martensitic transformations

Yang et al.'s pioneer work on the relationship between the shear angle and the surface relief angle of martensitic transformation (MT) was discussed, and its limitation was pointed out. Furthermore, a new universal method to determine the shear angle in MT was developed in this work. Firstly, the surface relief angle accompanying MT was measured by atomic force microscopy. Secondly, a trial-and-error method and an extended procedure were proposed for the calculation of the indices of the sample free surface. And finally, the limitation of Yang et al.'s method was eliminated using this method combined with Bergeon et al.'s model. The calculated shear angles for both fcc → hcp and fcc → bct MT using the current method were in good agreement with the theoretical values of the shear angles predicted by phenomenological theory of martensitic crystallography.

Transformation texture in deformed stainless steel

The development of transformation texture in a deformed austenitic stainless steel has been modelled using the crystallographic theory of martensite, and the interaction of martensite with the applied stress. It has thus been possible to explain published data on variant selection in martensite induced to form during the tensile deformation of austenitic stainless steel.

Internal Structure of B19 Martensite in AuTi Shape Memory Alloy

AbstractInternal twin of B19 martensite in equiatomic AuTi binary alloy was examined by conventional transmission electron microscopy observation and the phenomenological theory of martensite crystallography (PTMC). The crystal structure of martensite was B19 (orthorhombic) with the lattice parameters of 0.2944nm, 0.4900nm and 0.4633nm. Most of martensite plates were internally twinned by {111}typeI twin. <211>typeII twin was occasionally observed and {011}compound-twin relationship was observed at boundaries between adjacent martensite plates. However, no martensite plate entirely twinned by the <211>typeII twinning or the {011}compound twinning was observed. PTMC analysis showed that the invariant plane is formed only by the introduction of the internal twin of {111}typeI or <211>typeII twin in the present geometry of the transformation. Geometry of a typical martensite plate with internal twin of {111}typeI twin was in good agreement with that required for the formation of habit plane with the invariant plane character. The observed {111}typeI twin is, therefore, considered to be the lattice invariant shear to minimize the elastic strain energy due to the transformation.

Phase Transformation Crystallography of Lath Martensite

AbstractOur current understanding of martensitic transformations has been based on the Phenomenological Theory of Martensite Crystallography developed in the 1950s. Recently, a Topological Model of martensitic transformations has been presented wherein the habit plane is a semi-coherent structure, and the transformation mechanism is shown explicitly to be diffusionless. This approach is used here to model phase transformation crystallography of lath martensite in ferrous alloys. A range of network geometries is predicted corresponding to orientation relationships varying from Nishiyama-Wasserman to Kurdjumov-Sachs. Experimental observations from the literature of the dislocation and disconnection arrays, habit plane and orientation relationship are in good agreement with the model.

Atomic Force Microscopy Study and Qualitative Analysis of Martensite Relief in Zirconia

A recent report [S. Deville and J. Chevalier, J. Am. Ceram. Soc., 86[12], 2225 (2003)] has shown the new possibilities offered by atomic force microscopy (AFM) to investigate martensitic transformation‐induced relief in zirconia. In this paper, we studied qualitatively the surface relief resulting from martensitic tetragonal to monoclinic phase transformation in yttria and ceria‐doped zirconia by AFM. AFM appears as a very powerful tool to investigate martensite relief with great precision. The phenomenological theory of martensitic crystallography could be successfully applied to explain all the observed features. The formation conditions of martensite are discussed, as well as ways of accommodating locally the transformation strain, i.e., self‐accommodating variant pairs and microcracking. Variant growth sequences are observed. These observations bring new insights and explanations on the transformation initiation and propagation sequences.

Martensitic transformations in ‘unfamiliar’ systems

Abstract In stiff engineering materials, martensitic transformations are shear-dominant diffusionless processes, and their crystallographic features can be successfully predicted using the phenomenological theory of martensite crystallography (PTMC). Recently, an alternative approach has been developed wherein the interface structure is modelled in terms of interfacial dislocations. This model, referred to as the topological model (TM), provides insight into the transformation process and identifies a set of five criteria that must be met for a transformation to be diffusionless. In the case of stiff engineering materials, the crystallographic predictions of the PTMC and TM are very similar. However, the TM enables a broader range of transformations to be treated, and two examples of ‘unusual’ martensites are presented here. The first is a diffusionless transformation in a small elastically soft protein crystal. The second is a transformation in a prospective high-temperature engineering alloy which exhibits the characteristic crystallographic features of martensite but where concomitant diffusion occurs. In this case, four of the five criteria mentioned above that relate to conservation of substitutional atomic sites are satisfied.

Martensitic transformations in ?unfamiliar? systems

In stiff engineering materials, martensitic transformations are shear-dominant diffusionless processes, and their crystallographic features can be successfully predicted using the phenomenological theory of martensite crystallography (PTMC). Recently, an alternative approach has been developed wherein the interface structure is modelled in terms of interfacial dislocations. This model, referred to as the topological model (TM), provides insight into the transformation process and identifies a set of five criteria that must be met for a transformation to be diffusionless. In the case of stiff engineering materials, the crystallographic predictions of the PTMC and TM are very similar. However, the TM enables a broader range of transformations to be treated, and two examples of ‘unusual’ martensites are presented here. The first is a diffusionless transformation in a small elastically soft protein crystal. The second is a transformation in a prospective high-temperature engineering alloy which exhibits the characteristic crystallographic features of martensite but where concomitant diffusion occurs. In this case, four of the five criteria mentioned above that relate to conservation of substitutional atomic sites are satisfied.

Kinematic and Topological Models of Martensitic Interfaces

ABSTRACTThe Phenomenological Theory of Martensite Crystallography, developed fifty years ago, envisages martensitic interfaces to be invariant planes of the shape transformation. This theory has been very successful, but neither incorporates the notion of atomic relaxations at martensitic interfaces, nor explicitly demonstrates that such interfaces are glissile. A new model, called the Topological Model, is proposed that addresses these issues. Predictions of the habit plane and relative orientation of the crystals according to the two models are compared and contrasted.

Crystallography and migration mechanisms of planar interphase boundaries

A general and yet simple theory is developed to predict the orientation relationship, orientation, structure and migration mechanisms of planar interphase boundaries in phase transformations. In contrast to existing theories that are based essentially on matching of atoms or lattice sites within two parallel, closely-packed planes in the two lattices, the present theory involves consideration of matching of edges of closely-packed lattice planes. In terms of the present theory, planar interphase boundaries are defined by the Moiré plane resulting from the intersection between at least two sets of closely-packed lattice planes, and that such boundaries migrate in their normal directions by successive nucleation and lateral gliding, within the macroscopic interphase planes, of interfacial defects of Moiré ledges that have unique heights and displacement vectors. A brief comparison is provided between the present theory and approaches of phenomenological theory of martensite crystallography, invariant line, structural ledges and disconnections.

In situ SEM-EBSD observations of the hcp to bcc phase transformation in commercially pure titanium

This study presents in situ observations of the hcp (α) to bcc (β) phase transformation in commercially pure titanium at 882 °C using SEM imaging concurrent with crystal orientation determination using EBSD. Direct observations of the onset of the phase transformation are presented showing the early stages of the growth of β plates within α grains and allotriomorphic β along α–α grain boundaries. Intragranular β plates have a Burgers orientation relationship (OR) with the parent α grain and are lenticular in shape. These plates also have a tent surface relief and surface-traces consistent with habit planes predicted by the phenomenological theory of martensitic crystallography for pure titanium. These features suggest a military component to the growth mechanism. The β allotriomorphs have a Burgers OR with one of the α grains abutting at the boundary, but do not have surface relief characteristic of a military transformation. These are likely to grow by a civilian mechanism. The final stage of the transformation is a process of competitive growth of the two β forms, with the allotriomorphic β dominating by virtue of its faster moving α–β interfaces. Grain growth in the β stability field is more than an order of magnitude faster than that in the α field at temperatures near the phase transformation.

Displacive transformation of virus protein crystal

A crystalline protein undergoes a displacive transformation in the T-even bacteriophage. In the present work, the transformation mechanism is modelled in terms of interfacial dislocations whose motion gives rise to the observed deformation. The topological properties (Burgers vector, b, and 'overlap' step height, h) of the dislocations involved are defined rigorously and a recent theory is used that quantifies the diffusional flux arising due to their movement. The circumstance under which passage of transformation dislocations is diffusionless is identified. Thus, dislocation modelling is used successfully to describe a diffusionless displacive transformation in a process where the phenomenological theory of martensite crystallography cannot be applied.

A model of martensite formation in terms of interfacial defect mechanisms

The objective of this work is to demonstrate the consistency between a new model of martensite formation and the classical theory of martensite crystallography. Recent developments in the understanding of interfacial defects have enabled their topological character, i.e. Burgers vectors and step heights, to be defined rigorously. In addition, the material flux associated with their motion along an interphase interface has also been quantified. On this basis, a defect model has been developed in which an initially strained nucleus evolves via a diffusionless process into a martensite plate. A bcc to hcp transformation is illustrated, demonstrating the crystallographic equivalence of the dislocation model and the phenomenological theory.