Phenomenological Theory Of Martensite Crystallography Research Articles

Teoría cristalográfica de la transformación martensítica

La transformación martensítica es uno de los temas más investigados en la ciencia de los materiales durante el siglo XX. Precisamente la segunda parte de ese siglo se destacó por el desarrollo de diversas teorías relacionadas con la cinética de la transformación de esta fase, los mecanismos de nucleación y la forma como se produce el cambio de la estructura cristalina. En este trabajo se realiza la descripción de los diferentes conceptos que definen la cristalografía de la transformación martensítica, centrándose en la construcción y aplicación de los modelos cristalográficos más destacados: el modelo de Bain; el modelo de Wechsler, Lieberman y Read; y el modelo de Bowles y Mackenzie. Este desarrollo será realizado con base en características particulares de la transformación martensítica como su carácter no difusional, el tipo de intercara entre la fase madre (austenita) y la fase producto (martensita), la formación de la subestructura de defectos y el cambio de forma; todas estas descritas por medio de ecuaciones matemáticas que buscan predecir cómo se dará la transformación, más que en explicar el movimiento real de los átomos dentro de la estructura. Este desarrollo es conocido como la Teoría Fenomenológica de la Cristalografía de la Martensita (TFCM).

Orientation dependence of the martensite transformation in a quenched and partitioned steel subjected to uniaxial tension

The orientation dependence of the austenite-to-martensite transformation during uniaxial tensile testing was modelled using the phenomenological theory of martensite crystallography and the mechanical driving force. It was validated experimentally by means of electron backscatter diffraction measurements on a pre-defined zone of a quenched and partitioned steel during interrupted tensile tests. A close match is obtained between the predictions of the model and the experimental observations.

Pattern formation during cubic to orthorhombic martensitic transformations in shape memory alloys

The superelasticity and shape memory effect of shape memory alloys originate from martensitic transformations (MT) that produce self-accommodated polydomain structures. In order to understand the formation mechanism of various domain patterns, a phase field model of cubic to orthorhombic MT in NiTiPt and NiTiCu is formulated, through which microstructure evolutions dominated by long-range elastic interactions are simulated. A rich variety of morphological patterns are predicted and analyzed. In particular, autocatalytic events leading to multi-variant “pyramidal triangular” and “nested triangular” configurations in NiTiCu are revealed. These morphological patterns are beyond the reach of the classical phenomenological theory of martensitic crystallography (PTMC). The simulation predictions agree well with experimental observations. By distinguishing deformation variant from orientation variant, the theoretical connection and distinction between PTMC and phase field microelasticity theory are discussed, and their predictions are compared with experimental observations.

Non-classical {3 3 4}β type of twinned α′ martensite in a Ti–5.26 wt.% Cr alloy

Some uncommon crystallographic features of α′ martensite were characterized in the martensitic transformation in a water-quenched Ti–5.26wt.% Cr alloy. A pair of martensite plates, type K and type M, sit side-by-side and share a {334}β habit plane. However, they have different habit planes in terms of the hexagonal close-packed lattice. While the classical phenomenological theory of martensite crystallography (PTMC) is unable to explain the habit plane of type K martensite even though they contain {11¯01¯} internal twins, application of the edge-to-edge matching (E2EM) model succeeded in accounting for both the orientation relationship and the habit plane orientation of the two types of martensite. The elastic strain energy as a function of the thickness of type K martensite plates was calculated, and the result supports the preference of the E2EM model over PTMC in explaining this type of martensite. In addition, a self-accommodation mechanism for strain was proposed to maintain the macroscopic invariant plane, and reduce the overall elastic strain energy of the adjacent pair of martensite plates. The application of the E2EM model plus this self-accommodation mechanism provides a new perspective on understanding martensitic transformations and providing a link between the crystallography of displacive and diffusional transformations.

Transformation Mechanism of Preprecipitation NiMn Nanostructures

The transformation mechanism of constrained b.c.c NiMn (β phase) clusters coherently precipitated during isothermal aging of Fe-Ni-Mn maraging alloy at 753 K (480 °C) has been studied. Preprecipitation of β-NiMn phase was demonstrated using conventional and high-resolution transmission electron microscopy and confirmed by flanking of electron diffraction spots, X-ray diffraction sidebands, and the invariance of lattice parameter and peak breadths in the earlier stages of age hardening. The β-NiMn clusters were recognized with interfacial dislocation dipoles lying on {011}α planes and Burgers vectors of a0\( \left\langle {01\overline{1} } \right\rangle_{\alpha } \) type. During further aging, the β-NiMn clusters transformed martensitically into fct NiMn (θ phase) precipitates as envisaged by the characteristic microtwinning texture. Considering the anomalous elastic softness of β-NiMn alloy, the transformation was plausibly assumed to take place by the localized soft-mode mechanism in which the structural instability of clusters is stimulated by the strain field of the interfacial dislocations. Computerized calculations in accordance with the phenomenological theory of martensite crystallography indicated that microtwinning of martensitic θ precipitates occurs in a self-accommodating manner. Transformation of very small β clusters at earlier stages of aging is thermodynamically hampered by the interfacial energy barrier.

Quantitative Analysis of Variant Selection for Displacive Transformations Under Stress

The existing variant selection models for displacive transformations are mostly qualitative in nature and attempt to predict the bulk texture using several fitting parameters. Many of these models use Kurdjumov-Sach (K-S) type orientation relationships (ORs) and ignore the phenomenological theory of martensite crystallography. So far there has not been any attempt to assess variant selection in the level of individual variants within one austenite grain. In this work, new kinds of experiments and innovative mathematical models have been developed to critically assess the variant selection phenomenon during bainite transformation under externally applied stress. Volume fractions of individual variants in a austenite grain have been calculated for the first time. Patel and Cohen’s theory on variant selection has been used in a new mathematical framework. Hitherto unknown aspects of variant selection have been found, which is exciting and provides new insight into the subject.

The Topological Model (TM) of Martensite Transformations – some Improvements

A minor, but crucial, modification to the original version of the TM was recently proposed in order to ensure that the model predictions were entirely consistent with those of the phenomenological theory of martensite crystallography (PTMC). In the present paper an analysis based on the principles of the Frank-Bilby equation is used to derive this modified version of the two-dimensional TM equation for the habit plane orientation from first principles. A considerably simpler and more accurate expression for the tilt rotation is also presented. Finally, a simple method for using the TM approach to calculate the shape strain, its magnitude and direction is described. The results of the predictions made with this improved version of the TM are compared with those of the original TM and with the corresponding PTMC predictions.

Variant Selection in Austenitic Stainless Steel Samples after Cold Rolling and Tension Deformation

The deformation process can induce the precipitation of martensite in austenitic stainless steels. When shear stress is applied at temperatures near Ms, displacive transformation (martensitic transformation) mode is activated. When external stresses are applied, the work done contributes to a change in free energy either raising or lowering the Ms-temperature. Orientation relationships during austenite to martensite phase transformation were investigated in an austenitic stainless steel samples deformed by cold rolling and deformed in a tension test. EBSD (electron backscatter diffraction) and X-ray diffraction techniques were used to evaluate parent austenite texture and martensite texture after transformation. The observed orientation relationship between austenite and martensite was compared with the predicted orientation relationship by the phenomenological theory of martensite crystallography (PMTC). Aspects related to variant selection were discussed based on the criterion for the action of applied stress in the martensitic transformation postulated by Patel and Cohen. Results showed a very good agreement between measured and calculated results.

Comment on “A TEM study of martensite habit planes and orientation relationships in Cu–Al–Ni shape memory alloys using a fast Δ g-based method”

A recent study of Cu–Al–Ni alloys has demonstrated the convenience of using parallel Δ g ’s for measuring the irrational habit planes of martensite, but the paper lacks a theoretical basis. A key point that is missing is the link between the parallel Δ g ’s and the lattice-invariant shear direction in the phenomenological theory of martensitic crystallography (PTMC). After clarifying the equivalency between the PTMC and the parallel Δ g model, this work presents calculated results based on the PTMC and the Δ g model, showing consistency with the experimental results.

Mechanics of superelasticity in Ti–30Nb–(8–10)Ta–5Zr alloy

The superelastic behaviour of Ti–30Nb–10Ta–5Zr and Ti–30Nb–8Ta–5Zr (wt.%) biomedical alloys was investigated by tensile testing and in situ synchrotron X-ray diffraction. The phenomenological theory of martensite crystallography and texture prediction based on the Schmid law indicate that α ″ in Ti–30Nb–10Ta–5Zr forms in untwinned variants. Measurement of single-crystal elastic constants using an Eshelby–Kroener–Kneer self-consistent model shows that the 10-Ta alloy has a C ′ modulus 3 GPa higher than that of the 8-Ta alloy. That it nevertheless has a proof stress 35 MPa lower can be qualitatively explained by the differences in martensite crystallography. The results suggest that high tensile strength can be maintained for low modulus β -Ti in spite of martensitic transformation by optimizing transformation strains.

Quantitative Analysis of Variant Selection and Orientation Relationships during the γ-to-α Phase Transformation in Hot-Rolled TRIP Steels

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.

Shape-Strain Analysis of Martensite in Ceria-Doped Zirconia

We use the scanning-electron-microscope–electron-backscattering diffraction (SEM-EBSD), atomic force microscopy (AFM), and calculations based on the phenomenological theory of martensite crystallography (PTMC) to study two types of martensite observed in ceria-doped zirconia. The results indicate that a plate-type martensite has various habit planes such as {301}t, {100}t, and {10 1 0}t, which suggests the association of different lattice correspondences and lattice-invariant shears in PTMC. A pyramid-type martensite has only {301}t habit plane. The shape strains of the variants associated with these habit planes are effective in accommodating the shape strains of the transformation in the near-surface region, as proposed by Deville et al. (2004). Although pyramidal structures appear predominantly on surfaces near the (001)t plane, they also appear on surfaces near (100)t and (010)t planes. These results are understood from the shape strains calculated by the PTMC.

A crystallographic model of fcc/bcc martensitic nucleation and growth

A crystallographic model of face-centered cubic/body-centered cubic martensitic nucleation and growth has been developed in which the glissile martensitic interface is described in terms of discrete transformation and misfit dislocations within the framework of the Frank–Bilby equation. In the present model heterogeneous nucleation of a martensitic embryo occurs spontaneously by dissociation of an existing perfect dislocation under certain conditions, such as the catalysis on grain boundaries. Autocatalytic dislocation is proposed to be responsible for embryo growth, then nucleation and subsequent growth of a single embryo can be regarded as an autocatalytic process. As a natural result the crystallographic features of grown martensite are consistent with the phenomenological theory of martensite crystallography. Martensitic nucleation in this model agrees with many experimental observations.

Shape deformation by moving a glissile interface with one set of misfit dislocations

Transformation and misfit dislocations are used to describe the motion of glissile interfaces with one set of misfit dislocations in the framework of the Frank−Bilby equation. The sweep of these glissile interfaces brings about an invariant-plane-strain type shape deformation. Our approach explains the glissile motion of martensitic interfaces and small-angle symmetrical tilt grain boundaries. It is consistent with the phenomenological theory of martensite crystallography but more flexible.

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.

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.

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.

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.