Martensite Crystallography Research Articles

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.

A SIMPLE VECTOR ANALYSIS METHOD FOR MARTENSITE CRYSTALLOGRAPHY

The displacements of vectors in a habit plane (HP) are assumed to lie along a particu- lar Burgers vector, so that the misfit in the interface can be fully accommodated by a set of dislocations with that Burgers vector. This assumption is consistent with many models and experimental obser- vations. Based on this assumption, a simple method based on vector analysis has been developed. By applying this method to fcc/bcc system, the classical solutions from the phenomenal theory of martensite crystallography can be reproduced. In addition, a simple form of equation for general HP orientations satisfying the above assumption has also been derived. The present method provides a simple but general tool for analysis of irrational HP generated from either martensitic or diffusional transformations.

Martensitic interfaces and transformation crystallography in Pu–Ga alloys

The face-centered cubic (δ) to monoclinic (α) martensitic transformation in Pu–Ga is unusual because it produces a relative large change of volume up to 20%. Moreover, the transformation crystallography is not predicted satisfactorily by the classical phenomenological theories of martensite crystallography, which is based on the hypothesis that the habit plane is an invariant plane of the total shape change. In this study we use the recently developed topological model where the habit plane, i.e., the interface between the parent and martensite phases, is envisaged as a semi-coherent configuration with coherent terraces reticulated by a network of disconnections or transformation dislocations, and defects producing lattice-invariant deformation. The authors show explicitly that this network not only accommodates the coherency strains, so that no long-range strain field arises, but also produces diffusionless transformation by motion of the disconnections across the interface. It was show that the predicted habit plane inclination with respect to the parent and martensite phases in a Pu–Ga alloy is in good agreement with published experimental observations when the lattice-invariant deformation is \( (201)_{\alpha } /[10\overline{2} ]_{\alpha } \) twinning, as observed experimentally.

The effect of oxygen on α″ martensite and superelasticity in Ti–24Nb–4Zr–8Sn

β Phase elasticity, stress-induced α″ transformation and superelasticity in hot-forged Ti–24Nb–4Zr–8Sn–(0.08–0.40)O (wt.%) has been investigated by in situ synchrotron X-ray diffraction, Rietveld refinement and texture analysis. The β elastic constants were determined by Eshelby–Kröner–Kneer self-consistent modelling. A micromechanical model based on texture, martensite crystallography and Schmid law nucleation criteria was used to analyse the generation of non-linear strain. Oxygen increased the C ′ cubic shear constant. The β phase showed increased compliance along 〈1 1 0〉 β as precursor to transformation, which occurs above 0.15 wt.% O by growth of nanosized nuclei, and is nearly suppressed at 0.40 wt.% O by structural convergence of parent/martensite phases. The shape of the stress–strain curve is due principally to stress-induced martensitic transformation with high-symmetry {7 5 5} β habit planes, and is controlled by oxygen through its effect on the transformation strains and critical shear stress.

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.

Effect of Cooling Rate on Morphology and Crystallography of Lath Martensite in Fe-Ni Alloys

The development of blocks and subblocks in the lath martensite was observed with SEM/EBSD and TEM/Kikuchi diffraction patterns analyses. Morphology of lath martensite formed below Ms temperature was observed using step quenching method in 18 mass% Ni maraging steel. The development of lath martensite structure can be described as follow; lath groups with single K-S variant start to form at the austenite grain boundary. Next, other sub-blocks appear adjacent to the lath groups formed first and these lath groups form macroscopic blocks observed in optical microscopy. The morphologies of the lath martensite in Fe -23 mass% Ni alloy cooled at different cooling rates after austenitization were also observed. The packet size and block thickness decreases with increasing cooling rate, although the sub-block thickness do not change. A packet locally contains small packets with different relationship of close packed planes, and the amount of small packets increases with increasing the cooling rate.

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.

In-Situ Observation of Martensite Transformation of Low Carbon High Alloy Steel Using High Temperature Laser Scanning Confocal Microscopy and X-ray Diffraction by Synchrotron Radiation

Martensite transformation of Low carbon high alloy steel during cooling was in-situ observed by using high temperature laser scanning confocal microscopy and X-ray diffraction by Synchrotron radiation. The crystallography of martensite and retained austenite structure were analyzed by electron back scattered diffraction patterns (EBSD). From the test results it could be concluded that the austenite phase is stress- relieved by twin deformation when the martensite transformation is occurred.

In-situ Observation of Martensite Transformation and Retained Austenite in Supermartensitic Stainless Steel

Martensite transformation of supermartensitic stainless steel during cooling was in-situ observed by using high temperature laser scanning confocal microscopy and X-ray diffraction by Synchrotron radiation. The crystallography of martensite and austenite structure were analyzed which X-ray diffraction spots and electron back scattered diffraction patterns (EBSD). From the test results it could be concluded that the austenite phase is accommodated by rotation less that 3 degree of the crystallite when the martensite transformation is occurred. X-Ray diffraction integration strength of austenite was influenced by the transformation stress immediately after the martensite transformation. We consider that the diffracting power of parent phase of austenite increase during martensitie transformation, because the compression stress is accommodated, and the defect is introduced, resulting in the mosaic structure.

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.

Comparison of thermally induced and deformation induced martensite in Fe–29% Ni–2% Mn alloy

The morphology and crystallography of martensite either formed by cooling to subzero temperatures (thermal effect) or by compression deformation were compared for different austenite grain sizes of Fe–29% Ni–2% Mn alloy by transmission electron microscope (TEM). TEM observations revealed both ɛ and α′ martensite formation within large grained austenite phases by thermal effect whereas only α′ martensite formation was observed in small grained austenite phases. On the other hand, compression deformation effect caused only α′ martensite formation in both small and large grained austenite phases of Fe–29% Ni–2% Mn alloy. Thermally induced α′ martensite exhibited a lenticular morphology with partial twinnings that are peculiar to this kind of morphology. The crystallographic orientation relationship between austenite and thermally induced α′ lenticular martensites was found to be as Kurdjumov–Sachs (K–S) type relationship.