Phenomenological Theory Of Martensitic Transformations Research Articles

RELAXATION ROTATION DURING MARTENSITIC TRANSFORMATION AND SCATTERING OF MARTENSITE TEXTURE

In the our crystallographic theory of martensitic transformation, a new characteristic of martensitic transformation appears – a relaxation rotation, which was not in the generally accepted phenomenological theory of martensitic transformation. The relaxation rotation is necessary to obtain an invariant plane. The calculated angle of relaxation rotation for iron alloys with non-thermoelastic martensite is 1.75–1.85 degrees, for thermoelastic Geisler alloys with multilayer martensite 0.19–0.36 degrees. The relaxation rotation leads to the scattering of the texture of martensite. The scattering angles of single X-ray reflections of martensite in different alloys were measured and it was found that the scattering angle corresponds to the angle of relaxation rotation. This result shows that the our crystallographic theory of martensitic transformation describes the real mechanism of martensitic transformation.

Study of Microstructural Morphology of Ti-6Al-4V Alloy by Crystallographic Analysis and Phase Field Simulation.

Formation of a habit plane during martensitic transformation is related to an invariant plane strain transformation, which involves dislocation glide and twins. In the current work, the Phenomenological Theory of Martensitic Transformation (PTMT) is employed to study the crystallographic features while the phase field simulation is used to study the microstructure evolution for martensitic transformation of Ti-6Al-4V alloy. Results show that mechanical constraints play a key role in the microstructure evolution. It is shown that a twinned structure with very small twinned variants is geometrically difficult to form due to the lattice parameters of Ti-6Al-4V alloy. It is concluded that the predicted habit plane from the PTMT is consistent with results of the micro-elastic theory. The formation of a triangular morphology is favored geometrically and elastically.

Prediction of NiTi B19′ Martensite Twin Activation Below a Spherical Indenter Tip

The mechanical behavior of pseudoelastic NiTi is strongly affected by the properties of its twinned martensitic microstructures, which has been recently demonstrated by observations of an anisotropic material response during nanoindentation. In this paper, we apply the phenomenological theory of martensitic transformations to the multi-axial load case under a spherical indenter tip. We first calculate the elastic stress fields that trigger the martensitic transformation in anisotropic, linear-elastic finite element simulations. For , , and surface orientations of a single NiTi austenite grain, likely nucleation sites and the activated martensite correspondence variant pairs are then predicted. We further estimate the transformed martensitic volume and the resulting surface topography. In excellent agreement with recent experiments, four-, two-, and three-fold symmetries of the indents are observed; the orientation shows the largest and the orientation the smallest activated martensite volume. The tilt angles of the martensitic surface facets are about 1°, 5°, and 7° for the , , and orientations. Our results clearly highlight that dedicated anisotropic calculations in combination with a simple martensite twin selection criterion can be used to characterize the properties of small sample volumes subjected to the stress-induced martensitic transformation even under complex loading.

The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants.

The crystallography of displacive/martensitic phase transformations can be described with three types of matrix: the lattice distortion matrix, the orientation relationship matrix and the correspondence matrix. Given here are some formulae to express them in crystallographic, orthonormal and reciprocal bases, and an explanation is offered of how to deduce the matrices of inverse transformation. In the case of the hard-sphere assumption, a continuous form of distortion matrix can be determined, and its derivative is identified to the velocity gradient used in continuum mechanics. The distortion, orientation and correspondence variants are determined by coset decomposition with intersection groups that depend on the point groups of the phases and on the type of transformation matrix. The stretch variants required in the phenomenological theory of martensitic transformation should be distinguished from the correspondence variants. The orientation and correspondence variants are also different; they are defined from the geometric symmetries and algebraic symmetries, respectively. The concept of orientation (ir)reversibility during thermal cycling is briefly and partially treated by generalizing the orientation variants with n-cosets and graphs. Some simple examples are given to show that there is no general relation between the numbers of distortion, orientation and correspondence variants, and to illustrate the concept of orientation variants formed by thermal cycling.

Crystallographic variant selection of martensite at high stress/strain

The phenomenological theory of martensitic transformation is well understood that the displacive phase transformations are mainly influenced by the externally applied stress. Martensitic transformation occurs with 24 possible Kurdjomov-Sachs (K-S) variants, where each variant shows a distinct lattice orientation. The elegant transformation texture model of Kundu and Bhadeshia for crystallographic variant selection of martensite in metastable austenite at various stress/strain levels has been assessed in this present research. The corresponding interaction energies have also been evaluated. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed at different stress/strain levels. It has been investigated that the mechanical driving force alone is able to explain the observed martensite microtextures at all stress/strain levels under uniaxial tensile deformation of metastable austenite under low temperature at a slow strain rate. The present investigation also proves that the Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.

Stress induced martensite transformation texture in AISI 304 austenitic stainless steel

The phenomenological theory of martensitic transformation was applied to a tension induced martensitic transformation in an AISI 304 austenitic stainless steel in order to estimate the transformation texture. Input data were obtained from the published literature. Calculated pole figures were constructed assuming a variant selection process based on Patel and Cohen’s theory, which emphasises that a mechanical component of free energy is the driving force for martensitic transformation at temperatures above martensite start Ms. The results showed a remarkably good match between the calculated and published measured data.

A model for determining initial dislocation-densities associated with martensitic transformations

A three-dimensional multiple-slip dislocation-density-based crystal plasticity formulation, and specialised finite element formulations were used to determine the initial dislocation-densities associated with martensitic transformations in steel alloys. The analysis is based on modelling the shear part from the phenomenological theory of martensitic transformation to obtain both the transformation mobile and immobile dislocation-densities. The model was validated with experiments related to the transformation of lath martensite in high-strength low-alloying steels.

Zirconia nanoparticles: a martensitic phase transition at low temperature

The low temperature (450–600°C) amorphous to tetragonal and tetragonal to monoclinic phase transformations in zirconia nanoparticles, produced by an aqueous sol–gel route, are analysed in terms of their changes of lattice parameters and by using the phenomenological theory of martensitic transformation (Bowles–Mackenzie theory) to explore whether or not those crystallographic changes may be considered a martensitic transformation within the zirconia nanoparticles.

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.

Martensite crystallography—The role of the shape strain

The most significant characteristic of a martensitic transformation is the macroscopic change in shape of the region transformed—the shape strain. This results in a strain energy that opposes the transformation. The strain energy associated with a martensitic transformation can be calculated using the Eshelby equations for the strain energy of an oblate spheroid. The first aspect of the shape strain discussed in the paper is the reduction in the strain energy that results from the imposition of an appropriate applied stress—the familiar phenomenon of stress-induced martensitic transformation. An improved model for transformation toughening, which is based on using knowledge of the shape strain to calculate the characteristics of a stress-induced transformation, is described. The shape strain also dominates the crystallographic theories of the martensite transformation via the invariant plane strain concept that forms the basis of the very successful phenomenological theory of martensitic transformations (PTMT) developed just over half a century ago. This occurs when the transformed ellipsoid is infinitely thin (thickness to radius ratio t/ R = 0) and effectively ignores the surface energy of the interface. The paper explores the consequences of allowing the t/ R ratio to become finite and including a surface energy term. The analysis shows how this may be able to account for some of the characteristics of ferrous martensite that have, up to now, eluded explanation using the PTMT.

Martensitic transformation in zirconia: Part II. Martensite growth

Though the martensitic transformation in zirconia has been the object of a very large number of studies for the last decades, qualitative and quantitative observations of the formation and growth of relief induced by low temperature treatments has hardly ever been reported. In the first part of the study (Martensitic transformation in zirconia, Part I), we have demonstrated the excellent agreement between the atomic force microscopy quantitative observations and the outputs of the calculations derived from the phenomenological theory of martensitic transformation. The intermediate stages of transformation were nonetheless not considered. In this second part, the growth mechanisms of monoclinic phase resulting from the martensitic transformation in ceria-stabilized zirconia (10 mol% CeO 2) are investigated. Surface transformation is induced by aging treatments in water vapor at 413 K. The observations are rationalized by the recent analysis proposed for the crystallographic ABC1 correspondence choice, where the c t axis transforms to the c m axis. Three growth modes are observed and interpreted in terms of transformation strains accommodation. Microcracks formation is observed, explaining grain pop-out where the crystallographic disorientation between two adjacent grains is the largest. The influence of grain boundary paths on the surface relief features is demonstrated. Overall, our results strongly support the non-existence of a critical grain size for low temperature transformation, confirmed by the classical thermodynamics theory applied to this particular case.

A comparison of the phenomenological theory of martensitic transformations with a model based on interfacial defects

Structural models of martensitic interfaces are those where the habit plane (HP) is comprised of coherent terraces reticulated by arrays of interfacial defects. Such interfaces are shown explicitly to exhibit no long-range displacements and to move in a glissile manner by lateral motion of disconnections along the interface. We quantify predictions of HP and orientation relationship (OR) between the parent and product crystals for such models in terms of a reference lattice in an approach called a topological model (TM). These crystallographic quantities for the TM are compared with those of the phenomenological theory of martensite crystallography (PTMC). For the case of transformations resembling α to β in Ti, but where lattice invariant deformation is suppressed, the two models agree when the interplanar spacings of the terraces in the two crystals are the same. However, although the OR’s according to the two approaches are very similar, the predicted HP’s differ systematically when the terrace plane spacings are varied. The differences arise because the PTMC interfaces are unrelaxed configurations that are invariant planes of the geometrical shape transformation, whereas TM interfaces are physically invariant planes as a transformation progresses.

Martensite crystallography—the apparent controversy between the infinitesimal deformation approach and the phenomenological theory of martensitic transformations

The aim of this article is to demonstrate that the apparent controversy between the infinitesimal deformation (ID) approach and the phenomenological theory of martensitic transformations (PTMTs) in predicting the crystallographic characteristics of a martensitic transformation is entirely based on unjustified approximations associated with the way in which the ID calculations are performed. When applied correctly, the ID approach is shown to be absolutely identical to the PTMT. Nevertheless, there may be some advantages in using the ID approach. In particular, it is somewhat simpler than the PTMT; it is based on a physical concept that is easier to understand and, most important, it may provide a tool for investigating some of the features of martensitic transformations that have eluded explanation via the PTMT.

Atomistic simulations with slip boundary conditions

Dynamical variables are incorporated into Parrinello-Rahman simulations that allow for slipping of the simulation cell relative to its periodic images above and below a specified plane. Equations of motion are derived that show the slip to be determined by the dynamical balance of an internal virial traction and an external glide force. Elements of the phenomenological theory of martensitic transformations---namely, the existence of a habit plane and the fact that the macroscopic deformation of the new phase corresponds to an invariant plane shear---are introduced through the imposition of Lagrangian constraints on the dynamics of the cell and slip variables. A model structural transformation is simulated with and without slip, and with rational and irrational habit planes. The allowance of slip with an irrational habit plane dramatically lowers the barrier to the transformation. The results exhibit a remarkably wide variety of dislocation behavior, including edge and screw dislocations, slip, cross slip, dissociation, and twinning. An example of the physical processes thought to be responsible for the rapid propagation of the phase transformation in steels and shape memory alloys---a glissile dislocation interface---is also observed.

Tension–compression asymmetry of the stress–strain response in aged single crystal and polycrystalline NiTi

The purpose of this work is to thoroughly understand tension–compression asymmetry in precipitated NiTi using unique experimental results and micro-mechanical modeling. For the first time, tensile and compressive stress–strain behaviors were established on aged single crystals ([100], [110], and [111] orientations) and polycrystalline NiTi. The single crystal and polycrystalline Ti–50.8 at.% Ni materials were given both peak aged and over aged heat treatments. The drawn polycrystalline NiTi has a strong texture of the 〈111〉{110} type, thus it deformed in a manner consistent with the [111] single crystals. In contrast to the phenomenological theory of martensitic transformations (analogous to Schmid's law), the critical resolved shear stress required to trigger the transformation, τ crss, in the peak-aged single crystals was dependent on both the stress direction and crystallographic orientation. Using micro-mechanical modeling, the deviation from Schmid's law was attributed to the unique orientation relationship that exists between the Ti 3Ni 4 precipitates (their coherent stress fields) and the 24 martensite correspondence variant pairs. The over-aged single crystals generally obeyed Schmid's law within experimental error, consistent with the proposed micro-mechanical model. Qualitatively, the tension–compression asymmetry and orientation dependence of the recoverable strain level, ε 0, was consistent with the phenomenological theory for martensitic transformations. However, the peak- and over-aged single crystals generally both demonstrated smaller ε 0 magnitudes than predicted. The differences for both crystals were attributed to the inhibition of martensite detwinning coupled with several unique microstructural effects.

The Tetragonal to Monoclinic Martensitic Transformation in Zirconia

This paper reviews current knowledge of the martensitic tetragonal to monoclinic transformation that is the key to transformation toughening in zirconia ceramics. The most critical feature of this transformation is the shape strain, which not only governs the degree of toughening but, more important, determines whether or not stress-induced transformation will occur at the tip of a potentially dangerous crack. Determination of the shape strain by experiment is difficult, if not almost impossible, in zirconia but it is easily calculated by using the phenomenological theory of martensitic transformations. Therefore a major theme of the present paper is to demonstrate unequivocally that the phenomenological theory of martensitic transformations is capable of explaining all the reported microstructural and crystallographic features in these ceramics, and so can be used with confidence to provide the shape strain values, which are essential in developing a complete understanding of transformation toughening in zirconia.

The α2-to-O transformation in Ti-Al-Nb alloys

Abstract The α2-to-O transformation, with its characteristic microstructural features, occurs across the entire range of compositions in alloys based on the Ti3A1-Ti2AINb system. In this paper, we describe the isothermal decomposition of the α2-to the O(O1)-phase in a Ti-28.5 at.% A1–13 at.% Nb alloy, in the first detailed study of this transformation. Both parent and product phases are ordered with an identical site occupancy. The transformation is accomplished by a lattice distortion and a small composition change. The microstructural features and patterns that evolve during the diffusional growth and coarsening of the O-phase are shown to be dominated by the strain energy associated with the transformation. The orientation relationships, habit plane and the self-accommodating nature of the product variants are therefore explained by simple analyses in terms of the phenomenological theory of martensitic transformations.

Scanning tunneling microscope study of surface relief induced by the tetragonal-to-monoclinic transformation in a zirconia-yttria alloy

Surface relief induced by the tetragonal-to-monoclinic transformation in an arc-melted zirconia-yttria alloy has been investigated quantitatively, on a nanometer scale, with the scanning tunneling microscope. It was found by optical microscopy that two types of transformation products exist, the herringbone type and the acicular type. The surface relief of the herringbone and acicular products was successfully delineated by STM. The surface relief angles of the herringbone product were measured quantitatively, and they were in good agreement with results calculated from the phenomenological theory of martensitic transformation. Thus, STM was proved to be a useful tool for studying the surface relief resulting from a shear-type transformation, particularly when a quantitative measurement is needed for comparing the result with a predicted value from the phenomenological theory.

Roles of {101}<SUB>α</SUB> Twinnings in Martensitic Transformation of a 1.80 mass% Carbon Steel

In order to investigate the role of {101} α type twins or faults observed at the periphery of the martensite plate, the structure of the martensite in a 1.80 mass% C steel with a high tetragonality of 1.078 was studied by transmission electron microscopy, and in terms of the phenomenological theory of martensitic transformation. The periphery of the martensite contained two or three kinds of {101} α twins or faults in additon to the transformation twins of the (112)[111], system concentrated in the midrib

Transformation of lower bainite in hypereutectoid steels

The lower bainite transformation in five hypereutectoid steels (0.85 to 1.87 wt pet C) has been studied in the temperature range between 623 and 453 K by means of metallographic techniques. This paper brought conventional lower bainite into focus. The habit planes of ferrite and cementite platelets in lower bainite of a 1.10 wt pet C steel were close to (496)f and between (101)b and (112)b, respectively (subscriptsf, b, andc refer to the fee austenite, bec bainite ferrite, and bainite cementite, respectively). On the other hand, those in 1.80 and 1.87 wt pet C steels were close to (384)f and (101)b, respectively. The orientation relationship between austenite and bainite ferrite was the Kurdjumov-Sachs (K-S) relation and that between ferrite and cementite was the Isaichev relation for a 1.80 wt pet C steel. Application of the phenomenological theory of martensitic transformation to lower bainite in 1.80 and 1.87 wt pet C steels indicated that the lower bainite crystallography could be described by use of the (101) [−1−11]b system as the inhomogeneous shear, instead of the (112) [−1−11]b, system. The experimental and theoretical results suggest that lower bainite and martensite in 1.80 and 1.87 wt pet C steels have the same transformation inhomogeneity as the (101) [−1−1l]b system and their transformation mechanisms might be similar. The formation mechanism for lower bainite in a 1.10 pet C steel is still under consideration.