Crystallographic Theory Of Martensitic Transformations Research Articles

Relaxation Rotation during Martensitic Transformation in Alloys with Thermoelastic and Nonthermoelastic Martensite

It is shown that application of the crystallographic theory of martensitic transformation instead ofthe phenomenological one allows proper understanding of the mechanism of martensitic transformation incrystallographic analysis and computing, in addition to the previous characteristics, a new important characteristic,that is, the relaxation rotation of martensite crystallites to obtain the invariant plane. It is demonstratedthat the angle of relaxation rotation is most strongly dependent on the crystallographic systems of the original and final phases, as well as on the lattice parameters of these phases. It has been discovered that scatteringof the texture peaks of martensite, determined as the integral half-width of the texture maximum, is in linear proportion to the angle of relaxation rotation of martensite crystals.

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.

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

AbstractA computational framework is proposed to model anisotropic metallic polycrystals subjected to mechanically induced loadings. It enables the simulation of crystal‐plasticity‐like phenomena at finite strains. The unified framework of thermodynamically consistent constitutive equations is formulated such that it couples the crystallographic slip and martensitic transformation theories. The constitutive description for the slip plasticity evolution incorporates an anisotropic hyperelastic law with self and latent‐hardening. The mechanically induced martensite formation kinematics is based on the crystallographic theory of martensitic transformations. The complete set of highly coupled equations is expressed in a single system of equations and solved by a monolithic solution procedure. It is based on the Newton–Raphson methodology and incorporates the complete linearisation leading to asymptotic quadratic rates of convergence. The quasi‐static discretized evolution equations are integrated with a fully implicit scheme, except for the critical resolved slip stresses, which employ the generalized midpoint rule. The plastic flow is integrated with an implicit exponential integrator to exactly preserve the plastic incompressibility. Viscous regularizations for both deformation mechanisms are pursued to overcome numerical difficulties and model the behavior over a wide range of strain‐rate sensitivities. Numerical examples are presented to demonstrate the efficiency and predictive capability of the methodology.

Crystallographic Analysis and Mechanism of Martensitic Transformation in Fe Alloys

A new version of the crystallographic theory of martensitic transformation has been developed, where instead of Bain deformation, the deformation of the lattice was performed by a shear along the twinning system of crystals and an additional change in dimensions in three mutually perpendicular directions. In the proposed variant, the angle of relaxation rotation of martensite crystal was about 1.8°; in the standard phenomenological theory, it was 10°. The new version made it possible to establish the mechanism of lattice deformation upon martensitic transformation, to determine the angle of relaxation rotation, and to carry out crystallographic analysis of martensitic transformation in various alloys. The formation of crystals (laths) of dislocation martensite in medium-carbon steel was found to occur with redistribution of carbon.

Optimization Scheme of the Orientation Relationship from Crystallographic Statistics of Variants and its Application to Lath Martensite

In crystallographic theory of martensitic transformation, a slightly change of orientation relationship between lath martensite and prior austenite may indicate a different transformation mechanism and a change of mechanical property. Nevertheless, when the retained austenite can be hardly found in specimen, it is a great challenge to establish an accurate determination method for orientation relationship from the variant orientations only. Although some methods have been proposed, a reasonable evaluation of the solution accuracy is still waiting to be performed, and two further attentions should be addressed clearly: 1) significant improvement of calculation efficiency without sacrificing any solution accuracy; 2) effective elimination of the influence of the random cross-sections on the calculation. After an in-depth analysis of these issues, a new approach was developed involving two key steps in this paper. Firstly, an accurate clustering algorithm was developed to perform a statistic of all variants, which can give the most probable orientation and area fraction for each variant. Different from previous methods, the second step is to perform an optimization scheme established in this work, which takes variant fractions into consideration, to determine the optimal orientation relationship and orientation of prior austenite. In addition, the influence of the random cross-sections can be effectively eliminated by inputting the equally-weighted variants into the optimization scheme. Furthermore, in-situ high temperature EBSD examinations were first performed to validate solution accuracy, the corresponding results clearly indicated that the orientation of austenite obtained from this approach exhibited a high accuracy (with an error less than 1°), exceeding the accuracy achieved by the previous methods in addition to avoiding the possible deviation of using distorted retained austenite at room temperature. Indeed, the solution accuracy is contributed by the robust optimization scheme which strictly satisfies the criterion of a minimum average deviation between the measured and predicted orientation of martensitic variants. Another contributor to the accuracy is the good agreement between the clustered variant orientations and the measured data. Under the high accuracy, the variant-level calculation, which can save much computational time compared with pixel/domain-level calculation, is beneficial for the efficiency promotion.

Crystallographic Analysis and Mechanism of the Martensitic Transformation in the Heusler Alloy Ni47Mn42In11

The lattice parameters of the matrix of the modulated martensite crystal of the Ni47Mn42In11 alloy have been determined. Based on the phenomenological crystallographic theory of martensitic transformations, orientational relationships between the crystal lattices of the martensite matrix and the initial phase have been calculated, and the magnitude and the direction of the macroscopic shear, the habit plane, and the angle and the axis of rotation of the martensite plate have been determined. The mechanism of deformation upon the martensitic transformation has been established.

Giant tensile superelasticity originating from two-step phase transformation in a Ni-Mn-Sn-Fe magnetic microwire

Large recoverable strain of more than several percent arising from superelasticity in shape memory alloys is important for actuators, sensors, and solid-state refrigeration. Here, we report a Ni50.0Mn31.4Sn9.6Fe9.0 magnetic microwire showing a giant tensile recoverable strain of about 20.0% along the ⟨001⟩ direction of austenite at 263 K. The recoverable strain represents the largest value reported heretofore in Ni-Mn-based shape memory alloys and is also larger than that of the Ni-Ti wire available for practical applications at present. This giant tensile superelasticity is associated with the stress-induced two-step transformation, and the transformation sequence could be L21 (austenite) → 6M (six-layered modulated martensite) → NM (non-modulated martensite), as suggested by the temperature-dependent in-situ synchrotron high-energy X-ray diffraction experiments and the transformation strain calculation based on the crystallographic theory of martensitic transformation. In addition, this Ni50.0Mn31.4Sn9.6Fe9.0 microwire shows a transformation entropy change ΔStr of 22.9 J kg−1 K−1 and has the advantages of easy fabrication and low cost, promising for miniature sensor, actuator, and solid-state refrigeration applications.

Crystallographic analysis of the FCC → BCC martensitic transformation in high-carbon steel

Based on the phenomenological crystallographic theory of martensitic transformations, the following crystallographic characteristics of the tetragonal martensite in high-carbon steel have been calculated: orientation relationships between the crystal lattices of the bct martensite and fcc austenite; the magnitude and direction of the macroscopic shear; the habit plane; the angle and the axis of rotation of the crystal lattice of the martensite. The calculation was performed for three variants of lattice deformation: Bain deformation; two-shear Kurdjumov-Sachs deformation; and the deformation we suggested upon the analysis of the fcc-bcc transformation. In the last variant, a minimum rotation of the crystal lattice of martensite is required; consequently, this variant is closest to the real mechanism of the martensitic transformation. An expression has been derived that describes the interrelation between the degree of tetragonality of the crystal lattice of martensite and the magnitude of the shear deformation of the lattice. It has been shown that the 12 crystal-lographically equivalent variants of shear upon the formation of the lattice of the tetragonal martensite form three groups in each of which the martensite has the same tetragonality axis. For each variant of the shear, we have two equivalent variants of deformation of the martensite with invariant lattice. This results in 24 variants of orientation relationships.

In situ X-ray microdiffraction study of deformation-induced phase transformation in 304 austenitic stainless steel

The traditional phenomenological crystallographic theory of martensitic transformations can only explain the change in the shape and crystallographic orientation of a martensitic plate within a single parent crystal. It cannot predict the detailed transformation scenario for preferred selections of martensitic variants or the contributions of partial slip/twinning to local lattice distortion, especially in polycrystalline metals/alloys that exhibit grain-to-grain interactions throughout deformation-induced phase transformation. In this work, synchrotron-based X-ray microdiffraction was used to characterize changes in the local orientation, morphology and strain distribution inside individual martensitic plates, as well as the effect of parent orientation on variant selection in bulk polycrystalline 304 stainless steel (SS) during in situ uniaxial tensile loading at the low temperature of 210K. It was directly verified that the martensitic phase transformation in the studied 304 SS has two stages, transformation first from γ to ε in the nanoscaled lamella, and then from ε to α′ in the microbands. The selection of martensitic variants was predicted well by the minimum strain work criterion. Phase transformation-induced stress relaxation was evidenced by fluctuations in the (111) plane lattice strain accompanied by a strain gradient inside the martensitic plate, indicating a load transfer from the transformed grain to its neighbor. This leads to good stress/strain accommodation, as stresses can dissipate from the matrix into martensitic plates and nearby grains. Our experimental observations and theoretical analysis provide an in-depth understanding of the micromechanical behavior, particularly phase transformation-induced plasticity enhancement, of metals containing the metastable phase.

Crystallographic analysis of martensitic transformation in an iron-nickel alloy with twinned martensite

A variant of the crystallographic theory of martensitic transformations is proposed, based on a mechanism of lattice deformation in which the angle of rotation of a martensite plate is reduced to a minimum. In an iron-nickel alloy with twinned martensite, the least angle of rotation corresponds to the deformation of the austenite lattice by shear on the (111) plane in the $$\left[ {11\bar 2} \right]$$ direction proposed by Kurdyumov and Sachs as the first shear in the two-shear theory of martensite formation in steel.

Elucidation of microstructures produced in Ni51Fe22Ga27 ferromagnetic shape memory alloy

Both the magnetic and crystallographic microstructures in the ferromagnetic shape memory alloy Ni51Fe22Ga27 were extensively studied by electron holography, electron diffraction, dark-field image observations, and the phenomenological crystallographic theory of martensitic transformations. This study elucidated anomalies that were observed in the magnetic flux pattern before the onset of the martensitic transformation. Furthermore, the observations clarified the relationship between the magnetization vectors and the shape strain directions in the martensite variants that formed a self-accommodation group.

Micro-thermomechanical constitutive model of transformation induced plasticity and its application on armour steel

Based on the crystallographic theory of martensitic transformation and internal variable constitutive theory, a micromechanical constitutive model of martensitic transformation induced plasticity was developed. Plastic strains of product and parent phases as well as the volume fraction of each martensitic variant were considered as internal variables describing the microstructure evolution. The plasticity flow both in austenite and martensitic variants domain is described by J 2 flow theory. The thermodynamic driving force acting on these internal variables was obtained through the determination of the intrinsic dissipation due to plastic flow and the growth of martensitic domains. The evolution laws of the internal variables are derived, furthermore macroscopic response due to the change of internal variables is obtained. Thermomechanical behavior of armour steel under uniaxial loading was tested which showed a good agreement with experimental results.

Crystallographically based model for transformation-induced plasticity in multiphase carbon steels

The microstructure of multiphase steels assisted by transformation-induced plasticity consists of grains of retained austenite embedded in a ferrite-based matrix. Upon mechanical loading, retained austenite may transform into martensite, as a result of which plastic deformations are induced in the surrounding phases, i.e., the ferrite-based matrix and the untransformed austenite. In the present work, a crystallographically based model is developed to describe the elastoplastic transformation process in the austenitic region. The model is formulated within a large-deformation framework where the transformation kinematics is connected to the crystallographic theory of martensitic transformations. The effective elastic stiffness accounts for anisotropy arising from crystallographic orientations as well as for dilation effects due to the transformation. The transformation model is coupled to a single-crystal plasticity model for a face-centered cubic lattice to quantify the plastic deformations in the untransformed austenite. The driving forces for transformation and plasticity are derived from thermodynamical principles and include lower-length-scale contributions from surface and defect energies associated to, respectively, habit planes and dislocations. In order to demonstrate the essential features of the model, simulations are carried out for austenitic single crystals subjected to basic loading modes. To describe the elastoplastic response of the ferritic matrix in a multiphase steel, a crystal plasticity model for a body-centered cubic lattice is adopted. This model includes the effect of nonglide stresses in order to reproduce the asymmetry of slips in the twinning and antitwinning directions that characterizes the behavior of this type of lattices. The models for austenite and ferrite are combined to simulate the microstructural behavior of a multiphase steel. The results of the simulations show the relevance of including plastic deformations in the austenite in order to predict a more realistic evolution of the transformation process.

Crystalline damage growth during martensitic phase transformations

A thermomechanical model is developed within a large deformation setting in order to simulate the interactions between martensitic phase transformations and crystalline damage growth at the austenitic grain level. Subgrain information is included in the model via the crystallographic theory of martensitic transformations. The damage and transformation characteristics are dependent of the specific martensitic transformation systems activated during a loading process, which makes the model strongly anisotropic. The state of transformation for the individual transformation systems is represented by the corresponding volume fractions. The state of damage in the austenite and in the martensitic transformation systems is reflected by the corresponding damaged volume fractions. The thermodynamical forces energetically conjugated to the rate of volume fraction and the rate of damaged volume fraction are the driving forces for transformation and crystalline damage, respectively. The expressions for these driving forces follow after constructing the specific form of the Helmholtz energy for a phase-changing, damaging material. The model is used to analyze several three-dimensional boundary value problems that are representative of microstructures appearing in multiphase carbon steels containing retained austenite. The analyses show that the incorporation of damage in the model effectively limits the elastic stresses developing in the martensitic product phase, where the maximum value of the stress strongly depends on the toughness of the martensite. Furthermore, in an aggregate of randomly oriented grains of retained austenite embedded in a ferritic matrix the generation of crystalline damage delays the phase transformation process, and may arrest it if the martensitic product phase is sufficiently brittle. The response characteristics computed with the phase-changing damage model are confirmed by experimental results.

A theoretical model of the interaction between plastic distortion and configurational stress on the phase transformation front

We discuss a phenomenological model that describes the influence of plastic deformation on the evolution of an interface between martensite and the parent matrix. In development of the model it has been assumed that the rate of change of plastic distortion in the direction normal to the interface exhibits a functional relationship, which in general involves critical magnitudes of thermodynamic forces complemented by forces of pure mechanical character that originate from the mechanical stress fluxes acting on the interface. We have established a general theoretical model based on the fundamental principles of continuum mechanics in accord with the crystallographic theory of martensitic transformations. By using a special type of an asymptotic expansion procedure and homogenization technique we were able to derive an explicit constitutive relationship among the rate of plastic distortion, mechanical stress, crystallographic transformation tensor, and change of thermodynamic potential.

Crystallography of stress-induced [formula omitted] (trigonal) martensitic transformation in Au–49.5 at.%Cd alloy

The crystallography of B 2 - ζ 2 ′ (trigonal) stress-induced transformation in Au–Cd has been controversial. The present study was undertaken to clarify this issue by obtaining reliable experimental data, which enabled a critical test for the phenomenological crystallographic theory of martensitic transformation. The results revealed that the lattice invariant shear (LIS) was {1 0 0}〈0 1 1〉 C twinning in contrast to {0 1 1}〈1 0 0〉 C twinning, which was believed to be the case by all the previous investigators. The theoretical calculations using {1 0 0}〈0 1 1〉 C twinning agreed well with the observations in all respects. Therefore, the phenomenological crystallographic theory is shown to be well applicable to the present transformation. In addition to the stress-induced transformation, the morphologies of thermally induced martensites were examined, and two types of morphologies were observed: “roof-type” with LIS, and “herringbone-type” without LIS. Therefore, it is shown that transformations both with and without LIS are possible in the present transformation, and the previous discrepancy in LIS is rationalized.

Modelling of the effects of grain orientation on transformation-induced plasticity in multiphase carbon steels

The effects of grain orientation on transformation-induced plasticity in multiphase steels are studied through three-dimensional finite element simulations. The boundary value problems analysed concern a uniaxially-loaded sample consisting of a grain of retained austenite surrounded by multiple grains of ferrite. For the ferritic phase, a rate-dependent crystal plasticity model is used that describes the elasto-plastic behaviour of body-centred cubic crystalline structures under large deformations. In this model, the critical-resolved shear stress for plastic slip consists of an evolving slip resistance and a stress-dependent term that corresponds to the projection of the stress tensor on a non-glide plane (i.e. a non-Schmid stress). For the austenitic phase, the transformation model developed by Turteltaub and Suiker (2006 Int. J. Solids Struct. at press, 2005 J. Mech. Phys. Solids 53 1747–88) is employed. This model simulates the displacive phase transformation of a face-centred cubic austenite into a body-centred tetragonal martensite under external mechanical loading. The effective transformation kinematics and the effective anisotropic elastic stiffness components in the model are derived from lower-scale information that follows from the crystallographic theory of martensitic transformations. In the boundary value problems studied, the mutual interaction between the transforming austenitic grain and the plastically deforming ferritic matrix is computed for several grain orientations. From the simulation results, specific combinations of austenitic and ferritic crystalline orientations are identified that either increase or decrease the effective strength of the material. This information is useful to further improve the mechanical properties of multiphase carbon steels. In order to quantify the anisotropic aspects of the crystal plasticity model, the simulation results for the uniaxially-loaded sample are compared with those obtained with an isotropic plasticity model for the ferritic grains.

Crystallography of the tetragonal-to-monoclinic phase transformation in ceria-zirconia

A detailed understanding of the transformation toughening process in zirconia-containing ceramics requires the application of the crystallographic theory of martensitic transformation. Therefore, the crystallographic analysis of the tetragonal-to-monoclinic transformation in ceria-zirconia was performed by using both the infinitesimal deformation approach and Wechsler–Lieberman–Read phenomenological crystallographic theory. All crystallographic parameters such as the habit plane orientation, orientation relationship between the parent and product phases, the direction of the total shape deformation, the amount of the lattice invariant strain, etc. were calculated. The results obtained from the infinitesimal deformation approach were in agreement with those calculated from phenomenological crystallographic theory and also with experimental observations.

Computational modelling of plasticity induced by martensitic phase transformations

A time integration scheme is presented for the martensitic phase transformation model developed in recent theoretical work of Turteltaub and Suiker (A multi-scale thermomechanical model for cubic to tetragonal martensitic phase transformations 2005; Transformation-induced plasticity in ferrous alloys 2005). The phase transformation model can be used for analysing transformation-induced plasticity (TRIP) phenomena in ferrous alloys. The microstructural information for the phase transformation model is provided by the crystallographic theory of martensitic transformations. The transformation characteristics depend on the specific transformation systems activated during a loading process. The time integration scheme is formulated within a framework of finite deformations, where the stress-update algorithm is based on a fully implicit Euler backward discretization. A robust search algorithm is used for detecting the transformation systems activated during loading. The completion of the transformation process is prescribed by a constraint on the total martensitic volume fraction, which is accurately satisfied in the converged state using a sub-stepping algorithm. The computation of the consistent tangent operator is performed through a numerical differentiation method, which avoids the determination of extensive analytical derivatives and allows the model to be easily adapted if necessary. The ability of the algorithm to solve complex transformation-induced plasticity problems is illustrated with the aid of three-dimensional analyses, in which an aggregate of single-crystal grains of retained austenite embedded in a ferrite-based matrix is subjected to uniaxial tension. The response characteristics are in agreement with experimental findings of Jacques et al. (Philos. Mag. 2001; 81(7):1789; Metall. Mater. Trans. A 2001; 32A:2759) and Oliver et al. (Appl. Phys. A 2002; 74:S1143). Copyright © 2005 John Wiley & Sons, Ltd.

Martensitic transformation from α-Ti to β-Ti on rapid heating

Instead of conventional quenching martensitic transformation from β-Ti to α-Ti, unusual martensitic transformation from α-Ti to β-Ti induced by rapid heating has been achieved simply by using an electric current pulse. A large amount of the high-temperature martensitic phase remained in a Ti–6Al–4V alloy. We verified that such transformation is structurally and kinetically achievable, which agrees well with the phenomenological crystallographic theory of martensitic transformation.