Austenite-martensite Interface Research Articles

Effect of Si on the reversibility of stress-induced martensite in Fe–Mn–Si shape memory alloys

Fe–Mn–Si is a well-characterized ternary shape memory alloy. Research on this alloy has consistently shown that the addition of 5–6 wt.% Si is desirable to enhance the reversibility of stress-induced martensite vis-à-vis shape memory. This paper examines the effect of Si on the morphology and the crystallography of the martensite in the Fe–Mn–Si system. It is concluded that the addition of Si increases the c/ a ratio of the martensite, reduces the transformation volume change and decreases the atomic spacing difference between the parallel close-packed directions in the austenite–martensite interface (habit) plane. It is proposed that, in addition to austenite strengthening, Si enhances reversibility by reducing the volume change and the interfacial atomic mismatch between the martensite and the austenite. Although shape memory is improved, transformation reversibility remains limited by the necessary misfit dislocations that accommodate the atomic spacing differences in the interface.

Austenite–martensite interface in shape memory alloys

A two-scale phase field simulation is developed for austenite–martensite interface to understand the effects of crystalline symmetry and geometric compatibilities on the reversibility of structural phase transformations in shape memory alloys. It is observed that when the middle eigenvalue of martensite transformation strain is equal to zero, an exact austenite–martensite interface is formed with negligible elastic energy. On the other hand, when the middle eigenvalue is different from 0, an inexact interface between austenite and martensitic twin is formed, and the corresponding elastic energy increases with the increased magnitude of the middle eigenvalue, resulting in substantially higher energy barrier for austenite–martensite transformation, and thus higher thermal hysteresis in shape memory alloys.

A macroscopic constitutive model for shape-memory alloys: Theory and finite-element simulations

In this work, we develop a non-local and thermo-mechanically-coupled constitutive model for polycrystalline shape-memory alloys (SMAs) capable of undergoing austenite ↔ martensite phase transformations. The theory is developed in the isotropic metal-plasticity setting using fundamental thermodynamic laws and the principle of micro-force balance [E. Fried, M. Gurtin, Dynamic solid–solid transitions with phase characterized by an order parameter, Physica D 72 (1994) 287–308]. The constitutive model is then implemented in the ABAQUS/Explicit (2007) finite-element program by writing a user-material subroutine. The results from the constitutive model and numerical procedure are then compared to representative physical experiments conducted on a polycrystalline rod Ti–Ni undergoing superelasticity. The constitutive model and the numerical simulations are able to reproduce the stress–strain responses from these physical experiments to good accuracy. Experimental strain–temperature–cycling and shape-memory effect responses have also shown to be qualitatively well-reproduced by the developed constitutive model. With the aid of finite-element simulations we also show that during phase transformation, the dependence of the position i.e. the thickness of the austenite–martensite interface on the mesh density is heavily minimized when a non-local constitutive theory is used.

Low-energy morphology of the interface layer between austenite and twinned martensite

A micromechanical scheme is developed for predicting the morphology and interfacial energy of the interface layer between the parent phase and internally twinned martensite. Low-energy morphologies are determined by minimizing, with respect to shape parameters, the elastic microstrain energy associated with local incompatibility of transformation strains. The computational scheme involves a finite element solution to a problem of non-linear elasticity with eigenstrains, shape sensitivity analysis with respect to general shape parametrization and minimization employing a gradient-based algorithm. As an application, low-energy morphologies are studied for the austenite–martensite interface in the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy. Discussion of the results of the analysis includes comparison to alternative simplified methods in terms of the predicted morphologies and the corresponding interfacial energies.

Two-dimensional model for ferromagnetic martensites

We consider a recently introduced 2-D square-to-rectangle martensite model that explains several unusual features of martensites to study ferromagnetic martensites. The strain order parameter is coupled to the magnetic order parameter through a 4-state clock model. Studies are carried out for several combinations of the ordering of the Curie temperatures of the austenite and martensite phases and, the martensite transformation temperature. We find that the orientation of the magnetic order which generally points along the short axis of the rectangular variant, changes as one crosses the twin or the martensite-austenite interface. The model shows the possibility of a subtle interplay between the growth of strain and magnetic order parameters as the temperature is decreased. In some cases, this leads to qualitatively different magnetization curves from those predicted by earlier mean field models. Further, we find that strain morphology can be substantially altered by the magnetic order. We have also studied the dynamic hysteresis behavior. The corresponding dissipation during the forward and reverse cycles has features similar to the Barkhausen's noise.

A link between the shape of the austenite–martensite interface and the behaviour of the surface energy

Let Ω ⊂ R2 denote a bounded Lipschitz domain and consider some portion Γ0 of ∂Ω representing the austenite–twinned-martensite interface which is not assumed to be a straight segment. We prove that for an elastic energy density ϖ: R2 → [0 ∞) such that ϖ(0, ±1) = 0. Here, W(Ω) consists of all functions u from the Sobolev class W1, ∞(Ω) such that |uy| = 1 almost everywhere on Ω together with u = 0 on Γ0. We will first show that, for Γ0 having a vertical tangent, one cannot always expect a finite surface energy, i.e. in the above problem, the condition in general cannot be included. This generalizes a result of [12] where Γ0is a vertical straight line. Property (*) is established by constructing some minimizing sequences vanishing on the whole boundary ∂Ω, that is, one can even take Γ0 = ∂Ω. We also show that the existence or non-existence of minimizers depends on the shape of the austenite–twinned-martensite interface Γ0.

High-resolution electron microscopy study of ledge structures and transition lattices at the austenite–martensite interface in Fe-based alloys

In order to clarify how the lattices of austenite and martensite are connected at the interface on the atomic scale in the region within the width of the transformation twins or between slipped planes, a high-resolution electron microscopy study of the austenite–martensite interface was performed for Fe–23.0Ni–3.8Mn, Fe–30.5Ni–10Co–3Ti and Fe–8.8Cr–1.1C (mass %) alloys. Martensitic transformations occur at a low temperature in these alloys and exhibit various transformation characteristics, such as isothermal and athermal transformations, Kurdjumow–Sacks and Nishiyama orientational relationships, and a reversible mobile interface and a non-reversible interface in the reverse transformation. There were three important findings: (1) the (121)f interface is made up of two component planes, i.e. the terrace plane (111)f (//(011)b) and the ledge (0 0)f, and the average numbers of atom rows of [ 01]f (//[ 1]b) on these planes are 2.7–4.9 on (111)f and 1.3–2.6 on (0 0)f. These are different depending on the alloy, but the ratio of the atom rows of the former to the latter is about 2:1, in accordance with the observed habit plane of (121)f; (2) the neighbouring (0 0)f ledges are separated by about five to ten planes of (112)b; and (3) transition lattices from fcc to bcc (or bct) exist at the interface and the thickness of this transition lattice region is 0.2–0.8 nm. It is reasonably assumed that screw dislocations with a Burgers vector of 1/2[ 01]f (//1/2[ 1]b) reside at the ledge of the interface, which produces the lattice invariant deformation when they move with the interface. The complete scheme for the relaxation of the strain at the interface is considered to be as follows. First, transformation twins are introduced to relax the strain at the interface on the macroscopic scale, in accordance with the phenomenological theory, then screw dislocations are brought in at the ledges to release the strain between each of the twin-related martensite crystals and the austenite, and, finally, transition lattices are generated at the interface to relax the strain on the most microscopic scale, i.e. at the atomic level.

Simulation of an Austenite-Twinned-Martensite Interface.

Developing numerical methods for predicting microstructure in materials is a large and important research area. Two examples of material microstructures are Austenite and Martensite. Austenite is a microscopic phase with simple crystallographic structure while Martensite is one with a more complex structure. One important task in materials science is the development of numerical procedures which accurately predict microstructures in Martensite. In this paper we present a method for simulating material microstructure close to an Austenite-Martensite interface. The method combines a quasi-Newton optimization algorithm and a nonconforming finite element scheme that successfully minimizes an approximation to the total stored energy near the interface of interest. Preliminary results suggest that the minimizers of this energy functional located by the developed numerical algorithm appear to display the desired characteristics.

The behaviour of microstructures with small shears of the austenite-martensite interface in martensitic phase transformations

Let $\Omega \subset \Bbb{R}^2$ denote a bounded domain whose boundary $\partial \Omega$ is Lipschitz and contains a segment $\Gamma_0$ representing the austenite-twinned martensite interface. We prove $$\displaystyle{\inf_{{u\in \cal W}(\Omega)} \int_\Omega \varphi(\nabla u(x,y))dxdy=0}$$ for any elastic energy density $\varphi : \Bbb{R}^2 \rightarrow [0,\infty)$ such that $\varphi(0,\pm 1)=0$. Here ${\cal W}(\Omega)$ consists of all Lipschitz functions $u$ with $u=0$ on $\Gamma_0$ and $|u_y|=1$ a.e. Apart from the trivial case $\Gamma_0 \subset \reel \times \{a\},~a\in \Bbb{R}$, this result is obtained through the construction of suitable minimizing sequences which differ substantially for vertical and non-vertical segments.

HREM study on the ledge structures, transient lattices and dislocation structures at the austenite-martensite and austenite-bainite interfaces in Fe-based alloys

High-resolution electron microscopy (HREM) has been performed to know the atomic arrangement of the austenite-martensite interface and the austenite-bainite interface in Fe-based alloys. The alloys studied are Fe-23.0Ni-3.8Mn, Fe-8.8Cr-1.1C, Fe-30.5Ni-10Co-3Ti (mass %) for martensitic transformation and Fe-2Si-1.4C (mass %) for bainitic transformation. These alloys have various transformation characteristics depending on the alloy; for martensitic transformation, athermal and isothermal kinetics, the Kurdjumow-Sachs (K-S) and Nishiyama (N) orientation relationships, reversible and irreversible movement of the interface, and for bainitic transformation, upper bainite and lower bainite. All the interfaces observed had to be limited to {112} (macroscopically {225}) or very close to {112} because of the geometrical condition that the atom rows of f, b and b must be observed parallel to the interface, i.e., the edge-on orientation. The austenite-martensite interface is (121)f with the K-S orientation relationship of (111)f//(011)b and [101]f// [111]b, and the interface is basically composed of the terrace of (111)f and the ledge of (010)f, which have the average ratio of 2:1 for the number of atom rows of [101]// [111]b on these planes. This interface always accompanies the transient lattice region with the thickness of 0.4-1.0 nm, where the lattice changes continuously from fcc to bcc (or bct). No extra-half plane is observed at the (121)f interface over a large distance of 100-200 lattice planes. The interface for both the upper and lower bainites is close to (112)f with the N orientation relationship of (111)f//(011)b and [110]f//[100]b'. Contrary to the interface for martensite, this interface for bainite has many extra-half planes except when the interface is close to (112)f. The interface is basically made up of the terrace of (111)f//(011)b and the ledge of (011)b'//(112)f, and the height of the ledge is usually one or two atomic layers. No transient lattice region accompanies this interface. Transformation dislocations and a nucleating martensite are observed at the tip of growing martensite.

Prediction and observation of crack tip microstructure in shape memory CuAlNi single crystals

The formation of martensite at a notch tip in a CuAlNi shape memory alloy loaded in tension is studied. The geometry of the initial martensite plate to form at the notch is predicted theoretically, using the stress field at a crack tip in an anisotropic linearly elastic body together with a listing of all possible austenite–martensite interfaces from the Crystallographic Theory of Martensite (CTM). The stress field and CTM analyses are combined through a selection criterion based on computing the work available from the stress field to transform to each austenite–martensite interface. The resulting predictions are compared to experimentally observed microstructures in notched specimens of single crystal CuAlNi loaded in tension for eight notch orientations. Results show that the available work criterion accurately predicts the orientation, number and order of the austenite–martensite interfaces that initially form near a crack.

Characteristic features of shape memory effect and related transformation behavior in Fe-based alloys

Abstract Shape memory mechanisms, characteristic of Fe-based alloys, are discussed based on the microscopic observations with various scales ranging from micron meter to sub-nanometer. Most of the Fe-based shape memory alloys that may be technologically applicable in the future are associated with the fcc/bct and fcc/hcp transformations. The modes of the stress-induced martensitic transformation and its reverse transformation in these transformation systems, which are directly related to the shape memory effect, are examined in detail and it is concluded that the following conditions are the most important ones to achieve a good shape memory effect. In the case of the fcc/bct transformation, the tetragonality of the bct martensite must be large so that the twin boundary energy in martensite can be lowered, which results in that very fine transformation twins are completely extended through a martensite plate. A low twin-boundary energy in martensite is an important factor to reduce the density of dislocations residing at the austenite–martensite interface and make easy the reverse movement of the interface. In the extreme case of no dislocations at the interface, a thermoelastic transformation will be realized. A higher yield stress for slip in bct martensite is another factor to bring about the reversibly mobile interface. These are deduced from the detailed analysis of dislocations generated behind the reverse-moving interface on heating. In the case of the fcc/hcp transformation, the formation of extremely thin hcp martensite plates with uniform distribution in a deformed sample is most required to achieve a good shape memory effect. For such thin martensite plates to be produced, high densities of stacking faults must preexist on the primary slip system in austenite when an external stress is applied for shape change. A new mechanism for the formation of very thin martensite plates by an applied stress is presented. A low stress for inducing martensite transformation compared with the yield stress for slip in austenite, which results from the so-called ‘training’ treatment, may be a necessary but not sufficient condition for obtaining a good shape memory effect. Future directions of the research on Fe-based shape memory alloys are suggested.

Bulk and thin film microstructures in untwinned martensites

The microstructure in alloys for which the martensite phase is either the 9R or 18R long-period stacking order structure is investigated. A choice of a new unit cell to describe the lattice of the product phase is made, and it is found to give an exact austenite–martensite interface. A comparison with experimental observations for several different material systems supports this choice of unit cell, and the predictions of the shape strain and habit plane normal vectors are the same as those given by a phenomenological calculation. The approach followed here de-emphasizes the role of the internal defects within the unit cell of the martensite lattice in providing the mechanism by which compatibility between the phases is achieved. It is this reason that the name untwinned martensites is proposed to replace the older name faulted martensites. In addition, microstructures in thin film specimens of the alloys exhibiting the untwinned martensite are studied. In particular, a tent microstructure is constructed in a specially oriented film, and such microstructures have potential applications in micro-devices to act as either a pump or an actuator.

On the strain jump in shape memory alloys—A crystallographic-based mechanics analysis

The strain jump across the Austenite-Martensite (A-M) interface in single crystal Cu-14wt%Al-4.12wt%Ni Shape Memory Alloys (SMAs) under uniaxial tension was studied in this paper. A crystallographic-based mechanics analysis on the formation and microstructure of the interface was performed. By using the high sensitive Moire interference technique, the full-field deformation patterns during the transformation process were successfully recorded. The orientation of the habit plane (A-M interface) and the magnitude of the shape strain were determined precisely from the Moire fringe patterns. The theoretical predictions on the habit plane normal and the shape strain were compared with the measured results and good agreements were obtained.

Hierarchical microstructure in structural phase transitions

We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T0) we obtain the conditions under which branching of twins is energetically favorable. Above T0 a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.

HREM Observations of Continuously Changing Intermediate Structures between f.c.c. and b.c.c. at the Austenite-Martensite Interface

Continuous lattice change from f.c.c. to b.c.c. as a function of subnanometric distance is observed near the austenite-martensite interface in an Fe-Ni-Mn alloy transformed isothermally at low temperature. From detailed analysis of such lattice changes, it is concluded that the lattice deformation proposed by Kurdjumov and Sachs is the most appropriate one. The Bogers-Burgers mechanism on whit the Olson-Cohen nucleation model is based is found to he inadequate to explain the present observations.

Nonclassical Austenite-Martensite Interfaces

In the last 10 years a new theory of martensitic transformations based on nonlinear elasticity has been developed and intensively studied by J.M. Ball & R.D. James and others. Microstructures are understood in the theory as minimizing sequences for the total free energy, and are conveniently described using Young measures. For the case of the classical austenite-martensite interface, in which a pure phase of austensite meets a simple laminate of martensite, the formulae of the crystallographic theory of martensite for the orientation of the habit plane are recovered from the energy-minimization picture. The theory leads naturally to the prediction of more complex austenite-martensite interfaces, in which a pure phase of austenite meets a more complicated microstructure of martensite. The possible interfaces are computed in case that the martensite wells correspond to an orthorombic to monoclinic lattice transformation. Besides the classical interfaces, with simple laminate of martensite, new possible interfaces are presented which correspond for a larger set of lattice parameters. Then, for certain parameters, it can be concluded from the theory that possible interfaces are planes.

Hierarchical pattern formation in elastic materials

We study hierarchical structures such as branched twins in elastic materials based on a model of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential ( θ 6 model) in local strain, (2) strain gradient terms up to second order in strain and fourth-order in gradient, and (3) all symmetry-allowed compositional fluctuation-induced strain gradient terms which favor hierarchical structures and enable communication between macroscopic (cm) and microscopic (A˚) regions essential for shape memory. Below the transition temperature ( T 0 ) we obtain the conditions under which branching of twins is energetically favorable. This hierarchy of length scales provides a related hierarchy of time scales and thus the possibility of non-exponential decay. Results based on 2D simulations of the time-dependent Ginzburg-Landau (TDGL) equation are shown for twins, tweed and hierarchy formation. We also apply stability analysis to study the formation of modulated structures at early time and obtain an approximate phase diagram for the model.

High-resolution electron microscopy observations of transient lattices from fcc to bcc at the austenite martensite interface

Atomic arrangements of austenite fcc and martensite bcc near the interface in an Fe Ni Mn alloy have been observed by high-resolution electron microscopy. It is found that atom rows along the close-packed directions of two phases are completely coherent at the interface, but there exist deformed lattices which are neither fcc nor bcc. These lattices are regarded as transient lattices changing continuously from fcc to bcc lattice. By observation of these transient lattices we can deduce the lattice deformation in the fcc to bcc martensitic transformation. It is concluded that the lattice deformation proposed by Kurdjumow and Sachs is perfectly consistent with the observed atomic arrangements near the interface. The Bogers and Burgers mechanism is inadequate to explain the present observations. It is emphasized that the austenite martensite interface in the present alloy is not a monoatomic layer but has a width of about 0 7 nm in which the transient lattices are contained.

Hierarchical microstructure in structural phase transitions

Abstract We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T0) we obtain the conditions under which branching of twins is energetically favorable. Above T0 a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.