Austenite-martensite Interface Research Articles

Austenite-martensite interfacial patterns and energy dissipation of phase transformation in Ni-Mn-Ga single crystal

The martensitic phase transformation occurs in Shape Memory Alloys (SMA) via the nucleation/propagation of the Austenite-Martensite interface (A-M interface), which is a transition region (domain) between the two coexisting phases. For providing compatibility, the transition region consists of various martensitic twin structures (laminates), forming different interfacial patterns, such as parallel laminates and branching laminates. Due to the energy accumulation in the interfacial structures (e.g., elastic mismatch and twin-boundary surface energy), the interfacial patterns should be relevant to the driving force (energy dissipation) and the associated kinetics of the phase transformation. In this paper, we adopt a special thermal loading, small-temperature-gradient “heating-cooling-reheating”, to control the A-M interface's forward and reverse propagation to generate different interfacial patterns in a Ni-Mn-Ga single crystal SMA with the observation on the twin structures (by optical microscope and SEM) and the InfraRed measurement on the temperature hysteresis of the interface propagation (for characterizing the thermal driving force). Simple energetic analysis indicates that the thermal driving force (energy dissipation) is directly related to the stored energy in the interfacial structure, particularly the large mismatch elastic energy near the habit plane. This study not only provides the details of the various interfacial patterns and their dependence on the loading path, but also indicates the driving force and the associated mechanism about the pattern evolution to understand the phase transformation process.

A three-dimensional phase-field model for studying the orientation-dependent interface evolution in stress-induced martensitic phase transformation

In this study, we address the challenging task of predicting the motion of interfaces in stress-driven martensitic phase transformations within shape memory alloys. The novelty of our approach lies in the introduction of a monolithically solved thermodynamic-based phase-field method, specifically tailored for large strain conditions at the nanoscale for three-dimensional problems. To achieve this, we have developed a custom finite element software seamlessly integrated into the FEniCS open-source framework, providing a sophisticated and efficient tool for the examination of nanostructure evolution. Our investigation delves into five distinct and complex scenarios under diverse loading conditions for two– and three-dimensional problems, each presenting unique challenges: (i) a straightforward uniaxial tension scenario featuring a square domain with a pre-existing martensitic nucleus; (ii) the evolution of interfaces in a square sample incorporating a circular central nanovoid under biaxial tensile stress; (iii) the analysis of a rectangular beam subjected to horizontal and vertical compressive loads; (iv) the assessment of an initially voided rectangular beam experiencing mixed loading conditions; and (v) the three-dimensional simulations of cubic-to-tetragonal phase transformation using various orientation of the habit plane. In contrast to prior studies, our analysis not only explores the standard factors of habit plane reorientation and strain transformation values but also delves into the impact of nanovoids on austenite–martensite interface evolution.

Characterization on thermal hysteresis of shape memory alloys via macroscopic interface propagation

A specimen of Shape Memory Alloy (SMA) starts martensitic phase transformation normally by the nucleation of a macroscopic austenite-martensite interface at the specimen's boundary (i.e., the nucleation is sensitive to boundary conditions). By contrast, the interface propagation only needs to overcome the energy barrier of the incompatibility between the austenite and martensite phases (i.e., the interface-propagation driving force reflects material's intrinsic properties). In this paper, we observe the thermally induced forward and reverse quasi-static propagation of the macroscopic austenite-martensite interface in a Ni-Mn-Ga single-crystal bar. It is found that the temperature difference between the forward and reverse propagation is only 2.8 °C, which is obviously less than the thermal hysteresis evaluated from Differential Scanning Calorimetry measurement (6.3 °C) on the same material. This result not only gives a better characterization of the thermal hysteresis of the phase transformation, but also helps deeply understand the relation between the phase-transformation kinetics and the microstructures of the macroscopic austenite-martensite interface.

Uncovering the isothermal transformation dynamics and elemental diffusion behavior of reversed austenite in PH13-8Mo steel

The isothermal transformation kinetics and microstructural evolution of the reversed austenite significantly influence the properties of PH13-8Mo steel. However, the microscopic phase transformation behavior related to elemental diffusion during isothermal processes for PH13-8Mo steel needs further examination. Herein, we systematically investigate the isothermal transformation and elemental diffusion behavior of reversed austenite in PH13-8Mo steel. Phase transformation kinetic measurements unravel that the complete elimination of residual austenite can be achieved. Only hierarchical martensitic microstructure without austenite is detected after the solution-cooling treatment at 927 °C with a cooling rate of 10 °C/s, determining the critical martensite transformation start and finish temperature to be 176.6 °C, 11.6 °C. The isothermal kinetics of reverted austenite satisfy the Johnson-Mehl-Avrami relationship. The fraction of reversed austenite increases from 0.14 % at 510 °C to 8.73 % at 593 °C. Lath martensite boundaries with large kernel average misorientation values promote elemental diffusion at the interface. Further, the underlying behavior of elemental diffusion is elucidated during the isothermal aging process. The interfacial model indicates the growing width of the reversed austenite up to 100 nm and the compositional gradient formed by the elemental diffusion during aging for 0–5 h at 593 °C. The interdiffusion coefficient calculations interpret the diffusion direction of alloying element Ni from martensite to reversed austenite; Cr and Mo may form alloying carbides at the austenite-martensite interface; Al possesses the fastest diffusivity in martensite and austenite phases. The present work unveils the phase transformation kinetics of PH13-8Mo steel, achieving quantitative regulation for maraging stainless steel.

Coexistence of five domains at single propagating interface in single-crystal Ni[sbnd]Mn[sbnd]Ga shape memory alloy

Coexistence of both austenite and martensite during phase transformation is a common feature of all Shape Memory Alloys (SMAs). The martensite has different variants featuring characteristic deformations rotationally linked to each other due to the symmetries of the austenite parent phase, and the martensite variants can form twins with different mean characteristic deformations. Multiple-domain microstructures (consisting of austenite, martensite twins and individual martensite variants) evolve collectively within an SMA sample during the phase transformation, contributing thus to the material's macroscopic response (e.g., its global deformation). Particularly, the multiple domains can exist at the diffuse austenite-martensite interface nucleating and propagating in a single crystal in certain conditions. This implies an energy barrier for this interfacial structure, influencing the interface kinetics and the driving force (energy dissipation) of the phase transformation. In this paper, we report an experimentally observed interface consisting of five domains (austenite, one martensite variant and three twins) in a Ni–Mn–Ga single-crystal initially consisting of one martensite variant and subjected to a uniaxial thermal gradient. The compatibility analysis (performed from the characteristic strains of the three martensite variants having approximately a tetragonal symmetry) reveals that the five-domain interface is not a perfectly compatible pattern like the basic habit plane (consisting of only one twin compatible with austenite). However, its level of non-compatibility is similar to that of the quite common X-interface (four-domain coexistence) which is observed in many SMAs. Further, the significant effects of the thermal loading path and the material initial state (the initial martensite variant) on the domain pattern formation are demonstrated and analyzed. The experimental observation and the theoretical analysis of the domain patterns can provide hints to better understand diffuse interface kinetics and phase transformation hysteresis.

Microstructural mechanisms of hysteresis and transformation width in NiTi alloy from molecular dynamics simulations

Martensitic transformations in shape memory alloys are often accompanied by thermal hysteresis, and engineering this property is of prime scientific interest. The martensitic transformation can be characterized as thermoelastic, where the extent of the transformation is determined by a balance between thermodynamic driving force and stored elastic energy. Here we used molecular dynamics simulations of the NiTi alloy to explore hysteresis-inducing mechanisms and thermoelastic behavior by progressively increasing microstructural constraints from single crystals to bi-crystals to polycrystals. In defect-free single crystals, the austenite-martensite interface moves unimpeded with a high velocity. In bi-crystals, grain boundaries act as significant obstacles to the transformation and produce hysteresis by requiring additional nucleation events. In polycrystals, the transformation is further limited by the thermoelastic balance. The stored elastic energy can be converted to mechanisms of non-elastic strain accommodation, which also produce hysteresis. We further demonstrated that the thermoelastic behavior can be controlled by adjusting microstructural constraints.

Duplex and graded austenitic-to-martensitic steels by powder metallurgy: Interface diffusion and strength composite effect

Versatility of powder metallurgy was used to design new duplex and compositionally graded steels. Rapid consolidation by Spark Plasma Sintering (SPS) and longer consolidation by Hot Isostatic Pressing (HIP) were applied on two austenitic 316L and martensitic Fe-9Cr powders, either homogeneously blended or uniaxially graded before sintering.The microstructural investigations by micro-hardness, SEM, EDX and EBSD showed a continuous crystallographic structure at the austenite–martensite interface and a similar grain size in SPS and HIP samples, whereas a larger interdiffusion length of Cr and Ni was observed in the HIP sample, as confirmed by diffusion calculations. The tensile behaviour of materials could not be described by a simple law of mixtures. To better understand this phenomenon, the obtained materials were described as a composite and iso-strain and iso-stress models were used and discussed. The microstructural characterizations show that during the consolidation, diffusion of the chemical species modifies the nature and the respective fractions of phases, which explains the discrepancy between the models and the experimental mechanical behaviour of the duplex alloys.

Tension-compression asymmetric functional degeneration of super-elastic NiTi shape memory alloy: Experimental observation and multiscale constitutive model

The functional degeneration of super-elastic NiTi shape memory alloy (SMA) rods is investigated in the cyclic tension-unloading and compression-unloading experiments. The results show that the functional degeneration exhibits a strong tension–compression asymmetry, which originates from the initial 〈111〉 and 〈110〉 mixed textures along the axial direction of the rods, the polarity of martensite transformation, and the complex interaction between martensite transformation and dislocation slipping. Moreover, the dependence of functional degeneration on the applied stress level is discussed. To understand and predict the effect of initial texture on the cyclic deformation of polycrystalline NiTi SMA, a multiscale constitutive model is constructed at finite deformation. At the mesoscopic scale, two major inelastic deformation mechanisms, i.e., the transformation between austenite and martensite phases and the transformation-induced plasticity caused by the strain mismatch at the austenite–martensite interface, are considered. The total deformation gradient is multiplicatively decomposed into the martensite transformation, transformation-induced plasticity and elastic parts. The deformation gradient parts at the mesoscopic scale are obtained by upscaling these physical quantities at a smaller spatial scale (i.e., the microscopic scale). The proposed model is formulated within the framework of irreversible thermodynamics. The driving forces for martensite transformation and transformation-induced plasticity are derived according to the established Helmholtz free energy and Clausius-Duhem inequality. The complex interaction between martensite transformation and dislocation slipping, and the forward/reverse inheritance of dislocations caused by the moving austenite–martensite interfaces are considered. To calculate the overall cyclic responses of polycrystalline NiTi SMA at the macroscopic scale, the developed constitutive model is implemented into the finite element software ABAQUS/Explicit using a user-defined material subroutine. A polycrystalline representative volume element is constructed by introducing the initial 〈111〉 and 〈110〉 mixed textures observed in the experiment. By comparing the simulated results with the experimental data, the capability of the proposed model to predict the texture-induced tension–compression asymmetric functional degeneration is verified, and the influence of texture type on the cyclic deformation is discussed.

Fatigue and fracture of shape memory alloys in the nanoscale: An in-situ TEM study

This study is aimed at demonstrating the fatigue and fracture mechanisms in nanoscale NiTi shape memory alloy thin films. During functional fatigue, permanent strains are attributed to residual martensite pinned by Ni4Ti3 precipitates and interfacial dislocations parallel to type II internal twins of the martensite. These residual martensite-austenite interfaces acted as heterogeneous nucleation sites for stress-induced martensite in subsequent cycles thereby explaining the reduction in transformation stress. Finally, structural failure was observed to occur along the dislocation-rich austenite-martensite interface, making it the weakest link in the microstructure thus establishing a direct link between mechanisms of functional fatigue that result in the accumulation of permenant strain and mechanisms of structural fatigue that result in fracture. This work provides a comprehensive understanding of deformation mechanisms in nanoscale shape memory alloys and points to fundamental mechanisms that are applicable to macro scales.

A micromechanical constitutive model of high-temperature shape memory alloys

In this work, a new micromechanical constitutive model is constructed for high-temperature shape memory alloys. Different from the classical constitutive models, the microstructural patterns, heterogeneities of stress and strain fields at the microscopic scale are addressed. In the proposed model, three different inelastic deformation mechanisms, i.e., reversible martensitic transformation, irreversible transformation-induced plasticity, viscoplasticity, as well as their complex interactions, are considered. In addition to the well-known austenite and martensite phases, a new austenite-martensite interface phase is introduced to address the high local stress induced by the martensitic transformation. The modified Mori-Tanaka's homogenization scheme and Hill's interfacial operator are employed to determine the non-uniform stress fields of the three phases. To satisfy the thermodynamic compatibility of the proposed model, the driving forces and evolution equations of the three inelastic deformation mechanisms are derived based on the constructed Helmholtz free energy and the fundamental laws of irreversible thermodynamics. Inheritances of the plastic deformation induced by moving austenite-martensite (A-M) interface during repeated martensitic transformation and its reverse are incorporated. Temperature evolution caused by internal heat production and heat exchange with the ambient medium is also addressed. To validate the capability of the new constructed model, the predicted results of creep behavior and stress-assisted two-way shape memory effect of NiTiPd high-temperature shape memory alloys are compared with the experimental ones. The proposed model provides a theoretical tool for simultaneously analyzing the deformation behaviors at the macroscopic scale and underlying mechanisms at the microscopic scale.

Investigating the effect of nanovoid inelastic surface stress and the austenite–martensite interface inelastic stress on the martensitic growth at the nanovoid surface

Investigating the effect of nanovoid inelastic surface stress and the austenite–martensite interface inelastic stress on the martensitic growth at the nanovoid surface

Molecular dynamics simulations of austenite-martensite interface migration in NiTi alloy

The mechanism of austenite-martensite interface migration is a key component in understanding the phase transformations in shape memory alloys. It is also intimately tied to their observed hysteresis. Molecular dynamics simulations offer a unique capability to study phase transformations in detail, however, their associated timescales prevent the observation of interface formation via nucleation and growth near the transformation temperature. To address this challenge, we present a simulation methodology in which steady-state austenite-martensite interfaces are allowed to form close to equilibrium. The resulting structures contain well-defined interfaces which can be perturbed from equilibrium to study their migration. In NiTi specifically, the austenite-martensite interfaces are semicoherent, made up of terrace planes separated by structural disconnections. The disconnections advance via kink pairs and provide an atomic-scale mechanism for interface migration. The methodology and results presented here provide a foundation toward further leveraging molecular dynamics simulations to better understand how the atomic-scale structure of austenite-martensite interfaces impacts macroscopic properties such as hysteresis in shape memory alloys.

Concentration of transformation-induced plasticity in pseudoelastic NiTi shape memory alloys: Insight from austenite–martensite interface instability

Transformation-induced plasticity (TRIP) in pseudoelastic polycrystalline NiTi shape memory alloys (SMAs) is investigated through tensile tests combined with in-situ infrared and digital image correlation (DIC) observations, and a new TRIP concentration phenomenon is revealed. To this end, an instability evolution model for solid–solid phase transformation is established to explain the multi-scale mechanisms of TRIP in SMAs. It is shown that, during the stress-induced transformation, the local stress at the grain scale evolves discontinuously inside austenite–martensite mixtures, presenting the maximum magnitude at the austenite side of the transformation interfaces. This local stress field triggers TRIP although the macroscopic stress still evolves “smoothly” with a relatively low magnitude. As the temperature increases, a further plasticity in austenite is required to lower the discontinuity at the austenite–martensite interfaces. Due to the accumulation of the heat generated in transformed regions, the temperature at the moving transformation interface continuously increases till reaching the maximum at the end of the transformation. Therefore, TRIP is concentrated at the final transformation band fronts, manifesting as concentration peaks in the residual strain map. The concentration of TRIP also shows a strong rate/frequency dependence: when the loading rate increases, TRIP accumulates to a higher average density throughout the transformation region while the concentration is significantly relieved.

Hysteresis effect on austenite-martensite interface in Ni-Mn-Ga single crystal

The experiments on Ni-Mn-Ga single crystal shape memory alloy under a heating-cooling cycle demonstrate that the automatically generated twin laminate structure of the compatible austenite-martensite interface in the forward martensitic phase transition is significantly different from that in the reverse phase transition, even though the temperature hysteresis is small (As−Ms around 4 °C). Moreover, after the cooling-induced austenite → martensite transition, the remaining twin laminate is so fine (layer width around 1 μm) that the neighbouring twin boundaries merge with each other and disappear, making the fine twin laminate evolve into a single martensite variant (i.e., spontaneous detwinning). These observations provide insights into the relation between the hysteresis (phase-transition driving forces), austenite-martensite interface, and the basic material parameters such as twin boundary energy and softening modulus during the phase transition.

Growth Detection of Martensite-Austenite Interface by Magnetic Barkhausen Noise Technique

Growth Detection of Martensite-Austenite Interface by Magnetic Barkhausen Noise Technique

Asymptotic Self-Similarity of Minimizers and Local Bounds in a Model of Shape-Memory Alloys

We prove that microstructures in shape-memory alloys have a self-similar refinement pattern close to austenite-martensite interfaces, working within the scalar Kohn-Müller model. The latter is based on nonlinear elasticity and includes a singular perturbation representing the energy of the interfaces between martensitic variants. Our results include the case of low-hysteresis materials in which one variant has a small volume fraction. Precisely, we prove asymptotic self-similarity in the sense of strong convergence of blow-ups around points at the austenite-martensite interface. Key ingredients in the proof are pointwise estimates and local energy bounds. This generalizes previous results by one of us to various boundary conditions, arbitrary rectangular domains, and arbitrary volume fractions of the martensitic variants, including the regime in which the energy scales as varepsilon ^{2/3} as well as the one where the energy scales as varepsilon ^{1/2}.

A finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in NiTi single crystals

A 3D finite-strain constitutive model for the deformation response of NiTi at the single crystal level is proposed. The model accounts for reversible phase transformation from austenite to martensite habit plane variants, plastic deformation in the austenite phase, and rate effects induced from latent heat. It is developed within the formalism of irreversible thermodynamics with internal state variables based on the Eulerian logarithmic strain and its corrotational objective rate. The inelastic deformation is defined as an average over a representative volume element as classical in the micromechanics-based modeling approach. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite–martensite interface. It is accounted for by introducing an interaction term in the free energy, which is described through the Eshelby tensor by regarding the habit plane variants as ellipsoidal inclusions embedded in the austenite matrix, in order to accurately reflect the internal stress states that contribute to dislocation slipping. The numerical implementation of the model in an efficient scheme and its calibration are described in detail. The proposed model is validated by comparing simulations with available experimental data in single NiTi crystals. Numerical simulations of polycrystals are performed to obtain an insight into the interaction between phase transformation and plastic deformation induced by intergrannular constraints. The efficiency of the numerical implementation of the model is verified by simulations of indentation tests.

Magnetic Domain Structure Across the Austenite-Martensite Interface in Ni50Mn25Ga20Fe5  Single Crystalline Thin Foil by Lorentz Microscopy

The magnetic domain structure (MDS) at martensite transformation interface is relevant for complete understanding of functionalities in magnetic shape memory alloys. We study the MDS in Ni50Mn25Ga20Fe5 single crystalline foil using Lorentz transmission electron microscopy. The austenite-martensite interface is stabilized by decreasing foil thickness at the thickness of about 40 nm. The martensite in thicker region contains no twin domains and exhibits dense labyrinth MDS with magnetization out of plane. The austenite in thinner region exhibits broad magnetic domains with magnetization in plane. Within the interface region, these two distinct MDSs interpenetrate to each other, with labyrinth MDS of martensite gradually changing to broad magnetic domains of austenite. The changes from dense to broad domains do not follow exactly the underlying phase changes but occur on antiphase boundaries, revealing their role in the overall MDS formation and potential to decrease the transformation thermal hysteresis.

Explicit nonlinear finite element approach to the Lagrangian-based coupled phase field and elasticity equations for nanoscale thermal- and stress-induced martensitic transformations

In this paper, a nonlinear finite element procedure is developed to solve the coupled system of phase field and elasticity equations at large strains for martensitic phase transformations at the nanoscale. The transformation is defined based on an order parameter which varies between 0 for austenite to one for martensite. The phase field equation relates the rate of change of the order parameter to the Helmholtz free energy. Both the Helmholtz free energy and the transformational strain tensor depend on the order parameter, and the coupling between the phase field and elasticity equations occurs due to the presence of elastic energy in the Helmholtz free energy and the transformational strain in the total strain. The deformation gradient tensor is introduced as a multiplicative decomposition of elastic and transformational gradient tensors. A staggered strategy is used to solve the coupled system of equations so that first, the principle of virtual work is utilized to obtain the integral form of the Lagrangian equation of motion. It is then discretized and solved using the Newton–Raphson method which gives the displacements and consequently, the deformation gradient tensor. Next, since the order parameter is obtained from the phase field equation from the previous time step, the elastic deformation gradient tensor and the first Piola–Kirchhoff stress can be calculated and substituted in the phase field equation to find the order parameter for the current time step. The weighted residuals method is used to derive the finite element form of the phase field equation and the explicit method is used for its time discretization. The finite element procedure is well verified by comparing the obtained results with those from other simulations. Examples of thermal- and stress-induced phase transformations are presented, including austenite–martensite interface propagation and growth of preexisting martensitic regions. The developed algorithm and code can be advanced to solve kinetic problems coupled with mechanics at large strains for phase transformations and similar phenomena at the nanoscale.

Elastocaloric effect in bamboo-grained Cu71.1Al17.2Mn11.7 microwires

Bamboo-grained Cu71.1Al17.2Mn11.7 microwires with diameter ∼150 μm were created by Taylor-Ulitovsky method and subsequent annealing. The grain architecture dependent superelasticity (SE) and elastocaloric effects (eCE) were confirmed. The bamboo-grained microwires exhibited low stress hysteresis loss during SE due to the reduced constraints caused by grain boundary, which is favorable for the mobility of martensite-austenite interface. Consequently, a large isothermal entropy change ∼21 J/kg K with a wide temperature range 90 K was achieved. The produced adiabatic temperature change (ΔTad) reached −11.9 K under a maximum stress 400 MPa. A stable ΔTad of −5.6 K showing little degradation in 200 eCE cycles was found with applied stress 325 MPa. This work reveals a fact that the bamboo-grained Cu–Al–Mn microwire may act as a desirable material for miniature solid-state refrigeration devices.