Transformation Front Research Articles

Martensite Strain Memory in the Shape Memory Alloy Nickel-Titanium Under Mechanical Cycling

This paper describes an experimental study of stress-induced martensitic phase transformation in the SMA Nickel-Titanium. The rich local thermo-mechanical interactions that underlie transformation are examined using three-dimensional Digital Image Correlation (strain fields) and infrared imaging (thermal fields). We quantify the complex local interactions between released/absorbed latent heat and the extent of transformation, and explore the characteristics of the phase fronts and the evolution of martensitic volume fraction. We also quantify a strong strain memory in the martensite that forms in the wake of the phase transformation front. The accommodated strain in the martensite will remain constant during loading, even as the existing phase front propagates. There also exists a remarkable strain memory in the martensite that persists from cycle to cycle, indicating that the local elastic stress fields in the martensite are driven by a dislocation structure and martensitic nuclei that largely stabilize during the first loading cycle.

Instabilities induced by phase transformation fronts coalescence during the phase transitions in a thin SMA layer: Mechanism and analytical descriptions

Systematic experiments on stress-induced phase transitions in slender polycrystalline SMA specimens have revealed two interesting instability phenomena: the coalescence of two phase transformation fronts (a narrow zone between the pure austenite and pure martensite regions, which is also called the domain wall or macroscopic interface) during the loading process leads to a sudden stress drop and that during the unloading process leads to a sudden stress jump. In order to get an insight into these two phenomena, we carry out an analytical study on stress-induced phase transitions in a thin SMA layer. We derive a quasi-2D model with a non-convex effective strain energy function while taking into account the rate-independent dissipation effect. By using a coupled series-asymptotic expansion method, we derive a one-dimensional effective expression for the total energy dissipation, which only involves the leading order term of the axial strain. The equilibrium equations are obtained by maximizing the total energy dissipation, which can be solved analytically under suitable boundary conditions. The instability is then modeled as the switch of the layer’s configuration from a nontrivial solution mode to the trivial solution mode. The limit-point instability criterion is adopted to determine the bifurcation point. Descriptions for the whole coalescence processes are provided, which capture the morphology varies of the specimen and the accompanying stress drop or jump. It is revealed that the zero limit of the thickness-length ratio can lead to the smooth switch of nontrivial modes to trivial modes with no stress drop or jump.

On Peritectic Reactions and Transformations in Low-Alloy Steels

Differential thermal analysis (DTA) experiments on low-alloy steels with varying C, Si, Cr, and Mo contents indicated an increase in the difference between the liquidus and peritectic temperatures during solidification with the decrease in C and increase in Mo contents. In a number of the quenched samples, massive transformations of ferrite to austenite were observed. Electron microprobe analysis of the diffusion across a massive transformation front, along with the high growth rates estimated, gives strong reason to believe that these growths are uncontrolled by diffusion. As ferrite transforms to austenite during the peritectic reaction, shrinkage in volume occurs, causing elastic straining at the interface separating the two phases. It was shown through thermodynamic analysis of the equilibrium at the triple point that the increase in energy of the two phases due to this strain can result in undercooling below the equilibrium peritectic temperature and decreases in the equilibrium peritectic concentrations.

Mixed diffusion-controlled growth of pearlite in binary steel

A kinetic theory for the diffusion-controlled growth of pearlite is presented, which accounts simultaneously for diffusion through the austenite and via the transformation front. The simplified method abandons the need for mechanical equilibrium at the phase junctions and yet is able to explain experimental data on the growth rate of pearlite. Furthermore, unlike previous analyses, the deduced value for the activation energy for the interfacial diffusion of carbon is found to be realistic when compared with corresponding data for volume diffusion.

Evolution of the martensitic transformation in shape memory alloys under high strain rates

The specific properties of the shape memory alloys are mainly due to the martensitic transformation occuring in the material when mechanical or thermal loadings are applied. Here, the effect of strain rate on the transformation on an NiTi SMA is studied in tension. Different tests were performed at different strain rates in the range of 0,0001 /s to 15 /s. Two distinct methods were used to measure the extension rate of the martensitic phase region in the specimen: digital image correlation technique and infrared thermography (IR during quasi-static tensile tests only). For the dynamic tensile tests, a Split Hopkinson Tensile Bar set-up was used with a fast camera recording at 45’000 fps. A superimposition of DIC and IR measurements in time and space can be done during quasi-static tests and results show that the temperature peak, as expected, follows the transformation front. As a consequence of the former validation of the DIC procedure, the velocity of the transformation front at high strain rate is deduced from space-time figures. As a conclusion, in the range of strain rates investigated in this paper, no strain rate sensitivity is observed for dynamics of extension of the transformation region.

Interfacial energy and dissipation in martensitic phase transformations. Part I: Theory

A model of evolving martensitic microstructures is formulated that incorporates the interfacial energy and dissipation on three different scales corresponding to the grain boundaries attained by martensite plates, the interfaces between austenite and martensite plates, and the twin interfaces within martensite plates. Three different time scales are also considered in order to clarify the meaning of rate-independent dissipation related to instabilities at more refined temporal and spatial scales. On the slowest time scale, the process of deformation and martensitic phase transformation is investigated as being composed of segments of smooth quasi-static evolution separated by sudden jumps associated with creation or annihilation of interfaces. A general evolution rule is used in the form of minimization of the incremental energy supply to the whole compound thermodynamic system, including the rate-independent dissipation. Close relationship is shown between the evolution rule and the thermodynamic condition for stability of equilibrium, with no a priori assumption on convexity of the dissipation function. It is demonstrated that the extension of the minimum principle from the first-order rates to small but finite increments requires a separate symmetry restriction imposed on the state derivative of the dissipation function. Formulae for the dissipation associated with annihilation of interfaces are proposed that exhibit limited path-independence and satisfy that symmetry requirement. By exploiting the incremental energy minimization rule with the help of the transport theorems, local propagation conditions are derived for both planar and curved phase transformation fronts. The theory serves as a basis for the algorithm for calculation of the stress-induced evolution of martensitic microstructures along with their characteristic dimensions and related hysteresis loops in shape memory alloys; the examples are given in Part II of the paper.

The carbonatation of gypsum: Pathways and pseudomorph formation

In this paper, we present an experimental study of the interaction between gypsum (010) surfaces and aqueous solutions of Na 2 CO 3 with different concentrations. This interaction leads to the carbonatation (i.e., the transformation into carbonate minerals) of gypsum crystals, which under ambient conditions shows the characteristics of a mineral replacement and leads to the formation of pseudomorphs consisting of an aggregate of calcite crystals. Carbonatation progress was monitored by scanning electron microscopy (SEM) and glancing incidence X-ray diffraction (GIXRD). The carbonatation advances from outside to inside the gypsum crystal and occurs through a sequence of reactions, which involves the dissolution of gypsum and the simultaneous crystallization of different polymorphs of CaCO 3 [amorphous calcium carbonate (ACC), vaterite, aragonite, and calcite], as well as several solvent-mediated transformations between these polymorphs. The sequence in which CaCO 3 phases form is interpreted taking into consideration nucleation kinetics and the qualitative evolution of several chemical parameters in the aqueous solution. The textural characteristics of the transformed regions are described. The degree of faithfulness of the pseudomorphs obtained is related to the kinetics of the carbonatation process, which in turn depends on the initial concentration of carbonate in the aqueous solutions. Finally, changes in the rate at which the transformation front advances are discussed on the basis of both textural and physicochemical considerations.

TIPS AND TRICKS FOR CHARACTERIZING SHAPE MEMORY ALLOY WIRE: PART 3-LOCALIZATION AND PROPAGATION PHENOMENA

This is the third paper in our series to identify unusual phenomena and to provide recommendations for the thermo-mechanical characterization of shape memory alloy (SMA) wire. Part 1 provided some basic background of the martensitic transformations responsible for the shape memory effect and superelasticity 1 . The characterization of two typical NiTi SMA alloys began with differential scanning calorimetry (DSC) thermograms to measure their respective transformation temperatures, specific heats, and latent heats of transformation. It included an experiment for each alloy showing both shape memory and superelasticity, but in different temperature regimes. Part 2 reviewed the various methods for obtaining a fundamental set of isothermal mechanical responses and provided data on the same two SMA wire alloys over their relevant temperature windows 2 . In the process, it showed stress-induced transformations, which lead to an introduction of strain localization and propagation of phase transformation fronts. In this paper(Part 3), we narrow ourfocus on certain unusual phenomena occurring during superelastic tension responses, namely localization of strain and temperature fields. These are often overlooked by the novice, yet they play an important role in the kinetics of stress-induced phase transformation, and in turn, exacerbate the material response’s sensitivities to loading rate and ambient media (which will be the subject of the next paper in this series). Here, we introduce special experimental techniques for (otherwise) difficult to measure features in the underlying material response. We focus on the superelastic response of one of the two NiTi alloys that was used in our previous articles, that is, the alloy with an Austenite finish temperature (Af) below room temperature (designated as superelastic wire). Figure 1 shows four isothermal superelastic experiments, magnified from the set of fundamental mechanical responses of Fig. 8 in 2 . Each was done on a virgin specimen under elongation control at a slow rate, ˙L =± 1 × 10 −4 s −1 , in a temperature-controlled air chamber at different Editor’s Note: This ET feature series is intended as an introduction to this exciting area of experimental mechanics. It aims to increase awareness of active materials and to promote their consistent characterization by disseminating best practices from leading researchers in the field. Each article in the series will address the characterization of one commercially significant active material. Series editors: Nilesh D. Mankame and Paul W. Alexander.

Genesis of lateritic iron ore from banded iron-formation in the Capanema mine (Minas Gerais, Brazil)

Lateritic weathering of metamorphosed Proterozoic banded iron-formation (BIF), locally named itabirite in Brazil, produced large deposits of iron ore. At the Capanema iron-ore mine in the Quadrilatero Ferrifero in Minas Gerais state (southeast Brazil), the BIF is a bedded metasedimentary rock composed essentially of layers of hematite/kenomagnetite alternating with layers of quartz. The BIF is cut by dolerite dykes. The lateritic weathering of itabirite in wet tropical conditions resulted in a well-developed weathering mantle, with a specific succession of horizons of different chemical, mineralogical and textural compositions capped by a ferruginous duricrust or canga. The lack of alumina in the itabirite and the intense leaching of silica inhibited the formation of clay minerals. However, some alumina (from the weathered dolerite) is incorporated in secondary minerals. The process of alternating dissolution and reprecipitation of Fe and Al oxides and oxy-hydroxides controls the lateritic weathering. Eight different types of goethite (I–VIII) and three types of hematite (I–III) were identified based on texture, derivation and chemistry, related to five transformation fronts that include desilication, oxides dissolution, cementation, duricrust and erosion. Mass balance of the weathering column indicates varying iron redistribution (as goethite and hematite) through the profile, with an absolute enrichment of aluminium, locally derived from weathered dolerite. This alumina appears to act as an accelerant in the lateritisation process.

Diffuse interface model for high speed cavitating underwater systems

High speed underwater systems involve many modelling and simulation difficulties related to shocks, expansion waves and evaporation fronts. Modern propulsion systems like underwater missiles also involve extra difficulties related to non-condensable high speed gas flows. Such flows involve many continuous and discontinuous waves or fronts and the difficulty is to model and compute correctly jump conditions across them, particularly in unsteady regime and in multi-dimensions. To this end a new theory has been built that considers the various transformation fronts as ‘diffuse interfaces’. Inside these diffuse interfaces relaxation effects are solved in order to reproduce the correct jump conditions. For example, an interface separating a compressible non-condensable gas and compressible water is solved as a multiphase mixture where stiff mechanical relaxation effects are solved in order to match the jump conditions of equal pressure and equal normal velocities. When an interface separates a metastable liquid and its vapor, the situation becomes more complex as jump conditions involve pressure, velocity, temperature and entropy jumps. However, the same type of multiphase mixture can be considered in the diffuse interface and stiff velocity, pressure, temperature and Gibbs free energy relaxation are used to reproduce the dynamics of such fronts and corresponding jump conditions. A general model, based on multiphase flow theory is thus built. It involves mixture energy and mixture momentum equations together with mass and volume fraction equations for each phase or constituent. For example, in high velocity flows around underwater missiles, three phases (or constituents) have to be considered: liquid, vapor and propulsion gas products. It results in a flow model with 8 partial differential equations. The model is strictly hyperbolic and involves waves speeds that vary under the degree of metastability. When none of the phase is metastable, the non-monotonic sound speed is recovered. When phase transition occurs, the sound speed decreases and phase transition fronts become expansion waves of the equilibrium system. The model is built on the basis of asymptotic analysis of a hyperbolic total non-equilibrium multiphase flow model, in the limit of stiff mechanical relaxation. Closure relations regarding heat and mass transfer are built under the examination of entropy production. The mixture equation of state (EOS) is based on energy conservation and mechanical equilibrium of the mixture. Pure phases EOS are used in the mixture EOS instead of cubic one in order to prevent loss of hyperbolicity in the spinodal zone of the phase diagram. The corresponding model is able to deal with metastable states without using Van der Waals representation. The model’s predictions are validated in multi-dimensions against experiments of high velocity projectile impact onto a liquid tank. Simulations are compared to experiments and reveal excellent quantitative agreement regarding shock and cavitation pocket dynamics as well as projectile deceleration versus time. Then model’s capabilities are illustrated for flow computations around underwater missiles.

Abrupt Softening Phenomenon in a Shape Memory CuAlNi Single Crystal under Uniaxial Compression

Abrupt softening phenomenon was observed in a shape memory CuAlNi single crystal upon uniaxial compression. Sudden martensite variant(s) reorientation was found to be the reason behind this anomalous behavior. The significance of this finding is twofold. On one hand, it clearly demonstrates that the stress induced transformation can follow a sequence of the phase transformation (martensitic transformation, austenite to martensite) and then reorientation (from one martensite variant to another). On the other hand, the anomalous softening provides a good evidence for explaining the propagation of the phase transformation front.

Non-affine deformation in microstructure selection in solids II: Elastoplastic theory for thedynamics of solid state transformations

We study the nucleation dynamics of a model solid state transformation and the criterionfor microstructure selection. Using a molecular dynamics (MD) simulation, we had shownthat the dynamics of the solid is accompanied by the creation of transient non-affine zones(NAZ), which evolve with the rapidly moving transformation front. Guided by our MDresults, we formulate a dynamical continuum theory of solid state transformation, whichcouples the elastic strain to the non-affine deformation. We demonstrate that ourelastoplastic description recovers all qualitative features of the MD simulation. Weconstruct a dynamical phase diagram for microstructure selection, including regimes wheremartensite or ferrite obtains, in addition to making several testable predictions.

Numerical solution of the diffusion equation with moving boundary applied to modelling of the austenite–ferrite phase transformation

Modelling of the austenite–ferrite phase transformation by solving a diffusion equation with a moving boundary is the main aim of this work. The particular emphasis is put on the testing, to what extent models based on solving the diffusion equation are capable to describe properly the kinetics of transformation. Mathematical and numerical models describing γ−α phase transformation for granular ferrite were created. These models are based on the solution of the second Fick law for the 1D, 2D (the circle in the circle, the regular hexagon in the regular hexagon) and 3D (the sphere in the sphere) cases. Developed models were solved using the finite difference, as well as the finite element method. Results of the numerical simulations for ferrite volume fraction f f, ferrite grain size d α, and carbon segregation before the front of transformation were compared with the experimental data.

Modelling He I–He II phase transformation in long channels containing superconductors

The problem of heat transport during sub-cooling below λ point in long, narrow channels containing superconductors immersed in liquid helium is discussed. In order to describe the propagation of phase transformation front the travelling plane wave description with suitable change of variables has been adopted. Nonlinear temperature profile corresponding to the conductivity function in He II has been assumed. The heat diffusion equation is solved in the volume of He I with the assumption that the main contribution to the specific heat is due to helium and the main contribution to longitudinal conduction is due to superconductor. For one dimensional problem with the temperatures clamped at both extremities of the channel the closed form analytical solutions for temperature profile are obtained. Channels with discontinuity in diameter are also analysed. Experimental validation of the model is based on 54 m long superconducting lines applied in the Large Hadron Collider (LHC).

Phenomenological description of thermomechanical behavior of shape memory alloy

On the basis of a thermomechanical phenomenological model, we analyze the thermomechanical behavior of polycrystalline NiTi. Pseudoelastic response and strain-temperature response under fixed stress are studied by using finite element simulation. Calculated mechanical and thermal hysteresis behaviors of NiTi sheet are in good agreement with those observed experimentally. Hardening in stress–strain hysteresis loop and sharp change of strain in strain-temperature hysteresis loop are described by numerical simulation. The result from thermomechanically coupled calculation shows the phenomenon that phase transition occurs by nucleation and propagation of transformation fronts.

Reactive transport modeling of geochemical interactions at a concrete/argillite interface, Tournemire site (France)

Mineralogical and petrographical investigations of a borehole sealed by concrete (“engineered analogue” of concrete/clay interactions) overcored at the Tournemire site offer the possibility to perform reactive transport modeling over a timescale of 15 years, which is significantly longer than standard durations of laboratory experiments. The HYTEC code was used to simulate mineralogical evolutions in the Tournemire argillite matrix and along small fractures, as well as in concrete, assuming either thermodynamic equilibrium approach or kinetic control coupled to diffusive transfer. The mineralogical profiles calculated in thermodynamic equilibrium and with kinetics are very similar in the concrete. In contrast, kinetics of dissolution and precipitation reactions is found to be necessary for a better reproduction of the experimental observations in the argillite samples compared to thermodynamic equilibrium calculations, in particular with respect to the extent of the alkaline perturbation. The major effects observed when considering kinetics in the calculations are to smooth the sharpness and intensity of the mineralogical transformation fronts, these fronts being predicted to occur deeper inside the argillite matrix (<1 cm) and the fractures (⩽2 cm), as well as to lessen clogging of pores within the argillite. At 15 °C, the secondary mineral sequence simulated from the concrete to the argillite is: CSH/ettringite/carbonates at the concrete/argillite interface, followed by a zone of neoformation of clay-like phases and calcite, and a last zone with precipitation of calcite. Main discrepancies between the modeling results and the experimental observations are the precipitation of muscovite instead of K-feldspar and the neoformation of zeolites. Calculations also correctly predict that carbonates form at the concrete/argillite interface, which most probably result from concrete alteration and follow Ostwald’s step rule of mineral precipitation with a predominance of metastable vaterite over calcite.

Kinetics of Ni3Si2 formation in the Ni2Si–NiSi thin film reaction from in situ measurements

The kinetics of Ni3Si2 formation in the Ni2Si–NiSi thin film reaction were determined from simultaneous in situ x-ray diffraction (XRD) measurements, performed using a synchrotron source, and sheet resistance measurements. Samples consisted of 90nm Ni∕100nm polycrystalline-Si∕SiO2 stacks, of interest for fully silicided gate applications, on (100) Si. After initial formation of a Ni2Si∕NiSi bilayer, these films reacted to form Ni3Si2. The evolution of sheet resistance and of the intensity of XRD peaks were used to extract the fraction of Ni3Si2 formed during ramp and isothermal annealings. A Kissinger analysis was performed for ramp annealing with ramp rates of 1, 3, 5, 9, and 27°C∕s, obtaining the activation energy of Ni3Si2 formation, Ea=1.92±0.15eV. A Kolmogorov-Johnson-Mehl-Avrami analysis was performed for isothermal anneals, finding an Avrami exponent of 2.1±0.2, suggesting two-dimensional growth. This is consistent with a nucleation controlled process for Ni3Si2 formation, with nucleation sites at different positions in the thin film, and subsequent lateral two-dimensional propagation of the transformation front parallel to the film surface. Implications for Ni fully silicided gate applications are discussed.

Thermal effects in a mechanical model for pseudoelastic behavior of NiTi wires

A mechanical model for pseudoelastic behavior of NiTi wires is proposed with the aim to predict the behavior of Shape Memory Alloys(SMA) damping wire elements in model structures. We have considered at first a simple linearwise stress-strain relationship to describe the basic isothermal behavior of the SMA members. Then, this basic model is modified in order to include the effect of the strain rate. The model is based on detailed experimental characterization performed on a Ni rich NiTi superelastic wire which included the study of the localized character of the deformation and the local heat generation associated with the stress induced martensitic transformation occurring in these alloys. Heat conduction along the wire and heat interaction with the surroundings was also considered. In that way, the resulting local temperature field around the transformation front is assessed and its effect on the progression of the transformation is evaluated. It is shown how the simple mechanical model reproduces the global mechanical behavior, including the existence of a maximum in the damping capacity with the transformation rate.

Cryocrystallization during preparation of ferrites by cryochemical technology

Characteristics are considered for material prepared by cryochemical technology connected with its thermal conductivity and heat capacity, i.e., heat penetration coefficient. It is concluded that for rapidly occurring solidification it is desirable to use in calculations not the temperature of the cooling medium or substrate, but the contact temperature of interacting media, and this increases calculation accuracy. The effect of cooling rate with evaporation freezing of aqueous salt solutions of nickel, zinc, manganese and iron sulfate systems that are the starting material in the production of Ni-Zn and Mn-Zn ferrites, and also the properties of the salt and oxide powders obtained are studied. It is shown that under these conditions an effect arises of concentration supercooling of liquid, i.e., formation close to the phase transformation front of a region of supersaturated and supercooled solution that gives rise to loss of stability for the phase interface. The effect of cooling rate and frequency on material fineness and microstructure is analyzed. Features are demonstrated of solidification in a vacuum compared with other freezing methods.

The influence of lattice strain on pearlite formation in Fe–C

The effect of stress and strain on the transformation kinetics of pearlite is investigated by phase-field simulation. Strain is considered in terms of expansion/contraction during transformation and due to concentration gradients in austenite. It is demonstrated that due to the concentration dependence of the eigenstrain, an inhomogeneous stress distribution ahead of the transformation front enhances diffusion in the austenitic phase and reduces chemical supersaturation in both austenite and ferrite. The main result of the investigation is that transformation strain inhibits the cooperative growth mode of cementite and ferrite, as considered by the Zener–Hillert model, and provokes the salient growth of cementite needles ahead of the ferrite front, which we call “staggered growth”. The predicted growth velocities give the right order of magnitude compared to the experiment and close the gap between theoretical models based on diffusion only, and experimental observations.