Stress-induced Martensitic Phase Transformation Research Articles

Thermodynamic rationale for transformation-induced dislocations in shape memory alloys

Shape Memory Alloys (SMAs) undergo stress-induced martensitic phase-transformation affording a “superelastic” behavior with functional applications. Such behavior is undermined by the formation and accumulation of irreversible residual strains in each cycle. These residual strains arise from transformation-induced dislocation-emission and current understanding has postulated the microstructural role of emitted dislocations to accommodate lattice-mismatch while also observing a preference to occur during reverse-transformation. This study develops a thermodynamic framework to offer a causal explanation for dislocation-emission from Gibbs’ free energy considerations. Superelastic stress-strain curves for a reversible pathway without emitted-dislocations and for an irreversible pathway with emitted-dislocations are derived. The role of emitted-strain in relaxing the transformation-strain of the martensitic-inclusion and in accruing residual strain is proposed. It is shown that both pathways obey the first law of thermodynamics but it is the second law of thermodynamics that dictates the path preference. It is shown that the irreversible path achieves the critical condition for spontaneous reverse-transformation at a higher stress-level than the reversible path. Thus, the irreversible pathway initiates earlier during unloading and is thermodynamically selected during reverse-transformation. The driving-forces associated with the irreversible pathway are analyzed to establish the cause of emitted-dislocations and why it is thermodynamically preferred despite offering a higher lattice-friction barrier. Consequently, a new approach to target fatigue-resistant SMA properties is offered, focusing on the interplay of the individual driving-forces coming from the elastic strain-energy, work-interaction, and lattice-friction, as revealed by the thermodynamic framework.

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.

Interrelationships of stress-induced martensitic phase transformation and pitting corrosion in iron-based shape memory alloys

Orientation dependence of stress-induced martensitic transformation under compression and the influence of a corrosion attack on superelastic properties were investigated for Fe42.7Mn34.7Al13.4Ni7.7Cr1.5 (at.−%) single crystals. The results of incremental strain tests show that the crystallographic orientation has a considerable impact on the superelastic performance, eventually resulting from the formation of twinned or detwinned martensite to accommodate strain as well martensite variant interaction. In order to investigate the effect of a corrosive environment on the mechanical performance and martensitic transformation, compression specimens were immersed in a 5.0 wt.−% NaCl solution for 24 h before tested in incremental strain tests. The immersion of the compression specimens revealed a partial surface corrosion attack including localized pitting corrosion. The localized corrosion attack increased the number of active martensite plates, most probably due to an induced multiaxial stress state. Further investigations on specimens subjected to −6% compressive strain revealed that areas with retransformed martensite serve as nucleation zones for corrosion damage. Stress-induced corrosion cracks developed, which eventually deteriorate functional response.

Cryogenic temperature deformation behavior and shape memory mechanism of NiTiFe alloy

The excellent shape memory properties of NiTiFe alloys make them a popular choice for tube connection components and actuators in the aerospace industry. However, in order to obtain these properties, the alloy must undergo pre-deformation at specific cryogenic temperatures to induce the martensitic phase transformation. Despite their widespread use, the deformation behavior and shape memory mechanism of NiTiFe alloys at cryogenic temperatures remain unclear. To address this, we conducted a study investigating the deformation behavior and shape memory mechanism of Ni47Ti50Fe3 alloy at temperatures ranging from −190 °C to 150 °C using tensile tests, free recovery tests, and EBSD analysis. Our findings suggest that the deformation behavior of NiTiFe alloy can be classified into four classes corresponding to different deformation mechanisms. At temperatures above the Md (−15 to −30 °C), dislocation slip and {114}B2 deformation twinning occur without reversible strain. However, reversible and irreversible strains occur simultaneously at temperatures between −50 to −90 °C. At temperatures ranging from −110 to −150 °C, the reorientation/detwinning of the R-phase, stress-induced martensitic phase transformation, and yield stage of martensite occur in sequence. When the deformation temperature is within the range of −165–190 °C, the reorientation/detwinning of martensite occurs during the stress platform stage, and irreversible strain occurs during the yield stage of martensite. The best shape memory effect of the NiTiFe alloy is observed at deformation temperatures near Mf (−180 °C). Moreover, the reverse phase transformation temperatures increase with the increasing deformation amounts, even without plastic deformation. The temperature-dependent deformation map of NiTiFe alloy was obtained based on the tests conducted in this study, from which the influence of deformation temperatures on the different critical stresses and the deformation mechanism under different temperature conditions can be determined.

An interatomic potential for ternary NiTiHf shape memory alloys based on modified embedded atom method

NiTi-based high temperature shape memory alloys (HTSMAs) can operate in high temperature applications, where binary NiTi cannot function. NiTiHf is among the most popular HTSMAs due to its lower preparation cost and good thermal stability. Various aspects of material properties of NiTiHf and the effect of different factors, such as composition, heat treatment and precipitates, on its behavior is yet to be understood. Molecular dynamics (MD) simulations can provide insights to acquire such an understanding. However, MD simulations of NiTiHf have not been possible due to the absence of a reliable interatomic potential, which is a necessary tool for such simulations. In this study, density functional theory (DFT) simulations were employed and a ternary Second Nearest Neighbor Modified Embedded Atom Method (2NN MEAM) potential was calibrated for NiTiHf. To perform this study, the related unary and binary potentials were calibrated by fitting the values of their reproduced physical properties to the DFT results. The final ternary MEAM potential was checked for reliability and transferability by performing MD simulations. The results showed that the developed potential can appropriately capture the temperature-induced and stress-induced martensitic phase transformations in NiTiHf.

Excellent damping properties and their correlations with the microstructures in the NiTi alloys fabricated by laser-directed energy deposition

The NiTi alloys have superior damping properties, which mainly originate from the stress-induced martensite phase transformations. The stress-induced martensite phase transformation can be improved by the intrinsic Ni4Ti3 precipitation in the NiTi alloys fabricated by laser-directed energy deposition (L-DED), making L-DED a promising method for fabrication of NiTi alloys. Reported investigations on L-DED of NiTi alloys focus on their microstructural features and phase transformation properties. There are no investigations on the damping properties of the NiTi alloys fabricated by L-DED. For the first time, NiTi alloys with excellent damping properties are in-situ synthesized by L-DED, in this paper. The processing parameters are optimized to fabricate NiTi alloys with relatively uniform distributions of small-sized Ni4Ti3 precipitates, which will benefit the damping properties. Dynamic mechanical analysis (DMA) tests were utilized to quantify the damping properties of the NiTi alloys in in two oscillation modes (loading mode and creeping mode) according to the different load conditions in industrial applications. Experimental results show that the damping ratios are in a range of 0.02–0.2, which is comparable or larger than the values of the NiTi alloys fabricated with more complex structures or fabricated using more complex methods. It can be concluded that L-DED can be a promising method to fabricate NiTi alloys without the need for additional post-processing methods. Besides, the correlations between the superior damping properties with the microstructures are discussed.

Role of point defects in stress-induced martensite transformations in NiTi shape memory alloys: A molecular dynamics study

Shape-memory properties of equiatomic NiTi rely on the thermal- or stress-induced reversible martensitic phase transformation between the $B2$ and $B{19}^{\ensuremath{'}}$ phases. Irradiation defects suppress thermal-induced transformations, but their effects on stress-induced transformations are poorly understood. We use molecular dynamics to investigate the effect of vacancies, vacancy clusters, interstitials, and antisite defects on stress-induced transformations. All defects suppress the transformation, but vacancy clusters do so to the greatest extent, while antisite defects do so to the least extent. The responsible mechanisms are grain boundary pinning and chemical disordering.

Effects of ambient temperature on cyclic response and functional fatigue of shape memory alloy cables

In this paper, the effects of ambient temperature on the tensile response and superelastic fatigue behavior of the shape memory alloy (SMA) cable are investigated. The tested SMA cable is made of Nickel–Titanium and has an outer diameter of 8 mm with a 7 × 7 configuration. The SMA cables are subjected to an incrementally increasing loading protocol up to 14% strain amplitude under ambient temperatures varying from −20 °C to 60 °C. The effects of deformation amplitude and test temperature on stress-induced martensitic phase transformations are assessed. SMA cable specimens are also subjected to cyclic loading at a constant strain amplitude of 6% up to 1000 loading cycles at different test temperatures. The evolution of superelastic response with loading cycles is revealed by analyzing the maximum stress, residual deformation, hysteretic energy, and equivalent viscous damping ratio extracted from hysteretic curves. The results indicate that the ambient temperature considerably alters the superelastic behavior of SMA cables by shifting the stress-strain loops upward and narrowing them. When the ambient temperature is close to the reverse phase transformation temperature, the superelastic response degrades more progressively with both increasing loading amplitude and number of loading cycles. The least degradation in functional properties of SMAs takes place when the cable is tested at a temperature close to its austenitic transformation finish temperature, while increasing temperature decreases low cycle fatigue life of SMA cables when it is deformed up to the end of phase transformation. Overall, it is important to consider this temperature dependent response of SMA cables in applications where the cables will be subjected to varying outdoor temperatures.

Uncovering the role of nanoscale precipitates on martensitic transformation and superelasticity

We characterize the role of coherent nanoscale B2 Ni50Al50 precipitates on the temperature- and stress-induced martensitic phase transformation in nanocrystalline Ni63Al37 shape memory alloys using multi-million-atoms molecular dynamics (MD) simulations. We studied two types of precipitates: one with single crystal precipitates (SXP) and a second where grain boundaries cut through precipitates (PXP). Simulations reveal that the presence of B2 precipitates stabilizes the cyclic flag-shaped stress-strain response, characteristic of superelasticity, and reduces remnant strain. In contrast, single-phase nanocrystalline Ni63Al37 exhibits degradation of the reverse transformation during cyclic loading and, eventually, incomplete reversible transformation within a few cycles. This is consistent with previous experimental findings of ultra-low fatigue in Ni-Ti-Cu alloys with Ti2Cu precipitates. The simulations reveal that the presence of precipitates significantly improves the reversibility of the transformation by acting as elastic zones that partially shield the martensitic transformation and drive the reverse transformation. A detailed analysis of the MD trajectories reveals that the martensitic transformation of the matrix induces ultra-large elastic deformation in some of the B2 precipitates (approximately 12%) to the point of resulting in a martensite-like atomic structure.

Design of metastable β-Ti alloys with enhanced mechanical properties by coupling αS precipitation strengthening and TRIP effect

A strain-transformable microstructure was successfully designed in a metastable β Ti–7Mo–3Nb–3Cr–3Al alloy with enhanced mechanical properties, by introducing ∼28% α precipitates coupled with the TRIP effect, overcoming the traditional trade-off dilemma between strength and ductility in most metastable β-Ti alloys. The as-designed lamellar microstructure was predominantly deformed by stress-induced martensitic (SIM α") phase transformations, martensitic twinning and dislocation slip of the parent β grains and α laths. The β→α" transformation followed the [113]β//[112]α"//[-310]α"//[1-21]α" orientation relationship, with the {133}β habit plane predicted by the Phenomenological Theory of Martensite Crystallography (PTMC). A novel <211>α" type II martensitic twinning mode was also found, in addition to the {111}α" type I mode at SIM α"/α impinging region. The results show that, not only the lamellar α precipitates play a major role in precipitation strengthening, but they can also effectively block SIM α" propagation at the initial stages of deformation. However, SIM α" transmission across the α laths was also observed for large strains. Moreover, <c+a> pyramidal slip and shear of the α laths also contributed to the accommodation of internal stresses. Therefore, the origin of the enhanced tensile mechanical properties can be attributed to the combined effects of α precipitation strengthening coupled with the TRIP softening effect and the extra interaction stresses introduced by the α laths and other deformation products, validating the design concept. The current investigation may provide a novel strategy for designing new high-performance metastable β-Ti alloys.

A unique three-stage dependence of yielding behavior and strain-hardening ability in Ti-10V-2Fe-3Al alloy on phase fraction

Ti-10V-2Fe-3Al alloy represents one of the most widely adopted metastable β titanium alloys, the mechanical properties of which were influenced by several factors, including the grain size, phase fraction, precipitates, etc. In this study, we systematically investigated the effect of phase fraction on the tensile properties of equiaxed α+β dual-phase microstructures in Ti-10V-2Fe-3Al alloy. It is revealed that there existed a unique three-stage dependence of yielding behavior and strain-hardening ability on the phase fraction in this alloy. The change in β phase fraction (fβ) and corresponding phase composition not only determined the mechanical stability of β phase via equilibrium Mo content, but also altered the relative nano-hardness between the two phases by solid solution hardening. Specifically speaking, when fβ was larger than 80%, the β phase generally exhibited stress-induced martensitic phase transformation (SIMT) during loading. However, the β phase stability was continuously enhanced with decreasing fβ, leading to a progressive transition from double-yielding to single-yielding behavior. At 60% ≤ fβ < 80%, despite of the basically suppressed SIMT, there was a clear strain partitioning between the two phases due to a relatively large nano-hardness difference. This helped to maintain a reasonable strain-hardening ability by promoting geometrically necessary dislocations (GNDs) near the interphase boundaries. With further decrease of the β phase fraction (fβ < 60%), the nano-hardness of the two phases became much closer and as a result, the strain-hardening abilities were substantially deteriorated due to a lack of strain partitioning. Also, both the yield and ultimate tensile strength became much less dependent on the β phase fraction for microstructures in this region.

Crystal plasticity finite element simulation of NiTi shape memory alloy under canning compression based on constitutive model containing dislocation density

Crystal plasticity finite element (CPFE) simulation is employed for revealing plastic deformation mechanism of NiTi shape memory alloy (SMA) under canning compression at 400 °C, where only B2 austenite phase exists and it presents plastic deformation by dislocation slip without stress-induced martensite phase transformation and deformation twinning. Statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) densities are incorporated into crystal plasticity constitutive model for strain gradient. Texture evolution, stress and strain fields, SSD and GND densities are obtained on the basis of CPFE simulation. With progression of plastic deformation, γ-fiber (<111>) texture is gradually strengthened, which is further validated by the experimental data. Heterogeneous plastic deformation of NiTi polycrystalline cylinder model subjected to canning compression is illustrated by distribution of stress and strain based on all the slip systems, where stress concentration mainly emerges near the grain boundaries and large strain appears in the core location of NiTi polycrystalline cylinder. SSD density and GND density exhibit a heterogeneous distribution in the similar manner. Both SSDs and GNDs aggregate near the grain boundaries. SSD density increases with increasing plastic strain, whereas GND density decreases with increasing plastic strain. In addition, the total dislocation density increases with the increase of plastic strain. The developed CPFE model is an effective tool for simulating plastic deformation of NiTi SMA in the appropriate temperature range where dislocation slip is responsible for plastic deformation and work hardening is dominant during plastic deformation.

Study of the Fracture Behavior of Tetragonal Zirconia Polycrystal with a Modified Phase Field Model.

The superior fracture toughness of zirconia is closely correlated with stress-induced martensitic phase transformation around a crack tip. In this study, a modified phase field (PF) model coupling phase transformation and fracture is proposed to study the fracture behavior and toughening effect of tetragonal zirconia polycrystal (TZP). The stress-induced tetragonal to monoclinic (t–m) phase transformation around a static or propagating crack is characterized with PF simulations. It is shown that the finite size and shape of the transformation zone under different loads and ambient temperatures can be well predicted with the proposed PF model. The phase transformation may decrease the stress level around the crack tip, which implies the toughening effect. After that, crack propagation in TZP is studied. As the stress field is perturbed by the phase transformation patterns, the crack may experience deflection and branching in the propagation process. It is found that the toughness of the grain boundaries (GBs) has important influences on the crack propagation mode. For TZP with strong GBs, the crack is more likely to propagate transgranularly while, for TZP with weak GBs, intergranular crack propagation is prevalent. Besides that, the crystal orientation and the external load can also influence the topology of crack propagation.

Multi-scale simulations of fracture behavior in CeO2

Solid oxide fuel cells (SOFCs) are in a complex mechanical-thermal-electrochemical multi-field coupling condition, and traditional calculation methods are difficult to study from different scales concurrently. In this paper, we use a multi-scale method to investigate the mechanical properties of ceria. This multi-scale method cannot only obtain the micro-processes such as pre-phase transformation, phase transformation, and fracture represented by molecular dynamics (MD) calculations, but also acquire the displacement and stress fields by the finite element method (FEM). A center-cracked model is used to study the crack propagation and stress distribution near the crack tip. In the [100] crystal orientation, a stress-induced martensitic phase transformation occurs near the crack tip, while the [111] crystal orientation shows the characteristics of brittle fracture of ceramic materials. The stress-strain relationship calculated by this multi-scale method compares well with the results of MD simulations, which attests to its accuracy.

Stress-induced martensite phase transformation of FeMnSiCrNi shape memory alloy subjected to mechanical vibrating polishing

Abstract Fe66Mn15Si5Cr9Ni5 (wt.%) shape memory alloy (SMA) with γ austenite and e martensite was subjected to mechanical vibrating polishing and consequently its surface suffered from plastic deformation in the case of compressive stress. Almost complete e martensite transformation is found to occur in FeMnSiCrNi sample subjected to mechanical vibrating polishing, where stress-induced martensite transformation plays a predominant role. Stress- induced martensite transformation of FeMnSiCrNi SMA is closely related to the orientation of external stress. The complicated compressive stress which results from the mechanical vibrating polishing contributes to e martensite transformation from γ austenite of FeMnSiCrNi SMA. Mechanical vibrating polishing has a certain influence on the surface texture of e martensite of FeMnSiCrNi SMA, where texture appears in the polished FeMnSiCrNi SMA.

Mechanical behaviour of NiTiNb shape memory alloy wires– strain localisation and effect of strain rate

Over the past few years, shape memory alloys (SMAs) have received increased attention in civil engineering research due to their unique features such as superelasticity, shape memory effect (SME), high ductility and good corrosion resistance. SMAs, however, have complex material behaviour which depends on many parameters such as chemical composition, thermo-mechanical treatment and ambient temperature. SMAs exhibit high strain-rate sensitivity and strong strain localisation during the stress-induced martensitic (SIM) phase transformation. Both have serious implication in civil engineering applications. Strain rate effects and the strain localisation in SMAs have been commonly investigated separately in the literature which has been mostly focused on NiTi SMA. This paper investigates the strain localisation phenomenon, the effect of strain rate and their interaction in NiTiNb SMA. The digital image correlation (DIC) technique was used to investigate the strain localisation phenomenon. The effect of strain rates is investigated within the quasi-static range and varies from 3.3 × 10−5/s to 3.3 × 10−2/s in strain-controlled tests and 2 × 10−5/s to 2 × 10−1/s in displacement-controlled tests. Significant non-uniform strain distribution is observed during the SIM phase transformation, which progresses through the nucleation and broadening of the transformation bands (TBs). The nucleation of the TBs and the unloading strain recovery within the TBs show high strain-rate sensitivity. At high strain rates, the nucleation of a TB is accompanied by a significant stress-drop.

Thermodynamic behavior of NiTi shape memory alloy against low-velocity impact: experiment and simulation

The study of thermodynamic behavior of shape memory alloy (SMA) against impact is of great importance for the use of SMA as damping devices. This paper investigates the thermodynamic behavior of NiTi SMA sheet subjected to low-velocity impact loading, by means of experiment and explicit finite element (FE) analysis. First, the impact tests are carried out with different impact energies on the drop-weight impact system, the thermal response during the impact process is captured by the infrared camera. The impact force and the temperature rise achieve the maximum values of 8716 N and 46.93 ∘C at impact energy of 25 J. Then, an explicit Euler integration scheme is introduced to implement the SMA model (Wang et al., 2017, IJP) into finite element software ABAQUS by means of the explicit user-defined material subroutine VUMAT. Finally, the impact tests are simulated using the proposed numerical algorithm. Numerical results show good correlation with the experimental data, the maximum deviations between both for the impact force and the temperature are 5.78% and 0.63%, respectively. The analysis approach captures the prime thermodynamic features of SMA against low-velocity impact load such as superelastic deformation, stress-induced martensite phase transformation and temperature variation.

Microstructure and mechanical properties of novel Zr–Al–V alloys processed by hot rolling

In this study, the effects of vanadium (V) addition on the microstructures and mechanical properties of hot-rolled Zr–9Al–χV alloys (χ = 0, 2 and 4 at. %) were systematically investigated. Microscopic analyses indicated that the microstructures of hot-rolled Zr–9Al–χV alloys were sensitive to the V content. The hot-rolled Zr–9Al alloy was completely dynamically recrystallized and consisted of the α phase only, whereas the hot-rolled Zr–9Al–2V alloy consisted of partially recrystallized α and transformed β (α′ + β). The tensile tests showed that the difference between the ultimate and yield strengths of the hot-rolled Zr–9Al alloy approximated 20 MPa, whereas that of the hot-rolled Zr–9Al–2V alloy was about 200 MPa. The evident strain hardening of the hot-rolled Zr–9Al–2V alloy was caused by the mechanical contrast between the soft and hard components of the microstructure. The hot-rolled Zr–9Al–4V alloy consisted of large elongated β grains, in which equiaxed α and acicular α" grains were distributed. The engineering stress–strain curve of the hot-rolled Zr–9Al–4V alloy exhibited a double-yielding behaviour, which was caused by stress-induced martensite phase transformation: β→α".

Experimental investigation of thermomechanical behaviour of NiTi shape memory alloy under low-velocity impact loading

This paper experimentally investigates the thermomechanical behaviour of NiTi shape memory alloy (SMA) under low-velocity impact loading. The phase transformation temperatures of the NiTi material are measured by means of the Differential Scanning Calorimetry (DSC) method. The impact tests are carried out on a drop hammer impact system, wherein force sensor and infrared camera are used to capture the thermomechanical behaviour of NiTi SMA. Several prime material features of SMA, such as superelastic stress-strain response, stress-induced martensitic phase transformation, residual deformation, heat production and energy dissipation, are observed in the drop hammer test of the superelastic NiTi sheet. Considering the impact test is an approximate adiabatic process, the temperature variation on NiTi sheet is highlighted, due to the latent heat and intrinsic dissipation. This temperature variation will affect the mechanical behaviour of SMA, and therefore bring about complex thermomechanical coupling effect in the low-velocity impact test.

Effect of [formula omitted] dislocation on transformation stresses, nucleation, and growth for phase transformations between silicon I and silicon II under triaxial loading: Phase-field study

Stress-induced martensitic phase transformations (PTs) at a stationary 60∘ dislocation in single-crystalline Si are modeled by an advanced phase-field approach (PFA), which takes into account the lattice instability conditions obtained by atomistic simulations for the general stress tensor. Finite elastic, transformation, and plastic strains are considered. Finite element method (FEM) simulations elucidate two different mechanisms of nucleation and nanostructure evolution for two different stress-hysteresis cases. For a traditional finite-stress-hysteresis region, the PT starts with the barrierless nucleation of a thermodynamically-equilibrium-incomplete embryo, which loses its stability and grows forming a propagating martensitic band with distinct interfaces. However, in the unique zero-stress-hysteresis region, where PT for defect-free crystal occurs homogeneously through intermediate phases without nucleation, interfaces, and growth, the PT starts at a dislocation but spreads quasi-homogeneously, without interfaces, similar to the defect-free case; the macroscopic stress-strain curve is horizontal and without hysteresis during direct-reverse PTs. Despite large normal stresses produced by dislocation in the range of ±(6−12) GPa, a relatively small reduction in macroscopic PT stress by 1.6 GPa is quantitatively explained by mutually compensating contributions of stresses into lattice instability criterion.