Macroscopic Transformation Research Articles

Influence of cellulose nanofibers on the behavior of Pickering emulsions. Part II: Thixotropy and dynamic-mechanical tests

Nonlinear rheology of Pickering emulsions is used to further investigate the nonlinear and unrecoverable transformation of inner structures, which is beyond the linear viscoelastic regime of tiny structural disturbances. Exploring various rheological methods plays a vital role in emulsion applications, such as simulating the macroscopic structural transformation between static and liquidlike flow states, strain overshoot, and regeneration for broken structures. According to our previous studies, cellulose nanofibers (CNFs) Pickering emulsions are a typical system for investigating polymer-based emulsions with the auxiliary surfactant [didodecyldimethylammonium bromide (DDAB)] for enhancing CNF absorption. To further study different rheological properties by varying CNF or DDAB contents, multiple interval thixotropic test, large amplitude oscillatory shear, and concentration-time-dependent superposition are employed to study the linear viscoelasticity and structural transformation of nonlinear range. This research was conducted based on the previous published works [Cui et al., Materials 15, 8285 (2022)] as a further characterization for the same sample series.

Tension-compression asymmetry of metastable austenitic stainless steel studied by in-situ high-energy X-ray diffraction

This work studies the tension-compression asymmetry (TCA) of metastable austenitic stainless steel (MASS) in uniaxial loading depending on temperature. In-situ high-energy X-ray diffraction was used to simultaneously probe phase fractions, transformation kinetics, crystallographic texture, lattice strains, strain and stress partitioning between austenite and martensites during quasi-static tensile and compressive deformation at 24, 60 and 100 °C. Complementary relaxed-constraint crystal plasticity simulations and calculations of the mechanical driving force related to the formation of α’ and ε martensites were performed. At 24 °C, martensitic transformations (MTs) prevail, while at 100 °C dislocation slip is the dominant deformation mechanism for both load senses. Macroscopic stress-strain response and transformation behaviour exhibit TCA, with compression promoting the conversion of ε into α’. Transformation kinetics were analyzed in relation to shear banding and the geometric alignment of ε lamellas depending on load sense and temperature. A strong TCA was found for crystallographic texture, bearing signatures of grain rotation due to plastic slip and of MT in case of austenite (γ). For both load senses, the relative strengths of austenite and martensite texture fibres were related to the driving force anisotropy for α’ formation calculated based on the phenomenological theory of martensite crystallography. Texture evolution of α’ is largely controlled by the MT itself, not by grain rotation. Analysis of differently orientated austenite grain families revealed a pronounced TCA of the lattice strains, linked to the γ → ε MT. This was found to be a direct consequence of driving force and volume change related to ε formation. Furthermore, stress is shared differently between austenite and martensites in tension vs. in compression. γ hardens more and hence carries a larger portion of the total stress in compression than in tension. The origin for this TCA could be found in the elasto-plastic accommodation of the volume change related to α’ formation. These findings can aid the development of new material laws for MASSs that are sensitive to load-sense and temperature for advanced forming simulations.

Effect of retained austenite on the fatigue behavior of modified bainitic 100Cr6 steels considering local phase transformation

Since highly loaded components, such as roller bearings, tend to have relatively high lifetime scatter caused by microstructural defects, an increased defect tolerance of the material can improve the performance as well as the reliability of these highly stressed components. To increase the defect tolerance of the roller bearing steel 100Cr6, two different laboratory melts with either 1.5 wt.-% Al or 1.5 wt.-% Si in addition to the standard composition were developed. After an adapted heat treatment, both steels exhibited a bainitic microstructure with a relatively high content of retained austenite with more than 20 vol.-%. Considering the effects of the retained austenite, a defined mechanical stability is essential to avoid excessive deformation-induced transformation from the retained austenite into α′-martensite, which can lead to shape deviations in components. However, besides the increased deformability of the austenitic phase, local phase transformations in the vicinity of defects can increase the defect tolerance. The fatigue tests performed at ambient temperature (AT) and at T = 100 °C, show a higher fatigue strength of the Si-alloyed steel due to a refined microstructure and revealed for both steels a relatively high austenite stability, since no macroscopic phase transformation was observed. The high austenite stability can be explained by a relatively high carbon content of the austenitic phase. However, in contrast to the Al-alloyed steel, a decrease in the fatigue strength and in the defect tolerance due to the increased temperature were observed for the Si-alloyed steel, which indicates a more pronounced phase transformation at AT. The lower carbon content and the finer distribution of the retained austenite, when compared to the Al-alloyed steel, are supposed to be the reason. While a smaller carbon content decreases the phase stability, the refined austenite distribution results in a higher probability of retained austenite presence in the vicinity of a defect.

Strain-rate dependent deformation behavior of additively manufactured stainless steel with different fractions of δ-ferrite

The effect of strain rate on the tensile deformation behavior of additively manufactured CrNi stainless steel with different fractions of δ-ferrite (14 % in the as-built material and 6 % after the post-built solid-solution treatment) was revealed with the focus on the deformation stage of macroscopic strain-induced γ → α' martensitic transformation. Tension tests were performed with the initial strain rates of 5 ×10−4, 5 ×10−3, and 5 ×10−2 s−1 at two different temperatures, at which slow (300 K) and fast (183 K) kinetics of martensitic transformation were realized. Post-built solid-solution treatment provided a partial dissolution of the δ-ferrite in the additively manufactured steel specimens and assisted higher strain hardening at the stage associated with γ → α' martensitic transformation. Independently on δ-ferrite fraction and test temperature, an increase in the strain rate weakly influences the stress and strain, at which the stage of macroscopic strain-induced transformation starts, but visibly decreases the strain hardening rate at this deformation stage. The latter testifies the slower kinetics of strain-induced martensitic transformation at higher strain rates.

Cryogenic work-hardening behavior for a metastable austenitic stainless steel at liquid nitrogen temperature

An experimental study was conducted to analyze the undulated work-hardening behavior of S30408 metastable austenitic stainless steel at liquid nitrogen (LN2) temperature. The flow stress curve, work-hardening process, strength, and ductility were studied by uniaxial tensile tests at both room temperature (RT) and −196 °C. Based on the scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM) observations, the effects of the cryogenic temperature and deformation degree on the dislocation evolution, phase transformation, slip behavior, and hardening behavior were analyzed. The cryogenic work-hardening mechanism regarding the initial hardening, undulated hardening, and unstable hardening throughout the whole tensile process was elaborated. The correlation between macroscopic work-hardening and microscopic martensitic transformation accompanied by a localized dislocation strengthening was illuminated. It was revealed that the high strength of the austenitic steel during the cryogenic deformation process resulted from the α′-martensite transformation accompanied by dislocation strengthening. A critical point of phase content was obtained at a strain of 0.095 at −196 °C. The undulated work-hardening at cryogenic temperature was mainly attributed to the alternating evolution of the α′-martensite and austenite phases with a non-uniform deformation mode.

(Battery Division Early Career Award Sponsored by Neware Technology Limited) Design, Synthesis, and Characterization of Cathode Microstructures in Lithium Batteries

The propagation of redox reactions governs the electrochemical properties of battery materials and their critical performance metrics in battery cells. The recent research progress, especially aided by advanced analytical techniques, has revealed that incomplete and heterogeneous redox reactions prevail in many electrode materials. Advanced high-capacity cathode materials are mostly polycrystalline materials that exhibit complex charge distribution (the valence state distribution of the redox-active cations) due to the presence of numerous constituting grains and grain boundaries. The redox reactions in individual grains typically do not proceed concurrently due to their distinct geometric locations in polycrystalline particles. As a result, these unsynchronized local redox events collectively induce heterogeneous and anisotropic charge distribution, building up intergranular and intragranular stress. Therefore, these polycrystalline materials may exhibit weak mechanical stability, leading to undesired chemomechanical breakdown during battery operation. Grain engineering in polycrystalline materials provides a large playground to modulate the materials properties beyond controlling the chemical composition, and electronic and crystal structures. In particular, the anisotropic ion-conducting pathways in layered oxides make the grain crystallographic orientation a critical factor in determining the modality of the redox reactions in these materials.This presentation will discuss our recent progress in the design, synthesis, and characterization of cathode microstructures in lithium batteries.First, we will discuss how the charge distribution is guided by grain crystallographic orientations in polycrystalline battery materials. We elucidate the spatially resolved charge distribution in lithium layered oxides with different grain crystallographic arrangements and establish a model to quantify their charge distributions. While the holistic “surface-to-bulk” charge distribution prevails in polycrystalline particles, the crystallographic orientation-guided redox reaction governs the charge distribution in the local charged nanodomains. Compared to the randomly oriented grains, the radially aligned grains exhibit a lower cell polarization and higher capacity retention upon battery cycling. The radially aligned grains create less tortuous lithium-ion pathways, thus improving the charge homogeneity as statistically quantified from over 20 million nanodomains in polycrystalline particles. This study provides an improved understanding of the charge distribution and chemomechanical properties of polycrystalline battery materials.Second, we will discuss how the grain arrangement affects the thermal stability of polycrystalline cathode materials in rechargeable batteries. We performed a systematic in situ study on the Ni-rich polycrystalline cathode materials to investigate the fundamental degradation mechanism of charged cathodes at elevated temperatures, which is essential for tailoring material properties and improving performance. Using multiple microscopy, scattering, thermal, and electrochemical probes, we decoupled the major contributors to the thermal instability from intertwined factors. Based on our findings, the cathode grain microstructure has a forgotten yet important role in the thermal stability of polycrystalline rechargeable batteries. Oxygen release, as an important process during the thermal runaway, can be regulated through engineering grain arrangements. The grain arrangement can modulate the macroscopic crystallographic transformation pattern and oxygen diffusion length in layered cathodes to offer more possibilities for cathode material design and synthesis.Third, we will discuss our new understanding of particle behaviors in composite cathodes. We capture and quantify the particle motion during the solidification of battery electrodes and reveal the statistics of the dynamically evolving motion in the drying process, which has been challenging to resolve. We discover that the particle motion exhibits a strong dependence on its geometric location within a drying electrode. Our results also imply that the final electrode quality can be controlled by balancing the solvent evaporation rate and the particle mobility in the region close to the drying surface. We formulate a network evolution model to interpret the regulation and equilibration between electrochemical activity and mechanical damage of these particles. Through statistical analysis of thousands of particles using x-ray phase-contrast holotomography in a Ni-rich cathode, we found that the local network heterogeneity results in asynchronous activities in the early cycles, and subsequently the particle assemblies move toward a synchronous behavior. Our study pinpoints the chemomechanical behavior of individual particles and enables better designs of the conductive network to optimize the utility of all the particles during operation.

Effect of the grain arrangements on the thermal stability of polycrystalline nickel-rich lithium-based battery cathodes

One of the most challenging aspects of developing high-energy lithium-based batteries is the structural and (electro)chemical stability of Ni-rich active cathode materials at thermally-abused and prolonged cell cycling conditions. Here, we report in situ physicochemical characterizations to improve the fundamental understanding of the degradation mechanism of charged polycrystalline Ni-rich cathodes at elevated temperatures (e.g., ≥ 40 °C). Using multiple microscopy, scattering, thermal, and electrochemical probes, we decouple the major contributors for the thermal instability from intertwined factors. Our research work demonstrates that the grain microstructures play an essential role in the thermal stability of polycrystalline lithium-based positive battery electrodes. We also show that the oxygen release, a crucial process during battery thermal runaway, can be regulated by engineering grain arrangements. Furthermore, the grain arrangements can also modulate the macroscopic crystallographic transformation pattern and oxygen diffusion length in layered oxide cathode materials.

Microstructures and mechanical properties of NiTi shape memory alloys fabricated by wire arc additive manufacturing

Wire arc additive manufacturing (WAAM) has been proved to be a promising method to fabricate large expensive NiTi shape memory alloys with complex geometry. In this study, five layers of NiTi alloy with dimensions of 80 × 12 × 15 mm were deposited by the cold metal transfer (CMT) welding based WAAM process. The macroscopic morphology, microstructure evolution, phase transformation and mechanical properties of each layer were investigated and compared with each other. Each layer of the as-deposited NiTi wall shows a one-step B2→B19′ transformation during cooling and the martensitic transformation temperature (Ms) is lower than that of the as-received wire. For the first three layers, the columnar grains growing along the building direction have a larger length-to-diameter ratio and B2 is the main constituent phase. Coarse dendritic Ti2Ni/Ti4Ni2O precipitates are precipitated at the interior of the grains besides grain boundaries. However, grains in the subsequent layers become finer and the region near the top surface are characterized by equiaxed grains, and elliptical Ti2Ni/Ti4Ni2O precipitates mainly concentrate at grain boundaries. The heat-affected zone exhibits the lowest hardness of 233.34HV, followed by a gradually increase among the as-deposited layers and the highest hardness of 331.27HV was obtained at the 5th layer. The highest ultimate tensile strength of 652.46Mpa, together with the elongation of 13.66% and recoverable strain of 2.39% was obtained in the sample which is located at 11.5 mm height away from the substrate. This research provides an innovative method and insights for additive manufacturing NiTi shape memory alloys by introducing CMT based WAAM method.

Electron Collision Rate in Ultrashort Laser – Metal Interaction Inferred from Reflectivity Measurements

We study optical laser coupling of four metals (aluminum, copper, nickel and tungsten) upon single ultrashort 30-fs laser irradiation. Using dedicated experimental methodology, we carefully monitor the evolution of the material reflectivity integrated over the femtosecond pulse duration. We further apply the Drude-Lorentz formalism to infer the evolution of the effective electron collision rate eff as a function of applied fluence. The knowledge of this parameter is of paramount importance in any lasermatter interaction situation because of its immediate impact on laser energy coupling in material and on its subsequent macroscopic transformation.

A combined theoretical and experimental study of the phase coexistence and morphotropic boundaries in ferroelectric-antiferroelectric-antiferrodistortive multiferroics

The physical nature of the ferroelectric (FE), ferrielectric (FEI) and antiferroelectric (AFE) phases, their coexistence and spatial distributions underpins the functionality of antiferrodistortive (AFD) multiferroics in the vicinity of morphotropic phase transitions. Using Landau-Ginzburg-Devonshire (LGD) phenomenology and a semi-microscopic four sublattice model (FSM), we explore the behavior of different AFE, FEI, and FE long-range orderings and their coexistence at the morphotropic phase boundaries in FE-AFE-AFD multiferroics. These theoretical predictions are compared with the experimental observations for dense Bi1-yRyFeO3 ceramics, where R is Sm or La atoms with the fraction 0 ≤ y ≤ 0.25, as confirmed by the X-ray diffraction (XRD) and Piezoresponse Force Microscopy (PFM). These complementary measurements were used to study the macroscopic and nanoscopic transformation of the crystal structure with doping. The comparison of the measured and calculated AFE/FE phase fractions demonstrate that the LGD-FSM approach well describes the experimental results obtained by XRD and PFM for Bi1-yRyFeO3. Hence, this combined theoretical and experimental approach provides further insight into the origin of the morphotropic boundaries and coexisting FE and AFE states in model rare-earth doped multiferroics.

Light-Driven Rapid Peeling of Photochromic Diarylethene Single Crystals

Macroscopic transformation such as the molecular motors of biology is brought by transforming the protein using the chemical reaction of molecules by external stimuli. If it is possible to achieve it as machine-like in nanometer to micrometer size in photomechanical phenomena, there is a possibility of the application as driving devices of micro- or nanomachineries that drive without any electrical contact. Since light is useful to operate it without any direct contact as external stimuli and leads to rapid photochemical reactions, the operation at high speed can be expected. Here we newly found that crystals of a photochromic diarylethene exhibit a peeling behavior with astonishingly rapid velocity by photoirradiation to a lateral face in addition to separation behaviors such as jumping and cracking by photoirradiation to a well-developed face. The detail of the rapid photoresponsive peeling was discussed based on the molecular packings and the dependence on crystal size and photoirradiation conditions. These crystals can be potentially applied to macroscopic photomechanical actuators rapidly driven based on molecular machinery.

Strain wave pathway to semiconductor-to-metal transition revealed by time-resolved X-ray powder diffraction

One of the main challenges in ultrafast material science is to trigger phase transitions with short pulses of light. Here we show how strain waves, launched by electronic and structural precursor phenomena, determine a coherent macroscopic transformation pathway for the semiconducting-to-metal transition in bistable Ti3O5 nanocrystals. Employing femtosecond powder X-ray diffraction, we measure the lattice deformation in the phase transition as a function of time. We monitor the early intra-cell distortion around the light absorbing metal dimer and the long range deformations governed by acoustic waves propagating from the laser-exposed Ti3O5 surface. We developed a simplified elastic model demonstrating that picosecond switching in nanocrystals happens concomitantly with the propagating acoustic wavefront, several decades faster than thermal processes governed by heat diffusion.

Azobenzene Based Photo-responsive Mechanical Actuator Fabricated by Intermolecular H-bond Interaction

Photo-responsive mechanical actuator is a class of stimuli-responsive materials transferring light to mechanical energy through macroscopic transformation. To fabricate photo-responsive mechanical actuator, soft polymeric materials crosslinked with functional bridging structures are desired. Supramolecular interaction is a relatively common way to fabricate crosslinked materials due to its excellent self-assembly performance. And azobenzene and derivatives are ideal candidates of photo-responsive materials because of the unique photo-induced trans-cis isomerization. Here, a new kind of crosslinked materials based on supramolecular interaction between 4,4′-dihydroxyazobenzene and chitosan is reported. Under 355 nm irradiation, the macroscopic bending of polymeric materials occurs rapidly due to the photo-isomerization of 4,4′-dihydroxyazobenzene. Meanwhile, the photo-responsive mechanical actuator can also lift weight which is up to 200 times that of the actuator itself, and convert energy from light to mechanical work efficiently. This report suggests a new kind of photo-responsive actuator based on supramolecular interaction and may be helpful to contribute a theoretical basis to the design and synthesis of photo-responsive mechanical actuator suitable for large-scale manufacturing industrialization in future.

Giant Single-Crystal Shape Transformation with Wide Thermal Hysteresis Actuated by Synergistic Motions of Molecular Cations and Anions.

Manipulating the collective molecular movements to implement macroscopic mechanical response of bulk material is attractive and challenging. Here, an organic-inorganic hybrid single crystal is synthesized, which exhibits a giant macroscopic shape transformation with a remarkable thermal hysteretic feature. The colossal anisotropic shape change, which manifests as an abrupt elongation of ca. 9 % along the crystallographic c-axis and a concomitant contraction of ca. 9 % in a perpendicular direction, is induced by a significant reorientation of imidazolium, accompanied with a substantial configurational variation in CuBr4 2- complex anions. The synergistic motions of both the molecular cations and anions engender a remarkable large thermal hysteresis (>30 K) in the shape transformation of the single crystal, implying that this material may play a role in alternating memory media. Furthermore, due to the stable crystal lattice, a single crystal that demonstrates naked-eye detectable large shape transformation was used as a thermal actuator to spontaneously control an electric circuit by temperature variation.

Gradient-enhanced thermomechanical 3D model for simulation of transformation patterns in pseudoelastic shape memory alloys

Stress-induced martensitic transformation in polycrystalline NiTi under tension often proceeds through formation and propagation of macroscopic phase transformation fronts, i.e., diffuse interfaces that separate the transformed and untransformed domains. A gradient-enhanced 3D finite-strain model of pseudoelasticity is developed in this work with the aim to describe the related phenomena. The underlying softening response is regularized by enhancing the Helmholtz free energy of a non-gradient model with a gradient term expressed in terms of the martensite volume fraction. To facilitate finite-element implementation, a micromorphic-type regularization is then introduced following the approach developed recently in the 1D small-strain context. The complete evolution problem is formulated within the incremental energy minimization framework, and the resulting non-smooth minimization problem is solved by employing the augmented Lagrangian technique. In order to account for the thermomechanical coupling effects, a general thermomechanical framework, which is consistent with the second law of thermodynamics and considers all related couplings, is also developed. Finite-element simulations of representative 3D problems show that the model is capable of representing the loading-rate effects in a NiTi dog-bone specimen and complex transformation patterns in a NiTi tube under tension. A parametric study is also carried out to investigate the effect of various parameters on the characteristics of the macroscopic transformation front.

Microwave stimulation of dislocations and the magnetic control of the earthquake core

Microwave irradiation transforms the elasticity of solids into plasticity by controlling the dislocation mobility via magnetic interactions within the electron spin pairs on the dislocations. In ionic crystals, microwaves cause dislocations to accelerate and increase their mean free path, thus leading to a release of elastic energy; in covalent crystals, microwaves keep dislocations in place, thereby accumulating elastic energy and increasing the crystal strength. Microwave pumping at resonant Zeeman frequencies (in the magnetic resonance regime) is firm evidence of the concepts of electron spin pairs and of the magnetoplasticity phenomenon itself. However, the dominant contribution to the macroscopic transformation of elastic energy into plastic flow comes from nonresonant microwaves. These can be used to control the mechanics of diamagnetic solids, including, importantly, the earthquake focus. The observed correlation between magnetic events (such as magnetic storms and hydrodynamically generated high-power magnetic pulses) and their seismic and tectonic consequences (earthquake frequency and magnitude and deformations) indicates unambiguously that magnetically controlling the earthquake focus provides a realistic means to prevent a catastrophe by transforming large-magnitude earthquakes into weak, low-magnitude events.

Photoinduced repetitive separation of a supramolecular assembly composed of an amphiphilic diarylethene mixture.

A supramolecular assembly composed of a two-component mixture of amphiphilic diarylethenes, which have octyloxycarbonyl and N-octylcarbamoyl groups, showed a unique macroscopic transformation upon irradiation with UV light and subsequent standing in the dark. Unlike the pure compounds, the assembly was repetitively separated into a blue sphere and a red-purple sparse structure. Both the blue sphere and the sparse structure turned into colorless spheres upon irradiation with visible light and the divided colorless spheres showed the same response to UV and visible light. Phase diagrams based on the change in absorption spectra upon temperature change suggested that the transformation originates from a LCST transition. In the 0.5 : 0.5 mixture, in contrast to the pure compounds, the transition temperature sharply changed at around 50% of the fraction of the closed-ring isomer. TEM imaging showed that the 0.5 : 0.5 mixture with high photoisomerization yield formed a 10 nm-sized network. Judging from the phase diagram and TEM images, the separation is understood as the local phase transition of the regions with a high fraction of the closed-ring isomer.

Reaction Mechanism for the Hydrogen Evolution Reaction on the Basal Plane Sulfur Vacancy Site of MoS2 Using Grand Canonical Potential Kinetics.

We develop the grand canonical potential kinetics (GCP-K) formulation based on thermodynamics from quantum mechanics calculations to provide a fundamental basis for understanding heterogeneous electrochemical reactions. Our GCP-K formulation arises naturally from minimizing the free energy using a Legendre transform relating the net charge of the system and the applied voltage. Performing this macroscopic transformation explicitly allows us to make the connection of GCP-K to the traditional Butler-Volmer kinetics. Using this GCP-K based free energy, we show how to predict both the potential and pH dependent chemistry for a specific example, the hydrogen evolution reaction (HER) at a sulfur vacancy on the basal plane of MoS2. We find that the rate-determining steps in both acidic and basic conditions are the Volmer reaction in which the second hydrogen atom is adsorbed from the solution. Using the GCP-K formulation, we show that the stretched bond distances change continuously as a function of the applied potential. This shows that the main reason for the higher activity in basic conditions is that the transition state is closer to the product, which leads to a more favorable Tafel slope of 60 mV/dec. In contrast if the transition state were closer to the reactant, where the transfer coefficient is less than 0.5 we would obtain a Tafel slope of almost 150 mV/dec. Based on this detailed understanding of the reaction mechanism, we conclude that the second hydrogen at the chalcogenide vacant site is the most active toward the hydrogen evolution reaction. Using this as a descriptor, we compare it to the other 2H group VI metal dichalcogenides and predict that vacancies on MoTe2 will have the best performance toward HER.

Crystallography and consequence of the cubic-tetragonal-orthorhombic multi-step martensitic transformations in MnNi alloys

The crystallography of the martensitic transformations (cubic-tetragonal, tetragonal-orthorhombic and cubic-orthorhombic transformations) in MnNi alloys was studied by using the phenomenological crystallography theory of martensitic twinning. The results of habit plane, orientation relationship, macroscopic transformation strain of twinning martensite and angle of shear are obtained. The results show that the rotation angles between martensitic variants and their corresponding Bain variants are smaller than 1°, the angle of shear is smaller than 1° as well. The habit planes slightly deviate from rational {1 1 0}-type planes. Because of relatively small transformation strain and shear angle, the consequence of fcc-fct-fco multi-step transformation in MnNi alloys is mainly determined by transformation thermodynamics, rather than by the resistance of elastic energy.

Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys

Shape memory alloys, notably NiTi, often exhibit softening pseudoelastic response that results in formation and propagation of Lüders-like bands upon loading, for instance, in uniaxial tension. A common approach to modelling softening and strain localization is to resort to gradient-enhanced formulations that are capable of restoring well-posedness of the boundary-value problem. This approach is also followed in the present paper by introducing a gradient-enhancement into a simple one-dimensional model of pseudoelasticity. In order to facilitate computational treatment, a micromorphic-type regularization of the gradient-enhanced model is subsequently performed. The formulation employs the incremental energy minimization framework that is combined with the augmented Lagrangian treatment of the resulting non-smooth minimization problem. A thermomechanically coupled model is also formulated and implemented in a finite-element code. The effect of the loading rate on the localization pattern in a NiTi wire under tension is studied, and the features predicted by the model show a good agreement with the experimental observations. Additionally, an analytical solution is provided for a propagating interface (macroscopic transformation front) both for the gradient-enhanced model and for its micromorphic version.