Martensitic Phase Research Articles

Revealing contrary contributions of the magnetic and lattice entropy to the inverse magnetocaloric effect in magnetic shape memory alloy

In this work, we studied the nature and dilemma of the inverse magnetocaloric effect using Ni50Mn36In14 magnetic shape memory alloy. In this context, the inverse magnetocaloric effects of Ni50Mn36In14 magnetic shape memory alloy polycrystalline samples were investigated as a function of annealing heat treatments by the thermo-magnetometry method. Two forms of Ni49TiMn36In14 magnetic shape memory alloy were studied: one that predominantly undergoes a magnetic phase transition and the other that exhibits both a magnetic and martensitic phase transition. The magnetic behaviors and magnetocaloric properties of these alloys were analyzed to investigate the competition between magnetic and lattice contributions to the total entropy change. Finally, the mutually contradictory role of magnetic and lattice contributions was demonstrated.

Overcoming strength-ductility trade-off in Si-containing transformation-induced plasticity high-entropy alloys via metastability engineering

Benefiting from the transformation-induced plasticity effect has been recognized as a new approach to develop high-performance Si-containing high-entropy alloys with outstanding room-temperature strength-ductility balance. However, closely controlling the kinetics of deformation-induced α΄-martensite formation is essential to further boost ductility in addition to ultrahigh strength. In the present work, this aim was fulfilled by manipulating the chemical composition of the promising FeCoCrVMnSi system with the replacement of Mn with Ni and adjusting the Si content to fine-tune the stacking fault energy and the driving force of austenite to martensite transformation. The experimental results were obtained by EBSD, TEM, XRD, and tensile testing, and the results were supported by thermodynamic calculations, work-hardening analysis, and assessment of α΄-martensite formation kinetics. Accordingly, the single-phase Fe47Co30Cr10Ni5V8-xSix system was designed. In this system, the Fe47Co30Cr10Ni5V2Si6 alloy exhibited exceptional tensile strength (∼1.1 GPa) and total elongation (72 %), outperforming the competitive dual-phase Fe46Co30Cr10Mn5V2Si7 alloy. High strength was attributed to the high solid-solution strengthening effect as well as the volume fraction of α΄-martensite, while its ductility benefited from fine-tuned kinetics of martensitic phase transformation.

Antiferroelectric Ceramics for Energy-Efficient Capacitors by Theory-Guided Discovery.

Antiferroelectric ceramics, via the electric-field-induced antiferroelectric (AFE)-ferroelectric (FE) phase transitions, show great promise for high-energy-density capacitors. Yet, currently, only 70-80% energy release is found during a charge-discharge cycle. Here, for PbZrO3-based oxides, geometric nonlinear theory of martensitic phase transitions is applied (first used to guide supercompatible shape-memory alloys) to predict the reversibility of the AFE-FE transition by using density-functional theory to assess AFE/FE interfacial lattice-mismatch strain that assures ultralow electric hysteresis and extended fatigue lifetime. A good correlation of mismatch strain with electric hysteresis, hence, with energy efficiency of AFE capacitors is observed. Guided by theory, high-throughput material search is conducted and AFE compositions with a near-perfect charge-discharge energy efficiency (98.2%), i.e., near-zero hysteresis are discovered. And the fatigue life of the capacitor reaches 79.5 million charge-discharge cycles, a factor of 80 enhancement over AFE ceramics with large electric hysteresis.

Challenge of fabricating difficult-to-nitride materials: Formation of martensitic phase in (Fe0.8Co0.2)8N foil based on industrially suitable gas-nitriding process

Nitrogen-martensitic phase (Fe0.8Co0.2)8N was successfully synthesized by using an industrially suitable gas-nitriding process of a bulk foil. So far, the nitrogen-martensitic phase of the bulk material has not been synthesized at such a high Co content. We found that this is because the nitride was easily denitrided by elevating temperature. In this work, by exploiting a NH3 gas-nitriding process combined with quenching at a rapid cooling rate (>800 °C/s) in NH3 atmosphere, we found that nitrogen stayed at the surface layer of the foil. By using cross-sectional laser microscopy, the nitride region was observed as a 7-μm-thick layered shape at the surface of the 100-μm-thick foil. An x-ray diffraction technique revealed that the nitride layer was a martensitic phase that was characterized as a body-centered tetragonal structure with c/a = 1.04. These findings can be applied to nitriding and surface treatments for alloy systems in which a nitrogen solid solution is hardly formed. Our developed method is promising because the martensitic phase is expected to be formed in whole bulk by further optimizing parameters clarified in this work.

Laser-assisted manipulation of Volta potential pattern on the TC4 surface for improved hBMSCs osteogenesis

The Ti6Al4V (TC4) alloy, a prevalent biomedical material in orthopedics, still faces limitation of the insufficient osseointegration. To improve the bioactivity of TC4, introducing the electric environment onto the TC4 surface may be an effective way in the view of the necessity of endogenous electric microenvironment in bone regeneration. Herein, a Volta potential pattern was engendered on the TC4 surface via parallel laser patterning, so as to promote the osteogenic differentiation of cells. A 15 W laser successfully transformed the original α + β dual phase towards radially distributed lath-like martensite phase in the laser treated region. The atomic lattice distortion between the heterogeneous microstructures of the laser treated and untreated regions leads to a significant Volta potential fluctuation on the TC4 surface. The Volta potential pattern as well as the laser-engraved microgrooves respectively induced mutually orthogonal cell alignments. The hBMSCs osteogenic differentiation was significantly enhanced on the laser treated TC4 surfaces in comparison to the surface without the laser treatment. Moreover, a drastic Volta potential gradient on the TC4 surface (treated with 15 W power and 400 μm interval) resulted in the most pronounced osteogenic differentiation tendency compared to other groups. Modulating the electric environment on the TC4 surface by manipulating the phase transformation may provide an effective way in evoking favorable cell response of bone regeneration, thereby improving the bioactivity of TC4 implant.

Crystal plasticity based constitutive model for deformation in metastable β titanium alloys

Due to attractive mechanical properties, metastable β titanium alloys have become very popular in many industries including aerospace, marine, biomedical, and many more. It is often the complex interplay among the different deformation mechanisms that produces many of the sought-after properties, such as enhanced ductility, super-elasticity, and shape memory effects. Stress induced martensitic transformation is an important deformation mechanism for these alloys. Understanding of it and the influence it has on the microstructural evolution of materials is of great importance. To this end we have developed a crystal plasticity based constitutive model which accounts for both martensitic phase transformation and slip based plasticity simultaneously in metastable β titanium alloys. We present a new formulation for the evolution of martensite transformation, based on physical principles and crystal plasticity theory. To understand and demonstrate this feature of the model, a parametric assessment of the newly developed constitutive model is conducted. This is followed by first of its kind analyses of stress induced martensitic transformation in metastable β titanium alloys. We firstly present validations against uniaxial loading experiments for different metastable β titanium alloys exhibiting stress induced martensite transformation. As part of this, single crystal simulations in metastable β titanium alloys are used for the first time to investigate the interaction of individual transformation systems during unconstrained transformation. This study shows good agreement between the experimental and simulated responses during all stages of deformation in which elastic, transformation and finally the slip stage are exhibited. Relatively ‘strong’ and ‘weak’ orientations for transformation are observed, consistent with experimental studies. The work done here demonstrates the ability of this crystal plasticity finite element method to capture physical mechanisms while bringing new insight about the interaction of different deformation mechanisms in metastable β titanium alloys.

Zr and V-doped effect on Martensitic transformations and magnetic properties of NiMnIn shape memory alloy

In this study, the elements vanadium (V) and zirconium (Zr) were doped separately as a fourth element to the ternary NiMnIn Heusler magnetic shape memory alloy and the alloys were produced as ingots by arc-melting method. The shape memory properties, microstructures, magnetic and microstructural changes of these new alloys were investigated in detail. The vanadium (V) and zirconium (Zr) elements doped into the alloy caused a decrease in the transformation temperature values of the alloy, but did not cause a significant change in its magnetic properties. The master sample, which has low hysteresis, undergoes a phase transition from the martensite phase to the austenite phase due to an increase in the nucleation of austenite phases at the twinning boundaries. Here, the vanadium and zirconium doping of the alloy caused an increase in the strength and ductility values of the alloy and this caused the formation of the second phase. Due to the increase of this phase formation in the alloy, it can be said that there is a slight decrease in the shape retention of the alloy.

Experimental Investigation of Hot Forming of Zn‐Coated Hot‐Stamping Steel

An investigation on the thermal property, fracture mechanism of substrate and coating layer, liquid‐metal embrittlement (LME) crack, coating layer morphology, microstructure, and hardness of Zn‐coated hot‐stamping steel is presented. The effect of forming temperature on the LME is studied. The crack mechanism of substrate at elevated temperature is ductile fracture with various‐sized dimples. The inclusions in the dimples are also detected and researched. However, the fracture mechanism of coating layer and weld spot is different from that of substrate. At high temperature, the liquid Zn invades into the substrate with oxidation reaction, which reduces the thermal formability. The complex chemical reaction and different phase formation occur in the coating layer. The coating layer breaks and peels off from the substrate with sharp edge, indicating brittle fracture. The phase of substrate mainly transforms into martensite phase with the microhardness Vickers hardness 0.2 of 410–490.

Thermomechanics of phase transformation induced localization in NiTi tubes. Part I experiments

This two-Part study aims to illustrate and elucidate the effects of thermomechanical interactions in pseudoelastic NiTi structures that arise in the course of the reversible transformations between the austenitic and martensitic phases. Transformation leads to inhomogeneous deformation with the two phases coexisting and to latent heat-induced local heating/cooling. Part I first presents the results of displacement-controlled isothermal tension and compression experiments on NiTi tubes covering the pseudoelastic temperature regime. The experiments are conducted in a constant temperature circulating bath which suppresses thermomechanical interactions so the transformation front velocity is governed strictly by the applied displacement rate. The load/unload hystereses traced, quantify the transformation stresses and strains and will be used to calibrate the constitutive model of Part II. A set of isobaric experiments in which NiTi tubes are taken through a cool/heat cycle under constant stresses of different levels follow. The experiments are conducted in a custom small-scale environmental chamber with a circulating air stream run by a feedback temperature controller, coupled to load-controlled mechanical loading. The evolution of helical bands of the alternate phase is captured using digital image correlation. The results demonstrate that under such loading histories a strong interaction develops between the evolving inhomogeneous deformation, the latent heat and the surrounding environment. The speed of propagation of the helical fronts slows down or accelerates so as to match the rate at which heat is removed/added to the specimen by the airflow. Thus, here the evolution of localized deformation is strongly coupled to the interaction between the latent heats and heat transfer from the environment. The effect of the stress level on these events is examined through eight isobaric experiments, which provide a rich data set for evaluating constitutive models and structural analyses of these experiments such as those in Part II.

Application of the polyhedral template matching method for characterization of 2D atomic resolution electron microscopy images

High-throughput image segmentation of atomic resolution electron microscopy data poses an ongoing challenge for materials characterization. In this paper, we investigate the application of the polyhedral template matching (PTM) method, a technique widely employed for visualizing three-dimensional (3D) atomistic simulations, to the analysis of two-dimensional (2D) atomic resolution electron microscopy images. This technique is complementary with other atomic resolution data reduction techniques, such as the centrosymmetry parameter, that use the measured atomic peak positions as the starting input. Furthermore, since the template matching process also gives a measure of the local rotation, the method can be used to segment images based on local orientation. We begin by presenting a 2D implementation of the PTM method, suitable for atomic resolution images. We then demonstrate the technique's application to atomic resolution scanning transmission electron microscopy images from close-packed metals, providing examples of the analysis of twins and other grain boundaries in FCC gold and martensite phases in 304 L austenitic stainless steel. Finally, we discuss factors, such as positional errors in the image peak locations, that can affect the accuracy and sensitivity of the structural determinations.

Mechanical response and phase transformation characteristics of R-phase NiTi shape memory alloy under high strain rate compression

R-phase NiTi shape memory alloy (R-NiTi SMA) has many excellent properties, but there are application problems such as simple structure and high price. High velocity impact welding can effectively solve these problems, but the research on the mechanical response and phase transformation (PT) characteristics of R-NiTi SMA under dynamic deformation is lacking. Therefore, the quasi-static (0.001 s-1) and dynamic (500 s-1, 1000 s-1, 1500 s-1, 2000 s-1) compression experiments were conducted on R-NiTi SMA in this research. The results showed that the true stress-strain curves of R-NiTi SMA during deformation were characterized by three stages, including the superelastic, elastic, and plastic segments. The critical stress of austenite to R (A-R) and R to martensite (R-M) phase transformation increased with the increase of strain rate, and the phase transformation process gradually disappeared when the strain rate exceeded 1000 s-1, which was related to the velocities of A-R and R-M phase transformation. With the increase of strain rate, defects such as dislocations increased and hindered the phase transformation process during unloading, resulting in the increase of A-phase content. In addition, the enthalpy of the deformed samples decreased significantly and the temperature ranges of phase transformation increased slightly. This work deepens the understanding of the dynamic response of R-NiTi SMA and helps to expand the application of high strain rate processing technology in R-NiTi SMA.

Strengthening mechanism of abnormally enhanced fatigue ductility of gradient nanostructured 316L stainless steel

Structural materials with a good combination of high fatigue strength and high fatigue ductility are highly desirable in engineering applications. However, it remains a challenge to “break” the exclusive relationship between fatigue strength and fatigue ductility. The cylindrical 316L stainless steel specimens with a gradient nanostructured surface layer were prepared using surface mechanical rolling treatment (SMRT). Fully reversed strain-controlled tension–compression fatigue experiments indicated that the SMRT processed 316L specimens achieved simultaneous improvement of fatigue strength and fatigue ductility. The abnormal increase in fatigue ductility is attributed to the significant secondary cyclic hardening caused by the martensitic phase transformation and the transition in fatigue crack initiation mode. The martensitic phase transformation enhances the fatigue strength while reducing the proportion of plastic deformation in the controlled strain amplitude. The competition between the driving force and resistance of fatigue nucleation in different structural units results in the migration of fatigue crack initiation sites from the surface to subsurface, thereby prolonging the fatigue crack initiation life. This work reveals the synergistic strengthening mechanism of fatigue strength and fatigue ductility of a gradient nanostructured 316L stainless steel.

Intrinsic mechanism of grain size effect and grain boundary misorientation angle effect on crack propagation in martensitic steels

Grain size and grain boundary misorientation angle as two important parameters in the polycrystalline system have a significant influence on the mechanical properties of advanced martensitic steels. A phase field model is used to investigate the intrinsic mechanism of the effects of grain size and grain boundary misorientation angle on the crack propagation process which considers the coupling damage behavior between grains and grain boundaries in martensitic steels by means of the finite element finite method. The transgranular (through grain boundaries) and intergranular (along grain boundaries) failure can be simulated by this model through constructing a grain boundary energy function and using a specific order parameter to track crack propagation in the grain boundary area. This model can directly display the crack propagation path inside the grain (martensite and austenite phases) and grain boundary area with the stress distribution. The preferential cleavage planes in austenite and martensite phases are 111γ and 100α in grains with different orientations, respectively. Moreover, the simulation results show that the crack mainly bifurcates near the trifurcated grain boundary. The crack tip tends to induce transgranular fracture in low-angle grain boundaries and intergranular fracture in high-angle grain boundaries when it reaches the grain boundary area. Consequently, this model will be a powerful tool to investigate the influence of grain size and grain boundary misorientation angle on the mechanical properties of polycrystalline martensitic steels.

Phase transformation behavior and mechanical properties of NiTi shape memory alloys fabricated by directed laser deposition

Directed laser deposition shows promise as a method for fabricating complex structure NiTi shape memory alloy parts in engineering, aerospace, automobile, and biomedical fields. The dislocation density has an impact on phase transformation behavior and mechanical properties of NiTi manufactured by directed laser deposition. In this work, NiTi samples were produced by directed laser deposition, and the mechanism of martensitic phase transformation and its interactions with dislocation density were revealed through molecular dynamics. Laser power and scanning speed are the main factors affecting dislocation density, the phase compositions of the samples are B2, B19′, and Ti2Ni phase, and the samples with dislocation density below 2 × 1015 m−2 show single-step B2–B19′ martensitic transformation, stress plateau and improved elongation, the samples with dislocation density above the value exhibit no significant transformation peak and no stress plateau. The movement of (100) twin planes and the growth of advantageous variants are observed in the simulation which can explain stress-induced martensitic reorientation and the stress plateau phenomenon. The bending test suggested that the sample under the optimal parameters has an 85 % recovery ratio within 8 % pre-strain.

Nanoscale-precipitate-strengthened (Ni,Cu)-rich TiNiCu shape memory alloy with stable superelasticity and elastocaloric performance

This study aimed to enhance the stability of the superelastic and elastocaloric properties of a Ti49Ni41Cu10 shape memory alloy through a synergistic approach combining compositional design and precipitation hardening. The alloy was subjected to a 168-h aging treatment at 400 °C. The aging treatment increased the hardness of the alloy due to the formation of nano-scale C11b Ti(Ni,Cu)2 precipitates. The C11b Ti(Ni,Cu)2 precipitates exhibited a coherent interface with the matrix, contributing to the significant strengthening effect. The thickness of the precipitates was measured to be approximately 2 nm. Additionally, the lattice compatibility between the B2 parent and B19 martensite phases, determined to be 0.997 after aging, indicated a high level of compatibility between the two phases. The high compatibility and precipitate strengthening further contributed to the functional stability of the alloy. The 168-h aged Ti49Ni41Cu10 shape memory alloy showed excellent functional stability during thermal and deformation cycles. The peak temperature of B2 to B19 transformation only decreased by 0.2 °C after 10 thermal cycles and showed limited changes with a decrement of 3.2 °C after 10,000 superelastic cycles. The Ti49Ni41Cu10 SMA showed a large elastocaloric temperature drop of 18 °C at the 1st superelastic cycle and maintained a large temperature drop of 17 °C after 1000 cycles. These findings contribute to a deeper understanding of the microstructural changes and their impact on the functional properties of the Ti49Ni41Cu10 shape memory alloy. This study has demonstrated the potential for developing shape memory alloys with improved stability and performance by utilizing compositional design and precipitation hardening techniques.

Accelerated improvement in tensile superelasticity of electron beam directed energy deposition manufactured NiTi alloys by artificial thermal cycling combined with low temperature aging treatment

ABSTRACT The low-temperature aging treatment at 250°C can significantly improve the tensile superelasticity of NiTi alloys fabricated by electron beam directed energy deposition (EB-DED). However, it requires a very long aging duration (up to 200 h) to achieve excellent tensile superelasticity due to inherent coarse grain size. To accelerate the aging process, the high-density dislocations are introduced by artificial thermal cycling treatment prior to the aging treatment (the original dislocation content in EB-DED processed NiTi alloys is very low), which will promote the subsequent uniform precipitation of nanoscale Ni4Ti3 particles during low-temperature aging treatment. The phase transformation behaviour always maintains a stable two-stage martensitic phase transformation. Under a cyclic tensile test at 6% strain, 24 h aged sample with thermal cycling maintains a recovery rate exceeding 90% even after 10 cycles, comparable to the performance of the sample aged for 200 h without thermal cycling, indicating a substantial improvement in aging efficiency.

Phase transformation behavior and shape memory effect of nickel-titanium shape memory alloy using the magnetic field assisted wire electrical discharge machining

Nickel-titanium shape memory alloy (NiTi-SMA) can restore its original shape after deformation, making it show great application in the fields of biomedicine, aerospace, etc. The wire electrical discharge machining (WEDM) has the advantage of machining micro and complex structures, which can greatly promote the application of NiTi-SMA. However, there are issues such as heat affected layer (HAL) on the surface of WEDM, which can affect the functionality of NiTi-SMA. Therefore, when using WEDM to NiTi-SMA, more attention should be paid to the functional changes after machining. This article primarily examine is the impact of peak current and pulse on time on the phase transformation behavior, shape memory effect, and mechanical properties of NiTi-SMA during WEDM, and introduces into the magnetic field assisted (MFA) process to improve the machining performance of NiTi-SMA. The results indicate that the HAL formed on the surface of NiTi-SMA is primarily composed of the irreversible phase transformation of B2 austenite. This layer induces a hardening effect, resulting in an increase in the phase transition temperature and a decrease in the phase transition energy (∆HM-A), as a result, the martensitic phase transformation behavior is suppressed. When the peak current and pulse on time increase, the surface quality of the NiTi-SMA processed decreases. The thickness of the HAL and microhardness increase, causing an increase in the phase transition temperature of the NiTi-SMA processed samples. Additionally, the transformation energy ∆HM-A, shape recovery rate, and mechanical properties decrease, and after recovery, more surface cracks appear and show larger extensions. MFA-WEDM can improve the surface quality of NiTi-SMA processing, reduce the thickness of the HAL, and effectively enhance the phase transformation temperature and energy ∆HM-A of the NiTi-SMA processed samples. With a magnetic field strength of 0.45 T, the tensile shape recovery rates of 98%, 94.4%, and 91.0% were achieved at 2%, 5%, and 8% strain, respectively. This represents an improvement of 8.9% compared to the maximum shape recovery rate with conventional WEDM. At the same time, it also inhibits the generation and propagation of surface cracks after deformation recovery. Additionally, MFA-WEDM improves the mechanical properties of NiTi-SMA, and reduces the thickness of the brittle fracture region by 49.7% compared to conventional WEDM. Therefore, MFA-WEDM can effectively enhance the shape memory effect of NiTi-SMA. However, it is important to avoid excessive peak currents and pulse on time to achieve optimal shape memory functionality.

Revealing the Superior Post-Necking Elongation in the Fine-Grained Ti-6Al-4V ELI at Cryogenic Temperature

The mechanical properties of a fine-grained (FG) Ti-6Al-4V extra-low interstitial (ELI) alloy were investigated by tensile tests at 298 K and 77 K. The experimental results indicated that, at 77 K, the alloy exhibits a small uniform elongation of 2.65%, but has a fracture elongation of 19.2%, showing superior post-necking elongation. At 298 K, the alloy displays a single dislocation slipping, β→α″ phase transformation occurred, and 6.35% uniform elongation was obtained, whereas the coupling of dislocation slipping and twinning deformation behaviors dominated at 77 K. The limited uniform elongation is attributed to the absence of martensite phase transformation at 77 K, whereas the decent fracture elongation is ascribed to the resistance offered by twinning against plastic instability.

Ultraslow calorimetric studies of the martensitic transformation of NiFeGa alloys: detection and analysis of avalanche phenomena

We study the thermal properties of a bulk Ni55Fe19Ga26\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Ni}_{55}\\hbox {Fe}_{19}\\hbox {Ga}_{26}$$\\end{document} Heusler alloy in a conduction calorimeter. At slow heating and cooling rates (∼1Kh-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim {1}\\,\\hbox {K h}^{-1}$$\\end{document}), we compare as-cast and annealed samples. We report a smaller thermal hysteresis after the thermal treatment due to the stabilization of the 14 M modulated structure in the martensite phase. In ultraslow experiments (40mKh-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${40}\\,\\hbox {mK h}^{-1}$$\\end{document}), we detect and analyze the calorimetric avalanches associated with the direct and reverse martensitic transformation from cubic to 14 M phase. This reveals a distribution of events characterized by a power law with exponential cutoff p(u)∝u-εexp(-u/ξ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p(u)\\propto u^{-\\varepsilon }\\exp (-u/\\xi )$$\\end{document} where ε∼2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon \\sim 2$$\\end{document} and damping energies ξ=370μJ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi ={370}{\\upmu {\\rm J}}$$\\end{document} (direct) and ξ=27μJ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi ={27}{\\upmu {\\rm J}}$$\\end{document} (reverse) that characterize the asymmetry of the transformation.

Microstructure of Stress‐Induced Martensite in Micron‐Sized Zirconia Single Crystal Spheres

Martensitic phase transformation of zirconia (ZrO2), when realized from the superelastic effect, has immense potential in energy applications, such as micro‐actuation and high‐energy dissipation/damping. In this study, martensitic transformation in ZrO2 is studied using a newly developed microscale phase field model, which is scale‐independent and contains an averaged gradient term. The model is implemented using the FEniCS package in Python. With a thorough explanation of the model construction, the mechanics of phase transformation are detailed, and the material behaviors under different stress conditions are discussed. Mesh sensitivity, multivariant evolution, and the effect of particle size are analyzed to understand the martensite evolution in superelastic ZrO2. This work provides new insight into the martensitic phase transformation behaviors of micron‐sized spherical ZrO2 particles.