Microstructure Of Shape Memory Alloy Research Articles

Aqua jet integrated fiber laser machining of quaternary NiTiCuZr alloy

ABSTRACT Low thermal diffusivity of NiTi-based smart alloy results in concentrated heat accumulation during laser beam machining which rises to adverse thermal effects like heat-affected zones, residual stresses, and alterations in microstructure of shape memory alloy (SMA) system. The addition of Cu and Zr can reduce the thermal hysteresis in the phase transformation of NiTi SMAs. Minimizing thermal hysteresis is desirable in SMA applications where precise control of the phase transformation temperatures is required, such as in actuators, sensors, and medical devices. Therefore, aqua jet integrated laser (AJ-FLBM) machining is a suitable choice for smart materials that need to be machined with high precision and low heat affected zone. In this current research, the NiTiCuZr SMA is machined using AJ-FLBM to investigate the effects of process variables on surface characteristics measured using RSM-BBD approach. The surface quality was enhanced by 68.93% with a gradual decrease in laser power (P), cutting speed (CS), and an increase in frequency (F). Aqua jet integrated FLBM technique may reduce heat affected zone due to the removal of heat in areas near the cutting location. This was confirmed by the DSC test which reveals that optimal machining inputs do not alter shape memory properties.

Energy scaling laws for microstructures: from helimagnets to martensites

We consider scalar-valued variational models for pattern formation in helimagnetic compounds and in shape memory alloys. Precisely, we consider a non-convex multi-well bulk energy term on the unit square, which favors four gradients (±α,±β)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\pm }\\,\\alpha ,{\\pm }\\,\\beta )$$\\end{document}, regularized by a singular perturbation in terms of the total variation of the second derivative. We derive scaling laws for the minimal energy in the case of incompatible affine boundary conditions in terms of the singular perturbation parameter as well as the ratio α/β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha /\\beta $$\\end{document} and the incompatibility of the boundary condition. We discuss how well-studied models for martensitic microstructures in shape-memory alloys arise as a limiting case, and relations between the different models in terms of scaling laws. In particular, we show that scaling regimes arise in which an interpolation between the rather different branching-type constructions in the spirit of Kohn and Müller (Commun Pure Appl Math 47(4):405–435, 1994) and Ginster and Zwicknagl (J Nonlinear Sci 33:20, 2023), respectively, occurs. A particular technical difficulty in the lower bounds arises from the fact that the energy scalings involve various logarithmic terms that we capture in matching upper and lower scaling bounds.

Quantum annealing for microstructure equilibration with long-range elastic interactions

We demonstrate the use and benefits of quantum annealing approaches for the determination of equilibrated microstructures in shape memory alloys and other materials with long-range elastic interaction between coherent grains and their different martensite variants and phases. After a one dimensional illustration of the general approach, which requires to formulate the energy of the system in terms of an Ising Hamiltonian, we use distant dependent elastic interactions between grains to predict the variant selection for different transformation eigenstrains. The results and performance of the computations are compared to classical algorithms, demonstrating that the new approach can lead to a significant acceleration of the simulations. Beyond a discretization using simple cuboidal elements, also a direct representation of arbitrary microstructures is possible, allowing fast simulations with currently up to several thousand grains.

Influence of heat treatment on the phase transformation, thermodynamical parameters, crystal microstructure, and of Cu-Al-X (X: Cr, Ti) shape memory alloys

Shape memory alloys are known for their ability to return to their original shape under the influence of external factors (temperature, magnetic field and mechanical stress). Although NiTi-based alloys come to mind first when the shape memory effect is mentioned, CuAl-based alloys are very popular alternatives. The low cost of copper-based alloys is the biggest reason to study. In this study, the heat treatment effects of Cu-Al-X (X: Cr, Ti) (% weight) on some thermodynamic parameters, crystal structure and microstructure of shape memory alloy were investigated at three different temperatures (973 K, 1073 K and 1173 K). The changes in the thermal transformation of the samples were determined by DSC (Differential Scanning Calorimetry) and the changes in the crystal structure were determined by X-ray diffraction (XRD), Scanning Electron Microscope (SEM) and optical microscope device. According to DSC measurement, the temperature hysteresis of the samples decreased after the heat treatment. Besides, as the entropy change decreased, the thermal stability of the samples increased. It can be seen that the particle size of the CuAlCr alloy decreased with increasing temperature. The particle size of the CuAlTi alloy increased with increasing temperature. SEM and optical images showed that chromium (Cr) was more dissolved in the alloy compared to titanium (Ti) into CuAl alloy.

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

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

Rigidity of Branching Microstructures in Shape Memory Alloys

We analyze generic sequences for which the geometrically linear energy Eη(u,χ):=η-23∫B10e(u)-∑i=13χiei2dx+η13∑i=13|Dχi|(B10)\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} E_\\eta (u,\\chi )\\,{:}{=} \\,\\eta ^{-\\frac{2}{3}}\\int _{B_{1}\\left( 0\\right) } \\left| e(u)- \\sum _{i=1}^3 \\chi _ie_i\\right| ^2 \\, \\mathrm {d}x+\\eta ^\\frac{1}{3} \\sum _{i=1}^3 |D\\chi _i|({B_{1}\\left( 0\\right) }) \\end{aligned}$$\\end{document}remains bounded in the limit eta rightarrow 0. Here e(u) ,{:}{=},1/2(Du + Du^T) is the (linearized) strain of the displacement u, the strains e_i correspond to the martensite strains of a shape memory alloy undergoing cubic-to-tetragonal transformations and the partition into phases is given by chi _i:{B_{1}left( 0right) } rightarrow {0,1}. In this regime it is known that in addition to simple laminates, branched structures are also possible, which if austenite was present would enable the alloy to form habit planes. In an ansatz-free manner we prove that the alignment of macroscopic interfaces between martensite twins is as predicted by well-known rank-one conditions. Our proof proceeds via the non-convex, non-discrete-valued differential inclusion e(u)∈⋃1≤i≠j≤3conv{ei,ej},\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} e(u) \\in \\bigcup _{1\\le i\\ne j\\le 3} {\\text {conv}} \\{e_i,e_j\\}, \\end{aligned}$$\\end{document}satisfied by the weak limits of bounded energy sequences and of which we classify all solutions. In particular, there exist no convex integration solutions of the inclusion with complicated geometric structures.

A novel method for sample preparation of SMA spring for micro-structural studies

NiTi alloys are most widely used shape memory alloys (SMA). SMA in spring form is best suited for actuators as they can generate considerable forces and large displacements. Often it is necessary to know the micro structure of SMA to conclude their state as fully austenite or fully martensite at near room temperature. Sample preparation of wire for micro structural study is easier when compared to spring. This paper reveals a novel method of sample preparation for micro structural study using optical and scanning electron microscopes, of commercially available SMA spring in as received condition for which a prior history is unknown.

Quantitative Aspects of the Rigidity of Branching Microstructures in Shape Memory Alloys via H-Measures

Based on a geometrically linearized theory, we describe the partition into twins observed in microstructures of shape memory alloys undergoing cubic-to-tetragonal transformations in an ansatz-free ...

Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys

We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms of the problem parameters, which represent the shape of the nucleus, the quotient of the elastic moduli of the two phases, the surface energy constant, and the volume fraction of the two martensitic variants. We identify several different scaling regimes, which are distinguished either by the exponents in the parameters, or by logarithmic corrections, for which we have matching upper and lower bounds.

Modeling static microstructure of shape memory alloy via Legendre wavelets collocation method

The static microstructures of square-to-rectangular phase transformations are modeled in the current paper. Governing equations are described by the static Navier equations. The analysis of the simulation has been finished via Legendre wavelets collocation method. Microstructure evolutions of both 2D and 1D shape memory alloy (SMA) are capture well with a certain boundary condition and given mechanical loadings.

Analysis of austenite-martensite phase boundary and twinned microstructure in shape memory alloys: The role of twinning disconnections

An austenite-martensite phase boundary in shape memory alloys (SMA) is associated with a periodic microstructure of martensite twin lamellas. Microscopy studies show that the period, which represents the thickness of the twin lamellas, increases with the distance from the habit plane. This observation is often overlooked when the microstructure and energy of the austenite-martensite interface are evaluated. In this paper we introduce a model that reproduces the variation in the twin lamella period. For this purpose, the overall energy of the phase boundary and the accompanied twinned microstructure is formulated and minimized. In particular, the effect of twinning disconnections, via which twins are tapered or broaden, and the additional energy due to the disconnections, are considered. Fittings of model predictions with measurements based on microscopy images provide evaluations of the twin boundary and twinning disconnection energies. Comparison of the results with expressions based on the theory of dislocations indicates that interactions between disconnections play a dominant role in determining the overall energy of twinning disconnections.

Identification of crystal variants in shape-memory alloys using molecular dynamics simulations

Shape-memory alloys (SMA) have interesting behaviors and important mechanical properties due to the solid-solid phase transformation. These phenomena are dominated by the evolution of microstructures. In recent years, the microstructures in SMAs have been studied extensively and modeled using molecular dynamics (MD) simulations. However, it remains difficult to identify the crystal variants in the simulation results, which consist of large numbers of atoms. In the present work, a method is developed to identify the austenite phase and the monoclinic martensite crystal variants in MD results. The transformation matrix of each lattice is calculated to determine the corresponding crystal variant. Evolution of the volume fraction of the crystal variants and the microstructure in Ni-Ti SMAs under thermal and mechanical boundary conditions are examined. The method is validated by comparing MD-simulated interface normals with theoretical solutions. In addition, the results show that, in certain cases, the interatomic potential used in the current study leads to inconsistent monoclinic lattices compared with crystallographic theory. Thus, a specific modification is applied and the applicability of the potential is discussed.

Microstructural analysis and molecular dynamics modeling of shape memory alloys

Molecular dynamics (MD) is an effective tool for studying the microstructures in shape memory alloys at the atomic level. However, microstructural analysis of the results generated by MD is typically done by examining lattice constants or monoclinic angles, and only a limited set of the crystal variants can be identified. In the current work, a numerical method that can identify the crystal variants and multiple phases is proposed. By observing the pattern of the components in the transformation matrix of the lattice in the crystal, the corresponding variant of the lattice can be determined. The method is then applied to study the martensitic transformation induced by temperature and ultrahigh shear strain, and the resulting microstructures are verified by literature. Moreover, the microstructural evolution and the volume fraction variation of the crystal variants under ultrahigh shear strain are examined. The observed multiple stages of phase transitions imply that the current method is able to identify the austenitic, orthorhombic, trigonal (R phase), monoclinic, and body-centered orthorhombic crystal systems simultaneously. The proposed method also reveals that the nanometer-sized R phase is a transition zone that maintains the compatibility between the two phases in the different crystal systems. The proposed method is rapid, accurate, and sufficiently versatile to be applicable to other crystal systems and related materials.

Deformation concentration for martensitic microstructures in the limit of low volume fraction

We consider a singularly-perturbed nonconvex energy functional which arises in the study of microstructures in shape memory alloys. The scaling law for the minimal energy predicts a transition from a parameter regime in which uniform structures are favored, to a regime in which the formation of fine patterns is expected. We focus on the transition regime and derive the reduced model in the sense of $\Gamma$-convergence. The limit functional turns out to be similar to the Mumford-Shah functional with additional constraints on the jump set of admissible functions. One key ingredient in the proof is an approximation result for $SBV^p$ functions whose jump sets have a prescribed orientation.

Identification of crystal variants in shape-memory alloys using molecular dynamics simulations

Shape-memory alloys (SMA) have interesting behaviors and important mechanical properties due to the solid–solid phase transformation. These phenomena are dominated by the evolution of microstructures. In recent years, the microstructures in SMAs have been studied extensively and modeled using molecular dynamics (MD) simulations. However, it remains difficult to identify the crystal variants in the simulation results, which consist of large numbers of atoms. In the present work, a method is developed to identify the austenite phase and the monoclinic martensite crystal variants in MD results. The transformation matrix of each lattice is calculated to determine the corresponding crystal variant. Evolution of the volume fraction of the crystal variants and the microstructure in Ni-Ti SMAs under thermal and mechanical boundary conditions are examined. The method is validated by comparing MD-simulated interface normals with theoretical solutions. In addition, the results show that, in certain cases, the interatomic potential used in the current study leads to inconsistent monoclinic lattices compared with crystallographic theory. Thus, a specific modification is applied and the applicability of the potential is discussed.

Crystallographic Characteristics of Shape Memory Alloys

ABSTRACTThe martensitic microstructure of shape memory alloys is an aggregate of self accommodating plate groups. The principal character of this aggregate is its demonstration of pseudoplasticity, wherein a macroscopic shape change is brought about by extensive rearrangement and reorientation of the self accommodating martensite variants, and that of microstructural reversibility, wherein the polyvariant microstructure transforms back to the original grain of the parent phase after pseudoplastic deformation. These aspects of the shape memory intermetallic alloys are intriguing and, to a great extent, unsolved. The aim of this paper is to show that the underlying crystallographic interrelationships of the self accommodating microstructure of intermetallic alloys are responsible for the observed effect. The paper will discuss the relation between autocatalytic nucleation and self accommodation, the relation between microstructural reversibility and intervariant interfaces of the martensitic microstructure and the manifestations of microstructural irreversibility using results from the microstructural examination of the self accommodating microstructures.

Non-Chemical Potentials and Dissipative Forces in Thermoelastic Martensitic Transformation

*Institute of Metal Physics, National Academy of Sciences of the Ukraine,Department of Phase Transitions, 36 Vernadsky Str., 252142, Kiev, Ukraine**Departament de Fi´sica, Universitat Illes Balears. E-07071 Palma de Mallorca, Spain(Received October 16, 1997)(Accepted in revised form March 6, 1998)IntroductionDuring a martensitic transformation cycle, a shape memory alloy (SMA) runs a sequence of heterophasestates in which the fraction of martensitic phase increases continuously on cooling and decreases onheating showing a definite temperature hysteresis. At each step of both the forward and the reversetransformations the microstructure of SMA consists of a great number of plate-like martensite crystalsin an austenite matrix, appearing and growing on cooling and shrinking and disappearing on heating.Started with the works by Kurdjumov and Kurdjumov & Khandros (1–3), the problem of thermoelasticequilibrium in SMA remains still opened and has been the subject of extended discussions anddevelopments (4–13). Paskal & Monasevich (8, 9) postulated the existence of fraction dependent Gibbsfree energy potentials describing the direct and reverse martensitic transformation. They also derivedconstitutive thermodynamic force balance equations accounting for the temperature dependence of themartensite volume fraction in a global hysteresis cycle through minimisation of these, strictly speaking,non-equilibrium potentials. Some problems arise from this procedure: first, considering the configura-tion dependent thermodynamic functions as solely dependent on the martensite fraction is onlyphysically reasonable provided the microstructure sequence followed during the forward martensitictransformation is followed in the opposite sense during the reverse transformation. Such “microscopicreversibility” principle was qualitatively formulated by Olson & Cohen (5), who pointed out that growthand shrinkage of the martensitic plates take place in a well defined sequential order, the first platesformed on cooling being the last ones to disappear on heating. Second, introduction of non-equilibriumfree energies containing dissipative or frictional terms, and especially application of minimisationprinciple to them can be a source of misleading physical conclusions. Finally, the usual splitting of thefraction dependent thermodynamic potentials into pure chemical and non-chemical (elastic) compo-nents is practically useful, in the sense of their determination from the experiment, only if the purechemical equilibrium temperature T

The influence of surface energy on stress-free microstructures in shape memory alloys

Certain alloys such as In-Tl, Ni-Ti, Ag-Cd or Cu-Al-Ni display remarkable mechanical properties such as the shape memory effect or pseudo-elasticity. This behaviour is related to a solid-solid phase transformation which leads to a complicated microscopic arrangement of different phases. In recent studies such microstructures have been analyzed by the minimization of elastic energy. We discuss the influence of additional surface energy terms on the existence of stress-free microstructures both in the nonlinear and a geometrically linear setting.