Forward Transformation Research Articles

In situ characterization of the functional degradation of a [formula omitted] orientated Fe–Mn–Al–Ni single crystal under compression using acoustic emission measurements

Acoustic emission (AE) measurements were conducted in situ during cyclic compressive loading on an [001¯] orientated single crystal of Fe-Mn-Al-Ni shape memory alloy to study functional degradation of its superelastic response. The acoustic investigations were corroborated by optical microscopy, employing video imaging, and transmission electron microscopy. The analysis of acoustic emissions recorded during repeated loading and unloading sessions revealed two categories of AE signals that are differed by their characteristics in time and frequency domains. These two distinct types of AE signals were related to two underlying mechanisms: (i) the nucleation and reverse transformation of stress-induced (twinned) martensite, and (ii) the lateral growth and shrinkage of one dominant martensite variant and related dislocation activities, respectively. In addition, an asymmetry in the AE activity during forward and reverse transformation during mechanical loading and unloading was detected. In particular, an unexpected high AE activity was observed during the superelastic unloading of martensitic microstructure from the point of maximum load/strain. This effect was attributed to the reverse transformation of small, tiny areas of martensite as well as to unpinning and annihilation effects related to dislocations.

Experimental and numerical investigation of thermomechanical cycling of notched NiTi shape memory ribbon using SMA model accounting for plastic deformation

Shape memory alloys (SMAs) are being increasingly applied as thermally driven actuators. The commercially available SMA elements, however, frequently contain stress risers, either due to internal or surface defects or due to the required component shape. Stress risers represent a potential danger for the preliminary fatigue failure of such actuators but its actual mechanism is not very clear. This paper presents a combined experimental (2D DIC analysis of surface strains) and numerical analysis (SMA model with plastic deformation) of the stress, strain and phase fraction fields evolving in a thin NiTi shape memory ribbon with an artificial notch subjected to cyclic cooling-heating through transformation range under constant external force. It appeared that, even if only very low tensile stress is externally applied upon thermal cycling, local tensile stress at the notch tip sharply increases during the first cooling due to the forward martensitic transformation (MT) proceeding heterogeneously in space. This heterogeneity gives rise to plastic deformation at the notch-tip, which gradually accumulates upon thermal cycling and shields the notch tip from tensile overloading. Hence, fatigue performance of thermal NiTi actuator with stress riser depends very much on the plastic deformability of the alloy.

Simulation of isothermal reversible strain in the Ti40.7Hf9.5Ni44.8Cu5 alloy using a microstructural model

Recently it has been found that some NiTi-based alloys may undergo the forward martensite transition on isothermal holding. Moreover, such isothermal transformation under stress is accompanied by variation in reversible strain. At the same time, theoretical models do not allow describing the recoverable strain variation during holding. The aim of the present study was to adjust the microstructural model earlier developed by V. Likhachev and A. Volkov for describing strain variation due to the formation of the martensite phase on holding of NiTi-based alloys under a constant stress at temperatures within the temperature range of the forward martensite transformation. To take into account the possibility for isothermal martensite formation, a new suggestion was made, according to which the isothermal kinetics might be controlled by some relaxation process, which could change the local density of point defects and led to the fulfillment of thermodynamics condition for transformation. To include this assumption into the model some modifications have been added to constitutive equations. The modified microstructural model was used to simulate the strain variation, caused by isothermal martensite formation under various stresses. The influence of holding parameters (temperature and stress) on the maximum isothermal strain was found, and a good agreement between the simulated and experimental results was obtained. It was shown that the modified microstructural model allowed predicting the holding temperature and the stress at which the maximum isothermal strain can be found.

Inverse Transformation in Eddy Current Tomography with Continuous Optimization of Reference Defect Parameters.

This paper presents a methodology of inverse tomography transformation in eddy current tomography with the use of continuous optimization of reference defect parameters. Ferromagnetic steel samples with rectangular air inclusion defects of known dimensions were prepared and measured using an eddy current tomography setup. FEM-based (Finite Element Method based) forward tomography transformation was developed and utilized in inverse tomography transformation. The presented method of inverse tomography transformation is based on the continuous optimization of parameters that can describe the sample, such as the diameter and dimensions of the reference defect. The obtained results of inverse tomography transformation were in high accordance with the real parameters of the samples. Additionally, the presented method had acceptable repeatability. The obtained values of the sample parameters fit within the range of expanded uncertainty when compared to the real parameters of the sample.

Schema Compliant Consistency Management via Triple Graph Grammars and Integer Linear Programming

In the field of Model-Driven Engineering, Triple Graph Grammars(TGGs) play an important role as a rule-based means of implementingconsistency management. From a declarative specification of aconsistency relation, several operations including forward andbackward transformations, (concurrent) synchronisation, andconsistency checks can be automatically derived. For TGGs to beapplicable in realistic application scenarios, expressiveness interms of supported language features is very important. A TGG toolis schema compliant if it can take domain constraints, such asmultiplicity constraints in a meta-model, into account whenperforming consistency management tasks. To guarantee schemacompliance, most TGG tools allow application conditions to beattached as necessary to relevant rules. This strategy isproblematic for at least two reasons: First, ensuring compliance toa sufficiently expressive schema for all previously mentionedderived operations is still an open challenge; to the best of ourknowledge, all existing TGG tools only support a very restrictedsubset of application conditions. Second, it is conceptuallydemanding for the user to indirectly specify domain constraints asapplication conditions, especially because this has to be completelyrevisited every time the TGG or domain constraint is changed. Whiledomain constraints can in theory be automatically transformed toobtain the required set of application conditions, this has onlybeen successfully transferred to TGGs for a very limited subset ofdomain constraints. To address these limitations, this paperproposes a search-based strategy for achieving schema compliance. Weshow that all correctness and completeness properties, previouslyproven in a setting without domain constraints, still hold whenschema compliance is to be additionally guaranteed. Animplementation and experimental evaluation are provided to supportour claim of practical applicability.

A micromechanics-based constitutive model for nanocrystalline shape memory alloys incorporating grain size effects

A micromechanics-based model is developed to capture the grain-size dependent superelasticity of nanocrystalline shape memory alloys (SMAs). Grain-size effects are incorporated in the proposed model through definition of dissipative length scale and energetic length scale parameters. In this paper, nanocrystalline SMAs are considered as two-phase composites consisting of the grain-core phase and the grain-boundary phase. Based on the Gibbs free energy including the spatial gradient of the martensite volume fraction, a new transformation function determining the evolution law for transformation strain is derived. Using micromechanical averaging techniques, the grain-size-dependent superelastic behavior of nanocrystalline SMAs can be described. The internal length scales are calibrated using experimental results from published literature. In addition, model validation is performed by comparing the model predictions with the corresponding experimental data on nanostructured NiTi polycrystalline SMA. Finally, effects of the internal length scales on the critical stresses for forward and reverse transformations, the hysteresis loop area (transformation dissipation energy), and the strain hardening are investigated.

An Extended Three-Dimensional Finite Strain Constitutive Model for Shape Memory Alloys

AbstractA 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for smooth thermomechanical response; temperature dependence of the critical force required for (re)orientation, temperature, and load dependence of the hysteresis width; and asymmetry between forward and reverse phase transformation, and it is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated, and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, and nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, which further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments, and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.

Assessment of ocean wave spectrum using global Envisat/ASAR data and hindcast simulation

Wave mode of spaceborne synthetic aperture radar (SAR) is designed for the global ocean wave observations. Despite the fact that the significant wave height inferred from SAR measurements has been validated against model output and in-situ data, SAR's primary and unique capability for operational 2-dimensional spectral description of sea state remains to be fully evaluated. In this study, we extended the previous assessment approaches by introducing a new SAR image spectral parameter, the Mean rAnge Cross-Spectrum (MACS) that focuses on the isolated wave scales along the radar line-of-sight direction. MACS is an efficient variable in that it characterizes the local wave spectra properties without need of the non-linear wave inversion procedure. The assessment is based on the multiple-year data acquired by Envisat/ASAR wave mode, along with the collocated WaveWatch III (WW3) hindcast and the in-situ buoy-observed wave spectra, for which the SAR forward transformation is systematically performed to obtain the simulated image spectra. Inter-comparison between SAR-measured and WW3-simulated MACS demonstrates that the consistency is wavelength (or wavenumber) dependent. Three typical wavelengths, around 62 m for windsea, 168 m for intermediate waves and 342 m for swell, are selected to present the MACS comparison in detail. Comparable magnitude of SAR-measured and the simulated MACS is observed for the intermediate waves and swell, while larger simulation values are predicted for the windsea waves. Spatial distribution of MACS agrees well between these two data sets for all wavelengths with high correlation coefficients (>0.8) in most of the global ocean. One exception is in the extratropics where the quantitative difference is particularly notable. In the contrary, when comparing SAR-measured and buoys-simulated MACS, the agreement increases towards the shorter (<100 m) wavelengths. We also found that the large-scale atmospheric/oceanic features persistent on SAR images lead to the overestimate of SAR MACS at long wavelengths, which is expected to bias the wave inversion. The wave spectra retrieval performance shall advance as long as such impact is properly resolved.

Finite-time stabilization for a first-order hyperbolic system with integral kernel by boundary control

This paper consider the finite-time boundary stabilization for a first-order hyperbolic system with integral kernel and lower order term. Via choosing a suitable integral transformation converting the original system into a finite-time stable object system, then, we obtain the control law and certify the finite-time stabilization of the closed-loop system combined with the finite-time stability of object system and invertibility of forward transformation.

Solutions of the Multivariate Inverse Frobenius-Perron Problem.

We address the inverse Frobenius–Perron problem: given a prescribed target distribution , find a deterministic map M such that iterations of M tend to in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map; that is, a map under which the uniform distribution on the d-dimensional hypercube is invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via one-dimensional examples, and then use the factorization to present solutions in one and two dimensions induced by a range of uniform maps.

Microstructure and Magnetic Properties of Selected Laser Melted Ni-Mn-Ga and Ni-Mn-Ga-Fe Powders Derived from as Melt-Spun Ribbons Precursors

Selective Laser Melting was successfully used as a fabrication method to produce Ni-Mn-Ga and Ni-Mn-Ga-Fe ferromagnetic shape memory alloys. The starting material in a powder form with an average particle size of about 17.6 µm was produced by milling of as melt-spun ribbons. The microstructure, phase composition, and martensitic transformation behavior of both powder precursors and laser melted alloys were investigated by several methods, including high energy X-ray diffraction, electron microscopy, and vibrating sample magnetometry. The as laser melted materials are chemically homogenous and show a typical layered microstructure. Both alloy compositions have a duplex structure consisting either of austenite and 10M martensite (Ni-Mn-Ga) or a mixture of 14M and NM martensitic phases (Ni-Mn-Ga-Fe), contrary to the as milled powder precursors showing fcc structure in both cases. The forward martensitic transformation takes place at 336 and 325 K for Ni-Mn-Ga and Ni-Mn-Ga-Fe, respectively, while the magnetic response is much stronger for Ni-Mn-Ga than for the quaternary alloy. The results show that Selective Laser Melting allows for producing of good quality, homogenous materials. However, their microstructural features and consequently shape memory behavior should be tailored by additional heat treatment.

Architected material analogs for shape memory alloys

Architected material analogs for shape memory alloys

Pareto Optimal Design of a Fuzzy Adaptive Hierarchical Sliding-mode Controller for an X-Z Inverted Pendulum System

ABSTRACT The control problem of a three-degree-of-freedom (3-DOF) X-Z inverted pendulum as an unstable, multi-input-multi-output, under-actuated and high-order nonlinear system is facing many challenges. In this paper, a Fuzzy Adaptive Hierarchical Sliding-Mode Controller (FAHSMC) is optimally designed for the X-Z inverted pendulum system utilizing the Multi-Objective Genetic Algorithm (MOGA). To this end, at first, the state variables of this system are converted to the new state variables via five steps of a forward transformation process. In this transformation, the dynamical equations of the X-Z inverted pendulum system are reorganized to an appropriate form for control implementations. Then, the novel FAHSMC is designed for stabilization and tracking control of the system, and the stability analysis of the controller is proved via the Lyapunov stability theory. After that, the state and control variables of the X-Z inverted pendulum are computed through six steps of a backward transformation process. Ultimately, the MOGA is exerted for Pareto optimal design of the proposed control approach applied on the regarded X-Z inverted pendulum system. The tracking error of the cart position in the X-direction, the tracking error of the cart position in the Z-direction and the angle error of the pendulum are selected as three inconsistent objective functions for multi-objective optimization operations. Numerical results and diagrams illustrate that the proposed approaches can accurately converge the system states to the desirable trajectories in a short time and yield superior Pareto optimal fronts in comparison with the Hierarchical Sliding-Mode Controller (HSMC) and the Adaptive Hierarchical Sliding-Mode Controller (AHSMC).

Temperature Dependence of Martensite Variant Reorientation in Stress-Induced Martensite Aged Ni49fe18ga27co6 Single Crystals

In the present study, the temperature dependence of martensite variant reorientation in stress-induced martensite aged at 423 K along the [110]B2||[100]L10-direction Ni49Fe18Ga27Co6 single crystals was investigated in compression. This martensite aging induces a rubber-like behavior with a reversible strain of up to –16.0% along the [001]B2-direction in the temperature range from 248 K to 344 K, which is caused by L10-martensite variant reorientation. At higher temperatures between the forward and reverse transformation from 344 K to 382 K, the stress-induced martensite aged crystals demonstrate a two-stage stress-strain response with a reversible strain of up to –13.5%. The first stage is characterized by low critical stresses of σcr1 ≈ 1 – 15 MPa and an inverse elastocaloric effect (heat absorption) under loading. Super-elasticity is observed in the second stage with σcr2 ≥ 100 MPa. In this temperature range, the martensite variant reorientation occurs through reverse and then forward martensitic transformation.

Thermo-mechanical characterisation of NiTi-based shape memory alloy wires for civil engineering applications

Shape Memory Alloys (SMAs) exhibit a complex material behaviour due to thermo-mechanical coupling. At present, the understanding of their material behaviour under different thermo-mechanical loading conditions relevant to civil engineering applications is lacking even though they have been widely used in the past decade or so, for example mechanical behaviour at constant stress but variable temperature loading has not received much attention in civil engineering. In this study a comparative analysis of the mechanical behaviour of various NiTi-based SMAs is carried out to investigate: (1) stress-elongation and stress-temperature response under direct tensile loading; (2) thermo-mechanical behaviour under constant stress condition but under variable temperature loading (to investigate their ability to exhibit shape memory effect, if any, while carrying load); and (3) the ability to develop and retain recovery stress at room and sub-zero temperatures. Essentially, all these tests aim at investigating the potential/limitations of the SMAs in civil engineering in particular re-centring and heat-activated prestressing applications. The results from this study showed that at a constant stress of 600 MPa a large forward transformation strain, in the range of 5%–11%, is produced in NiTi-based SMAs when the temperature is lowered to or below the room temperature. This material behaviour of NiTi-based SMAs could be detrimental in many civil engineering applications of NiTi-based SMAs. However, all NiTi-based SMAs used in this study were found to have a good potential for re-centring applications, but only austenitic NiTi-based SMAs were found suitable for long-term prestressing applications. The maximum recovery stress developed on heating with constrained boundary conditions ranged between 230–750 MPa.

Metal artifact reduction method based on a constrained beam-hardening estimator for polychromatic x-ray CT

Beam hardening in x-ray computed tomography (CT) is inevitable because of the polychromatic x-ray spectrum and energy-dependent attenuation coefficients of materials, leading to the underestimation of artifacts arising from projection data, especially on metal regions. State-of-the-art research on beam-hardening artifacts is based on a numerical method that recursively performs CT reconstruction, which leads to a heavy computational burden. To address this computational issue, we propose a constrained beam-hardening estimator that provides an efficient numerical solution via a linear combination of two images reconstructed only once during the entire process. The proposed estimator reflects the geometry of metal objects and physical characteristics of beam hardening during the transmission of polychromatic x-rays through a material. Most of the associated parameters are numerically obtained from an initial uncorrected CT image and forward projection transformation without additional optimization procedures. Only the unknown parameter related to beam-hardening artifacts is fine-tuned by linear optimization, which is performed only in the reconstruction image domain. The proposed approach was systematically assessed using numerical simulations and phantom data for qualitative and quantitative comparisons. Compared with existing sinogram inpainting-based and model-based approaches, the proposed scheme in conjunction with the constrained beam-hardening estimator not only provided improved image quality in areas surrounding the metal but also achieved fast beam-hardening correction owing to the analytical reconstruction structure. This work may have significant implications in improving dose calculation accuracy or target volume delineation for treatment planning in radiotherapy.

Martensite and reverse transformation temperatures of TiAu-based and TiIr-based intermetallics

Dependence of transformation temperatures of TiAu- and TiIr-based Intermetallics on Valence Electron Ratio (VER), number of valence electrons (ev) and average atomic number of the alloys (Z) were investigated. The alloys mostly have medium numbers of valence electrons (6.5 ≤ ev ≤ 7.3) near 7 with a limited number of TiAu-based alloys belonging to high valence electron group with ev more than 7.50 and relatively narrow range of average atomic numbers (Z = 41–53). The forward and reverse phase transformation temperatures, Ms and As of AuTi-based alloys sharply increase with the average atomic number of the alloys. The investigated TiIr alloy compositions have almost similar average atomic numbers (49.5–50.2). Clear correlations between transformation temperatures and VER were found. Ms and As both decrease from around 1550 °C to as low as 17 °C respectively, with increasing VER from 0.131 to 0. 174. The dependence of transformation temperatures on valence electron ratio is discussed based on the variations of elastic properties and atomic bonding due to composition change in these alloys.

Efficient Synthesis of Linearly Polarized Shaped Patterns Using Iterative FFT via Vectorial Least-Square Active Element Pattern Expansion

A novel method is presented to efficiently synthesize linearly polarized shaped patterns for antenna arrays mounted on complex platforms surrounded with many scatters. The vectorial active element patterns (Vec. AEPs) are adopted to include the mutual coupling and complex platform effect. The vectorial least-square (LS) active element pattern expansion (Vec. LSAEPE) method is developed to approximate each Vec. AEP as the radiation from a virtual subarray with identical element patterns, so that the fast Fourier transform (FFT) can be utilized to efficiently perform the forward and backward transformations between the excitation distribution and the vectorial array pattern including mutual coupling. An energy-based weighted averaging method is introduced to merge the excitation vectors obtained from copolarization (CoP) and cross-polarization (XP) pattern synthesis in each iteration and consequently the obtained final excitation vector can simultaneously meet both the CoP and XP pattern requirements. The method is called the iterative Vec. LSAEPE-FFT significantly extends the FFT-based synthesis technique to be capable of controlling the CoP main lobe shape, sidelobe distribution, and the XP level. Three examples for synthesizing different shaped patterns for different antenna arrays on complex platforms are conducted to validate the effectiveness of the proposed method. A comparison with some other representative methods is also provided to verify the advantages of the proposed method in both accuracy and efficiency.

Valence Electron Ratio for Design of Shape Memory Alloys with Desired Phase Transformation Temperatures

Dependence of phase transformation temperatures of TiPd- and TiPt-based shape memory alloys on valence electron ratio (VER), number (ev/a), and average atomic number of the alloys (Z) are investigated. The alloys have medium numbers of valence electrons (6.6 ≤ ev/a ≤ 7.3) that are near 7 and a wide range of the average atomic number (Z = 25–54). The forward and reverse phase transformation temperatures, Ms and (As), increase with average atomic number of the alloys, respectively. Clear correlations between transformation temperatures and VER are found. Ms and (As) both decrease from around 1184 °C (1175 °C) to as low as 20 °C (32 °C), respectively, with increasing VER from 0.134 to 0.270. Temperature hysteresis of the thermoelastic transformation in these alloys tends to decrease with increasing VER. Dependence of transformation temperatures and temperature hysteresis of these shape memory alloys on VER is discussed based on the variations of elastic moduli and atomic bonding due to composition change.

Lattice Defects Generated by Cyclic Thermomechanical Loading of Superelastic NiTi Wire

Cyclic instability of stress–strain–temperature functional responses of NiTi is presumably due to the plastic deformation accompanying martensitic transformation proceeding under external stress. In order to obtain systematic experimental evidence on this, we have performed series of cyclic thermomechanical loading tests (10 cycles) on superelastic NiTi wires with nanocrystalline microstructure, evaluated accumulated unrecovered strains and analysed permanent lattice defects created during the cycling by TEM. The accumulated unrecovered strains and density of lattice defects increased with increasing temperature and stress, at which the forward and/or reverse transformation proceeded. It did not correlate with the temperature and stress applied in the test as such. If the martensitic transformation proceeded at low stress ( 250 MPa), the responses were very unstable (large accumulated unrecovered strains and high density of dislocations and deformation bands). A scheme allowing for estimating the cyclic instability of functional behaviours of various NiTi wires in wide range of thermomechanical loading tests was introduced.