Elastic Transformation Research Articles

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.

Characterization and modeling of three-dimensional self-healing shape memory alloy-reinforced metal-matrix composites

In this work, three-dimensional metal-matrix composites (MMCs) reinforced by shape memory alloy (SMA) wires are modeled and simulated, by adopting an SMA constitutive model accounting for elastic deformation, phase transformation and plastic behavior. A modeling method to create composites with pre-strained SMA wires is also proposed to improve the self-healing ability. Experimental validation is provided with a composite under three-point bending. This modeling method is applied in a series of finite element simulations to investigate the self-healing effects in pre-cracked composites, especially the role of the SMA reinforcement, the softening property of the matrix, and the effect of pre-strain in the SMA. The results demonstrate that SMA reinforcements provide stronger shape recovery ability than other, non-transforming materials. The softening property of the metallic matrix and the pre-strain in SMA are also beneficial to help crack closure and healing. This modeling approach can serve as an efficient tool to design SMA-reinforced MMCs with optimal self-healing properties that have potential applications in components needing a high level of reliability.

EXAMINING THE EFFECT OF SHAPE, SIZE AND DISTANCE OF POPS IN THE NON-LINEAR BEHAVIOR OF STEEL SHEAR WALLS

The shape and place of the holes of shear walls are effective on tensions and the elastic and non-elastic transformation and also the formability, bending resistance and capacity of absorbing energy at times of earthquakes. Thus, it is necessary to pay attention to the non-linear behavior of steel shear walls with pops and consider some strategies for reinforcing the sides of the pops. The goal of this project is studying and deeper understanding of the strength and weakness points of pops, the effect of shape and place of pops on the functioning and behavior of shear walls in the non-linear area of steel shear walls. For this purpose, we present the results of a numeric study on steel shear walls with pops. The analyses are done by the limited components Abaqus program and are calibrated by experimental results. An area of subjects that is studied in the steel shear walls with pops includes final load, and load-displacement curves. The numeric results for steel shear walls with pops would also be compared. Finally, the calculated numeric results will be compared with the experimental results. Final load and load-displacement curves gained by the numeric analysis show a good adaptation with the results gained from related experiments. Results of numeric analysis in most cases indicate that this method is a conservative one. Thus, we could use this method in designing applications.

StructMap: Elastic Distance Analysis of Electron Microscopy Maps for Studying Conformational Changes

Single-particle electron microscopy (EM) has been shown to be very powerful for studying structures and associated conformational changes of macromolecular complexes. In the context of analyzing conformational changes of complexes, distinct EM density maps obtained by image analysis and three-dimensional (3D) reconstruction are usually analyzed in 3D for interpretation of structural differences. However, graphic visualization of these differences based on a quantitative analysis of elastic transformations (deformations) among density maps has not been done yet due to a lack of appropriate methods. Here, we present an approach that allows such visualization. This approach is based on statistical analysis of distances among elastically aligned pairs of EM maps (one map is deformed to fit the other map), and results in visualizing EM maps as points in a lower-dimensional distance space. The distances among points in the new space can be analyzed in terms of clusters or trajectories of points related to potential conformational changes. The results of the method are shown with synthetic and experimental EM maps at different resolutions.

Elastic stress transmission and transformation (ESTT) by confined liquid: A new mechanics for fracture in elastic lithosphere of the earth

We report on a new mechanical principle, which suggests that a confined liquid in the elastic lithosphere has the potential to transmit a maximum applied compressive stress. This stress can be transmitted to the internal contacts between rock and liquid and would then be transformed into a normal compressive stress with tangential tensile stress components. During this process, both effective compressive normal stress and tensile tangential stresses arise along the liquid–rock contact. The minimum effective tensile tangential stress causes the surrounding rock to rupture. Liquid-driven fracture initiates at the point along the rock–liquid boundary where the maximum compressive stress is applied and propagates along a plane that is perpendicular to the minimum effective tensile tangential stress and also is perpendicular to the minimum principal stress.Liquid-driven fractures and dikes propagate along the axes of cylindrical zones that are perpendicular to the minimum compressive principal stress in rocks in non-tectonic regions. The minimum depth for liquid-driven fracture, which is induced by a spherical confined liquid and an isolated magma chamber in the elastic lithosphere, ranges from 2 to 6km, whereas dikes with hemi-cylinder-shaped ends propagate upwards closer to the surface under gravity. Transmission of pumping pressure, i.e. the pressure differences on the underside of a dike that is connected with a chamber, from the source magma chamber to intermediate and shallow chambers increases liquid pressure and also the effective tensile tangential stress and therefore leads to new fractures and dike formation and to upwards transport of magmas that have stagnated in the intermediate chamber.Tectonic stress alters local stress fields in the surrounding country rocks and therefore synchronously varies the local effective tensile tangential stress and the nature and geometry of the liquid-driven fractures.

Deformation of metallic glasses: Recent developments in theory, simulations, and experiments

We review recent research into elastic and plastic deformation of metallic glasses, with an emphasis on making connections between developments in theory and simulation (largely from the physics community) and experimental results (largely from the metallurgy community). Topics covered include strain measurement via scattering techniques, non-affine atomic displacements during elastic deformation, shear transformations, constitutive equations, shear bands, and strain hardening. Where possible we connect the observed behavior and properties to the structure of the glass on the atomic- and nano-scales.

Influence of prestress on shock behavior of polycrystalline iron via atomistic simulations

Plasticity behavior and phase transition of metal Fe subjected to shock loading have attracted considerable attention in shock physics community, in particular for underlying relationship between them. Experimental examinations and atomistic simulations on shocked Fe have displayed a three-wave structure: elastic wave, plastic wave and transformation wave. However, these studies are primarily limited to the one-dimensional planar case. Recently, owing to the rapid development of experimental techniques, investigating dynamic property of shocked metal has extended to the multi-dimensional loading conditions, such as cylindrical or spherical shocks. In this regard, fruitful findings are achieved, for example, twinning ratio in polycrystalline Fe under implosive compression is found to be much higher than that under planar shock, implying that the the complex stress state plays a critical role. In this paper, we explore the effects of prestress on plasticity and phase transition of shocked polycrystalline iron. The imposed presstress normal to the impact direction in one-dimensional planar shocking represents the varying deviatoric stress, and does not nearly affect the principal stress. The utilized empirical potential for iron could describe the plasticity dislocation and phase transition very well. The simulations show that as the prestress increases, the shock speed at elastic stage and Hugoniot elastic limit increase, which is in accordance with the theoretical analyses based on shock wave theory and experimental measurement. Meanwhile the plastic wave speed increases more quickly and catches up with the transformation wave more easily, resulting in a steep shockwave front. Atomistic snapshots show that plasticity dislocation stemming from the grain boundary precedes phase transition, where most of BCC atoms are transformed into the HCP atoms and shear stress significantly decreases. Further observations from these images find that plastic zone becomes narrower with increasing prestress, representing a shorter plastic relaxation time, which accelerates the completion of phase transition. This rapid phase transition process is also indicated by quantitatively evaluating the ratio of transitioned closed packed atoms as a function of evolution time. The origin based on the atomistical prediction model of Fe phase transition is attributed to the fact that higher prestress gives rise to the larger von-Mises stress for easier dislocation emission while lower one cannot. But the final transformed atoms are independent of prestress. Additionally, the measured free surface velocity profiles from planar and cylindrical impact loading validate the simulations conducted here. These findings will help to understand experimentally the microscopically dynamic evolution of Fe, imposed by complex stress state.

Stress state of rocks surrounding excavations under variable Young’s modulus

Deep-level mining needs extra data on physical behavior of rocks at great depths (under high stresses). Without such data, any computations for deep-level technologies based on analogy with shallowdepth technologies are non-diagnostic. Elastic moduli of rocks may depend on the accumulated plastic deformation and their reduction is considerable in the known tests of metals. It seems interesting to study the influence of this property of rocks on distribution of residual stresses and displacements. Elastic transformation of an excavation after drivage (relief of stresses) largely affects surrounding rock mass and results in origination of a transition layer around the excavation. A local drop of deformation energy takes place in the surrounding rocks, which reduces stress concentration. The problem is studied based on an analytical solution obtained for a deep round excavation subjected to constant value compressive stresses at infinity and a solution taking into account the Young modulus. The article offers an algorithm for geomechanical condition of rocks and determines ranges for stresses and displacements in the zone of influence of excavation. Examples of calculations are given, and the results are discussed.

Reconstruction-Incorporated Respiratory Motion Correction in Clinical Simultaneous PET/MR Imaging for Oncology Applications.

Simultaneous PET and MR imaging is a promising new technique allowing the fusion of functional (PET) and anatomic/functional (MR) information. In the thoracic-abdominal regions, respiratory motion is a major challenge leading to reduced quantitative and qualitative image accuracy. Correction methodologies include the use of gated frames that lead to low signal-to-noise ratio considering the associated low statistics. More advanced correction approaches, previously developed for PET/CT imaging, consist of either registering all the reconstructed gated frames to the reference frame or incorporating motion parameters into the iterative reconstruction process to produce a single motion-compensated PET image. The goal of this work was to compare these two—previously implemented in PET/CT—correction approaches within the context of PET/MR motion correction for oncology applications using clinical 4-dimensional PET/MR acquisitions. Two different correction approaches were evaluated comparing the incorporation of elastic transformations extracted from 4-dimensional MR imaging datasets during PET list-mode image reconstruction to a postreconstruction image-based approach. Eleven patient datasets acquired on a PET/MR system were used. T1-weighted 4D MR images were registered to the end-expiration image using a nonrigid B-spline registration algorithm to derive deformation matrices accounting for respiratory motion. The derived matrices were subsequently incorporated within a PET image reconstruction of the original emission list-mode data (reconstruction space [RS] method). The corrected images were compared with those produced by applying the deformation matrices in the image space (IS method) followed by summing the realigned gated frames, as well as with uncorrected motion-averaged images. Both correction techniques led to significant improvement in accounting for respiratory motion artifacts when compared with uncorrected motion-averaged images. These improvements included signal-to-noise ratio (mean increase of 28.0% and 24.2% for the RS and IS methods, respectively), lesion size (reduction of 60.4% and 47.9%, respectively), lesion contrast (increase of 70.1% and 57.2%, respectively), and lesion position (changes of 60.9% and 46.7%, respectively). Our results demonstrate significant respiratory motion compensation using both methods, with superior results from a 4D PET RS approach.

Saliency-aware food image segmentation for personal dietary assessment using a wearable computer

Image-based dietary assessment has recently received much attention in the community of obesity research. In this assessment, foods in digital pictures are specified, and their portion sizes (volumes) are estimated. Although manual processing is currently the most utilized method, image processing holds much promise since it may eventually lead to automatic dietary assessment. In this paper we study the problem of segmenting food objects from images. This segmentation is difficult because of various food types, shapes and colors, different decorating patterns on food containers, and occlusions of food and non-food objects. We propose a novel method based on a saliency-aware active contour model (ACM) for automatic food segmentation from images acquired by a wearable camera. An integrated saliency estimation approach based on food location priors and visual attention features is designed to produce a salient map of possible food regions in the input image. Next, a geometric contour primitive is generated and fitted to the salient map by means of multi-resolution optimization with respect to a set of affine and elastic transformation parameters. The food regions are then extracted after contour fitting. Our experiments using 60 food images showed that the proposed method achieved significantly higher accuracy in food segmentation when compared to conventional segmentation methods.

A 3-D constitutive model for pressure-dependent phase transformation of porous shape memory alloys

Porous shape memory alloys (SMAs) exhibit the interesting characteristics of porous metals together with shape memory effect and pseudo-elasticity of SMAs that make them appropriate for biomedical applications. In this paper, a 3-D phenomenological constitutive model for the pseudo-elastic behavior and shape memory effect of porous SMAs is developed within the framework of irreversible thermodynamics. Comparing to micromechanical and computational models, the proposed model is computationally cost effective and predicts the behavior of porous SMAs under proportional and non-proportional multiaxial loadings. Considering the pressure dependency of phase transformation in porous SMAs, proper internal variables, free energy and limit functions are introduced. With the aim of numerical implementation, time discretization and solution algorithm for the proposed model are also presented. Due to lack of enough experimental data on multiaxial loadings of porous SMAs, we employ a computational simulation method (CSM) together with available experimental data to validate the proposed constitutive model. The method is based on a 3-D finite element model of a representative volume element (RVE) with random pores pattern. Good agreement between the numerical predictions of the model and CSM results is observed for elastic and phase transformation behaviors in various thermomechanical loadings.

Topological Coding and Its Application in the Refinement of SIFT

Point pattern matching plays a prominent role in the fields of computer vision and pattern recognition. A technique combining the circular onion peeling and the radial decomposition is proposed to analyze the topology structure of a point pattern. The analysis derives a feature which records the topological structure of a point pattern. This novel feature is free from isometric assumption. It can resist various deformations such as adding points, suppressing points, affine transformations, projective transformations and elastic transformations to some degree. A refinement solution of the well known scale invariant feature transform (SIFT) algorithm is also proposed based on the probabilistic analysis of this feature. Experimental results show that the proposed refinement solution for SIFT using this feature is effective and robust.

Theory of vibrational anomalies in glasses

The theory of elasticity with spatially fluctuating elastic constants (heterogeneous-elasticity theory) is reviewed. It is shown that the vibrational anomalies associated with the boson peak can be qualitatively and quantitatively explained in terms of this theory. Two versions of a mean-field theory for solving the stochastic equation of motion are presented: the coherent-potential approximation (CPA) and the self-consistent Born approximation (SCBA). It is shown that the latter is included in the former in the Gaussian and weak-disorder limit. We are able to discuss and explain cases in which the change of the vibrational spectrum by varying an external parameter can be accounted for by changing the Debye frequency (elastic transformation) and cases in which this is not possible. In the latter case a change in the distribution of the elastic moduli has occurred.

Plastic and transformation interactions of pores in shape memory alloy plates

A three-dimensional constitutive model for shape memory alloys (SMAs) is developed along the lines of the Stebner–Brinson (SB) implementation of the Panico–Brinson model. Plastic kinematic hardening behavior is simulated in addition to elastic deformation and phase transformation. A series of finite element simulations is carried out using this model to investigate the localization effects of the stress and strain field on NiTi plates with structured arrays of pores. The application of this model on porous architectures provides insight into how geometric features influence the mechanics of the structure. The incorporation of plastic deformation shows a marked decrease in the maximum stress levels; these results are more consistent with experimental data as compared to the original SB model. Furthermore, the new results demonstrate that clustered pores lead to more distributed stresses and transformation compared to a dispersed configuration of pores, indicating the importance of pore geometry in determining the stress and strain distribution. The improved model provides a practical tool toward design and optimization of porous SMA structures.

NiTiCu 형상기억합금의 피로특성

Recently, the actuator worked by the driving recovery-force of the thermo elastic martensitic transformation of shape memory alloys(SMA) has been studied. This paper presents a study on the fatigue life of shape memory alloy (SMA) actuators undergoing thermally induced martensitic phase transformation under various stress levels. shape memory recoverable stress and strain of Ti-44.5at.%Ni-8at.%Cu alloys were by means of constant temperature tensile tests. Differential scanning calorimetry (DSC) was employed in order to investigate the transformation characteristics of the alloy before the tests. the results were summarized as follows. The martensite inducing stress incerased with the increasing of the Cu-contents. The fatigue life decreased with the increasing of the test load and the Cu-content. The data acquired will be very useful during the design process of an SMA NiTiCu element as a functional part of an actuator.

Transformational volume holography.

We analyze the bulk elastic transformation of volume holograms as a general approach for three-dimensional pupil engineering. The physical relationship between transformation and the resulting point spread function is discussed by deriving the corresponding analytical expressions. For affine transformations, an analytical solution is directly possible. However, for nonaffine transformations, the analytical solution is not straightforward and we must turn to quasi-analytical solutions using the approximation of the stationary phase. Transformational volume holography offers richer design flexibility and real-time adjustment capabilities for imaging systems.

Non rigid respiratory motion correction in whole body PET/MR imaging

Respiratory motion in PET/MR imaging leads to reduced quantitative and qualitative image accuracy. Correction methodologies include the use of respiratory synchronized gated frames which lead to low signal to noise ratio (SNR) given that each frame contains only part of the count available throughout an average PET acquisition. In this work, 4D MRI extracted elastic transformations were applied to list-mode data either inside the image reconstruction or to the reconstructed respiratory synchronized images to obtain respiration corrected PET images. Five patient datasets acquired on the SIEMENS mMR PET/MR system were used. T1-weighted 4D MR images were registered to the end expiration MR image using an elastic B-spline registration algorithm to derive deformation matrices used to account for the respiratory motion. The derived matrices were subsequently applied during the List Mode OSEM PET image reconstruction of the original emission list-mode data. The corrected images were compared with those produced by applying the elastic transformation after reconstructing PET frames followed by summing the realigned gated frames, as well as with uncorrected motion averaged images. Significant improvement was obtained by using any of the two respiratory motion correction techniques compared to uncorrected motion average images (>30% differences in tumor position and size and 25% SNR increase). Both correction approaches lead to nearly equivalent improvements (differences of <8% and <6% for the lesion FWHM and the SNR respectively). A list-mode reconstruction based respiratory motion correction for PET has been implemented and its performance evaluated. This approach was based on the use of elastic transformations derived from 4D MRI during PET image reconstrucion. Our results show significant respiratory motion compensation when compared to the motion average PET images, with slightly better contrast and SNR compared to an equivalent 4D PET image space elastic motion correction method.

Indirect determination of martensitic transformation temperature of sintered nickel-free Ti–22Nb–6Zr alloy by low temperature compression test

Nickel-free Ti–22Nb–6Zr alloys were fabricated by conventional powder metallurgy sintering method. X-ray diffractometer (XRD) investigation showed that the as-sintered alloys mainly consisted of β phase, with a few needle-like α phase precipitates. Differential scanning calorimetry (DSC) measurement in the temperature ranging from −70°C to 400°C and constant stress thermal cycling test by dynamic mechanical analysis (DMA) were unable to reveal the martensitic start temperature of sintered Ti–22Nb–6Zr alloys. Therefore low temperature compression tests were carried out to evaluate their phase transformation behavior indirectly. There was an obvious drop of both Young’s modulus and recoverable strain at −85°C∼−80°C in the Young’s modulus-temperature and recoverable strain–temperature curves of sintered Ti–22Nb–6Zr alloys respectively, which was attributed to the occurrence of thermal elastic martensitic transformation at this temperature. At the testing temperature of −85°C, a superelasticity of as high as 5.9% was achieved in the sintered alloys. The results had revealed that sintered Ti–22Nb–6Zr alloys own a great superelasticity intrinsically and would exhibit a much greater superelasticity at room temperature if their martensitic transformation start temperature (Ms) were closer to room temperature. Along with their noble biocompatibility, sintered nickel free Ti–22Nb–6Zr alloys are thus thought to be potentially competitive biomaterials for biomedical applications.

Variation in kinetics of martensitic transformation during partial thermal cycling of the TiNi alloy

Abstract A method of differential scanning calorimetry has been used for the study of variation in the kinetics of thermal elastic martensitic transformation during the thermal cycling of the equiatomic TiNi alloy through the different fractions of forward or reverse martensitic transformation temperature ranges. The results of the study have shown that “partial cooling” cycling results in damage to the crystalline structure in “transforming” and “austenite” volumes independently of whether or not “austenite” volumes undergo martensitic transformation during partial cycling. The structure damage in “martensite” volumes does not occur during “partial heating” cycling. It is caused by the fact that internal stresses relax through plastic strain in the austenite phase, resulting in an increase in defect density or the reorientation of martensite crystals in the martensite phase without the accumulation of defects.

Numerical Simulation with Thorough Experimental Validation to Predict the Build-up of Residual Stresses during Quenching of Carbon and Low-Alloy Steels

A mathematical model to calculate the build-up of residual stresses during quenching of carbon (AISI 1045) and low-alloy (AISI 4140 and 4340) cylindrical steel bars is proposed. The model is implemented as a combination of the commercial software AC3®, to simulate the microstructure evolution, and Abaqus®, to model the heat transfer and the elastic, plastic, thermal, and phase transformation strains/stresses by the finite element method. All steel properties required in the model are calculated as an average of the properties of individual microconstituents (austenite, pearlite, bainite, or martensite) weighted by their local volume fractions, enabling the model application to any type of carbon or low-alloy steel. To thoroughly verify the simulation results, experimental measurements were carried out in cylindrical bars quenched in stirred water and these measurements were compared with model results. The heat transfer coefficient between the bar and the water was calculated by an inverse solution technique, resulting in the constant value of 7200 W m–2 K–1 for the whole quenching period. For the low-alloy steels, measured and calculated volume fractions of martensite in the bar cross sections are in very good agreement, but for the carbon steel, large discrepancies are observed in the fractions of most constituents. Tangential and axial residual stresses were measured on the lateral surface of the quenched bars using the X-ray diffraction method. These stresses, which are compressive, agree well with those calculated by the present model, showing discrepancies generally lower than 10%.