Applied Strain Field Research Articles

Cumulative effects of primary radiation damage in alloy 800H: An atomistic simulation study

Fe-Ni-Cr-based alloys, including alloy 800H, are used as structural materials in nuclear reactors such as the PWRs and BWRs, but also are considered as candidate materials for advanced reactors. In this work, we report a molecular dynamics (MD) study of the effect of irradiation and alloy composition on the microstructure and mechanical behavior of alloy 800H. Our results of primary irradiation damage suggest a larger spontaneous recombination distance for Cr compared to other alloy components, thereby suggesting that Cr may increase the tolerance of the alloy 800H to primary defect production. The progressive accumulation of irradiation events through cascade overlap results in the growth of defects and their agglomeration into clusters, but also induces the formation of dislocations. Irradiation-induced mechanical degradation was also investigated for the single crystal, and based on our observations two degradation mechanisms were proposed: the nucleation and glide of dislocations, promoted by the dynamics of interstitial atoms and vacancies defects under applied strain field, and the rapid activation of slip systems by the combined effect of the foregoing and generated dislocations, vacancies and interstitial atoms. We also found that increasing Ni or Cr substantially limits the irradiation-induced mechanical degradation. Finally, our MD findings highlight the strengthening of alloy 800H by increasing Ni content, and the degradation of the Young modulus induced by the increase of Cr content.

Two new in-plane torsion tests for the investigation of self-heating under pure shear cyclic loading

The fatigue limit under a pure shear loading is very complex to determine for thin sheet materials. In this paper, two new specimen geometries are proposed to assess the fatigue limit under this condition using self-heating measurements for isotropic material. Both new geometries are disc-shaped with particular designs to promote a homogeneous stress field. Strain gauge measurements confirmed that the applied strain fields correspond to a pure shear condition. The thermal fields were imaged by an infrared camera, demonstrating the validity of using a 0D thermal approach. In this way, fatigue limits under pure shear loading could be determined.

Phenomenology of chiral Dzyaloshinskii-Moriya interactions in strained materials

We use phenomenological symmetry arguments to demonstrate that while chiral magnetic (Dzyaloshinskii-Moriya) interactions are conventionally restricted by symmetry to appear in a limited set of noncentrosymmetric materials, they may arise in a material with any symmetry when coupled to a strain field. We derive point-group specific free-energy functionals that capture the relationship between an applied strain field and chiral magnetic couplings, demonstrating how strain may offer highly selective control over magnetic textures. Finally, we discuss several examples of common strain configurations that may lead to out-of-plane modulation in the magnetic moment of a quasi-two-dimensional film as required for applications in magnetic devices.

The critical strain - A crossover from stochastic activation to percolation of flow units during stress relaxation in metallic glass

The stress relaxation processes of strained Zr50Cu50 metallic glass (MG) are investigated by molecular dynamics simulations. We provide the direct evidence for the strain-accelerated relaxation which can be attributed to the activation of flow units in MGs. Moreover, a crossover from stochastic activation to percolation of flow units corresponding to a critical applied strain can be observed. The temperature influence on the strain-accelerated dynamics is also discussed. Our results may be helpful for the understanding of the relaxation dynamics under applied strain field and deepen the comprehension of the nature of MG.

Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide

We present a detailed mechanism of, and the effect of homogeneous strains on, the migration of uranium vacancies in ${\mathrm{UO}}_{2}$. Vacancy migration pathways and barriers are identified using density functional theory and the effect of uniform strain fields are accounted for using the dipole tensor approach. We report complex migration pathways and noncubic symmetry associated with the uranium vacancy in ${\mathrm{UO}}_{2}$ and show that these complexities need to be carefully accounted for to predict the correct diffusion behavior of uranium vacancies. We show that under homogeneous strain fields, only the dipole tensor of the saddle with respect to the minimum is required to correctly predict the change in the energy barrier between the strained and the unstrained case. Diffusivities are computed using kinetic Monte Carlo simulations for both neutral and fully charged state of uranium single and divacancies. We calculate the effect of strain on migration barriers in the temperature range 800\char21{}1800 K for both vacancy types. Homogeneous strains as small as $2%$ have a considerable effect on diffusivity of both single and divacancies of uranium, with the effect of strain being more pronounced for single vacancies than divacancies. In contrast, the response of a given defect to strain is less sensitive to changes in the charge state of the defect. Further, strain leads to anisotropies in the mobility of the vacancy and the degree of anisotropy is very sensitive to the nature of the applied strain field for strain of equal magnitude. Our results suggest that the influence of strain on vacancy diffusivity will be significantly greater when single vacancies dominate the defect structure, such as sintering, while the effects will be much less substantial under irradiation conditions where divacancies dominate.

Research on non-uniform strain profile reconstruction along fiber Bragg grating via genetic programming algorithm and interrelated experimental verification

A new heuristic strategy for the non-uniform strain profile reconstruction along Fiber Bragg Gratings is proposed in this paper, which is based on the modified transfer matrix and Genetic Programming(GP) algorithm. The present method uses Genetic Programming to determine the applied strain field as a function of position along the fiber length. The structures that undergo adaptation in genetic programming are hierarchical structures which are different from that of conventional genetic algorithm operating on strings. GP regress the strain profile function which matches the ‘measured’ spectrum best and makes space resolution of strain reconstruction arbitrarily high, or even infinite. This paper also presents an experimental verification of the reconstruction of non-homogeneous strain fields using GP. The results are compared with numerical calculations of finite element method. Both the simulation examples and experimental results demonstrate that Genetic Programming can effectively reconstruct continuous profile expression along the whole FBG, and greatly improves its computational efficiency and accuracy.

An organotypic uniaxial strain model using microfluidics

Traumatic brain injuries are the leading cause of disability each year in the US. The most common and devastating consequence is the stretching of axons caused by shear deformation that occurs during rotational acceleration of the brain during injury. The injury effects on axonal molecular and functional events are not fully characterized. We have developed a strain injury model that maintains the three dimensional cell architecture and neuronal networks found in vivo with the ability to visualize individual axons and their response to a mechanical injury. The advantage of this model is that it can apply uniaxial strains to axons that make functional connections between two organotypic slices and injury responses can be observed in real-time and over long term. This uniaxial strain model was designed to be capable of applying an array of mechanical strains at various rates of strain, thus replicating a range of modes of axonal injury. Long term culture, preservation of slice and cell orientation, and slice-slice connection on the device was demonstrated. The device has the ability to strain either individual axons or bundles of axons through the control of microchannel dimensions. The fidelity of the model was verified by observing characteristic responses to various strain injuries which included axonal beading, delayed elastic effects and breakdown in microtubules. Microtubule breakdown was shown to be dependent on the degree of the applied strain field, where maximal breakdown was observed at peak strain and minimal breakdown is observed at low strain. This strain injury model could be a powerful tool in assessing strain injury effects on functional axonal connections.

Cyclic strain anisotropy regulates valvular interstitial cell phenotype and tissue remodeling in three-dimensional culture

Many planar connective tissues exhibit complex anisotropic matrix fiber arrangements that are critical to their biomechanical function. This organized structure is created and modified by resident fibroblasts in response to mechanical forces in their environment. The directionality of applied strain fields changes dramatically during development, aging, and disease, but the specific effect of strain direction on matrix remodeling is less clear. Current mechanobiological inquiry of planar tissues is limited to equibiaxial or uniaxial stretch, which inadequately simulates many in vivo environments. In this study, we implement a novel bioreactor system to demonstrate the unique effect of controlled anisotropic strain on fibroblast behavior in three-dimensional (3-D) engineered tissue environments, using aortic valve interstitial fibroblast cells as a model system. Cell seeded 3-D collagen hydrogels were subjected to cyclic anisotropic strain profiles maintained at constant areal strain magnitude for up to 96h at 1Hz. Increasing anisotropy of biaxial strain resulted in increased cellular orientation and collagen fiber alignment along the principal directions of strain and cell orientation was found to precede fiber reorganization. Cellular proliferation and apoptosis were both significantly enhanced under increasing biaxial strain anisotropy (P<0.05). While cyclic strain reduced both vimentin and alpha-smooth muscle actin compared to unstrained controls, vimentin and alpha-smooth muscle actin expression increased with strain anisotropy and correlated with direction (P<0.05). Collectively, these results suggest that strain field anisotropy is an independent regulator of fibroblast cell phenotype, turnover, and matrix reorganization, which may inform normal and pathological remodeling in soft tissues.

Development of a synchrotron biaxial tensile device for in situ characterization of thin films mechanical response

We have developed on the DIFFABS-SOLEIL beamline a biaxial tensile machine working in the synchrotron environment for in situ diffraction characterization of thin polycrystalline films mechanical response. The machine has been designed to test compliant substrates coated by the studied films under controlled, applied strain field. Technological challenges comprise the sample design including fixation of the substrate ends, the related generation of a uniform strain field in the studied (central) volume, and the operations from the beamline pilot. Preliminary tests on 150 nm thick W films deposited onto polyimide cruciform substrates are presented. The obtained results for applied strains using x-ray diffraction and digital image correlation methods clearly show the full potentialities of this new setup.

Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field

This paper examines the evolution of an axisymmetric two-dimensional vortex in a steadily rotating strain field and the dynamical interactions that can enhance vortex spreading through resonant behaviour. Starting with a point vortex localized at the origin, the applied strain field generates a cat's eye topology in the co-rotating streamfunction, localized around a radius rext. Now the vortex is allowed to spread viscously: initially rext lies outside the vortex, but as it spreads, vorticity is advected into the cat's eyes, leading to a local flattening of the mean profile of the vortex and so to enhanced mixing and spreading of the vortex. Together with this is a feedback: the response of the vortex to the external strain depends on the modified profile. The feedback is particularly strong when rext coincides with the radius rcat at which the vortex can support cat's eyes of infinitesimal width. There is a particular time at which this occurs, as these radii change with the viscous spread of the vortex: rext moves inwards and rcat outwards. This resonance behaviour leads to increased mixing of vorticity, along with a rapid stretching of vorticity contours and a sharp increase in the amplitude of the non-axisymmetric components. The dynamical feedback and enhanced diffusion are studied for viscously spreading vortices by means of numerical simulations of their time evolution, parameterized only by the Reynolds number R and the dimensionless strength A of the external strain field.

Whole Bone Strain Quantification by Image Registration: A Validation Study

Quantification of bone strain can be used to better understand fracture risk, bone healing, and bone turnover. The objective of this work was to develop and validate an intensity matching image registration method to accurately measure and spatially resolve strain in vertebrae using microCT imaging. A strain quantification method was developed that used two sequential microCT scans, taken in loaded and unloaded configurations. The image correlation algorithm implemented was a multiresolution intensity matching deformable registration that found a series of affine mapping between the unloaded and loaded scans. Once the registration was completed, the displacement field and strain field were calculated from the mappings obtained. Validation was done in two distinct ways: the first was to look at how well the method could quantify zero strain; the second was to look at how the method was able to reproduce a known applied strain field. Analytically defined strain fields that linearly varied in space and strain fields resulting from finite element analysis were used to test the strain measurement algorithm. The deformable registration method showed very good agreement with all cases imposed, establishing a detection limit of 0.0004 strain and displaying agreement with the imposed strain cases (average R2=0.96). The deformable registration routine developed was able to accurately measure both strain and displacement fields in whole rat vertebrae. A rigorous validation of any strain measurement method is needed that reports on the ability of the routine to measure strain in a variety of strain fields with differing spatial extents, within the structure of interest.

Development of a Biaxial Tensile Module at Synchrotron Beamline for the Study of Mechanical Properties of Nanostructured Films

AbstractWe have developed on the DIFFABS-SOLEIL beamline a biaxial tensile machine with synchrotron standard for in-situ diffraction characterization of thin polycrystalline metallic film mechanical response. The machine has been designed to test cruciform substrates coated by the studied film under controlled applied strain field. Technological challenges comprise the fixation of the substrate, the generation of a uniform strain field in the studied (central) volume, the operations from the beamline pilot. Tests on W and W/Cu multilayers films deposited on polyimide substrates are presented.

An analytical solution for the load distribution along a fibre in a nonwoven network

This paper develops a method to analyse the load distribution along a half fibre in a nonwoven or fibre composite where force is transferred into the fibre at any set of discrete contacts. The force transferred at each contact is assumed to be proportional to the displacement of the contact relative to the applied strain field. The constant of proportionality between displacement and force can be set independently for each contact. The cross-sectional area and elastic modulus of each segment between contacts can also be set independently. It was shown that the displacement, due to the applied strain, at each contact could be expressed in terms of the displacement at the last contact at the end of the fibre. As the displacement at the last contact was the sum of the previous contacts, each multiplied by a stress transfer coefficient, the stress distribution along the fibre could be solved analytically. The debonding of fibres from a paper sheet under load was simulated. The fibre load–network strain curve was found to be highly sensitive to the configuration of the crossing points. The method of analysis has application to nonwoven networks such as paper as well as nonwoven fibre composites.

Scaling of the $E(J)$ Characteristics in the ITER Type ${\rm Nb}_{3}{\rm Sn}$ Strands in Relation to the Applied Strain and Magnetic Field

Voltage- current characteristics VCC(epsiv, B, 4.2 K) have been measured in the range of the applied axial tensile strain (epsiv) from 0% to 0.93% at magnetic fields 10 T and 12 T for ITER type bronze processed Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strand and for similar strand with enhanced mechanical strength in which part of stabilizing copper was replaced by high strength high conductivity microcomposite Cu-Nb material. The results of description of the electric field-current density characteristics E(J,epsiv,B,4.2 K) are presented. To describe experimental database E( J) versus strain and magnetic field the relation is used containing four fitting parameters. Three parameters,namely: C, T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (0) and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c2</sub> (0, epsiv) describe. Additional parameter characterizes the smoothness of E( J). Good agreement of experiment and calculation has been obtained.

Active Elasticity of Gels with Contractile Cells

Cells play an active role in the maintenance of mechanical homeostasis within tissues and their response to elastic forces is important for tissue engineering. We predict the collective response of an ensemble of contractile cells in a three-dimensional elastic medium to externally applied strain fields. Motivated by experiment, we model the cells as polarizable force dipoles that change their orientation in response to the local elastic strain. The analogy between the mechanical response of these systems and the dielectric response of polar molecules is used to calculate the elastic response function. We use this analogy to evaluate the average cell orientation, the mean polarization stress, and the effective elastic constants of the material, as a function of the cell concentration and matrix properties.

Turbulent plane wakes subjected to successive strains

Six direct numerical simulations of turbulent time-evolving strained plane wakes have been examined to investigate the response of a wake to successive irrotational plane strains of opposite sign. The orientation of the applied strain field has been selected so that the flow is the time-developing analogue of a spatially developing wake evolving in the presence of either a or an streamwise pressure gradient. The magnitude of the applied strain rate a is constant in time t until the total strain e(sup at) reaches about four. At this point, a new simulation is begun with the sign of the applied strain being reversed (the original simulation is continued as well). When the total strain is reduced back to its original value of one, yet another simulation is begun with the sign of the strain being reversed again back to its original sign. This process is done for both initially favourable and initially adverse strains, providing simulations for each of these strain types from three different initial conditions. The evolution of the wake mean velocity deficit and width is found to be very similar for all the strained cases, with both measures rapidly achieving exponential growth at the rate associated with the cross-stream expansive strain e(sup at). In the favourably strained cases, the wake widths approach a constant and the velocity deficits ultimately decay rapidly as e(sup -2at). Although all three of these cases do exhibit the same asymptotic exponential behaviour, the time required to achieve this is longer for the cases that have been previously strained (by at approx. equals 1). These simulations confirm the generality of the conclusions drawn in Rogers (2002) regarding the response of plane wakes to strain. The evolution of strained wakes is not consistent with the predictions of classical self-similar analysis; a more general equilibrium similarity solution is required to describe the results. At least for the cases considered here, the wake Reynolds number and the ratio of the turbulent kinetic energy to the square of the wake mean velocity deficit are determined nearly entirely by the total strain. For these measures the order in which the strains are applied does not matter and the changes brought about by the strain are nearly reversible. The wake mean velocity deficit and width, on the other hand, differ by about a factor of three when the total strain returns to one, depending on whether the wake was first favourably or adversely strained. The strain history is important for predicting the evolution of these quantities.

The role of recrystallisation on the deformation behaviour of calcite rocks: large strain torsion experiments on Carrara marble

The rheological, microstructural and textural evolution of Carrara marble was studied during experimental deformation in torsion up to very large shear strains ( γ=0.4–50). Experiments were performed at constant angular displacement rates corresponding to shear strain rates of 6×10 −5–3×10 −3 s −1, a confining pressure of 300 MPa and temperatures of 500, 600 and 727 °C. Microstructures and crystallographic preferred orientations (CPO) were analysed using light microscopy and electron backscatter diffraction (EBSD). At all conditions deformation occurred dominantly by dislocation creep, even up to very large shear strains. After peak stresses ( γ≤2), recrystallisation mostly by subgrain rotation caused weakening (5–20%), grain size reduction and a change in the CPO. A monoclinic CPO that formed at small strains at all temperatures evolved into two different large strain CPOs at different temperatures. At large strains, even after complete recrystallisation, the CPO continued to strengthen and a secondary foliation was formed at a steep angle to the shear zone boundary. This secondary foliation was continuously reset by both subgrain rotation and grain boundary migration recrystallisation and eventually overprinted the primary foliation. Misidentifying the primary and secondary foliations could result in misinterpretation of the applied strain field. More generally, information about the amount of strain is lacking for microstructures and CPOs of highly deformed ultramylonites.

Influence of an applied strain field on microstructural evolution during the α 2 → O-phase transformation in Ti–Al–Nb system

We investigate the influence of an applied homogeneous strain on the coherent α 2 ( DO 19) to O-phase transformation in Ti–Al–Nb alloys using a phase-field approach. The emphasis is on the effect of the applied strain on the two-phase morphology, as well as the equilibrium volume fractions of different orientation domains of the O-phase. It is found that the applied homogeneous strain field does not change the essential features of the morphological patterns, but does alter the relative amount of each orientation domain and the equilibrium volume fraction of the O-phase. When the applied strain is of the same order of magnitude as the stress-free transformation strain, the initial two-phase mixture becomes unstable and transforms into a single O-phase.

Experimental verification of response of embedded optical fiber Bragg grating sensors in non-homogeneous strain fields

One of the advantages of optical fiber sensors is their ease of embedment within a structure for non-destructive strain monitoring. In particular, Bragg grating sensors are written directly into an optical fiber hence remaining unobtrusive. In addition, several gratings can be written in series along a single fiber, permitting sensing at discrete points throughout the strain field. However, in regions of strong strain gradients, measuring the strain at discrete points may not be sufficient. One solution is to write a Bragg grating longer than the strain region of interest and use the change in its spectral response to determine the applied strain field as a function of position along the fiber. This paper presents an experimental verification of the response of an embedded optical fiber Bragg grating (OFBG) to applied non-homogeneous strain fields. Optical fiber Bragg grating sensors were embedded in four epoxy specimens of different forms so as to apply known strain functions along the gauge length when the specimen is under uniaxial tension. The complete spectral response of the Bragg gratings was then measured as a function of increasing load. The results are compared with analytical calculations, based on the piecewise-uniform period assumption for chirped gratings. Finally, the use of these spectra is discussed as possible basis functions for the resolution of an arbitrary applied strain distribution.

Reaction rate imaging

It has long been recognized that common experimental observables such as species concentrations are not generally reliable markers of flame front topology, heat release rate, or reaction rate. We show that with proper selection of excitation transitions, the planar laser-induced fluorescence (PLIF) signals of two spatially correlated species can be used to determine a bimolecular reaction rate in flames. This measurement technique provides a spatial marker of a species-specific bimolecular reaction region as well as a measure of the relative forward rate of that reaction. Our primary focus is the CO+OH reaction due to its significance in H−C−O mechanisms and the feasibility of simultaneous OH and CO PLIF imaging. The reaction rate diagnostic was applied to methane/air-based Bunsen flames and an acoustically forced vortex-flame interaction. Measured reaction rate, CO LIF, and OH LIF profiles extracted from the Bunsen flame images agreed reasonably well with theoretical estimates, and the measured reaction rate was observed to intensify near the flame tip. Measurements in a vortex-flame system indicated entrainment of CO directly into the vortex core, but only minor reaction rates occurred in the core due to low oxidizer (OH) concentration. On the primary flame surface, the forward reaction rate initially increased threefold due to enhanced reactive scalar mixing resulting from the applied strain field. The vortex passage caused the base of the CO+OH reaction surface to detach and lift similar to OH, with the base of the CO surface detaching later in time. For the majority of cases considered, the topologies of the reaction rate fields were distinctly different than those of the individual reactive scalars, suggesting that insight into CO oxidation by OH can be improved by the use of rate imaging diagnostics.