Non-uniform Strain Research Articles

Rhombohedral distortion and percolation phenomena in B-site substituted perovskite ferroelectrics with enhanced piezoelectric response

High-energy x-ray diffraction coupled with atomic pair distribution analysis and large-scale computer simulations are used to study the relationship between the local structure and piezoelectric response of an exemplary ferroelectric from the $\mathrm{BaTi}{\mathrm{O}}_{3}$ family where Ti is partially replaced by nonferroelectric Ce. Our results indicate that, likely, the increase in the piezoelectric response observed for Ce concentration 10% is due to an increased local rhombohedral distortion of the perovskite lattice. Despite a further increase in the distortion, the piezoelectric response for Ce concentration >10% decays quickly, likely because of rapidly increasing nonuniform strain fields due to the size mismatch between Ti- and Ce-centered octahedra and loss of electric dipoles due to the nonferroactivity of the latter. Thus, the transition between the observed two regimes of piezoelectric response does not appear to involve a crossing of a morphotropic phase boundary where the crystallographic symmetry changes abruptly but is likely to be percolative in nature. A similar behavior, referred to as tricritical phenomenon, is observed with other B-site substituted ferroelectrics from the $\mathrm{BaTi}{\mathrm{O}}_{3}$ family, indicating the presence of a common structural origin. Our results highlight the importance of chemical substitution-driven rhombohedral distortions in achieving control over the piezoelectric response of perovskite ferroelectrics, thereby providing a different perspective on the ongoing effort to improve their performance in practical applications.

Feasibility on accurate measurement of non-uniform strain field through contact methods

When straight material filaments do not remain straight after deformation, the strain varies spatially. These spatially varying strain fields arise because of (1) non-uniform distribution of boundary traction, (2) presence of residual stress in the reference configuration, (3) the body being inhomogeneous. The strain measured using devices such as extensometer and strain gauge assumes that the strain is uniform over the gauge length, irrespective of the strains actual variation. Here the accuracy of the strain estimated using contact strain measurement techniques is investigated by assuming that the uniaxial strain (not stress) varies periodically along the measurement axis. A tight bound for the error in the measured strain is obtained and verified through numerical simulation. This study’s significant finding is that for gauge length of strain measurement about two times the periodicity of the strain variation, the measured strain’s value would be repeatable but with a significant error. Thus, one has to be cautious about the magnitude of the estimated non-uniform strain.

Simultaneous measurement of temperature and strain based on peak power changes and wavelength shift using only one uniform fiber bragg grating

Many efforts have been devoted to simultaneous measurements of strain and temperature by FBG sensors and several improving techniques have been resulted and implemented on the measurement. Most of them are based on two or more FBGs configurations or a single non-uniform FBG implementation. We propose simultaneous measurement of temperature and strain based on peak power changes and Bragg wavelength shifts using only one uniform fiber Bragg grating (FBG). We placed a ramp with the angle of θ, similar to a tilted cantilever beam, on an assumptive structure and stuck a uniform FBG on it. When a uniform strain applied to a structure, the cantilever beam converts it to a non-uniform strain distribution along with itself and consequently the uniform FBG. By creating this non-uniform strain distribution, the peak power of the reflection spectrum of the FBG will be sensitive to strain changes. In addition, the Bragg wavelength shift will be sensitive to both temperature and strain parameters. According to our simulation, temperature sensitivity of 14.15 pm/°C is obtained for FBG sensor without any changes in the peak power. The strain sensitivity of 0.7837 pm/με, and a nonlinear sensitivity according to a quadratic function for peak power variation are also observed.

Effect of coarse aggregate size on non-uniform stress/strain and drying-induced microcracking in concrete

Non-uniform stresses, strains and microcracking of the concretes with three coarse aggregate sizes (5–10 mm, 10–16 mm, 16–20 mm) dried under 40% relative humidity (RH) for 60 days were quantified using digital image correlation and lattice fracture modelling. The influencing mechanism of coarse aggregate size on the drying-induced microcracking of concrete was clarified: (1) As the coarse aggregate size decreases, propagation paths of microcracking are increased, which increase the number of small microcracks and release the drying shrinkage force from mortar phase. (2) Tensile stress shells surrounding the coarse aggregates become thinner, thereby decreasing the area of large microcracks. As the coarse aggregate size decreased from 16-20 mm to 5–10 mm, the average thickness of tensile stress shells decreased from 2.13 mm to 1.09 mm at the beginning of drying, and the area of the microcracks >5 μm in width decreased from 796.6 mm2/m2 to 340.2 mm2/m2 at 60 days since drying.

Simultaneous measurement of temperature and strain using a single fiber bragg grating on a tilted cantilever beam

Importance of simultaneous measurement of temperature and strain by fiber Bragg grating (FBG) sensors has led to innovation of several renewing techniques. Most of them are based on two FBGs configurations or one non-uniform FBG implementation. Both temperature and strain changes can result in Bragg wavelength shift in reflected spectrum from a uniform FBG. We propose using full width at half maximum (FWHM) of the reflection spectrum as a cross-sensitivity indicator for simultaneous measurement of temperature and strain using only one FBG. When a non-uniform strain is applied to a sample which a uniform FBG is stuck on it, in addition to the Bragg wavelength, FWHM of the reflection spectrum changes. This FWHM change besides the Bragg wavelength shift is used to obtain simultaneously strain and temperature. When a uniform strain is applied to the sample, we get the help of cantilever beam concept. We place a ramp with an angle of θ, similar to a tilted cantilever beam, on a sample under test and stick a FBG on the ramp. A uniform strain applied to the sample, creates a strain gradient along the cantilever beam and of course along the FBG causing a change in the FWHM of reflection spectrum. This FWHM change besides the Bragg wavelength shift is used to obtain simultaneously strain and temperature. In our simulation results, temperature sensitivity of the FBG is 14.2 pm/℃ for Bragg wavelength with no change in the FWHM and strain sensitivity is 0.453 pm/μe for Bragg wavelength and a nonlinear sensitivity according to a quadratic function for FWHM variation.

Spin-thermoelectric transport in nonuniform strained zigzag graphene nanoribbons

We study a nonuniform strain in zigzag graphene nanoribbons for producing the spin-thermoelectric effects, using the mean-field Hubbard approximation and a Green's function approach. Our theoretical results show that a sinusoidal-shaped inhomogeneous strain with electron-electron interaction could induce a different effect on each edge of zigzag nanoribbons and finally generate a spin semiconductor with a tunable spin-dependent band gap. The strength of strain also controls the magnitude of magnetization in each edge. Interestingly, pure spin current and a giant spin Seebeck coefficient can be produced even at low values of strain by applying a thermal gradient and without magnetic elements. These results pave a practical way toward improved design for spin-thermoelectric applications through strain engineering.

Texture and grain boundary engineering in nickel coating with tungsten addition and its effect on the coating corrosion behavior

Nickel‑tungsten (NiW) alloy coatings (~2, 4, 7, 10, and 13 wt% tungsten) were electrodeposited over mild steel. Corrosion rate (icorr value) decreased for the initial addition of tungsten (~2, 4, and 7 wt%) to reach a minimum of 7 wt% tungsten. For higher tungsten additions (10 and 13 wt%), the corrosion rate again increased to values that were 88% higher than the pristine Ni coating. Between pristine Ni and Ni-7 wt% W, a 51% decrease in the icorr value was measured. Between Ni-7 wt% W and Ni-13 wt% W, a 72% increase in the icorr value was noticed. The highest corrosion rate for Ni-13 wt% W was attributed to small-sized grains and a high fraction of high-angle grain boundaries (HAGBs). The high corrosion rate in pristine Ni coating was attributed to high coating strain and non-uniform strain distribution, a low fraction of Ʃ3 CSLs, absence of twist grain boundaries (special boundaries), and high fraction Ʃ9 CSLs (which possess high grain boundary energy than Ʃ3 CSLs). The lowest corrosion rate in Ni-7 wt% W coating was attributed to lower HAGB fraction than the Ni-13 wt% W coatings, a relatively higher fraction of Ʃ3 CSLs, and uniform strain distribution.

Effects of premature contact in maxillary alveolar bone in rats: relationship between experimental analyses and a micro scale FEA computational simulation study.

The aim of the investigation was to evaluate the maxillary alveolar bone morphology, bone architecture, and bone turnover in relation to the mechanical strain distribution in rats with dental premature contact. Fifty 2-month-old male Wistar rats were used. The premature contact group (N=40) received a unilateral (right side) resin cementation on the occlusal surface of the upper first molar. The animals were distributed in 4 subgroups according to the periods of euthanasia: 7, 14, 21, and 28 days after cementation (N=10, for each period). For the control group (N=10), the teeth were kept without resin, featuring a normal occlusion. The pieces including the upper first molars, alveolar bone, and periodontal tissue were processed to histological and immunohistochemical evaluation of RANK-L and TRAP protein expression. A three-dimensional bone microarchitecture analysis was performed, where the heads of animals were scanned using microtomography and analyzed using CT-Analyser software (Bruker, Kontich, Belgium). In the computer simulation by finite element analysis, two micro-scaled three-dimensional finite element models of first molar and dentoalveolar tissues were constructed, in representation of control and premature contact groups, using Materialise MIMICS Academic Research v18 (Materialise, Leuven, Belgium). The analysis was set to simulate a maxillary molar biting during the power stroke phase. The total deformation, equivalent strain, and minimum principal strain distribution were calculated. The expression of RANK-L and TRAP presented higher positive ratio in the 7-day period compared to the control group. The three-dimensional morphometry showed decrease of bone volume in the premature contact, with significant values between the control and the 7-day and 14-day groups (P = 0.007). In FEA, the premature contact model presented a uniform compressive strain distribution in the alveolar bone crest compared to a non-uniform compressive strain distribution in the control model. The results from FEA, 3D bone microarchitecture, and histological and immunohistochemical analyses showed that a model with dental traumatic occlusion resulted in changes of alveolar bone mechanobiology and, consequently, its morphology. These results could be applied in dental treatment planning bringing biological and mechanical feedback to provide an effective mechanism to obtain physiological bone loss responses. Furthermore, this association between experimental and computational analyses will be important to figure out the alveolar bone response to mechanical stimulation in different clinical conditions.

Influences of structural anisotropy and heterogeneity on three-dimensional strain fields and cracking patterns of a clay-rich rock

In this study, three-dimensional non-uniform strain fields and cracking patterns of a clay-rich rock are investigated. Uniaxial compression creep tests are performed on samples drilled in five different orientations with respect to bedding planes. A digital volume correlation method is applied to X-ray micro-tomographic images taken during the creep tests to calculate both full local strain fields and average global strains. Both instantaneous and time-dependent strains, respectively, induced by applied stress and creep mechanism are analysed. Strain heterogeneity inside samples is quantified by calculating strain concentration zones, which are correlated with the presence of stiff inclusions. Cracking patterns of samples are characterized through reconstructed X-ray micro-tomographic images. Correlations between major cracking patterns and strain concentration zones are investigated.

Age and Sex Differences in Load-Induced Tibial Cortical Bone Surface Strain Maps.

ABSTRACTBone adapts its architecture to the applied load; however, it is still unclear how bone mechano‐adaptation is coordinated and why potential for adaptation adjusts during the life course. Previous animal models have suggested strain as the mechanical stimulus for bone adaptation, but yet it is unknown how mouse cortical bone load‐related strains vary with age and sex. In this study, full‐field strain maps (at 1 N increments up to 12 N) on the bone surface were measured in young, adult, and old (aged 10, 22 weeks, and 20 months, respectively), male and female C57BL/6J mice with load applied using a noninvasive murine tibial model. Strain maps indicate a nonuniform strain field across the tibial surface, with axial compressive loads resulting in tension on the medial side of the tibia because of its curved shape. The load‐induced surface strain patterns and magnitudes show sexually dimorphic changes with aging. A comparison of the average and peak tensile strains indicates that the magnitude of strain at a given load generally increases during maturation, with tibias in female mice having higher strains than in males. The data further reveal that postmaturation aging is linked to sexually dimorphic changes in average and maximum strains. The strain maps reported here allow for loading male and female C57BL/6J mouse legs in vivo at the observed ages to create similar increases in bone surface average or peak strain to more accurately explore bone mechano‐adaptation differences with age and sex. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC. on behalf of American Society for Bone and Mineral Research.

A micro-mechanical constitutive model for heterogeneous rocks with non-associated plastic matrix as implicit standard materials

In this work, we shall propose a new micro-mechanical constitutive model for the estimation of effective elastic-plastic behaviors of heterogeneous rocks. A bi-potential based incremental variational (BIV) approach is developed in order to take into account non-uniform local strain fields of constituents. The studied materials are composed of a non-associated and pressure sensitive plastic matrix, elastic inclusions and/or voids. For clarity, the local behavior of matrix is first described by an elastic perfectly-plastic model. Based on the bi-potential theory to dealing with non-associated plastic flow, the solid matrix is considered as pertaining to implicit standard materials (ISMs). The effective incremental bi-potential and macroscopic stress tensor are then estimated through an extension of the incremental variational method initially established for generalized standard materials(GSMs). The accuracy of the BIV model is verified by comparing the model’s predictions with the reference results obtained from direct finite element simulations. Furthermore, by assuming that the general formulation obtained for the perfectly plastic matrix remains valid for each loading increment, the BIV model is extended to considering that the solid matrix exhibits an isotropic hardening by using an explicit algorithm. The accuracy of the extended BIV model is also validated by a series of comparisons with the reference solutions obtained by direct finite element simulations for both inclusion-reinforced composites and porous materials. Both local and macroscopic responses are compared. As an example of application, the extended BIV model is finally applied to estimating the mechanical responses of typical claystone and sandstone under different loading paths.

Mechanical Manipulation of Silicon-based Schottky Diodes via Flexoelectricity

Silicon-based Schottky barrier diodes (SBDs), as a two-terminal circuit element, are widely used in modern industries due to its low cost and better compatibility with the complementary metal oxide semiconductor (CMOS) technology. Flexoelectricity resulting from strain gradient is a distinctive electromechanical coupling phenomenon compared to piezoelectricity resulting from strain. Flexoelectricity can exist in any dielectric due to the non-uniform strain breaking symmetry of materials. In this paper, we utilize the induced flexoelectric polarization to tune the behavior of a SBD made of metal and p-type Silicon. Making use of conductive atomic force microscopy (C-AFM), we measured current-voltage of the fabricated Si-based SBD under different tip forces. In order to conduct a quantitative study on the tuning effect of flexoelectricity on the performance of the fabricated Si-based SBD, we introduce an effective barrier height and provide a modified current equation according to the classical thermionic emission theory. The results show that flexoelectricity plays a significant role in dictating the Schottky barrier height, maximum rectified current (density), reverse saturation current (density), rectification ratio, and open voltage of the fabricated SBD. In addition, based on the Hertzian contact model and the measured data, the nonzero flexoelectric coefficients of the used p-type silicon are obtained.

Experimental and numerical investigation of the cylinder-dome transition region of a pressure vessel

The difference in stiffness between cylindrical and dome regions of a filament wound composite pressure vessel may cause undesirable bending in the cylinder-dome transition region. Because of the bending, strain distribution may be non-uniform in the transition region. Therefore, accurate modeling that captures non-uniform strain distribution in the transition region is crucial for a safe pressure vessel design. In this study, a pressure vessel with a metallic liner was designed. Three identical pressure vessels were manufactured. One of the vessels was cut for detailed geometric investigation. The section of the transition region was investigated using an optical microscope. The termination of each hoop layer and resin pockets under the helical layers were clearly observed at the micro-scale. Also, measurement of layer by layer thickness and fiber volume fraction were performed. Other vessels were pressurized until the burst pressure. Fiber direction strain was measured using strain gauges that were mostly attached to the transition region to capture the non-uniform strain distribution. Two finite element models were created to analyze the transition region. The first finite element model was created with design parameters. The second finite element model was established by considering the findings obtained from the microscopic analysis. Strain distributions obtained from the strain gauges and finite element analyses were compared. In contrast to the first finite element model, strain distribution in the transition region was perfectly matched with the second finite element model. Thus, important aspects of analyzing the transition region of a pressure vessel were addressed for designers.

Determination of true stress strain characteristics of structural steels using Instantaneous Area Method

This paper presents recent research findings on true stress strain characteristics of normal strength S275, S355 and high strength S690 steels to EN 10025:2005. It aims to provide generalized constitutive models for analysis and design of steel structures. Comprehensive experimental and numerical investigations into mechanical properties of the structural steels have been carried out based on test results of nine monotonic tensile tests. Non-uniform stress and strain distributions within the necked region are found when the test coupons are under very large deformation. After corrections to the stress and strain non-uniformities by Instantaneous Area Method with successive approximations, true stress strain characteristics of the tested steels were successfully quantified as generalized constitutive models. Moreover, the microstructures of the typical structural steels haven been carefully examined, and their microstructural constituents are successfully quantified by Digital Image Analytics. The research findings are very important for subsequent numerical investigations into the structural performance of steel structures under very large deformations up to fracture. The authors are grateful for the financial supports from the Research Grants Council of the Government of Hong Kong SAR, and the CNERC for Steel Construction (HKB).

Programmable Strain Gradients in 3D Hydrogels for Guiding Complex Tissue Architecture

Biological tissues experience various stretch gradients in the body which act as mechanical signaling from the extra-cellular environment to cells. These mechanical stimuli are transferred to cell sensor proteins, triggering essential signaling cascades regulating cell migration, differentiation and tissue remodeling. Previous studies have successfully applied simple, uniform stretch to 2D elastic substrates in order to analyze the response of living cells. However, the ability to induce non-uniform strains in controlled gradients, particularly in 3D hydrogels, has proven challenging.In this study, we manipulated the geometry of 3D fibrin hydrogels embedded in punctured silicone rubber strips. The strips were then stretched using a dedicated stretching device [1,2] and imaged in real-time under confocal microscopy. The resulting strains and internal fiber alignment gradients were analyzed and compared to finite element simulations. Strain gradient control through geometric manipulation and external stretch was confirmed with a linear relationship between strain magnitude and fiber alignment in the stretch direction. Additionally, fibroblast cells embedded in the fibrin gels were found to align along the stretch direction in a gradient manner that correlate to the developed strain gradients. The experimental and simulation data confirm our ability to custom design mechanical gradients in 3D hydrogels and control cell alignment, offering a framework for further elucidation of cell response to mechanically induced signaling and providing a platform for programming cellular behavior and differentiation. [1] A. Roitblat Riba, S. Natan, A. Kolel, H. Rushkin, O. Tchaicheeyan, A. Lesman. Straining 3D hydrogels with uniform z-axis strains while enabling live microscopy imaging. Annals of Biomedical Engineering (2019). https://doi.org/10.1007/s10439-019-02426-7. [2] A. Kolel, A. Roitblat Riba, S. Natan, O. Tchaicheeyan, E. Saias, A. Lesman. Controlled Strain of 3D Hydrogels under Live Microscopy Imaging. Journal of Visualized Expirements. (Pending Publication). e61671. In-press (2020).

Axial stress–strain behavior of carbon FRP-confined seawater sea-sand recycled aggregate concrete square columns with different corner radii

This paper presents an experimental study on the axial stress–strain behavior of carbon fiber-reinforced polymer (CFRP)-confined seawater sea-sand recycled aggregate concrete (SSRAC) columns. Forty-two circular and square specimens were tested under axial compression, and the effects of the aggregate replacement ratio, CFRP thickness, and corner radius were investigated. The results indicated that, by replacing natural aggregates with recycled aggregates (RAs), the CFRP-confinement effectiveness can be enhanced, showing a higher enhancement ratio in the ultimate strength and strain. The effect of the corner radius ratio on the ultimate condition of CFRP-confined SSRAC is also more pronounced compared with CFRP confined natural aggregate concrete (NAC). This conclusion was also validated by the nonuniform hoop strain distribution for specimens with varying corner radius ratios. The difference in CFRP confinement efficiency caused by the recycled aggregate replacement and corner radius is accurately captured by the DIC (Digital image correlation) measurement system. By reasonably taking the coupling effect of RAs and the corner radius ratio into account for the confinement efficiency parameter, the proposed ultimate strength and strain model for CFRP-confined SSRAC demonstrates a satisfactory performance when compared with test results.

Post-gel polymerisation shrinkage profiling of polymer biomaterials using a chirped fibre Bragg grating

A strain profile measurement technique using a chirped fibre Bragg grating (CFBG) sensor by implementing an integration of differences (IOD) method is reported in this paper. Using the IOD method the spatial distribution of strain along the length of the CFBG is extracted from its power reflectance spectra. As a proof of concept demonstration, the developed technique is applied to measure the polymerisation shrinkage strain profile of a photo-cured polymer dental composite which exhibits a non-uniform strain distribution attributed to the curing lamp characteristics. The result from the CFBG technique is compared with that of an FBG array embedded in the dental composite and is correlated with the degree of conversion of the material which also depends on the curing lamp intensity distribution. This technology will have significant impact and applications in a range of medical, materials and engineering areas where strain or temperature gradient profile measurement is required in smaller scales.

Enhanced superconducting performance in solution-derived YBa2Cu3O7−δ films using parallel ion-beam structure modification method

Surface modification of superconductors has been extensively researched. However, such modification usually degrades the superconducting properties by creating rough surface morphologies and non-superconducting phase impurities, with the exception of the antidot method modification. Here, a new parallel ion-beam structure modification (PISM) method proves extraordinarily effective in improving the superconductivity of solution-derived YBa2Cu3O7−δ (YBCO) films. Experimental results demonstrate that the surface morphologies of the treated YBCO films become smoother than the pristine samples, and large-sized pores, needle-like a-axis grains, and/or secondary-phase impurities are almost completely removed. Treatment by the PISM method affords remarkable increase ratios ΔJc of the critical current density by 128.9% or more, where greater improvements are achieved by increasing the Ar+ ion bombardment time. The current-carrying capacity is improved by newly generated impurities, i.e., Ba‒Cu‒O phases acting as Δl volume pinning centers, and drastic shortening of Cu‒O bonds derived from the non-uniform compressive strain.

Flexoelectric effect in dielectrics under a dynamic load

Health monitoring of structures can be improved if a more universal two-way electromechanical coupling, the flexoelectric effect, is utilized. It is a coupling between the electric polarization and the strain gradients. In the direct flexoelectricity, the electric polarization is induced by strain gradients, which yield also a finite higher-order stress tensor in the considered phenomenological theory. Because of the size-effect in higher-grade theories of continua, the polarization in piezoelectric solids under a non-uniform strains in nano-sized structures is significantly influenced by flexoelectricity. This effect is substantially enhanced near the crack defects, in regions with large strain gradients. The mixed finite element method (FEM) is developed from the variational formulation of flexoelectric boundary value problems. The C0 continuous approximation is applied independently for both the displacements and displacement gradients. The kinematic constraints between them are satisfied by collocation at some internal points of elements. The developed computational method is applied to general 2D boundary value problems with cracks under a dynamic load. The influence of flexoelectricity on the induced electric potential and the crack opening displacement is investigated.

Numerical simulation and experimental study on non-uniform strain during hot compression of aluminium alloy

The finite element numerical simulation of hot compression deformation process of B93 aluminium alloy was carried out by DEFORM-3D software. Besides, the microstructure characteristics of deformed specimens in different regions and the relationship between non-uniform strain and dynamic recrystallisation during deformation were analysed by experimental study. The results show that the hot compression process of B93 aluminium alloy obviously exhibits a nonuniform characteristic of deformation, the region with the largest equivalent strain is the most prone to deformation. Also, in the largest equivalent strain zone, dynamic recrystallisation reacts the most complete, and the grain size reaches the minimum value. Nonuniform deformation show a rising tendency with the increase of strain rate and deformation temperature, and the influence of strain rate on nonuniform deformation is slightly greater than that of deformation temperature. The most suitable hot working process for the alloy is 410~430°C/0.001~0.01s-1.