Measurement Of Strain Fields Research Articles

Strain field measurements over 3000 °C using 3D-Digital image correlation

With the development of aerospace and fusion engineering, understanding the mechanical behavior of materials under high-temperature conditions has become increasingly important. However, few studies are devoted to the ultra-high temperature range of 2000–3000 °C. In this study, with the aim of developing non-contact measuring techniques of mechanical deformation under ultra-high temperature, a high heat flux (~300 MW) comprehensive experimental platform is established, which includes a vacuum chamber, a three-dimensional digital image correlation (3D-DIC) system, infrared radiation thermometers and an electron beam heating system. Using the electron beam heating technique, the tungsten specimen can be heated to over 3000 °C. Owing to the use of a vacuum chamber, the thermally induced airflow disturbance at high temperature can be completely removed. Tantalum carbide (TaC) powder is chosen as the speckle material and speckle fabrication technology is developed to adapt ultra-high temperatures under vacuum conditions. In order to suppress the blackbody radiation at high temperature, three schemes based on blue light sources, self-radiating light sources and a dual wavelength optical filter technique are designed for three temperature ranges from room temperature to 3067 °C. Afterwards, full-field thermal deformation of the tungsten specimen above 3000 °C was determined based on the above strategies using the 3D-DIC technique. The feasibility and accuracy of the proposed methods are verified by comparing the measurement results with the thermal expansion strain data and model from available databases and literature. The standard deviations in different temperature intervals are 50 με for 25–1200 °C, 100–200 με for 1200–1800 °C and less than 500 με for 1800–3067 °C. The proposed methods and technologies are expected to lay a foundation for further developments in strain field measurements at ultra-high temperature.

Localized strain fields in honeycomb materials with convex and concaved cells

Characterizing the local deformations and strain fields in ligaments of periodic honeycomb materials is instrumental to applications such as cores of sandwich structure as well as honeycomb shaped tunable phononic crystals, compliant metamaterials, and 4D printed shape memory materials. Such applications employ honeycomb shaped materials whose nonlinear behavior is controlled by localized deformations in their ligaments. These local deformations can exhibit values and complex non-uniform states that far exceed the overall macroscopic deformations and strains sustained by the honeycomb material in value and complexity. Each of the aforementioned applications can be better designed with an improved understanding of the evolution of local strain fields in honeycombs' ligaments during their deformation. This work aims to characterize the local strains and deformations developing in honeycomb ligaments near honeycombs’ macroscopic onset of yielding. Finite element computations and the full field strain measurement technique digital image correlation (DIC) are used to measure and characterize the local deformations in the ligaments of concaved and convex honeycombs. Results show nonlinear strain gradients and significant localization in deformed ligaments. Moreover, complex state of stress comprising biaxial normal stresses and shear stresses exists near plastic zones.

Rate dependent behaviour and dynamic strain localisation of three novel impact resilient titanium alloys: Experiments and modelling

The tensile behaviour of three ductile titanium alloys, Ti0.7Al4V, Ti1Al4V and Ti3Al2.5V, conceived for impact containment applications, is characterised at quasi-static, intermediate and high strain rates. Tests have been performed using a screw driven mechanical system and a bespoke in-house developed split Hopkinson tension bar equipped with ultra-high speed photographic equipment. The three alloys present noticeable strain rate sensitivity. Ti1Al4V is characterised by the lowest flow stress and highest ductility of the three alloys. Ti3Al2.5V higher flow stress but lowest strain to failure while Ti0.7Al4V has similar flow stress but larger engineering failure strain compared to Ti3Al2.5V. The dynamic true strain rate, determined by measuring the time history of the minimum cross-section diameter during necking, reaches values up to one order of magnitude higher than the nominal strain rate. This phenomenon, occurring during dynamic strain localisation, is of fundamental importance for understanding and modelling the dynamic behaviour of ductile alloys designed to withstand impact loading. The experimental results are used to determine the material parameters of the Johnson-Cook (JC) and Khan–Huang–Liang (KHL) models, which are incorporated in the ABAQUS/explicit code for finite element simulations of the dynamic tensile tests. It is found that the KHL model predicts the experimentally measured strain field, deformed geometry, effective strain rate and macroscopic force-displacement response during the high strain rate experiments with significantly better agreement than the JC model.

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation.

A procedure using digital image correlation (DIC) to detect cracks on welded specimens during fatigue tests on resonance testing machines is presented. It is intended as a practical and reproducible procedure to identify macroscopic cracks at an early stage and monitor crack propagation during fatigue tests. It consists of strain field measurements at the weld using DIC. Images are taken at fixed load cycle intervals. Cracks become visible in the computed strain field as elevated strains. This way, the whole width of a small-scale specimen can be monitored to detect where and when a crack initiates. Subsequently, it is possible to monitor the development of the crack length. Because the resulting images are saved, the results are verifiable and comparable. The procedure is limited to cracks initiating at the surface and is intended for fatigue tests under laboratory conditions. By visualizing the crack, the presented procedure allows direct observation of macrocracks from their formation until rupture of the specimen.

Characterizing fracture response of cracked transversely graded materials

Property gradation along a crack front makes conventional fracture mechanics analyses challenging. This issue is addressed in the present study through a combination of full-field measurements and modeling. We develop a novel experimental setup that consists of a synchronous dual Digital Image Correlation (DIC) system, facilitating in situ measurement of displacement and strain fields on both sides of a transversely precracked multi-layered structure subjected to uniaxial tensile load. By measuring the evolution of stress intensity factors developed on the opposite sides of the sample, we explore the mechanisms of crack initiation and propagation in the examined graded sample. Our experimental measurements are supplemented by a finite element analysis that elucidates the deformation and fracture response of the internal layers for which surface measurement is not possible. Finally, based on experimental and numerical observations, we develop a simple model that allows for prediction of critical far-field loads at which transversely graded structures fail. The capability of our proposed model in predicting tensile failure loads is demonstrated through a brief study of the influence of gradient function on the load bearing and fracture resistance in various graded structures.

Model-Based Digital Image Correlation for Noncontact Deformation Measurement of Strain Field and Mechanical Property

This paper presents a new method that combines a physics-based model and finite-element (FE) based digital image correlation (DIC) with an interfacial continuity condition for simultaneous deformation measurements of strain field and material mechanical properties. The dual-domain global DIC method incorporates a model-based kernel that offers useful physical insights into the complex deformation and constrains the solutions to the iterative minimization of the DIC criterion, which leads to a faster convergence. Unlike local subset-based and global FE-based methods where the DIC is formulated to solve for the nodal displacements, the model-based DIC that accounts for complex deformation in the specific region is formulated to identify system parameters. Both domains, along with their interface and the continuity condition enforced on the global displacement field, are discretized and solved simultaneously in a single calculation. The dual-domain global DIC method has been investigated by comparing reconstructed strain fields and estimated parameters against targets simulated using the commercial FEA software COMSOL and published experimental data. Unlike FE-DIC which is noise sensitive, the model-based DIC is robust against the Gaussian noise effects.

Overcoming high luminance gradient using serial exposure time method for synchronous full-field measurement of temperature and deformation.

The high-temperature optical method has been widely used for evaluating structural materials subjected to high temperature. Obtaining high-quality images of a specimen surface in such a harsh environment is detrimental for the accurate measurement of temperature and strain field. However, the high-temperature environment poses many challenges on these measurements, e.g., the large luminance gradient on the sample surface would jeopardize the image quality when using the full-field optical method. In order to overcome this issue, we propose here a simple and effective algorithm to obtain image sequences with serial exposure times. This algorithm incorporates exponentially decreasing exposure times to successfully reduce the disturbance caused by large luminance gradient, as will be shown by the verification on samples tested both in arc wind tunnel and oxy-propane torch flame. In comparison to the images with single exposure time, further experiment carried out on C/SiC sample up to 1100°C shows that image sequences with different exposure times can be effectively obtained by the image fusion technique. The calculation of the deformation and temperature fields using the image sequence method gives more accurate and reasonable results.

Discontinuous and inhomogeneous strain distributions under monotonic and cyclic loading in textured wrought magnesium alloys

The present work investigates the deformation behaviour of strongly textured AZ31B wrought magnesium sheets under monotonic as well as cyclic mechanical loading. Of special focus is the distribution of strain, which is investigated employing optical strain field measurements on the specimen surfaces. Microstructural investigations of the material after loading provide detailed information on the underlying deformation characteristics. The investigations show that bands of twinned grains (BTGs) form up once twinning occurs. These BTGs consist of solely {101‾2} tension twins and are clearly delimited to the adjacent absolutely twin-free regions. Most importantly, strain fields are strongly inhomogeneous and discontinuous due to these BTGs with considerably higher compressive strain inside BTGs, both after monotonic and cyclic loading. During the first few load cycles, BTGs are observed to grow and the formation of new BTGs can occur. Additionally, a significant hardening is found during the first load cycles, most likely caused by residual twins and unretwinnable twins. However, material behaviour stabilizes after a few load cycles and remains approximately constant for most of a specimen's lifetime. The presented specific deformation characteristics are important for understanding and describing the material. Modelling the investigated material behaviour is not yet completely feasible with phenomenological constitutive models, which is why important modelling aspects are discussed.

Through-thickness strain field measurement using the mirror-assisted multi-view digital image correlation

A low-cost, easy-to-implement and effective mirror-assisted multi-view digital image correlation (multi-view DIC) technique, which uses only a regular two-camera stereo-DIC system and two planar reflective mirrors, is proposed for the full-field through-thickness strain (TTS) measurement of sheet samples. The front and rear surfaces of a plate-shaped sample are reflected by the mirrors and form two virtual surfaces behind the mirrors. The virtual surfaces are simultaneously captured and subsequently reconstructed by the stereo-DIC system. Furthermore, by utilizing the speckle patterns premade on the two mirrors, the 3D shapes of real surfaces can be estimated from the reconstructed virtual surfaces. By subtracting the 3D coordinates of the rear surface from those of the front surface, the full-field thickness distributions and TTS maps of the sample can be calculated. Compared with the regular multi-view DIC, which requires at least four cameras, the proposed technique has the prominent advantages of direct full-field TTS measurement by using only two cameras and simple implementation procedures. Two real experiments, including the full-field TTS measurement of a sheet sample subjected to in-plane translation and the thinning limit estimation of an advanced high-strength steel specimen subjected to uniaxial tensile loading, well validated the efficacy and accuracy of the developed technique.

Validating 3D two-parameter fracture mechanics models for structural integrity assessments

In-situ fracture tests were carried out on the I12 beamline at the Diamond Light Source. Four Al-Ti metal-matrix composites, with two crack lengths, were studied to assess for the impact of in-plane constraint. Synchrotron X-ray computed tomography and synchrotron X-ray diffraction were used to measure total strain and elastic strain respectively. In this work, the measured elastic strains in the samples are detailed as a function of applied load and compared against those predicted from a 3D elastic-plastic finite element model. The modelled strains increased asymptotically towards the tip of the electro discharge machined notch. The experimental results do not highlight the same response, which is due to a combination of blunting and low experimental spatial resolution. Far field experimental and measured strain fields converged, notably in the test piece containing a long notch (a/W = 0.5) and higher levels of constraint.

Finite element modeling for deep-drawing of aluminum alloy sheet 6014-T4 using anisotropic yield and non-AFR models

The predictive capability of a non-associated flow rule (non-AFR) for the strong plastic anisotropy was assessed. Based on Hill’s 48 function, a constitutive model under a non-AFR was established for aluminum alloy 6014-T4 sheet, in which the plastic potential function and the yield function were identified by Lankford coefficients (r-values) and yield stresses, respectively. Two constitutive models applying Hill’s 48 and Yld2000 functions under the AFR were also established for the comparison with the non-AFR Hill’s 48 model. These constitutive models were numerically carried out on Abaqus/Explicit by user subroutine (VUMAT). The representational ability of constitutive models was assessed in terms of the predictions on yield stresses and r-values. To further verify the simulated results, deep-drawing experiments of a cylindrical cup and a seat pan were performed. Simulation results were compared with the experiments from the aspects of the forming force, the earing profile, and the measured strain field using ex situ 3D DIC (Digital Image Correlation). Comparison results showed that non-AFR Hill’s 48 model gives the best overall prediction performance and requires less effort than the AFR Yld2000 model, indicating the effectiveness and superiority of non-AFR.

Microscopic Measurement of Strain Fields with Digital Image Correlation and Comparison to Finite Element Modelling

Digital Image Correlation (DIC) has become more and more important in the field of material characterization and research, especially for strongly anisotropic fiber reinforced materials. Its big advantage over the conventional methods like strain gauges or point based video-extensometers is the full field strain and displacement measurement and the ability to analyze three-dimensional displacements. Although theoretically, the concept of the DIC as a pure image-based method allows it to work on every imaginable scale, its main field of application is in the range, where the region of interest (ROI) has a size between 10 −2 m to 10 −1 m. In this case, imaging is accomplished with the use of high-resolution black and white digital cameras. This work is focused on a smaller scale with ROI sizes between 10 −4 m to 10 −3 m, where a digital microscope is used to create the images. The innovative idea behind this work is using the natural surface structure of a polished carbon fiber reinforced Polyamide-6 sample, produced by automated fiber placement, as a statistical pattern instead of the usual speckle pattern applied to the area to be investigated. This way the stress and strain distributionin different regions of the investigated sample area can be evaluated and displayed, while the sample is exposed to an increasing mechanical load in form of a three-point bending test. The resulting strain and displacement fields are compared to finite element modeling of the ROI. To provide an accurate model, the image of the sample is first segmented into fiber, matrix and voids using “Trainable Weka Segmentation” and the resulting phases mapped with the corresponding material properties. To compute the resulting strains in the sample, the measured displacements from the DIC on the edges of the ROI were used as boundary conditions for the simulation. Simulation and experimental results clearly point out the inhomogeneity of the strain field in these samples. Due to the presence of fiber rovings and the presence of voids, local strain values exceed the global average by up to 4 %.

Fabrication of a simple and easy-to-make piezoelectric actuator and its use as phase shifter in digital speckle pattern interferometry

In this report, design and assembly of a simple, easy-to-make and low-cost piezoelectric actuator (PZA) with one degree of freedom for application in phase-shifting interferometry is described. The PZA is designed in a way that its components can easily be manufactured and assembled. In the developed PZA, a series of ring-shaped piezo-ceramics are assembled inside a stainless steel case and through a couple of plate springs are preloaded. Planar electrodes are cut from a thin beryllium copper plate using wire-cut EDM and used on top and bottom sides of each ceramic plate. The supply voltage is applied to the electrodes by a designed control electronic circuit connected directly to a computer through a standard parallel port. A graphical user interface is developed in the MATLAB environment for controlling the converter. The electromechanical response of the PZA is studied by applying a calibration procedure based on using a Michelson interferometer. It is shown that by increasing the DC voltage from 0 to 200 V, the PZA has a good linear response. By using the PZA for strain field measurement in a rectangular steel plate, it is shown that the linear response of the designed PZA makes it a suitable candidate for use in Carre phase-shifting interferometry.

A practical and effective regularized polynomial smoothing (RPS) method for high-gradient strain field measurement in digital image correlation

Digital image correlation (DIC) is an effective tool for studying the deformation of tested materials. However, high-gradient strain field (HSF) measurement remains a challenging issue in DIC, because multifold factors have a significant effect on the first correlation calculation step of the original displacement and the exact strain reconstruction in the second post-processing step. In this study, we focus on the second step. The formerly proposed local Hermite has been proven as an accurate and robust method, yet substantial programming work is involved in constructing a Hermite element. To solve this issue, a regularized polynomial smoothing (RPS) method is proposed, which replaces the Hermite function of the polynomial. The RPS applies the same kernel function as the point-wise least-squares (PLS) method for easy implementation. Tikhonov regularization and the generalized cross-validation (GCV) function are also used to decrease unavoidable noise and weaken the dependence on window size. The experiments demonstrate that, in the matched/overmatched case, Tikhonov regularization in RPS can greatly decrease the degree of morbidity caused by ill-posed problems in the PLS method, thereby ensuring smoothness and stability of the solution. Moreover, the influences of window size and polynomial order of both the RPS and PLS are also closely studied. In conclusion, the proposed RPS provides a practical, robust and accurate method for HSF measurement.

Critical response analysis of steel deck pavement based on viscoelastic finite element model

ABSTRACT Orthotropic steel deck (OSD) bridges have gained increasing popularity around the world and the steel deck pavement is essential to extend the service life of the bridge. To optimise the design method for OSD pavements, this study evaluated the critical response of this type of pavement using the viscoelastic finite element (FE) model. Firstly, the FE model was elaborated and comprehensively complemented with field strain measurements to simulate the OSD pavement response. Secondly, the critical responses including critical strain, shear stress and deflection of the OSD pavement under various loading and pavement conditions were predicted via the proposed model. It was found that in FE model, a moving load better simulated the field truck loading than a pulse one, while quasi-static and dynamic analysis algorithms provided nearly identical response predictions. The positions of critical horizontal strains were temperature-dependent. Critical strains and deflections dropped with the load motion speed and rose with temperature, while the critical shear stresses exhibited the opposite trend. Moreover, the investigated three types of critical responses were found to be similarly influenced by the layer thickness variation but showed different patterns under varying bonding conditions.

Nd3+ and Nb5+ Co‐Substitution Inducing a Large Electrocaloric Response in Na0.5Bi0.5TiO3 Lead‐Free Ceramics

Nd3+ and Nb5+ co‐substituted (Na0.5Bi0.49Nd0.01)Ti1–xNbxO3 lead‐free ceramics are synthesized by conventional solid‐state reaction method. The X‐ray diffraction study revealed that NBNT‐Nb‐0 (x = 0.00) ceramics exhibit single phase monoclinic crystal with Cc phase while NBNT‐Nb‐1 (x = 0.00) ceramics exhibited a dual phase with coexistence of monoclinic and tetragonal systems. The temperature‐dependence dielectric study revealed the existence of ferroelectric and antiferroelectric transformations in two independent regions. Further temperature‐dependent strain vs. electric field measurements strengthen the ferroelectric to antiferroelectric transformation in the present ceramics. The induced electrocaloric effect (ECE) response showed that a significant change in temperature (ΔT) is obtained at 50 kV cm−1 fields: about 0.69 K for NBNT‐Nb‐0 and 0.81 K for NBNT‐Nb‐1 ceramics, respectively. The maximum isothermal entropy change (ΔS) is found to be 0.95 and 1.02 Jkg−1 K−1 for NBNT‐Nb‐0 and NBNT‐Nb‐1 ceramics obtained at 50 kV cm−1, respectively. The simultaneous presence of ECE response and isothermal change in entropy (ΔS) is an open window for great potential applications in the field of electronic devices.

Use of distributed optical fibre as a strain sensor in textile reinforced cementitious matrix composites

This study focused on using optical fibres embedded into the core of textile reinforced cementitious matrix composites (TRCMCs) as strain sensors. These composites have been increasingly used for strengthening and rehabilitating existing constructions and civil engineering structures. Our aim was to assess the embedding capability, strength, and feasibility of strain measurements of a material which exhibited multiple early cracks when loaded in tension.To this end, the Rayleigh backscattering technique was chosen, which allowed performing full field strain measurements with millimetric spatial resolution. Two standard mechanical tests were performed on the composite specimens with embedded optical fibres: the three-point bending test on a cementitious matrix beam, compared to the theoretical results using the beam theory, and a direct tensile test on a textile reinforced specimen, compared to the results of surface strain gauges.These results emphasised that implementing optical fibres using the Rayleigh backscattering technique would be a feasible approach to finely analyse the mechanical behaviour of cementitious matrix composites.

Microstructure-based modelling and Digital Image Correlation measurement of strain fields in austenitic stainless steel 316L during tension loading

The present work aims to compare the local strain fields on the microscopic scale of an austenitic stainless steel 316L sample during tension loading, obtained by experimental measurements and simulations. Experimentally, Digital Image Correlation (DIC) technique is used to track the strain maps during the specimen loading. Microstructure-based Finite Element (FE) models based on two different approaches for the material behaviour, Crystal Plasticity (CP) and Sistaninia-Niffenegger Fatigue (SNF) ones, provide the numerical results. The quality of the outcomes reinforces the use of a combination of these techniques to study the residual strain localization in the microstructure, as well as its evolution during the deformation process. Whereas the calculated and measured strain and stress fields showed good agreement in the elastic range, as expected, significant differences were found between CP and SNF approaches at large plastic strains.

Digital image correlation (DIC) for measurement of strains and displacements in coarse, low volume-fraction FRP composites used in civil infrastructure

Accurately measured strains are critical when investigating the application of Fiber Reinforced Polymer (FRP) materials, but traditional mechanical strain measurement methods have several critical drawbacks related to the installation process and the recording capabilities of the devices. FRP materials typically used in the civil engineering field feature large asymmetries and heterogeneity originated from the manual installation procedures, as opposed to the highly controlled FRP fabrication methods used in other fields that result in more homogeneous materials. The feasibility of using an optical full-field Digital Image Correlation (DIC) technique for measurement of strain fields on FRP materials used in the civil engineering industry has been investigated and the level of error in the DIC method when using more traditional methods was determined. The main advantage of using DIC over more traditional methods, which is the capacity of DIC to measure full field strains instead of strains at isolated points, has been demonstrated by providing exemplar measurements of various specimens of FRP materials. The reported strain fields are examples of what was obtained during an experimental campaign to understand the behavior of FRP anchors and other materials. The main conclusions drawn from the observation of those strain fields are discussed.

Measurement of creep strain field at crack tip using Digital Image Correlation

Measurement of creep strain field at crack tip using Digital Image Correlation