Showing papers in "Strain in 2016"

The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

Abstract: The grid method is a technique suitable for the measurement of in-plane displacement and strain components on specimens undergoing a small deformation. It relies on a regular marking of the surfaces under investigation. Various techniques are proposed in the literature to retrieve these sought quantities from images of regular markings, but recent advances show that techniques developed initially to process fringe patterns lead to the best results. The grid method features a good compromise between measurement resolution and spatial resolution, thus making it an efficient tool to characterise strain gradients. Another advantage of this technique is the ability to establish closed-form expressions between its main metrological characteristics, thus enabling to predict them within certain limits. In this context, the objective of this paper is to give the state of the art in the grid method, the information being currently spread out in the literature. We propose first to recall various techniques that were used in the past to process grid images, to focus progressively on the one that is the most used in recent examples: the windowed Fourier transform. From a practical point of view, surfaces under investigation must be marked with grids, so the techniques available to mark specimens with grids are presented. Then we gather the information available in the recent literature to synthesise the connection between three important characteristics of full-field measurement techniques: the spatial resolution, the measurement resolution and the measurement bias. Some practical information is then offered to help the readers who discover this technique to start using it. In particular, programmes used here to process the grid images are offered to the readers on a dedicated website. We finally present some recent examples available in the literature to highlight the effectiveness of the grid method for in-plane displacement and strain measurement in real situations.

Experimental Investigations of Fracture Process in Concrete by Means of X-ray Micro-computed Tomography

Abstract: The paper describes investigation results on fracture in notched concrete beams under quasi-static three-point bending by the X-ray micro-computed tomography. The two-dimensional (2D) and three-dimensional image procedures were used. Attention was paid to width, length, height and shape of cracks along beam depth. In addition, the displacements on the surface of concrete beams during the deformation process were measured with the 2D digital image correlation technique in order to detect strain localisation before a discrete crack occurred. The 2D fracture patterns in beams were numerically simulated with the finite-element method using an isotropic damage constitutive model enhanced by a characteristic length of micro-structure. Concrete was modelled as a random heterogeneous four-phase material composed of aggregate, cement matrix, interfacial transitional zones and air voids. The advantages of the X-ray micro-computed tomography were outlined.

Testing Concrete E‐modulus at Very Early Ages Through Several Techniques: An Inter‐laboratory Comparison

Abstract: These researches were performed thanks to the 'Hubert Curien' Partnerships passed, on one hand, between IFSTTAR & ULB (Tournesol project) and, on the other hand, between IFSTTAR & the University of Minho (Pessoa project - Proc 441, together with the Portuguese Foundation for Science and Technology - FCT). A special thank is addressed to the Campus France agency (http://www.campusfrance.org) for their management of these partnerships. The authors are also grateful to the financial support provided by FCT (Portuguese Foundation for Science and Technology) through PhD grant (SFRH/BD/80682/2011) to the third author and the research project EXPL/ECM-EST/1323/2013. The second, fourth and last four authors would like to thank the Belgian national founds for scientific research (FNRS) for their financial support to the Universite Libre de Bruxelles.

Theoretical analysis on the measurement errors of local 2D DIC: Part I temporal and spatial uncertainty quantification of displacement measurements

Abstract: This study presents a theoretical uncertainty quantification of displacement measurements by subset-based 2D-digital image correlation. A generalized solution to estimate the random error of displacement measurement is presented. The obtained solution suggests that the random error of displacement measurements is determined by the image noise, the summation of the intensity gradient in a subset, the subpixel part of displacement, and the interpolation scheme. The proposed method is validated with virtual digital image correlation tests.

Methods in mechanical testing of arterial tissue: a review

Abstract: Mechanical testing of arterial tissue can provide unique insights into its behaviour. As measurement and computational techniques continue to advance, new applications can be discovered that increase the accuracy of characterising tissue behaviour. This review provides an overview of the general considerations involved in testing arterial tissue and discusses the more commonly employed in vitro techniques used to assess the mechanical properties of arterial tissue, as well as emerging techniques. The more common methods discussed are uniaxial, planar biaxial and inflation testing. With the increasing precision and versatility of optical measuring systems and the rising interest in the mechanical behaviour of vessels with complex geometries and material properties, we also discuss the emerging trend of full-field measurement systems. Mechanical testing can be combined with bioreactor techniques to characterise the dynamic remodelling of arterial tissue in response to its mechanical environment. The analysis and characterisation provided by advanced mechanical testing techniques can produce and inform more accurate surgical simulations, as well as aid in the risk prediction and modelling of pathological conditions.

Theoretical Analysis on Strain Transfer Error of FBG Sensors Attached on Steel Structures Subjected to Fatigue Load

Abstract: Fibre Bragg grating (FBG) sensors have been increasingly adopted to detect the dynamic strain of structures. When the sensor is attached on the surface, adhesive material is employed to assist the installation, which leads to indirect contact of sensing fibre and the monitored structure. To correct the strain transfer error induced by the shear lag effect and improve the measurement accuracy of FBG sensors under dynamic response, strain transfer mechanism of a three-layered testing model constituted of sensing fibre, adhesive layer and host material has been studied in this paper. Laboratory test on steel beam attached with FBG sensor under fatigue load has been projected to investigate the feasibility of the derived strain transfer formula, and numerical simulation by MATLAB has been used as a supporting tool to offer the reference dynamic strain. Based on the analysis, sensitive parameters that affect the strain transfer coefficient have been discussed to instruct the application design of FBG sensors. Results indicate that strain transfer coefficient under dynamic response is much lower than that in static state, and error modification is particularly significant; in the dynamic testing model, bonded length, shear modulus and thickness of adhesive layer are more sensitive, which should be precisely selected in practical engineering to guarantee the effective strain measurement.

Optimised experimental characterisation of polymeric foam material using DIC and the Virtual Fields Method

Abstract: This article presents a methodology to optimise the design of a realistic mechanical test to characterise the material elastic stiffness parameters of an orthotropic PVC foam material in one single test. Two main experimental techniques were used in this study: Digital Image Correlation (DIC) and the Virtual Fields Method (VFM). The actual image recording process was mimicked by numerically generating a series of deformed synthetic images. Subsequent to this, the entire measurement and data processing procedure was simulated by processing the synthetic images using DIC and VFM algorithms. This procedure was used to estimate the uncertainty of the measurements (systematic and random errors) by including the most significant parameters of actual experiments, e.g. the geometric test configuration, the parameters of the DIC process and the noise. By using these parameters as design variables and by defining different error functions as object functions, an optimisation study was performed to minimise the uncertainty of the material parameter identification and to select the optimal test parameters. The confidence intervals of the identified parameters were predicted based on systematic and random errors obtained from the simulations. The simulated experimental results have shown that averaging multiple images can lead to a significant reduction of the random error. An experimental determination of the elastic coefficient of a PVC foam material was conducted using the optimised test parameters obtained from the numerical study. The identified stiffness values matched well with data from previous tests, but even more interesting was the fact that the experimental uncertainty intervals matched reasonably well with the predictions of the simulations, which is a highly original result and probably the main outcome of the present paper.

Elastic Full‐Field Strain Analysis and Microdamage Progression in the Vertebral Body from Digital Volume Correlation

Abstract: The strain distribution in vertebral body has been measured in vitro in the elastic regime but only on the bone surface by means of strain gauges and digital image correlation. Digital volume correlation (DVC) based on micro-computed tomography (micro-CT) images allowed measurements of the internal strain distribution in bone at both tissue (trabecular and cortical bone) and organ (vertebra) levels. However, DVC has been mainly used to investigate failure of the vertebral body but has not yet been deployed to investigate the internal strain distribution in the elastic regime. The aim of this study was to investigate strain in the elastic regime and up to failure inside the vertebral body, including analysis of strain in all directions. Three porcine thoracic vertebrae were loaded in a step-wise fashion at increasing steps of compression (5, 10 and 15%). Micro-CT images were acquired at each step of compression. DVC successfully provided the internal strain distribution both in the elastic regime and up to failure. Micro-CT images successfully identified regions of failure initiation and progression, which were well quantified by DVC-computed strains. Interestingly, the same regions where failure eventually occurred experienced the largest strain magnitude also for the lowest degrees of compression (yet in the elastic regime).

Damage Investigation in A319 Aluminium Alloy by X-ray Tomography and Digital Volume Correlation during In Situ High-Temperature Fatigue Tests

Abstract: The aim of this work is to analyse the strain field heterogeneity in an aluminium alloy subjected to low-cycle fatigue at high temperature. In the cylinder heads produced by a lost-foam casting process, the microstructure of the studied alloy consists hard intermetallic phases and large gas and microshrinkage pores. In order to study the influence of this complex 3D microstructure on fatigue crack initiation and propagation at 250 °C, an experimental protocol using laboratory and synchrotron tomography, finite element simulation and a new digital volume correlation platform have been used. The results showed the role of pores in the crack nucleation and highlighted the importance of hard phases in the crack propagation, thanks to the resolution on the DVC measurement.

Non-destructive Examination of Loads in Regular and Self-locking Spiralock® Threads through Energy-resolved Neutron Imaging

Abstract: Energy-resolved neutron transmission imaging is utilised for in situ comparisons of strain distributions in fastened assemblies with regular and self-locking Spiralock® female threads. The strain maps measured within torqued steel bolts indicate that for a Spiralock® thread, the load is distributed over a larger section of the fastener, making this type of thread more suitable for fastening of assemblies subject to transverse vibrations.

Bragg Edge Neutron Transmission Strain Tomography in Granular Systems

Abstract: The advent of pixelated detectors for time-of-flight neutron transmission experiments has raised significant interest in terms of the potential for tomographic reconstructions of triaxial strain distributions. A recent publication by Lionheart and Withers [WRB Lionheart and PJ Withers, “Diffraction tomography of strain”, Inverse Problems, v31:045005, 2015] has demonstrated that reconstruction is not possible in the general sense; however, various special cases may exist. In this paper, we outline a process by which it is possible to tomographically reconstruct average triaxial elastic strains within individual particles in a granular assembly from a series of Bragg edge strain measurements. This algorithm is tested on simulated data in two and three dimensions and is shown to be capable of rejecting Gaussian measurement noise. Sources of systematic error that may present problems in an experimental implementation are briefly discussed.

Optimization of a Cruciform Specimen Geometry for the Identification of Constitutive Parameters Based Upon Full-Field Measurements

Abstract: A methodology is proposed to optimize a specimen shape in a biaxial testing machine for the identification of constitutive laws based on full-field measurements. Within the framework of Finite Element Model Updating (FEMU) and Integrated Digital Image Correlation (IDIC), the covariance matrix of the identified material parameters due to acquisition noise is computed and its minimization is the basis of the proposed shape optimization. Two models are investigated; first, a linear elastic law, and second, an elastoplastic law with linear kinematic hardening. Two optimal fillet radii sets are assessed for the two investigated laws based on the minimization of the identification uncertainty.

Digital Image Correlation and Noise‐filtering Approach for the Cracking Assessment of Massive Reinforced Concrete Structures

Abstract: This paper describes the use of Digital Image Correlation (DIC) techniques for the cracking assessment of reinforced concrete (RC) massive beams and walls. DIC is known to provide accurate and detailed information on displacement and strain fields. Non-contact measurements can be used to evaluate concrete cracking of destructive tests carried out on a wide range of specimen scales. When applied to large RC structures tested outdoors or in difficultly controllable conditions, DIC-based methods may lead to erroneous results. In this study a post-processing procedure is presented to cope with noisy full-field measurements. The proposed cracking assessment approach is validated on a large experimental campaign. Four points bending tests are carried out on RC beams: firstly on full-scale rectangular beams and then on mock-ups scaled down by 1/3. In addition, fours RC walls are tested under in-plane cyclic shear up to failure. Digital images taken throughout the tests are processed by DIC techniques to provide in-plane displacement and strain fields. Full-field measurements are post-processed by the noise-filtering technique and the cracks patterns are identified. Crack widths are measured and compared with measurements obtained from conventional point-based sensors (linear variable differential transformer LVDT and fibre-optic FO transducers). The proposed DIC-based post-processing provides accurate estimation of cracks width for most of the tests. The analyses carried out on the two groups of RC beams show a scale-effect on the cracks width.

Theoretical Analysis on the Measurement Errors of Local 2D DIC: Part II Assessment of Strain Errors of the Local Smoothing Method–Approaching an Answer to the Overlap Question

Abstract: In this paper, the strain error of subset-based two-dimensional digital image correlation (DIC) is theoretically derived. Analytical solutions are provided to estimate the strain error. A dimensionless factor is proposed, namely the overlap magnifier, which reveals the dependency of the strain error on the DIC regularisation parameters, that is, subset size, step size and strain window size. The derived equations are validated numerically and experimentally. The estimated random strain error is in good accordance with the experimental data. The proposed derivation can be readily extended to stereo DIC.

Adaptive Isogeometric Digital Height Correlation: Application to Stretchable Electronics

Abstract: A novel adaptive isogeometric digital height correlation (DHC) technique has been developed in which the set of shape functions, needed for discretization of the ill-posed DHC problem, is autonomously optimized for each specific set of profilometric height images, without a priori knowledge of the kinematics of the experiment. To this end, an adaptive refinement scheme is implemented, which refines the shape functions in a hierarchical manner. This technique ensures local refinement, only in the areas where needed, which is beneficial for the noise robustness of the DHC problem. The main advantage of the method is that it can be applied in experiments where the deformation mechanisms are unknown in advance, thereby complicating the choice of suitable shape functions. The method is applied to a virtual experiment in order to provide a proof of concept. A second virtual experiment is executed with stretchable electronics interconnects, which entail localized buckles upon deformation with complex kinematics. In both cases, accurate results were obtained, demonstrating the beneficial aspects of the proposed method. Moreover, the technique performance on profilometric images of a real experiment with stretchable interconnects was demonstrated.

In vivo Identification of the Passive Mechanical Properties of Deep Soft Tissues in the Human Leg

Abstract: Goal: A non-invasive method is proposed to identify in vivo the passive mechanical properties of deep soft tissues in the human leg. How: Force-displacement curves in response to a localized compression of the calf are measured with a custom made experimental setup. The material parameters of a finite element model are then calibrated against the experimental curves using a genetic algorithm. A thorough investigation of the efficacy of this method to identify such mechanical properties is conducted through a design of experiments analysis and mixed numerical - experimental validations. Results: It is the first time that a thorough analysis is conducted to really separate the contribution of deep and superficial tissues in the response to compression tests and this permits to estimate the parameters of deep soft tissues on four subjects independently of the response of their other tissues. Two strain energy density functions are compared. It is shown that a 2nd order reduced polynomial better describes the passive mechanical behavior of the deep soft tissues of the leg than the neo-Hookean model.

Fast and Dense 2D and 3D Displacement Field Estimation by a Highly Parallel Image Correlation Algorithm

Abstract: This paper describes a fast method for estimation of dense 2D and 3D displacement fields from image correlation. It is based on a previously published local, or window-based, optical flow algorithm which is ideally suited for parallel processors. We describe the algorithm, its extension to stereo image correlation and its implementation on Graphical Processing Unit (GPU). We present the properties of the estimated displacement fields on simulated images and evaluate their accuracy on real data from a rigid body movement experiment. The main features of the method are a dense output (i.e. a 2D or 3D displacement vector per pixel) and a highly parallel structure which allows very high computational performance. A pair of 4 megapixels stereoscopic images is processed in less than 0.2 s. on a Titan GPU. Finally, we present and comment several experimental results obtained with the proposed method during mechanical experiments conducted at ONERA.

Analysis of Accuracy of Biaxial Tests Based on their Computational Simulations

Abstract: Design of biaxial tension testing rig has a significant influence on quality of the measured stress–strain data. The paper analyses the effect of test parameters on the accuracy of results. Finite element simulations of biaxial tension tests were realized, and the resulting stress–strain curves (evaluated in the same manner as in real experiments) compared with the input ones by means of coefficient of determination R2. The investigated parameters were type (hooks or narrow clamps), number (2÷5) and size (0.25÷5 mm) of gripping elements, specimen size (18÷33 mm), testing protocol (different displacement ratios) and specimen material (healthy artery, aneurysm tissue, elastin and intraluminal thrombus). Numerical results were compared with experiments on porcine aortas carried out with two clamps and four hooks per edge. Experiments were evaluated with respect to the obtained quality of fit and maximum achievable stresses under equibiaxial load. Two or three hooks and two narrow clamps per edge give the best accuracy for small specimens. Larger hook diameter increases the accuracy for low numbers of hooks. Non-equibiaxial protocols show worse accuracy than equibiaxial ones. For large specimens, four and five hooks are the best choice. The experiments revealed that higher stresses can be induced by two clamps setup (median 433 versus 257 kPa in circumferential direction and median 454 versus 333 kPa in axial direction). Quality of the fit was slightly but consistently higher with the four hooks setup (mean R2 = 0.984 versus 0.9797). The number of gripping elements should be chosen with respect to the need to ensure uniform force distribution along the specimen edge. Both narrow clamps and hooks achieved a comparable accuracy regardless of material. High numbers of hooks and wide clamps should be avoided for small specimens. Compared with hooks, use of narrow clamps allowed us to reach higher load until specimen rupture.

Identification of Added Mass in the Composite Plate Structure Based on Wavelet Packet Transform

Abstract: A new concept has been introduced that the combination of rotational mode shape with two-dimensional wavelet packet transform to detect the added mass (damage) in a glass fibre reinforced polymer composite plate structure. Wavelet packet transform is an advanced signal processing tool that can magnify the abnormality features in the signal. Rotational mode shapes are sensitive to damage in beam and plate structures. The proposed method employs an added mass, which slides to different locations to alter the local and global dynamic characteristics of the structure. Finite element analysis is carried out to obtain the first three rotational bending mode shapes, from the damaged plate structure, then used as input to two-dimensional wavelet packet transform. The numerical results of normalised diagonal detail wavelet packet coefficients show a peak at single or multiple added mass (damage) locations of a plate structure for two different boundary conditions. This method seems to be sensitive to relatively small amount of damage to the plate structure. A simple parametric study is carried out for the damage extent quantification. In addition, investigation with noise-contaminated signals shows its feasibility in the real applications.

Dynamic Deformation of Clamped Circular Plates Subjected to Confined Blast Loading

Abstract: In this paper, the dynamic deformation of thin metal circular plates subjected to confined blast loading was studied using high-speed three-dimensional Digital Image Correlation (3D DIC). A small-scale confined cylinder vessel was designed for applying blast loading, in which an explosive charge was ignited to generate blast loading acting on a thin metal circular plate clamped on the end of the vessel by a cover flange. The images of the metal plates during the dynamic response were recorded by two high-speed cameras. The 3D transient displacement fields, velocity fields, strain fields and residual deformation profiles were calculated by using 3D DIC. Some feature deformation parameters including maximum out-of-plane displacement, final deflection, maximum principal strain and residual principal strain were extracted, and the result was in good agreement with that simulated by AUTODYN. A dimensionless displacement was introduced to analyse the effects of plate thickness, material types and charge mass on the deflection of metal plates. DIC is also proven to be a powerful technique to measure dynamic deformation under blast loading.

Measurement of the Appearance and Growth of Tow Buckling Defect in the Frame of Complex Shape Manufacturing Process by Using Fringe Projection Technique

Abstract: During the manufacturing of composite complex shape parts, defects such as tow buckles characterised by out of plane elevation may appear. The parameters controlling the appearance and growth of the defect are not completely understood and need to be investigated. A device capable of reproducing tow buckles has been used to study the tow buckling phenomenon. Several techniques able to measure out of plane elevations are discussed to detect the appearance and evaluate continuously the growth of the tow buckle in relation to its size and shape. The fringe projection technique was chosen as it gives the best compromise between the size of the defect to measure and its resolution. If the in-plane bending angle is the main criterion at the origin of the tow buckle appearance and growth, it is not the only one. This work shows that the fabric architecture such as the space between the tows perpendicular to the one showing the buckle is also crucial to control the buckle’s appearance and growth. It also shows that the differential bi-axial loading of the fabric as well as the stiffness of the tows in the three main directions greatly in fluences the appearance of the defect.

A Closer Look at the Diffuse and Localised Necking of A Metallic Thin Sheet: Evolution of the Two Bands Pattern

Abstract: Plastic strain localisation in a sheet specimen was monitored by electronic speckle pattern interferometry during uniaxial tensile tests. The experiments were carried on in the diffuse and localised necking stages until fracture. A kinematic model, which is independent of material characteristics, was used to describe the whole strain rate field with two crossing localisation bands inclined with respect to the tensile direction. Then, the physical features of localisation, such as the width of the two bands, their inclination angles and their maximum strain rates are identified by least-square from the displacements fields and their evolutions are followed from the onset of diffuse necking up to the failure. In particular, the effect of the average strain rate is considered and bandwidth evolution is analysed in detail. It was found that: The band structure appears early, as soon as diffuse necking starts; The separation, in terms of strain rate or bandwidth, of the two bands corresponds to the transition between diffuse and localised necking. The localised necking stage can be divided into two sub-stages: in the first one, the two bands continue to evolve but at different rates, and in the second one, one of the bands stabilises. The transition between the two sub-stages is influenced by the crossbeam velocity; The inclination of the band leading to fracture remains quite stable, while the other rotates towards a situation perpendicular to the tensile direction; The band width decreases exponentially versus the maximum local strain. The two bands follow the same evolution path, but one of them progressively lags behind the other until it stops deforming. Although the average strain rate was only varied by a factor two, it was found that, when the strain rate increases, the two bands stay together longer and thus that the onset of localised necking is delayed.

Addendum to ‘Characterising the Strain and Temperature Fields in a Surrogate Bone Material Subject to Power Ultrasonic Excitation’

Abstract: Recently, a very interesting article was published in Strain where a rigid polyurethane foam specimen was submitted to longitudinal vibrational excitation in the ultrasonic range. The authors showed that it was possible to measure time-resolved strain response maps by combining digital image correlation and ultra-high-speed imaging. The objective of this discussion is to propose further analysis of the data published in that article, showing that it is possible to extract meaningful values for Young’s modulus by using the acceleration field in the specimen as a load cell. The aim here is not to provide a complete solution to this problem but to alert the readers on the possibilities offered by this kind of test. This method is an interesting alternative where the energy is input repeatedly instead of in one go as in impact-basedtests. Full-field vibration measurements have already been used in the past to identify stiffnesses but only in bending and at much lower strain rates. This article shows that the method can be extended to cover a much wider strain rate range. Finally, only global stiffness values were identified then, whereas here, maps of stiffnesses can be derived.

Exploring a Multi‐modal Experimental Approach to Investigation of Local Embedment Behaviour of Wood under Steel Dowels

Abstract: A multi-modal experimental approach for analysing the embedment behaviour of timber connections with steel dowels is proposed in this study. In this approach, a standard mechanical embedment test on single-dowel connections is combined with an optical measurement of surface deformations of the connection based on digital image correlation principle and an X-ray micro-computed tomography examination of the deformations in the dowel-wood interface. The latter is conducted on cylindrical cores including the dowel hole, physically extracted from the loaded specimen at three characteristic points of the load-deformation curves. The major challenge of this procedure is disrupted load transfer between the cylindrical core specimens and the external material they were plugged in for further analysis. Despite its challenges and limitations, the method revealed a potential for an unprecedented insight into the micromechanics of dowel connections and for effective correlation of the micro-level observations with the external macroscopic load-deformation characteristics.

A new Method for Processing Time Averaged Vibration Patterns: Linear Regression

Abstract: Speckle-based interferometry systems are useful tools for measuring vibration patterns at harmonically vibrating objects. The standard method for processing the speckle patterns acquired is to eliminate additive background noise and speckle phase, yielding Bessel-type fringe patterns whose values are proportional to the absolute value of the Bessel function. Fringes are covered by multiplicative speckle intensity noise on the Bessel-modulated vibration amplitude. Sine–cosine filtering is not an option because the Bessel-type fringe pattern is not a phase pattern, and thus, sine–cosine filtering would only degrade the results. Improvements can be reached by involving additional measurements acquired in the stationary state. An alternative method for processing vibration patterns using linear regression is proposed, yielding patterns where the vibration amplitude is an argument of a true Bessel function, not its absolute value. As a result, spatial frequencies of the vibration fringe pattern are only half of those obtained with standard methods, and results can be filtered and normalised conveniently. While other contributions to improve the results rely on determining indexed skeletons for high Bessel fringe densities, the proposed method aims at a very limited number of low-order fringes, allowing demodulation of the Bessel fringe pattern based on the actual Bessel values in the pattern. The method provides an effective alternative for spatial filtering. Phase differences between the stationary and vibrating states have an adverse effect on the results. Two methods, capable of handling phase jumps of 2π in the phase difference distribution, are presented to correct this.