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

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.     

Characterisation of Indentation‐Induced Pattern Using Full‐Field Strain Measurement

Abstract: In this study, digital image correlation (DIC)‐based strain analysis software was successfully developed. Its strain resolution lies in the order of 2.3 × 10^?4–3.1 × 10^?4. Full‐strain field measurement was used to study indentation‐induced plastic patterns around the spherical indenter for a polycrystal and a single crystal of pure aluminium. During indentation, the pure aluminium specimen of the single crystal revealed a symmetric indentation pattern of von Mises strain. The piling‐up around the residual impression was successfully and directly characterised by examining the sign of strain ?_X and ?_Y in the X and Y directions. However, the inward, out‐of‐plane movement results in an error in calculating in‐plane strain referred to as a ‘distortion strain’ using two‐dimensional DIC.     

Ultra‐High‐Speed Full‐Field Deformation Measurements on Concrete Spalling Specimens and Stiffness Identification with the Virtual Fields Method

Abstract: For one decade, spalling techniques based on the use of a metallic Hopkinson bar in contact with a concrete sample have been widely employed to characterise the dynamic tensile strength of concrete at strain rates ranging from a few tens to hundreds of s^?1. However, the processing method based on the use of the velocity profile measured on the rear free surface of the sample (Novikov formula) remains quite basic. In particular, the identification of the whole softening behaviour of the concrete material is currently out of reach. In the present paper, a new processing technique is proposed based on the use of the virtual fields method (VFM). First, a digital ultra‐high‐speed camera is used to record the pictures of a grid bonded onto the specimen. Then, images of the grid recorded by the camera are processed to obtain full‐field axial displacement maps at the surface of the specimen. Finally, a specific virtual field has been defined in the VFM equation to use the acceleration map as an alternative ‘load cell’. This method applied to three spalling tests with different impact parameters allowed the identification of Young's modulus during the test. It was shown that this modulus is constant during the initial compressive part of the test and decreases in the tensile part when microdamage exists. It was also shown that in such a simple inertial test, it was possible to reconstruct average axial stress profiles using only the acceleration data. It was then possible to construct local stress–strain curves and derive a tensile strength value.     

Influence of Wooden Board Strength Class on the Performance of Cross‐laminated Timber Plates Investigated by Means of Full‐field Deformation Measurements

Although cross‐laminated timber (CLT) plates are increasingly used in high‐performance building structures, a tailored composition of them or, at least, a performance‐based classification scheme is not available. Especially, the influence of the quality of the ‘raw’ material (wooden boards) on the load carrying capacity of CLT elements is hardly investigated yet. For this reason, within this work, bending tests on 24 CLT plates consisting of wooden boards from three different strength classes have been carried out. The global mechanical response as well as the formation of failure mechanisms were investigated, including a full‐field deformation measurement system, which allowed for a qualitatively as well as quantitatively identification of board failure modes. Interestingly, no influence of the board strength class on the elastic limit load of the CLT plates was observed, but the situation was different for the load displacement history beyond the elastic regime, where basically, two different global failure mechanisms could be distinguished. The obtained knowledge about the ‘post‐elastic’ behaviour of CLT plates may serve as a basis for the optimisation of CLT products and the development or improvement of design concepts, respectively. Moreover, the obtained large ‘post‐elastic’ capacity reserve of CLT consisting of high quality boards could lead to a better utilisation of the raw material.     

Modelling Strategies for Property Identification Based on Full‐Field Surface Displacement Data

Abstract: The use of full‐field displacement measurements in mechanical testing provides detailed response information that can be used, in conjunction with modelling and optimisation, for precise material property identification. One limitation of this technique is that the collection of response data and the sectioning of a specimen to reveal the material microstructure are both destructive tests and mutually exclusive, as the displacement measurement occurs only on the exposed surface. Therefore, modelling of an experiment to interpret a full‐field experiment requires assumptions about the structure of the material below the visible surface. This study evaluates the effects of several possible modelling assumptions on the errors in model‐predicted response and on the resulting material property estimates. A 3‐D microstructural model, for which the subsurface grain geometry and orientations are known, provides the basis for comparison of several common modelling assumptions based on the grain geometry and orientations on the visible surface of a specimen.     

Full‐Field Vibration Measurement by Time‐Average Speckle Interferometry and by Doppler Vibrometry – A Comparison

Abstract: Identification of dynamic material properties, non‐destructive testing and study of vibroacoustic behaviour of different structures require the use of complex, pointwise and full‐field measurements, which are capable of providing data for experimental modal analysis or model updating. Nowadays, among other techniques, optical non‐contact techniques represent the favourite choice as they do not add mass, stiffness or damping to the structure under test. When the range of vibration amplitudes allows it, most of these techniques are based on interferometric principles. Development of laser sources and detectors leads to a continuous improvement of vibration measurement techniques. However, a hard choice still has to be made between spatial resolution and temporal resolution. Another difficult choice is between space bandwidth product and energetic sensitivity of the detector. While the number of pixels of a camera is continuously increasing, the pixel size seems limited at its lower end. The paper presents a comparative study of the vibration amplitude fields as measured by two full‐field non‐contact techniques, speckle interferometry and laser Doppler vibrometry, and predicted by finite‐element model. The measurements concern the free and the forced vibrations of a thick, composite plate with free boundaries.     

Performance Assessment of a Numerical Simulation Tool for Wooden Boards with Knots by Means of Full‐Field Deformation Measurements

In wooden boards, knots and the resulting fibre deviations in their vicinities are mainly responsible for qualitative downgrading of timber elements. Thus, the development of reliable numerical simulation tools for the determination of effective strength and stiffness properties of timber elements and, in a next step, for the development and evaluation of grading criteria is highly desirable. Due to the complexity of such tools, a comprehensive validation is required. Within this work, the suitability of full‐field deformation measurements for four‐point bending tests on wooden boards with knots is evaluated first. Next, the test series is used to validate a previously developed three‐dimensional numerical simulation tool, which combines a geometrical model for the grain course and a micromechanical model for a density and moisture dependent characterisation of the clear‐wood material. The digital image correlation technique proved to be capable to reproduce the strain fields in the vicinity of knots under bending load. Moreover, a very good correlation between numerical and experimental results was obtained.     

Diffusing‐Wave Spectroscopy Contribution to Strain Analysis

Abstract: We present a new full‐field strain measurement method based on diffusing‐wave spectroscopy. Our technique makes it possible to measure strains in the vicinity of the surface of highly light‐scattering materials. Its main feature is an extreme sensitivity: the range of deformations measured is 10^?5–10^?3. To validate the measurements, experimental results from several plane stress configurations are compared with theoretical and numerical calculations. Furthermore, we propose an extension of the method for non‐scattering materials.     

3D Residual Stress Field in Arteries: Novel Inverse Method Based on Optical Full‐field Measurements

Abstract: Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress‐free configurations that evolve over time. This gives rise to residual stresses contributing to the homoeostatic state of stress in vivo as well as adaptations to perturbed loads, disease or injury. The existence of residual stresses in an intact but load‐free excised arterial segment suggests compressive and tensile stresses, respectively, in the inner and outer walls. Accordingly, an artery ring springs open into a sector after a radial cut. The measurement of the opening angle is commonly used to deduce the residual stresses, which are the stresses required to close back the ring. The opening angle method provides an average estimate of circumferential residual stresses but it gives no information on local distributions through the thickness and along the axial direction. To address this lack, a new method is proposed in this article to derive maps of residual stresses using an approach based on the contour method. A piece of freshly excised tissue is carefully cut into the specimen, and the local distribution of residual strains and stresses is determined from whole‐body digital image correlation measurements using an inverse approach based on a finite element model.     

An Approach to Analyse Errors Introduced in the Random Grid Strain Measurement Method

Abstract: The present work refers to the errors imposed by the recently introduced random‐grid mesh‐free full field strain measurement method. Excluding systematic errors of the digital camera, the method itself is not an error‐free procedure. A possible cause of errors could be the misplacement of the spot‐centre (centroid) with regard of the spot boundaries. Another cause of errors is the limited order of approximation in the field function. A third one, emerges from the so‐called ‘sub‐pixel effect’. This kind of error is difficult to trace, so direct comparison between the results of the method and exact solutions is required. In the present work, proper analytical or numerical derivations of those errors are presented and reasonable upper limits are estimated. Finally, numerical and experimental examples are presented to demonstrate the accuracy of the method.     

A Multigrid PGD‐based Algorithm for Volumetric Displacement Fields Measurements

The use of a finite elements‐based Digital Volume Correlation (FE‐DVC) leads to lower measurement uncertainties in comparison to subset‐based approaches. However, the associated computing time may become prohibitive when dealing with high‐resolution measurements. To overcome this limitation, a Proper Generalised Decomposition solver was recently applied to 2D digital image correlation. In this paper, this method is extended to measure volumetric displacements from 3D digital images. In addition, a multigrid Proper Generalised Decomposition algorithm is developed, which allows to use different discretisations in each term of the decomposition. Associated to a coarse graining of the digital images, this allows to avoid local minima, especially in presence of large displacements. Synthetic and practical cases are analysed with the present approach, and measurement uncertainties are compared with standard FE‐DVC. Results show that such an approach reduces the computational cost (when compared to FE‐DVC) whilst maintaining lower measurement uncertainties than standard subset‐based DVC.     

Application of High Magnification Digital Image Correlation Technique to Micromechanical Strain Analysis

Abstract: This paper describes an experimental apparatus and its application for the full‐field measurement of heterogeneous strains at high magnifications. The apparatus consists of an image acquisition and analysis system, an optical microscope and a stable tensile stage. Magnified images of the specimen surface are acquired and analysed using the digital image correlation (DIC) method. The response of the heterogeneous microstructure of a nodular cast iron is investigated during a tensile test. Strains obtained by using the DIC method and averaged over the observation window correlate with strain measurements simultaneously obtained by using an extensometer. The strain maps of DIC reveal the heterogeneous development of plasticity in the nodular cast iron microstructure. The apparatus has the potential to investigate material behaviour at the microscopic scale.     

A Review of the Challenges and Limitations of Full‐Field Measurements Applied to Large Heterogeneous Deformations of Rubbers

Abstract: This paper presents an overview of the use of full‐field measurement techniques, more precisely digital image correlation (DIC) and coupled DIC and infrared thermography, for the material and structure characterisation of rubber reported in the literature. Even though such techniques have increasingly been applied for approximately 30 years for moderate deformations in metal and composite materials, they are still under‐employed in the measurement of full kinematic and thermal fields in the case of large deformations undergone by rubber materials. To date, the applications addressed are crack propagation at both macroscopic and microscopic scales, model validation and constitutive parameter identification.     

Identification of Specimen Position and Orientation Using Standard Deviation of Intensity in Phase‐Shifting Digital Holography1

Abstract: Phase‐shifting digital holography is a useful method to measure the displacement distribution and the strain distribution of an object surface. The complex amplitude distribution of an object surface is obtained as the complex amplitude distribution at a reconstruction distance. It is, however, difficult to measure the reconstruction distance by actual measurement. We discovered that the standard deviation of the intensity on the reconstructed image becomes the maximum value when the reconstruction distance is the same as the actual optical path length. The displacement distributions are obtained for the x‐, y‐ and z‐directions. When the normal direction of an object surface inclines from the z‐direction, the displacements defined on the xyz‐coordinate system should be transformed into the object coordinate system. It is, therefore, required to develop a measurement method of the orientation of the object to obtain the parameters for transforming from the xyz‐coordinate system into the object coordinate system. In this paper, the method to identify the position and the orientation of a specimen using the standard deviation of the intensity distribution is proposed.     

Perspective Measurement of the Out‐of‐plane Displacement and Normal Strain Field Distributions Inside Glass Fibre‐reinforced Resin Matrix Composite

A depth‐resolved wavenumber‐scanning interferometer (DRWSI) was built up to measure the out‐of‐plane displacement and normal strain field distributions on the front surface, rear surface and internal glass fibres of a glass fibre‐reinforced resin matrix composite before and after loading. Series of the fringe patterns were recorded, while the wavenumber of the laser, monitored online by an optical wedge, was scanned by tuning the temperature. Random sampling Fourier transform is used to overcome the non‐linearity of the wavenumber series. In the end, the distributions of the out‐of‐plane displacements and normal strain field are presented as the applied loads were 10 µm, 20 µm and 30 µm, respectively. In conclusion, DRWSI is a suitable method to measure the mechanical properties inside resin composite non‐destructively.     

Direct strain tensor approximation for full‐field strain measurement methods

Full‐field strain measurement techniques are based on computing the spatial derivatives of numerical or functional approximations of the underlying displacement fields extracted from digital imaging methods. These methods implicitly assume that the medium satisfies the strain compatibility conditions, which are only true in the case of a continuum body that remains continuum throughout its deformation history. In the present work, we introduce a method that can be used to calculate the strain components directly from typical digital imaging data, without the need of the continuum hypothesis and the need for displacement field differentiation. Thus, it enables the measurement of strain fields from imaged surfaces that may or may not contain discontinuities. Numerical comparisons are performed on the basis synthetic data produced from an analytical solution for an elastically orthotropic open‐hole domain in tension. For performance comparison purposes, the mean absolute error distributions are calculated for the cases of both the traditional meshless random grid method, and the direct strain method introduced herein. It is established that the more refined representation of strain provided by our present approach is more accurate everywhere in the domain, but most importantly, near its boundaries. Published 2013. This article is a US Government work and is in the public domain in the USA.     

50th Anniversary Article: Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method

This paper deals with noise propagation from camera sensor to displacement and strain maps when the grid method is employed to estimate these quantities. It is shown that closed‐form equations can be employed to predict the link between metrological characteristics such as resolution and spatial resolution in displacement and strain maps on the one hand and various quantities characterising grid images such as brightness, contrast and standard deviation of noise on the other hand. Various numerical simulations confirm first the relevance of this approach in the case of an idealised camera sensor impaired by a homoscedastic Gaussian white noise. Actual CCD or CMOS sensors exhibit, however, a heteroscedastic noise. A pre‐processing step is therefore proposed to first stabilise noise variance prior to employing the predictive equations, which provide the resolution in strain and displacement maps due to sensor noise. This step is based on both a modelling of sensor noise and the use of the generalised Anscombe transform to stabilise noise variance. Applying this procedure in the case of a translation test confirms that it is possible to model correctly noise propagation from sensor to displacement and strain maps, and thus also to predict the actual link between resolution, spatial resolution and standard deviation of noise in grid images.     

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

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.     

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

The behaviour of the cancellous bone surrogate material, rigid polyurethane foam (PUF), subject to power ultrasonic vibration excitation has been studied, with the purpose of identifying a methodology to investigate the effects that ultrasonic surgical devices have on biological tissue materials. To characterise the vibrational response to ultrasonic excitation, non‐contact measurement of the full in‐plane displacement field of PUF plate specimens was performed by combining the use of an ultra‐high speed camera and 2D digital image correlation. To investigate the thermal response, an infrared camera was used in real time to detect the temperature field. The measured surface displacement and strain fields of the PUF specimens and the thermal response are compared with data from an analytical model, and two different finite element models using Abaqus and PZFlex . The close agreement between calculated and measured data provides initial confidence in the use of the models for predicting the effects of ultrasonic excitation on tissue materials. The measurement data demonstrate the success of the experimental method for measuring vibrational responses in a hard tissue surrogate material at the ultrasonic frequencies associated with power ultrasonic surgical devices.