On noise prediction in maps obtained with global DIC

International audienceA predictive formula giving the measurement resolution in displacement maps obtained using Digital Image Correlation was proposed some years ago in the literature. The objective of this paper is to revisit this formula and to propose a more general one which takes into account the influence of subpixel interpolation for the displacement. Moreover, a noiseless DIC tangent operator is defined to also minimize noise propagation from images to displacement maps. Simulated data enable us to assess the improvement brought about by this approach. The experimental validation is then carried out by assessing the noise in displacement maps deduced from a stack of images corrupted by noise. It is shown that specific image pre-processing tools are required to correctly predict the displacement resolution. This image pre-processing step is necessary to correctly account for the fact that noise in images is signal-dependent, and to get rid of parasitic micro-movements between camera and specimen that were experimentally observed and which corrupt noise estimation. Obtained results are analyzed and discussed

The grid method for in-plane displacement and strain measurement: a review and analysis

International audienceThe 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

Strict upper bounds of the error in calculated outputs of interest for plasticity problems

International audienceThis paper introduces a new computational technique for deriving guaranteed upper bounds of the error in calculated outputs of interest for plasticity problems under quasi-static conditions. This approach involves the resolution of some nonstandard additional problems, for which resolution techniques are given. All sources of error (spatial and temporal discretization, iteration stepping) are taken into account

On the propagation of camera sensor noise to displacement maps obtained by DIC - an experimental study

International audienceThis paper focuses on one of the metrological properties of DIC, namely displacement resolution. More specifically, the study aims to validate, in the environment of an experimental mechanics laboratory, a recent generalized theoretical prediction of displacement resolution. Indeed, usual predictive formulas available in the literature neither take into account sub-pixel displacement, nor have been validated in an experimental mechanics laboratory environment, nor are applicable to all types of DIC (Global as well as Local). Here, the formula used to account for sub-pixel displacements is first recalled, and an accurate model of the sensor noise is introduced. The hypotheses required for the elaboration of this prediction are clearly stated. The formula is then validated using experimental data. Since rigid body motion between the specimen and the camera impairs the experimental data, and since sensor noise is signal-dependent, particular tools need to be introduced in order to ensure the consistency between the observed image noise and the model on which prediction hypotheses are based. Pre-processing tools introduced for another full-field measurement approach, namely the Grid Method, are employed to address these issues

Une nouvelle procédure d’identification des paramètres de lois cohésives

L’objectif est ici d’introduire un nouvel outil de caractérisation de lois cohésives, modèle le plus couramment utilisé pour décrire et simuler le phénomène de délaminage. Cet outil est basé sur une méthode de corrélation d’image globale, où la définition de l’espace de recherche cinématique est adéquatement choisie. Après avoir présenté le principe de cette méthode, on s’intéresse à sa validation, ainsi qu’à son comportement au bruit. Cette validation est réalisée numériquement, (i) en construisant un ensemble d’images à l’aide d’un outil de simulation évolué du délaminage et (ii) en identifiant à partir de ces images les caractéristiques du comportement de l’interface

Effect of interpolation on noise propagation from images to DIC displacement maps

International audienceThis paper introduces and validates a new prediction of sensor noise propagation from images of randomly marked surfaces to displacement maps obtained by Digital Image Correlation (DIC). Images are indeed often affected by sensor noise, which propagates to DIC output. We consider here the 2D global DIC (G-DIC), for which this output is the in-plane displacement calculated at a set of nodes. Predictive formula for the resolution of the displacement at these nodes is already available in the literature. The contribution of the present paper is to revisit this formula to take into account the interpolation required by sub-pixel displacement. A generalization is also proposed to predict the displacement resolution throughout the field of view. It is then extended to several kinds of DIC. The correlation procedure is thoroughly described in order to emphasize the role of the interpolation. A numerical assessment on synthetic data validates the new prediction and shows the improvement brought about by the proposed formula

Concurrent tracking of strain and noise bursts at ferroelastic phase fronts

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Removing quasi-periodic noise in strain maps by filtering in the Fourier domain

International audienceQuasi-periodic noise due to various reasons often corrupts strain maps obtained with full-field measuring systems. The aim of this didactic paper is to show how to remove this noise by changing some Fourier coefficients involved in the two-dimensional (2D) Fourier transform of these strain maps. The basics of the 2D Fourier transform of images, which is a common tool in image processing but that is only scarcely employed in the experimental mechanics community, are first briefly recalled. Several procedures employed for removing undesirable frequencies in strain maps are then discussed. Three different examples illustrate the benefit of this approach

Determining displacement and strain maps immune from aliasing effect with the grid method

International audienceSpatial aliasing may affect methods based on grid image processing to retrieve displacement and strain maps in experimental mechanics. Such methods aim at estimating these maps on the surface of a specimen subjected to a loading test. Aliasing, which is often not noticeable to the naked eye in the grid images, may give spurious fringes in the strain maps. This paper presents an analysis of aliasing in this context and provides the reader with simple guidelines to minimize the effect of aliasing on strain maps extracted from grid images

Concurrent tracking of strain and noise bursts at ferroelastic phase fronts

Many technological applications are based on functional materials that exhibit reversible first-order ferroelastic transitions, including elastocaloric refrigeration, energy harvesting, and sensing and actuation. During these phase changes inhomogeneous microstructures are formed which fit together different crystalline phases, and evolve abruptly through strain bursts related to domain nucleation and the propagation of phase fronts, accompanied by acoustic emission. Mechanical performance is strongly affected by such microstructure formation and evolution, yet visualisation of these processes remains challenging. Here we report a detailed study of the bursty dynamics during a reversible stress-induced martensitic transformation in a CuZnAl shape-memory alloy. We combine full-field strain-burst detection, performed by means of an optical grid method, with the acoustic tracking of martensitic strain avalanches using two transducers, which allows for the location of the acoustic-emission events to be determined and the measurement of their energies. The matching of these two techniques reveals interface formation, advancement, jamming and arrest at pinning points within the transforming crystal