A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A coaxial cable sensor device with periodic impedance discontinuities along the length of its cable. The cable comprises an inner conductor, insulating material disposed around the length of the inner conductor, and an outer conductor disposed around the insulating material. The periodic impedance discontinuities are created by physical deformations or material alterations to at least one of the inner conductor, the outer conductor, and the insulating material. The sensor device may be used to measure temperature, pressure, strain, and acoustic waves in building structures, and is well suited for down-hole or underwater applications.

Coaxial cable bragg grating sensor

The “planar” digital image correlation technique needs a single CCD camera to acquire the surface patterns of a zone of a specimen in the underformed and deformed states. With these two images, one can determine in-plane displacement and strain fields. The digital image correlation technique used herein is based on Fast Fourier Transforms, which are very effective in reducing the computation cost. Its performance is assessed and discussed on artificial signals and in a real experimental situation. The technique is utilized to analyze experimental results of a plane shear experiment and validate a damage meso-model describing different degradations in a C/C composite material.

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Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model

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.

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

Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components

Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I

Our purpose is the direct strain measurement from the interrogation of a crossed grating marked on the surface of a specimen. The observation of the object through a master grid (as in moire method) is replaced by a direct characterization of the pattern using a Fourier transform. This gives direct access to the modification of the pitches which leads to quantification of the strain without the intermediary of a fringe pattern. The comparison between the undeformed and deformed states allows the determination of the magnitude and orientation of principal strains and of the local rigid-body rotation. We describe three analysis techniques, one using the diffraction phenomenon, another utilizing a numerical spectral evaluation and third combining diffraction and phase-shifting procedure. These grid interrogations have different domains of application and a suitable choice of these analysis techniques allows a very large measurement range (10−5 to high strain according to the grating resistance).

Grating Interrogations: from Small to Large Strain Measurement

La photomecanique , qui regroupe l’ensemble des metrologies optiques, offre une large palette de techniques de mesure sans contact, souvent mises a profit pour l’identification du comportement mecanique des materiaux dans les laboratoires comme pour le suivi des procedes de fabrication ou la tenue de structures dans l’industrie.

Mesures en mécanique par méthodes optiques

A grid method is used to experimentally determine the in-plane displacement fields around a crack tip in a Single-Edge-Notch (SEN) tensile polyurethane specimen. Horizontal displacement ux-exp and vertical displacement uy-exp are expressed as functions of circular coordinates centred on the crack tip. These are compared with the approximate solutions of linear elastic fracture mechanics with a view to studying the applicability to polymers. The results show that this solution is not in agreement with the experiments at the focused on the vicinity of a crack tip. Taking this into account, an FEA program is developed with CAST3M for the purpose of comparing the experimental displacements and the numerical data. New formulations of displacements ux and uy are then developed. These formulations are derived from the principle of superposition and based on Arakawa’s formulation. With the displacement gradients obtained from the FEA and the new formulations, the determination of J-integrals is found to be in very good agreement with those derived from numerical calculation. Consequently, the proposed formulations can give displacement fields compatible with the J-integral calculation for the region near the crack tip. An application based on an experimental test is proposed to evaluate the performances of the proposed formulations.

Mario Cottron

Papers

Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I

Grating Interrogations: from Small to Large Strain Measurement

Mesures en mécanique par méthodes optiques

In Plane Displacement Formulation for Finite Cracked Plates Under Mode I Using Grid Method and Finite Element Analysis

Calculation of J-integrals using experimental and numerical data: Influences of ratio (a/W) and the 3D structure