Alexis Lagarde

Photoelastic analysis of a three-dimensional specimen by optical slicing and digital image processing

The authors show a nondestructive method for obtaining the isochromatic and isoclinic fringes in a three-dimensional photoelastic specimen. The basic idea is to delimit a slice between two plane laser beams. The properties of polarization of the scattered light (Rayleighs law) and the interference possibilities of the diffused beams are used. By introducing speckle pattern properties, the correlation factor of the two scattered beams is similar to the illumination given in a plane polariscope for the investigation of a slice (in a classical frozen-stress technique). The authors use a monochromatic laser beam, a CCD camera and a personal computer. Because they cannot obtain the correlation factor directly, they do a statistical analysis of the speckle patterns. The variance (function of the correlation factor) is computed from the light intensities of three images corresponding to the speckle pattern for plane 1 alone, plane 2 alone, and both planes together.

Numerical spectral analysis of a grid: Application to strain measurements

Abstract We present a nondestructive and noncontact extensometry technique, which has been developed in order to study the behavior of different materials such as polycarbonate, araldite, urethane, etc. A spectral analysis of a crossed grating marked on the surface of a specimen and recorded by a charge coupled device camera is presented. The procedure is based on the use of a bidimensional fast Fourier transform algorithm coupled with an interpolation process. It leads to the accurate determination of frequencies. Numerical simulations have been made to evaluate the strain sensitivity; it depends on both the initial phase and the number of cycles characterizing the grid. Theoretically, the strain sensitivity can reach 10 -5 in best cases, but practically it is notbetter than 10 -4 . Several applications on different materials are presented: polyurethane, paper and cloth.

Two-wavelength method for full-field automated photoelasticity

A new method for the whole-field determination of the isoclinic angle α and the isochromatic parameter ϕ is presented. The problems appearing during the calculation of these two parameters are solved with the use of two different wavelengths. Indeed, when a monochromatic light is used as an incident light, α is not measurable at the points where ϕ is equal to 2kπ. In this method, each monochromatic light can compensate for the influence of ϕ to obtain the isoclinic angle for the entire model. Also, most of the methods calculate the fractional fringe order that is unwrapped afterward to obtain the isochromatic parameter. This unwrapping process needs an initialization, which cannot be automatic with only one isochromatic fringe pattern. The use of two wavelengths permits a complete automatic unwrapping of the isochromatic parameter, even for the initialization of the process.

Grating interrogations: from small to large strain measurement

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 moiré 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).

Separation of isochromatic and isoclinic patterns of a slice optically isolated in a 3-D photoelastic medium

Abstract We show a nondestructive experimental method which gives the isochromatic and isostatic patterns of slice optically isolated in a three dimensional photoelastic model. We used a nondestructive method of optical slicing developed in our laboratory. In this method, the photoelastic model is optically sliced by two plane laser beams. The analyze of the scattered light gives fringes equivalent to the ones obtained in a plane polariscope (isochromatic and isoclinic fringes). In order to separate the isochromatic and the isoclinic fringes, we recorded several images for different polarization orientations and we separated the isoclinic and isochromatic fringes using the Fourier transform. Then the isostatics pattern is plotted. We show a test of a punctual loading on the top of a prismatic specimen and the possibilities of our method in an industrial case of a model realized by stereolithography technique.

Shadow moire by phase shifting method and applications

The shadow moire is one of the optical techniques which is able to give level lines of an object with respect to a master grating plane. Level lines result from the interferences between the lines of the master grid and their shadow projected by a ponctual source light. The sensitivity of this procedure is a few tenths of millimeters in best cases. A complete study is presented showing the influence of the different parameters. It is shown that only one possibility is available. We then propose an automated procedure based on a 2D FFT algorithm to determine precisely the phase shift value introduced by a coarse object translation. Finally, the presented applications on 3D shape reconstruction and out-of-plane displacement field measurement show the potentiality of shadow moire is greatly improved with an accuracy of 0.02 mm.

Optical methods applied to the investigation of fracture mechanics

Because of the increase of catastrophic crack propagations at the middle of this century, it became necessary to develop a fracture theory in order to extend the life of structures and for evident reasons of security. These first search works have given a better understanding of the fracture in a linear medium by defining the stress distribution around a crack-tip. The stress singularity is then characterized for each fracture mode by a factor independent of the mechanical properties of the material, the stress intensity factor. This linear theory is always useful because of the common employment of brittle materials. A few decades after, the progress in the study of non-linear behaviors has induced a theory of ductile fracture. For this kind of material, the singularity amplitude is then characterized by the energy release rate. These theoretical works have required the development of experimental methods to test some results to understand special fracture phenomena. Among the experimental methods, the optical ones, which allow non-contact and so non-disturbing measurements, are every powerful. The advent of the laser, the use of image processing and numerical procedure to analyze the experimental data allows by optical methods the determination of stresses or kinematic values with a high precision. Our purpose is to present a few optical methods and the associated analysis techniques developed in our laboratory which seem to be well adapted to measure characteristic parameters of brittle or ductile fracture.

Improvement on phase-shifting method precision and application on shadow moiré method

Phase shifting technique is more and more employed in photomechanic even on optical methods which are not well adapted for it, particularly for shadow moire method where the phase shift is realized by translating the object. In such case, good results are obtained only if translation is executed with high accuracy. We present the effect of unaccuracy phase shift evaluation on the form and amplitude of calculated phase error. In this article, we propose a new automated procedure based on the use of a 2.D. F.F.T. algorithm to determine precisely the phase shift value introduced by a coarse object translation. We finally present an application on the out-of-plane displacement measurement on bended plate in corrugated paper. An order of largeness is given for await precision on such measurement.

Improvement of local strain measurement by grid method: new optical device and quasi-heterodyne technique

Among optical strain measurement methods, the grid method is a powerful one. Progresses in the technique of information processing have contributed to develop classical analysis (optical and numerical Fourier transform). We propose a new optical device that allows the interference of diffracted beams from two crossed gratings of parallel lines marked on the specimen surface. The analysis of the interference fringes during loading provides the geometry of the gratings and so leads to the strain determination. The proposed method is insensitive to the specimen translations and presents a range from 105, with the use of a phase-shifting technique, to a few 102. Using experimental traction tests, we compare this method with the classical ones and we develop the performances of the proposed method (sensitivity and large measurement range).

High Speed Local Strain Determination from Grating Diffraction

The spectral analysis of grating allows, for static loading, the direct measurement of local strains at the surface of a body. This grating analysis is achieved by two ways (optical diffraction phenomenon or numerical Fourier transform) in order to determine at each step of load pitches and orientations of crossed grating. Our purpose is to extend this strain measurement method to investigate dynamic problems. The grating interrogation is performed using optical diffraction of a laser beam with an oblique incidence. In order to separate the diffracted beams during the dynamic event, we associate with each strain state a specific angle of the incident laser beam. This procedure allows to record 23 strain states at a maximum frequency equal to 1 MHz. The diffracted spots can be stored by two ways (film and CCD camera) and their analysis gives a strain sensitivity of 2.10−4.