Identification of isochromatic fringes

In simple cases of static-photoelastic analysis, the numbering of the isochromatic fringes does not present unusual difficulties. In more complex cases, in particular wave propagation, the problem may be so difficult that few investigators attempt the analysis. In this paper guidelines to number the isochromatic fringes are presented. Advantage is taken of some topological properties as well as of the time and space derivatives of these isochromatic fringes. Several examples are discussed to illustrate the use of the guidelines. It is observed that under most conditions the guidelines are sufficient to number the whole field of isochromatics on photographs taken with the commonly used monochromatic light.     

Improving fringe definition by pseudo-solarization

A method is described for obtaining well-defined fringes as well as fractional fringes in photoelastic stress analysis. It is based on an edge effect which occurs during the pseudo-solarization of films during development. Sharp fractional fringes are obtained throughout the field of the model with a high degree of accuracy. The technique can be used with all types of polariscopes.     

Application of numerical and optical evaluation schemes for particle image velocimetry

Application of particle image velocimetry (PIV) techniques for measurement of fluid velocities typically requires two steps. The first of these is the photography step in which one or more exposures of a particle field are taken. The second step is the evaluation of the particle pattern and production of appropriate velocities. Each of these steps involves optimization which is usually specific to the experiment being conducted and there is significant interaction between photographic parameters and evaluation characteristics.Among the various evaluation techniques suggested for analysis of PIV images is the evaluation of the scattered interference pattern (Young's fringes) by numerical Fourier transform. An alternative to the numerical calculation of the Fourier transform of the Young's fringes has been suggested, using a modified liquid crystal television as an optical correlator to allow the transform to be performed optically. Both transform techniques are affected by the quality of the input function, specifically the Young's fringes.This paper will compare the performance of optical and numerical Fourier transform analysis of Young's fringes using speckle images. The repeatability and an estimate of the accuracy of the particle displacement will be shown for each method. A brief examination of the effects of small particle number density of PIV evaluation will also be presented. Finally, for a small part of an actual unsteady flow, the optical and numerical Fourier transform analysis methods will be compared.     

Nano-moire method

Nano-moiré method presented in this paper is an experimental technique which allows direct measurement of nanoscopic mechanical parameters, such as displacement, strain and dislocation distribution. The basic idea is the formation of moiré fringes when a HREM (high resolution electron microscopy) image of crystal material is superimposed with a unidirectional grating. Fourier filtering technique is used to increase the contrast of fringes and to multiple the fringes. This method has atom-size sensitivity and spatial resolution, and relatively large range. It provides a new experimental technique with very high sensitivity and spatial resolution for nanomechanics. The project supported by the National Natural Science Foundation of China     

Full-field surface-strain and displacement analysis of three-dimensional objects by speckle interferometry

A method of full-field measurement of displacements as well as strain on arbitrarily curved surfaces is introduced. The speckle effect of coherent light is utilized to produce fringes due to displacements. Unlike the fringes produced by holographic interferometry, these fringes have a unique interpretation in relating to displacements and they localize on the surface. Three measurements are required to determine the three components of displacement; and, knowing the geometry of the object, its surface strains can be deduced. Three ways of recording displacement fringes, namely, real time, double exposure and superposition, are described.     

微型计算机对全息位移与应变分析的冲击

本文的中心是微型计算机与图象处理机在全息干涉法的位移与应变分析中的作用。首先将考虑数据采集问题,即如何将条纹图转变为计算机中的数据,在这一部分将讨论从图形数据化到固态电视摄象机等一系列问题。然后考虑成像区域物点的正确辨别问题以及成像区域与对应的有限元分析的网格点之间转换问题。此后,将考虑对条纹插值,算出网格点位置的应变或位移的问题。最后,将给出由全息分析的数据得出位移或应变值的数学公式。     

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.     

MOIRÉ INTERFEROMETRY WITH ENHANCED RESOLUTION

The implementation of this method is relatively simple. It does not require any modification to interferometric systems already in use. It can be used in the analysis of large as well as very small fields, including measurements under a microscope.
A fringe pattern with a carrier is recorded in a single exposure, just as in the standard procedure. As a consequence, any possible instability of the interferometer does not affect the accuracy of the measurements. Further, the spatial resolution of the measurements is not compromised.
Since only one exposure is needed for a given displacement component this method can be applied to dynamic as well as static measurements.
It should be emphasized that even though the number of electronically generated fringes can be arbitrary, the sensitivity is the same as in ordinary moire interferometry as long as the data are taken at the lines of minimum intensity. The improvement is in the increase of the number of data points taken at the locations of maximum resolution. In other words, all the data are taken at the maximum resolution.
This method applies not only to moire interferometry but to any experimental technique based on two-beam interference, as long as the fringe pattern has good contrast.     

Diffraction theory of optical interference moiré and a device for production of variable virtual reference gratings: A moiré microscope

Optical interference moiré methods are analyzed using Fraunhoffer diffraction theory to relate general large surface deformations to the fringes observed. This analysis determines the Almansl strain in the current configuration from the gradients of the fringe number function. The analysis shows the advantages of an experimental scheme that allows the virtual reference grating to be varied. The ability to vary the virtual reference grating results in a larger dynamic range and the ability to maintain a fringe spacing for maximum accuracy. A moiré microscope has been constructed which has this ability. Digital image processing coupled with optical filtering and phase control is used to enhance the accuracy of the fringe measurements. The variable virtual-reference-grating capability is demonstrated by using it to highlight several aspects of the deformation field near a crack tip in a single crystal of iron-silicon.     

Carrier fringe method of moiré interferometry for tiny strain measurements in micro-field

In this paper, we demonstrate a new optical method for tiny strain measurements based on the principle of carrier fringes of moire interferometry. A cross-line grating with frequency of 1200 lp/mm is replicated on the specimen surface, and the strain can be deduced from the changes in carrier fringes before and after the deformation of an object. Four coherent laser beams are used to obtain the carrier fringe patterns of field U and V. Both theoretical analysis and numerical simulation indicate that the ideal accuracy of strain can be controlled within a range of ±1με. Case study of a plane extension experiment shows that the measurement accuracy of strain can be controlled within the range of ±10με. The average strain values of every row of field U and every column of field V can be obtained by using this method, and approximated strain of every pixel in the whole-field can be further acquired, and thus it is possible to measure tiny strains occurred in a micro-field. The technology in this paper can provide comprehensive information for analyzing related mechanical content in the field of MEMS.     

Towards RGB photoelasticity: Full-field automated photoelasticity in white light

In this paper a new full-field method for the automatic analysis of isochromatic fringes in white light is presented. The method, named RGB photoelasticity, eliminates the typical drawbacks of the classical approach to photoelasticity in white light which requires a subjective analysis of colors and an experienced analyst to acquire and interpret the results. The proposed method makes it possible to determine retardations uniquely in the range of 0–3 fringe orders. For this purpose the isochromatics are acquired by means of a color video camera and the colors are decomposed in the three primary colors (red, green and blue) and compared to those stored in a calibration array in the system. Furthermore, the influence of various spurious effects on the accuracy of the proposed method is experimentally evaluated.     

Limitation of fourier transform photoelasticity: Influence of isoclinics

The application of the Fourier transform to photoelasticity was used in the evaluation of the retardation using a carrier system of fringes. In photoelasticity, the light intensity from the analyzer in a circular polariscope depends on both the retardation (isochromatics) and the isoclinic parameter. The theoretical analysis shows that the angle between the principal stresses in the model and in the carrier system of fringes influences the evaluation of the retardation (isochromatics), as occurs when misaligned compensators (namely, Babinet) are used. As a consequence, this method may not be applied as a full-field technique, although the error is small if the angle between the principal stresses in the model and in the carrier is less than 25 deg. Numerical simulations and experimental tests were conducted to corroborate this prediction.     

Photoelastic studies of ultrasonic waves in a large plate

This paper presents the results of a series of experiments which were conducted to study the feasibility of using the photoelastic method to observe ultrasonic waves in a large plate on quantitative basis. The frequency used was as high as 0.79 MHz. Due to inherent limitations of the power of the ultrasonic driving systems, very low fringe orders were produced. In order to analyze low-order fringes quantitatively, a dynamic compensating system was developed and used. The photoelastic fringes were recorded with the aid of the dynamic compensator by a still camera with a flashlight source synchronized with the oscillator pulses. The analysis of the photographic record was carried out with the aid of a microdensitometer. The photoelastic method is found to be feasible for observing ultrasonic waves in transparent media. The attenuation of stress waves was determined. The dynamic compensating system developed in this investigation was found to be satisfactory.     

Hyperstatic Method of Photoelasticity

A new hyperstatic method to measure nonlinear strains is introduced—using birefringent coating and reflection polariscope—to separate the principal strains from fringes and isoclinics—combines equilibrium consideration in shear difference method with compatibility consideration wherein the second order differential equation is converted into difference equation to separate the principal strains in elastoplastic range treating it as a statically indeterminate (hyperstatic) problem. An erratum to this article can be found at     

A fringe-compensation technique for stress analysis by reflection holographic interferometry

The use of holographic interferometry for stress analysis of nontransparent objects is limited by rigid-body displacements of the object. These displacements can alter the fringe patterns and often cause the fringes to disappear completely. A technique of compensation for this deterioration of the fringe pattern forreal-time holographic interferometry is described in this paper. It is especially designed to permit the accurate measurement of the out-of-plane component of strain near regions of stress concentration in plates that are subjected to in-plane loading. It is first shown that the fringes caused by a pure rigid-body displacement can be eliminated almost completely by translations of the hologram and rotation of the illumination wave. This procedure is first described when the displacement is known; then when it is unknown. A method to estimate the error made in the correction is presented. In actual stress-analysis problems, the object is both rigidly displaced and strained. Assuming the rigid displacement is known and corrected as previously, the analysis is developed to relate the fringe pattern to the strain-related displacement. This analysis takes into account the optical modifications of the system that are necessary to achieve the rigid-body-displacement correction. When the rigid-body displacement is unknown, the method is shown still to be workable through the use of various symmetries and boundary conditions. Two sample interferograms are presented as illustrations. Quantitative treatment of data from one of these are presented in a companion paper.     

Experimental and numerical study of a spiral structure at the periphery of an aspirated rotor–stator cavity

The purpose of this paper is to study the range of existence, the process of transition and the phase velocity of the spiral structure in an aspirated rotor–stator cavity. Experience shows that for a given flow rate and rotation, a whole range of azimuthal wave numbers are possible. Some are highly stable while others on the fringes of this range are subject to multiple transitions that depend on the fluctuations of the flow. Numerical simulation offers the advantage of enabling control over the wave number and the disturbance of the flow. Both approaches enable us to better understand the dynamics of this instability.     

Constructing pure digital secondary moiré patterns

A new method of constructing pure digital secondary moiré patterns of equal-strain fringes is proposed in this paper. By this method, a pure secondary moiré pattern, without trace of primary moiré fringes, is obtained directly from common digital moiré patterns regardless of how low or high the fringe density. The pure secondary moiré patterns eliminate the backnoise of primary fringes and give the strain value at every point over the whole strain field. This technique can significantly increase the measurement accuracy and the range of moiré techniques.Paper was presented at the 1988 Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Automatic order-determination of transient in-plane displacement moire patterns

This paper presents a fringe-carrier method that eliminates sign ambiguity of transient moire fringes which can be used to automatically determine the relative orders. A fringe carrier is preset in the static state of the specimen and the dynamic in-plane displacements are recorded as the modulation to the frequency of the carrier fringes when the specimen is loaded by impact. According to a modulating criterion developed from the modulation degree, the fringes of the transient moire patterns keep monotonical in orders so that they can be automatically encoded in grey levels by a digital image system. The moire orders purely caused by dynamic loadings are evaluated by subtracting the grey-value of the unmodulated carrier image from that of the modulated carrier images encoded by their orders. With the subtracted moire orders the strain components can be obtained, and, correspondingly, the histograms of dynamic displacement moire images are shown with order variation by image-difference. The project supported by Alexander von Humboldt Foundation of Germany and the National Natural Science Foundation of China     

Experiment and modelling of birefringent flows using commercial CFD code

It is well-known that certain fluids are birefringent and when flows are viewed in polarised light interference fringes are observed. The fringes are caused by a phase shift in the light passing through the fluid and are proportional to the integral of the maximum shear strains in the fluid. In order to understand what is happening within the three dimensional flow and overcome the difficulties due to this integration, additional computational or experimental information is needed.

In this work, a commercially available computer code (Fluent) is used for the first time to model the flows. The flow data are then exported to a spreadsheet where the shear rates are integrated across the field and then banded for graphical output. The results from this are then compared to results generated from birefringent flow experiments and the agreement is found to be good since the modelled fringes show the same patterns as those in the experiment. This novel use of computational and experimental techniques together will allow quantitative analysis of three-dimensional flows in the future.

Currently, there are still a lot of empirical variables involved in fitting the computational fringes to the experiment, but the results of this preliminary study show that this is a promising approach to this type of problem.