Photoelastic Problem Research Articles

Isochromatic photoelastic phase map unwrapping: temporal versus spatial approach

A comparison of temporal and spatial unwrapping on a photoelastic isochromatic phase map is discussed. The analytical results show that the two-dimensional Macy’s spatial unwrapping can yield a quite good retrieval if an inconsistency-free isochromatic map is to be treated as is true in most of the photoelastic problem cases. While only temporal wrapped data are provided for the phase retrieving work, the success strongly depends on providing the correct changing ratio between the two (or more) temporal states, (e.g., percentage variation of load or wavelength step). The simulation of an incorrect ratio of the temporal isochromatic work on the accuracy of the retrieving work is performed. Experimental results show that temporal unwrapping error is more easily occurs near a highly stressed zone.

Reconstruction of structural damage based on reflection intensity spectra of fiber Bragg gratings

We present an approach for structural damage reconstruction based on the reflection intensity spectra of fiber Bragg gratings (FBGs). Our approach incorporates the finite element method, transfer matrix (T-matrix), and genetic algorithm to solve the inverse photo-elastic problem of damage reconstruction, i.e. to identify the location, size, and shape of a defect. By introducing a parameterized characterization of the damage information, the inverse photo-elastic problem is reduced to an optimization problem, and a relevant computational scheme was developed. The scheme iteratively searches for the solution to the corresponding direct photo-elastic problem until the simulated and measured (or target) reflection intensity spectra of the FBGs near the defect coincide within a prescribed error. Proof-of-concept validations of our approach were performed numerically and experimentally using both holed and cracked plate samples as typical cases of plane-stress problems. The damage identifiability was simulated by changing the deployment of the FBG sensors, including the total number of sensors and their distance to the defect. Both the numerical and experimental results demonstrate that our approach is effective and promising. It provides us with a photo-elastic method for developing a remote, automatic damage-imaging technique that substantially improves damage identification for structural health monitoring.

Stress field tomography based on 3D photoelasticity

A tomographic method for identification of stress fields based on 3D photoelasticity has been developed. A second order tensor field tomographic method based on the general inverse problem of 3D photoelasticity, previously developed by the authors, is found to be highly sensitive to errors in photoelastic observations. In this study a new tomographic method for stress field with fairly high robustness to errors in photoelastic observations has been developed by introducing both equilibrium condition and linear elasticity to the previously developed general tensor field tomographic method. This new stress field tomographic method expands unknown 3D stress distributions as a linear combination of independent set of basis functions and a new inverse problem is posed: identify the amplitudes of basis functions based on photoelastic observations. Just as the inverse problem of 3D photoelasticity, this newly posed inverse problem is also nonlinear and ill posed. Unlike conventional approaches to 3D photoelasticity, both these nonlinearity and ill-posedness are properly treated using a load incremental approach. Load incremental approach chops the nonlinear solution space into segments with unique solutions by conducting photoelastic observations at sufficiently small increments in external load. Validating both numerically and experimentally, it is shown that this new stress field tomographic method has sufficient robustness against errors in photoelastic observations and is applicable to experimental stress measurements.

Inverse problem of photoelastic fringe mapping using neural networks

This paper presents an enhanced technique for inverse analysis of photoelastic fringes using neural networks to determine the applied load. The technique may be useful in whole-field analysis of photoelastic images obtained due to external loading, which may find application in a variety of specialized areas including robotics and biomedical engineering. The presented technique is easy to implement, does not require much computation and can cope well within slight experimental variations. The technique requires image acquisition, filtering and data extraction, which is then fed to the neural network to provide load as output. This technique can be efficiently implemented for determining the applied load in applications where repeated loading is one of the main considerations. The results presented in this paper demonstrate the novelty of this technique to solve the inverse problem from direct image data. It has been shown that the presented technique offers better result for the inverse photoelastic problems than previously published works.

Load Extraction from Photoelastic Images Using Neural Networks

Photoelastic materials develop colored fringes under white light when subjected to mechanical stresses, which can be viewed through a polariscope. This technique has traditionally been used for stress analysis of loaded components, however, this can also be potentially used in sensing applications where the requirement may be measurement of the stimulating forces causing the generation of fringes. This leads to inverse photoelastic problem where the developed image can be analyzed for the input forces. However, there could be infinite number of possible solutions which cannot be determined by conventional techniques. This paper presents neural networks based approach to solve this problem. Experiments conducted to prove the principle have been verified with theoretical results and finite element analysis of loaded specimens. The developed technique, if generalized, can be implemented for whole-field analysis of the stress patterns involving complex fringes under different loading conditions. This can also provide direct visualization of the stress field, which may find application in a variety of specialized areas including biomedical engineering and robotics.

Use of Mueller matrices in the photoelastic determination of the stress distribution in a model for a solid propellant rocket grain

We introduce some basic optical rules dealing with Mueller matrices as phenomenological descriptors of optical devices. Specific simple examples illustrate how all the Stokes parameters of a beam passing through a system of several devices can be determined by the multiplication of the individual Mueller matrices of the respective system components and the Stokes vector of the incident beam. Two resulting families of interference fringes in the (visible) emerging field of the de- vices considered are separated from each other by the introduction of suitable additional system components. The ''isochromatic'' family of fringes can thus be isolated from the ''isoclinic'' family, and a natural application to photoelastic problems becomes evident. Thus, a second purpose is to use this technique and these fringes to photoelastically determine the stress distribution in a disk with a square perforation, when the disk is subjected to a uniformly distributed pressure, acting at its outside or at its inside periphery. This enables the visualization and quantification of the stresses developed during the burning of the grain. The size of the square hole and the radii of the fillets at the corners of the square are variables of the study. Results are given as stress concen- tration factors, in dimensionless form, and are of use to the designer of solid propellant rocket grains. An analogy is given to suggest another application at longer wavelengths to calibrate or discriminate between some radar signals in the microwave region. © 2003 Society of Photo-Optical

Tensor field tomography based on 3D photoelasticity

A new method for non-destructive measurement of arbitrary 3D stress state using photoelasticity has been developed. The new approach, namely, load incremental approach, is an attempt to solve the non-linear inverse problem of 3D photoelasticity by considering change in stress state for a load increment and linearizing the non-linear governing equation. As long as the applied load increment is small and photoelastic images are taken with high resolution in load increment, this method works and can reconstruct arbitrary 3D stress state. Numerical simulations clarify the effect of (i) the material sensitivity, (ii) the number of the observations and (iii) the constraint on the observation directions on the performance of the proposed method. These results provide the fundamental data for designing the experimental setup for 3D photoelasticity.

光弾性を用いた三次元応力場計測のための逆解析手法の開発

A new method for non-destructive measurement of arbitrary 3D stress state using photoelasticity has been developed. The new approach proposed here, namely, load incremental approach, is an attempt to solve the nonlinear inverse problem of 3D photoelasticity by the linearization of the governing equation based on high resolution in load increment. As long as the applied load increment is small enough, this method works and can reconstruct arbitrary 3D stress state.Results from numerical simulations show the effect of i) the number of the observations, ii) the independency of the observation directions, and iii) the material sensitivity on the performance of the proposed method.

Experimental comparison of solution methods for the axisymmetric photoelastic problem

A method of component separation in axisymmetric photoelastic problems based on the use of the compatibility condition is experimentally tested against the more common methods of oblique incidence and subslicing. The results show the method to be comparable in accuracy, but to have the distinct advantage of not requiring additional measurements other than those in the meridional plane.

Closed-Form Inversion of the Axisymmetric Integrated Photoelasticity Equations

The purpose of the present Note is to show how the general axisymmetric photoelastic problem can be solved using only the integrated data. Indeed, the axisymmetric problem is reduced to a quasi-plane problem in that only a fringe photograph plus a plot of the family of isoclinics is sufficient to yield a complete solution. The formulation includes the treatment of thermoelastic and residual stress problems.

Simplification of the axisymmetric photoelastic problem

The axisymmetric photoelastic problem is reformulated in such a way that data taken from only the meridional plane is sufficient to obtain a solution.

Numerical evaluation of photoelastic data from discontinuous models

Equations are developed which allow the solution to the photoelastic problem of obtaining the boundary loads causing the internal stress pattern on a block of material when the isoclinics and isochromatics from within the block are known. The method uses the well known line integral theory and Flamant's solution for the stress distribution in a semi-infinite plane due to a point load. The problem is solved without having to start at a boundary of known loading, which is the approach generally used in evaluating photoelastic data. This new method offers great facility and reliability when examining discontinuous models, such as rock or soil systems. Data which have been obtained from carefully controlled experiments on blocks of various sizes are analysed by a numerical method using the developed equations. The calculated boundary loads are then compared with the average applied boundary loads, which are imposed by contact. It is found that the distributions of the applied loads on the boundary are affected by local stress concentrations. In general, the average values agree well with the computed boundary loads, except, however, for the case of applied boundary shear. After examining the relatively large single blocks, some typical results of boundary loads on specific blocks within blocky models are examined. Here the results of the numerical method described in this paper are compared with results obtained from the shear difference method.

Effects of stress-induced optical activity in photoelasticity

In this paper, photoelastic problems involving optical activity are analysed using Stokes parameters. A set of differential equations equivalent to the Maxwell-Neumann equations is derived which yields results with greater ease than other currently available methods. A few specific problems are solved by using these equations. A brief discussion on the use of scattered light methods in problems with optical activity is also included.

A solution of the photoelastic problem by photometry

A solution of the photoelastic problem by photometry

Determination of small dilatations and surface stress by birefringence measurements

Birefringence induced in a suitably oriented transparent optically isotropic body by a zone which has undergone a dilatation is used to determine the local dilatation in that zone from a solution of the photoelastic problem. Dilatations < 10 10−6 have been determined, a sensitivity of measurement greater than in conventional interferometry, using specimens of modest optical specification. Local dilatations have been determined in transparent zones 0.2 mm or more in thickness. Mean dilatations have been determined in opaque layers or in zones too thin to observe (some < 1 μm thick) from birefringence in the unaffected zone. Problems which arise in the measurements are discussed. Applications are described. Instrumentation and automation techniques are given. It appears possible to extend sensitivity to measure dilatations < 10 −7, which would be the equivalent of determining the effect of inserting a sheet of molecular dimensions.

The preparation and use of a stress-sensitive material in multi-layer photoelastic models

There are many applications for a stress-sensitive material in research and teaching when considering photoelastic problems. The particular material selected by the authors is a polyurethane rubber sold under the trade name ‘Solithane’. Engineers reading existing technical publications might feel that Solithane is too difficult and too expensive to use as a research tool. The authors hope to show in this article that, for very little cost, and with a modicum of care, it can be prepared and used in the most modest space. The basic composition and preparation of the final rubber under laboratory conditions are described including practical aspects of model preparation. A range of rubbers of differing elasticity were prepared, their properties tested, and the results of these tests are given. It is suggested how and why this material should lend itself to the construction of multi-layer models with particular reference to geological and mining problems. Photographs are included of apparatus used, and of problems being investigated.

Intensity Method for Stress-Optical Measurements

The formalisms of the Mueller calculus and the Poincaré sphere are applied to the photoelastic problem and a general intensity method for measurement of stress-optical constants is derived. This general method overcomes certain limitations of some of the existing methods and hence is about ten times more sensitive. The power of the new method is indicated by utilizing the frozen stress in a specimen for dispersion measurements without externally stressing it. We have measured the stress-optical dispersion of fused silica and calcium fluoride by this technique, over the range from 250 to 580 mμ.

Closure to “Discussions of ‘Further Work on the General Three-Dimensional Photoelastic Problem’” (1956, ASME J. Appl. Mech., 23, pp. 134–135)

Closure to “Discussions of ‘Further Work on the General Three-Dimensional Photoelastic Problem’” (1956, ASME J. Appl. Mech., 23, pp. 134–135)

Further Work on the General Three-Dimensional Photoelastic Problem

Abstract It is known that purely photoelastic procedures cannot solve the general three-dimensional stress problem. Photoelasticity furnishes data from which only the principal shears can be determined, but not the principal stresses. A new, general, and practical method of solution which has been described previously (1, 2) is reviewed briefly, and possible variations in procedure are discussed. This method combines the photoelastic data from frozen stress patterns with a numerical integration of one of the differential equations of equilibrium in Cartesian coordinates. The actual principal stresses at each point of a homogeneous and isotropic body of arbitrary shape subjected to a general system of loads are thereby determined. The method has been applied previously to a sphere subjected to diametral compressive loads of 172 lb. The present paper contains the results from a second sphere subjected to 79.6 lb which show that the degree of reproducibility of results is high. Very good agreement is also shown to exist with a theoretical solution of the same problem by Sternberg and Rosenthal (3) The paper also contains the solution of a short rectangular parallelepiped loaded through a small flat circular die. The investigation was conducted in the Photoelastic Laboratory of the Mechanics Department of Illinois Institute of Technology.

Three-Dimensional Photoelasticity

The classical Sommerfeld-Runge method for deriving the laws of geometric optics in isotropic inhomogeneous media from Maxwell's equations is applied to problems in ``weakly'' anisotropic and inhomogeneous media. This leads to a generalized Hamilton-Jacobi partial differential equation for the phases of the two waves (eikonals) which can propagate with finite velocity in such a medium. If one restricts oneself to a limited class of stress distributions, one derives a very powerful method of solving axially and spherically symmetric problems which would be very difficult to treat by the direct solution of the classical equations of elasticity. The Maxwell-Neumann law is derived in variational form so that, in principle, one can estimate in any given case the error involved in the conventional assumption that the paths are straight lines instead of the actual Fermat paths. The last section treats the so-called general problem of photoelasticity in which the principal stress directions in the plane of the wave front rotate arbitrarily as the latter propagates through the medium. Again the Sommerfeld-Runge method gives one a solution which claims that if the rate of rotation is small in a wavelength one can ignore the contributions of the rotation to the integrated phase. An experiment is proposed to check this claim.