Digital Photoelasticity Research Articles

Adaptive Quality Guided Phase Unwrapping Algorithm for Whole‐Field Digital Photoelastic Parameter Estimation of Complex Models

Abstract: With advancements in digital image processing and data acquisition, a separate branch of photoelasticity namely digital photoelasticity came into existence. Here, intensity information of the acquired image is used for the evaluation of whole‐field photoelastic parameters. Digital photoelasticity provides only wrapped phasemaps of isoclinics and isochromatics and they have to be unwrapped in different ways for getting the continuous‐phase values. In the case of the isochromatic phasemap, ambiguity removal prior to unwrapping is essential. In this paper, a 10‐step phase‐shifting methodology is proposed and a new strategy for obtaining the isochromatic phasemap free of ambiguity is demonstrated. Isoclinic unwrapping is performed by a new adaptive quality guided algorithm. Adaptive in the sense that isoclinic phase unwrapping is done autonomously even in the presence of isotropic points/π jumps occurring in the isoclinic phasemap. The isochromatic phasemap is also unwrapped using the quality guided path follower. The methodology is validated for the problem of a ring under diametral compression and later shown for three other models which have complex stress fields. Wherever possible, the parameters obtained by the new methodology are compared with analytical or numerical methods and the comparison is quite good.

Determination of the stress intensity factors due to corrosion cracking in ferroconcrete by digital image processing reflection photoelasticity

Nucleation of corrosion cracking can be detected and analyzed by digital image processing reflection photoelasticity by which the process mechanisms of crack extensions due to corrosion are quantitatively estimated. This study examines the distribution of expansion stress measured in initial cracking and partial cracking stages. Based on optical linear elastic fracture mechanics, the relation between the stress intensity factors and increment extensions are generated in different corrosion times. The accuracy of the method is demonstrated by comparisons of the predictions, the experimental predictions, and the numerical results.

Study of shear transfer in Al/epoxy joint by digital photoelasticity

An improved six-step phase-shifting method is proposed for calculating full-field shear stress based on a four-step color phase-shifting method in digital photoelasticity. The method was verified using a disk under diametral compression and then applied to an aluminum alloy/epoxy joint for studying the shear transfer behavior. Experimental results revealed that the isochromatic fringe order and shear stress at the bonding interface are distributed continuously and increased with compression. In particular, an antisymmetric thermal residual shear stress appears at the bonding interface, because of the difference in the thermal expansion coefficients of Al and the resin. This indicates that the thermal residual shear stress at the bonding interface is self-balanced and reaches a peak at the edges of the bonding interface. The load transfer is realized by the shear band from the bonding interface to the bottom support. Basically, the bonding interfacial shear stress is balanced with the load.

A Study of Stress Analysis for a Residual Stress Model by Digital Photoelasticity

The stress analysis for a model with initial stresses, which we term a residual stress model, is performed by digital photoelasticity. The stresses applied on the residual stress model are obtained by analyzing both the initial stresses and the resultant stresses. The method used for analyzing the stresses applies the principle of superposition of the stress to photoelasticity, which is a well-known technique in the field of elasticity. In the digital photoelasticity technique used, the principal stress direction and the relative phase retardation  are analyzed by photoelastic techniques using linearly polarized light. This technique overcomes the phase difference error associated with a quarter-wave plate by employing incident light at three different wavelengths, and using an unwrapping technique that allows and  to be determined using the arctangent function. A residual stress model produced by a disk containing frozen stresses that was subjected to a diametral compressive load at an angle of 31 was used to experimentally test this method. The values of the stresses of the loaded disk model analyzed were in good agreement with corre- sponding theoretical values at all locations far from the loading points of the residual stress model.

An adaptive scanning scheme for effective whole field stress separation in digital photoelasticity

In photoelasticity, the method of obtaining the individual values of principal stresses/normal stresses separately is referred to as stress separation. Shear difference method is one of the widely used techniques for stress separation in digital photoelasticity. Normally a simple raster scanning approach is used in shear difference method in which stress separation is carried out for all the lines within the model domain by either row-wise horizontally or column-wise vertically starting from the boundary pixels. This requires the presence of a free boundary to start the integration scheme for every row of interest, which is not always possible in most of the practical problems. In order to overcome this, in this paper, an adaptive scanning scheme is proposed so that stress separation can be carried out even if there is only one free boundary pixel available in the model. The new scanning scheme is validated using the theoretically generated data for the problem of a ring subjected to internal pressure. Later, the applicability of this scheme is demonstrated by using two other example problems.

Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods

An experimental method is given for determination of three-dimensional axial stress distribution in polarization-maintaining optical fibers. The method relies on using phase-shifting digital photoelasticity for gathering several integrated retardation maps for multiple angular position of object and using them as input data for tomographic procedure. The experimental data obtained for panda-type fiber show the regions of high stress in the core and stress member areas of the fiber cladding. The obtained results are in good agreement with the theoretical values known from literature. Also measurement of refractive index distribution in the fiber was done by means of microinterferometric tomography. Interesting correlation between the stress and refractive index distributions is shown and explained.

Assessment of autonomous phase unwrapping of isochromatic phase maps in digital photoelasticity

Photoelasticity is the only whole-field experimental technique which can analyse both 2-D and 3-D elasticity problems. In digital photoelasticity one gets two phase maps, one corresponding to principal stress direction (isoclinic) and the other corresponding to principal stress difference (isochromatic). The phase maps for both isoclinics and isochromatics are to be unwrapped differently for obtaining continuous phase values. Autonomous phase unwrapping is one of the challenging issues and this paper focuses on recent advances on isochromatic phase map unwrapping. A comparative study of different autonomous phase unwrapping algorithm is done by solving a bench mark problem and a stress frozen slice with cut-outs. The need for domain delimiting in addition to domain masking is brought out while using autonomous phase unwrapping algorithms.

Full-Field Isoclinic Evaluation in Digital Phase-Shifting Photoelasticity Applied to C-Shaped Model

The full-filed evaluation of the isoclinic parameter in digital photoelasticity is presented. The proposed method is based on the four-step color phase shifting technique and the phase unwrapping (PU) algorithm. It is experimentally applied to an eccentrically loaded split ring (C-shaped model). Experimental results show that the isoclinic-angle map obtained is almost free from the influence of the isochromatic parameter and the isoclinic values lie in the physical range, −π/2 to +π/2, regardless of the presence of the isotropic point or region.

Whole field evaluation of stress components in digital photoelasticity—Issues, implementation and application

In photoelasticity, the method of obtaining the individual values of principal stresses/normal stresses separately is referred to as stress separation. Shear difference is one of the widely used techniques for stress separation in photoelasticity and one needs the value of fringe order and the isoclinic angle free of noise at every pixel over the domain. For accurate parameter determination, a ten-step phase shifting approach which uses a plane polariscope for isoclinic determination and a circular polariscope for isochromatic determination is proposed. A new quality guided approach for isoclinic unwrapping is developed. Isochromatic phasemap free of ambiguous zones is obtained by a new methodology and is unwrapped by a quality-guided approach. Whole field evaluation of stress components and its representation is then presented. The models used in this study are intentionally subjected to moderate loads showing a high level of isochromatic–isoclinic interaction. In view of this, the isoclinic data has several kinks which is found to cause streak formation in the whole field representation of separated stress components. An outlier smoothing algorithm is proposed for getting a smooth variation of the digital photoelastic parameters over the domain. Use of such smoothed data for stress separation has removed the streaks and has also greatly improved the accuracy of the separated stress components.

Plotting of Isoclinic Phasemap from Finite Element Results and its Use in Digital Photoelasticity

Digital photoelasticity is an experimental method for determining stresses in 2D and 3D models. In digital photoelasticity one gets a wrapped isoclinic phasemap. The main issue with wrapped isoclinic phasemaps is that the isoclinic values obtained do not uniformly represent the principal stress direction of one of the principal stresses consistently over the entire domain. These zones are labelled as inconsistent zones. Such zones need to be identified and corrected to get unwrapped values of continuous isoclinic phase values. In this paper, a method is developed to plot the simulated wrapped and unwrapped isoclinic phasemap from 2D Finite Element (FE) results so that one can use this as a convenient tool for identification and correction of inconsistent zones in isoclinic phasemaps obtained experimentally for complex problems. The method is explained by using the problem of a circular disc under diametral compression. The application of this method for handling complex problems is demonstrated by solving the cantilever bending of a binocular specimen.

On Phase‐Shifting Integrated Photoelasticity

Abstract: The development of phase‐shifting photoelasticity of plane specimens began 21 years ago. Meanwhile, the method was also applied to bodies with three‐dimensional stresses, where the secondary principal stresses and their directions generally vary along the path of a probing light beam. In the theory of integrated photoelasticity, a three‐dimensional body is represented by an equivalent model with three characteristic parameters, which are the characteristic retardation or phase, and the primary and secondary characteristic directions. Results are commonly tested in plainly stressed specimens at oblique incidence or in a cylindrical body composed of three discs under diametral compression, where the load axes vary from disc to disc. In this study, I verify the applicability of some polariscope arrangements in integrated photoelasticity by means of a bent‐beam specimen which exhibits rotating principal directions along the light path. This device enables continuous variation of the stress field. Furthermore, an approximate analytical solution of the characteristic parameters is available. The following three major arrangements of optical elements were investigated: (i) linear polariscope in white light; (ii) linear polariscope in monochromatic light; and (iii) circular polariscope in monochromatic light in the dark‐ and bright‐field arrangement as well as in the half‐tone or grey‐field arrangement. Results are discussed and compared with the literature of two‐ and three‐dimensional digital photoelasticity.

Expansion stress analysis of ferroconcrete corrosion by digital reflection photoelasticity

This study used digital photoelastic birefringent coatings, to measure the expansion stress of a steel bar boundary with concrete caused by corrosion. The distribution of expansion stresses were measured in the initial cracking and partial cracking stages. A numerical model was used to estimate and compare the expansion stress generated by the steel bar during different corrosion and crack stages. The feasibility of applying digital image processing photoelasticity to long-term monitoring and measurement of steel bar corrosion and expansion stress was verified by the consistent results obtained.

A New Six-Step Phase Shifting Technique Using Mixed-Polariscope in Digital Photoelasticity

Photoelasticity is one of the most widely used techniques for experimental stress and strain analysis. With the availability of low cost digital image processing systems, a separate branch of photoelasticity known as digital photoelasticity came into existence providing whole-field values of the isoclinics (θ) and isochromatics (N) in a true sense. Among the several methods available for data acquisition, phase shifting / polarization stepping techniques are most widely used for their simplicity and accuracy. In this paper a new digital photoelastic method based on phase shifting using monochromatic light source is presented. It provides full field values of θ and N. The arrangement is carefully chosen with the intention of reducing the influence of quarter wave mismatch error in the evaluation of θ and N. The methodology is validated for the benchmark problem of a disk under diametral compression.

High Frequency Quantitative Photoelasticity Applied to Jet Engine Components

For sometime, reflection photoelasticity has been used in a qualitative manner as an aid to the placement of strain gauges in vibration tests on turbine and compressor blades. Often, the motivation for such tests is the validation of numerical models used in life-time predictions. Strain gauges supply data at a small number of discrete points, whereas the photoelastic fringe patterns provide information over the whole field of view. Digital photoelasticity based on phase-shifting allows these fringe patterns to be processed into maps of surface strain data that can be used to verify the computational results. Digital photoelasticity has been developed over the last two decades utilising spectral or phase approaches sometimes combined with Fourier analysis; and in most reported applications only idealised case studies are considered. Recently, the application of digital photoelasticity in high frequency blade tests has been developed as a robust methodology that can be applied using standard equipment or using solid-state polariscopes. The paper includes descriptions of the methodology and exemplar results to demonstrate the efficacy of this advanced application of photoelasticity for full-field validations of numerical modelling.

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).

A novel approach for ambiguity removal in isochromatic phasemap in digital photoelasticity

Phasemaps obtained by phase shifting techniques in digital photoelasticity contain ambiguous zones. To obtain total fringe order by phase unwrapping, the phasemap should be free of ambiguous zones. A new method is developed, which uses a dark field image for ambiguous zone identification and its correction. This methodology is explained and validated by solving a benchmark problem. As ambiguous zones are of arbitrary shape, an advanced boundary extraction method developed in-house is used for effecting the correction in practical problems. The performance of the new methodology is demonstrated by using the problem of a ring under diametral compression and a slice cut from a stress frozen model.

Phase shifting photoelasticity in white light

The availability of image acquisition systems has led to the development of digital photoelasticity both in monochromatic and white light. In particular white light has been used mainly with the following methods: Spectral Content Analysis, RGB photoelasticity and phase shifting photoelasticity. Phase shifting photoelasticity in the colour domain has been used effectively for the determination of the isoclinic parameter in order to reduce the influence of the isochromatic fringes. The method has been also proposed for the determination of the isochromatic fringe order. This paper concerns the general characteristics of phase shifting photoelasticity in the colour domain. Special attention is drawn towards the influence of spectral content of the light source, the spectral response of the colour camera filters, the dispersion of the birefringence and the error of quarter wave plates.

On the Calibration of Optical Full-Field Strain Measurement Systems

There are no standard reference materials suitable for the calibration of full-field optical strain measurement systems. This is hindering the uptake of the technology by industrial end-users since optical metrology instrumentation and procedures cannot be easily integrated into quality assurance systems. The EU-funded SPOTS project is developing a physical reference material (PRM) and measurement protocol that should provide the basis of a calibration standard for establishing the traceability of strain values obtained with optical devices. This paper describes a PRM based on a parametric design of monolithic four-point bend test that can reliably generate a known strain field over a range of specimen sizes. Measurements acquired from strain gauges and LVDTs compared well with data obtained from ESPI, digital image correlation, photoelasticity and thermoelasticity studies, demonstrating excellent repeatability and inter-laboratory reproducibility.

Comparative Study of Evaluation of Primary Isoclinic Data by Various Spatial Domain Methods in Digital Photoelasticity

With the advent of PC-based digital image processing systems, automation of parameter estimation based on intensity processing from the entire field has now become simpler. Various methods for obtaining the isoclinic parameter using plane, circular, and mixed polariscopes have been reported in the literature. A comparative study has been conducted on the performance of these methods both qualitatively and quantitatively. The focus of the study is on how these algorithms provide the basic isoclinic data. To illustrate the performance, theoretically simulated and experimentally recorded images for a ring under diametral compression is used. The role of background light intensity and quarter-wave plate mismatch on the experimental evaluation of isoclinic data is brought out.

On the effects of a crack propagating toward the interface of a bimaterial system

This paper deals with the influence of matrix cracks on the failure mode of bimaterial systems and composite materials. In order to investigate such an influence, the stress field near a crack embedded into the more yielding material and propagating perpendicularly to the interface, has been analyzed by using systematic numerical simulations. Such analysis has shown that the crack propagation give rises to transversal stresses that can damage the reinforcing materials when this has low modulus, as glass fibers, or low transversal strength, such as carbon fibers. Moreover, the longitudinal stress concentration can damage the reinforcing material only if this has high stiffness, as in the case of aramid and carbon fibers. Also, the numerical results have permitted to implement simple formulas that allows the user an accurate evaluation of the SIF as well as to predict possible debonding or fiber splitting phenomena. Finally, the SIFs evaluated numerically have been corroborated by experimental tests carried out by using an efficient procedure based on RGB digital photoelasticity.