Digital Photoelasticity Research Articles

A CAE approach for the stress analysis of gear models by 3D digital photoelasticity

The use of numerical and experimental methods to determine the stress field of mechanical components is well known. In particular, 3D photoelasticity can be considered the only experimental technique for the complete stress state evaluation of 3D components. The advent of rapid prototyping techniques has allowed the manufacturing of complex models in a matter of hours by using birifrangent materials. The present paper is focused on the description of a Computer Aided Engineering (CAE) approach which combines Finite Element (FE) simulations and automatic photoelastic investigations for the stress analysis of face gear drives, made by stereolithography. Computer Aided Design (CAD) geometries, used to manufacture the stereolithographic models, are directly used to perform FE analyses, thus allowing the stress analysis process to become simpler and easier. The substantial agreement observed between experimental and numerical results proved the potentialities of the adopted approach and the usefulness of FE simulations to optimize photoelastic analyses through cost- and time-effective experiments even for complex 3D shapes.

Flexural effects of sandwich beam with core junctions under in-plane bending

An improved six-step phase shifting method in digital photoelasticity was applied to calculate the full-field shear stress of cores in sandwich beam under in-plane bending. The load transfer and local stress concentration at the core junctions were investigated. The load transfer was realized by shear bands which connect the top and bottom sheet faces through adhesively bonded interfaces in the sandwich beam. The shear stress on both sides of the core junctions distributed continuously under pure bending, but distributed discontinuously and antisymmetrically under three-point bending. Different to the case under pure bending, the apparent shear stress concentrations existed on the core junction lines under three-point bending and maximized at the three-phase joints.

A simple approach to photoelastic calibration of glass using digital photoelasticity

Quantification of residual stresses in glass articles necessitates the knowledge of photoelastic constant of the glass material. The recent developments in digital photoelasticity have increased its applicability in residual stress analysis of glass. In this paper, photoelastic calibration of the glass material has been performed using the carrier fringe method (CFM) and phase shifting technique (PST) in digital photoelasticity. The retardations measured by both of these techniques are used for the calculation of photoelastic constant of the glass material and they were found to be in good agreement with each other. Calibration of glass by CFM is recommended for industrial applications since it requires only a few images as compared to PST.

Separation of Isochromatics and Isoclinics Phasemaps for the Photoelastic Technique with use Phase Shifting and a Large Number of High Precision Images

Abstract Digital photoelasticity is an important optical metrology follow-up for stress and strain analysis using full-field digital photographic images. Advances in digital image processing, data acquisition, procedures for pattern recognition and storage capacity enable the use of the computer-aided technique in automation and facilitate improvement of the digital photoelastic technique. The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phaseshifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate a larger sequence of images. Each image represents a pattern and a measurement of the stresses present in the object. A decrease in the mean errors was obtained by increasing the number of observations. A reduction in the difference between the theoretical and experimental values of stresses was obtained by increasing the number of images in the equations for calculating phase. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations. The proposed method with many images and high accuracy is a good alternative to the photoelastic techniques.

The Study on Residual Stress Testing of Humidity Effect and Distribution Law for PMMA

Polymethyl methacrylate (PMMA) has shown some excellent performances. However the humidity environment affects mechanical properties of PMMA seriously. In this work, the digital phase-shifting photoelasticity is used to test the humidity stress of the boundary according to which we concluded that the boundary stress decreases gradually from the boundary to the inner. The mathematical model of the boundary stress distribution is established based on the distribution law of the boundary stress. This mathematical model can be used to predict the effect of the humidity environment to the boundary stress, and guide PMMA to use safely.

New numerical method for the photoelastic technique

The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phase-shifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate a larger sequence of images. Each image represents a measurement of the stresses present in the object. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations.

New numerical methods for the photoelastic technique with high accuracy

The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phase-shifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate equation of phase with a larger sequence of images. Each image represents a pattern and a measurement of the stresses present in the object. A reduction in the difference between the theoretical and experimental values of stresses was obtained by increasing the number of images in the equations for calculating phase. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations.

Experimental characterization of interlaminar shear failure in sandwich structures under three-point bending

We applied an improved six-step phase-shifting method in digital photoelasticity to an adhesively bonded aluminum/epoxy/aluminum sandwich structure in order to study interlaminar shear failure behavior. Before and after three-point bending, a self-balanced thermal residual shear stress appeared on the interface because of the difference in thermal expansion coefficients between aluminum faces and epoxy core interlayer. At the beginning of loading, the shear stress in the core layer distributes continuously and forms shear bands tilting at a 45° direction. It then joins with the upper and bottom aluminum faces in order to realize the shear load transfer. As the bending load increases, the maximum interface shear stress occurs near the supports and a partially debonded region appears at the interface. The interfacial shear stress in the partially debonded region decreases rapidly until a shear failure occurs. A load–flexibility curve of the vibration-damping–type sandwich structure agrees well with the theoretical prediction of a laminated beam.

Flexural effects of sandwich beam with a plate insert under in-plane bending

The local stress concentrations in sandwich beam with a plate insert under in-plane bending are concerned in the study. An improved six-step phase shifting method in digital photoelasticity is employed to calculate the whole-field shear stress.The shear load transfer is realized by shear bands which connect the top and bottom sheet faces through adhesively-bonded interfaces. The plate insert plays a role in load transfer in the sandwich structure, and the fact that debonding might occur at more sites of the interfaces may also leads to the failure of the structure. The local stress concentrations at the insert end change with the load under three-point bending loads, while they remain as the initial residual shear stress under four-point bending loads. The local stress concentration effects generated by the plate insert is essentially caused by the mismatch of elastic properties of the core materials and the irrational geometry of the insert.

RGB photoelasticity applied to the analysis of membrane residual stress in glass

The measurement of residual stresses is of great relevance in the glass industry. The analysis of residual stress in glass is usually made by photoelastic methods because glass is a photoelastic material. This paper considers the determination of membrane residual stresses in glass plates by automatic digital photoelasticity in white light (RGB photoelasticity). The proposed method is applied to the analysis of membrane residual stresses in some tempered glass. The proposed method can effectively replace manual methods based on the use of white light, which are currently provided by some technical standards.

Improvement of digital photoelasticity based on camera response function

Studies on photoelasticity have been conducted by many researchers in recent years, and many equations for photoelastic analysis based on digital images were proposed. While these equations were all presented by the light intensity emitted from the analyzer, pixel values of the digital image were actually used in the real calculations. In this paper, a proposal of using relative light intensity obtained by the camera response function to replace the pixel value for photoelastic analysis was investigated. Generation of isochromatic images based on relative light intensity and pixel value were compared to evaluate the effectiveness of the new approach. The results showed that when relative light intensity was used, the quality of an isochromatic image can be greatly improved both visually and quantitatively. We believe that the technique proposed in this paper can also be used to improve the performance for the other types of photoelastic analysis using digital images.

Experimental Study on Stress Field Parameters of an Interface Crack in Aluminum/ Epoxy

Standard experimental tests including photoelasticity in the evaluation of stress intensity factors in crack tip has been regarded widely. A least-squares method is used to determine the stress field parameters of interface crack in Aluminum/ epoxy bimaterial and its evolvement. Based on multi-parameter stress field equations and the least-squares principle, a set of over-determined nonlinear equations is established by fitting the isochromatic phase field obtained by digital phase-shifting photoelasticity in this paper. An iterative procedure based on Newton-Raphson method is utilized to estimate the unknown stress field parameters. Interface crack experiments reveal that the modulus of combined stress intensity factor increases with the applied loads and however its phase angle holds the line on the condition of same loading direction. On the other hand, the modulus of combined stress intensity factor increases with the loading direction from 30o to 75o under the same applied load, however, its absolute phase angle decreases and is independent of the loads.

Application of High Speed Image Correlation for Measurement of Mode Shapes of a Car Bonnet

For the analysis of vibrations and mode shape extraction in particular the use of optical full-field measurement techniques has grown during the last years. Beside techniques like Digital Speckle Pattern Interferometry, Moiré, Thermography or Photoelasticity the Digital Image Correlation techniques have already been successfully proven to be an accurate displacement analysis tool for a wide range of applications.

Sensitivity of isoclinic data using various phase shifting techniques in digital photoelasticity towards generalized error sources

Photoelasticity is a whole field experimental technique to obtain stress fields in both 2-D and 3-D elasticity problems. The accuracy of parameter evaluation by digital photoelastic techniques depends on the choice of the optical arrangements for parameter estimation, the inherent error in optical elements and any misalignments introduced during experimentation. A generic approach to simulation of error in digital photoelasticity by Jones calculus is presented in this paper. Of late it has been shown that the quarter-wave plate mismatch error is varying and is not a constant value. The present simulation accounts for inherent variable error in quarter-wave plates and also accommodates the error arising due to the optical misalignment of the various optical elements. The applicability of the new methodology is shown for different phase shifting techniques. A comparative study among various techniques is done regarding sensitivity to general error sources and it is found that the ten-step method is the least sensitive among them all. Therefore usage of the ten-step method is thus recommended while using manual polariscope for digital photoelastic applications.

Adaptive Smoothing for Isoclinic Parameter Evaluation in Digital Photoelasticity

Abstract: In digital photoelasticity, one gets whole field information of isoclinic and isochromatic parameters based on intensity processing. Isoclinic values are undefined at isochromatic fringe contours and this appears as noise in the isoclinic phasemap which affects stress separation adversely. A new adaptive smoothing algorithm to remove the noise due to isochromatic‐isoclinic interaction that automatically takes care of the isotropic points and π jumps present in the isoclinic phasemap is proposed. It is validated for the benchmark problem of a ring under diametral compression and verified for an angled bracket.

Digital photoelasticity – A comprehensive review

Digital photoelasticity has rapidly progressed in the last few years and has matured into an industry-friendly technique. This review thematically classifies all the developments in digital photoelasticity and highlights the relative merits and drawbacks of the various techniques. The overall objective is to provide enough information and guidance to allow an end-user to make an informed choice on the type of technique to be used in a particular situation.

Noise-Free Determination of Isochromatic Parameter of Stereolithography-Built Models

Recently, stereolithography, one of the rapid prototyping (RP) techniques, has simplified the process of making three-dimensional (3-D) photoelastic models. One of the issues in stereolithography-made models is the noise due to porosity of the model. This is undesirable for data handling in digital photoelasticity. A preliminary study showed that the thickness of the slice has an influence on the appearance on the noise. In this paper, use of 10-step phase-shifting technique (PST) and refined three-fringe photoelasticity (RTFP) is explored to determine the isochromatic data as accurately as possible. A slice cut from a 3-D model of a spline shaft made of stereolithographic material is used for isochromatic determination. It is found that with suitable postprocessing, the quantitative results obtained from 10-step PST and RTFP are comparable. The relative merits of these two techniques for analysing stereolithographic models are brought out.

Influence of the Resin Layer Thickness at the Interface of Hybrid Metal-composite Co-cured Joints

As discussed in literature, the accurate analysis of the modern co-cured joints between composite materials or between a metal and a composite material (hybrid joints) is complicated by the influence of the interface resin layer on the interface singular stress field. In such joints, in fact, there is not a proper adhesive layer and the thickness of the resin layer, that plays the role of the adhesive, is not constant due to the presence of the reinforcing fibers in the composite adherent. For this reason several authors assume that a generic co-cured joint can not be studied as a simple bi-material joint, without considering the particular characteristics of the actual resin layer. This problem is also involved into the development of reliable design methods able to give accurate predictions of the joint efficiency. In this work, by theoretical analyses performed by using the Lekhnitskii theory, numerical simulations carried out by means of the boundary element method and experimental investigations based on the combined use of the generalized Dundurs parameters and digital photoelasticity, the influence of the resin layer on the singular stress field at the interface of a generic hybrid metal-composite joint, has been investigated.

Measurement of Applied Stresses and Residual Stresses on a Residual Stress Model by Applying Two Different Loads

Applied stresses on a residual stress model have previously been obtained by measuring the residual stresses and the resultant stresses generated by applying a load. The present paper reports that the applied stresses and the residual stresses on the residual stress model can be obtained by measuring two resultant stresses generated by applying loads of two different magnitudes. In the proposed method, the residual stresses need not be obtained from the residual stress model before applying a load. The residual stress model used to test the proposed method is a circular disk with frozen stresses that is subjected to a diametral compressive load at a certain angle. The applied stresses and the residual stresses on a residual stress model were experimentally and precisely obtained by digital photoelasticity using linearly polarized light.

Application of Real-Time Photoelastic Analysis to Single Fibre Fragmentation Tests

One of our main research areas is the trans-scale modelling of damage in composite materials, which consist of a polymer matrix and carbon or glass fibres in different material combinations and geometrical arrangements. From the local stress redistribution in the fibre-matrix interphase and in the surrounding matrix material information on the parameters of microscopic damage models for composite materials can be obtained. Owing to the difficult interface characterisation based on the properties of the single material components, a photoelastic analysis of single fibre fragmentation tests is performed. In addition to the qualitative visual interpretation in polarized light, an enhanced quantitative analysis in combination with digital photoelasticity using a four image phase shifting method will be applied [1]. As the sequential capturing of images might cause incorrect results, these four pictures are grabbed simultaneously. This allows for continuous testing. Additionally, errors due to the relaxation behaviour of the matrix material can be avoided. To this, a modular optical system consisting of a variable long distance microscope and a beam dividing module proposed by [2] was developed. It allows for the simultaneous projection of four different filtered images of one microscopic scene to the four quadrants of a CCD chip. This special equipment gives the possibility to apply quantitative photoelasticity to tensile tests performed on standard testing machines. This paper explains the measurement hardware and discusses the main problems and realised solutions from picture capturing through image processing to real-time photoelastic analysis at the present state of development. Exemplary results for the qualitative analysis of selected material combinations and different manufacturing processes are shown.