Method In Digital Photoelasticity Research Articles

Three-wavelength digital photoelasticity.

A three-wavelength photoelasticity method is proposed to simplify the optical setup and speed up data acquisition. By recording six intensity images with circularly polarized illuminations of three close wavelengths, the phase retardation and corresponding inner stress can be computed accurately with a correspondingly developed computational algorithm. Since the mechanical rotations of wave plates and polarizers required by classic photoelasticity techniques are avoided, the data acquisition of this proposed method is very speedy, and measurement of a dynamic sample can be achieved with a very simple and compact optical setup. Besides theoretical analyses, numerical and experimental evidences are also used to confirm the feasibility of this suggested three-wavelength digital photoelasticity method.

Experimental study on the interaction between two cracks by digital photoelasticity method: construction of the Williams series expansion

The multi-point Williams series expansions for the near-crack-tip fields in the vicinity of two interacting cracks in an isotropic linear elastic material are experimentally and numerically determined. The experimental method used to study the interaction of two cracks is the digital photoelasticity method which is applied for determination of coefficients of the higher-order terms of the Williams series expansion for a plate of finite width with two interacting cracks. The digital image processing tool for handling of the entire set of experimental data isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is relied on the classical Ramesh technique but enables to scan the experimental image in any direction and to analyse the image after any number of logical operations. The realized digital image analysis allows us to extract photoelastic data from the entire field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns in the vicinity of the crack tips are converted into text file and then the points of isochromatic fringes with minimum light intensity are used for estimating linear elastic fracture mechanics parameters. The multi-parameter stress field description with the first fifteen terms is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two interacting cracks using 1) the classical over-deterministic method in the form based on the stress field and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is demonstrated that the BFGS method has indisputable advantages over the classical over-deterministic method. The significance of higher-order terms in the Williams expansion is proved for the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement. This verifies the experimental analysis

Importance of the Higher Order Terms of the Williams series expansion: Experimental Aspects and Finite Element Simulations

The study is devoted to the multi-point Williams series expansion for the crack-tip fields in isotropic linear elastic materials and methods of estimating the coefficients of higher order terms in the power expansion. It is shown that higher order terms are very important in processing of the experimental data obtained from interference – optic methods. It is demonstrated that the accurate interpretation of the experimental data requires keeping, considering and evaluating the higher order terms of the Williams expansion. A large cohort of experiments on cracked specimens from optically sensitive materials using digital photoelasticity method was performed. The interference fringe patterns obtained show that the correct description of the stress fields in the vicinity can be given if we take into account higher order terms in the asymptotic presentation of the near crack tip fields. Two interference-optical methods were used. Digital photoelasticity method and digital holography interferometry technique are applied for determination of the coefficients of the Williams series expansion. It is shown that we can restore theoretically the stress field in the vicinity of the crack tip if at least fifteen terms in the power expansion are hold. The classical over-deterministic method is used for the evaluation of the coefficients.

Computational and experimental identification of coefficients of the Williams series expansion by considering higher order terms in the cracked specimens through digital image analysis

In the study, digital photoelasticity method is used for finding of the linear elastic fracture mechanics parameters for a plate of finite width with two inclined interacting cracks. The digital image processing tool for the whole set of experimental data namely isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is based on the well-known Ramesh technique but allows us to scan the image in any direction and to analyse the image after any number of logical operations. The performed digital image analysis allows us to extract photoelastic data from the whole field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns near the crack tips were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-point stress field description is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two inclined interacting cracks using 1) the algorithm based on the classical over-deterministic method and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is shown that the latter method has undeniable advantages over the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement.

Photoelastic study of a double edge notched plate for determination of the Williams series expansion

In this work, digital photoelasticity method is applied for assessment of the crack tip linear fracture mechanics parameters for a plate with double edge notches and different other crack configurations. The overarching objective of the study is to obtain the coefficients of the Williams series expansion for the stress and displacement fields in the vicinity of the crack tip by the digital photoelasticity technique for the double edge notched plate. The digital image processing tool for experimental data obtained from the photoelasticity experiments is developed and utilized. The digital image processing tool is based on the Ramesh approach but allows us to scan the image in any direction and to analyse the image after any number of logical operations. In the digital image processing isochromatic fringe analysis, the optical data contained in the transmission photoelastic isochromatics were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-parameter stress field approximation is used. The mixed mode fracture parameters, especially stress intensity factors (SIF) are estimated for specimen configurations like double edge notches and inclined center crack using the proposed algorithm based on the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different cracked specimens. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values estimated using the proposed method are compared with analytical / finite element analysis (FEA) results, and are found to be in good agreement.

Extracting fracture mechanics parameters (higher-order coefficients of Williams series expansion) from FEM analysis and digital photoelasticity method

The paper describes new algorithms and procedures proposed for determining fracture mechanics parameters from finite element analysis using the over deterministic method. The multi-parameter crack tip stress field description is used. The algorithms and procedures based on multi-parameter stress field representations in series form are shown to be a powerful tool for reliable and accurate parameter determination. The technique is aimed at the determination of coefficients of the Williams series expansion from finite element analysis and is based on the over deterministic approach. The methodology is illustrated and applied to several cases of cracked specimens. Examples are presented for crack-tip fields recorded using digital photoelasticity. The results of finite element analysis are compared with the digital photoelasticity experiments. The results are in good agreement. The principal stresses obtained from finite element method are in good agreement with the isochromatic fringe patterns obtained by the photoelasticity method. Explanation has been made for giving guidance to a user on how best to approach implementation of the method from a practical standpoint.

The digital photoelasticity method and finite element analysis for determination of the multi-point crack-tip field series expansions for notched semi-disks

The digital photoelastic method for the construction of the multi-point crack-tip series expansions in isotropic elastic semi-disks is employed. The series of cracked specimens in the form of the semi-disk with vertical and inclined notches from optically active materials (polycarbonates) were produced and tested under three-point bending. The principal intent of this experimental procedure of the phototelasticity technique was estimation of the amplitude coefficients in the Williams expansion in which the non-singular high-order terms are taken into account. The first ten coefficients in the multi-point series expansion have been ascertained. To retrieve the points belonging to the isochromatic fringe patterns and having the minimum light intensity the digital image processing scheme was utilized. The scheme of the over-deterministic method for evaluation of the amplitude coefficients (fracture mechanics parameters) is applied. Additionally, the problem was reduced to the problem of minimizing the objective function which is the quadratic form for the stress field in terms of unknown fracture mechanics parameters. The finite element analysis for the same series of the notched specimens was performed. The demeanour of the stress field in the neighbourhood of the notch tip for different types of mixed mode loading was elucidated from finite element analysis. The coefficients of the asymptotic presentation of the stress and displacement fields are recovered from finite element results. It is shown that the multi-point coefficients are in good agreement with experimental observations.

Higher-order coefficients of the Williams series expansion for near crack-tip fields and their extraction from FEM experiments and digital photoelasticity method

Multi-parameter stress field near the Mode I crack tip in an isotropic linear elastic material is presented. The coefficients of the Williams series expansion of the stress field in the vicinity of the Mode I crack in the isotropic linear elastic material are obtained by the digital photoelasticity technique and by finite element analysis. The main objective of this study is to determine first fifteen coefficients with good accuracy and to compare the numerical results with the analytical solution for the infinite plate with the central crack. It is shown that the coefficients of the higher-order terms of the Williams series expansion are extracted with good accuracy. Comparison of the coefficients of the Williams series known from the theoretical solution for an infinite plate with the central crack and the coefficients extracted from the photoelasticity method and from finite element analysis is given. The FEM analysis is performed for a series of cracked specimens with a small crack and for a series of cracked specimens considered in the phototelasticity experiments. It is shown significant importance of higher-order terms in the Williams series expansion.

Photoelastic evaluation of stress fields and coefficients of multi-parameter asymptotic expansion of the crack-tip stress field

In this work, digital photoelasticity method is appliedfor estimation of the crack tip fracture mechanics parameters for a plate with double edge notches and different crack configurations.The digital image processing tool for experimental data obtained from the photoelasticity experiments is developedand utilized. The digital image processing tool is based on the Ramesh approach but allows us to scan the image in any direction and to analyse the image after any number of logical operations. In the digital image processing fringe analysis, the optical data contained in the transmission photoelasticisochromatics were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-parameter stress field approximation is used. The mixed mode fracture parameters, especially stress intensity factors (SIF) are estimated for specimen configurations like double edge notches and inclined center crack using the proposed algorithm based on the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different cracked specimens. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

A new integral equation method for calculating interacting stress intensity factor of multiple crack-hole problem

In this paper, a new integral equation method is proposed based on elementary solutions and superposition principle to study multiple crack-hole problem under both remote and surface stresses. Several typical crack-hole problems are solved in order to compare the calculation results of interacting stress intensity factors (SIFs) obtained by the newly proposed method with those obtained by Green’s function method, dislocation density method, finite element method and digital photo-elasticity method, and further to investigate the effect of loading conditions and crack-hole geometric parameters on SIFs. Research results show that there exists a neutral inclination angle α0 of the crack (with x-axis) for eliminating the crack-hole interaction when σx∞ ≥ σy∞. Increase of σx∞ is helpful for cracking arrest and the compressive stresses on crack and hole surfaces are helpful for crack propagation. In addition, the normal stress (p) on the crack surface only affects KI and α0 of KI, while the normal stress (n) on the hole surface affects both KI and α0 of KI, and KII and α0 of KII. The hole radius (R) and the crack-hole spacing distance (t) have little effect on α0 of KI and KII. The new integral equation method not only has almost the same calculation results of SIFs as the Green’s function, dislocation density and finite element methods, but also has advantage of simplicity and wide applicability over Green’s function and dislocation density methods in calculating the interacting SIFs of the cracks under both remote and surface stresses.

Experimental evaluation of coefficients of multi-parameter asymptotic expansion of the crack-tip stress field using digital photoelasticity

In this study coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate are obtained by the use of the digital photoelasticity method and finite element analysis. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give more accurate estimation of stress, strain and displacement fields and to extend the domain of validity for the Williams series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. The developed tool allows us to find points that belong to isochromatic fringes with minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. Numerical simulations of the same cracked specimen as in the experimental photoelasticity method are performed. The higher-order coefficients are extracted from finite element method calculations implemented in Simulia Abaqus software package and the outcomes are compared to experimental values. The plate with a small central crack has been considered either. This kind of the cracked specimen has been utilized for comparison of coefficients of the Williams series expansion obtained from finite element analysis with the coefficients known from the theoretical solution based on the complex variable theory in plane elasticity. It is shown that the coefficients of the Williams series expansion match with good accuracy.

DETERMINATION OF THE WILLIAMS SERIES EXPANSION’S COEFFICIENTS USING DIGITAL PHOTOELASTICITY METHOD AND FINITE ELEMENT METHOD

In the present work, photoelastic and finite element methods have been employed to study the near crack tip fields in isotropic linear elastic cracked bodies under mixed mode loading. The investigated fracture results have been obtained for a series of cracked specimens by testing plates with two parallel cracks, two inclined parallel cracks, three-point bend specimens, four-point bend specimens, inclined edge crack triangular shape specimens subjected to symmetric three point bend loading. The multi-parameter Williams series expansion is used for the crack tip field characterization. Digital photoelasticity method is utilized for determination of the Williams series expansions coefficients. The unknown coefficients in the multi-parameter equation are determined using a linear least squares method in an over-deterministic manner. Together with the experimental determination of the fracture mechanics parameters finite element method is invoked to describe the crack tip stress field. Coefficients of higher order terms are either found numerically by finite element method. A good agreement is found between the numerical and experimental results. The significant advantages using multi-parameter equations in the analysis of the stress field are shown and the errors that a study with a limited number of terms produce is demonstrated. The comparison with finite element analysis highlighted the importance and precision of the photoelastic observation for the evaluation of the fracture mechanics parameters. The experimental SIF, T-stress values and coefficients of higher-order terms estimated using the digital photoelasticity method for the extensive series of cracked specimens are compared with finite element analysis (FEA) results, and are found to be in good agreement.

Interference-optical methods in mechanics for the multi-parameter description of the stress fields in the vicinity of the crack tip

Digital photoelasticity method is used to analyzeexperimentally the complete Williams series expansion of the stress and displacement fields in the vicinity of the crack tip in isotropic linear elastic plates under Mixed Mode loading. The distribution of the isochromatic fridge patterns is employed for obtainingthe stress field near the crack tip by the use of the complete Williams asymptotic expansion for various classes of the experimental specimens (plates with two collinear cracks under tensile loading and under mixed mode loading conditions). The higher order terms of the Williams series expansion are taken into account and the coefficients of the higher order terms are experimentally obtained. The stress field equation of Williams up to fifty terms in each in mode I and mode II has been considered. The comparison of the experimental results and the calculations performed with finite element analysis has shown the importance and significant advantages of photoelastic observations for the multi-parameter description of the stress field in the neighborhood of the crack tip.

Computational methods of phase shifting to stress measurement with photoelasticity using plane polariscope

The photoelastic technique has seen some renewed interest in past few years with digital images and image processing new methods becoming readily available. However, further research is needed to improve the precision, the accuracy and the automation of photoelastic technique. The aim of this research work is to get new numerical equations for the phase-shifting method in digital photoelasticity using a plane polariscope. The model was developed to plane polariscope because of the simplicity and low cost of this equipment. To develop the phase shift and respective intensity equations only the analyzer is rotated. A ring under diametral compression is used for the experimental validation. From these intensity equations, the equations for isoclinic and isochromatic parameters are deduced by applying a new numerical technique. This approach can be used to calculate the isoclinic and isochromatic parameters using any number of images. Several analysis are performed with different number of photographic images. The results showed errors reduce when more phase-stepped images are utilized. Hence, one concludes that the uncertainties in results due to effects of errors on photoelastic images can be reduced with a larger amount of phase-stepped images.

Numerical Methods for the Photoelastic Technique using Phase Shifting

AbstractThe 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 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.

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.

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.

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.