Photoelastic Isochromatic Fringe Research Articles

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

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.

Numerical Computation of Complex Stress Intensity Factors of Interface Cracks in Bi-Materials Based on Photoelastic Theory

This paper presents a new numerical method for obtaining the complex stress intensity factor with an interface crack in bi-materials using photoelastic isochromatic fringe numbers N. The theoretical solution of stress field at the crack tip was deduced from Muskhelishvilis stress function and an undetermined term σ0 which is a function of material properties was added to this theoretical solution. A partial differential iterative equation with fast convergence was formed by applying the photoelastic theory. The complex stress intensity factor K=K1+iK2 and σ0 were obtained by Newton-Raphson iteration method and K domain was discussed. The simulant photoelastic isochromatic fringe pattern could be generated through image processing and numerical calculation according to K and σ0. The simulant isochromatic fringe pattern accords with experimental photoelastic isochromatic fringe pattern, so it is practicable for this numerical method of obtaining the complex stress intensity factor.

Numerical Computation of Complex Stress Intensity Factors of Interface Cracks in Bi-Materials Based on Photoelastic Theory

This paper presents a new numerical method for obtaining the complex stress intensity factor with an interface crack in bi-materials using photoelastic isochromatic fringe numbers N. The theoretical solution of stress field at the crack tip was deduced from Muskhelishvilis stress function and an undetermined term σ0 which is a function of material properties was added to this theoretical solution. A partial differential iterative equation with fast convergence was formed by applying the photoelastic theory. The complex stress intensity factor K=K1+iK2 and σ0 were obtained by Newton-Raphson iteration method and K domain was discussed. The simulant photoelastic isochromatic fringe pattern could be generated through image processing and numerical calculation according to K and σ0. The simulant isochromatic fringe pattern accords with experimental photoelastic isochromatic fringe pattern, so it is practicable for this numerical method of obtaining the complex stress intensity factor.

Stress analysis of a stepped rounded D‐ring with a ratio of H1/H2 = 3.0 under uniform squeeze rate and internal pressure by photoelastic experimental hybrid method

AbstractStresses occurring in a stepped rounded D‐ring designed to have a ratio of H1/H2 = 3.0 and compressed to 20% squeeze and pressurized with internal pressures of 0 MPa, 0.98 MPa, 1.96 MPa, 3.92 MPa, 4.9 MPa and 5.89 MPa are analyzed using photoelastic experimental hybrid method. It was observed that when a pressure of 0 MPa and 20% compression are applied, the photoelastic isochromatic fringes of the stepped rounded D‐ring with a ratio of H1/H2 = 3.0 were almost symmetrical. However, as the applied internal pressure increased, the circular portion of the D‐ring moved over the step on the front side along the points 1r–2r towards the restraining wall of the front side of the groove. During the motion of the circular portion, the space between the restraining wall and the step on the front side was slowly filled; but unlike the D‐ring with a ratio of H1/H2 = 1.0 where complete filling occurred earlier before extrusion, complete filling of this space delayed until the portion of the D‐ring near the extrusion gap extruded. It was further noted that an internal pressure of up to 5.89 MPa was required to initiate extrusion in the D‐ring with a ratio of H1/H2 = 3.0.

Internal stress analysis of a stepped rounded D-ring under a uniform squeeze rate and internal pressure using a photoelastic experimental hybrid method

Internal stresses occurring in a stepped rounded D-ring compressed to 20% squeeze and pressurized with internal pressures of 0, 0.98, 1.96, 2.94, 3.92 and 4.9 MPa are analyzed using a photoelastic experimental hybrid method. At a pressure of 0 MPa and 20% squeeze, the photoelastic isochromatic fringes of the stepped rounded D-ring were almost symmetrical. As the internal pressure increased, the isochromatics shifted and curved towards the extrusion gap. By supplying a radius of 0.33 mm at the corners of the stepped D-ring, the high stresses at the sharp corners were reduced by up to 25%. These results further indicate that extrusion of the stepped rounded D-ring occurred at an internal pressure of 4.9 MPa which was about 25% higher than the pressure at which the extrusion of the stepped unrounded D-ring occurred.

Experimental Evaluation of Mixed Mode Stress Intensity Factor for Prediction of Crack Growth by Phoelastic Method

Determination of stress intensity factors K I, K II, and constant stress term, σ ox is investigated. A theory of determining the stress intensity factors using photo-elastic method is formulated taking three stress terms. Three-parameter method of fracture analysis for determining the mixed mode stress intensity factors under biaxial loading conditions from photo-elastic isochromatic fringe data is used. A special biaxial test rig is designed and fabricated for loading the specimen biaxially. A simplified and accurate method is proposed to collect the data from isochromatic fringes. Taking specimen geometry and boundary conditions into account, regression models are developed for estimation of fracture parameters.

Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error

The Fourier transform method, widely applied in photomechanics for the automated analysis of interferometric fringe patterns, has been recently extended to the photoelastic isochromatic fringe patterns analysis. Unfortunately, its use in photoelasticity involves some limitations that have not been completely highlighted in literature. This work deals with the influence of the quarter-wave plate tolerance on the evaluation of the retardation. Both theoretical and experimental analyses have shown that the quarter-wave plate error does not affect the retardation only if the principal stress directions in the model and in the carrier are aligned. In general, instead, the tolerance of the quarter-wave plates leads to an amplification of the retardation error due to the influence of the isoclinics with a subsequent restriction of the field in which the method can be applied. For instance, using common quarter-wave plates and tolerating a maximum retardation error of about 0.03 fringe order, than the Fourier transform method cannot be applied as a full-field technique but only in the model zones in which the misalignment between the principal stresses in the model and in the carrier is less than 15°.

Photoelastic inverse problem solution for a biaxially loaded infinite plate with a hole

AbstractThis paper presents an inverse problem solution for the case of photoelastic isochromatic fringes around the hole of a biaxially uniformly loaded infinite plate for two problems. Problem 1 relates to an infinite plate in which the circular hole is drilled first and then the loads are applied. Problem 2 is the residual stress problem in which the hole is drilled after the biaxial load is applied to the infinite plate. This “hole method” solution may be used for all cases of biaxial, far field uniform loading conditions.

Catalogue of photoelastic fringes for a biaxially loaded infinite plate with a hole

AbstractThis paper presents a typical catalogue of “virtual” photoelastic isochromatic fringes around the hole of a biaxially loaded infinite plate for two problems. Problem 1 relates to an infinite plate in which the circular hole is drilled first and then the loads are applied. Problem 2 is the residual stress problem in which the hole is drilled after the biaxial load is applied to the infinite plate. Use of this catalogue allows visualisation of the stress distribution around the hole, and a first approximation to the solution of the inverse problem using photoelasticity.

Theoretical photoelastic stresses in three dimensional body with elastic contact

An understanding of the Hertz contact theory is important for investigating the failure strength and behavior of rolling and/or slipping mechanical-structural components. Two simple special cases including a circular contact and line contact patch have been solved in the closed form solution. However, there are many unsolved complicated cases where the contact areas become elliptical contact patches. In this paper, a simple stress field generated in contact bodies under general loading conditions is derived. The stress field derived in this paper is utilized to generate theoretical three dimensional photoelastic isochromatic fringe patterns. Some of the theoretical isochromatic fringe patterns are compared with published experimental results. The agreement between the theoretical and the experimental results are found to be good.

Photoelastic investigation of stress intensifications in the interacting nozzle attachment region of pressure vessels

In this paper, the problem of determining the opening mode (mode I) stress intensity factor (SIF) from the photoelastic isochromatic fringe pattern associated with a surface crack located in the ligament region between two radial nozzle-cylinder junctions of pressure vessel has been investigated. The objective is to determine the influence of geometry, size and location of the surface flaw with respect to the radial nozzles. Starting from the crack tip stress field formulation of Etheridge and Dally using three parameters (1)† a new method suited to the analysis of photoelastic data obtained from a single isochromatic fringe loop to extract the SIF has been introduced. This new method has been used to predict SIFs for a range of pressure vessel nozzle spacings when photoelastic models are subjected to internal pressure loading.

Stress intensity factor determination from isochromatic fringe patterns—A review

It is the aim of this paper to present an overview of the major publications and persons that have contributed to the development in the area of determining stress intensity factors (SIF) from photoelastic isochromatic fringe patterns. The authors task concludes with a reference list at the end of the paper, which contains a total number of 147 publications and 129 authors, starting with the well known papers by Post, Wells and Post from the fifties, and terminating with papers published in 1986. For convenience a separate, alphabetic listing of authors is also provided. Although most of the papers compiled deal with applications of the techniques, a good deal of the papers are devoted to development of the methods. Static loading conditions are studied in the majority of the papers, but dynamic cases are also covered. Almost all other aspects of the problems are covered in the papers listed, e.g. mode I, mixed-mode conditions, two- and three-dimensional problems, near- and far-field effects, and plate bending problems, to mention a few.

A three-point flexure test configuration for improved sensitivity to metal/ adhesive interfacial phenomena

Abstract A three-point flexure test was used to evaluate the effects of chemical surface treatments on the performance of adhesively-bonded structures of Ti6A14V. A single adherend/adhesive structure rather than a double adherend sandwich configuration is shown to be sensitive to pre-bonding adherend surface treatments. Data is presented which relates mechanical properties with chemically treated adherend surfaces. Photoelastic isochromatic fringes were recorded simultaneously with the flexure test as a means to monitor stress distribution, failure initiation, and crack propagation.

Photoelastic investigation of bolted joints in composites

In this paper, the methods of photo-orthotropic elasticity are applied to the study of bolted joints in composites. The photoelastic models are E-glass fibre-reinforced epoxy strips loaded through a cylindrical pin, simulating bolt loading without lateral pressure. A special loading arrangement is devised so that the photoelastic response around the hole is not obscured. Quasi-isotropic and unidirectionally-reinforced specimens are tested, with ratios of end distance to hole diameter varying from 2 to 6. Photoelastic isochromatic fringe patterns are presented along with the shear stress distribution for the quasi-isotropic models.

A new method of determining the stress intensity factor K from isochromatic fringe loops

This paper describes the four parameter method of analysis for determining the stress intensity factor K. Dynamic photoelastic isochromatic fringe patterns associated with cracks propagating in centerpin loaded, eccentric-pin-loaded and crack-line-loaded SEN specimens of Homalite 100 were recorded. Data was obtained for tests over a range of crack velocities from arrest to the terminal velocity of 14,900 in. sec (378 m sec). Six measurements describing the size and shape of the experimental isochromatic loops were used to determine the stress intensity factor K by employing a comparison function to match analytical and experimental results. The analytical isochromatic loops were generated with a Westergaard stress function of the form Z(z) = K √2πz {1 + β( z a}) and a superimposed normal stress σ Ox = αK|√2 πz which acts parallel to the direction of crack extension. Results were obtained by the computer program (FRACTURE) for different values of the four parameters to give 8925 analytical fringe loops. Another computer program (SEARCH) was used to find a small group of solution which given very low values of the comparison function f c . The final solution which contains the value of K was obtained from the small group by selecting the most consistent solution. The results obtained for Homalite 100 show that K min and K k are nearly the same and that ȧ increases abruptly from 0 to about 10,000 in./sec (254 msec) for modest increases in K above 400 psi √in. (4.4 × 10 5 Nm 3 2 ). Further increases in crack velocity require significant increases in K until terminal velocity is