Photoelastic Method Research Articles

Compressive failure of thermally strengthened glass spheres — Why are Prince Rupert's drops so strong?

This paper aims to elucidate the exceptional high strength of Prince Rupert's Drops (PRDs). PRDs are idealized as thermally strengthened Glass Spheres (SGSs), and their compressive failure mechanisms are investigated experimentally and numerically. The distributions of residual stress within SGS specimens are quantitatively characterized using an integrated photo-elastic method. Uniaxial compression tests conducted on these specimens reveal that the compressive residual stress present on the sphere's surface significantly enhances its strength. High-speed video images demonstrate that SGSs fail at the equatorial region, in contrast to annealed glass spheres (AGS) which typically fracture near the Hertzian contact zone. Numerical simulations suggest that the residual stress mitigates the maximum principal stress on the surface of SGSs, thereby impeding the development of flaws on the surface of the specimens. Ultimately, failure of SGS specimens under pressure occurs due to the “squeezing” effect, in contrast to AGSs which commonly fail due to contact indentation.

New high sensitivity approach for a quantitative visualization of the continuous whole-field stress evolution in digital photoelasticity

Digital photoelasticity is a widely used technique for experimental stress analysis on mechanical models subjected to loading conditions, due to its ability to reveal the stress information through color fringe patterns and consequently demodulate it computationally to achieve a quantitative evaluation. In this process, some limitations persist, such as, expertise dependence, experimental repeatability, sensitivity to load increments, and weak performance under experimental conditions, especially in time-dependent scenarios. In response to these weaknesses, the method “Quantitative Visualization of the Continuous Whole-Field Stress Evolution” introduced the ability to perform a complete demodulation of the fringe patterns generated in time-dependent applications, achieving high performance compared to conventional photoelasticity methods. This paper proposes a new highly sensitive approach for a quantitative visualization of the continuous whole-field stress evolution in digital photoelasticity by incorporating an inverse signal process and a multi-stage strategy. The algorithm aims to ensure the performance under high fringe order conditions while exhibiting high sensitivity in cases where the maximum stress obtained is less than one fringe order. The results presented validate its effectiveness in demodulating full-field stress distributions, especially in scenarios where the loading condition induces fringe orders less than one, thus contributing to the broader applicability of digital photoelasticity.

Visualization Of Nanoparticle Orientation Structures Inside Complex Fluids Using Polarized Light Imaging Technique

The present paper reports on the effect of 3D-oriented particles on birefringence using the concept of 'rheooptics', a technique for identifying changes in the internal structure or flow dynamics of complex fluids from changes in optical anisotropy (birefringence). We used the photoelastic method, as a kind of polarized light imaging technique, to visualize the internal orientation structure induced by applying shear stress to cellulose nanocrystal (CNC) suspensions under shear flow. Two different rheometers (concentric cylinder and parallel plate-type) that can easily combine a birefringence measurement system were introduced to Transverse rotation Longitudinal rotation perform the shear flow induction, and the birefringence was measured and compared from vertical and horizontal directions for shear. The birefringence measurements from different directions provide an opportunity to investigate the effect of 3D-oriented CNCs on birefringence, which is a novelty of the present study. The measured birefringence was fitted with the empirical equation proposed in the previous study and followed the power law of applied shear rate with the same exponent, independent of the shear direction at the time of measurement This result suggests that there is a common physical background that gives birefringence a power law. This exponent was different from the values given in previous studies and is explained by differences in the particle interaction behaviour based on the concentration of suspensions and CNC length. Note that the proportionality coefficients differ by a factor of 10, clearly indicating differences due to the direction of birefringence measurement. These results indicate that birefringence due to transverse rotation of the CNC is more sensitive to shear stress than to longitudinal rotation.

Experimental Analysis Of Flow Birefringence In Jeffery-Hamel Flow

The photoelastic method, a stress field measurement method in solid mechanics, is being considered for application to fluids. In previous studies, simple shear flow and uniaxial extensional flow experiments have shown a relationship between the measured phase retardation and the velocity field. However, no clear relationship has been shown for extensional and shear combined flow fields. The objective of the present study is to clarify the relationship between the velocity field and the measured phase retardation in an extensional-shear combined flow. For this objective, photoelastic measurements were conducted in a steady flow field using the Jeffery-Hamel flow, which is an extensional-shear combined flow with an analytical solution for the velocity field. Comparison with the analytical velocity field showed that birefringence was proportional to the 0.88 and 0.92 power of the deformation in the shear or extensional-dominated region, respectively. The results show that the birefringence Δ_n followed the power law of extensional rate ε^{0.95} where it is dominant. Whereas shear is dominant, Δ_n proportional to a power-law of γ^{0.88} holds. These results are consistent with previous studies using shear flow and uniaxial extensional flow. Furthermore, it is shown that in the extensional-shear combined flow, the sum-of-squares root of two equations suggests that the theory developed mainly for solids could also be applied to fluids.

Photoelasticity-based stress field analysis of glass under 1064 nm laser irradiation

Laser-induced thermal cracking in glass cutting surpasses traditional methods. Understanding dynamic thermal stresses is crucial for exploring mechanisms and controlling trajectories. We developed a real-time stress measurement system using the photoelastic method. Scanning soda-lime glass with a 1064 nm laser at various speeds, we analyzed stress changes with a finite element model. Results revealed phase entanglement issues, resolved by phase unwrappling. Stress differences peaked at 105 MPa (2 mm/s) and 78 MPa (4 mm/s). 2 mm/s scanning led to wider, longerwrapp cracks than 4 mm/s due to higher stress levels. Simulation and experimental results agreed, enhancing stress analysis comprehensively.

Revealing physical interactions of ultrasound waves with the body through photoelasticity imaging

Ultrasound is a ubiquitous technology in medicine for screening, diagnosis, and treatment of disease. The functionality and efficacy of different ultrasound modes relies strongly on our understanding of the physical interactions between ultrasound waves and biological tissue structures. This article reviews the use of photoelasticity imaging for investigating ultrasound fields and interactions. Physical interactions are described for different ultrasound technologies, including those using linear and nonlinear ultrasound waves, as well as shock waves. The use of optical modulation of light by ultrasound is presented for shadowgraphic and photoelastic techniques. Investigations into shock wave and burst wave lithotripsy using photoelastic methods are summarized, along with other endoscopic forms of lithotripsy. Photoelasticity in soft tissue surrogate materials is reviewed, and its deployment in investigating tissue-bubble interactions, generated ultrasound waves, and traumatic brain injury, are discussed. With the continued growth of medical ultrasound, photoelasticity imaging can play a role in elucidating the physical mechanisms leading to useful bioeffects of ultrasound for imaging and therapy.

Relation between edge stress, bending strength, surface stress and fracture pattern of thermally toughened glass

Thermally toughened safety glass must meet safety requirements in the building industry. Here, destructive tests are defined in the product standards, which must be carried out on small, standardized format (360 mm × 1100 mm) glass elements to determine the fracture pattern and bending strength. This is costly and not in the interests of sustainability. As part of the quality control of optical anisotropy effects in thermally toughened glass, isochromatic scans that can provide information on the edge stress are acquired. The evaluation of the isochromatics and retardations at the edge with deduction of the edge stress and transfer to bending strength and fracture pattern could provide essential findings for assuring the safety requirements of thermally toughened glass. In this experimental investigation, the surface and edge stress were measured on standardized format thermally toughened safety glass, with different edge processing and glass thicknesses from three different suppliers. Afterwards, the fracture pattern is controlled, or the bending strength is analyzed in a destructive four-point bending test. Conclusively, the results from the photoelastic and destructive tests are compared to determine whether the photoelastic measurement methods used to measure surface and edge stress can be employed as quality control.

Holographic method for stress distribution analysis in photoelastic materials

<p>An alternative method to obtain the internal stress distribution in photoelastic materials using digital holography (DH) is presented. Two orthogonally polarized holograms were used to obtain the phase maps and analyzed using the proposed approach. This method directly determines the stress distributions from the phase differences obtained in the reconstructed phase maps, unlike methods obtained by photoelasticity. Optical information, such as index of refraction, phase differences, etc., are not measured directly in traditional photoelasticity. However, this approach was validated with both the finite element method and the RGB (red, green, and blue) photoelasticity method that is traditionally used.</p>

Experimental determination of the strength of toughened glass in the area of near-edge holes

For tempered glass, edge distances for drilled holes in point-fixed glazing must be observed. For production reasons, the European product standard EN 12150 for thermally toughened safety glass requires a minimum edge distance of two times the thickness t. When transferring loads from the glass pane, it is necessary to consider whether and to what extent residual stresses of the tempering process are present in the remaining area between the edge and the hole. The German design standard DIN 18008-3 specifies a blanket distance to the edge of 80 mm for cylindrical holes, which is frequently undercut in construction practice. In this case, the strength of the tempered glass used may not be applied for structural analysis, and only the strength of annealed glass may be assumed instead. Because of this discrepancy, this study experimentally investigated the strength behavior of toughened glass with cylindrical near-edge holes via photoelasticity and destroying four-point bending test. The pre-stress zones of a glass pane are qualitatively compared using the monochrome wavelength photoelasticity method, and the surface compressive stress is measured at points near the hole. Then, the fracture stress of the drilled specimen is determined by four-point bending tests and the necessary numerical simulation using the finite element method of the bending test. The various test methods are intended to provide information on the distribution of the residual stresses and thus on the strength of the toughened glass when the edge distance is lower than the distance required in DIN 18008-3—and by this update the rules.

Stress distribution and roof subsidence of surrounding strata considering in situ coal conversion and CO2 mineralization backfilling: Photoelastic experiments using 3D-printed models of mining faces and goafs

Coal, a reliable and economical fuel, is expected to remain the primary energy source for power generation for the foreseeable future. However, conventional mining and utilization of coal has caused environmental degradation and infrastructure damage. An in situ coal conversion method has been proposed to mitigate environmental problems and reduce CO2 emissions resulting from coal extraction and utilization. This method involves the in situ conversion and utilization of coal, backfilling of waste rock, and CO2 mineralization to backfill the goaf. In this study, the impact of mining and conversion activities on the surrounding strata was evaluated to ascertain the effectiveness and advantages of the in situ coal conversion method. Transparent stope models were created using three-dimensional printing technology. The stress distribution and deformation characteristics of the surrounding strata were examined using photoelasticity and digital image correlation methods. The results were compared with those obtained using the traditional backfill mining method. The comparison revealed that the disturbance to the surrounding strata was 14.4 times less in the in situ conversion method than in the traditional backfill mining method. Additionally, the disturbance height at the roof and the disturbance depth at the floor were 4.2 and 2.1 times lower, respectively. The roof subsidence in the in situ conversion method was 1.97 times less than that in the traditional backfill mining method. These results confirm the advantages of minimizing the disturbance to surrounding rocks and controlling the subsidence of roof strata.

Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out

A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain.

Advancing instantaneous photoelastic method with color polarization camera

Digital photoelasticity is an essential experimental method. For dynamic objects and transient stress fields, the utilization of the instantaneous photoelastic method becomes necessary. Existing instantaneous photoelastic methods, represented by the conventional RGB method and instantaneous phase shifting techniques, encounter a significant challenge in simultaneously obtaining both the isochromatic and isoclinic parameters while ensuring a considerable measurement range for the isochromatic fringe order (retardation). This severely limits the application scope of instantaneous photoelasticity. In this paper, a novel approach is proposed by introducing a color polarization camera into the field of photoelasticity. The proposed method enables simultaneous determination of the full-field continuous isochromatic fringe order and the isoclinic parameter, ensuring a considerable measurement range for the isochromatic fringe order. Additionally, the obtained isoclinic parameter is consistent, eliminating the need for tedious and time-consuming phase unwrapping procedures. To validate the accuracy and effectiveness of the method, it was applied to standard problems involving a disc and a ring under diametral compression and an instantaneous problem concerning a rotating blade. The proposed method expands the application potential of instantaneous photoelasticity, enabling the resolution of a broader range of problems.

Influence of race thickness on contact stress of inner and outer races of angular contact ball bearing using photoelastic experimental hybrid method

Influence of race thickness on contact stress of inner and outer races of angular contact ball bearing using photoelastic experimental hybrid method

A photoelastic method for stress analysis of granular terrain beneath a wheel

This paper presents a photoelastic method for the stress analyses of granular terrains beneath a traveling wheel. Recently, wheel terramechanics have been studied using various advanced techniques such as particle velocimetry and machine learning. However, the dynamic profiles of the stress distributions in soil have not been directly observed. In this paper, we propose a photoelastic method to experimentally demonstrate the two-dimensional stress analysis of a granular terrain. This method uses photoelastic disks as terrain particles; thus, the internal stress and propagation of the granular terrain can be visualized using the interference fringe of light. This study aimed to observe the dynamic behavior of grains, typically simulating circular or spherical objects of the granular terrain. To demonstrate the photoelastic method for simulated ground, we developed a single-wheel testbed using photoelastic materials. Moreover, the effects of mixing with non-photoelastic materials were investigated to simulate steady states with small and large wheel-slip conditions. This paper presents a force chain analysis of the photoelastic particles beneath a single traveling wheel. The force chain structure was geometrically compared with the propagation angle and length. In addition, the orientational orders of the force chains were quantitatively evaluated under both small and large wheel slip conditions. The experimental results confirmed that the photoelastic method can reveal dynamic changes in the internal stress structures of granular terrain beneath the wheel under various slip conditions.

Elliptically polarized light photoelasticity based on LCD.

We propose a three-wavelength elliptically polarized light photoelasticity method for high efficiency and low-cost stress measurement. By illuminating the sample with two different forms of elliptically polarized light for each wavelength sources, twelve images are acquired. From these images, phase delay and the principal internal stress difference are precisely computed using developed algorithms. Our proposed method based on an LCD panel has the unrivalled advantage that elliptically polarized light can be automatically adjusted, which reduces the mechanical rotation of the system, in contrast to the traditional six-step phase-shifting photoelasticity method, which requires manual rotation for circularly polarized light. In addition, the system has the potential to theoretically expand the area of illumination infinitely, thereby expanding the measurement area. The viability of the suggested methods is confirmed with numerical simulation and stress measurement.

Experimental study on the influence of explosive stress wave on the dynamic crack propagation characteristics under biaxial confining pressure

The effect of biaxial confining pressure on dynamic crack and the interaction between explosive stress wave and dynamic crack are studied based on dynamic photoelastic method in this experiment. The experiment consists of five groups, primarily focusing on the angle at which the stress wave encounters the crack. The experimental results reveal two main fractures: mode I fracture and mixed-mode fracture. The influence of biaxial confining pressure on stress waves and dynamic cracks differs between these two fracture modes. Additionally, the Newton-Raphson iteration method is employed to analyze and calculate the fringe pattern of the crack tip at various stages. Subsequently, the calculation results are used to reconstruct the photoelastic fringe. To validate the accuracy of the calculation method, the reconstructed photoelastic fringe pattern is compared with the experimental results. The results show that the presence of confining biaxial pressure enhances the crack initiation toughness, propagation toughness and propagation speed. It also improves the crack's resistance to the impact of the incident stress wave from all directions. When the stress wave interacts with the crack, the photoelastic fringe patterns at the crack tip can be categorized into two main types. One is primarily influenced by the stress wave, while the other is primarily influenced by the stress field at the crack tip. To extract accurate crack tip information, it is essential to analyze the fringe pattern dominated by the stress field at the crack tip.

Effect of shatterproof polymer film application on the fracture types and strength of glass subject to bending load

Shatterproof polymer films are widely for windows used because they can be easily installed on existing glass windows to improve safety. Applying them to glass plates has been reported to not only prevent fragments from scattering but also increase load-bearing capacity and penetration resistance. However, the clarification of their mechanism and quantitative evaluation are still insufficient because the effect of film application on the strength and failure mode of glass under quasi-static loading has not been investigated. In this study, three-point bending tests and fracture surface observations were conducted on a float glass with a shatterproof polymer film. The stress field formed inside the glass was visualised during the tests using the photoelastic method. By varying the support span of the specimen, the deformation mode was varied to generate three types of failures: bending, shear caused by Hertzian contact stress, and mixed-mode failures. Under the conditions in the present study, the breaking loads of the specimens with and without film were almost the same; however, the fracture surface observation indicated that the area subjected to shear failure caused by Hertzian contact stress was larger with film application. Finally, the effect of the film thickness on the breaking load due to bending deformation was theoretically predicted.

Characterization of the photoelastic dispersion coefficient using polarized digital holography.

The photoelastic dispersion coefficient represents the relationship between stress and the differences in refractive indices in a birefringent material. However, determining the coefficient using photoelasticity is challenging, as it is difficult to determine the refractive indices within photoelastic samples that are under tension. Here we present, for the first time, to our knowledge, the use of polarized digital holography to investigate the wavelength dependence of the dispersion coefficient in a photoelastic material. A digital method is proposed to analyze and correlate the differences in mean external stress with differences in mean phase. The results confirm the wavelength dependence of the dispersion coefficient, with an accuracy improvement of 25% compared to other photoelasticity methods.

Application of artificial neural networks for stress state analysis based on the photoelastic method

The present article proposes an evolutionary development of the photoelasticity method for measuring stresses based on annular photoelastic sensors application along with stress pattern recording with the aid of a digital camera and its recognition using artificial neural networks. The analysis of the modern application of the photo-elasticity method for various problems within the theory of strength is presented. The principle of operation of photoelastic sensors based on the photoelasticity effect is considered. Optical patterns in an annular photoelastic sensor are presented for various values of the horizontal stress. The calculation of the stress state of the sensor for the following full-scale experiment has been performed, the estimate of the threshold conditions under which the sensor can be applied has been performed. As a result of a laboratory experiment, a dataset of 1500 isochromatic images has been assembled. A subspecies of a neural network, namely a convolutional neural network, has been applied as a machine learning algorithm. Different combination of models and optimizers have been employed. The application of downhole sensors for continuous monitoring of alterations in the rock mass stress state and the integration of this data into a digital field model based on Internet of Things technologies has been proposed.

Practical method for improving the accuracy of weakly stressed birefringence detection by circularly polarized instantaneous photoelasticity.

Due to the mismatch between the quarter-wave plate and the wavelength of the light source, the circularly polarized field photoelastic stress analysis method has an impact on the measurement of the phase delay and the stress direction angle. In particular, the measurement of the phase delay is inaccurate for weakly stressed samples with phase delays less than a quarter-wavelength. In this paper, we first give a method for calculating the mismatch value δ, which requires only one air calibration without prior calibration of the parameters of the quarter-wave plate with other equipment. We then introduce δ into the correction process for the phase delay, derive the correction equation, and give a theoretical comparison of the relative error curves. The results show that the correction method can theoretically limit the maximum amount of error. Finally, we have verified the accuracy of the method by measurements of the internal lens stress before and after the correction and by stitching measurements on SiC wafers.