Three-dimensional photoelasticity by stress freezing

Three-dimensional photoelasticity by the stress-freezing method has been considered to be one of the most powerful methods of experimental stress analysis. Its principles were well established more than thirty years ago, but its use outside the academic world has steadily declined. The reasons are cost and time needed to generate the desired information. This presentation summarizes fifteen year's effort to develop-stress-freezing photoelasticity into a responsive and inexpensive tool for stress analysis in the industrial environment. The whole procedure of stress-freezing photoelasticity is reviewed and evaluated from a cost-effectiveness point of view. The basic properties of model materials, the method of model casting, and the method of mold preparation are discussed in detail. The methods of model slicing, measurement of fringe order, and evaluation of stresses in models are reviewed together with available equipment. Finally, several applications of developed procedures are described in detail.     

Photoelastic analysis of contact stresses in the presence of machining irregularities

Three-dimensional stress-freezing photoelasticity is used to analyze the stress distributions in a shaft with a shrink-fit ring. Of particular concern is the stress redistribution when machining irregularities are present at the contact surface. Details of the model manufacture, data reduction, and analysis are given.     

New model materials for photoelasticity and photoplasticity

Two new materials are proposed as models for photoelasticity and photoplasticity. One is cast resin fully cured epoxy-phenol alloy which is made by the mutual cross linking of pre-condensed resins of epoxy and phenol. While epoxy-phenol alloy resin is available only for photoelasticity, the other, polycarbonate resin, is useful not only for photoelasticity, but also for photoplasticity. Polycarbonate is very tough and has large values of both photoelastic stress sensitivity and modulus of elasticity. The excellent cold workability of polycarbonate is proved by a deep-drawing test. Hence the photoplastic results obtained from a polycarbonate model can be applied by analogy to the plastic stress analysis in other ductile materials. Both resins are very transparent even in the plastic state.     

三维光弹性中预应力结构的应力冻结研究

本文提出用三维光弹性应力冻结法模拟分析预应力钢筋混凝土结构中的应力。通过模拟体与实体结构的相似性研究,给出了模型载荷比例系数Cq参数,通过参数合理的选取,有效的解决了应力冻结水平预测这一技术关键;用光弹性应力二次冻结法,将结构预应力和负载应力冻结在同一试件中;应分析精度对模型尺寸的要求,采用了精密浇铸的方法制作模型。此外,还研制了受力清晰明确的加载系统。对这些涉及应力冻结的若干关键问题结合工程实例进行探讨。实验应力分析结果与有限元数值法一致性较好。     

Photomechanical properties of some birefringent polymers around their glass transition temperatures

This paper describes an investigation and comparison of the optical and mechanical properties of the three polymers—PMMA (polymethyl methacrylate), CT200 and MY750 (both based on bisphenol-A epichlorohydrin). The work was undertaken with the specific purpose of assessing the suitability of these polymers for use in contact studies involving three-dimensional photoelasticity and the stress-freezing technique. The optical property investigated was the variation of photoelastic fringe constant with maximum stress-freezing temperature. The mechanical properties sought were the variation of Young's modulus with temperature and the stress-strain behavior at the stress-freezing temperature. The effects of the magnitude of stress and the soak time in the thermal cycle were also investigated for the MY750 resin. The results provide the optimum peak temperature for the thermal cycle to achieve repeatable values of Young's modulus and fringe constant during stress freezing. The nonlinear stress-strain behavior is quantified and should be a useful reference. The dependence of strain on load and soak time is also shown and is useful in specifying the optimum cycle time for stress freezing and the appropriate stress level. It was concluded that the resin MY750 was the most suitable for photoelastic applications which involved high localized stress, such as contact problems or fracture mechanics studies.     

Acoustical birefringence and the use of ultrasonic waves for experimental stress analysis

Stress-induced optical birefringence in transparent materials has long been a common technique of stress analysis. Although stress-induced acoustic birefringence was discovered more than 20 years ago, its development and actual applications are still limited. This paper will look at the similarities and differences between the propagation of light waves in photoelastic materials and the propagation of ultrasonic waves in deformed solids. Critical comparisons of the experimental methods employed in photoelasticity with those available in modern ultrasonic measuring technique show why previous studies on ultrasonic measurement of stresses were not very successful. A new experimental technique is devised for using ultrasonic waves for stress analysis. The technique employs a single rotatable 10-MHz shear transducer as the transmitter and receiver of ultrasonic pulses. The enlarged display of the 10-MHz modulated-pulse pattern of reflected echoes provides a convenient way to determine the directions of principal axis of the stress within ±3 deg. The pulse-echo-overlap method is used to measure the absolute velocities of the two principal shear waves. The difference in principal stresses is then calculated from the velocity measurements. Test results of common structural-aluminum and steel specimens under uniaxial compression show a linear relation between the velocity changes and the applied stress. Ultrasonic measurements of stress distribution in a 6.35-cm diameter, 1.9-cm-thick aluminum disk under diametric compression are also reported. Paper was presented at Third SESA International Congress on Experimental Mechanics held in Los Angeles, CA on May 13–18, 1973.     

Half-fringe photoelasticity: A new approach to whole-field stress analysis

This paper presents a new method for whole-field stress analysis based on a symbiosis of two techniques—classical photoelasticity and modern digital image analysis. The resulting method is called ‘half-fringe photoelasticity (HFP)’. Classical photoelasticity demands materials with high birefringence, which leads to extensive use of plastics as model materials. Since the behavior of these materials is often different from that of the prototype materials, their use distorts the similitude relationships. In many contemporary problems this distortion is untenable. HFP offers a way out of this dilemma. It permits materials and loads to be chosen so that no more than one half of a fringe order appears in the area of interest. Thus, for example, glass, which behaves linearly up to high stress levels and over a wide range of temperatures, could be used as model material. Alternatively, models from polymeric materials could be used under very low load in order to stay within the linear part of the stress-strain diagram and to prevent large deformations. The half-fringe-photoelasticity system, which is described here, utilizes the resulting low levels of birefringence for effective stress analysis. This paper describes the system. It outlines a calibration routine and illustrates its application to two simple problems using glass models.     

Design and evaluation of the poleidoscope: A novel digital polariscope

The goal of recent research in digital photoelasticity has been fast, reliable, and accurate full-field photoelastic data that will allow the technique to play a valued role in assessing material and structural integrity. A novel design for a polariscope that allows simultaneous capture of multiple images is described, and a prototype instrument is evaluated using both transmission and reflection photoelasticity. The design offers the potential for real-time data acquisition and processing of high-speed events, using a number of different approaches to digital photoelasticity. The evaluation of the instrument arranged for the phase-stepping method demonstrated that it was capable of providing results of comparable quality and accuracy to manual analysis and more conventional methods of acquiring phase-stepped images.     

Nondestructive residual-stress measurement in a wide-flanged rolled beam by acoustoelasticity

X-ray stress analysis is a standard nondestructive stress-measurement technique, but its use is limited in the sense that only a surface layer is surveyed. Recently, acoustoelasticity has emerged as a technique for nondestructive stress analysis. Acoustoelasticity makes use of stress-induced acoustic-birefringent effects. It gives stress distributions averaged through the thickness of a specimen. This technique is attractive because it does not require a transparent plastic model as photoelasticity does. However, much should be done before this method is established as a standard nondestructive technique of stress analysis. The most important among them is to separate stress-induced birefringence from that introduced by texture structure. For special cases, such as axisymmetric stress distributions and when a stress-free region is knowna priori, residual-stress distributions can be evaluated nondestructively. In this paper, we measured residual-stress distribution in a wide-flanged rolled beam by using a recently developed T-type transducer. The results were compared to those obtained from conventional destructive methods.     

Towards stress freezing in birefringent orthotropic composite models

Birefringent composite models are fabricated using epoxy resin reinforced with unidirectionally oriented glass fibers. The mechanical and photoelastic properties of the material at room temperature are determined. To explore the possibility of application of stress-freezing technique to birefringent composite models, the behavior and properties of this material are studied at elevated temperature (at stress-freezing temperature of the resin). The properties of the material at room and at elevated temperatures are reported. The feasibility of stress freezing glass-fiber-reinforced epoxy composites with low-fiber-volume fraction is discussed.     

正交异性动态光弹性方法的几个基本问题的研究

文章对适用于动态研究的正交异性光弹性复合材料进行了分析，详细说明了光弹性复合材料中残余双折射的确定方法；基于静态下Ｈｙｅｒ和Ｌｉｕ应力－光性定律，提出了正交异性动态应力－光性定律，并对正交异性材料的动态力学参数及动态光弹性常数给出了实用的标定方法；最后，利用三个单轴压缩试件（０°，９０°及４５°），采用动态应变测量方法，证实了单轴应力状态下正交异性动态应力－光性定律的正确性。     

Contact stress in stranded cable

An experimental study of interstrand contact stresses existing in a stranded cable while it rests in its supporting clamp has been made using the stress-freezing photoelastic technique. Comparing the results with the Hertz contact-stress theory made it possible to establish criterion for suspension-clamp design.     

Photovisco-elastoplastic behavior of polycarbonate material under creep and tension tests

Polymers are widely used as photomechanical models of a prototype material (often a metal). Photoplasticity is one of the methods used in order to show the behavior of plastic materials stressed beyond the linear elastic limit. To illustrate this process we have analyzed the photovisco-elastoplastic behavior of polycarbonate as a photoplastic material. In this paper a technique for local and simultaneous measurement of birefringence and principal strains is presented. The mechanical and optical properties, at room temperature, have been evaluated by means of uniaxial tension tests. A series of creep tests has been carried out in order to study the photovisco-elastoplastic behavior of polycarbonate. In two different experiments we analyzed nonlinear birefringence and the amplitude of the corresponding strains. We could thus evaluate the distribution of strains and the distribution of uniaxial stress for each birefringence state and vice versa.     

Highlights of the optical anisotropy of unstressed transparent polymeric plates

The photoelastic effect is cumulative, therefore the presence of material birefringence in unstressed transparent polymers might lead to erroneous photoelastic analyses. This presence is more influential in the scattered-light photoelasticity. Direct-transmission polariscopes are not suitable for detecting all material birefringence in normally illuminated plates because the birefringence in question coincides with the wave normal of the propagating light. The present paper describes phenomenologically the presence of the material birefringence in an arbitrarily selected group of unstressed cross-linked polymers and presents means of their determination. The material-birefringence information obtained can be used as a means of taking proper precautions for conducting faultless scattered-light photoelastic analyses. Octagonally shaped plates were machined to permit data acquisition using four different light-propagation directions. The orientation and diffusion of molecular chains appear to be the major source of the material birefringence observed.     

Determination of the full-field stress and displacement using photoelasticity and sampling moiré method in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.     

The existence of real distinct slownesses in photoelastic media

The continuum mathematical models of photoelasticity rely upon the ability of an optical medium, rendered anisotropic by the presence of a stress field, to sustain two transmitted light waves, with distinct slownesses and polarisations. The purpose of this paper is to examine the mathematical models with a view to determining whether they validly support birefringence over a wide range of material properties and impressed stress fields, and to determine conditions under which birefringence is guaranteed by the mathematical models. The classical models of Maxwell and Neumann and the recent finite deformation model of Smith and Rivlin are treated. In each case the secular equation is given and conditions are derived in the form of inequalities for the existence of distinct real slowness solutions. Methods of direct inspection and function extremisation are employed to verify these inequalities, with the aid of a geometric analogy. It is found that for magnetically isotropic media the distinctness of the three eigenvalues of the dielectric tensor is a necessary and sufficient condition for birefringence for all directions of propagation. For magnetically anisotropic media, birefringence is guaranteed by the distinctness of at least two of the eigenvalues of the matrix product of the dielectric tensor and the specific magnetic reluctance tensor.     

Analysis of cylindrical shells of nonuniform thickness using two-dimensional photoelastic models

An experimental method is described whereby symmetrically loaded cylinders of nonuniform thickness are analyzed using two-dimensional photoelastic models mounted on elastic foundations. The technique is most conveniently applied to ring-stiffened or notched cylinders. The particular model studied simulated a notched cylindrical pressure vessel which had been previously studied with three-dimensional photoelasticity. The stress-concentration factors at the base of the notch, found using both methods, showed excellent agreement. An analysis was also performed which allows estimation of the error involved when a beam-on-elastic-foundation model does not rigorously simulate a cylinder.     

Temperature and time influence in the stress freezing of the epoxy Hysol 4290

Disks of the photoelastic epoxy known as Hysol 4290 have been subjected to constant load at various temperature levels and the birefringence has been recorded as time elapsed (creep test). Also disks of the same material were loaded at the critical temperature and then cooled, each to a different temperature level and, after they reached thermal equilibrium, the loading was removed while the temperature was maintained constant (recovery test). The effect of time on the fringe value is given for both groups of tests using the temperature as a parameter. Finally, tensile specimens have been subjected to various loads at the critical temperature and fringe response and failure recorded. The results obtained may be useful for the design of experiments and, in some cases, to shorten the time required to conduct a three-dimensional photoelasticity investigation using the “freezing” method.     

Full-field separation of principal stresses by combined thermo- and photoelasticity

The combined use of thermoelastic stress analysis and full-field reflection photoelasticity based on the phase-stepping technique has been developed for twodimensional problems. The first method determines the sum of the principal stresses, the latter evaluates the difference of the principal stresses. Thus the principal stresses were separated at each point in the field of view without reference to neighboring points. An evaluation of this approach has been performed using a tensile plate with a central circular hole. The results show that the analysis carried out combining thermo- and photoelasticity incurred errors no larger than those of each system working independently.