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.     

数字光弹性法综述

将光弹性法与计算机图像处理技术相结合 ,来自动采集光弹性数据和分析应力的方法 ,称为数字光弹性法 ,与传统光弹性法相比 ,它可以进一步提高实验速度和精度。本文详细讨论了以下两个方面 :一是光弹性条纹的细化和倍增处理技术 ;二是自动确定光弹性参数的技术 ,包括相移法、傅立叶变换法、逐步载荷法、广谱分析法和RGB光弹性法等。通过对近二十年来国内外在这些方面的研究、应用和进展作了综述 ,认为采用白光的彩色域相移技术计算光弹性等倾角 ,结合采用白光源或三色光源的相移法来确定光弹性等色线级数 ,有望成为解决静态二维和三维冻结模型薄切片应力分析的最佳方法 ;另外 ,设计一种能实时和同步采集多幅条纹图的实验装置 ,通过相移法来自动获取动态光弹性数据 ,是数字动态光弹性法很有前景的发展方向     

Photoelastic Tomography with Linear and Non-linear Algorithms

Tomography is a powerful method for the investigation of the internal structure of 3D objects from human bodies to atomic reactors. Classical tomography has been elaborated for the determination of scalar fields, i.e. fields, each point of which is characterized by a scalar. Due to that, algorithms of classical tomography can not be directly applied by investigating stress fields since stress is a tensor. In this paper it is shown that photoelastic tomography can be based on the equations of integrated photoelasticity. In the linear approximation the problem of stress field tomography is decomposed into a number of problems of scalar field tomography for single components of the stress tensor. In the non-linear case the axisymmetric stress field can be determined using a genetic algorithm. The paper is illustrated by several examples.     

Phase Shifting Full-Field Interferometric Methods for Determination of In-Plane Tensorial Stress

A new method that combines phase shifting photoelasticity and transmission Coherent Gradient Sensing (CGS) is developed to determine the tensorial stress field in thin plates of photoelastic materials. A six step phase shifting photoelasticity method determines principal stress directions and the difference of principal stresses. The transmission CGS method utilizes a standard four step phase shifting method to measure the x and y first derivatives of the sum of principal stresses. These stress derivatives are numerically integrated using a weighted preconditioned conjugate gradient (PCG) algorithm, which is also used for the phase unwrapping of the photoelastic and CGS phases. With full-field measurement of the sum and difference of principal stresses, the principal stresses may be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions. The method is demonstrated for a compressed polycarbonate plate with a side V-shaped notch. The experimental stress fields compare well with theoretical stress fields derived from Williams solution for a thin plate with an angular corner.     

A novel instrument for transient photoelasticity

A new instrument has been developed for the photoelastic analysis of transient events. The instrument is based on the Phase-Stepped Images Obtained Simultaneously (PSIOS) system developed by Patterson and Wang, which enables four phase-stepped photoelastic images to be collected simultaneously. Where the new instrument differs is that the original instrument requires four cameras to collect the four images, whereas the new instrument requires only one camera. This makes the use of phase-stepping viable for events, in which the fringe order varies with time. Three examples are given of the use of the instrument in static and dynamic photoelasticity to generate full field maps of isochromatic fringes. The instrument has been found to work well and significantly increases the potential for the use of photoelasticity to study transient and possibly dynamic events. J.W. Hobbs was a Research Associate, R.J. Greene was a Research Associate     

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。     

Photoelastic validation of a theoretical solution for an edge cracked disk

In this paper, the theoretical solution developed by Vaughan and Wu for the stress analysis of a circular disk with a radial edge crack extending to its center is validated by photoelasticity. The photoelastic results include the fullfield isochromatics as well as measurements of the maximum shear stress at a number of test points. Additionally, the experimental stress intensity factor is extracted from the photoelastic data by Irwin's two-parameter method. Good agreement is observed when the theoretical stress field and stress intensity factor are compared with the experimental results. It is concluded that the Vaughan-Wu solution can be confidently applied in fracture mechanics analyses. The application of such a solution to the stress analysis of two-dimensional bodies with complex geometries subjected to complex loading is also noted.     

复合材料光弹性分析的工程方法

本文在推导均衡光弹性复合材料应力(应变)—光定律的基础上,导出了均衡光弹性复合材料的近似应变—光定律。然后加以推广,提出适用于一般光弹性复合材料的近似应变—光定律.精度分析及实验验证表明:作为工程计算,在采用本文推荐的参数时,光弹性复合材料可视作各向同性材料进行光弹性分析。     

正装结构非线性应力应变累加规律研究

基于有限位移理论的正装结构非线性分析理论对解决超大跨度、柔性结构的非线性计算有重大意义.文中探讨了正装结构非线性的分析特点,研究了其应变场与应力场的Kirchhoff应力张量与Lagrange应变张量的适用性,提出了正装结构非线性分析中应力场与应交场的累加规律,导出了拖动坐标法的虚功增量方程,以此对杆系结构非线性分析常用的CR法和UL列式进行了精度比较分析.文中研究成果可为正装结构的非线性分析提供理论指导.     

电子散斑和全息光弹法相结合测量透明材料的应力强度因子K1

全息光弹性中等和线是获得断裂力学中应力强度因子的一种有效方法之一。但用传统的全息光弹性方法获取等和线需暗房，要经过显影定影及再现，而且不能直接数字化使其应用受到限制。本文提出一种将全息光弹性与相移电子散斑干涉（Electric Speckle Pattern Interferometry，简称ESPI）有机结合的方法，不但克服传统全息光弹性的不足，而且使全息光弹性实现了数字化。文中将这一方法成功应用于有预制裂纹的三点弯曲试件上，定量求得其应力强度因子（Stress Intensity Factor，简称SIF）K1，而且实验值和理论值具有相一致的结果。     

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.     

Photoelastic model measurement with rotated principal axes by scattered-light photoelasticity

The method of measurement of a three-dimensional photoelastic model with rotated principal axes has not yet been fully experimentally established. It is known that a three-dimensional photoelastic model can be reduced to an optically equivalent model. In this paper, the optically equivalent model is realized from a stratified model consisting of two layers of the frozen stress model. The secondary principal stress direction and the relative phase retardation of the frozen disk model in the stratified frozen stress model are determined for the entire field from Stokes parameters obtained by scattered-light photoelasticity using unpolarized light. The accuracy of these values is confirmed by a comparison with results only from the frozen stress disk model.     

材料破坏过程中应力分布的数值光弹图

 介绍应用材料破坏过程分析(MFPA)系统进行材料破坏过程应力 场分析的“数值光弹”方法. 给出了几种材料试样在外部载荷作用 下变形或破坏时的内部应力分布条纹图. 结果表明(MFPA)系统为研 究材料破坏过程中的应力分布提供了一种简单易行的分析方法.     

Photoelasticity for stress analysis under high hydrostatic pressure

Experimental research relative to pressure effects on the mechanical behavior of materials is frequently handicapped by the difficulties associated with making load and deformation measurements in a hostile environment. The application of photoelasticity in high-pressure experiments provides a means for studying the effect of hydrostatic stress on varying stress fields. The purpose of this paper is to examine the feasibility of using the photoelastic method of stress analysis in a high-pressure environment. The unusual feature of this application is the finite elastic deformations suffered by the photoelastic model under high pressure. As a result, the mechanical and stress-optical properties of the model materials are functions of pressure. Another important feature in this study is the selection of a suitable model material. Since the model must come into contact with the liquid pressure media, chemical and absorption resistance are essential considerations. Although it was found that photoelastic investigations can be carried out at high pressure, limitations are imposed by the presence of the optical vessel and pressurized fluid.     

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.     

Evaluation of an applied plane-stress tensor distribution using ultrasonic shear waves

Most acoustoelastic stress measurements using shear waves that have been carried out so far are strongly related to photoelastic experiments: the velocity difference of the birefringent waves is evaluated. Absolute time-of-flight measurements potentially give more information about stresses but are also likely to be inaccurate. A technique is developed enabling time-of-flight and polarization angle measurements in an aluminum plate that are reproducible within 1/3 ns and one-deg respectively. Based on a previous calibration of the acoustoelastic effect, a plane-stress tensor field caused by applying a load to an aluminum 2024-T351 compact-tension specimen is evaluated. The results are compared to those of a finite-element analysis.     

同震断层三维裂纹扩展波动时域超奇异积分法

应用波动时域超奇异积分法将P波、S波和磁电热弹多场耦合作用下同震断层任意形状三维裂纹扩展问题转化为求解以广义位移间断率为未知函数的超奇异积分方程组问题;定义了广义应力强度因子,得到裂纹前沿广义奇异应力增量解析表达式;应用波动时域有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以三维矩形裂纹扩展问题为例,通过典型算例,研究了广义应力强度因子随裂纹位置变化规律;分析了同震断层裂纹扩展中力、磁、电场辐射规律.      

Automated Stress Separation Along Stress Trajectories

A procedure for the separation of principal stresses in automated photoelasticity is presented. It is based on the integration of indefinite equations of equilibrium along stress trajectories, also known as Lamè–Maxwell equations. A new algorithm for precise and reliable stress trajectory calculation, which is an essential feature of the procedure, has also been developed. Automated stress separation is carried out along stress trajectories starting from free boundaries. Experimental tests were performed on a disc in diametral compression and on a ring with internally applied pressure. Full-field principal stress values were obtained and results were compared with those from the theory of elasticity and with those obtained from the classical shear difference method. It was shown that the proposed method is more accurate and less affected by the presence of residual stresses or experimental errors at the boundaries than the shear difference method. In addition, the method requires little human interaction and is therefore well-suited for automated photoelasticity.     

The double-light-beam method in three-dimensional scattered-light photoelasticity

This paper presents a new scattered-light photoelasticity technique which may be called the double-light-beam measurement method. Principal-stress directions and relative retardations related to the principal-stress differences can be measured at any point within an ordinary three-dimensional photoelastic model by this method. This method does not need double loading and the quantities to be measured depend only on the relative light intensity. Moreover, the output signals alternate, providing improved accuracy and stability. If supported by an appropriate program-control and digital processing system, the double-light-beam method can be used to quickly determine the internal stress distribution in ordinary three-dimensional photoelastic models.     

Development of a Hybrid Method of Reflection Photoelasticity for Crack Problems in Anisotropic Plates

Reflection type photoelastic experiment can be used more effectively than a transmission type photoelastic experiment especially in industrial fields. Moreover, composite materials have been widely used in engineering applications and structures because of their outstanding advantages which individual isotropic components do not have. The development of these materials requires a promising technique such as reflection photoelasticity to analyze their behaviors in service. Unfortunately, there are few experimental studies based on this technique. Therefore, a hybrid method based on this technique was developed in this research to analyze the fracture behavior of opaque anisotropic materials. The application of this method will help to understand the fracture behaviors of anisotropic materials used in engineering components and structures. The validity of this method was verified by comparison of the results obtained from this method with ones obtained from the hybrid methods for isotropic material on the same isotropic specimen. The reflection type photoelastic experiment for orthotropic materials was then applied to orthotropic plates with a central crack of various inclination angles. Using this hybrid method for anisotropic materials, stress intensity factors and separated stress components were obtained at the vicinity of the crack-tip in orthotropic plates from only the isochromatic fringe patterns of the isotropic coating material.