全场数字化测量光弹性等倾角的五步彩色相移法

通过把相移法与光学彩色信息图像处理技术相结合 ,提出了一种确定全场光弹性等倾角的五步彩色相移法。模型置于白光照射下 ,在起偏镜与分析镜不同设置的平面偏振光场中 ,用彩色数码照相机分别采集五幅等色线与等倾线相耦合的条纹图 ,根据相移法基本原理 ,就可以确定在 0～π/2范围内的等倾角。经过对径压缩圆盘的检验 ,实验结果与理论完全相符。该方法改进了单色光相移法的不足 ,对实验应力分析及其在工程结构强度设计中的应用将起积极的促进作用     

数字光弹性中五步彩色相移法及其应用

把相移法与光学彩色信息图像处理技术相结合,提出全场数字化确定主方向角的光弹性五步彩色相移法。其主要优点是采用最简单的白光平面偏振仪光学系统,由数码照相机采集五幅等色线与等倾线相互耦合的彩色条纹图,经计算机进行处理后,就可以得到[O～π／2]范围内单纯连续的等倾角相图;为了减少测量误差,在相移法中引入背景光强参与运算。对实验中存在的三种主要误差因素进行了定量分析,给出了具体的误差控制指标。用对径压缩圆盘问题的理论仿真模拟结果、基本实验和复杂平面及空间实际问题进行检验和对比,表明本方法是正确可行的。     

基于移相法的光学玻璃应力等倾角全场数字化测量

提出了一种用四步移相法实现光学玻璃应力等倾角全场数字化测量的方法。用数码相机拍摄椭圆偏振光场转过不同角度时的四幅出射光强图像,根据移相法的原理计算出在0°～90°范围内的等倾角β。通过对具有典型应力分布的光学玻璃进行实验验证表明,计算结果与实际情况相符。     

Phase shifting photoelasticity in white light

The availability of image acquisition systems has led to the development of digital photoelasticity both in monochromatic and white light. In particular white light has been used mainly with the following methods: Spectral Content Analysis, RGB photoelasticity and phase shifting photoelasticity. Phase shifting photoelasticity in the colour domain has been used effectively for the determination of the isoclinic parameter in order to reduce the influence of the isochromatic fringes. The method has been also proposed for the determination of the isochromatic fringe order. This paper concerns the general characteristics of phase shifting photoelasticity in the colour domain. Special attention is drawn towards the influence of spectral content of the light source, the spectral response of the colour camera filters, the dispersion of the birefringence and the error of quarter wave plates.     

光强和方位角误差对光弹性五步彩色相移法的影响

为了了解相移法中的各种参数所产生的误差对最终结果的影响 ,对一些主要参数做深入的误差分析是十分必要的。针对五步彩色相移法所用的白光入射平面偏振场的特点 ,只考虑光强、起偏镜和分析镜方位角所引起的误差影响就可以了。提出一个分析和评估这些误差源对五步彩色相移法确定等倾角参数所产生影响的方法 ,这对合理设计实验装置和执行正确的实验条件将起到积极的作用     

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).     

Digitally whole-field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique

This paper presents a whole-field method for automatic determination of the isoclinic parameter φ in photoelasticity. The method determines φ in the true phase interval (-π/2<φ+π/2) based on the four-step color phase-shifting approach and a new unwrapping method based on simple logic operations, a binary image and a gray-scale mask. A plane polariscope with a white light source is used for capturing raw photoelastic fringe images. The theoretical validation of the method is done with the problem of a circular disk under compression. Comparisons between theoretical and experimental results are also demonstrated. The experimental confirmation for the proposed method is tested with the photoelastic model having an isotropic point(s) and/or a singular point(s). The results show the method permits the reliable isoclinic parameter to be determined in the true phase interval with almost no defects of the isochromatic parameter.     

Whole field evaluation of stress components in digital photoelasticity—Issues, implementation and application

In photoelasticity, the method of obtaining the individual values of principal stresses/normal stresses separately is referred to as stress separation. Shear difference is one of the widely used techniques for stress separation in photoelasticity and one needs the value of fringe order and the isoclinic angle free of noise at every pixel over the domain. For accurate parameter determination, a ten-step phase shifting approach which uses a plane polariscope for isoclinic determination and a circular polariscope for isochromatic determination is proposed. A new quality guided approach for isoclinic unwrapping is developed. Isochromatic phasemap free of ambiguous zones is obtained by a new methodology and is unwrapped by a quality-guided approach. Whole field evaluation of stress components and its representation is then presented. The models used in this study are intentionally subjected to moderate loads showing a high level of isochromatic–isoclinic interaction. In view of this, the isoclinic data has several kinks which is found to cause streak formation in the whole field representation of separated stress components. An outlier smoothing algorithm is proposed for getting a smooth variation of the digital photoelastic parameters over the domain. Use of such smoothed data for stress separation has removed the streaks and has also greatly improved the accuracy of the separated stress components.     

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten‐step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. 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.     

数字光弹性相移法中全场等倾角和等差线相位

以径向受压圆盘为例,从弹性力学的角度详细分析了模型全场等倾角相位的情况,分析第一主应力的方向,在六步相移法的基础上提炼出圆盘全场等倾角相位和等差线的真实相位。采用有限元软件MARC与形函数拟合相结合的方法模拟径向受压圆环六步相移图和等差线相位图,可以推广到没有解析解或者解析解复杂的应力模型的光弹性实验模拟。通过径向受压圆盘实验验证了方法的可行性,实现光弹法中自动提取全场等差线的信息。     

Numerical analysis of phase-stepping interferometric photoelasticity for plane stress separation

A phase-stepping method for interferometric photoelasticity is proposed to determinate whole-field plane stress components. Isopachic phase can be obtained by rotating polarizer, second quarter-wave plate and analyzer at definite optical arrangements. On the other hand, isochromatic and isoclinic phases can be determined in a circular polariscope arrangement. Furthermore, a load-stepping method is adopted to overcome the wrong mathematic sign of the isochromatics in the ambiguity regions and the influence of initial interferometric fringes on the isopachics. Light intensities and phase-stepping formula for the proposed method are derived using Jones calculus. Simulation of a circular disk under diametral compression demonstrates the feasibility of the proposed method.     

Real-time phase-shift ing techniques for determining the photoelastic parameters: a theoretical comparison

Among data acquisition techniques in digital photoelasticity, the integrated phase shifting technique (IPST) can real-time analyze the photoelastic parameters at a video rate of the high speed CCD camera. In this paper, fourteen algorithms are described by different configurations of the rotating an analyzer at a constant rate and an output quarter-wave plate at another constant rate. The theoretical comparisons of the algorithms are given by the simulated phase distributions of the isochromatic and isoclinic parameters of the disk under two cases that the load keeps unchangeable or linearly increasing in exposure time of the camera. Then a guideline is given to alleviate the influence of the load changing with time on the IPST.     

Fourier transform profilometry based on composite structured light pattern

In Fourier transform profilometry (FTP), the zero frequency of the imaged patterns will influence the measurement range and precision. The π phase shifting technique is usually used to eliminate the zero order component, but this method requires the capture of two fringe patterns with a π phase difference between them, which will impede the real time application of the method. In this paper, a novel method is proposed, in which a composite structured light pattern is projected onto the object. The composite structured light pattern is formed by modulating two separate fringe patterns with a π phase difference along the orthogonal direction of the two distinct carrier frequencies. This method can eliminate the zero frequency by using only one fringe pattern. Experiments show that there is no decrease in the precision of this novel method compared with the traditional π phase shifting technique.     

Error analysis of phase shifting by varying the incident angle of parallel beams in shadow Moiré

A phase shifting technique by varying the incidence angle of parallel beams in a shadow Moiré has been demonstrated in the present investigation. Error of phase shifting with this technique is evaluated, since it is not a stringent technique in theory. Furthermore measures in order to increase its accuracy have been suggested. Feasibility of the proposed phase shifting technique has been verified with experiments. It was found that the difference between the recommended and conventional phase shifting techniques could be significantly optimized to be less than 5%.     

Photoelastic Analysis with a Single Tricolor Image

A new approach to simultaneous measurement of isochromatics and isoclinics from a single image using a tricolor light, called as the tricolor photoelastic technique, is proposed in order to enable and facilitate the analysis of time varying phenomena. Not only an apparatus of experiment but the whole analysis system and procedure are developed. Using a color digital camera and a tricolor light source under linear polarization, fringe order and the principal direction of birefringence are obtained from a piece of color image data by a single shot using the method proposed. It is emphasized that this method can be applicable to time varying phenomena in which good repeatability and reproducibility of experiments are not expected, since multiple exposures are not necessary for sufficient data acquisition in the completion of stress analysis.     

New approaches to the full-field analysis of photoelastic stress patterns

This paper presents two new methods that provide a complete solution for the automatic fringe analysis of photoelastic data. Previous solutions have not yet provided a complete full-field analysis of both fringe sets (isochromatic and isoclinic) over a multiple number of fringes with an automatic measurement of absolute magnitude. This paper reviews previous approaches and discusses the options along which this work has been directed. Specifically, two new algorithms are presented. Firstly, the combination of phase maps at three wavelengths in order to remove the isochromatic ambiguity at every π turning point, that would occur in a single phase map. Additionally, this algorithm allows the automatic measurement of absolute magnitude, providing the neutral axis is within the field of view. Secondly, a new method is proposed that removes the areas of 2π ambiguity in an isoclinic phase map by cross-correlating regions of low modulation at two different wavelengths. The algorithms are demonstrated by applying them to the analysis of an engine connecting rod. The rod was manufactured as a full-scale three-dimensional model in araldite (Ciba-Geigy CT200), from which a central slice was taken after having been stress frozen.     

Elliptically polarized white light photoviscoelastic technique and its application to viscoelastic fracture

The present paper demonstrates the successful application of the photoviscoelastic technique using elliptically polarized white light to the stress field evaluation of the crack growth in a viscoelastic strip. Using the proposed technique, which can determine both isochromatic and isoclinic parameters simultaneously from a single color image, the time-dependent stress state around a slowly propagating crack tip in a viscoelastic strip plate is successfully analyzed. Then, the time-dependent stress intensity factor extended for linearly viscoelastic materials is evaluated from the experimental results using a method based on the least squares. The results show that the proposed critical stress intensity factor for fast crack growth may be considered as a characteristic property of the material under monotonically increasing load.     

Automated photoelasticity: weighted least-squares determination of field stresses

The three-wavelength approach to phase-stepping photoelasticity as developed by the author is extended to determine automatically full-field stress tensor values. The only need for the user to calibrate the results is to give the material fringe value and the value of a stress at a single point. Four phase-stepped images illuminated by three wavelengths of light, that differ by prescribed increments, are collected using a semi-circular polariscope and an RGB CCD camera. A ramped phase map for the isochromatic parameter (α) is produced in the wrapped range −π/2<απ/2 that can be calibrated automatically. The value of the isoclinic angle (θ) is determined in the wrapped range −π/4<θπ/4. A discrete cosine transform algorithm has been developed to separate the stresses into Cartesian components. A convenience of the method is that accurate results can be obtained using a least-squares error minimisation process. The results obtained from experimental testing of a disc-in-compression specimen using transmission photoelasticity presented in comparison with theoretical solutions demonstrate the accuracy of the new approach.     

Instantaneous phase shifting arrangement for microsurface profiling of flat surfaces

Phase shifting interferometry is a well-established technique for non-contact surface profile measurement. Though phase shifting technique has many advantages, it is marred by a few inaccuracies due to the vibration and mechanical movement of the phase shifter itself. Significant amount of work is reported to theoretically compensate these error sources. But for a few works, prominent achievements have not been reported in eliminating these error sources in phase shifting interferometry. In this paper, a novel optical layout, in combination with instantaneous phase shifting interferometry is described. Experiments were carried out with this setup on a super mirror with a λ/20 surface roughness, to demonstrate the validity of the principle.