Noise removal in three-fringe photoelasticity by adaptive colour difference estimation

Three-fringe photoelasticity (TFP) can give the total fringe order from a single-colour isochromatic fringe field. In TFP, the total fringe order is obtained by comparing the colour of the unknown photoelastic fringe pattern with a calibration specimen. Comparison is conventionally done by minimising the colour difference error. This leads to misidentification of fringe order in some regions. A new colour difference formula is proposed with an additional term, which ensures continuity of fringe order data over the domain. Fringe order data obtained by conventional TFP is used as base data and the new method is termed as refined TFP. To enable applicability of the technique to arbitrary geometries, a new boundary identification technique is developed. The new method is demonstrated with some example problems.     

平面偏振光场光弹性实时相移法

光弹性法可广泛用于二维、三维应力或应变场的研究。根据偏振相移法的原理,提出一种新的积分相移法,并设计了用于全场等倾线和等差线实时分析的光弹性仪。在正交偏振光场下,按一定速度同步旋转起偏镜和分析镜,CCD摄像机可连续获取四幅相移光弹图像,由CCD像敏单元积分获得其光强值,通过所提出的相移法运算,可以迅速地得出全场等倾角和等差线的相位值。该方法和装置不仅可用于光学原件及玻璃制品的高速检测,而且也可用于随时间缓慢变化的光弹性分析中。     

A numerical comparison of real-time phase-shifting algorithms

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 linear 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.     

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).     

Noise removal in three-fringe photoelasticity by median filtering

In three-fringe photoelasticity, the total fringe order is obtained by comparing the colour of the unknown photoelastic fringe pattern with a calibration specimen. Comparison is conventionally done by minimising the colour difference error using the least square method. This can give the total fringe order from a single-colour isochromatic field. This technique, however, leads to misidentification of fringe order in some regions. Some researches have proposed boundary identification technique to remove this error. Whilst this ensures continuity of fringe order data over the domain, this does not provide accurate results for every region. A simpler method has been proposed in this paper using median filtering which can be easily undertaken using any standard image processing software. The method is demonstrated with the help of a simple example of disc under diametral compression.     

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.     

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.     

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.     

实时确定光弹性参数的积分相移法

积分相移法可以实时测量光弹性参数,在光弹性实验的某些变载测试中将有一定的发展潜力。推导了积分相移法三种典型算法,通过对径压缩圆盘问题的理论仿真模拟,考察了载荷变化对积分相移法的影响,给出了降低这种影响的具体措施。     

Study of shear transfer in Al/epoxy joint by digital photoelasticity

An improved six-step phase-shifting method is proposed for calculating full-field shear stress based on a four-step color phase-shifting method in digital photoelasticity. The method was verified using a disk under diametral compression and then applied to an aluminum alloy/epoxy joint for studying the shear transfer behavior. Experimental results revealed that the isochromatic fringe order and shear stress at the bonding interface are distributed continuously and increased with compression. In particular, an antisymmetric thermal residual shear stress appears at the bonding interface, because of the difference in the thermal expansion coefficients of Al and the resin. This indicates that the thermal residual shear stress at the bonding interface is self-balanced and reaches a peak at the edges of the bonding interface. The load transfer is realized by the shear band from the bonding interface to the bottom support. Basically, the bonding interfacial shear stress is balanced with the load.     

Review of RGB photoelasticity

Automatic methods of photoelasticity have had a significant progress with the development of automatic acquisition and image processing methods. This article concerns RGB photoelasticity, which allows the determination of the photoelastic retardation using, usually, a single acquisition of the isochromatic fringes in white light by a colour camera. In particular, the article presents an overview of the main characteristics of RGB photoelasticity that is influence of the quarter-wave plate error, number of acquisitions, type of light source, determination of low and high fringe orders, methods for searching the retardation, scanning procedures, calibration on a material different from that under test, combined use of the RGB and phase shifting methods. A short section on the applications of RGB photoelasticity completes the article.     

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.     

An investigation of cracking in brittle solids under dynamic compression using photoelasticity

Crack initiation in brittle materials was experimentally studied using photoelasticity under dynamic loading conditions with particular attention to the frictional characteristics of the microcracks. Two pieces of Homalite-100 were bonded except central region to prepare plate specimens with an inclined center crack. An edge of the specimen was impacted with and without lateral confinement. In situ photoelastic (isochromatic) fringes were obtained using a high-speed camera. Initial direction and profile of wing crack was the same as in static loading tests. Effect of crack surface roughness and lateral confinement on fringe pattern is discussed. Average speed of wing crack propagation was about 100 m/s and wing cracks from a crack with higher friction coefficient propagated faster than from a smooth crack.     

Photoelasticity stress analysis using carrier fringe and FFT techniques

A novel carrier fringe technique for photoelasticity stress analysis is described and verified experimentally. Linear carrier fringes generated by using a quartz wedge are superimposed on fringes formed by the stressed model. The resultant fringe pattern is then captured using a charge coupled device camera and stored in a digital frame buffer. A fast Fourier transform method is then used to process the complete photoelastic fringe image over the whole surface of the model. The experiment also uses a minimum spanning tree phase unwrapping strategy to create a continuous map of the whole stress field. Finally, the whole principal stress difference field has been calculated and plotted from one single exposure showing the methods' potential for use as a reflection analysis system suitable for application to nonstationary objects and complicated stress patterns.     

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.     

相移法获取三维光弹特征相位差的方法

对于三维光弹模型,次主应力及其方向沿入射光连续变化,根据光学等效的原理,可以将三维光弹模型等效为一个包含线性相位延迟器和旋光器的光学模型。在集成光弹法中,对于每一个测量点,研究者必需通过实验获取三个特征参数。提出了一种用于确定集成光弹中全场特征相位差的五步相移法,给出了偏振光场中元器件的设置方法,并运用Jones算子推导出相移法得出的光强公式。最后使用斜射法对径向受压圆盘进行实验,验证了方法的有效性。     

Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique

In this paper a new whole field technique for determination of characteristic parameters in integrated photoelasticity using phase-shifting methodology is proposed. Appropriate optical arrangements necessary for this are presented and the intensity equations are obtained by Jones calculus. The new methodology is verified experimentally for the problem of a circular disk under diametral compression viewed in oblique incidence.     

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°.     

平面偏振光场光弹性实时相移法的误差分析

研究了在获取图像的过程中转角变化、偏振片方位角误差及试件所受的载荷变化对平面偏振光场光弹性实时相移法的影响。通过理论分析与数值模拟,讨论了在不同条件下等倾角相位误差。等倾角相位误差随着每场转角变化的增加而增大;偏振镜方位角误差使等倾角相位产生平移;试件所受的载荷变化会引起所采集的光弹性图像误差,对等倾角的计算结果会产生较大的影响。研究结果对合理设计光弹性实验装置、正确评价和执行实验技术具有积极的指导作用。