An adaptive scanning scheme for effective whole field stress separation in digital photoelasticity

In photoelasticity, the method of obtaining the individual values of principal stresses/normal stresses separately is referred to as stress separation. Shear difference method is one of the widely used techniques for stress separation in digital photoelasticity. Normally a simple raster scanning approach is used in shear difference method in which stress separation is carried out for all the lines within the model domain by either row-wise horizontally or column-wise vertically starting from the boundary pixels. This requires the presence of a free boundary to start the integration scheme for every row of interest, which is not always possible in most of the practical problems. In order to overcome this, in this paper, an adaptive scanning scheme is proposed so that stress separation can be carried out even if there is only one free boundary pixel available in the model. The new scanning scheme is validated using the theoretically generated data for the problem of a ring subjected to internal pressure. Later, the applicability of this scheme is demonstrated by using two other example problems.     

Tensor field tomography of residual stresses

An approximate method is proposed for determining residual stresses in elonagted transparent articles featuring weak variation of the stress field along the axis. The proposed method is a generalization of the well-known method of determining internal stresses in optic fibers based on the integrated photoelasticity measurements. Complete determination of the stress tensor components is performed within the framework of the concept of temperature-dependent residual stresses.     

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.     

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.     

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.     

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。     

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.     

Stress evaluation of Through-Silicon Vias using micro-infrared photoelasticity and finite element analysis

The Through-SiliconVias (TSV) is a key component of three dimensional electronic packaging. Obtaining its stresses is very important for evaluating its reliability. A micro-infrared photoelasticity system with a thermal loading function was built and applied to characterize the stresses of the TSV structure. Through testing it was found that the stress of each TSV is different even if their fabrication technology is exactly the same, that different TSVs obtain their stress free states at different elevated temperatures, and that their stress free states are maintained even when the temperature is further elevated. A finite element model was used to quantitatively determine the stresses of a TSV under different stress-free temperatures. Different virtual photoelasticity fringe patterns were then created based on the principle of photoelasticity and the simulated stresses. Comparing the virtual fringe patterns with the experimental pattern, an appropriate virtual photoelasticity fringe pattern and the corresponding stresses of TSV were determined     

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。     

Whole-field digital measurement of principal stress directions in photoelasticity

A method that uses three light-field isoclinic images and the associated light-field unloaded model (or white) images for whole-field digital determination of the principal stress directions in photoelasticity is presented. Relevant theory is derived and explicit conditions for directly determining the directions to the range 0–π/2 are given. Tests of this method on a directly loaded two-dimensional disc and a stress frozen photoelastic slice are demonstrated. The results agree well with the values obtained from the manual method and/or the theory.     

Integrated photoelasticity for nondestructive residual stress measurement in glass

The paper gives a review of integrated photoelasticity and of its application for residual stress measurement in glass. By considering the basic theory of the method, two particular cases, the case of weak birefringence and that of constant principal stress axes, are picked up. It is shown that integrated photoelasticity is actually optical tensor field tomography. Its peculiarities in comparison with scalar field tomography are considered. Since directly integrated photoelasticity allows for the measurement of only some of the stress components, analytical or numerical methods are to be used for complete determination of the stress field. Nonlinear optical phenomena, interference blots and fringe bifurcation, are briefly considered. Several examples illustrate the application of the method.     

The case of weak birefringence in integrated photoelasticity

The main difficulties connected with the application of integrated photoelasticity are as follows: (1) in general (when rotation of the principal axes is present) one has to measure three characteristic parameters for each ray (instead of two in two-dimensional photoelasticity and in the frozen stress method); (2) the characteristics parameters are connected with the stress distribution in a very complicated manner: to determine the stress distribution from their basis is difficult.If the birefringence is weak, then measurements can be simplified. In the latter case a usual plane polariscope may be used for measurements, and simple approximate integral relationships between the experimental data and the distribution of birefringence on the ray are valid, if rotation of the principal axes is moderate. The paper attempts to establish the domain where application of these relationships is justified. By the aid of numerical experiments it is shown that simple integral relationships can be applied if optical retardation is less than a quarter of a wavelength and rotation of the principal axes is less than π/6. In the latter case by investigating a three-dimensional model the parameter of isoclinic and the optical phase retardation are measured exactly in the same way as by investigating a two-dimensional model.     

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).     

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。     

Fresnel integral in the complex form: Its new representation,interpretation, and application in problems of wave beam diffraction

A new representation for the complex Fresnel integral, allowing for its transformation into the trigonometric form, and its new interpretation based on the 2D Cornu spiral and a 3D spiral with a smooth envelope surface have been obtained. Within this representation the integral is separated into a constant part and a rapidly oscillating additive. The former is responsible for the geometrical-optical field transport, and the latter implements diffraction. This separation is exact. Based on this approach, we have proposed and implemented a new method for solving the problems of wave beam propagation in the near-field zone on a large-scale grid at large optical distortions of the wavefront, with a transport of the initial-wave amplitude and phase. The amplitude is approximated by a step or linear function, and the phase is approximated taking into account the local linear tilt and focusing of the wavefront. The physical meaning of the solutions obtained is established. The approach proposed allows one to perform regular calculations of wave field propagation in the near-field zone on a large-scale grid (up to ∼10 points within aperture) at large initial wavefront aberrations (up to ∼100λ or more).     

Residual stresses deriving from holographic interferometry data on a base of inverse problem solution

A transition model, which is capable of obtaining both membrane and bending residual stress components from initial experimental information, is developed for thin-walled plane structures. The determination of residual stresses is based on the combined implementing of the hole-drilling method and reflection hologram interferometry. Required input data are obtained by simultaneous measurements on through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Superimposed residual stresses field, which consists of both membrane and bending components, is a reason for the various deviations of each specific fringe pattern from an ideal form. This fact is a clear experimental indication of the bending stress contribution in a total stress field. Two ways of decomposition of superimposed residual stresses field are proposed and analysed in detail. Emphasis is laid on a careful quantitative formulation of the inverse problem needed for an accurate deriving both membrane and bending residual stress components. It is shown that an availability of two-side initial data is both an essential and necessary condition of such a formulation. Detailed analysis of an accuracy of the results obtained is performed. This analysis is based on a wide set of both actual interferograms and analogous reference fringe patterns related to superimposed residual stress field under study. Comparing residual stress values obtained proceeding from one-side and two-side data are presented for different types of superimposed field of interest.     

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.     

Three-dimensional computer modeling of electromagnetic fields: A global lookback lattice truncation scheme

A new lattice truncation scheme for the finite difference time domain approach to the solution of Maxwell's equations has been developed. The problem space is truncated near the sources and the field components on its boundary are generated from those field values known at retarded times on an interior surface one cell from it with an integral representation of the electromagnetic field. The numerical implementation of this global lookback scheme is discussed. Examples which have been used to determine its characteristics and its validity are given.