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.     

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.     

Numerical simulation of isopachic parameter determined by phase-stepping interferometric photoelasticity: errata

The authors regret that errors occurred in the previous paper[1]. If the polarizer and analyzer are generally represented by Pβ with arbitrary angle β to the reference axis in Fig. 1,original Eq. (8) can be rewritten as     

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.     

Digital shifting photoelasticity with optical enlarged unwrapping technology for local stress measurement

In this paper, photoelasticity combined with phase shifting technology is used to obtain stress distribution within the stress concentration zone. Both the optical enlarged unwrapping technology and the combined path shear difference technology are provided for evaluating the local stress information. By means of a phase shifting photoelastic experiment of a diametric-compressed disc, the stress components surrounding the local loading zone are determined. The results show not only a good improvement compared with conventional photoelastic analysis but also a good agreement with theoretical data.     

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     

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.     

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).     

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.     

Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis

Combining color imaging with phase shifting, a technique named five-step color phase shifting is presented to determine the whole-field isoclinic parameter. Relevant theory is derived and explicit conditions for directly determining the isoclinic parameter in the range of [0,π/2] are given. The unloaded light intensity of the model is systematically studied. A color camera recorded five isoclinic images coupled with isochromatics from a plane polariscope with five different settings, respectively. Experiments have been carried out with a circular disk under diametral compression and errors have been analyzed and estimated. This technique utilizes white light, which avoids undefined isoclinics near the locations where the isochromatics exist and will have active effect on experimental stress analysis and structural strength design.     

Theoretical analysis of third order interferometric autocorrelation signals for enhanced sensitivity towards pulse chirp and asymmetry

In this paper, we report theoretical analysis of third order interferometric autocorrelation to achieve enhanced sensitivity towards pulse chirp and asymmetry. The analysis is based on interferometric correlative envelope (ICE) functions and ICE difference signals derived from interferometric autocorrelation signals. The third order ICE signals are compared with second order ICE signals obtained from a second order interferometric autocorrelation signals. It is shown that one out of six third order ICED signals may be used to obtain simultaneous detection and measurement of pulse chirp as well as pulse asymmetry of the chirped ultrashort laser pulse. This is in contrast to use of two out of three second order ICED signals for simultaneous detection of pulse chirp and asymmetry.     

Numerical-experimental hybrid method for stress separation in digital gradient sensing method

A numerical-experimental hybrid method for the stress separation in the digital gradient sensing (DGS) method is proposed in this study. In the proposed hybrid method, boundary conditions for a local finite element model, that is, nodal force along boundaries are inversely determined from experimental values obtained by the digital gradient sensing method. The hybrid method follows two stages. In stage 1, the DGS method measures the Cartesian stress gradient components directly and, subsequently, the sum in Cartesian stresses at all interesting points on the surface; stress sum are used to compute the unknown boundary conditions for the local model. In stage 2, the individual stress components are calculated by the direct finite element method using the computed boundary conditions from stage 1. The effectiveness is demonstrated by applying the proposed method to a stress concentration problem involving concentrated load acting on an edge of a large planar sheet. The individual stress components thus determined are summed and compared with analytical stress sum, confirming the effectiveness and accuracy of the proposed technique.     

Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers

We present a robust and accurate numerical algorithm for calculating energy-minimizing wavelengths of equilibrium states for diblock copolymers. The phase-field model for diblock copolymers is based on the nonlocal Cahn–Hilliard equation. The model consists of local and nonlocal terms associated with short- and long-range interactions, respectively. To solve the phase-field model efficiently and accurately, we use a linearly stabilized splitting-type scheme with a semi-implicit Fourier spectral method. To find energy-minimizing wavelengths of equilibrium states, we take two approaches. One is to obtain an equilibrium state from a long time simulation of the time-dependent partial differential equation with varying periodicity and choosing the energy-minimizing wavelength. The other is to directly solve the ordinary differential equation for the steady state. The results from these two methods are identical, which confirms the accuracy of the proposed algorithm. We also propose a simple and powerful formula: h = L¹/m, where h is the space grid size, L¹ is the energy-minimizing wavelength, and m is the number of the numerical grid steps in one period of a wave. Two- and three-dimensional numerical results are presented validating the usefulness of the formula without trial and error or ad hoc processes.     

Evidence of microphase separation in controlled pore glasses

The phase separation of a mixture of water and isobutyric acid (iBA) confined in the pore space of Controlled Pore Glass (CPG) 10-75 has been studied by ¹H NMR relaxometry and ¹H-pulsed field gradient (PFG) diffusion measurements. For an acid-rich mixture (mass fraction 54 wt% iBA), evidence of a phase separation process in the pores was obtained, which occurs in a temperature window between 32 and 39 °C, as indicated in the PFG data by an anomalous temperature dependence of the diffusion coefficient and in the relaxation data by a bi-exponential magnetization decay. The phase separation temperature of the mixture in the pore is slightly lower than in the bulk mixture of the same composition (41 °C) and extends over a finite temperature range. A qualitative model of the phase separation process in the pores is developed, which assumes a temperature-dependent domain-like structure of the liquid below the phase transition temperature and a breakdown of these domains upon reaching the transition temperature.     

Uncertainty analysis of temporal phase-stepping algorithms for interferometry

We have addressed the problem of the uncertainty evaluation of phase values rendered by two popular algorithms: the N-bucket and the (N + 1)-bucket, both used to exploit temporal phase-stepping techniques. These algorithms, are mainly affected by errors in the calibration of the piezoelectric transducers used to achieve the phase shift, external vibration and optical noise. We have characterized and compared the influences of these errors on the phase uncertainty. We applied a Monte Carlo-based technique of uncertainty propagation that allowed us to consider in the uncertainty evaluation the simultaneous contributions of different error sources. The uncertainty evaluation was performed for phase values in the range (0, 2π), with different values of N and assuming that the phase was calculated from fringe patterns generated by using either Moiré interferometry or electronic speckle-pattern interferometry. We found that the uncertainties associated with the phases rendered by both algorithms are similar and they can be significantly affected by the optical noise and the value of N.     

Structural analysis of the phase separation in magnetic semiconductor (Zn,Cr)Te

We have studied the structural properties of the phase separation in Zn_1−xCr_xTe films grown by MBE with a relatively high Cr composition x∼0.2. In the combined analyses using TEM and EELS, it has been revealed that the Cr-aggregated regions are composed of precipitates of the hexagonal structure, which are formed in a particular crystallographic relation with the zinc-blende (ZB) structure of the matrix that the c-plane of the hexagonal structure nearly parallel to the (1 1 1) plane of the ZB structure. In the XRD measurements, the diffraction from the hexagonal precipitates has been detected in the ω-scan. From the measurements on the series of films grown at different temperatures, it has been suggested the hexagonal precipitates were formed in a larger quantity with the increase in growth temperature.     

Low-and high-dimension limits of a phase separation model

We study a simple zero-temperature model for phase separation of a binary alloy, in which nearest-neighbor interchange can occur if the fraction of AB pairs is not thereby increased. We present analytic results for the one-dimensional case and numerical results for the infinite dimensionality limit on a Cayley tree. In neither limit does the final fraction of AB pairs agree with the dimension-independent result found previously ind=3, 4, 5.