Error analysis for determination of stress intensity factors from isochromatic crack tip fringe patterns

A statistical error analysis for the stress intensity factor as determined by the classical apogee point method is represented. Random errors in the measurements of apogee distance, tilt angle and crack tip position are considered the most typical sources for inaccuracies in the determination of the stress intensity factor.     

Characterization of isochromatic fringe patterns for a dynamically propagating interface crack

The isochromatic fringes surrounding a crack propagating along a bimaterial interface have been developed and characterized. A parametric investigation has also been conducted to study the influence of various fracture parameters on this isochromatic fringe pattern. The relevant fracture parameters of interest were the crack-tip velocity, the mode mixity of loading and the non-singular stress field component. In all the cases the fringe pattern was compared with the more familiar patterns that are generated for the case of crack propagation in homogeneous media. It was found that both the crack tip velocity and the mode mixity of loading have a significant effect on the size and shape of the isochromatic fringe pattern surrounding a crack tip propagating along a bimaterial interface. However, the non-singular stress field component was found not to have a substantial effect on the fringe pattern. This is in contrast with the case of crack propagation in homogeneous media, where the non-singular stress field component determines the tilt of the fringe contours. The paper also presents an appropriate scheme to analyze experimental fringe contours to extract the various fracture parameters of interest. Finally, this scheme is employed to analyze actual experimental data from a typical bimaterial interface fracture experiment.     

A new method of determining the stress intensity factor K from isochromatic fringe loops

This paper describes the four parameter method of analysis for determining the stress intensity factor K. Dynamic photoelastic isochromatic fringe patterns associated with cracks propagating in centerpin loaded, eccentric-pin-loaded and crack-line-loaded SEN specimens of Homalite 100 were recorded. Data was obtained for tests over a range of crack velocities from arrest to the terminal velocity of 14,900 in. sec (378 m sec).Six measurements describing the size and shape of the experimental isochromatic loops were used to determine the stress intensity factor K by employing a comparison function to match analytical and experimental results. The analytical isochromatic loops were generated with a Westergaard stress function of the form $\text{Z(z) =}\text{K}\text{√2πz}\text{{1 + β(}\text{z}\text{a})}$ and a superimposed normal stress σ_Ox=αK|√2πz which acts parallel to the direction of crack extension. Results were obtained by the computer program (FRACTURE) for different values of the four parameters to give 8925 analytical fringe loops. Another computer program (SEARCH) was used to find a small group of solution which given very low values of the comparison function f_c. The final solution which contains the value of K was obtained from the small group by selecting the most consistent solution.The results obtained for Homalite 100 show that K_min and K_k are nearly the same and that ? increases abruptly from 0 to about 10,000 in./sec (254 msec) for modest increases in K above 400 psi √in. (4.4 × 10⁵$\text{Nm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$). Further increases in crack velocity require significant increases in K until terminal velocity is     

Complete fringe order determination in scanning white-light interferometry using a Fourier-based technique

White-light interferometry uses a white-light source with a short coherent length that provides a narrowly localized interferogram that is used to measure three-dimensional surface profiles with possible large step heights without 2π-ambiguity. Combining coherence and phase information improves the vertical resolution. But, inconsistencies between phase and coherence occur at highly curved surfaces such as spherical and tilted surfaces, and these inconsistencies often cause what are termed ghost steps in the measurement result. In this paper, we describe a modified version of white-light interferometry for eliminating these ghost steps and improving the accuracy of white-light interferometry. Our proposed technique is verified by measuring several test samples.     

Evaluation of optical coherence quantitation of analytes in turbid media by use of two wavelengths

We introduce a novel method for determining analyte concentration as a function of depth in a highly scattering media by use of a dual-wavelength optical coherence tomography system. We account for the effect of scattering on the measured attenuation by using a second wavelength that is not absorbed by the sample. We assess the applicability of this technique by measuring the concentration of water in an Intralipid phantom, using a probe wavelength of 1.53 mum and a reference wavelength of 1.31 mum. The results of our study show a strong correlation between the measured absorption and the water content of the sample. The accuracy of the technique, however, was limited by the dominance of scattering over absorption in the turbid media. Thus, although the effects of scattering were minimized, significant errors remained in the calculated absorption values. More-accurate results could be obtained with the use of more powerful superluminescent diodes and a choice of wavelengths at which absorption effects are more significant relative to scattering.     

Fourier fringe processing by use of an interpolated Fourier-transform technique

Recently a powerful Fourier transform technique was introduced that was able to extract the phase from only one image. However, because the method is based on the two-dimensional Fourier transform, it inherently suffers from leakage effects. A novel procedure is proposed that does not exhibit this distortion. The procedure uses localized information and estimates both the unknown frequencies and the phases of the fringe pattern (using an interpolated fast Fourier transform method). This allows us to demodulate the fringe pattern without any distortion. The proposed technique is validated on both computer simulations and the profile measurements of a tube.     

Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element

Recently, the authors (Karihaloo and Xiao, 2001a-c) extended the hybrid crack element (HCE) originally introduced by Tong et al. (1973) for evaluating the stress intensity factor (SIF) to calculate directly not only the SIF but also the coefficients of the higher order terms of the crack tip asymptotic field. Extensive studies have proved the versatility and accuracy of the element for pure mode I problems. This study is to show the versatility of the element for mode II and mixed mode cracks. Accuracy of the SIF and coefficients of higher order terms is validated by comparing with the available results in the literature, or results obtained by the boundary collocation method, which is powerful for relatively simple geometries and loading conditions.     

Pulse-laser electroholography by use of interference fringe patterns captured by a CCD

Digital holography is combined with a pulse-laser electroholographic system for a real-time three-dimensional display. Owing to the one-dimensional characteristics of the Bragg-regime acousto-optic spatial-light modulator, vertical parallax cannot be generated from the acoustic signal propagating along the fan-shaped beam direction of the incident laser. To obtain a proper interference pattern, we attach a horizontal slit to the confocal lens system for recording the fringe data, significantly reducing the bandwidth of the vertical fringe data. When the bandwidth-reduced fringe data are displayed by use of a pulse-laser electroholographic system, the clarity and the quality of the image are found to be appreciably improved.     

Thulium:ZBLAN blue fiber laser pumped by two wavelengths

We demonstrate and analyze an upconversion blue fiber laser pumped by two wavelengths. Lasing at 0.48 mum with very low pump threshold power is obtained from a Tm-doped fluorozirconate fiber that is counterpropagating pumped by 1.21- and 0.649-mum light. We employed a rate-equation analysis using parameters obtained by fitting to the experimental data to predict the 0.48-mum output characteristics as a function of fiber length and output reflectivity.     

Direct index of refraction measurements at extreme-ultraviolet and soft-x-ray wavelengths

Coherent radiation from undulator beamlines has been used to directly measure the real and imaginary parts of the index of refraction of several materials at both extreme-ultraviolet and soft-x-ray wavelengths. Using the XOR interferometer, we measure the refractive indices of silicon and ruthenium, essential materials for extreme-ultraviolet lithography. Both materials are tested at wavelength (13.4 nm) and across silicon's L2 (99.8 eV) and L3 (99.2 eV) absorption edges. We further extend this direct phase measurement method into the soft-x-ray region, where measurements of chromium and vanadium are performed around their L3 absorption edges at 574.1 and 512.1 eV, respectively. These are the first direct measurements, to our knowledge, of the real part of the index of refraction made in the soft-x-ray region.     

Recovery of absolute phases for the fringe patterns of three selected wavelengths with improved anti-error capability

Abstract

In a recent published work, we proposed a technique to recover the absolute phase maps of fringe patterns with two selected fringe wavelengths. To achieve higher anti-error capability, the proposed method requires employing the fringe patterns with longer wavelengths; however, longer wavelength may lead to the degradation of the signal-to-noise ratio (SNR) in the surface measurement. In this paper, we propose a new approach to unwrap the phase maps from their wrapped versions based on the use of fringes with three different wavelengths which is characterized by improved anti-error capability and SNR. Therefore, while the previous method works on the two-phase maps obtained from six-step phase-shifting profilometry (PSP) (thus 12 fringe patterns are needed), the proposed technique performs very well on three-phase maps from three steps PSP, requiring only nine fringe patterns and hence more efficient. Moreover, the advantages of the two-wavelength method in simple implementation and flexibility in the use of fringe patterns are also reserved. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.     

Stabilized phase-shifting fringe analysis by use of current-induced frequency modulation of laser diodes

A closed-loop phase-shifting Fizeau-type interferometer was constructed that uses direct frequency modulation of a laser diode. The interferometer is servo controlled entirely in the phase domain, where optical phases are detected by two-frequency optical heterodyning. A detailed study of stabilization of the interferometer under feedback control was conducted both experimentally and theoretically. The interferometer showed good stability against vibration up to 200 Hz. The stabilization factors obtained experimentally are in good agreement with the theoretical calculations. The phase-shifting experiment was accomplished with high precision as well as with high stability against external disturbances. The profile measurement of a mirror surface was made with a phase-shifting analysis algorithm, and good measurement reproducibility of lambda/60 in the root-mean-square value was obtained for ten measurements within a period of 20 min.     

Direct extraction of phase gradients from Fourier-transform and phase-step fringe patterns

An approach to computing pixel-by-pixel gradients of optical phase directly from digitally encoded Fourier-transform or phase-stepped fringe patterns is described. This approach can be classified as a phase unwrapping but is really a sine-cosine demodulation technique that finds its roots in the differential cross-multiplier phase-demodulation technique commonly used by the optical fiber sensor community. This technique is algorithmically simple, does not rely on a computation of the arctangent, and therefore is not subject to some of the limitations of the standard phase-unwrapping methodologies. The proposed phase-gradient technique is demonstrated by the calculation of strain fields from moir6 interferometric fringe patterns.     

A new method for the theoretical determination of isochromatic fringes in plane elasticity crack problems

International Journal of Fracture -     

Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform

A novel technique that uses a fan two-dimensional (2D) continuous wavelet transform (CWT) to phase demodulate fringe patterns is proposed. The fan 2D CWT algorithm is tested by using computer generated and real fringe patterns. The result of this investigation reveals that the 2D CWT technique is capable of successfully demodulating fringe patterns. The proposed algorithm demodulates fringe patterns without the requirement of removing their background illumination prior to the demodulation process. Also, the algorithm is exceptionally robust against speckle noise. The performance of the 2D CWT technique in fringe pattern demodulation is compared with that of the 1D CWT algorithms. This comparison indicates that the 2D CWT outperforms its 1D counterpart for this application.     

The generation of phase singularities at millimetre wavelengths by the use of a blazed grating

Abstract

A specially configured reflection blazed grating has been designed for operation at millimetre wavelengths to enable the efficient conversion of an incident plane wave into a beam with a phase singularity.     

Analytical determination of reflection-peak wavelengths of chirped sampled fiber Bragg gratings

An analytical expression for calculating the position of the reflection-peak wavelength of a chirped sampled fiber Bragg grating (C-SFBG) is obtained for what is believed to be the first time. Using Fourier theory, the chirped sampling function of the C-SFBG is expanded, and an equivalent local Bragg period is then obtained to derive the expression of the peak wavelength. The calculated results based on the expression are in excellent agreement with the numerical reflection spectra obtained by the conventional transfer-matrix method.