A Measurement Method for Birefringent Plate using Elliptically Polarized Light

Abstract:  The principal axis ψ and total relative phase retardation ρ _tot of a birefringent plate are obtained automatically using an elliptically polarized incident light source and a phase unwrapping technique. The technique overcomes the error associated with the quarter-wave plate by making use of incident light of different wavelengths, and the unwrapping technique allows ψ and ρ _tot to be determined using an arctangent function without interpolation or construction of a calibration table. The proposed method is validated analytically and experimentally for a circular disk under diametral compressive load.     

Phase unwrapping method for three-dimensional stress analysis by scattered-light photoelasticity with unpolarized light

In scattered-light photoelasticity with unpolarized light, the secondary principal stress direction psi and the relative phase retardation rho in a three-dimensional stressed model with rotation of the principal stress axes can be obtained by use of Stokes parameters. For completely automated stress analysis, measurements of the total relative phase retardation and the secondary principal stress direction over the entire field are required, and it is necessary to unwrap psi and rho. A phase unwrapping method is thus proposed for the determination of these values based on scattered-light photoelasticity. The values are easily obtained via an arctangent function, overcoming the error associated with the quarter-wave plate by employing an incident light of different wavelengths. The proposed technique provides automated and nondestructive determination of the total relative phase retardation and the secondary principal stress direction in a model exhibiting rotation of the principal stress axes.     

Phase unwrapping through demodulation by use of the regularized phase-tracking technique

Most interferogram demodulation techniques give the detected phase wrapped owing to the arctangent function involved in the final step of the demodulation process. To obtain a continuous detected phase, an unwrapping process must be performed. Here we propose a phase-unwrapping technique based on a regularized phase-tracking (RPT) system. Phase unwrapping is achieved in two steps. First, we obtain two phase-shifted fringe patterns from the demodulated wrapped phase (the sine and the cosine), then demodulate them by using the RPT technique. In the RPT technique the unwrapping process is achieved simultaneously with the demodulation process so that the final goal of unwrapping is therefore achieved. The RPT method for unwrapping the phase is compared with the technique of least-squares integration of wrapped phase differences to outline the substantial noise robustness of the RPT technique.     

Fiber bragg grating strain sensor demodulation with quadrature sampling of a mach-zehnder interferometer

A simple and highly sensitive phase-demodulation technique is proposed, and its use for a fiber Bragg grating strain sensor is experimentally demonstrated. Sampling a phase-modulated Mach-Zehnder output with controlled time delay produced two quadrature data streams that have relative quadrature phase difference (90 degrees ). The Bragg wavelength-dependent phase information is extracted by application of digital arctangent function and phase unwrapping to the quadrature signals. By use of this technique with a reference grating, strain sensing at as much as a 30-kHz sampling rate was obtained with strain resolution of 3.5 microstrains and 6 nanostrains/ Hz in quasi-static and dynamic strain measurements, respectively.     

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch-crack problem is treated in two different ways: if the non-dimensional crack length l /ρ ( l = crack length; ρ= notch root radius) is smaller than the transition crack length l _T/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ ρ is larger than l _T/ρ, the notch-crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, l _T, and for the geometric factor F = K _I/(1.1215K_tσ√π l ) are developed for various notch problems for the crack length range l ≦ l _T. It is found that the stress (σ_yy) normalized by the peak stress (σ_peak), σ_yy/σ_peak, for the pre-cracked component is very similar to the geometric factor for short cracks.     

Assessment of the period to fatigue macrocrack initiation near stress concentrators by means of strain parameters

A new approach to the experimental assessment of the local strain at a stress concentrator has been presented. It is based on a procedure of notch opening displacement measurements at certain points in the vicinity of a notch related to the effective notch radius ρ _eff = ρ + d * , where ρ is the notch radius and d * is a material constant. Different stress concentrators in structural elements were modelled for a wide variation of notch radii ( ρ = 0.1–6.5 mm) and different geometries of specimens. Hence, a basic relationship, which directly relates the local strain range Δ ε* to the period of fatigue macrocrack initiation N _i has been established. Thus, by applying the value of Δ ε* , assessed from a direct measurement at the notch root, it is possible to determine the period N _i to initiate a fatigue macrocrack of length a _i = d * for some structural components of complicated geometry.     

THE STRESS INTENSITY FACTOR OF SMALL CRACKS AT NOTCHES

Abstract— It was found in a previous publication that stress fields around notches are quantitatively very similar, if the peak stress at the notch root (σ_peak) and the notch root radius ( ρ ) are the same. As a consequence, small cracks (length l ) should have the same stress intensity factor, if σ_peak and ρ are similar. This implies that the geometry factor C in
should primarily depend on l/ρ only, and not on other dimensions. Available data on calculated K values was analysed, which confirmed the similarity concept. An equation for C as a function of l/ρ was obtained. It was shown that K -values calculated with this equation are an accurate approximation for the stress intensity factor of small cracks at notches.     

Characteristic angle, light intensity and their correlation to wavelength in three dimensional photoelastic media

The interaction of the photoelastic parameters, the normalised light intensity I_n the characteristic angle ψ, and their link to the stress state parameters, the ratio of bending and direct stresses P and the angle of divergence θ of the stress components σ^M and σ^N have been examined by employing different wavelengths. The analysis of the experimental data shows that the correlation diagrams of these parameters demonstrate similar characteristic curves. Measurements also show a preferable range of wavelength within which the wavelength of light source should be selected. So far the results are valid for thin plates, thin shells of rotationally symmetric conditions and similar structures.     

部分编码结构光三维测量技术的研究

提出了一种部分编码结构光三维面形测量方法,将相位展开技术与条纹编码结合起来,既有效地减少了投影和拍摄的图像数量又提高了相位展开的可靠性.该方法利用部分编码技术对相邻的多根条纹进行整合,减小了条纹密度,然后再对整合后的条纹相位进行展开,最终得到整个图像的相位分布.实验证明,该方法可以较大程度地减少重建所需的画幅数,同时具有良好的精度和可靠性.     

Retrieving ESPI Map of Discontinuous Objects via a Novel Phase Unwrapping Algorithm

Abstract:  This work presents an effective scheme for the phase unwrapping of electronic speckle pattern interferometry (ESPI) map of discontinuous objects. ESPI is a highly effective measurement approach for industry and academia. However, due to the speckle noise, its unwrapping job is quite difficult, especially, when treating ESPI maps obtained from the deformation field of an object containing height discontinuities. The minimum L^p norm method developed by Ghiglia and Romero can treat the aforementioned problem with acceptable accuracy, but takes a long time to run. Therefore, this study presents a novel method based on a hybrid of the regional algorithm proposed by Gierloff, the branch cut method presented by Goldstein et al . and the (spatially) parallel unwrapping method with region-referenced algorithm developed by Huang and He. The proposed algorithm can retrieve ESPI maps with height discontinuities within acceptable accuracy and effectiveness.     

Unified approach for rough phase measurement without phase unwrapping by changing the sensitivity factor

Phase evaluation is extraordinarily important in optical, acoustic and radar techniques where coherent signals are employed as information carriers. In most of the cases, phase information are obtained from an inverse trigonometric function and wrapped into ?π to π. A phase unwrapping process is thus required to obtain the final unwrapped phase which represents the ultimate physical quantity to be measured. One-dimensional phase unwrapping is easily achieved by adding or subtracting an integer multiple of 2π to the wrapped phase to establish a smooth phase map. Two-dimensional phase unwrapping, however, is quite troublesome and an elegant unwrapping routing should be chosen in most of the cases to deal with phase residues caused by noise and other error sources. It would be valuable if two-dimensional phase unwrapping can be avoided and the physical quantity obtained directly. In the past, researchers have proposed other methods such as the multiple wavelengths approach which incorporates information from multiple wavelengths to eliminate the need for phase unwrapping. In this study, we extend the multiple wavelengths approach by varying the sensitivity factor, which is more convenient and cost-effective, to achieve the aim of requiring no phase unwrapping. Furthermore, an elegant phase derivative approach is used to solve the phase ambiguity problem in the multiple wavelengths method. Both simulation results and real experiment data of shadow moiré and shearography demonstrate the usefulness of this method, especially for discontinuous surface profile measurements such as steps. Advantages and disadvantages for the proposed method are also discussed in this paper.     

Measurement of interfacial fracture parameters using coherent gradient sensing (CGS)

An optical interferometry called coherent gradient sensing (CGS) has been extended for mapping interface crack tip fields and for evaluating fracture parameters. The optical technique is a double grating shearing interferometer with an on line spatial filtering arrangement. The method offers real time full field measurements and can be used both in transmission made and reflection mode. The interferometer measures small angular deflections of light rays which can be further related to in plane gradients of _x + _y in transmission through elasto-optic relations. Direct interfacial crack tip measurements in a high stiffness mismatch PMMA-aluminium bimaterial system are performed. A variety of crack tip mode mixities are studied using asymmetric four point bend specimens subjected to different far field mechanical loads. The. complex stress intensity factors and the associated phase angles are measured from CGS patterns using an asymptotic expansion field. The measurements are compared with finite element results.     

An investigation into the location of crack initiation sites in alumina, polycarbonate and mild steel

The effects of notch root radius on fracture toughness and crack initiation sites have been investigated in this paper using three different classes of materials. Data on alumina which represent ceramics, mild steel from the metals ffeily and polycarbonate representing plastics were obtained and analysed. The locations of crack initiation sites have been pinpointed by scanning electron microscopy. These identified sites more or less are located within the critical process zone or the theoretical plastic zone. The critical process zone size ( D _c ) or the theoretical plastic zone size ( R _YF ) are independent of the notch root radius unlike the plain-strain fracture toughness of notched specimens [ K _{IC (ρ)].} The authors emphasize why the parameters D _c and R _YF are useful for a quantitative evaluation of the reliability of structural materials.     

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.     

FRACTURE TOUGHNESS CALIBRATION OF THE Si3N4/Fe JOINT SYSTEM: A PARAMETRIC STUDY

Abstract— A fracture toughness calibration of the Si₃N₄/Fe joint system has been performed for various mixed-mode loading conditions and for different thicknesses of the metal interlayer. The asymmetric four-point-bend loading geometry was used. The values for the calibration function ( Y ) as well as the mode mixity (ψ)of the system increase on increasing the thickness of the metal. As the loading conditions change from mode II to mode I the dependence of both parameters on metal thickness is more intensive.     

Study of influence of notch root radius on fracture behaviour of extra deep drawn steel sheets

Fracture tests are carried out on extra deep drawn steel CT specimens containing notches with different values of notch root radius (ρ= 0.07–0.75 mm). Experimental findings clearly show a critical notch root radius (ρ_c) below which the fracture toughness remains independent of ρ and above which it varies linearly with ρ. The 3D finite element analysis shows that the location of maximum stress level causing crack initiation is in the vicinity of notch tip. The maximum stress level is independent of ρ; however, its location is shifted away from notch tip along unbroken ligament length with increase in ρ.     

A CRACK CLOSURE STUDY TO PREDICT THE THRESHOLD BEHAVIOUR OF SMALL CRACKS

Abstract— The small crack problem is addressed within the applicability of Linear Elastic Fracture Mechanics as the result of crack closure phenomenon. The variation of crack closure stress intensity factory K _op as a function of crack length, a , was determined in two materials, namely a A508 steel and a 2024A1 alloy. These results were obtained on two-dimensional small cracks ( a ≫ 0.1 mm) which were machined from long fatigue cracks. These measurements of K _op in addition to data published in the literature on a nodular cast iron and a 9Cr–1Mo steel yield to a unique characteristic function: K _op/ K _o= 1 –exp(– ka ) in which k is the only parameter to characterize the small crack effect. A prediction of the threshold behaviour of small and long cracks on A508 steel is made using the results of crack closure measurements.     

NON-ISOTHERMAL FATIGUE CRACK GROWTH IN HASTELLOY-X

Abstract— Non-isothermal fatigue crack growth tests were performed on Hastelloy-X single edge notch specimens in which strain and temperature were varied simultaneously. Conditions were selected to include nominally elastic and nominally plastic conditions and temperatures up to 925°C. The crack growth rates were first reported as a function of the strain intensity factor (δ K _ε) derived from a crack compliance analysis. Out-of-phase (ε_max at T _max) cycling showed faster crack growth rates than isothermal or in-phase (ε_max at T _max) cycling under elastic straining. Under fully plastic cycling, the opposite results was observed, i.e. crack growth rates under isothermal cycling are faster than under TMF cycling. On a δ K _ε-basis, a strain range effect was observed. All the results were rationalized using a corrected stress-intensity factor (δ K _eff) computed from the actual load, the closing bending moment caused by the increase compliance with crack length, and with the effective opening stress. Each mode of fracture was found to be characterized by a unique crack growth rate vs δ K _eff curve. On a δ K _eff-basis, the isothermal crack growth rates at T _min and T _max provide an upper and a lower bound for the TMFCG rates. The effectiveness of δ K _eff to correlate crack growth rates under fully plastic cycling is discussed in detail.     

CTODi MEASURED BY MEANS OF A MODIFIED CHARPY-V-SPECIMEN

Abstract— Measurements of CTOD_i on Charpy-V-specitnens of mild steel St 37 and pressure-vessel steel 22NiMoCr37 have been carried out. Slotted and precracked specimens have been used besides the original V-notched ones. A definition of CTOD = 2(R – R_o) has been proposed which corresponds to δ₄₅, defining the CTOD of fatigue cracks. The symbols R_o and R represent the original and the actual crack tip radii respectively. Additionally, this definition presents the opportunity to measure CTOD and CTOD_i by a direct metallographic method. It is demonstrated that COD testing, based on the hinge model, can also be applied to slotted bars, delivering CTOD and CTOD_i values which are equal to those evaluated by direct metallographic measurements.
The results obtained on four different tip radii, R_o, show a linear increase of CTOD_i as a function of R_o, which is steeper for the softer material St 37. The extrapolation to the tip radius R_o=0 gives a CTOD_i, which is equal to those determined from precracked specimens.     

Fringe-scanning method using a general function for shadow moiré

We describe a new high-resolution three-dimensional measurement method for shadow moiré. The method is based on the principle of using shadow moiré to produce moiré fringes and a fringe-scanning technique. In this method, a general function, instead of an arctangent function, is used for detecting the shape of an object. One can subsequently analyze the general function using numerical analysis with a digital computer. Two systems for static and dynamic measurements are proposed.

Experimental results show that measurement accuracies in static and dynamic measurement systems are obtainable to greater than 1/50 and 1/40 fringes, respectively.