Three-dimensional speckle interferometric investigation of the stress-intensity factor along a crack front

The variation in Mode I stress-intensity factor throughout the thickness of an ASTM standard compact tension specimen was determined using scattered-light speckle interferometry. Two very thin sheets of coincident coherent light traveling in opposite directions were passed through a Plexiglas specimen normal to the crack faces. A double-exposed photograph of the scattered-light speckle pattern was taken while the specimen was subjected to a small load increment. From this double-exposed photograph, the change in the crack-opening displacement could be determined. From the information about the crack-opening displacement in the region of the crack tip, the stress-intensity factor was calculated for various interior planes and on the surface of the specimen. For the compact tension specimen tested, the stress-intensity factor did not vary throughout the specimen's thickness. The method of scattered-light speckle interferometry proved to be very powerful in solving this complex three-dimensional problem.     

Photoelastic analysis of a three-dimensional specimen by optical slicing and digital image processing

The authors show a nondestructive method for obtaining the isochromatic and isoclinic fringes in a three-dimensional photoelastic specimen. The basic idea is to delimit a slice between two plane laser beams. The properties of polarization of the scattered light (Rayleigh's law) and the interference possibilities of the diffused beams are used. By introducing speckle pattern properties, the correlation factor of the two scattered beams is similar to the illumination given in a plane polariscope for the investigation of a slice (in a classical frozen-stress technique). The authors use a monochromatic laser beam, a CCD camera and a personal computer. Because they cannot obtain the correlation factor directly, they do a statistical analysis of the speckle patterns. The variance (function of the correlation factor) is computed from the light intensities of three images corresponding to the speckle pattern for plane 1 alone, plane 2 alone, and both planes together.     

Application of the Fourier transform in electronic speckle photography

In speckle photograph technology, to determine the displacement of the points on the surface of the measured body, the conventional method is to put the film which has recorded the speckle patterns before and after displacement into a system of optical Fourier transforms. After filtering on the spectrum plane, the experimentalist can obtain the displacement information from the interference pattern on the image plane. Instead of setting up a complex optical Fourier transform system, we consider the speckle field as a light intensity function of 2 dimensions, which will change with different positioning of the points. After working on the function's discrete Fourier transform (DFT), according to one of the properties of Fourier transformation, the displacement of the measured point is involved in the phase of its spectrum. Having extracted the displacement information from the phase, we obtain the distribution of the displacement field. In this paper, we deduce the expression for the displacement field by using Fourier transformation under conditions of both equal and unequal displacement and show their applications.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

Study of basic patterns of light scattering in aqueous solution of milling yellow

Basic characteristics of light scattering in an aqueous solution of milling yellow are presented in a form of relations between the scattered radiant power, states of polarization of primary radiation and scattered radiation, observation angle and azimuthal angle.It is found that the state of polarization of the scattered light in milling-yellow solution can be utilized as a foundation of reliable photoelastic scattered-light techniques for flow analysis. However, Rayleight's model of scattering is nnt directly applicable.Paper contains data on major parameters of light scattering, knowledge of which is necessary to correctly design flowbirefringence experiments. In particular, these data can be used to develop a set of conditions and constraints for designing of particular scattered-light flow-birefringence experiments, and of corresponding transfer functions.     

Characteristic relations of flow birefringence

The general problems of the flow-induced birefringence in liquids have been presented and discussed in Part 1 of this paper, in which some particular responses of an aqueous solution of NGS 1828 were presented, namely, the pertinent mechanical responses and the birefringence responses in transmitted radiation. This paper presents the optical responses of NGS 1828 observed in the scattered radiation. It is shown that the scattered-light techniques can become a powerful and indispensable tool of flow-birefringence techniques, if the actual patterns of light scattering are taken into account. Proof is given that the light scattering and the related birefringence cannot be described by Rayleigh's mathematical model of scattering (Part 1, Ref. 51). The optical effects of the modulation of the primary beam and the scattered beam, called scattered primary isochromatics and scattered secondary isochromatics, are described in terms of the parameters of the system. A practical example is presented. Samples of typical recordings of light-intensity modulation by typical flow patterns are given in the form of scattered primary and secondary isochromatics and integrated isochromatics. One type of intensity modulation enables the determination of shear-strain rate at an interior point in the flow field. Using the determined shear-strain rates at the interior points, a velocity profile along the axis of symmetry of a rectangular-conduit flow was obtained. The results so obtained were satisfactory when compared with the results of direct volumetric measurement. The other type of intensity modulation reveals the nonuniform distribution of birefringence along the path of the transmitted light in the rectangular-conduit flow. The results presented in Part 1 of this paper, are complementary to the results presented below.     

Rectilinear and circular analysis of a plane slice optically isolated in a three-dimensional photoelastic model

Because of the coherence of scattered light, it is possible to produce a speckle image from a plane beam of light passing through a transparent model. When two plane parallel beams of light are transmitted through the model the slice between the beams is then optically isolated. The two speckle patterns corresponding to the two beams are superposed and provide optical data relative to the slice (principal stress directions, birefrengence), the data being collected on high contrast photographic plates or by optical filtering to obtain the square of the contrast. The isoclinic and isochromatic fringes are shown to exist. The concepts of rectilinear or circular analysis are extended to the observation of a plane slice in a three-dimensional model without freezing or cutting the model.     

Scattering of elastic waves by a surface-breaking crack

Scattering of incident surface waves and incident body waves by a surface-breaking crack is investigated in a two-dimensional geometry. By decomposing the scattered fields into symmetric and antisymmetric fields with respect to the plane of the crack, two boundary value problems for a quarter-plane have been obtained. The formulation of each boundary-value problem has been reduced to a singular integral equation which has been solved numerically. For incident surface waves the back-scattered and forward-scattered surface waves have been plotted versus the dimensionless frequency. Curves are also presented for the scattered displacement fields in the interior of the body generated by incident body waves, both versus the angle of incidence and versus the dimensionless frequency.     

Assessment of electronic shearography for structural inspection

Electronic shearography (ES), a laser interferometry technique, has the potential for large-scale structural inspection and for identifying cracks and strain anomalies. A system based on this technology could possibly be used for noninvasive inspection of structures with high insensitivity and robustness. One major problem is the existence of largerigid body motions in typical engineering structures such as bridges and high-rise buildings. These rigid-body motions are large enough to cause a complete decorrelation of the characteristic speckle pattern that is obtained by illuminating the object surface. This nullifies any possibility of interference between speckled images obtained at different stages of loading, as is necessary for interferometry applications. A systematic study was conducted to characterize the speckle pattern obtained from typical civil structures as a function of the illumination and imaging system. Experiments were carried out to quantify speckle decorrelation as a function of object motion and instrumentation characteristics. A fracture mechanics based finite element (FEM) analysis was carried out on an existing fractured bridge to determine the strains and displacements. The results of these studies were subsequently used to define the parameters of a structural inspection system based on ES for field applications.     

An automatic system for scattered-light photoelasticity

This paper describes the recent development of an automatic data-collecting-and-interpreting system for a dual-observation method in scattered-light photoelasticity. The system incorporates a flexible relay optic, photon counting and computer techniques. Photoelastic parameters are evaluated from the photon counts by means of an electronic digital computer. Evaluation procedures have been improved so that the effect of absorption of scattered light is eliminated.     

A geometrical approach to holographic interferometry

Geometrical considerations are used to obtain quantitative data for the components of the displacement vector. Use is made of a dual-beam illumination and a variant is described, using point light sources and a single point of observation. Contour lines for the displacement vector in the viewing direction and in a perpendicular direction are obtained as the algebraic sum and difference of two interference patterns. Densification of the initial pattern is used to obtain moiré patterns for the out-of-plane and in-plane displacements of flat Surfaces and for the derivatives of these displacements. To determine the complete displacement field of objects of arbitrary shape, one holographic plate is sufficient, using two times two-point light sources.     

Full-field surface-strain and displacement analysis of three-dimensional objects by speckle interferometry

A method of full-field measurement of displacements as well as strain on arbitrarily curved surfaces is introduced. The speckle effect of coherent light is utilized to produce fringes due to displacements. Unlike the fringes produced by holographic interferometry, these fringes have a unique interpretation in relating to displacements and they localize on the surface. Three measurements are required to determine the three components of displacement; and, knowing the geometry of the object, its surface strains can be deduced. Three ways of recording displacement fringes, namely, real time, double exposure and superposition, are described.     

Three-dimensional stress-relief displacements from blind-hole drilling: a parametric description

Optically-based interferometric techniques are finding increased application to the quantitative determination of near surface stress states. Unlike the standardized strain-gage method of hole drilling, however, some optical methods are sensitive to all three components of the displacement field produced by drilling of the stress-relieving hole. Analysis of the resulting fringe patterns necessitates a full knowledge of such motions. Here, direct formulae, which relate stress-relief displacements to radial position and azimuth, relative hole dimensions, residual or applied stress, and Poisson's ratio, are constructed from an extensive series of finite element calculations. The final formulae are derived from a large set of trial formulae that best describe the displacements according to a statistical regression analysis. The formulae are generally valid for hole depth/diameter ratios from 0.5 to 4.0, for Poisson's ratios from 0.05 to 0.45, and over radial distances from the hole axis from 2 to 20 times the hole radius, although these validity ranges can vary with hole depth. The equations are compared to an existing strain-gage hole-drilling standard and are used to forward model a speckle interferometer fringe pattern recording stress-relief displacements in an acrylic block.     

An adaptive procedure for defect identification problems in elasticity

In the context of inverse problems in mechanics, it is well known that the most typical situation is that neither the interior nor all the boundary is available to obtain data to detect the presence of inclusions or defects. We propose here an adaptive method that uses loads and measures of displacements only on part of the surface of the body, to detect defects in the interior of an elastic body. The method is based on Small Amplitude Homogenization, that is, we work under the assumption that the contrast on the values of the Lamé elastic coefficients between the defect and the matrix is not very large. The idea is that given the data for one loading state and one location of the displacement sensors, we use an optimization method to obtain a guess for the location of the inclusion and then, using this guess, we adapt the position of the sensors and the loading zone, hoping to refine the current guess.Numerical results show that the method is quite efficient in some cases, using in those cases no more than three loading positions and three different positions of the sensors.     

Measurement of surface displacement normal to the line of sight

Two methods for measuring the displacement of a surface normal to the line of sight are described and experimental results presented. The displacement in either case may consist of a simple lateral or rotational shift of the body in total, or it may consist of small local displacements due to some type of mechanical stress. The displacement is displayed as a system of interference fringes over the image of the surface. The first method permits observation of the displacement fringes in real time; or, if a double exposure is recorded, the fringes can be observed directly on the doubly exposed photograph in white light. The second method requires spatial filtering of the image after recording a double exposure of the surface before and after displacement. However it permits selection of the component of displacement in any direction normal to the line of sight with a continuously variable sensitivity from the single (doubly exposed) transparency. Both methods are noncontacting, use only a single laser beam for illuminating the object and require no previously constructed grids or rulings.     

DVC中内部散斑质量评价及计算体素点的优化选择

数字体图像相关方法(digital volume correlation, DVC)是一种可测量物体内部三维全场变形的先进实验力学测试技术, 通过分析由体图像成像设备(如X-ray CT)获取的物体变形前后的三维体图像, DVC可获得物体内部具有亚体素精度的三维变形信息. 在应用DVC测量内部变形时, 被测试样体图像的内部散斑质量对其测量精度有着重要影响. 本文从DVC算法位移测量误差的理论分析和数值模拟实验两方面证实了DVC的位移测量误差与计算子体块的灰度梯度平方和(sum of square subvolume intensity gradient, SSSIG)值呈负相关关系, 即: 计算子体块的SSSIG值越大, 其位移测量精度越高, 因此SSSIG可用于体图像内部散斑质量的定量评价. 尽管直接增加计算子体块尺寸可以增加SSSIG, 但是较大计算子体块内更多的计算点会导致计算量的显著增加. 为此, 本文进一步提出一种计算体素点优化选择方法, 该方法通过将计算子体块中灰度梯度较小的体素点剔除出计算, 以实现在增大计算子体块尺寸的同时不会显著增加计算量. 模拟和真实实验结果显示了该计算体素点优化选择方法的有效性.      

Stress analysis by combination of holographic interferometry and boundary-integral method

The paper describes a hybrid experimental and numerical method analysis of bodies. It consists of the experimental method of double-aperture speckle interferometry and the boundary-integral method. The interference patterns allowing evaluation of the displacement vector are obtained by the speckle interferometry. The boundary displacements obtained experimentally are conveniently used for the calculation of stresses in the body by the boundary-integral method. Some examples bear witness of the effectiveness and accuracy of the hybrid technique.     

Application of digital speckle pattern interferometry for fluid velocimetry in wind tunnel flows

This paper shows the feasibility of using digital speckle pattern interferometry (DSPI) as a fluid velocimetry technique in high speed gaseous flows. The light scattered from an illuminated plane was recorded with a CCD camera at the same time as a uniform reference beam. A fibre optic was used to bring this reference beam from the laser cavity to the CCD camera. The comparison of two subsequent frames gives information about the velocity field. DSPI was applied to a Von Karman street flow set up in a wind tunnel. Particle image velocimetry (PIV) measurements were also obtained for comparison with the information provided by DSPI. A system for increasing the measurement region when using short coherence length lasers is proposed. Received: 15 June 2000/Accepted: 8 September 2000     

Application of scattered-light photoelasticity to doubly connected tapered torsion bars

This paper reports the use of scattered-light photoelasticity to solve the doubly connected tapered-shaft problem. Some techniques are presented which help realize more fully the potential of scattered-light photoelasticity. These include the use of a continuousemission gas laser as a light source for the polariscope, the use of a photometer arrangement to read fringe spacings, and the use of curve-fitting techniques to analyze the data. Also, some design features for constructing a scattered-light polariscope are presented.     

Scattered-light rosette

A newly developed concept, called thescattered-light, rosette, is used to determine the state of stress on a free surface. Three simultaneous, polarized-light beams intersecting at a surface point yield sufficient scattered-light photoelastic data to evaluate the stresses at a surface point. After initial calibration, the surface-stress analysis consists of a series of photographs, one photograph for each point of interest. General equations are derived which are valid for any three light beams intersecting at a surface point on a stressed, photoelastic material. Simplifications of the general equations and techniques are also noted. Stresses obtained from the scattered-light-rosette analysis are compared with the known solutions for two problems.