A compact polariscope/shearing interferometer for mapping stress fields in bimaterial systems

A compact optical device, which is a combination of a polariscope and a shearing interferometer (PSI), is described for mapping stress fields in bimaterial systems. The PSI device uses commercially available wave plates, and a calcite crystal for beam duplicating. It can operate in a variety of modes, including as a circular polariscope and as a shearing interferometer. In its polariscope mode, it can be used on birefringent materials such as Homolite and epoxy; in its shearing mode, it can be used on optically isotropic materials such as polymethylmethacrylate (PMMA) and glass. As an example, the device is used to obtain full-field maps of stress fields in the vicinity of an interfacial crack in an epoxy-PMMA bimaterial plate.     

A combination optical method of lateral shearing interferometry and caustics

A novel experimental technique is presented that combines the optical method of caustics and the full-field lateral shearing interferometer of coherent gradient sensing (CGS) in one setup. Collimated light transmitted through a deformed specimen is separated into two legs. One is processed by the lateral shearing interferometer and is recombined with the other on a single image plane. By adjusting the optical path length of each leg, a combination lateral shearing interferogram/caustic image is generated. When this technique is applied to a fracture specimen, information about the stress intensity factor can be obtained from the caustic and the CGS interference fringes for exactly the same deformation field. This allows for a direct comparison between the two methods when investigating phenomena such asK-dominance, three-dimensional deformation and so on. In this paper, the technique is presented in detail, and its feasibility is tested by application to mode I and mixed-mode crack tip deformation fields.     

Techniques for the determination of absolute retardation in photoelasticity

The purpose of this paper is to give an interpretation to the fringes observed in holographic interferometry when plane-polarized light or circularly polarized light is utilized. It is shown that, when plane-polarized light is utilized and both the loaded and the unloaded states are considered, the obtained patterns are formed by the superposition of three families of fringes: the two families of absolute optical retardation and the family of relative retardation. The intensity distribution is also a function of the orientation of the plane of polarization, and along the points where the plane of polarization is parallel to one of the principal directions, only one of the families of absolute retardation is observed. By utilizing circularly polarized light, the dependence on the orientation of the principal axis is eliminated and patterns consisting of the superposition of the three above-mentioned families are obtained. If only the loaded state is considered, the holographic interferometer behaves as an ordinary polariscope with the reference beam playing the role of the analyzer. The relationships between the observed families are discussed. Examples of application to the disk and ring under diametral compression are also given.     

An experimental study of dynamic delamination of thick fiber reinforced polymeric matrix composites

Dynamic delamination of thick fiber reinforced polymeric matrix composite laminates is investigated using optical techniques and high-speed photography. The laminates used in this work are graphite/epoxy fiber reinforced, 65 percent fiber volume fraction, composite plates consisting of 48 plies (6 mm plate thickness). Two different laminate layups are tested: a quasi-isotropic arrangement and a unidirectional arrangement. The experimental setup consists of 152 mm×152 mm square plates impact loaded in an outof-plane configuration using a high-speed gas gun. Impact speeds range from 1 m/s to 30 m/s. Real-time imaging of the laminate out-of-pane displacement is performed using the lateral shearing interferometer of coherent gradient sensing (CGS) in conjunction with high-speed photography. Onset of dynamic delamination can be observed, and quantities such as delamination speeds (in some cases up to 1800 m/s) are measured and reported. A brief comparison is made with dynamic fracture experiments of the same material conducted in a separate study.     

Dual hologram shearing interference technique for wind tunnel flow fields testing

 A novel optical diagnostic technique, dual hologram shearing interferometry, for measuring density gradients of different phase objects is proposed and demonstrated. The lateral shearing is achieved by using a phase grating. A holographic interferometer has been developed and designed on the base of a single pass Z type conventional schlieren device. The interferometer’s scheme is insensitive to acoustical disturbances, similarly to the conventional schlieren layout, and is capable of recording holograms with a continuous wave laser during the wind tunnel run. The features of the technique make it tolerant to both the temporal coherence of the laser light source and to the relatively low, schlieren quality optical windows of the wind tunnel’s test section. The obtained reconstructed lateral shearing interferograms with a large region of overlap have high contrast and may have an arbitrary orientation and/or spacing of the background interference fringes. It is believed that the proposed approach will become a useful tool for visualization and accurate mapping of the density gradients of gas dynamic flow fields, in wind and shock tunnels, where acoustic noise problems may dramatically affect reference beam holographic schemes. Received: 9 January 1997 / Accepted: 12 April 1997     

单箱三室箱梁剪力滞效应的试验研究

为开展单箱三室箱梁剪力滞效应的试验研究,制作了有机玻璃简支箱梁模型,对试验模型进行了分级加载。对该试验箱梁进行集中加载,分别作用于跨中截面四腹板上方、两对称边腹板上方和两对称中腹板上方。采用DH3816应变采集仪测得跨中及四分之一跨截面各关键点应变值,用百分表测得箱梁各关键截面挠度值。测量得到的截面应力分布规律验证了箱梁截面剪力滞效应的存在。对该有机玻璃简支箱梁,利用有限元方法和模型试验方法,研究了3种集中力工况下截面的剪力滞分布规律。结果表明,集中力作用下单箱三室箱梁各翼板间存在明显的剪力滞效应,且荷载的横向作用位置对箱梁截面剪力滞效应影响较大。     

基于空间光调制器获得空心光束的数值模拟和实验研究

光镊技术中,会聚的空心光束形成的能量光阱可用来捕获吸光性颗粒或操纵吸光性颗粒沿光轴方向运动。采用Gerchberg-Saxton(GS)算法计算所需相位,并将相位载入相位型空间光调制器来获得空心光束。为了提高会聚的空心光束能量,对空间光调制器相位屏进行预处理,叠加数字闪耀光栅位相,实现了将四个一级衍射谱闪耀至零级干涉极大位置,空心光束能量提高到原来的4.7倍。为了消除空间光调制器二维光栅结构所形成的零级谱亮斑以及高级谱的影响,在相位屏上加入球面波相位,使得空心光束衍射谱平面与零级谱平面的空间位置分离,并采用带通滤波器将空间光调制器的零级谱亮斑和高级谱滤掉。采用高度会聚透镜将所得空心光束会聚为微米尺寸,可应用于捕获吸光性颗粒。另外,利用离散傅立叶变换的平移原理实现空心光束实时平移,该方法可应用于实时操纵吸光性颗粒移动。     

Analysis of plane and cylindrical nonlinear hyperelastic waves in materials with internal structure

A comparative analysis of two types of hyperelastic waves—plane waves (with plane front) and cylindrical waves (with curved front)—is offered. The propagation of the waves is studied theoretically for quadratically nonlinear hyperelastic media and numerically for a class of unidirectional fibrous composite materials. Hyperelasticity is described using the classical Murnaghan potential and a structural model of the first order—the model of effective constants. The internal structure of materials is described by this model and is at the micro-or nanolevels in numerical analysis. Particular attention is given to the evolution of the wave profile. It is studied in three stages: (i) derivation of nonlinear wave equations, (ii) construction of solutions in the form of plane and cylindrical waves, and (iii) numerical analysis of the evolution of these waves in composites with microlevel (Thornel) or nanolevel (Z-CNT) fibers. The main similarities and differences between plane longitudinal and cylindrical waves are shown. The most unexpected result is the striking difference between the evolution patterns numerically observed for plane and cylindrical wave profiles __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 21–46, October 2006.     

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.     

Local thickness and wave velocity measurement of wavy films with a chromatic confocal imaging method and a fluorescence intensity technique

This work presents two different methods for measuring the thickness of wavy films. The first one is a new non-intrusive technique called “chromatic confocal imaging method” which uses two optical properties—the confocal image and the chromatic aberration of a lens. The accuracy of this technique depends on the optical components, the local gradient of the film thickness and the accuracy of the refractive index used. The second method for simultaneous measurements of film thickness and wave velocity is based on a fluorescence intensity technique. Film thickness and wave velocity measurements of silicone films with different viscosities are presented for Reynolds numbers from 2 to 700 and various inclination angles. The experimental data agree well with the results from published experimental and theoretical studies.     

Solutions of the integral equations for shearing stresses in two-material curved beams

In the same way as shearing stresses for curved beams made of one material, the problem of evaluating the shearing stresses of composite curved beams is also reduced to one of solving the integral equations. Solving directly two integral equations can derive the formulae of shearing stresses, which satisfy not only the equilibrium equations but also the static boundary conditions on the boundary surfaces of the beams. The present analysis will be used to investigate the shearing stresses of a cantilevered curved beam made of two materials, which is loaded by a concentrated force at its free end. The comparison between the numerical results of shearing stresses obtained using the equations developed in this paper and a three-dimensional finite element analysis shows excellent agreement.     

Three-dimensional imaging of a turbulent jet using shearing interferometry and optical tomography

The 3-D density field of a round, neutrally buoyant turbulent jet is obtained using a finite-fringe, shearing interferometer. A He–Ne laser beam (λ=632.8 nm) is subdivided into six beams of equal intensity, which intersect a helium–argon jet flowing from a vertical nozzle. Two-dimensional projection data of the jet are captured simultaneously from six viewing directions distributed over 140°. The desired phase is removed from the spatial carrier using the Fourier transform method. A tomographic reconstruction technique, using a truncated Fourier–Bessel expansion is performed to obtain the complete 3-D density field. The Reynolds number, based on the exit mean velocity and the nozzle diameter, is 5890. Received: 22 December 1999/Accepted: 20 January 2000     

Slope-contour fringe multiplication by Fresnel diffraction

Coherent collimated monochromatic light emitted from a He?Ne laser was used to illuminate a transparent sheet specimen in plane stress. The light emerging from the specimen was concentrated by a thin positive lens on a coarse amplitude grating placed at the vicinity of the focus of the lens and projected on a ground-glass screen. The strongly coherent light of the laser was diffracted at the coarse grating. The deformed lateral surfaces of the loaded specimen worked as a thin lens of continuously variable focal length, which was interposed in the path of the beam and distorted the diffraction image. The pattern yielded the partialslope contours of the thickness variation in a direction normal to the rulings of the grating. Positioning the grating within the focal distance of the lens resulted in a predominant Fresnel diffraction of the opaque strips of the grating. Placing the grating beyond the focal plane created a Fresnel diffraction of the open slits. Both diffraction patterns yielded a high multiplication of fringes which increased considerably the accuracy of the experimental results.     

Experimental analysis of thermal fields in horizontally eccentric cylindrical annuli

This paper presents new experimental results on thermal field and heat transfer in a two-dimensional annulus between horizontally eccentric cylinders. The study is conducted by means of optical techniques, for 1.07×10⁴≤Ra _L≤8.27×10⁴ and a wide eccentricity range. The horizontal eccentricity of the inner cylinder substantially alters the thermal field and the geometry of the plume, but, in analogy to the behaviour for vertical eccentricity, the average Nu is slightly affected in the investigated range of eccentricity. The concentric geometry is also considered mainly to validate the experimental technique and evaluate the accuracy of the adopted methodology by comparison with available results. Both shearing interferometer and reference beam interferometer are obtained by means of Wollaston prisms with appropriate splitting angles, so that the temperature and local Nu distributions may be evaluated quantitatively from the original pictures via digital image processing.     

Analytical estimates of the contact zone area for a pressurized flat-oval cylindrical shell placed between two parallel rigid plates

The paper presents an analytical estimate for an area of contact for a thin-walled noncircular cylindrical shell placed between two parallel rigid plates with an initial gap and then pressurized hydrostatically up to the contact appearance. The Euler–Bernoulli beam is used to model the shell deformation under the plane strain assumption. Such a simplification allows one to obtain the simplest closed-form estimate for the contact zone area. The first approximation is obtained neglecting the deformation of the curvilinear segments of the flat oval shell cross-section while the solution for the curved beam loaded by the homogeneous pressure is considered as a second approximation. The accuracy of the proposed analytical solutions as well as their usability in the preliminary design of thin-walled elements of various cooling systems is validated by the results of both numerical simulations and experimental tests.     

Absolute phase measurement in extrinsic Fabry-Perot optical fiber sensors using multiple path-match conditions

This paper describes the use of the first and second optical return paths in a moderate-to-high finesse Fabry-Perot sensor to measure the absolute phase in extrinsic Fabry-Perot interferometry (EFPI) sensors. A path-matched differential interferometry (PMDI) using a highfinesse EFPI sensors, a low-finesse Fabry-Perot readout interferometer and a broadband light source consisting of amplified spontaneous emission (ASE) from an erbium-doped fiber amplifier (EDFA) is used to illustrate the idea. The first and second multiple paths in the Fabry-Perot readout sensor are used to provide two distinct path-match conditions from the same scanning Fabry-Perot readout interferometer. The difference in fringe numbers between the centers of two orders of interference fringe packets formed by the distinct path-match conditions makes possible a simple method of measuring the cavity length of EFPI sensors, which in turn can be used to measure absolute phase and the corresponding strain. Sensor cavity length measurement using the multiple return paths in the high-finesse Fabry-Perot sensor is correlated to that measurement using the modulation transfer function found using an optical spectrum analyzer; the multiple return path technique is then used to make strain measurements on a cantilever beam. Comparisons with resistance strain gage measurements are favorable. Characterization tests indicate that the proposed technique has a cavity length measurement resolution on the order of 1.1 μm, which translates to a strain resolution of 28 με for a 4-cm gage length sensor.     

The oblique-plate impact experiment

An experimental method is presented for the study of one-dimensional plane waves corresponding to combined pressure and shear. The experiment involves the impact of two skewed flat plates. A projectile plate is accelerated using a gas gun and made to impact a target plate in a vacuum chamber. The projectile and target plates are parallel, but inclined relative to the axis of the gun so that the particle velocity in the target has components both normal and parallel to the plane of impact. The particle velocity at the target rear (free) surface is recorded as a function of time. The normal velocity component is monitored using a laser velocity interferometer; the transverse motion is monitored using a shadow technique. The measured wave profiles can be compared to theoretical predictions based on one-dimensional-wave theory.     

Slope and curvature measurement by a double-frequency-grating shearing interferometer

This paper describes a shearing interferometer capable of the direct measurement of the slopes and curvatures of reflecting plates. The wavefront shear is produced by a double-frequency grating which is simply a grating containing two closely spaced frequencies. The first-order waves associated with each frequency form the interferogram, the contours of which are related to the model's slope or curvature depending upon system arrangement and recording procedure. Four arrangements are described: two for slope and two for curvature. In one, the slope contours are obtained directly and in real time. In the second slope arrangement, an extra spatial-filtering step is necessary to obtain the slope contours. However, this arrangement, as opposed to the first, measures the slope only due to the loading, compensating for initial model slope and optical-system aberrations. The two curvature techniques can be described as double-shearing interferometers having a primary and secondary shear. The primary shear for both arrangements is provided by the double-frequency grating. In one technique, the secondary shear is provided by a translation of the recording film between two exposures during the recording step. A subsequent spatialfiltering step displays the curvature fringes. The second technique requires only a single exposure and places a beam splitter at the location of one of the first-order diffraction spectra during the filtering step. The field equations defining the fringe values are derived for all four arrangements with experimental results also being given.     

Three-Dimensional Elasticity Solutions for Rectangular Orthotropic Plates

A state space approach for three-dimensional analysis of rectangular orthotropic elastic plates subjected to external loads on the top and bottom faces is developed. Through Hamiltonian variational formulation via Legendre’s transformation, the basic equations of elasticity are formulated into the state space framework in which the state equation exhibits Hamiltonian characteristics and the associated eigensystem possesses symplectic orthogonality. By means of separation of variables and eigenfunction expansion, three-dimensional elasticity solutions for orthotropic rectangular plates with two opposite edges simply supported and the other two arbitrary—which can be any combinations of simply-supported, clamped, and traction-free edges—are determined in a systematic way. The existing elasticity solution for the fully simply-supported plate is recovered. The through-thickness variations of the displacements and stresses are evaluated within the context.     

三维电子散斑干涉法在检测残余应力中的应用

本文提出一种新的大错位三维电子散斑干涉法,并将其和钻 法检测残余应力技术结合起来,其特点一是利用三个激光器,从不同的方向照射被测物体,二是在被测物附近放置一参考物,利用大错位棱镜,使物体表面的信息和参考物上的信息都进及ＣＣＤ中,可以得到与三个位移场有关的电子散斑干涉条纹图,并可以运算和分离获得独立的ｕ,ｖ和ｗ场信息,本文介绍了大错位三维电子散斑干涉法的原理、方法和系统,并将其应用于钻孔法释放残余应