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.     

Two holographic blind-hole methods for measuring residual stresses

The relationship between the displacements and stresses relieved from blind-hole drilling is introduced via an easily understandable concept in this paper. Combining this concept with holographic interferometry, two holographic blind-hole methods for measuring residual stresses are established. The first is a new technique which requires measuring three out-of plane displacements; and the second is a modification of another technique which requires measuring two out-of plane displacements. Each of the two methods needs only one interference fringe pattern and is demonstrated by using it to measure a known residual stress in an aluminum specimen.     

Residual-stress determination through combined use of holographic interferometry and blind-hole drilling

Holographic interferometry is used to determine in-plane radial displacements due to release of residual stresses by hole drilling. A method is derived for relating radial displacements measured in three directions of illumination to the state of residual stress, analogous to relations used in the conventional strain-rosette technique. Residual stress is produced by an interference fit of two circular tubes. Agreement between stress determined holographically with a computed value and with that determined by the conventional technique is good. Advantages of the holographic technique in overcoming various shortcomings of the conventional technique are discussed. A modification of the holographic technique involving data collection in only two directions of illumination is described.     

Displacement and strain measurement with automated grid methods

An image-processing-based automated grid method is investigated to determine the method's displacement and strain accuracy limits, and how these limits are influenced by the choice of camera-calibration models. A CCD camera and a PC-based frame grabber are used to record grid spot motion, then ordering and centroiding are used to identify each spot and calculate their individual displacements. The displacements are fitted with a moving biquadratic surface, and the strains are obtained by analytical differentiation of that surface. Camera-calibration models which are considered include various combinations of image-perspective transformation, image stretching, and elliptical-lens distortion. The strain and displacement accuracy are explored through rigid-body motion and uniaxial tension tests. In the process, sensitivity to in-plane and out-of-plane rigid-body translation, and extreme sensitivity to in-plane rigid-body rotation (for non-synchronized frame grabbers) are confirmed. It is found that under the best conditions the displacement accuracy is 015 pixels and that the strain accuracy is 120 microstrain. Finally, the automated grid method is used to investigate the strains developed in an aluminum perforated strip subjected to uniaxial tension.     

The Equations of Motion of a Plate with Residual Stress

We consider a three-dimensional body which is at rest in a cylindrical configuration of height 2ε. We assume that the material is residually stressed and that it responds elastically to deformations from the reference configuration. Under appropriate assumptions on the data, and using weak-convergence methods, we determine the limit, as ε goes to zero, of the elasto-dynamic problem. The plate problem obtained, as in the case without residual stress, splits into two problems: one governing the in-plane displacement and the other determining the out-of-plane motion.     

In-plane and out-of-plane displacement measurement by ultrasonic speckle correlation method (USCM)

When an object moves, ultrasonic speckles backscattered from its surface will follow the object to move. From the Kirchhoff diffraction theory and the correlation principles of random signals, the necessary condition for keeping the correlativity between the speckle fields before and after the objective displacement was deduced. Based on this condition, the formulas for the relationship between the speckle displacement and the objective displacement were obtained. Practical measurement was performed. Ultrasonic digital speckle correlation method was used to measure the in-plane displacement and out-of-plane displacement of an object. The displacements of the objective surface were evaluated after the displacements of the speckles were determined.This method can be also used to measure the displacements of an inner objective surface. A mountain-climbing search method was proposed, which enabled us to find the maximum correlation coefficient in the correlation operation quickly and efficiently. The experimental results showed good agreement with the theoretical predictions.     

A fringe-compensation technique for stress analysis by reflection holographic interferometry

The use of holographic interferometry for stress analysis of nontransparent objects is limited by rigid-body displacements of the object. These displacements can alter the fringe patterns and often cause the fringes to disappear completely. A technique of compensation for this deterioration of the fringe pattern forreal-time holographic interferometry is described in this paper. It is especially designed to permit the accurate measurement of the out-of-plane component of strain near regions of stress concentration in plates that are subjected to in-plane loading. It is first shown that the fringes caused by a pure rigid-body displacement can be eliminated almost completely by translations of the hologram and rotation of the illumination wave. This procedure is first described when the displacement is known; then when it is unknown. A method to estimate the error made in the correction is presented. In actual stress-analysis problems, the object is both rigidly displaced and strained. Assuming the rigid displacement is known and corrected as previously, the analysis is developed to relate the fringe pattern to the strain-related displacement. This analysis takes into account the optical modifications of the system that are necessary to achieve the rigid-body-displacement correction. When the rigid-body displacement is unknown, the method is shown still to be workable through the use of various symmetries and boundary conditions. Two sample interferograms are presented as illustrations. Quantitative treatment of data from one of these are presented in a companion paper.     

Surface effects in the deformation of an anisotropic elastic material with nano-sized elliptical hole

We examine the effect of surface energy on an anisotropic elastic material weakened by an elliptical hole. A closed-form, full-field solution is derived using the standard Stroh formalism. In particular, explicit expressions for the hoop stress, normal, in-plane tangential and out-of-plane displacement components along the edge of the hole are obtained. These expressions clearly demonstrate the effect of elastic anisotropy of the bulk material on the corresponding field variables. When the material becomes isotropic, the hoop stress agrees with the well-known result in the literature while both the in-plane tangential and out-of-plane displacements vanish and the normal displacement is constant along the entire boundary of the elliptical hole.     

球形压痕的残余变形分析

球形压痕技术在材料力学属性，诸如硬度，弹性模量等的测量中得到了广泛的应用。应用Twyman-Green及云纹干涉法并配合相移技术，本文对IN783合金进行了一系列的球形压痕实验研究，并对残余压痕的面内（u,v）及离面（w）变形场进行了定量测量和分析。应用面内变形测量结果，进一步对试件表面的应力一应变分布进行了分析和计算，并在离面变形场的基础上，确立了压痕周围的弹塑性边界，从而进一步应用面内的分析结果，得到材料的屈服强度。应用压痕实验的接触半径和压力并配合Tabor经验公式，本文进一步得到了材料的应力应变曲线。实验结果与已知的IN783合金相吻合。对所涉及的一系列压痕实验，本文也进行了二维有限元分析并得到了比较一致的结果。     

Residual Stress Determination Using Cross-Slitting and Dual-Axis ESPI

Hole-drilling and Electronic Speckle Pattern Interferometry (ESPI) are used to measure residual stresses in metal specimens. The slitting method is chosen as an alternative to the more commonly used hole-drilling method because it involves less material removal and leaves large areas of highly deformed material available to be measured. However the conventional single-slitting method is sensitive only to the stress component perpendicular to the slit direction, and thus has a strong directional bias. Conventional ESPI has a similar bias because it responds to surface displacements in a specific sensitivity direction. In this paper, a novel cross-slitting method with dual-axis ESPI measurements is proposed to address both directional biases. Cross-slitting is introduced as a means of releasing all in-plane stress components. The dual-axis ESPI system uses diagonal-mirror and shutter devices to provide surface displacement measurements in orthogonal in-plane directions. The combination of the cross-slit and dual-axis measurement gives isotropic sensitivity to the in-plane residual stress components. Experimental measurements are described that illustrate the capability and effectiveness of the cross-slitting/ESPI technique.     

A method of three-dimensional strain measurement on non-ideal objects using holographic interferometry

Holographic interferometry has been applied to determine the components of tensile, compressive and shear strain in the surface layer of a non-ideal object subjected to high values of stress. The method consists of determining the three components of the vector displacement at a sufficient number of discrete points on the surface of the object. Functions in the form of truncated power series are fitted to the fringe order-distance data using the method of least squares. Interpolation of these functions is then carried out to obtain the fringe-order numbers at closely spaced equal intervals. The displacement in each interval is calculated and the displacement-distance relationship is then numerically differentiated to obtain strain. Components of stress at a particular point are then estimated by multiplying the strain value by the appropriate modulus. These stresses result from the application of considerable forces that are likely to cause large rigid-body displacements unless the object can be satisfactorily restrained. The difficulty of providing the required restraining forces has been avoided by mounting the object on a kinematic mount from which it can be removed before stressing and replaced afterwards. The accuracy of relocation of the object is sufficient to ensure the satisfactory formation of holographic interference fringes. As the use of the two-exposure holographic method results in a direction ambiguity of the displacement vector at any point of the surface, this method is complemented by electrical strain measurement. The strain is sampled in two convenient orthogonal directions at some part of the surface. The application of the uniqueness theorem of elasticity then permits the direction of displacement to be uniquely specified at any point of the surface. The electrical strain measurement also provides a check of the strain values determined by interferometry at various positions on the surface. This check is necessary since precise knowledge of the surface geometry of a non-ideal object may be lacking. Incorrect assumptions made about the geometry are shown to result in serious errors in the evaluation of strain. The method described has been used to estimate the stresses in the vicinity of a threaded hole in a sample of pipe for representative values of torque applied in screwing a connecting member into the pipe. Possible reasons for failure of the pipe in service are then deduced.     

Residual stress determination using blind-hole drilling and digital speckle pattern interferometry with automated data processing

A combined system of blind-hole drilling and digital speckle pattern interferometry that performs automated data analysis is used to determine the magnitude of the residual stress induced in an aluminum plate subjected to uniaxial tension. The authors perform a finite element analysis of the blind-hole drilling process to adjust the analytical model commonly used for residual stress determination. The relieved displacement field due to the introduction of the blind hole is determined by the evaluation of the optical phase distribution. Using more than 300 values of this displacement field, the magnitude of the residual stress is determined and compared with the applied stress value.     

Diffraction Assisted Image Correlation: A Novel Method for Measuring Three-Dimensional Deformation using Two-Dimensional Digital Image Correlation

Digital Image Correlation (DIC) provides a full-field non-contact optical method for accurate deformation measurement of materials, devices and structures. The measurement of three-dimensional (3D) deformation using DIC in general requires imaging with two cameras and a 3D-DIC code. In the present work, a new experimental technique, namely, Diffraction Assisted Image Correlation (DAIC) for 3D displacement measurement using a single camera and 2D-DIC algorithm is presented. A transmission diffraction grating is placed between the specimen and the camera, resulting in multiple images which are then used to obtain apparent in-plane displacements using 2D-DIC. The true in-plane and out-of-plane displacements of the specimen are obtained from the apparent in-plane displacements and the diffraction angle of the grating. The validity and accuracy of the DAIC method are demonstrated through 3D displacement measurement of a small thin membrane. This technique provides new avenues for performing 3D deformation measurements at small length scales and/or dynamic loading conditions.     

部分相干光云纹干涉法测三维位移场

本文提出了一种用部分相干光可同时获得面内位移和离面位移场的云纹干涉法。该法具有装置简单,无需防震,可用于观场测量等特点。文中论述了此法的基本原理,应用波前干涉理论和付里叶光学理论对变形前后波前的干涉、记录和再观进行了分析,导出了计算公式。实现了透射物体和反射物体表面的面内位移分量(U_0,V_(45),U_(90))和离面位移(w)的全场同时测量,典型实验证明,实验值与计算结果符合较好。     

An Out-of-Plane Motion Compensation Strategy for Improving Material Parameter Estimation Accuracy with 2D Field Measurements

In-plane surface displacements, when measured with 2D Digital Image Correlation (2D-DIC), are very sensitive to out-of-plane displacement components. Any out-of-plane motion of the surface can pollute the measured field by introducing artificial displacements. These displacements are difficult to separate from the underlying response of the surface and thereby limit the application of 2D-DIC in inverse problems where the test specimen has significant motion in the out-of-plane direction. In the context of inverse problems, we propose to partially relax this condition of no out-of-plane motion in 2D-DIC. With this approach, only the out-of-plane rigid-body motion of the specimen surface, which is initially in-plane, needs to be avoided while the requirement of surface deformations to be primarily in-plane is essentially waived. Compensation, based on the pinhole camera model, for out-of-plane displacements of the surface in response to applied load is included within the error function of the minimization problem. The improvements in material parameter estimation, obtained by using the proposed compensation strategy, are demonstrated by an example. The proposed technique makes it possible to utilize 2D-DIC with a simple conventional lens for an increased number of inverse problems; and in the process avoiding the computational and experimental difficulties associated with 3D measurement methods as well as the high cost and magnification limitations of a telecentric lens.     

Experimental observation of stress waves propagating in laminated composites

The theoretical research on stress waves propagating in laminated composites has been reported by many authors. However, there has been little work on experimental studies of stress waves in those materials. This paper presents an experimental investigation on stress waves propagating parallel to the layers of a laminated composite. A sandwich laminated composite consisting of two aluminum facings and an epoxy core is used as a specimen. The stress wave in the specimen is observed by use of high-speed holographic interferometry with a pulsed laser. In order to obtain the relative fringe orders, the interference fringe pattern in the reconstructed image is treated as an image-processing system with a personal computer. For the calculation of the in-plane displacement, an approximate relative-fringe-order method is used. The in-plane displacements obtained at some sampling points on the surface are smoothed by using a spline function. Distributions of the in-plane displacement and the shear stress are then obtained quantitatively over the whole analyzed field.     

基于大型炉体焊接残余应力测试的盲孔法研究

为提高炉体焊接残余应力测试精度,对传统的盲孔法进行改进,即在测点打孔后多次扩孔并增加孔深;通过对SM400ZL钢焊接残余应力测试时的应变释放系数A,B进行实验标定,得出多组应变释放系数值,计算可得残余应力的估算值,并对不同状况下的残余应力值进行比较.通过大拉力标定试验得出SM400ZL钢盲孔的孔边塑性变形对测量精度的影响和塑性修正公式.结果表明,改进的盲孔法能够更准确地测得焊接残余应力值,测量结果经塑性修正,最大误差减小到2%以下.测试方法和结果可直接在相关的工程实际中应用.     

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提出了用超声散斑干涉法来测量物体的位移,并且基于数字干涉和相移-频移技术对超 声散斑数字干涉测量法进行了初步的理论推导. 为了验证理论分析的结果,对一铝试件进行 了离面位移和面内位移的试验测量. 试验结果显示理论分析是正确的,在测量位移和变形时 此方法是有效可行的.     

MEASUREMENT OF NON-UNIFORM RESIDUAL STRESSES BY COMBINED MOIRE INTERFEROMETRY AND HOLE-DRILLING METHOD： THEORY, EXPERIMENTAL METHOD AND APPLICATIONS

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements. The project supported by the FRAMATOME ANP     

Phase-stepped fractional moiré

Two computer-aided methods have been developed for analysis of in-plane and out-of-plane surface displacements of structures under load. Both methods are whole-field techniques which combine phase-stepped geometric moire with video and computer technologies. With these methods, a displacement field of interest is determined by computer-processing phase stepped, geometric moiré image data with fringe ordering done automatically within the software. The theory of the techniques is described and results of accuracy tests and application problems are given. It is shown that very good agreement is obtained between theory and experiment for in-plane strain determinations. For out-of-plane displacement determinations errors are only a few percent over the entire field of view. The application problems discussed are: (1) the measurement of composite column buckling, and (2) the determination of the shape of a slightly distorted, thin aluminum plate.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.