Rapid interpretation of moiré photographs

The paper describes the possibilities of rapidly and conveniently obtaining results by means of the reflection moiré method. The moiré photographs are produced with the aid of a screen provided with a finely ruled grid. The contrast of the photographs is increased by optical means. By displacement of two equal moiré photographs, moiré fringes of second order for the curvature or the twist are obtained. It is shown how charts can be produced which indicate:

1. The distribution of the bending moments
2. The distribution of the bending moments for which the reinforcement should be designed
3. The distribution of the shear forces and the magnitude of the bearing reactions.

     

The moiré-grid analyzer method for the analysis of finite strain

Elements of Lagrangian finite-strain tensor are derived in terms of moiré-fringe intercepts with grid analyzer axes (Ξ,η); they are shown to be independent of the relative angle between the analyzer and the undeformed specimen grids. The role of the initial mismatch λ and initial rotation θ ₀ on initial patterns and patterns under finite strains are discussed. Aluminum tensile-test pieces photoengraved with 133 lines per inch (lpi) grid are tested; analyzer grid of 142 lpi is used. The axial strains calculated from moiré-fringe intercepts with (ξ,η), are in good agreement with average strain obtained from 3-in. gage length.     

Displacement and Strain Measurement by Circular and Radial Gratings Moiré Method

Direct digital moiré method of circular and radial gratings with its phase shifting technique is proposed and applied in a mixed-mode fracture problem of large deformation materials. Circular and radial curves are used as both reference and specimen gratings in this digital moiré method for deformation measurement. And phase shifting technique is automatically implemented directly on circular and radial fringes, which facilitates obtaining displacement fields in polar coordinate system, radial u _r and circumferential u _θ , and strain fields ε _r, ε _θ , ε _rθ are calculated subsequently. Application of the direct digital moiré method of circular and radial gratings in a mixed-mode fracture problem with large deformation illustrates the process of this method, and also demonstrates its feasibility and validity for large deformation materials.     

The transfer-grid method,a practical Moiré stress-analysis tool

A practical and simple moiré stress-analysis technique is described. The grid is applied to any part by a transfer method, like a decal, not necessitating mechanical engraving or photoetching nor any special environmental care. The moiré fringes are observed remotely from the part without master contact. This is done through the use of a projection device and a master held in a plane where the projected image of the working grid is formed. Limitations of the method, as well as its applications, are discussed.     

Optical differentiation of the displacement patterns using shearing interferometry by wavefront reconstruction

Two techniques of moiré-pattern differentiation are described and implemented. One of the techniques is extremely simple since the grid printed in the model provides both the displacement information and the shearing mechanism required to display the displacement derivatives. This technique can only be applied to the derivatives in the direction parallel to the projected displacement. To find the derivativs in the direction perpendicular to the projected displacement, a double-exposure technique is utilized. Experimental and theoretical values of the derivatives show a good agreement. In view of the speed with which the differentiation can be performed as compared to any other methods, the proposed techniques seem to be valuable practical tools for moiré work. The optical differentiation is very attractive, but to be useful in the case of small deformations, it must produce patterns with large density of fringes. The techniques described in this paper offer a simple solution to this problem.     

Basic optical law in the interpretation of moiré patterns applied to the analysis of strains—part 1

The objective of this paper is to generalize the optical law that relates the displacement field to the fringes of moiré patterns. Until now, a discontinuous relationship has been applied. Displacements that are equal to an integral number of times the master grid pitch or half the master grid pitch are related to the points of maximum and minimum light intensity, respectively. The generalized optical law gives a continuous relation-ship between displacements and light intensities. By applying this law it is possible to increase the precision of moiré far beyond the actual limits.     

Accuracy of the Sampling Moiré Method and its Application to Deflection Measurements of Large-Scale Structures

Measuring accurate displacement distributions for large-scale structures is an important issue and a very challenging task. Recently, a simple and accurate phase measurement technique called sampling moiré method [Exp Mech 50–4:501–508, (2010)] has been developed for small-displacement distribution measurements. In this method, the phase distribution of moiré fringes can be analyzed from a single grating image by simultaneously performing down-sampling image processing and intensity-interpolation to generate multiple phase-shifted moiré fringe images. In addition, the phase of the original grating can also be obtained from the phase of the moiré fringe by adding the phase of the sampling grating. In this study, the measurement accuracy of the sampling moiré method was analyzed through computer simulations and a displacement measurement experiment. Four factors of the sampling moiré method were investigated, including the sampling pitch, the order of the intensity-interpolation, random noise, and the form of grating. The results show that determining the optimal sampling pitch is an important factor for obtaining better results but it is not critical. In addition, a practical application of the sampling moiré method is presented that involves a deflection measurement on a 10-meter-long crane. The experimental results demonstrate that submillimeter deflections of the crane can be successfully detected.     

The moiré method of zonal and line gratings

The theory of moiré fringes produced by zonal gratings interfering with line gratings of equal or slightly different pitch was developed. Differential equations relating the pitches of the two gratings to the interfringe spacing of the moiré pattern produced were established. It was shown that the moiré fringes produced belong to families of confocal ellipses, parabolas or hyperbolas in the cases where the zonal-grating pitch (p _m ) is greater than, equal to, or smaller than the line reference-grating pitch (p _r ). These patterns yielded all the displacement components of a two-dimensional strain field. Therefore, they are sufficient for the complete determination of the strain and stress distribution in any elastic or plastic plane-stress problem. As an illustration, the method has been applied to the determination of the lateral-contraction-ratio function of a polymeric substance (cold-setting pure epoxy resin) in creep at various steps of temperature.     

A moiré microscope for finite deformation micro-mechanical studies

A new version of a moiré microscope is presented that embodies the theory of optical moiré interferometry. To interrogate the deformed specimen grating, the device uses a transmission diffraction grating that allows for a simple and quick change of the virtual reference grating vector without disturbing the optical alignment of the other components in the optical train. To analyze deformation from the acquired moiré interference fringe patterns, the displacement light-itensity moiré optical law introduced by Sciammarella is revisited. The analysis of deformation is consistent with the continuum principles of finite deformation and can readily be used to obtain micro-mechanical quantities of interest such as the local strains, stretches and rotations.     

Study on fracture behavior of ferroelectric ceramics under combined electromechanical loading by using a moiré interferometry technique

This paper discusses an in situ observation of fracture behavior around a crack tip in ferroelectric ceramics under combined electromechanical loading by use of a moiré interferometry technique. The deformation field induced by the electric field and the stress concentration near the crack tip in three-points bending experiments was measured. By analysis of the moiré images it is found that under a constant mechanical load, the electric field almost has no effect on the crack extension in the case that the directions of the poling, electric field and crack extension are perpendicular to each other. When the poling direction is parallel to the crack extension direction and perpendicular to the electric field, the strain decreases faster than that calculated by FEM with and without electrical loading as one goes away from the crack tip. In addition, as the electric field intensity increases, the strain near the crack tip increases, and the strain concentration becomes more significant. The project supported by the National Natural Science Foundation of China (10132010, 10025209, 10232023)     

A new application of isodensitometry in the moiré technique

Some years ago, isodensitometry was introduced into the moiré technique in order to improve the sensitivity of this method. The application of the Sabattier effect gives now a new possibility to produce more lines of equal displacement. The obtained experimental data are the additional lines and the moiré fringes of full or half order. This method is applied on a beam under pure bending and a circular ring loaded diametrically. It will be shown in this paper that the calibration of the displacement curves can be accomplished by a calibration bar or by ‘self calibration’ which will be done on the same model to be studied. Further, the photographic process can be influenced in a way that different lines of equal displacement can be produced for a given system of moiré fringes. The additional lines are shifted here by choosing different times of exposure.     

Fabricating Parameters Optimization of High Frequency Grating by Multi-scanning Electron Beam Method

The electron-beam moiré method uses a high frequency grating to measure microscopic deformation. Increasingly fine gratings are being developed to achieve increasingly high resolutions in microscopic stress analysis. In this study, we improve the electron grid fabricating technique by using a common scanning electron microscope (SEM). An error analysis for the multi-scanning grating was performed by a sampling moiré method. The grating manufacturing parameters strongly affect the superfine grating quality. A high accelerating voltage or a short working distance yield better results generally. A set of optimal parameters is suggested based on a minimum-error criterion. A cross-line grid with a frequency of 10,000 lines/mm and a parallel grating with a frequency of 13,000 lines/mm were successfully fabricated.     

The moiré grid-analyzer method for strain analysis

The complete state of strain throughout an extended field can be determined from a single photograph by the moiré grid-analyzer method. Grids are used for the active, or specimen screen, and for the rigid analyzer screen. Hence, two families of moiré fringes appear simultaneously, providing displacements inx andy directions throughout the field. Interweaving of moiré fringes so as to disguise the identity of each family is prevented by use of an initial pattern. The initial pattern also eliminates uncertainties in assignment of moiré fringe orders throughout the field, and it provides numerous data points in any local region for reliable evaluation of fringe gradients. A rigorous derivation is presented for interpretation of such patterns in terms of strains. Errors in computed shear strains caused by analyzer misalignment are automatically canceled. The effects of rigid-body rotation of elements within the specimen are routinely eliminated in strain computations. Since calculated strains are independent of analyzer orientation, no fine control of analyzer alignment is required, and small shifts of analyzer position during the experiment are permissible. Accordingly, the moiré grid-analyzer method not only makes possible analysis of problems that previously could not be approached, but also offers vast simplifications for all extended-field moiré analyses.     

An investigation into the stresses in double-lap adhesive joints with laminated composite adherends

The mechanics of double-lap joints with unidirectional ([0₁₆]) and quasi-isotropic ([0/90/?45/45]_2S) composite adherends under tensile loading are investigated experimentally using moiré interferometry, numerically with a finite element method and analytically through a one-dimensional closed-form solution. Full-field moiré interferometry was employed to determine in-plane deformations of the edge surface of the joint overlaps. A linear-elastic two-dimensional finite element model was developed for comparison with the experimental results and to provide deformation and stress distributions for the joints. Shear-lag solutions, with and without the inclusion of shear deformations of the adherend, were applied to the prediction of the adhesive shear stress distributions. These stress distributions and mechanics of the joints are discussed in detail using the results obtained from experimental, numerical and theoretical analyses.     

An electron moiré method for a common SEM

In the electron moiré method, a high-frequency grating is used to measure microscopic deformation, which promises significant potential applications for the method in the microscopic analysis of materials. However, a special beam scanning control device is required to produce a grating and generate a moiré fringe pattern for the scanning electron microscope (SEM). Because only a few SEMs used in the material science studies are equipped with this device, the use of the electron moiré method is limited. In this study, an electron moiré method for a common SEM without the beam control device is presented. A grating based on a multi-scanning concept is fabricated in any observing mode. A real-time moiré pattern can also be generated in the SEM or an optical filtering system. Without the beam control device being a prerequisite, the electron moiré method can be more widely used. The experimental results from three different types of SEMs show that high quality gratings with uniform lines and less pitch error can be fabricated by this method, and moiré patterns can also be correctly generated.The project supported by the National Natural Science Foundation of China (10662005) and JSPS fellowship in Japan. The English text was polished by Keren Wang.     

Moiré-fringe measurement

A simple technique and an apparatus layout, for measuring moiré-fringe spacings, used in conjunction with the moiré replica technique, are introduced. Results of measurements, using this new technique for evaluation grid spacings show an agreement of more than 99.9 percent between the actual grid spacing and those evaluated using the proposed apparatus.     

Strain analysis of composites by moiré methods

Moiré techniques were developed, adapted and applied to the determination of strain fields in filamentary composite laminates. Conventional techniques, using 1000 line-per-inch (Ipi) arrays bonded or photoprinted onto the specimen, were applied to glass-epoxy and boron-epoxy specimens with holes and cracks. Techniques for tenfold fringe multiplication were also applied to glass-epoxy and boron-epoxy laminates with holes. A reflective surface of glass-like smoothness was produced on the specimen and a 500 dot-per-inch grid photoprinted on it. A rigid distortion-free camera was used for recording replicas of the specimen grid by projection photography. These replicas were analyzed with a 200 line-per-millimeter (5080 Ipi) grating for reconstruction of moiré-fringe patterns. These patterns were analyzed by graphical and mechanical differentiation using second-order moiré. Strain distributions and strain-concentration factors were in very good agreement with theoretical and other experimental results.     

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.     

The principle and application of sticking film moiré internnferometry

This paper presents a new method for obtaining a high-resolution one-dimensional or two-dimensional moiré pattern on a specimen. The technique uses a holographic film that adheres to the specimen. The film is twice exposed by a virtual holographic grating, then it is removed from the specimen, devellped, fixed, bleached, and illuminated. This process produces clearly visible moiré patterns. The method is used to measure elastic modulus values of some materials, deflection and longitudinal displacement of a beam, stress-intensity factors (SIF), crack-opening displacement (COD,J integral, and a dynamic deformation. This paper explains the principles of the method, derives two displacement equations of two-dimensional moiré interferometry, and discusses the reliability, range of application, and measuring precission of the new method.     

A new optical system for moiré methods

A new optical system for moiré methods is proposed in which the light path from the model grating and that from the master grating are diffent. They are combined by mirrors to form moiré patterns. Its application to Ligtenberg's reflective moiré method extends the method to dynamic problems and also facilitates the use of linearmismatch fringes. It can also be applied to in-plane moiré method in cases where deformation is large and diect contact with model grating is to be avoided.