The grid-shift technique for moiré analysis of strain in solid propellants

Moiré principles and procedures were surveyed with a view toward adaptation to measurement of complex strain distribution in solid propellants. Compliant coating and photosensitive materials were selected for grid reproduction. The most flexible of the several possible procedures for recording moiré data was found to be grid photography. A novel “grid-shift” technique employing coarse grids was developed for point-by-point determination of surface displacement derivatives, and the grid-shift relations for large strain and large rotation were derived. The technique is extremely versatile, permitting the analysis of strain of dynamically deformed specimens in nonambient environmental conditions of temperature, pressure or atmosphere. The utility of the technique was demonstrated by application to static and dynamic problems.     

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.     

Moiré interferometry at VPI & SU

A relatively easy technique for producing high-frequency gratings on specimens extends moiré techniques into the high-sensitivity domain. Whole-field patterns of inplane displacement components are obtained with grating frequencies of 1200, 2400 and 4000 l/mm (30,480, 60,960 and 101,600 l/in.). Moiré interferometry is a case of two-beam interference, characterized by extensive range, excellent fringe contrast and fringe localization on the specimen surface. It is a reflection technique, compatible with opaque specimens and live observation of deformation.     

Surface topography by multisource moiré patterns

Moiré patterns produced by interference of a series of periodically arranged linear light sources with a line-specimen grating of similar pitch are located at a plane parallel to the sources and the specimen grating and at some distance away from these planes. A transparent or reflecting specimen located at a distance from the specimen grating distorts the image of the multisource projected on the specimen grating due to its surface irregularities and forms a moiré pattern. This pattern yields the partial-slope contours of the topography of the specimen along a direction normal to the lines of the grating. Two such contour patterns taken at mutually perpendicular directions are sufficient to yield the complete topographic picture of the surface. The method was used for determining gradients of thickness variations in two-dimensional specimens due to lateral contraction. The technique is highly accurate in determining the values of thickness in such cases, since the integration of the slope of thickness variation along any traverse of the specimen is a steady and accurate process.     

Precision strain standard by moiré interferometry for strain-gage calibration

Moiré interferometry is proposed as an alternative to extensometers to define the strain field used for calibration of electric strain gages. Measurements were conducted with a real reference grating of 1200 lines/mm (30,480 ?/in.), a gage length of 41.67 mm (1.640 in.), and a strain excursion of 2000 μm/m. Results showed a standard deviation of 1.1 μm/m at each load level and probable error within 2 μm/m for the 2000 μm/m excursion. Critical factors for accuracy are change of gap between specimen and reference gratings that might occur during loading, and the quality of collimation of incident light. A hollow uniaxially loaded test specimen interrogated by moiré interferometry is recommended for a strain standard of 99.9-percent accuracy.     

The moiré method for measuring large-plane nonhomogeneous deformations

Moiré-fringe equations have been developed for directly determining the components of Green's and Cauchy's deformation tensors from measurements of fringe pitch and angle. The equations, which were previously verified for large-plane homogeneous deformations, are used to determine the deformation-tensor components for nonhomogeneous strain fields. The results are compared to theoretical values. Specifically, the deformations investigated are pure bending of a rectangular block, and extension of a tapered plane specimen.     

Sharpening and multiplication of moiré fringes

Moiré fringe sharpening is produced when the widths of clear and opaque bands in a pair of super-imposed screens are complementary. Fringe multiplication is produced when the frequency of lines in the reference screen exceeds the frequency in the specimen screen by an integral factor. The number of moiré fringes then formed corresponds to the greater frequency. The conditions of formation of these moiré patterns are presented and demonstrated. Intensity distribution across projected images of moiré fringes is discussed.     

Moiré topography of curved surfaces

A physical surface presents a macroscopic curvature and a microscopic curvature, associated with roughness, which is superimposed on the former. Moiré techniques developed in this paper deal with the measurement of partial slopes and macroscopic curvatures of cylindrical and conical shells due to loading. Two distinct techniques are presented, capable of measuring both the undeformed shape of the shell, as well as small departures from the initial shape due to loading. The first one yields the deflection-contour pattern of the loaded shell by bringing into interference the lines of a reference grating, placed close to the matt surface of the shell, and their shadows cast on this surface. The second one provides patterns of partial-slope contours by bringing into interference the reflected lines of a reference grating, placed at a distance apart from the specularly reflecting surface of the shell, and a second grating named the specimen grating. For the complete definition of the surface, an orthogonal set of partial-slope contour or curvature patterns is needed. Either method is sufficient for the evaluation of the moment and strain distribution of the loaded shell, with the second method being more sensitive and accurate. Illustrative examples are given for both methods.     

New optical methods of moiré fringe multiplication

Photographs or other replicas of relatively coarse specimen screens can be analyzed with sensitivities corresponding to screens of many thousands of lines per inch (lpi). Moiré fringe multiplication is accomplished by collecting specific groups of diffracted beams emanating from two moiré screens in series. Three methods are described and multiplication by factors as high as 30 are demonstrated. Sensitivity and accuracy are increased by the fringe-multiplication factor. Usefulness of full-field mechanical differentiation techniques is extended to cases of correspondingly lower strains. These fringe-multiplication methods apply to both bar-and-space screens and transparent diffraction gratings.     

Measurement of strain fields near coldworked holes

Residual strains near coldworked holes were measured for several degrees of radial expansion. Moiré-grating photography created magnified replicas of deformed gratings. Fringe patterns with sensitivity multiplication and S/N improvement were obtained by optical data processing and by using slotted apertures for photography. Computer data reduction and plotting provided the required strain maps.     

A technique for reducing the fringe frequency in large-displacement holography

The analytical method of superposition is combined with the experimental technique of multiple-exposure holography to decrease the sensitivity of holographic measurement by at least an order of magnitude. Moiré fringes of a lower frequency are produced which simultaneously extend the range of measurement to larger displacements. The method is demonstrated for the case of a clamped circular plate subjected to a concentrated load centrally applied.     

Wave motion in anisotropic media by dynamic photomechanics

Photomechanical techniques are developed for studying wave propagation in anisotropic media such as fiber-reinforced composites and rocks. Moiré fringes in transparent and opaque materials, and isochromatic fringes in transparent composites, are photographed at rates up to over one-million frames/second. A Beckman and Whitley 189 framing camera is utilized with illumination provided by argon flashbombs or a special electronic flash.     

Displacement field around a circular hole in a viscoelastic plate

Moiré experimental techniques are used to measure displacement fields in viscoelastic plates undergoing large deformations at elevated temperatures. These experimental procedures are applicable to determining displacement fields in nonlinear materials. As preliminary information, the material properties are determined from creep studies. The moiré method is used to determine the strains under constant load and isothermal conditions. Tests are conducted for several combinations of load and temperature for 2.5 decades of time. Assuming thermorheologically simple behavior, the data are shifted to establish the creep extensional compliance over ten decades in time. The constitutive equations are formulated as integral equations, the kernels of which are the functions that were measured in this work. These equations are solved exactly for the infinitesimal case. The finite case is then approximated by an incremental superposition of a series of successiye infinitesimal solutions. The results are applied to a plate initially containing a circular hole, and are shown to agree closely with the experimental measurements.     

Moiré interferometry with embedded grids-effect of optical refraction

Optical refraction resulting from refractive index gradients in nonhomogeneously stressed models is investigated as a limitation on the usefulness of moiré interferometry employing embedded grids. Apparent displacements caused by internal refraction are estimated for static and dynamic cases; Boussinesq's problem, and the problem of a spherically expanding pulse, respectively. Refraction effects are found to be far larger in the dynamic case. Moiré observations of motions in models loaded by pellet impact are compared with independently measured motion histories. Anomalies in the moiré data are found to agree fairly well with predicted refraction effects for a spherically expanding pulse. It is concluded that optical refraction effects are potentially quite detrimental to observation of transient internal motions using moiré interferometry.     

A dynamic moiré method for deformation measurement of curved surfaces

A simple method is proposed for obtaining moiré patterns, and information is given on the deformation of curved surfaces. The experimental arrangement is based on the projection-moiré principle and consists of a projector and a camera. A transparent object, e.g., a shell with line gratings, is projected onto the focal plane of this projector and superposed there with a reference grating which describes the undeformed state of the curved surface in the form of a transparent picture. Moiré patterns are obtained by simultaneously superposing the projected line grating in the shell's deformed state and the reference grating. They present a general picture of the behavior of the object during loading, such as during impact if the patterns are recorded with a high-speed camera.     

Experimental study of the failure mechanism and strength characteristics of fiber bundles and composites

The primary aim of this investigation was to establish the strength characteristics of S-glass fiber bundles and composites subjected to quasi-static loading. Ten glass-bundle specimens and glass-fiber unilayer specimens, each containing thirty-one approximately equally spaced fibers (S-glass, 0.00485-in. diameter) were prepared and tested in an Instron machine at three strain rates (0.0265 in./in./min, 0.66 in./in./min and 26.5 in./in./ min). Grid lines were placed on composite specimen producing interference moiré fringes with a reference master grid placed in front of the specimen. The specimens were observed photographically during deformation. The experimental bundle strength compares well with that obtained on the basis of Daniels' theory. The experimental standard deviation is, however, much larger than that predicted theoretically. The experimental mean composite strength is compatible with that obtained on the basis of rule of mixtures and Gücer-Gurland models. The Zweben crack-propagation criterion [E ₂(f _C )=1] gives too low a value for the composite strength. A new criterion [E ₃(f_C)=1] is suggested for the present test series. Due to the rather large standard deviation and the small number of test samples it was not possible to quantitatively evaluate the effect of rate of straining. However, it is observed that, within the range of strain rates employed, the effect of strain rate on bundle and composite strengths does not exceed 20 percent and 10 percent, respectively.     

Application of Moiré Interferometry to the Characterization of Orthotropic Materials in the Antisymmetric Configuration using the Virtual Fields Method

Moiré interferometry is an effective full-field deformation measurement technique and has been utilized for mechanical behavior analysis of materials and structures. For isotropic materials, Moiré patterns can be obtained by performing standard tests, such as, tensile and bending tests, to calculate the displacement and strain. Then, the mechanical properties can be characterized. However, standard tests are not sufficient to characterize the mechanical parameters of anisotropic materials due to the complexity of their material properties. Thus, in this work, Moiré interferometry was combined with the Virtual Fields Method to obtain the four in-plane elastic constants (Q₁₁, Q₂₂, Q₁₂, and Q₆₆) of orthotropic materials in the form of a diametrically compressed disk. Firstly, according to finite element method simulation results, optimized parameters can be achieved when the principal direction of the material does not coincide with the loading direction, making the loading configuration antisymmetric. Therefore, Moiré interferometry experiment was simulated to demonstrate the feasibility of measurement in the antisymmetric configuration. Finally, the Q₁₁, Q₂₂, Q₁₂ and Q₆₆ values of a unidirectional carbon fiber composite were measured in a real Moiré interferometry experiment using the proposed method, yielding results that agreed closely with those obtained using the strain gauges.     

Edge-effect studies in fiber-reinforced laminates

Experimental and theoretical studies of edge effects in rectangular composite strips under tension are discussed. The objective of the study was to investigate the effect of various parameters, including reinforcement material, fiber orientation and the structure of the reinforcement, on the various quantities which are observed in the vicinity of free edges in multidirectionally reinforced laminates. Of particular interest was the confirmation of theoretical results related to differences in response of graphite- and boron-reinforced laminates. Experiments consisted of moiré measurements of surface-displacement patterns which were compared with theoretical predictions, and examination of failure levels. The experiments were carried out on AVCO 5505 boron and Whitaker 5206 MODMOR II graphite-reinforced angle-ply laminates in which both stacking sequence and fiber orientation were varied parametrically. Moiré techniques were developed which allowed observation of displacements on both the wide surface and along the narrow edge of 1 in.-wide × 16-ply-thick (.085 in.-.105 in.) laminates.     

Application of the moiré method for use with cylindrical surfaces

The paper describes how the Moiré reflective technique can be used to determine transverse-bending moments in a cylindrical shell. A cylindrical screen is used and the pattern of lines on it is reflected in the shell which acts as a lens and reduces the apparent pitch. When a photograph of the unloaded shell is considered, the lines on the negative are found to vary only slightly in width so that within the limits of movement of the ray reflected from the shell the pitch can be considered uniform. Loading the shell alters its radius and this alters the pitch of the lines as they appear on the photographic plate. It is shown that this change in line width does not affect the fringe pattern. Since the length of the reflected ray increases at distances away from the center of the photograph, a correction has to be applied to fringes at these points to obtain the correct change of slope. Photographs of the fringe pattern are obtained for various angular positions round the shell and, from these photographs, graphs of fringe against position round the shell are plotted. After correction, the slope of these graphs allows the bending moment at a point to be calculated. It is noted that transverse and radial deflections can influence the fringe pattern and this is allowed for. By taking photographs of the unloaded shell and measuring the widths of lines on the negative, the radius of the shell can be calculated and compared with spherometer readings. Knowing the bending moment at a point, the change in radius is calculated and the calculated final radius compared with that obtained from measurements on the separate photograph of the loaded shell. Finally, the deflections on the transverse center line are calculated from the fringe patterns and compared with deflection-gage readings.     

Hole-drilling method using grating rosette and Moiré interferometry

The hole-drilling method is one of the most wellknown methods for measuring residual stresses. To identify unknown plane stresses in a specimen, a circular hole is first drilled in the infinite plate under plane stress, then the strains resulting from the hole drilling is measured. The strains may be acquired from interpreting the Moire signature around the hole. In crossed grating Moire interferometry, the horizontal and vertical displacement fields （u and v） can be obtained to determinate two strain fields and one shearing strain field. In this paper, by means of Moire interferometry and three directions grating （grating rosette） developed by the authors, three displacement fields （u, v and s） are obtained to acquire three strain fields. As a practical application, the hole-drilling method is adopted to measure the relief strains for aluminum and fiber reinforced composite. It is a step by step method; in each step a single laminate or equivalent depth is drilled to find some relationships between the drilling depth and the residual strains relieved in the fiber reinforced composite materials.