A localized hybrid method of stress analysis: A combination of moiré interferometry and FEM

A method of combining moiré interferometry and the finite-element method to effect localized stress analysis is presented. The displacement data from local regions of interest in the optical experiment are used as boundary conditions for the finite-element stress analysis. The stability of the method is examined with data from simple numerical models one of which corresponded to the stress analysis of a pin-loaded plate with friction. These studies show that the method requires the sensivity of moiré interferometry for successful implementation, i.e., displacement data accuracy within 0.1 μm or 4 μin. This localized hybrid method of stress analysis provides a powerful and efficient method for the reduction of experimental data.     

An experimental investigation of losipescu specimen for composite materials

A detailed experimental evaluation of the losipescu specimen tested in the modified Wyoming fixture is presented. Moiré interferometry is employed to determine the deformation of unidirectional and cross-ply graphite-epoxy specimens. The results of the moiré experiments are compared to those from the traditional strain-gage method. It is shown that the strain-gage readings from one surface of a specimen together with corresponding data from moiré interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to twisting. A localized hybrid analysis is introduced to perform efficient reduction of moiré data, producing whole-field strain distributions in the specimen test sections.     

An intelligent hybrid method to automatically detect and eliminate experimental measurement errors for linear elastic deformation fields

In a previous study, to minimize or eliminate the errors and noises associated with a full-field experimental measurement and subsequent fringe analysis such as moiré interferometry, the authors derived a variational principle minimizing the experimental measurement errors. Furthemore, on the basis of this variational principle, the authors developed an intelligent hybrid method. In several test simulations, the method has demonstrated the automatic detection and elimination of randomly incorporated errors into known correct finite element displacement fields. In this study, a fringe analysis method is developed together with the two-dimensional fast Fourier transform method. Then, experimentally recorded moiré fringe patterns are analyzed by the fringe analysis method. The conventional and intelligent hybrid analyses are carried out using the analyzed fringe information as input data. The present method verifies the automatic detection of experimental errors and noises, and the simultaneous automatic elimination of those experimental errors. This method also makes it possible to obtain a fairly smooth visualization of higher order information such as the stress and strain distributions.     

Integration of laser-speckle and finite-element techniques of stress analysis

A study of the combined use of laser-speckle and finite-element methods for stress analysis is described. The speckle technique provides displacement data which can be directly input to a finite-element computer program for the determination of stresses. The displacement data can be used as boundary conditions for the examination of a subregion of the structural component to be analyzed. A substantial reduction in computational effort can be realized over conventional finite-element analysis of the entire structure. Also, a sizeable reduction in the required amount of experimental data may occur since direct numerical differentiation of the data is not required for strain evaluation. Acceptable accuracy may be obtained even when experimental displacement data may be too scarce for traditional numerical differentiation. Random error in experimental displacement is illustrated to have localized effects on the calculated stress field. Paper was presented at 1983 SESA Spring Meeting held in Cleveland, OH on May 15–19, 1983.     

Measurement of energy release rates for delaminations in composite materials

Conventional measurements of energy release rates,G _I andG _II, for delaminations in composite materials, generally utilize loads, crack lengths and simple standard specimen geometries. In this work, a more widely applicable measurement method, using phase shifting moiré and the J integral, is presented. The experimental technique described requires only fringe-pattern information and the elastic constants for the measurements—thus it can be used when the standard methods are inapplicable. Using conventional double-cantilever beam and end-notched flexure specimens, the energy release rate has been measured simultaneously by the moiré method and the standard methods, with good agreement found between the two. This development will for the first time permit the experimental validation of new finite-element routines as they are developed.Paper was presented at the 1993 SEM Spring Conference on Experimental Mechanics held in Dearborn, MI on June 7–9.     

Iosipescu shear characterization of polymeric and metal matrix composites

The paper outlines the results of an experimental/analytical investigation of deformation and stress fields in the test section of graphite/epoxy and boron/aluminum Iosipescu specimens using high-resolution moiré interferometry and finite-element analysis. Very good correlation between experimental and analysis is demonstrated for the graphite/epoxy speciments. This, in turn, justifies the use of correction factors employed in the previous investigations to eliminate differences in the inital shear moduli obtained from 0-deg and 90-deg losipescu specimens. The significant discrepancies observed in the case of boron/aluminum specimens are attributed to localized yielding at the notch tips caused by the clamping action, the associated in-plane bending effects and changing boundary conditions due to slippage in the grips.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Whole-field residual stress measurement in rail using moiré interferometry and twyman/green interferometry via thermal annealing

A novel whole-field residual stress measurement technique is developed using moiré interferometry and Twyman/Green interferometry coupled with thermal annealing. The technique is successfully applied to residual stress measurement in rail. In the measurement, a high temperature resistant 1200-lines/mm cross grating is made on a rail transverse slice surface. The whole-field residual stress relief is achieved by thermal annealing. Moiré interferometry and Twyman/Green interferometry are employed to obtain the in-plane and out-of-plane deformations generated by the residual stress relaxation. The whole-field strain redistribution due to the residual stress relief is calculated, and the whole-field residual stress distribution, including the possible stress concentration, is then obtained. Because of the three-dimensional nature of the residual stress relaxation and the measurement, the three-dimensional residual stress reconstruction sometimes becomes possible based on some plausible assumptions. In this paper, the principle of the experimental theory, technique and procedures are described. Three-dimensional residual stress reconstruction in a rail using a transverse slice is shown. Its comparison to the hole-drilling method with moiré interferometry is also presented.     

Hybrid elastostatic and thermostatic analysis from measured data

An effective hybrid method is demonstrated for stress analysis and heat transfer. Measured information is represented and differentiated analytically, while the number of unknown coefficients and amount of experimental input data needed are reduced through field equations. The approach is accurate, full-field, employs arbitrarily shaped elements, does not require a smoothing parameter and is well suited for computer-vision techniques. The concept is presently illustrated by moiré strain analysis, although it can be extended to other disciplines.     

Constructing pure digital secondary moiré patterns

A new method of constructing pure digital secondary moiré patterns of equal-strain fringes is proposed in this paper. By this method, a pure secondary moiré pattern, without trace of primary moiré fringes, is obtained directly from common digital moiré patterns regardless of how low or high the fringe density. The pure secondary moiré patterns eliminate the backnoise of primary fringes and give the strain value at every point over the whole strain field. This technique can significantly increase the measurement accuracy and the range of moiré techniques.Paper was presented at the 1988 Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Exact interpretation of moiré fringe patterns in digital images

Geometric moiré enjoys the advantages of simplicity of technique and equipment, and the ability to use white light. However, resolution has been hampered by difficulties in employing more than 40 per mm. The present paper illustrates the aspects of a digital imaging system relevant to the determination of fractional fringes, and enables reliable analysis from extremely few fringes.In applying digital imaging to moiré analysis it is imperative that not only the optical characterization but also the features of the image recording system be well understood. Digitization, spatial-averaging operation and the aperture modulation are the most significant features critical to the interpretation of the digital image recorded.This paper seeks to illustrate the interaction of the moiré technique with the characteristics of a specific image recording system. Examples are presented which experimentally define the nature of moiré fringes recorded with a relatively standard digital imaging system. Further examples are presented which illustrate the influences of the features of this imaging system on the interpretation of the moiré pattern.     

The moiré method applied to three-dimensional elastic problems

The purpose of this paper is to develop the technique of moiré for three-dimensional strain and stress analysis. The classical problem of contact of a sphere with a semi-infinite space is studied, and experimental results are compared with those of Hertz's solution. Results show that the method is accurate and has a high sensitivity. The results prove also that the strain distribution in a very small region with a steep gradient can be detected quite precisely.Paper was presented at the 1964 SESA Spring Meeting held in Salt Lake City, Utah, on May 6–8.     

Deformation measurement during powder compaction by a scanning-moiré method

The mechanical behavior of powders during compaction has been studied in previous papers. It has been shown that a moiré method may be used to determine the resulting strain distribution. Some difficulties were encountered, however, in the method used. In the present paper, therefore, an image-processing system employing a personal computer to analyze the moiré pattern is introduced. Many strain distributions obtained in this way from moiré-fringe patterns are presented. Further, using this image-processing system, a scanning-moiré technique is developed in which the master grating is replaced by the scanning lines of a television camera. The use of image processing in conjunction with the mismatch technique allows measurement of both small and large strains from one image picture.Paper was presented at 1982 SESA Spring Meeting held in Oahu and Maui, HI on May 23–28.     

Investigation of displacement fields in an abrasive waterjet drilling process: Part 1. Experimental measurements

The transient state of displacement fields in the machining zone of a target material during abrasive waterjet impinging and drilling was investigated. A moiré interferometry experimental setup for recording displacement fields and a dynamometer for measuring the reaction force were developed. Whole fields of surface displacement fields and the reaction force of the ceramic and polycarbonate target materials were successfully recorded when the specimen was being pierced by high-pressure abrasive waterjet (AWJ). This paper demonstrates that bothu andv displacement fields of a workpiece during AWJ drilling can be recorded in real time and simultaneously by the moiré interferometry experimentation. The measured surface displacement distributions and the machining forces will be used to drive a finite element model in the second part of this investigation, in which the authors study the stress and strain state for the target material associated with the jet-materials interaction during the jet penetration process.     

Moiré holographic analysis of reinforced plate models

This paper deals with an extension of moiré holography for structural analysis on reinforced plate models. It is shown that unequal optical paths, caused by lack of uniform thickness, are compensated for and do not alter the moiré fringe patterns. Moreover, a simple technique is described for replicating high-sensitivity moiré gratings on Plexiglas models. The validity of the method has been satisfactorily tested on plate models with different geometries.Paper was presented at the 1988 SEM Spring Coinference on Experimental Mechanics, held in Portland, OR on June 5–10.     

Out-of-plane deflections of metallic and composite pin-loaded coupons

The projection shadow moiré technique was employed to determine an out-of-plane contouring history of aluminum, [(+45/–45)]_3S , [(0/90₃,0] _S and [(0/90/+45/–45)]_2S fiberglass epoxy pin-loaded specimens experimentally. The contouring interval was limited to 0.0254 mm by experimental concerns. Qualification of the projection shadow moiré optical arrangement was initially accomplished by the out-of-plane contouring of a clamped, centrally loaded, circular aluminum plate. Experimental results indicate significant out-of-plane displacements in the bearing region of the coupon at load levels well below ultimate. Effects of material anisotropy could be seen in the fiber-oriented shape of the displacement contours. Comparisons with three-dimensional finite-element results indicate that experimental out-of-plane contours were significantly larger than their finite-element counterparts in the region above the pin for the [(+45/–45)]_3S , [(0/90)₃, 0] _S laminates. These deviations increased with increasing pin-load level. These variations could be attributed to linear-elastic through-thickness moduli assumptions as well as through-thickness finite-element mesh coarseness.     

Measurement of residual stress using interferometric moiré: A new insight

The use of interferometric moiré and hole drilling to determine residual stress has been well reported and accepted for stress fields whose principal directions can be predicted well enough to permit the moiré grids to be aligned with the principal strain axes. When the principal strains do not align themselves with the grid axes, a third strain component can be obtained by working with the diagonal pitch of the moiré grid, but this requires resetting the optical bench to the lower frequency. Diffraction efficiency is lost, with an additional loss in sensitivity. In this paper, the authors determine the shear strain component by observing the rotation of the moiré fringes in close proximity to the hole. The results of experiments on a specimen containing a model residual stress distribution are presented and compared with the theoretical prediction. Finally, the isothetic contours, based on elastic theory, were computed and plotted for several cases to verify this proposition. These results and the expected residual stress distribution are also compared to the experimentally obtained moiré fringes.     

Measurement of bending stresses in shells of arbitrary shape using the reflection moiré method

The basic equation for fringe formation in the case of reflection moiré applied to surfaces of arbitrary curvatures is derived. A practical point-by-point solution for the application of this method is introduced, and the corresponding simplified equations are given. The technique is applied to an industrial problem, the stress analysis of a shell-shaped door.     

Moiré interferometry: Advances and applications

Recent applications of moiré interferometry at VPI & SU and related developments of laboratory techniques are reviewed. The applications are studies of composite bodies, including micromechanics and macromechanics of composites, thermal strains and residual strains. The techniques section discusses steady-state thermal strain measurements, carrier fringes, and advances in methods for producing specimen gratings. With its high sensitivity, high spatial resolution and extensive displacement range, moiré interferometry has matured into a powerful technique for measuring inplane deformations of complex materials and structures.Invited paper was presented at the 1990 SEM Fall Conference on Hologram Interferometry and Speckle Metrology held in Baltimore, MD on November 5–8.     

Moiré interferometry determination of residual stresses in the presence of gradients

The full-field technique of high-sensitivity moiré interferometry in conjunction with a multiple-hole-drilling procedure is applied to residual-stress measurements in the presence of gradients. The method arrives at residual-stress estimates starting from in-plane displacement components. Successful applications of the method to problems simulating the nonuniform transverse residual stresses of welded joints are reported.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Fracture process zone analysis of concrete using moiré interferometry

The fracture process zone (FPZ) ahead of a crack tip in concrete and mortar beams subjected to threepoint bending was studied using moiré interferometry. A large FPZ can occur in concrete before the external load reaches its maximum value. Comparing the experimental results between concrete and mortar suggests that the aggregate contributes to the formation of the large FPZ in concrete. The formation of this large FPZ makes concrete less brittle than mortar. The effect of the FPZ on the fracture property, such as stress intensity factor, is investigated by combining moiré interferometry measured displacements with the smoothing FEM method. The study shows that a large FPZ significantly affects the value of the stress intensity factor.