Moiré interferometry combines the concepts and techniques of geometrical moiré and optical interferometry. In his definitive monograph, Guild1 shows that all moiré phenomena can be treated as cases of optical interference, although moiré generated by low-frequency bar-and-space gratings can also be explained by obstruction or mechanical interference. Moiré interferometry is capable of measuring in-plane displacements with very high sensitivity. A sensitivity of 2.4 fringes/µm displacement is demonstrated for all the patterns in this chapter except Figs. 4.7 and 4.45, where the sensitivity is 4.0 and 1.2 fringes/µm displacement, respectively. In Chapter 5, the sensitivity is even higher.

Experimental TechniquesVolume 13, Issue 6 p. 25-28 METAL-FORMING STUDIES BY MOIRÉ INTERFEROMETRY S.D.K. Barbat, S.D.K. Barbat S.D.K. Barbat is associated with the University of Michigan, department of Mechanical Engineering and Applied Mechanics, Ann ArborSearch for more papers by this authorY. Guo, Y. Guo MI. Y. Guo (SEM Member) is associated with Virginia Polytechnic Institute and State University, Department of Engineering Science and Mechanics, Blacksburg, VA.Search for more papers by this authorR.S. Rao, R.S. Rao R.S. Rao is associated with the University of Michigan, Department of Mechanical Engineering and Applied Mechanics, Ann Arbor, MI.Search for more papers by this authorD. Post, D. Post D. Post (SEM Member) is associated with Virginia Polytechnic Institute and State University, Department of Engineering Science and Mechanics, Blacksburg, VA.Search for more papers by this author S.D.K. Barbat, S.D.K. Barbat S.D.K. Barbat is associated with the University of Michigan, department of Mechanical Engineering and Applied Mechanics, Ann ArborSearch for more papers by this authorY. Guo, Y. Guo MI. Y. Guo (SEM Member) is associated with Virginia Polytechnic Institute and State University, Department of Engineering Science and Mechanics, Blacksburg, VA.Search for more papers by this authorR.S. Rao, R.S. Rao R.S. Rao is associated with the University of Michigan, Department of Mechanical Engineering and Applied Mechanics, Ann Arbor, MI.Search for more papers by this authorD. Post, D. Post D. Post (SEM Member) is associated with Virginia Polytechnic Institute and State University, Department of Engineering Science and Mechanics, Blacksburg, VA.Search for more papers by this author First published: June 1989 https://doi.org/10.1111/j.1747-1567.1989.tb01032.xAboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume13, Issue6June 1989Pages 25-28 RelatedInformation

Moire interferometry provides contour maps of in-plane displacement fields with high sensitivity and high spatial resolution. It has matured rapidly as an invaluable tool for engineering analyses, proved by many industrial and scientific applications. With the typical reference grating frequency of 2400 lines/mm, the contour interval is 0.417 mu m displacement per fringe order. For microscopic moire interferometry, sensitivity corresponding to 17 nm per contour has been achieved. Reliable normal strains and shear strains are extracted from the displacement data for bodies under mechanical, thermal and hydrostatic loading.

Moiré interferometry is introduced as an outgrowth of moiré fringe multiplication. Coherent laser light enabled the practical implementation of virtual reference gratings and high-frequency specimen gratings. Reliable analysis of shear depended upon the ideas in a little-known paper. These three facets are the essence of current techniques. Present-day applications are exemplified by work in electronic packaging and composite materials. Several significant advances are forecast to further broaden the usefulness and appeal of moiré interferometry.

In the past decade, the optical method called moire interferometry has matured rapidly to emerge as an invaluable tool, proved by many industrial and scientific applications. It has been applied to numerous problems in engineering mechanics. It measures in-plane displacement fields with high sensitivity and high spatial resolution. This paper reviews current practices of moire interferometry and its extensions. Applications in diverse fields are addressed to demonstrate the wide applicability of the method, especially the recent applications for thermal deformation analyses of microelectronics devices. Speculation on future developments and practices is presented.

Moire interferometry and shadow moire are extraordinarily versatile and effective methods for determining in-plane and out-of-plane displacement fields, respectively. The basic concepts are reviewed for both methods, topics on practice and analysis are addressed, and numerous examples of important applications are presented.The moire data are received as whole-field fringe patterns, or contour maps, of displacements. For moire interferometry with the typical reference grating frequency of 2400 lines/mm, the contour interval is 0.417 mu m per fringe order; the sensitivity is 2.4 fringes per mu m displacement. Orthogonal U and V displacements are measured, and normal and shear strains are determined from these in-plane displacement fields. For microscopic moire interferometry, sensitivity corresponding to 17 nm per fringe contour has been achieved by means of the optical/digital fringe multiplication algorithm.The patterns of moire interferometry are characterized by excellent fringe contrast and spatial resolution, including patterns from complex applications. The applications reviewed here address laminated composites, including the study of free-edge effects along the cylindrical surface of holes in laminated plates; thermal deformation of microelectronics devices; the damage wake along a crack path, and a micromechanics study of grain deformations in titanium.The examples of shadow moire show the out-of-plane displacements W for prebuckling and post-buckling of columns; and W displacements of electronic packages subjected to temperature changes. Phase-stepping analyses were used for the electronic packages to increase sensitivity, providing 12.54 mu m per fringe contour. Since W is typically much larger than U and V, the sensitivity of shadow moire can be adjusted to serve broad categories of engineering applications.

The deformation on cylindrical surfaces of holes in tensile-loaded laminated composite specimens was measured using new moiré interferometry techniques. Two composite tensile specimens, fabricated from IM7/5250-4 pre-preg with ply layups of [0°4/90°4]3s and [+30°2/-30°2/90°4]3s, were examined using the newly developed moiré interferometry techniques. Circumferential and thickness direction displacement fringe patterns (each 3° wide) were assembled into 90°-wide mosaics around the hole periphery for both composite specimens. Distributions of strain were calculated with high confidence on a sub-ply basis at select angular locations. Measured strain behavior was complex and displayed ply-by-ply treands. Large ply-related variations in the circumferential strain were observed at certain angular locations around the periphery of the holes in both composites. Extremely large ply-by-ply variations of the shear strain were also documented in both composites. Peak values of shear strain approached 30 times the applied far-field axial strain. Post-loaded viscoelastic shearing strains were recorded that were associated with the regions of large load-induced shearing strains. Large ply-group related variations in the thickness direction strain were observed in the [+30°2/-30°2/90°4]3s specimen. An important large-scale trend was observed where the thickness direction strain tended to be more tensile near the outside faces of the laminate than near the mid-ply region. The measured strains were compared with the three-dimensional analysis technique known as Spline Variational Elastic Laminate Technology (SVELT), resulting in a very close match and corroborating the usefulness of SVELT.

In this paper, high sensitivity laser moire interferometry was used for observation and analysis of in-situ damage initiation and growth in random fiber composite beams. The technique was found to be very effective. The general approach was to load the beams to successively increasing load levels, and then unload, observing the residual field. Damage showed up as anomalies in the fringe patterns. In the four-point-bend tests, it was found that observable microscopic failure initiated in the tension region first at about 40% of the ultimate failure load, while failure initiation in the compression region started at about 50% of the ultimate failure load. To determine the effect of this early and asymmetric damage growth in the tension and compression regions, the neutral axis shift of the beam was determined as a function of increasing load. This was done by reloading the beams (after observing the residual field) to a small load well below any damage threshold. It was found that very little shift occurs indicating the stiffness of the beam was largely unaffected by the microstructural damage over a major range of loading including close to failure. This unexpected behavior is most likely caused by progressive failure of the chopped fibers in orientations at or near 90° to the length of the beam.

An experimental analysis was conducted on a bimaterial plate subjected to a uniform change of temperature. Whole-field displacement measurements U and V were made on the free surface by means of high-sensitivity moire interferometry, and stresses were calculated from these data. Stresses resembled those of stress singularities, but they reached finite tensile and compressive peaks on opposite sides of the interface. The peaks and a severe stress gradient between them occurred in a narrow zone of about ±25 μm from the interface. The results pertain to an elastic three-dimensional body.

This chapter excerpts material from a series of tests of thick laminated composites in compression.1 As illustrated in Fig. 7.1, the graphite/epoxy specimens were cut from thick-walled cylinders with two different stacking sequences (i.e., the sequence of fiber directions in successive plies of the laminate). They are called quasi-isotropic and cross-ply laminates. In-plane and interlaminar compression tests were conducted, with the compressive loads applied parallel and perpendicular to the plies, respectively. Note that the coordinate system maintains x perpendicular to the plies and y parallel to the plies. The loading fixture of Fig. 4.10 was used.

Many fields of study require deformation measurements of tiny specimens or tiny regions of larger specimens. The mechanics of microelectronic assemblies is an example, where the ever increasing demand for closer packing exacerbates the problems of thermal stresses. Other fields include crack-tip analyses in fracture mechanics; grain and intragranular deformations of metals and ceramics; interface problems; etc. Moiré interferometry adapted for such micromechanics studies is the subject of this chapter.

Brief descriptions of several studies are presented in this chapter. Diverse experiments are described where the common thread is composite materials. They address the mechanics of highly complex bodies. These examples were chosen to demonstrate the broad scope of moiré interferometry and to express the virtue of whole field observations. These are not in-depth reports. Instead, numerous fringe patterns are shown and discussed to familiarize the reader with real-world analysis.

The main focus of this chapter is potential limitations imposed by the aperture of the camera lens. Numerical and experimental investigations were performed to validate moiré interferometry for extremely large strain gradients and discontinuities.