The magic of carrier fringes in moiré interferometry

Practical applications in which carrier fringes are used with moiré interferometry for strain measurements are presented. Examples illustrate how moiré carrier fringes are applied to obtain the desired data in complex laminated composite specimens. In many cases, carrier fringes permit extraction of much more detailed information, with procedures that are easier and more accurate than those using loadinduced fringes alone. The fringe vector for carrier fringes is introduced and its application to the interpretation of fringe patterns is explained. In moiré interferometry, the carrier fringes are produced easily by adjustments of optical elements that control the virtual reference grating.     

Automated fringe pattern analysis for moiré interferometry

The theory of an automated fringe-pattern analysis using temporal phase stepping method for moiré interferometry is presented. The automated method provides a fast and accurate strain measurement for moiré interferometry. Measurements on a tapered composite specimen with a dropped ply are shown to highlight the capability of this technique to obtain the strain distribution, particularly around the region with a dropped ply.     

Recent Applications of Moiré Interferometry

Moiré interferometry has been a valuable experimental technique for the understanding of the mechanical behavior of materials and structures. Over the last decade less emphasis has been placed on the development of the technique and more towards applications. This paper is a review article on recent applications using moiré interferometry in the fields of microelectronics devices, material characterization, micromechanics, residual stress, composite materials, fracture mechanics, and biomechanics. The general principles of moiré interferometry and advancement of techniques will not be discussed in this text, but references will be provided.     

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     

Using Carrier Fringes to Study the High Temperature Deformation Behavior of a BGA Package Under Extended Dwell Times

There is a compelling need to experimentally understand solder joint deformation behavior at high temperatures over an extended period of time. Accordingly, the deformation behavior of solder joints in a Ceramic Ball Grid Array (CBGA) package mounted on an organic FR4 board under extended dwell time at a high temperature has been studied using laser moiré interferometry. The warpage and the in-plane horizontal deformation of the ceramic substrate and the organic board as a function of time were determined. The variation of the normal strains and shear strains in the solder joints with time were also investigated. It was found that increased sensitivity was necessary to accurately determine the strains in the small sized solder joints. A new method utilizing carrier fringes to increase the sensitivity of the moiré interferometry system is proposed and has been used to determine the strains in the small sized solder joints. Increased sensitivity can be obtained merely by changing the incident angle of the laser light on the surface of the specimen, thereby making it unnecessary to use expensive phase shifting apparatus with the traditional laser moiré system.     

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.     

Surface and interior strain fileds measured by multiple-embedded-grid moiré and strain gages

Surface and interior straini fields in thick specimens of polycarbonate have been measured by an embedded-multiple-grid moiré method. Interior gratings are photographed through intervening gratings. Coherent optical processing of grating records creates moiré fringe pattern. A correction procedure was developed to eliminate moiré errors caused by strain-induced gradients of refractive index. This procedure utilizes the refraction distribution as obtained from observation of a grating from opposite sides of a specimen. No measurements other than the normal moiré observations are required in order to find actual strains. The correction technique should be useful in refining the results obtained when other optical methods are used in three-dimensional situations. The method is utilized to determine strains on the surfaces and at the mid-and quarter-planes of thick compact tension specimens. Results obtained, after correction, agree with measurements made with embedded strain gages. Maximum tensile strain occurs on the midplane. The findings are rationalized by consideration of thickness and proximity to the crack tip.     

The governing equations for moiré interferometry and their identity to equations of geometrical moiré

The equations prescribing the gradient and inclination of fringes in moiré interferometry are derived from the basic laws of diffraction and interference. A vectorial representation of three-dimensional diffraction employs incidence and emergence vectors in the plane of the grating; the representation is especially well suited for this type of analysis. The corresponding equations for geometrical moiré are derived by a remarkably direct vectorial method. The analyses prove that the patterns of moiré interferometry and geometrical moiré are governed by identical relationships. Paper was presented at 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14, 1985.     

Investigation of shrinkage-induced stresses in stereolithography photo-curable resins

An experimental study has been undertaken to investigate the shrinkage characteristics of acrylic-based and epoxy-based stereolithography (SL) photopolymer resin systems after they have been laser cured and post-cured under ultraviolet (UV), and thermal exposure. The induced residual stresses and strains were determined by the shadow moiré and the hole-drilling strain-gage methods. Out-of-plane displacements (warpage) of acrylic-based post-cured resin plates were recorded by means of the shadow moiré method and correlated to the shrinkage strains by theoretical analysis. The induced residual stresses in the epoxy-based cylindrical resin specimens were determined from strains of three-element strain-gage rosettes of the blind-hole drilling method. Results are presented for the shrinkage stresses and strains for both material systems as a function of the post-curing process (UV, thermal). It was found that the shrinkage strains in the acrylic-based photopolymer resin were of considerable magnitude, while thermal post-curing resulted in higher shrinkage stresses for both material systems. The values of the shrinkage stresses compare well with those of the existing literature.     

Residual surface stresses in laminated cross-ply fiber-epoxy composite materials

Residual (curing) stresses in a cross-ply laminated plate are related to the strains released when individual plies are separated. Released displacements are determined using high-sensitivity moiré interferometry and linearized strain-displacement equations are used to determine residual strains. Elastic orthotropic stress-strain relations are used to calculate residual stresses remote from free-edges of a [90₂₀/0₂₀/90₂₀] graphite-epoxy cross-ply panel. The measured strains compare favorably with those predicted by laminated plate theory. In a second example, the circumferential and radial residual strains and stresses at the end-section of a thick-walled cross-ply graphite-epoxy cylinder are determined. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas NV on June 8–11.     

Immersion interferometer for microscopic moiré interferometry

The basic sensitivity of moiré interferometry has been increased beyond the previously conceived theoretical limit. This is accomplished by creating the virtual reference grating inside a refractive medium instead of air, thus shortening the wavelength of light. Various optical configurations of moiré interferometry for operation in a refractive medium are introduced and one of them has been put into current practice. A very compact four-beamimmersion interferometer has been developed for microscopic viewing, which produces a basic sensitivity of 4.8 fringes per μm displacement (contour interval of 0.208 μm per fringe order), corresponding to moiré with 4800 lines per mm. Its configuration makes it inherently stable and relatively insensitive to environmental disturbances. An optical microscope is employed to obtain high spatial resolution. The method is demonstrated for deformation of a thick graphite/epoxy composite at the 0/90-deg ply interface. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13, 1991.     

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.     

Nano-meter Displacement Measurement by Phase Analysis of Fringe Patterns Obtained by Optical Methods

0Introduction Inordertomonitorthehealthofstructures,straingagesanddisplacementtransducersare usuallyused.Thereasonisthatmanyrulesorcodesforinspectionofstructuresrequiretousestrain gagesanddisplacementtransducers,anditiseasytousethem.However,thesemethodsarebasically one pointmeasurementmethods.Theyareexpensiveandtime consumingfordistributionanalysis.Opticalmethodssuchasgrating projection,geometricmoir啨,moir啨interferometry,holographic interferometryandspeckleinterferometryareusefultomeasuredi…     

Local time—Temperature-dependent deformation of a woven composite

Moiré interferometry is utilized to investigate the time-temperature-dependent deformation of a woven composite substrate used in multilayer circuit board applications. Creep tests are performed at temperatures ranging from 27 to 70°C, and the resulting longitudinal and transverse displacement fields are measured via moiré interferometry. Measured displacement fields reveal the influence of fabric architecture on woven composite response. The deformation fields in the plane of the composite for loading along both warp and fill directions consist of a periodic arrangement of high-strain and low-strain regions in accordance to the interlacing bundle architecture. The deformation fields over the cross-section of the composite indicate that neighboring unit cells are subjected to equal and opposite bending moment even when the composite is loaded in uniaxial tension.     

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.     

Dynamic moiré measurement of strains induced in a titanium tube plate during the rolling of a series of tubes

The strains developed in a tube plate by the process of roller expansion of tubes were measured by moiré interferometry. The maximum strains during the process were recorded by photographing the fringe patterns during rolling at a rate of five frames per second. The tubes were rolled according to a prearranged pattern, and the deformations over the whole tube-plate element were recorded between the rolling of successive tubes; by this means, the effect of each tube rolling on the overall strain pattern was assessed.     

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.     

Phase-stepped ESPI and moiré interferometry for measuring stress-intensity factor andJ integral

Electronic-speckle-pattern interferometry and moiré interferometry have been used to calculateK ₁ andJ for compact tension specimens. Automated-fringe-pattern analysis enables the full-field of data to be used with the minimum of operator intervention. Measurements are shown to be accurate to within 10 percent. TheJ-measurement procedure employed could form the basis of an automatic-fault detection system.     

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.     

The development of orthogonal bicolored moiré fringes

This paper presents the results of an investigation to develop new techniques to enhance the moiré method of mechanical interferometry. The program demonstrated the practicality of developing the use of orthogonal bicolored moiré fringes with the unique capability to selectively display either set of fringes while obscuring the other set. An interpolation method for the determination of fractional fringe orders is also discussed.