Robert Czarnek

Free Edge Strain Concentrations in Real Composite Laminates: Experimental-Theoretical Correlation

The magnitude of the maximum shear strain at the free edge of axially loaded theta (2)/-theta(2)(s) and (+ or - theta(2) (s) composite laminates was investigated experimentally and numerically to ascertain the actual value of strain concentration in resin matrix laminates and to determine the accuracy of finite element results. Experimental results using moire interferometry show large, but finite, shear strain concentrations at the free edge of graphite-epoxy and graphite-polyimide laminates. Comparison of the experimental results with those obtained using several different finite element representations showed that a four node isoparametric finite element provided the best and most trouble free numerical results. The results indicate that the ratio of maxium shear strain at the free edge to applied axial strain varies with fiber orientation and does not exceed nine for the most critical angle which is 15 deg.

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.

High sensitivity moiré interferometry with compact achromatic interferometry

Abstract Experimental observations and measurements are the sources of information essential for correct development of mathematical models of real structural materials. Moire interferometry offers high sensitivity in full-field measurements of in-plane displacements on the surface of a specimen. Although it is a powerful method in experimental stress analysis, it has some shortcomings. One is that existing systems require highly coherent light. The only sufficient source of light for this application is a long cavity laser, which is relatively expensive and at best cumbersome. Another shortcoming is that measurements must be performed in a vibration-free environment, such as that found on a holographic table. These requirements limit the use of existing moire interferometers to a holographic laboratory. In this paper a modified concept of compensation is presented, which permits the use of a chromatic source of light in a compact moire system. The compensator provides order in the angles of incident light for each separate wavelength, so that the virtual reference grating created by each wavelength in a continuous spectrum is identical in frequency and spatial position. The result is a virtual reference grating that behaves exactly like that created in coherent light. With this development the use of a laser diode, which is a non-coherent light source of tiny dimensions, becomes practical. The special configuration of the optics that create the virtual grating allows its synchronization with the specimen grating and leads to an interferometer design that is relatively insensitive to the vibrations found in a mechanical testing laboratory. Sensitivity to relative motion is analyzed theoretically. This development provides the oppurtunity to apply moire interferometry to solid mechanics problems that cannot be studied in an optics laboratory. Experimental verification of the optical concepts is provided. A compact moire interferometer based on the presented idea was developed for measurements of deformation on a testing machine. Its application in both coherent and temporally non-coherent light is demonstrated.

Real-time optical differentiation for moire interferometry

Real-time methods for differentiation of in-plane displacement fields produced by the moire interferometry technique are introduced. Two approaches are developed: (1) optical shearing of displacement patterns and (2) superposition of two lateral shear interferograms of wavefronts from 2 diffraction orders of the specimen grating. Coherence problems are circumvented by polarization effects. In both cases additive-type moire fringes give the map of displacement derivatives of the object under load. The issue of carrier patterns and extraneous fractional fringe order is clarified. Experimental verification of the principle is presented.

Deformation of a Metal-Matrix Tensile Coupon with a Central Slot: An Experimental Study

A metal-matrix specimen was investigated using high-sensitivity moire interferometry. The specimen was a 6-ply [0/±45]s boron-aluminum tensile coupon with a central slot. In-plane displacement fields were analyzed at various load levels from 15 to 95% of the failure load. Normal and shear strains were determined from displacement gradients. Highly localized plastic slip zones occurred in the ductile aluminum matrix tangent to the ends of the slot. Shear strains in the slip zone were an order of magnitude greater than the largest normal strains in the specimen. The shear-strain concentration factor γxy/ϵff rose dramatically with the onset of plastic slip and continued to rise gradually with load to 95% of the failure load. Upon unloading, shear strains in the slip zone remained precariously high. The maximum normal strain occurred at the end of the slot, where the normal-strain concentration factor ϵy/ϵff diminished as the load increased.

Super high sensitivity moiré interferometry with optical multiplication

Abstract A new method has been developed for increasing the sensitivity of the moire interferometry method, which yields an order of magnitude improvement. The new method offers this improvement without sacrificing the resolution or simplicity of the experimental procedure, making it unique from other methods suggested in the literature. The accomplished results open a number of possible applications in micro- and macro-mechanics, and provide data in a form easy to accommodate by automated fringe processing systems.

Three-mirror, four-beam moiré interferometer and its capabilities

Abstract A short history and description of the basic principles of moire interferometry lead to the introduction of a three-mirror, four-beam moire interferometer. The theory of operation of the instrument is provided. Some variations of the system are discussed with recommendations for specific applications.

Shear-strain contours from moire interferometry

Whole-field contour maps of shear strains γxy are derived from displacement fields obtained by moiré interferometry with 2400 ℓ/mm (60,960 ℓ/in.). Cross-derivatives of displacements are obtained by mechanical differentiation. They are summed by graphical additive moiré. The high sensitivity of moiré interferometry permits quantitative analysis in the small-strain domain.

Shear strains in a graphite/PEEK beam by moiré interferometry with carrier fringes

A multispan quasi-isotropic graphite-PEEK beam exhibited dramatic shear strains in the interlaminar region between plies. Shear strains in the plies themselves varied in basic accord with fiber direction. The large anomalous shear strains were developed near the center of the beam height, where shear stresses were large. High-sensitivity moiré interferometry with 2400l/mm (60,960l/in.) was used. A new technique of data extraction was developed, using carrier fringes to transform the pattern to one in which fringe slopes are proportional to derivatives of displacement. This technique enhanced detection and measurement of highly localized shear-strain gradients.

Moiré interferometry with ±45-deg gratings

Specimen gratings with rulings oriented +45 deg and −45 deg to they axis can be used to determine theu andv displacement fields, i.e., the displacements in thex andy directions. The fringe patterns are identical to those obtained with (X) and (Y) specimen gratings. The analysis leading to this conclusion is presented. A vector quantity related to the fringe gradient in the interference pattern is defined and found effective for visualizing and describing the image-forming rays. Advantages relate to construction of apparatus for moiré interferometry.