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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 1 — Jul. 6, 1998
  • pp: 35–44
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Applications of holographic interferometry to structural and dynamic analysis of an advanced graphite-epoxy composite component

Howard Fein  »View Author Affiliations


Optics Express, Vol. 3, Issue 1, pp. 35-44 (1998)
http://dx.doi.org/10.1364/OE.3.000035


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Abstract

It was undertaken to apply holographic techniques to characterize the dynamic behavior and structure of an advanced graphite-epoxy composite part and its ancillary mounting geometry. Holograms of the vibrational modes of the structure are used to accurately map the nodes, maxima, minima, and geometry of the induced motion. Holograms of the displacement patterns of mechanical and thermally induced stress in the structure are also used to map the location and extent of nonuniformities, discontinuities, and micro-structural defects in the volume and mounting of the composite material. Holographic data was imaged by a photo-thermoplastic based holocamera system configured for off-axis holograms and coupled to high resolution video capture for subsequent image analysis.

© Optical Society of America

1. Introduction

2. Methods

Stress induced displacements of the object under study cause each type of hologram to generate patterns of bright and dark lines which appear superimposed on the object. These are called interference fringes and define isobars of displacement on the surface of the object. The displacement characteristics are determined by the direction of the motion and stress producing the fringes. The most useful observations of interest to this discussion correspond to out-of-plane, or nearly out-of-plane displacement. Specific geometries and symmetries in the holographic fringe patterns map the behavior of the structure and can readily show distortions resulting from material, structural, or processing anomalies as changes in the topography of the surface of the object. Derivation of the magnitude of displacement is defined from the fringe pattern by the fringe density (number of fringes). This is well understood [10

10. C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 155, 180.

]. In the case of Real-Time and Multi-Exposure holograms, the displacement at any given point on the object is derived by counting the number of fringes to that point. Since the fringes are cosinusoidal in nature, each represents a nominal displacement value equal to 1/2 the wavelength of light with which the hologram was recorded, thus total out of plane displacement is given simply by:

D=(2)
(1)

where D is the total displacement in the orthogonal direction out of plane, N is the number of fringes, and λ is the wavelength of the laser light employed in recording the hologram. Absolute magnitude calculation depends on the viewing angle and is considered in these experiments to describe displacement in the orthogonal, out of plane direction.

For Time-Average holograms the displacement is derived from a fringe pattern that is modulated by the coefficients of the zero crossings of a Bessel function of the first kind of order zero as given by

D=(ξnλ4π)
(2)

where D is the total displacement, ξn is the coefficient of the nth zero of the Bessel function (corresponding to the nth fringe counted from the zero displacement nodal fringe), and l is the wavelength of the laser light. The absolute magnitude of the displacement analytically derived in this fashion also depends on the Sensitivity Vector in relation to the orthogonal, out of plane direction.

3. Procedure

Holograms were made with exposures controlled radiometrically by measuring the optimum energy density at the holographic plate. This method insured the high contrast ratios desired in interferograms of this type. The object beam was configured to illuminate the structure under study while the reference beam illuminated the holographic plate directly. Either real-time, time-average, or multi-exposure holograms of the composite structure assembly were possible in this configuration.

Figure 1. Off-Axis Holographic Interferometry Configuration

Time average holograms of the vibrational modes of the structure identified the resonant frequencies and mapped the nodes, maxima, minima, and geometry of the induced motion. Holograms of the displacement patterns of induced stress in the structure are used to map the location and extent of nonuniformities, discontinuities, micro-cracks, and other structural defects in the volume and mounting of the component. Such data can be readily compared to the requirements imposed by the operational environment and allows the true, real-world behavior of the structure to govern its optimum design, engineering, and especially, operational inspection.

Data has been taken for several specimens of an advanced polymer matrix composite control structure assembly. The composite structure assembly under test is an advanced aerodynamic guidance fin. Mass loading, composite thickness, shape, as well as material density, homogeneity, and constraint were postulated to have great effect on the vibrational mode shapes, frequencies, and structural fringe patterns. Inclusions, flaws, and anomalies in the structural volume of the material were also expected to be highly discernible in the holographic fringe patterns as well. A schematic representation of the graphite-epoxy composite structure and it’s mounting geometry with an accompanying photo of the actual mounted assembly is illustrated in figure 2. Different constraint and stress geometries were applied to this assembly in order to develop an understandable characterization of its structural and vibrational dynamics.

Figure 2. Composite structure schematic diagram and photo of the actual assembly in place for holographic imaging. Photographic point of view from this image and all holograms is directly along a line of sight orthogonal to the object center. The structural curve is not apparent from this aspect. Fringe patterns will be superimposed over structure image in following data.

The assembly was mounted and a holographic exposure made while it was in an “undisturbed” state (isolated from any induced vibrations or stresses). The resulting hologram was left in place superimposed on the image of the fin itself to produce a realtime holographic image which was displayed on the monitor. The real-time holographic images are observed while the fringe patterns are optimized by micrometrically adjusting the position of the holographic camera to negate rigid body motion anywhere in the holographic system which could affect the useful data. The interference fringes which were produced by subsequent mechanical or vibrational stress mapped the displacement characteristics.

Mechanical and structural characteristics were subsequently investigated by employing real-time holograms to identify interesting and significant displacement patterns produced during the application of mechanical clamping stress, thermal stress, and direct bending stress on the fin itself to observe its behavior. Multi-exposure holograms were then employed to map the differential “before and after” behavior and subsequently recorded so the complete motion geometries caused by the induced stresses in the assemblies are easily defined.

4. Results

4.1 Modal analysis

Figure 3. The holographic fringe pattern shown here defines the primary bending mode of the structure. The frequency in this case was nominally 56 Hz. It is seen to be a clear displacement phenomenon whose amplitude increases linearly from the mounting clamp assembly of the component.
Figure 4. This fringe geometry illustrates strong torsional displacement pattern produced at a nominal frequency of 121 Hz. The nodal ridge dividing the high amplitude fringe groups on the image top and bottom corners denotes that a phase change occurs between them. This defines a high stress point which could result if the inherent noise spectrum of the structure in its operational configuration includes a component at this frequency.

Figure 5. First bending/conjugate mode at 545 Hz.
Figure 6. Second bending/conjugate mode at 564 Hz.

Figure 7 shows the image of a hologram made at a higher frequency complex mode. The bright nodal area of essentially zero displacement is very broad and significant. The fringe pattern symmetry indicates even force and stress distribution in the assembly and the higher displacement areas are seen at the extreme right edge and Figure 7. Higher order complex mode is a superposition of a second bending and second torsional mode at 1.61 kHz. The broad nodal area varies smoothly into the sharp nodal lines in both torsional and bending stress showing the location of changes in direction between the high displacement edges and corners.

Figure 7. Higher order complex mode is a superposition of a second bending and second torsional mode at 1.61 kHz. The broad nodal area varies smoothly into the sharp nodal lines in both torsional and bending stress showing the location of changes in direction between the high displacement edges and corners.

4.2 Mechanical analysis

The effects of mechanically induced stress are observed using previously described methods of real-time holography to examine behavior under conditions in which mechanical and thermal stress imbalances have been purposely applied to examine the response of the structure as it is affected by the applied stress. Examples of mechanically induced stress effects are shown in figures 8 and 9. Fringe geometries are progressively more complex as the displacement changes across the surface resulting from localized stress applied to the structure substrate. It was desired to investigate the characteristics of displacement fringe geometry when the assembly behavior was modified by material and mounting anomalies.

Figures 8 and 9 are holograms whose fundamental fringe geometries have been distorted by nonisotropic mounting constraints. The distortion defines the effect of non-uniform constraint and loading on the structure as asymmetries in the fringe patterns.

Figure 8. Constraint induced stress gradient.
Figure 9. Differential stress loading.

Figure 8 shows a real-time hologram which maps a high stress gradient in a simple bending geometry. Direct mechanical force was applied out of plane in the direction of the viewer uniformly at the free edge of the fin assembly from the back. The fringe pattern indicates that constraint is fairly isotropic along the image left side at the clamping mount assembly. The fringes defining large non-uniform displacements induced by the direct mechanical stress to the free right edge of the component are seen to vary considerably from an expected pattern of purely straight vertical fringes. This type of non-uniform effect could contribute to anomalous behavior or even component failure in the operational environment.

Figure 9 illustrates a hologram whose fringe pattern clearly denotes the result of highly differential loading on the imaged specimen. The stress concentration identified by the concentric fringes in the mounting clamp area contrast distinctly with the adjacent vertical fringe continuity which is expected to manifest in a continuous fashion over the entire surface under normal conditions. This situation is indicative of constraint or mass loading anomaly at the clamping mount which could also contribute to a catastrophic component failure in operation.

Figure 10 shows a multi-exposure hologram of the composite component responding a purposely applied thermal stress. The fringe pattern shows a distortion characteristic of a buried flaw in the composite substrate. The effect of this anomaly, though captured in the volume of the composite material, clearly induces a highly localized displacement at the surface of the composite substrate. Such flaws, in the nature of inclusions, entrapped gas, delaminations, as well as other fabrication errors, can be easily identified.

Figure 10. Internal structural flaw identified when local thermal stress from a 15 degree C increase in temperature is applied to the back of the composite material. The non-uniform displacement distribution indicates the location and extent of the internal flaw.

5. Conclusion

It has been demonstrated that holographic interferometry can be successfully employed to characterize certain aspects of the vibration induced behavior of an advanced graphite-epoxy composite flight control structure. The frequency dependent characteristics of the structure are shown to be highly dependent on the assembly’s mechanical geometry and mounting constraints. Further analysis is underway to investigate the dependence on substrate materials and processing.

Complete vibration analysis depends on a direct comparison of the of the actual composite structure assembly configuration with associated operational noise spectrum to show its true effect on the complete mechanical system. If the spectrum does not contribute significant energy at the frequencies of excitable modes then the components of the assembly will experience minimal stress in the operational environment. If the converse is seen, the analysis enables the identification of the appropriate geometry for application of stiffening or damping constraints to change the mode shapes or strengths and shift or prevent their excitation.

Holographic analysis has also proven to be a uniquely effective method of defining and analyzing structural characteristics. These techniques also enable the identification of the appropriate geometry for application of structural or other composite substrate changes to modify the geometry of stress or obviate structural anomalies and flaws. The holographic data is, in many cases, ultimately employed to help define parameters for finite element modeling and modification of the substrate material itself or its processing to eliminate anomalous behavior. Holographic methods were included in ongoing development and subsequent testing of the prototype assemblies illustrated and have proven to be the most effective method of evaluating the characteristics of interest.

References and links

1.

H. Fein, “The Application of Holographic Interferometry to the Characterization of the Dynamics of a Complex Bonded Structure,” Proc. SPIE , Adhesives Engineering, 1999, 248–253, (1993). [CrossRef]

2.

H. Fein, “Holographic Evaluation of the Material and Dynamic Characteristics of Bonded Compliant Structures,” Proceedings of International Conference on the Applications of Lasers and Electro-Optics, (ICALEO) Laser Materials Processing 77, 604–610 (1993).

3.

H. Fein, “An Application of Holographic Interferometry to Evaluate the Material Characteristics of Cast Compliant Structures,” in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 15, D.O. Thompson and D. E. Chimenti, eds., (Plenum, New York, 1996). [CrossRef]

4.

H. Fein, “Holographic Interferometry Applied to the Characterization and Analysis of the Dynamic and Modal Behavior of Complex Circuit Board Structures,” Proc. SPIE , Practical Holography VIII 2176, 256–261 (1994). [CrossRef]

5.

Howard Fein, “Applied Holographic Interferometry as a Nondestructive Method for the Dynamic and Modal Analysis of an Advanced Graphite Epoxy Composite Structure,” in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 16, D.O. Thompson and D.E. Chi-menti, eds., (Plenum, New York, 1997).

6.

C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 227.

7.

C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 179–183.

8.

C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 229.

9.

“Instant Holocamera,” (Newport Corp., Fountain Valley, Ca., 1981).

10.

C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 155, 180.

OCIS Codes
(090.2880) Holography : Holographic interferometry
(120.4290) Instrumentation, measurement, and metrology : Nondestructive testing
(120.7280) Instrumentation, measurement, and metrology : Vibration analysis

ToC Category:
Research Papers

History
Original Manuscript: February 17, 1998
Revised Manuscript: March 26, 1998
Published: July 6, 1998

Citation
Howard Fein, "Applications of holographic interferometryto structural and dynamic analysis of anadvanced graphite-epoxy compositecomponent," Opt. Express 3, 35-44 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-35


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References

  1. H. Fein, "The Application of Holographic Interferometry to the Characterization of the Dynamics of a Complex Bonded Structure," Proc. SPIE, Adhesives Engineering, 1999, 248-253, (1993). [CrossRef]
  2. H. Fein, "Holographic Evaluation of the Material and Dynamic Characteristics of Bonded Compliant Structures," Proceedings of International Conference on the Applications of Lasers and Electro-Optics, (ICALEO) Laser Materials Processing 77, 604-610 (1993).
  3. H. Fein, "An Application of Holographic Interferometry to Evaluate the Material Characteristics of Cast Compliant Structures," in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 15, D.O. Thompson and D. E. Chimenti, eds., (Plenum, New York, 1996). [CrossRef]
  4. H. Fein, "Holographic Interferometry Applied to the Characterization and Analysis of the Dynamic and Modal Behavior of Complex Circuit Board Structures," Proc. SPIE, Practical Holography VIII 2176, 256-261 (1994). [CrossRef]
  5. Howard Fein, "Applied Holographic Interferometry as a Nondestructive Method for the Dynamic and Modal Analysis of an Advanced Graphite Epoxy Composite Structure," in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 16, D.O. Thompson and D.E. Chimenti, eds., (Plenum, New York, 1997).
  6. C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 227.
  7. C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), pp. 179-183.
  8. C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 229.
  9. "Instant Holocamera," (Newport Corp., Fountain Valley, Ca., 1981).
  10. C. M. Vest, Holographic Interferometry, (Wiley, New York, 1979), p. 155, 180.

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