• DTDHandbook
• Contact
• Contributors
• Sections
• 1. Introduction
• 2. Fundamentals of Damage Tolerance
• 3. Damage Size Characterizations
• 4. Residual Strength
• 5. Analysis Of Damage Growth
• 6. Examples of Damage Tolerant Analyses
• 7. Damage Tolerance Testing
• 0. Damage Tolerance Testing
• 1. Introduction
• 2. Material Tests
• 3. Quality Control Testing
• 4. Analysis Verification Testing
• 0. Analysis Verification Testing
• 1. Structural Parameter Verification Techniques
• 0. Structural Parameter Verification Techniques
• 1. Compliance
• 2. Moiré Fringe
• 3. Photoelasticity
• 4. Crack Growth Rate
• 2. Residual Strength Methods-Verification
• 3. Crack Growth Modeling-Verification
• 5. Structural Hardware Tests
• 6. References
• 8. Force Management and Sustainment Engineering
• 9. Structural Repairs
• 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
• 11. Summary of Stress Intensity Factor Information
• Examples

# Section 7.4.1.2. Moiré Fringe

The moiré fringe technique for obtaining the stress-intensity factor for a through-thickness crack (two-dimensional geometry) is based on the measurement of in-plane displacements (or strains) in the crack tip region.  The moiré fringes, which leads to displacement or strain measurements, are developed as a result of an interference created by an optical mismatch of two grid patterns; one pattern is the model grid which is placed on the structure, the other is the reference grid which has the same pattern as the model grid in the unloaded condition.  As the moiré fringes are converted to, say, displacement measurements in the crack tip region, the displacement (d) of the crack surfaces close to the crack tip is related to the stress-intensity factor (K) through the relation (plane stress-linear elasticity assumed)

 (7.4.3)

where E is the elastic modulus and r is the distance from the crack tip.  Typically, measurements are made of the displacement as a function of distance from the crack tip; and, the collection of these results are used with a linear regression equation to estimate the value of K.

Continuing evolvement of the moiré interferometry techniques have produced methods for increased displacement sensitivity which are covered by a review paper by Post, et al. [2000]  In a method called microscopic moiré interferometry, two techniques have evolved which are used sequentially:  a) an immersion interferometer uses a fluid coupling media to produce virtual reference gratings of 4800 lines/mm – double the usual basic sensitivity, b) a complementary technique uses optical/digital fringe multiplication by fringe shifting, along with an efficient algorithm to generate an enhanced contour map of the displacement field.   The two advances work in concert to result in an overall sensitivity multiplier as high as 24X.

Even planar surfaces are no longer a strict requirement for using moiré.  Work by Boeman [1991] and later expanded by Mollenhauer [1997] have developed innovative methods for imaging the inner surfaces of bolt holes in composite plates.

Other variations include shadow moiré, which is useful for higher in-plane displacements, again as with regular moiré, increased sensitivities can be obtained using the optical/digital fringe multiplication techniques.

In work by Epstein and Dadkah [1993], applications to fracture mechanics solutions have been pursued.  Moiré interferometry measures the stress intensity factor local to the crack-tip without relying on compliance calculations, a savings in instrumentation complications for both fracture and corrosion studies.  Portable field units have been developed at Idaho National Engineering Lab for extending the use to maintenance and field activities.

A comprehensive review of experimental mechanics techniques and applications is included in Rastogi [2000].