1st Edition
Strain and Temperature Measurement with Fiber Optic Sensors
FROM THE AUTHORS' PREFACE
Sensors operating on interferometric principles and mounted inside optical fibers have recently been considered for measuring strain and temperature. Indeed, such sensors have successfully been employed for measuring pressure or temperature in fluids. Fiber optics sensors are especially adept for such measurements because sensors immersed in fluids can easily be calibrated by tests.
Unfortunately, the use of fiber optic sensors inside solids is not as straightforward. Owing to the complex interactions between the sensor and the surrounding material, the relationship between the sensor output and the parameters of interest, namely the strain and temperature inside the material, cannot be determined by simple tests. And without the appropriate relationships, fiber optic sensors do not provide meaningful information. In general, the relationship providing the bridge between the sensor output and the engineering values of strain and temperature must be established via analytical models. The major aim of this book is to present such models for extrinsic and intrinsic Fabry-Perot sensors and for Bragg grating sensors embedded in or mounted on the surface of isotropic or anisotropic solids or immersed in fluids.
The scope of the book is limited to the theory of fiber optic strain and temperature sensors. Accordingly, we have taken as our starting point the demodulated sensor signals. The hardware needed to produce these signals is not discussed. It is presumed that the reader is familiar with and has access to the sensor, light source, light detector and demodulator required for generating signals which can then be analyzed and interpreted by the methods presented in the book.
The problem necessitates complex analytical developments. To assist the reader, the significant results are summarized in tables, and numerical examples are given illustrating the calculation procedures.
List of Symbols
1. The problem: Numerical examples - Note on the symbols
I. Sensor strains and temperature
2. Introduction
3. Stresses and strains in the material
4. Stresses and strains in the sensor
5. Anisotropic uncoated sensor in a generally anisotropic material
6. Orthotropic uncoated sensor in an orthotropic material: Displacement continuity conditions - Stress continuity conditions
7. Transversely isotropic uncoated sensor in a transversely isotropic material
8. Transversely isotropic uncoated sensor in an isotropic material
9. Isotropic uncoated sensor in a transversely isotropic material
10. Isotropic uncoated sensor in an isotropic material
11. Sensors not embedded in a solid: Surface mounted sensor - Sensor immersed in a fluid
12. Effects of the coating: Out-of-plane shear applied - Axisymmetric loading - Non-axisymmetric in-plane loading - Observations
13. Summary of results: Extrinsic Fabry-Perot sensors - Plane strain and plane stress conditions
II. Optical and geometric properties of the sensor
14. Introduction
15. Optical properties of the sensor: Transversely isotropic sensor - Isotropic sensor - Summary of results
16. Geometric properties of the sensor: Fabry-Perot sensor - Bragg sensor - Summary of results
17. Summary of results
III. Sensor output
18. Introduction
19. Fabry-Perot sensor output in terms of the sensor optical and geometric properties: Reflected light intensity-Low finesse Fabry-Perot sensor - Reflected light intensity-High finesse Fabry-Perot sensor
20. Fabry-Perot sensor output in terms of the sensor strains and temperature: - Transversely isotropic intrinsic Fabry-Perot sensor - Isotropic intrinsic Fabry-Perot sensor - Extrinsic Fabry-Perot sensor - Non-embedded Fabry-Perot sensors - Summary
21. Fabry-Perot sensor output in terms of the farfield strains and temperature: Uncoated transversely isotropic or isotropic intrinsic Fabry-Perot sensor in a generally anisotropic material - Transversely isotropic intrinsic Fabry-Perot sensor in a transversely isotropic material - Transversely isotropic intrinsic Fabry-Perot sensor in a transversely isotropic material - Isotropic intrinsic Fabry-Perot sensor in an isotropic material - Extrinsic Fabry-Perot sensor - Summary
22. Bragg sensor output in terms of the sensor optical and geometric properties
23. Bragg sensor output in terms of the sensor strains and temperature: Transversely isotropic Bragg sensor - Isotropic Bragg sensor - Non-embedded Bragg sensors - Summary
24. Bragg sensor output in terms of the farfield strains and temperature: Transversely isotropic intrinsic Bragg sensor in a transversely isotropic material - Transversely isotropic intrinsic Bragg sensor in an isotropic material - Isotropic intrinsic Bragg sensor in a transversely isotropic material - Isotropic intrinsic Bragg sensor in an isotropic material - Summary
IV.Demodulation
25. Introduction
26. Geoptic strain
27. Demodulation: Low finesse Fabry-Perot sensor - High finesse extrinsic Fabry-Perot sensor - High finesse intrinsic Fabry-Perot sensor - Bragg sensors - Summary
28. Geoptic strain in terms of the farfield strains and temperature
V. Strain and temperature measurement
29. Introduction
30. Measurements of the farfield strains and temperature with seven sensors: The effects of uncertainties
31. Measurement of the farfield strains and temperature with n sensors
VI. Sensor selection and calibration
32. Introduction
33. Sensor selection: Sensor selection process
34. Sensor properties: Intrinsic Fabry-Perot and Bragg sensors - Thermooptic coefficient for an extrinsic Fabry-Perot sensor - Summary
VII. Computer code
APPENDICES
A. Transformation matrices
B. Stiffness and compliance matrices
C. Thermal expansion coefficient
D. Continuity conditions (uncoated sensors)
E. Derivative of the stress function
F. Stress-strain relationship at points A and B
G. Solution for es5 and es6 for an orthotropic uncoated sensor in an orthotropic material
H. Solution for es2 through es4 for a transversely isotropic uncoated sensor in a transversely isotropic material
I. Continuity conditions (coated sensors)
J. Pockel constants
K. Solution of the wave equation
L. Traveling wave intensity
M. Change in the geoptic strain-High finesse Fabry-Perot
BIBLIOGRAPHY, INDEX
71 tables, 42 figures
Biography
Regis J. Van Steenkiste
