Is it a measure of fiber optic “elasticity”? Is fiber optic elasticity better than steel wire?
I. Physical Definition of Fiber “Young’s Modulus”
Young’s Modulus (commonly denoted as E) is a physical quantity that describes the ability of an isotropic linear elastic material to resist tensile or compressive strain (i.e., the material’s stiffness). Its physical definition is the ratio of normal stress \sigma to normal strain \epsilon within the material’s elastic deformation limit:
E = \frac{\sigma}{\epsilon}
- Numerical Value for Silica Fiber:** The Young’s Modulus for standard fused quartz silica (\text{SiO}_2) core and cladding materials is approximately E \approx 72\text{ GPa} (Gigapascals).
When the fiber is coated with polyurethane, polyimide, or metallic materials, or encapsulated in a metal tube/polymer to form a sensor, the apparent elastic modulus of the overall structure will change accordingly, depending on the composite cross-sectional area and modulus of each layer.
II. Is Young’s Modulus a Measure of “Elasticity”?
In physics and materials mechanics, “elasticity” needs to be understood from two perspectives: stiffness against deformation and range of elastic recovery.
1. Stiffness Against Tension/Deformation (Rigidity Dimension)
Young’s Modulus measures the material’s ability to resist tensile deformation when subjected to force. A larger modulus indicates a “harder” material, meaning it experiences less relative elongation (strain) under the same tensile force.
- Quartz Fiber:** E \approx 72\text{ GPa}
- Ordinary Structural Steel Wire:** E \approx 200\text{--}210\text{ GPa}
Comparison Conclusion: Under the same cross-sectional area and equal tensile force, the elongation strain of a quartz fiber is approximately 3 times that of steel wire. From the perspective of “stiffness against tensile deformation,” steel wire is “harder” (has a higher modulus) than optical fiber.
2. Limit of Elastic Deformation Range (Dimension of Fully Recoverable Deformation)
If “elasticity” refers to the ability of a material to return to its original shape without plastic deformation after being stretched, then optical fiber performs significantly better than steel wire.
- High-Strength Quartz Fiber:** Due to its extremely high material purity and absence of grain boundary defects, quartz glass exhibits near-perfect pure linear elastic behavior (without yielding until fracture), provided its surface is free from micro-cracks. High-strength coated fibers (e.g., selected polyimide-coated fibers) can withstand elastic strains up to 1\%\text{--}2.5\% (i.e., 10000\ \mu\epsilon \text{ -- } 25000\ \mu\epsilon) without residual plastic deformation.
- Ordinary Steel Wire:** Typically enters the plastic deformation stage after reaching a yield limit strain of 0.2\%\text{--}0.5\% (i.e., 2000\ \mu\epsilon \text{ -- } 5000\ \mu\epsilon), and cannot recover its original length after unloading.
Comparison Conclusion: The recoverable linear elastic strain range of optical fiber is much larger than that of ordinary steel wire.
III. Engineering and Fiber Bragg Grating (FBG) Sensing Applications
In Fiber Bragg Grating (FBG) stress and strain measurements, the elastic modulus of the material is a core physical parameter for calculating the actual force experienced.
According to Hooke’s Law, when using FBG strain sensors to detect a workpiece, the measured physical relationship is:
\text{Stress on Workpiece} = \text{Elastic Modulus of Workpiece} \times \text{Strain}
For engineering scenarios requiring precise strain or stress measurements, protective encapsulation is typically achieved using specialized tubing with specific moduli. Examples include OFSCN® Alloy Tube Packaged Fiber Bragg Grating strain sensor and OFSCN® Fiber Bragg Grating Stress Sensor. The sensor’s wavelength-strain relationship (displacement/strain sensitivity, in units of \mu\epsilon/\text{pm}) is calibrated at the factory. Combined with the known elastic modulus of the structural component material, the mechanical stress experienced by the workpiece can be accurately converted.
