How hard is quartz glass, and how much tensile strength can it withstand?
Quartz glass (silicon dioxide, \text{SiO}_2) serves as the primary substrate material for modern communication and sensing optical fibers. Its mechanical properties exhibit a unique duality: at the microscopic level, it possesses extremely high stiffness and theoretical strength; however, at the macroscopic level, its actual load-bearing capacity is limited due to its brittle nature and the presence of surface microcracks.
This document provides a detailed explanation from three perspectives—physical concepts, mathematical calculations, and engineering applications—to address the questions: “How hard is quartz glass?” and “What is the maximum tensile force an optical fiber can withstand?”
I. What is the “Young’s Modulus” of Optical Fiber?
Young’s Modulus (Young’s Modulus) is a physical quantity that describes the ability of a solid material to resist deformation. Within the elastic limit, it is the ratio of tensile stress ( \sigma ) to tensile strain ( \varepsilon ):
E = \frac{\sigma}{\varepsilon}
For the quartz glass used in optical fibers (fused silica), its Young’s Modulus E typically ranges between 72\ \text{GPa} and 73\ \text{GPa} (i.e., 7.2 \times 10^{10}\ \text{Pa} to 7.3 \times 10^{10}\ \text{Pa}).
What does this mean?
This value indicates that quartz glass has very high stiffness. For comparison, the Young’s Modulus of aluminum is approximately 69\ \text{GPa}, and that of copper is approximately 110\ \text{GPa}. This means that under the same tensile force, a bare quartz fiber’s resistance to deformation is even slightly greater than that of a metal aluminum wire of the same cross-sectional area.
II. What is the Maximum Tensile Force a Quartz Fiber Can Withstand?
To assess the maximum tensile force a fiber can withstand, we must base our calculations on the standard single-mode fiber dimensions (cladding outer diameter 125\ \mu\text{m}).
The cross-sectional area A of the fiber’s quartz cladding is:
A = \pi \times r^2 = \pi \times (62.5 \times 10^{-6}\ \text{m})^2 \approx 1.23 \times 10^{-8}\ \text{m}^2
Depending on the application scenario, the tensile strength of optical fibers can be categorized into the following three levels:
1. Proof Test Strength—The Minimum Guarantee Against Failure
To eliminate macroscopic defects and severe surface microcracks from the manufacturing process, standard optical fibers must pass a tensile proof test before leaving the factory.
- Proof Stress：Typically 100\ \text{kpsi} (approximately 700\ \text{MPa} or 0.7\ \text{GPa}).
- Corresponding Strain：Approximately 1\% (i.e., 10000\ \mu\varepsilon).
- Tensile Force：F = \sigma \times A \approx 7 \times 10^8\ \text{Pa} \times 1.23 \times 10^{-8}\ \text{m}^2 \approx 8.6\ \text{N}This means that qualified fibers leaving the factory can withstand a tensile force of at least approximately 8.6\ \text{N} (equivalent to the gravitational force of about 0.88\ \text{kg}) instantaneously without breaking.
2. Short-Term Ultimate Tensile Strength—The Laboratory Limit
In the absence of severe environmental degradation and with an intact surface coating, the short-term ultimate tensile strength of a high-quality bare quartz fiber measured in a laboratory can reach around 5\ \text{GPa}.
- Ultimate Tensile Force：F \approx 5 \times 10^9\ \text{Pa} \times 1.23 \times 10^{-8}\ \text{m}^2 \approx 61.5\ \text{N}This is equivalent to a hair-thin bare optical fiber being able to lift approximately 6.2\ \text{kg} momentarily. This fully demonstrates the high strength of quartz glass in a defect-free state.
3. Long-Term Safe Working Tension—Engineering Design Guideline
Because quartz glass is susceptible to “static fatigue” (i.e., under long-term tensile stress and the action of atmospheric moisture, microcracks slowly propagate), to ensure the fiber does not break during its lifespan of over 25 years, engineering design typically limits the long-term static working strain to within a safety margin of 0.2\%.
- Safe Working Stress：Approximately 144\ \text{MPa}.
- Long-Term Safe Tensile Force：F \approx 1.44 \times 10^8\ \text{Pa} \times 1.23 \times 10^{-8}\ \text{m}^2 \approx 1.77\ \text{N}Therefore, for bare optical fibers themselves, it is recommended not to exceed a long-term static tensile force of 1.7\ \text{N} (equivalent to a force of 0.18\ \text{kg}). If greater tensile force needs to be withstood, protection must be provided by outer armored structures such as stainless steel tubes, aramid yarns, or alloys.
III. Application of Mechanical Principles in Fiber Bragg Grating (FBG) Sensing
The Young’s Modulus of optical fiber is the fundamental basis for calculations in Fiber Bragg Grating (FBG) sensors. According to Hooke’s Law, within the elastic deformation range of a material, there is a direct linear relationship between the stress and strain of an object being measured:
\text{Stress} = \text{Elastic Modulus} \times \text{Strain}
By precisely measuring the minute shifts in the reflected wavelength of an FBG, highly accurate strain data can be obtained, which can then be used to calculate the stress distribution within a structure.
For example, the OFSCN® Fiber Bragg Grating Stress Sensor, designed by Beijing Dacheng Yongsheng Technology Co., Ltd. based on this physical principle, uses standard single-mode optical fiber operating within a safe strain range as its core sensing medium:
OFSCN® Fiber Bragg Grating Stress Sensor
This sensor undergoes rigorous strain-wavelength calibration before leaving the factory. In practical engineering applications, users input the calibrated first-order coefficient into the demodulation equipment. Combined with the elastic modulus (Young’s Modulus) of the measured structural component (such as rebar, concrete, aluminum alloy, etc.), multi-physical quantity calculations and monitoring can be accurately achieved.
The core optical fiber used internally is a high-quality bare optical fiber produced based on the standard G.652D optical fiber preform:
