Relationship Between Quartz Tube Wall Thickness and Pressure Resistance (Part 3 of 6)

Proportional Relationship Between Wall Thickness and Pressure Resistance

The pressure resistance of quartz tubes (especially internal pressure, i.e., internal load) is directly related to wall thickness. However, it is not a simple linear proportional relationship, as it is influenced by multiple factors such as material strength, geometric dimensions, and temperature. The key analysis is as follows:

1. Theoretical Calculation Formula (Thin-Walled Cylinder Model)

For internal pressure (internal load), the pressure resistance of quartz tubes can be estimated using the thin-walled pressure vessel formula:

• P = Maximum allowable internal pressure (MPa)
• σ = Tensile strength of quartz (~50 MPa, decreases at high temperature)
• t = Wall thickness (mm)
• D = Inner diameter (mm)

Key Conclusion:

• Pressure resistance P is directly proportional to wall thickness t (greater thickness → higher resistance).
• Pressure resistance P is inversely proportional to inner diameter D (smaller diameter → higher resistance).

Calculation Example

Inner Diameter D (mm)	Wall Thickness t (mm)	Theoretical Pressure P (MPa)	Actual Safe Pressure (MPa)
7.75	1.0	12.9	3–5
7.75	2.0	25.8	6–10
7.75	3.0	38.7	10–15
10.0	1.0	10.0	2–4

Note: In practical applications, a safety factor (typically 3–5 times) must be considered. Therefore, the rated commercial pressure values of quartz tubes are much lower than the theoretical ones.

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2. Actual Relationship Between Wall Thickness and Pressure Resistance

• (1) Standard Quartz Tubes (Wall Thickness 1–2 mm):
  • Inner diameter 5–10 mm: Typical pressure resistance 1–5 MPa
  • Inner diameter >10 mm: Pressure resistance decreases further (e.g., ID 20 mm, WT 2 mm → only ~1 MPa)
• (2) High-Pressure Quartz Tubes (Wall Thickness 3–5 mm):
  • Inner diameter 5–10 mm: Pressure resistance 10–20 MPa (requires seamless + annealing process)
  • Applications: High-pressure chemical reactions, supercritical fluid experiments
• (3) Extremely Thick-Walled Tubes (Wall Thickness >5 mm):
  • Pressure resistance can exceed 30 MPa, but cost is high, weight increases, and heating uniformity may be affected.

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3. Other Key Factors Affecting Pressure Resistance

• (1) Temperature:
  Quartz tensile strength decreases by about 30%–50% at 500°C, requiring increased wall thickness or reduced working pressure.
• (2) Material Defects:
  Micro-cracks, bubbles, and other defects significantly reduce actual pressure resistance. Optical-grade, defect-free quartz tubes should be selected.
• (3) End Sealing:
  Tube ends are prone to rupture under high pressure. Flanges/metal encapsulation should be used for enhanced support.

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4. Requirement Verification (Inner Diameter 7.75 mm, 10 MPa)

Minimum Wall Thickness Calculation:

But in practice, the following must be considered:

• Safety factor (3–5 times) → Wall thickness ≥ 2.5–3.0 mm
• High-temperature strength reduction → Recommended wall thickness ≥ 3.5 mm

Recommended Solution:

• Custom quartz tube parameters: ID 7.75 mm, OD ≈14–15 mm (WT ≥ 3.5 mm)
• Material: High-purity fused quartz (SiO₂ > 99.99%)
• Process: Seamless drawing + annealing

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5. Conclusion

Wall thickness is directly proportional to pressure resistance, but inner diameter, temperature, and material quality must also be considered.

For high-pressure experiments (10 MPa) with high-purity fused quartz (SiO₂ > 99.99%), without considering temperature fluctuations:

• A wall thickness of ≥3.5 mm must be used.
• Seamless + annealing process should be prioritized, and leak testing must be conducted before delivery.
• If further optimization (weight reduction/cost saving) is needed, sapphire tubes (pressure resistance >100 MPa) or specially designed high-pressure quartz tubes may be considered.