The difference between internal pressure resistance and external pressure resistance of quartz tubes (Part 2 of 6)

The pressure resistance of quartz tubes varies depending on whether they are subjected to internal pressure (internal pressure) or external pressure (external pressure), and is mainly influenced by material mechanical properties, structural shape, and failure mode.

Taking the structural shape of inner and outer circles as an example, here are the key differences:

1. Comparison of internal pressure resistance (internal pressure) vs. external pressure resistance (external pressure)：

Characteristics	Internal pressure resistance (internal pressure)	External pressure resistance (external pressure)
Direction of force	Internal pressure expands outward	External pressure compresses inward
Destruction Mode	Tensile rupture (tube wall torn apart)	Buckling instability (tube wall collapse)
Key influencing factors	The tensile strength of quartz (~50 MPa)	The compressive strength of quartz (~1100MPa)However, it is limited by geometric stability in practice.
Typical voltage withstand value	Standard quartz tube:1~3MPa Thickened/high-pressure tube:5~20MPa	Standard quartz tube:0.1~0.5MPa Thickened/high-pressure tube:1~5MPa
Applicable scenarios	High-pressure reactor, fluid delivery pipe	Vacuum environment, external pressure test

(1) Internal pressure resistance (internal pressure)

2. Detailed analysis

Failure mechanism: Quartz is a brittle material with low tensile strength (~50MPa). Under high pressure, the pipe wall is subjected to circumferential tensile stress and is prone to cracking at weak points (such as microcracks and bubbles).

The hoop stress formula (thin-wall theory) is expressed as:

Variables Explanation:

σhoop​: Hoop stress (MPa)

P: Internal pressure (MPa)

r: Inner radius (mm)

t: Wall thickness (mm)

Key Notes:

Applicability: Valid for thin-walled tubes(t/r≤0.1)

Safety Factor: Actual design stress should include a 3–5x safety margin.

Limitation: Neglects axial stress and end effects.

Example Calculation:
For a tube with

r=5mm, t=1mm, and P=10MPa:

(Compare to quartz’s tensile strength ~50MPa to assess failure risk.)

Reference Standards:

ASME BPVC Section VIII (Pressure Vessels)

ISO 3585 (Fused Quartz Specifications)

Let me know if you need derivations or edge-case adaptations (e.g., thick-wall theory).

If

≥50MPa，the quartz tube may rupture.

Calculation for this case:

Quartz tube with an inner diameter of 7.75 mm and a wall thickness of 1 mm, theoretical pressure resistance:

However, the actual safety pressure is only 1 to 3 MPa (defects and temperature effects must be taken into account).

(2) External Pressure Resistance (Outer Pressure)
Failure Mechanism: While quartz has high compressive strength (~1100 MPa), slender tubes are prone to buckling (similar to a straw being crushed).

Critical Buckling Pressure (Simplified Euler Formula):

E = Elastic modulus of quartz (~72 GPa)

ν = Poisson’s ratio (~0.17)

D = Outer diameter (mm)

t = Wall thickness (mm)

Key Notes:

1.This formula applies to thin-walled tubes under uniform external pressure.

2.Actual safe pressure should apply a safety factor (typically 3–5×).

3.Geometric imperfections (e.g., ovality) significantly reduce P critical

Example: For a tube with D=10mm andt=1mm:

P critical ≈1.5MPa (theoretical),

Practical safe pressure<0.5MPa

Example Calculation:

For a quartz tube with outer diameter = 10 mm and wall thickness = 1 mm, the critical buckling pressure is calculated as:

Note:

The actual safe external pressure is typically < 0.5 MPa (must account for geometric imperfections).

3. Your Application Scenario Analysis  

(1) Internal CO₂ High Pressure (10 MPa)  

Requirement: Inner diameter 7.75 mm, capable of withstanding 10 MPa.  

Issue: Standard quartz tubes (wall thickness 1–2 mm) cannot meet the requirement (theoretically requires ≥3 mm wall thickness).

Solution:  

Custom-made thick-walled quartz tubes (e.g., wall thickness 3–5 mm, outer diameter ≈14–17 mm).  

Use sapphire tubes (pressure-resistant >100 MPa, but high cost).

Translated with DeepL.com (free version)

4. Conclusion

Internal pressure resistance (internal pressure): Limited by tensile strength, ordinary quartz tubes can withstand pressures of 1 to 3 MPa. For pressures of 10 MPa, thicker tubes must be custom-made.

External pressure resistance (external pressure): Limited by buckling stability, pressure resistance is typically less than 0.5 MPa. External compression must be avoided.

• Your experiment:  
• Internal pressure of 10 MPa → High-pressure custom quartz tubes (wall thickness ≥ 3 mm) must be used.
• Considering a heating temperature of 500°C → Compressive strength decreases by 30%–50% at high temperatures → Theoretical wall thickness ≥ 3 mm × 2 = ≥ 6 mm.
• Considering uncertainties in quartz tube purity, processing, and transportation, appropriate redundancy is provided → Redundant thickening of 2 mm (wall thickness ≥ 8 mm).
• External pressure → Ensure that the heater is installed without additional mechanical stress.

It is recommended to purchase high-purity quartz tubes with a purity of no less than 99.9%:

“Inner diameter 7.75 mm, wall thickness ≥ 8 mm, static pressure resistance 10 MPa”