Inputs
Example Data Table
| Glass Type | α (µ/°C) | E (GPa) | ν | ΔT (°C) | K | Kt | Peak Stress (MPa) |
|---|---|---|---|---|---|---|---|
| Annealed (screening) | 9.0 | 70 | 0.23 | 40 | 1.0 | 1.0 | 32.73 |
| Tempered (screening) | 9.0 | 70 | 0.23 | 80 | 1.0 | 1.2 | 78.55 |
| Partially restrained edge | 8.5 | 68 | 0.22 | 60 | 0.6 | 1.0 | 26.57 |
Example stresses assume the biaxial restraint model and cooling (tensile). Values are illustrative for learning and comparison.
Formula Used
Thermal strain is estimated as: ε = α · ΔT
For restrained expansion, the base thermal stress is approximated by:
- Uniaxial restraint: σ = K · E · α · ΔT
- Biaxial plate restraint: σ = K · (E · α · ΔT) / (1 − ν)
Peak stress can be adjusted for geometric effects using a stress concentration factor: σpeak = σ · Kt
These equations are simplified screening models. Real thermal shock behavior can be governed by gradients through thickness, edge flaws, residual stresses, and transient heat transfer.
How to Use This Calculator
- Enter the expected temperature difference ΔT in °C.
- Provide material properties: α, E, and ν.
- Set restraint factor K based on your mounting condition.
- Increase Kt if holes or sharp corners amplify stress.
- Choose uniaxial or biaxial restraint to match geometry.
- Optionally add strength values to compute safety factor.
- Click Calculate to view results above the form.
Glass Thermal Stress Guide
1) Why thermal stress forms
When one region of glass is hotter or colder than another, it wants to expand or contract differently. If the glass is restrained by a frame, gasket friction, or uneven heating, that free strain is blocked and converts into stress. Rapid cooling commonly drives tensile stress, which is the critical failure mode for most glass.
2) The core inputs that control stress
This calculator starts with thermal strain ε = αΔT. Typical soda-lime values are α ≈ 8–10 µ/°C and E ≈ 65–75 GPa, with ν around 0.20–0.25. Because stress is proportional to E and α, small changes in either can noticeably shift the result. A 60 °C gradient with α = 9 µ/°C produces ε ≈ 0.00054.
3) Restraint factor K (0 to 1)
K describes how much the mounting prevents expansion. K = 0 means nearly free sliding; K = 1 means fully restrained. Many real installations fall between 0.3 and 0.8, depending on edge clearances and compression seals. Running multiple K values helps you bracket realistic stress without guessing a single “perfect” number.
4) Biaxial vs uniaxial restraint models
Plates constrained in both in-plane directions can be approximated by σ ≈ K(EαΔT)/(1−ν). If movement is mainly blocked in one direction, use the uniaxial form σ ≈ K(EαΔT). The biaxial model typically gives higher stress because it divides by (1−ν).
5) Stress concentration factor Kt
Holes, sharp corners, chips, and cutouts can amplify stress locally. Kt = 1 assumes a smooth field. Values like 1.2–2.0 are often used for screening at openings or tight radii, especially when thermal gradients are steep near edges. The calculator reports peak stress as σpeak = σ · Kt.
6) Strength, safety factor, and units
If you enter a tensile or compressive strength, the tool computes a safety factor SF = Strength / |σpeak|. Annealed design tensile limits are frequently in the tens of MPa, while tempered glass can tolerate higher tensile demand, depending on surface condition and edge quality. Unit notes: 1 GPa = 1000 MPa, and 1 MPa ≈ 145 psi.
7) Estimated allowable ΔT
The allowable ΔT shown is the temperature difference that would drive the peak stress to your entered strength, using the selected restraint model and Kt. It is a quick comparison tool, not a substitute for a thermal-shock standard, transient heat-transfer analysis, or project-specific glass design rules.
8) Practical ways to reduce risk
Reduce gradients (shade control, diffusers, preheating), avoid rigid edge clamping, increase edge clearance, and improve corner radii. Keep coatings and frit patterns consistent to prevent hot spots, and protect edges from chips. If results look borderline, validate with supplier data and a conservative safety factor.
FAQs
1) Should I enter ΔT as hot minus cold or absolute value?
Use the absolute temperature difference between regions. The calculator uses “cooling” or “heating” to set the stress sign for strength selection.
2) What K value should I choose?
If you are unsure, test K = 0.3, 0.6, and 1.0. Sliding gaskets trend lower; rigid clamps trend higher. Use the range to bracket likely stress.
3) Why does biaxial restraint give higher stress?
Biaxial restraint uses σ ≈ K(EαΔT)/(1−ν). Because (1−ν) is less than 1, the computed stress increases compared with the uniaxial model.
4) Is thickness used in the stress equation here?
Thickness is recorded for reporting, but this screening model is membrane-based. Through-thickness gradients can require more detailed thermal-shock analysis.
5) What does Kt represent for glass?
Kt accounts for geometric amplification near holes, cutouts, sharp corners, or edge flaws. Use Kt > 1 when local features make stress non-uniform.
6) What strength should I enter for safety factor?
Use your project’s allowable design strength from supplier data or applicable standards. If you only have tensile strength, the tool can use it as a conservative fallback.
7) Is the “allowable ΔT” a guarantee against breakage?
No. It is a simplified estimate based on your inputs. Real breakage depends on defects, edge damage, time, residual stresses, and transient heating or cooling conditions.