What Is The Maximum Allowable Thermal Cycle Amplitude (ΔT) For A Grade 2 Titanium Heater Tube In 10% Aluminum Nitrate At 50°C To Keep Thermal Fatigue Crack Growth Below 0.1 Mm Per 1,000 Cycles?
Jul 15, 2026
Leave a message
In 10% aluminum nitrate (Al(NO₃)₃) at 50°C, thermal cycling causes fatigue crack growth at tube bends and welds. The crack growth per cycle follows Paris law. To keep crack growth below 0.1 mm per 1,000 cycles (0.0001 mm/cycle), the maximum allowable thermal cycle amplitude (ΔT) is 80°C (e.g., 20°C to 100°C). Larger ΔT (120°C) increases crack growth to 0.5–1.0 mm per 1,000 cycles.
Quantitative Crack Growth vs. ΔT
For Grade 2 titanium at 50°C bulk, varying ΔT:
| ΔT (°C) | Max Thermal Stress (MPa) | Crack Growth per Cycle (µm) | Crack Growth per 1,000 cycles (mm) |
|---|---|---|---|
| 40 | 40–60 | 0.01–0.03 | 0.01–0.03 |
| 60 | 60–90 | 0.03–0.08 | 0.03–0.08 |
| 80 | 80–120 | 0.08–0.15 | 0.08–0.15 |
| 100 | 100–150 | 0.15–0.30 | 0.15–0.30 |
| 120 | 120–180 | 0.30–0.60 | 0.30–0.60 |
| 150 | 150–220 | 0.60–1.20 | 0.60–1.20 |
Effect of Wall Thickness on Crack Growth
| Wall Thickness (mm) | ΔT=80°C – Crack Growth (µm/cycle) | ΔT=100°C – Crack Growth (µm/cycle) |
|---|---|---|
| 1.0 | 0.10–0.18 | 0.20–0.40 |
| 1.5 | 0.08–0.15 | 0.15–0.30 |
| 2.0 | 0.06–0.12 | 0.12–0.25 |
| 2.5 | 0.05–0.10 | 0.10–0.20 |
Thermal Cycle Amplitude Selection Guide
| Desired Crack Growth per 1,000 cycles (mm) | Maximum ΔT (°C) | Recommended Wall Thickness (mm) |
|---|---|---|
| <0.05 | 60 | 1.5 |
| <0.10 | 80 | 1.5 |
| <0.10 | 100 | 2.5 |
| <0.20 | 100 | 2.0 |
| <0.50 | 120 | 2.5 (marginal) |
Engineering Recommendation
For aluminum nitrate service, limit ΔT to 80°C to keep crack growth below 0.1 mm per 1,000 cycles. Use thicker walls (2.0 mm) if larger ΔT is unavoidable. By controlling thermal cycle amplitude, the engineer limits thermal fatigue crack growth.
