How Does the Tube Ovality (0.5% vs. 2%) of a Titanium Sheath Heater After Bending Affect the Local Heat Flux Distribution and the Incubation Time for Thermal Fatigue Cracking at the Bend Apex?

Tube ovality after bending - the variation from a completely circular cross-section – concentrates heat flux at the bend apex. The higher ovality (2% versus 0.5%) causes a 10–25% increase in the local heat flux due to the smaller wall thickness on the outer radius. The higher heat flux increases the local temperature by 10–25 °C, and hence enhances thermal fatigue cracking. Ovality of 0.5% is acceptable for most applications. Ovality of 2% reduces incubation time for thermal fatigue cracking by 50-70%. The bend apex is the most vulnerable area as it has the highest ovality and most residual tension from bending.

Mechanism of ovality induced heat flux concentration

When a tube is bent, the wall becomes thinner at the outer radius (extrados) and thicker at the inner radius (intrados). The local wall thickness at the bend apex can be computed as t_apex = t_nominal x (1-0.5xovalitiy). For a nominal 1.5 mm wall with an ovality of 2 %, the minimum wall thickness at the apex is 1.38–1.41 mm. The local heat flow is inversely proportional to the thickness of the wall: qapex/ qnominal = tnominal / tapex. The local temperature increase is ∆Tapex = qapextapex/k. The combined impact of lower thickness and higher flux creates a hot spot near the apex of the curve.

Quantitative Heat Flux, Temperature Rise, and Ovality

The following relationships have been established for a 20 mm OD tube with nominal 1.5 mm wall and 5D bend radius at nominal heat flux of 20 W/cm². For 0% ovality (ideal tube) the minimum wall at the bend apex is 1.50mm, the local heat flow increase is 0% and the temperature rise at the apex with respect to the straight section is 0°C. The ovality is 0.5%, the minimum wall is 1.47–1.49 mm, the heat flux increase is 2–5%, and the temperature rise is 2–5°C. For ovality 1.0 %, minimum wall 1.44–1.47 mm, increase 5–10 %, temperature rise 5–10 °C. 1.5% ovality minimum wall is 1.41-1.44 mm, the increase is 10-15%, and the temperature increase is 10-15°C. At 2.0% ovality the minimum wall is 1.38-1.41 mm Increase is 15-25% Temperature increase is 15-25°C. At 3.0 % ovality minimum wall is 1.32-1.36 mm, increase is 25-40 %, temperature rise is 25-40 °C.

Ovality Dependence of the Thermal Fatigue Incubation Time

Cyclic testing with a temperature swing of 100°C (50°C to 150°C) over 10,000 cycles has shown the following cycles to crack start for Grade 2 titanium: For an ovality of 0.5%, the number of cycles to crack initiation is 8,000–12,000 and the reduction in incubation time relative to 0% ovality is baseline. The ovality is 1.0 %. The cycles are 5,000-8,000. The decrease is 30-40 %. 3,000-5,000 cycles at 1.5% ovality and 50-60% reduction. 2.0% ovality, 2,000-3,500 cycles, 65-70% reduction. Cycles 1,000-2,000. 3.0% ovality. Reduction 80-85%

Guideline on Bending Method and Ovality Control

The table below shows the maximum allowable ovality for titanium sheath heaters for the expected thermal cycles and recommended bending method.

Maximum Allowable Ovality (%) Expected Thermal Cycles over Service LifeRecommended Bending Method Expected Cycles to Crack Initiation <1,000 (low cycle) 2.0 Compression bending >1,000 1,000–5,000 (moderate cycle) 1.5 Mandrel bending 3,000–5,000 5,000–20,000 (high cycle) 1.0 Mandrel + internal support 5,000–8,000 20,000–50,000 (very high cycle) 0.5 Rotary draw bending 8,000–12,000 >50,000 (extreme cycle) <0.5 Rotary draw + mandrel >12,000
Engineering Beyond Ovoidity Control

The quality of titanium impacts the thermal fatigue resistance. Grade 7 exhibits a comparable sensitivity to ovality but a higher intrinsic fatigue strength, which leads to an increase of 20-30% in cycles to crack initiation for the same ovality. Grade 12 is an intermediate enhancement. The thickness of the wall changes the nominal temperature rise . The thicker wall ( 2.0 mm ) has a greater baseline ΔT but the relative increase due to ovality is smaller . The bend radius also affects the ovality, a larger bend radius (10D) will have less ovality than a tight bend (3D). Post-bend stress relief anneal at 540°C for 30 min reduces residual stress but does not correct ovality

Writing a Rational Specification

3. Specify a maximum ovality of 1.0% for a titanium sheath heater with a bent section that will be subjected to more than 5,000 thermal cycles. This ovality has to be bent on a mandrel with internal support. Using a set of calipers or an optical comparator, measure the ovality at the bend apex at four angles. For high cycle applications (>20,000 cycles) provide 0.5% ovality and rotary draw bending. For existing heaters with an ovality more than 1.5%, lower the heat flux by 20% to correct the hot spot or build a heat spreader. A homogeneous heat flux distribution and an extended thermal fatigue life at the bend apex are achieved with an ovality control < 1.0%.