What Maximum Allowable Hoop Stress at 500°C Internal Sheath Temperature Governs the 100,000-Hour Creep Rupture Life of 316 Stainless Steel Heater Tubing

Design Stress Basis for Service Life at Elevated Temperature

For 316 stainless steel sheathed electric heating tubes used in high temperature air or gas heating applications with internal metal temperatures of 500 °C, and in the inner wall of sheaths immersed in lower temperature fluids, the maximum allowable hoop stress for a 100,000 hour creep rupture life is an important design parameter. For a room temperature design, the yield strength is the basis for the permissible stress whereas for a high temperature design for creep limited operation, the stress levels are such that the component will not rupture by creep cavitation and grain boundary cracking within its design life. For 316 stainless steel at 500 °C, the average stress to cause rupture in 100,000 hours (about 11.4 years of continuous operation) is about 120-140 MPa, depending on the specific heat chemistry and grain size. The maximum allowed hoop stress is 80-95 MPa with usual safety factor of 1.5 for design against creep rupture (ASME Section VIII Division 2 method). The article gives quantified data of creep rupture stress for 316 heater sheaths in the temperature range 450 °C to 650 °C and a methodology to calculate safe operating pressure and wall thickness for elevated temperature service.

Creep Rupture Mechanism and the Larson-Miller Criterion

For 316 stainless steel creep rupture occurs by grain boundary cavitation and crack propagation . Time to rupture varies with temperature according to an Arrhenius relation and with stress according to an inverse power law. The Larson-Miller parameter (LMP = T × (C + log t_r), where T is absolute temperature in Kelvin, t_r is rupture time in hours and C is a material constant usually 15-20 for austenitic stainless steels) is a way of extrapolating short-term creep test data to extended service lives. Extensive testing has been performed on 316 to determine a 100,000 hour creep rupture strength at 500 °C between 110 MPa (lower bound, 95 % confidence) and 150 MPa (upper bound) with a normal mean of 130 MPa. The rupture strength at 100,000 hours is 60-90 MPa at 550 °C. And at 600 °C it lowers to 30-50 MPa. At 650 °C the 100,000 hour rupture strength is just 15-25 MPa. This is below the hoop stress from internal pressure in most heater designs and means that 316 cannot attain 100,000 hour life at 650 °C no matter how thick the wall is, because creep rupture will be inescapable. The practical result is that 316 sheathed heaters built for 100,000 hour (11.4 year) continuous service must be constructed such that the maximum operating sheath temperature is not greater than 530-550 °C depending on the internal pressure.

Allowable Hoop Stress, Quantified for 100,000 Hour Life.

Table 4.3 shows the maximum permissible hoop stress for 316 stainless steel heater tubing with a creep rupture life of 100,000 hours at temperatures between 450 °C and 650 °C. Three stress values are supplied, i.e. the mean stress to rupture (50% survival), the lower bound stress (95% survival, API/ASME design basis), and the suggested design permissible stress (lower bound divided by a safety factor of 1.25-1.5 depending on code. For design of the heater using the specified acceptable stress, the maximum internal pressure should be calculated from the thin-wall hoop stress formula: P max = 2 t σ allow / D mean, where t is the wall thickness, D mean is the mean diameter.

Temperature (°C) Mean Rupture Stress (MPa) 100,000 hr Lower Bound (95% Survival) Rupture Stress (MPa) Recommended Design Allowable Stress (MPa) (SF = 1.4 on lower bound) Maximum Hoop Stress for 100,000-hr Life (MPa) Typical Application Limit 450 210-250 180-210 130-150 130 Unlimited service 475 170-200 145-175 100-125 110 Safe for most heaters
500 120-150 100-130 70-95 85 Standard design basis 525 85-110 70-95 50-70 60 Derated design required 550 60-80 45-65 30-45 40 Short-life or low-stress only 575 40-55 30-45 20-30 25 Marginal for continuous service 600 25-40 18-30 12-20 15 Not recommended for 100,000-hr 625 15-25 10-18 7-12 10 Unacceptable for long life
650 10-15 5-10 3-7 5 316 not suitable; upgrade alloy
Converting Internal Pressure and Wall Thickness to Allowable Stress

The recommended design permissible hoop stress for a conventional 316 heater sheath of 10 mm outer diameter and 1.5 mm wall thickness (mean diameter 8.5 mm) is 85 MPa at 500 °C, which gives a maximum internal pressure of P_max = (2 1.5 85) / 8.5 = 30 MPa (300 bar). This is well above any feasible pressure in immersion heater service, demonstrating that creep rupture at 500 °C is not the limiting factor for such a heater – other problems such as oxidation or thermal fatigue will dominate. At big diameter sheaths or high temperature creep becomes limiting. For a 20 mm OD sheath with 2.0 mm wall (mean diameter 18 mm) at 550 °C (allowable stress 40 MPa) the maximum internal pressure is merely Pmax = (2 2.0 40) / 18 = 8.9 MPa (89 bar). This may be too little for a heater at 550 °C in a pressurised system (e.g. superheated water or steam at 80-100 pressure). The designer should increase wall thickness, lower the temperature by reducing power density, or update the material.

Factors Affecting Creep Rupture Strength

Creep rupture strengths in table are for 316 completely annealed ASTM 6-8 (30-50 m) grain size. Three things alter these values. The first is grain size. Coarse grained material (ASTM 3-5, 50-80 µm) demonstrates 10-20 % stronger creep rupture strength at the same temperature than fine grained material because grain boundaries are the dominant creep cavitation sites and coarser grain sizes mean fewer boundaries per unit volume of material and hence a lower density of cavities. Going to a minimum grain size of ASTM 5 can provide an added margin. The second component is prior cold work: 10-20 % cold work boosts initial strength but causes quick stress release and recrystallisation around 500-600 °C, leading to poorer long-term creep strength than fully annealed material. Fully annealed is better for creep limited service. The third point is the distribution of carbides. Material with fine intragranular carbides (from correct solution annealing) gives precipitation strengthening which increases creep resistance. Coarse, grain boundary carbides (sensitisation) diminish creep strength as the carbides act as nucleation locations for cavities. Fine intragranular carbides inside a solution annealed microstructure are necessary for creep constrained applications

Practical Determination of Sheath Temperature for Creep Life Calculations

The temperature of the inner sheath (the metal temperature at the inner wall which regulates the creep of the pressure-containing cross-section) of the heater in service is higher than the temperature of the outer sheath measured in the process fluid. The temperature difference across the wall is ΔT = (q × t) / k where q is heat flow (W/m2), t is wall thickness and k is thermal conductivity of 316 (about 20 W/m·K at 500 °C). For a typical water heater with outer jacket temperature 90°C and wall thickness 1.5 mm, the inner jacket temperature is just 1-2°C higher which is negligible. If the outer sheath temperature is 600°C, the inner sheath temperature may be 620-630°C because of the temperature decrease across the wall, which will greatly reduce the creep life. The heat flux should be used to determine the calculated inner wall temperature when creep rupture data are used rather than the recorded outer temperature. Creep is not the life-limiting failure mode in the majority of immersion heating applications in liquids. For air and gas heating above 500 °C outside temperature, creep has to be specifically considered.

Summary: Application of Creep Rupture Data to the Design of 316 Heaters

For 316 stainless steel encased heaters with an internal temperature of 500 °C, the maximum permitted hoop stress for a 100,000 hours (11.4 years) creep rupture life is 85 MPa (recommended design allowable). This stress value permits regular small diameter sheaths (10 mm OD, 1.5 mm wall) to cope with internal pressures up to 300 bar – much beyond normal service conditions. At 550 °C allowed stress is reduced to 40 MPa and at 600 °C to 15 MPa, making creep rupture life limiting for many heater designs. Engineers needing 316 sheaths for high temperature service must calculate the inner wall temperature from the heat flux and wall thickness, then select wall thickness and operating pressure such that the resulting hoop stress does not exceed the allowable values in the table for the desired service life. The architecture described here links creep rupture stress with temperature, time and safety parameters so that customers can construct 316 encased heaters which will operate continuously for 100,000 hours without creep failure.