Engineering guide
This module performs the fatigue analysis of spherical shells under cyclic loading to TRD 303 Annex 1, part of the German Technical Rules for Steam Boilers (TRD). From the pressure and temperature cycles of operation — minimum and maximum cycle pressure, minimum and maximum cycle temperature, and the temperature differences during start-up and shutdown — the allowable number of load cycles to technical crack initiation is determined. Stress concentration factors for thermal stresses and for the edge of openings capture the local stress increase.
The verification is required whenever a steam boiler component is operated cyclically rather than predominantly statically: frequent start-ups and shutdowns, load-following operation or sliding-pressure operation generate alternating pressure and thermal stresses that limit service life. On the material side, the yield strength, tensile strength, modulus of elasticity, coefficient of thermal expansion and thermal diffusivity enter the calculation; for water-wetted components, the influence of corrosion on the crack initiation curve is taken into account.
The TRD rules were withdrawn at the end of 2012. For the fatigue life assessment of existing boilers, however, TRD 303 Annex 1 remains the familiar reference method; for new designs, EN 12952-3 (fatigue analysis) and EN 12952-4 (in-service life monitoring) take over this role.
Scope
- Spherical shells subject to cyclic stressing
Typical workflow
Define the load cycles
Minimum and maximum cycle pressure and the associated cycle temperatures are established from the operating profile. The governing cycle temperature determines which material property values are used; the temperature differences during start-up (negative) and shutdown (positive) describe the transient thermal stress contributions.
Record geometry and material properties
The mean diameter of the spherical shell follows from the outside and inside diameters; the analysis wall thickness is obtained by deducting the allowances for wall thickness undertolerance and corrosion. On the material side, the yield strength at 20 °C and at the governing cycle temperature, the tensile strength, modulus of elasticity, Poisson's ratio, coefficient of thermal expansion and thermal diffusivity are required.
Determine the stress range
The pressure-induced membrane stress range is amplified by the shape factor of the spherical shell and the stress concentration factor at the edge of openings. The thermal stress contributions from the start-up and shutdown temperature differences are captured via the stress concentration factor for thermal stresses and superimposed on the pressure contributions.
Determine the allowable number of load cycles
Using the governing stress range, the crack initiation cycle count is read from the crack initiation curves, distinguishing between water-wetted and non-water-wetted surfaces. Safety factors on the number of cycles and on the stress range yield the allowable number of load cycles; finally, the conditions of validity of the verification are checked.
Frequently asked questions
When is the static verification to TRD 303 sufficient, and when is Annex 1 required?
The TRD rules provide a simplified screening criterion based on the number and range of the expected pressure and temperature cycles. For predominantly static loading — infrequent start-ups and shutdowns, small pressure fluctuations — the strength verification of TRD 303 is sufficient. For load-following operation, sliding-pressure operation or frequent start-ups, the cyclic loading must be quantified per Annex 1.
Why does it matter whether the component is water-wetted?
On water- or steam-wetted surfaces, the medium acts corrosively on emerging micro-cracks (corrosion fatigue in combination with the protective magnetite layer). The crack initiation curves for water-wetted components therefore lie well below those in air, particularly at high cycle counts. Assigning the wrong category leads to a substantial overestimate of the allowable number of cycles.
What does the crack initiation cycle count mean, as opposed to the cycles to failure?
The method evaluates the number of cycles up to technical crack initiation at the most highly stressed location, usually at the edge of an opening. Crack initiation does not yet mean failure of the component, but it is the criterion beyond which intensified recurring inspections or other measures become necessary. Safety factors on cycle count and stress range cover the scatter of the curves.
What role do the temperature differences during start-up and shutdown play?
During start-up, the inner surface is hotter than the mean wall, producing compressive thermal stresses (negative temperature difference); during shutdown, the sign reverses. These thermal stresses superimpose on the pressure stresses and can dominate the total stress range. A boiler's allowable rates of temperature change are derived directly from this verification.
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