Thermo-mechanical fatigue modelling white paper


Pressure equipment is often subject to cyclic loading during service, accumulating irreversible damage due to degradation of the material in response to alternating stresses. This type of loading can lead to the initiation of cracks, which may propagate resulting in sudden failure of the structure at stress amplitudes lower than the tensile yield strength of the material. This mode of failure can be predicted assuming conservative rules with the combined use of the Finite Element Method (FEM) and fatigue theory.

Different types of loads can lead to fatigue failure. Temperature and pressure oscillations are usually included in the design specification of vessels and other pressure equipment together with other mechanical loading oscillations. Relevant technical standards propose a clear methodology to conduct calculations including stress and fatigue failure prediction. In particular ASME VIII-2 and PD-5500 are widely used for these purposes. Standards and codes also provide the input needed to post-process the stress distribution calculated by the FEA method.

Thermal fatigue analysis

The fatigue analyst of pressure equipment must pay extra attention to some geometric features like welds, bolting, clamps and supports as these detailed areas will probably be the ones limiting the fatigue useful life of the entire system. The use of codes will aid the analyst in this matter as standards normally provide a set of curves (S/N curves) that include the information gathered after numerous tests of specimens containing welds and other features similar to those under consideration.

The calculation methodology usually includes two main stages:

Technical approach

PRE Technologies specialises in the finite element analysis (FEA) approach to perform stress and fatigue analyses of pressure equipment under the loads specified by the client with the objective of assessing the expected useful life for the different components or assemblies.

The analysis of the different assemblies involves the use of FEA coupled methods. The outputs from the stress analysis are used to complete a fatigue analysis in accordance with the methodology contained within the PD-5500 or ASME VIII-2 codes. The steps that are followed along the technical delivery of the project are discussed below (for PD-5500 only).

FEA modelling

The work is based on the examination of the thermally and mechanically induced stresses on the equipment for a whole cycle. To facilitate the analysis two different FEA models are created. The first model will be used to calculate the temperature field on the vessel or reactor under the given conditions and the second will add other cyclical mechanical loads to obtain the alternate stress that will eventually lead to fatigue failure. A third stage might be required to evaluate the locally relevant stresses where the global model accuracy is deemed not sufficient.

Heat exchanger FEA

A summary of the stages involved is detailed in the next list:

As mentioned, sub-modelling of some regions is often utilised to provide an accurate analysis of stress concentrations due to small features, discontinuities or stress risers not included in the global model. This can be, for instance, the nozzle regions or the baffle/coil welds in vessels and heat exchangers.

Some assumptions are normally made based on PRE technologies’ experience in FEA fatigue modelling: Heat exchanger FEA fatigue analysis

Fatigue assessment

The fatigue assessment methodology is based on the recommendations of the standard used (for this example the PD-5500 standard). This standard recommends the use of previously simplified fatigue analysis and screening methodology assuming conservative rules. PRE technologies perform this analysis to assess the need of fatigue evaluation as part of the best practices in fatigue failure prediction methods. The use of FEA models can greatly improve the use of manual calculations normally used in this type of preliminary conservative analysis.

A further detailed analysis is performed using the stress ranges obtained from the FE analysis. This analysis involves more detail and the use of S/N curves to predict the damage factor for each identified set of loads. The first stage in this procedure is to calculate the stress historic of each of the identified critical regions. Principal stresses will be computed and amplitude will be used together with S/N curves to assess the potential fatigue failure.

The fatigue curves in PD-5500 are derived from welded samples tested based on the mean minus two standard deviations of the S-N curves corresponding to 97.7% probability of survival. These fatigue curves basically incorporate mean stress, so the effective stress ranges do not need to be corrected due to mean stresses, leading to a removal of every constant load presented in the cycle considered.

The fatigue curves are associated with figures of welded joints. The direction and location of the principal stress is used to determine which of the seven fatigue curves is to be applied. In the figure on the right the PD-5500 S-N curves for austenitic steel are presented.

Heat exchanger fatigue curves

The classification of welds and directions of principal stress in complex loading cases are not always obvious. In case of multi-axial stress state governing the cycle, the algebraic difference between the maximum and the minimum stresses regardless of the direction will be assumed as the alternating stress input in the S-N curves. Principle of conservatism is always used by the PRE technologies engineers to ensure the predicted results are within reasonable safety margins.

In order to comply with the specification assessment, the following steps are taken:

PRE Technologies' engineers possess vast experience applying this methodology to a variety of pieces of equipment, including separator vessels, chemical reactors, compressors, cyclones, spools and pipeline sections.

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