Level 1 pipeworks calculations - thermal and fatigue gradients

The calculation of industrial piping systems is one of the practical applications of the finite element method. The specific features of piping systems are taken into account in particular through flexibility coefficients, which act as inertia reducers, and stress intensifier coefficients, which a posteriori increase the calculated stresses according to the nature of the element studied.

A small number of piping systems require special vigilance: these are the primary circuit piping systems in nuclear power plants, known as Level 1.

The highly sensitive nature of these pipes may require the deployment of powerful calculation resources (3D modeling, elastoplastic analysis), but in the majority of cases calculations are carried out in the elastic domain with wire elements.

Nevertheless, more precise and comprehensive rules are implemented in the codes, and additional physical phenomena must be integrated into the analysis. In particular, the estimation of maximum stresses, or more precisely their maximum amplitude of variation, must include the effects of thermal gradients associated with heat diffusion through the pipe thickness.

Part of this article is therefore devoted to the presentation of these thermal gradients, to which a linearization process is applied, enabling them to be broken down into three distinct parts, corresponding to as many types of stress. A distinction is made between the linearized part (linear variation across the thickness), which induces a bending stress, the non-linearized part, which has only localized effects, and the mean value, which has no effect in the absence of any major discontinuity (change in cross-section or material). The equations then retain some or all of these effects, depending on their purpose, which may be to verify the elastic behavior of the system, or to justify it against fatigue. In the latter case, all the effects of thermal gradients are retained.

Fatigue is a complex phenomenon, for which many uncertainties exist. The method used in piping calculations is based on the use factor calculation technique, which quantifies the damage sustained by the installation. The aim is to study the state variations imposing the greatest stress, and then to associate a maximum number of occurrences (number of cycles) with them, in order to maximize the damage.

The example in the last section of this article gives a complete presentation of the calculation methodology, applied to a point located at the interface of a section change, i.e. a point of major discontinuity. This example includes seismic loads (primary inertial part and secondary part), thermal transients and fatigue calculations.