This paper gives a highlight about pressure vessel (PV) methods of design to initiate new engineers and new researchers to understand the basics and to have a summary about the knowhow of PV design. This understanding will contribute to enhance their knowledge in the selection of the appropriate method. There are several types of tanks distinguished by the operating pressure, temperature and the safety system to predict. The selection of one or the other of these tanks depends on environmental regulations, the geographic location and the used materials. The design theory of PVs is very detailed in various codes and standards API, such as ASME, CODAP ... as well as the standards of material selection such as EN 10025 or EN 10028. While designing a PV, we must design the fatigue of its material through the different methods and theories, we can find in the literature, and specific codes. In this work, a focus on the fatigue lifetime calculation through fracture mechanics theory and the different methods found in the ASME VIII DIV 2, the API 579-1 and EN 13445-3, Annex B, will be detailed by giving a comparison between these methods. In many articles in the literature the uniaxial fatigue has been very detailed. Meanwhile, the multiaxial effect has not been considered as it must be. In this paper we will lead a discussion about the biaxial fatigue due to cyclic pressure in thick-walled PV. Besides, an overview of multiaxial fatigue in PVs is detailed. KEYWORDS. Pressure vessel design; ASME VIII; Multiaxial fatigue; Fracture mechanics; Cumulative damage
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