Research on determining the lifetime of an expansion bellows designed to compensate the difference in expansion between the shell and the tubes in a fixed tube sheet heat exchanger has never ceased because of its Importance in a heat exchanger. The main function of the expansion bellows is to absorb the difference in expansion between the shell and the tube bundle while resisting the axial thermal deflection and the equivalent internal pressure on the shell side. TEMA-9  edition attaches great importance to the finite element method in the case of an expansion bellows because of the disadvantages of the old design methods, which lead to overestimation and stress overload in the bellows. The objective of this work is to study the damage in the most stressed zone of the expansion bellows in order to construct a numerical simulation tool of the rupture to determine the lifetime that an expansion bellows can support during the operating conditions of a fixed tube heat exchanger. In a first step, the ANSYS FEM calculation code will allow the determination of the critical zone where the Von Mises is maximum and where potential cracks can develop. In a second step, a post-processor based on the concept of Continuum Damage Mechanics and using Newton's iterative method will be applied to this critical area for the determination of the bellows critical lifetime. The maximum lifetime will be the value of the number of cycles that corresponds to the critical value of the DC damage (crack initiation).
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