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The mechanism of failure of heat exchanger and steam generator tube-to-tubesheet joints is related to the level of residual stresses produced in the tube expansion and transition zones during the expansion process and their variation during operation. The accurate prediction of these stresses based on the plastic and creep properties of the joint materials involved can help to design for better leak tightness and strength. Existing design calculations are based on an elastic perfectly plastic behavior of the expansion joint materials and do not account for creep. The proposed model is based on a linear strain hardening material behavior and considers the joint contact pressure relaxation with time. The interaction of the tube and the tubesheet is simulated during the process of the application of the expansion pressure and operation. The effects of the gap, material strain hardening and creep properties are to be emphasized. The developed model results are validated and confronted against the more accurate numerical FEA models.