Issue 47

A. Chouiter et alii, Frattura ed Integrità Strutturale, 47 (2019) 30-38; DOI: 10.3221/IGF-ESIS.47.03 35 f eq s      (8)   1 2 2 p n h trE E E N P            (9) This nonlinear system is iteratively solved according to the Newton method (Benallal et al, [15]) for each iteration (s), we have: : 0 ; : 0 p f h h f h p c c c                    (10) Where f and h is their partial derivatives taken at time (t n +1) at each iteration (s). The "corrections" c   and Cp are defined by:         1 1 p n s and S S C P P c             (11) The iteration (s = 0) corresponds to the elastic predictor. When P and   are determined, E P and D are calculated from their discretized forms and the stresses are determined by:   1 ij ij D      The method developed above has been implemented in the ANSYS commercial code and the post-processor. It will use as data, the parameters of the material and the components of the total deformations. As result, it will give, a function of the internal pressure in the fixed tube-plate heat exchanger and the difference of expansion exerted on the bellows, the damage value, the cumulative plastic deformation and the stress components σ ij at each step, until initiation of macroscopic cracks at the critical zone (Von Mises maximal stress value). This will permit to determine the number of maximum service cycles that the expansion bellows can withstand as a function of the variations in internal pressure and thermal expansion. V ALIDATION O F T HE M ETHODOLOGY s mentioned earlier in this paper, the objective of the present work is to develop a model that can predict the critical cycle life of expansion bellows for fixed tube sheet heat exchanger. As an example of application, we consider an expansion which material and geometrical properties has been taken from ASME Sec II Part D [17] (see Tab. 1 and Fig. 6). Figure 6 : Two-dimensional model of wall expansion bellow. A (12)