PSI - Issue 14

S.C.S.P. Kumar Krovvidi et al. / Procedia Structural Integrity 14 (2019) 855–863 S.C.S.P. Kumar Krovvidi / Structural Integrity Procedia 00 (2018) 000–000

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2. Preliminary design Preliminary design of the bellows for nuclear applications is carried out by standards of EJMA. Failure modes such as in-plane stability and column stability of the bellows are addressed during the preliminary design. The bellows which are suitable for ½-inch bellows sealed valve are considered in the present case study. The material of construction of the bellows is SS316LN. The specifications of the bellows and the design details of the bellows as per EJMA are given in Table 1. The equation for predicting the life (N c ) of the bellows as per EJMA is given by 6 3.4 1.86 10 54000 c t N S          Where, S t is the total stress range computed as per the expressions given in EJMA [2] . Table 1: Design specifications and the geometrical details of the bellows S.No Parameter Value 1 Design Pressure (P) : 0.3 MPa 2 Design temperature (T) : 293 K 3 Axial movement (x) : 20 mm (±10 mm) 4 Design Code for preliminary design : Standards of EJMA 5 Inner diameter of the bellows (Db) : 29 mm 6 Length of the bellows (Lb) : 83 mm 7 Number of convolutions : 20 8 Depth of convolution (w) : 7 mm 9 Number of plies (n) : 1 10 Ply thickness (tp) 0.2 mm 11 Number of cycle as per EJMA (Nc) :48500 12 Limiting design pressure based on In-plane stability (Psi) : 0.4 MPa 13 Limiting design pressure based on column stability (Psc) : 0.1 MPa * * In bellow-sealed valves, the limiting design pressure is not governed by column stability as the bellows are guided internally by the stem of the valve. 3. Analysis 3.1. Linear elastic analysis and estimation of cycle life as per RCC-MR In general, formed bellows operate in elasto-plastic range. RCC-MR (2007) gives the method to find the elasto plastic strain range in the bellows based on simple linear elastic analysis. The methodology for finding the elasto plastic strain range based on the RCC-MR is summarized in Fig. 2. The linear elastic strain is enhanced to consider the plastic strain at the point of examination. The linear elastic finite element analysis was carried out on bellows geometry using ABAQUS 6.14 FE software. Figure 3 gives the geometry of the bellows used for the analysis. Young’s modulus (E) of 200GPa and Poisson ratio (  ) of 0.3 are considered during the linear elastic analysis. Single convolution of the bellows is modeled using axisymmetric shell elements. One end of the bellows is fixed simulating its connection with the valve body and the other end is subjected to axial displacement and an internal pressure of 0.3 MPa. Three loading cases are considered in this work. Since single convolute axisymmetric model is considered in the analysis, the displacement loading of ±0.5 mm, ±0.625 mm and ±0.75 mm are imposed in the FE model corresponding to three loading cases of ±10 mm, ±12.5 mm and ±15 mm axial movements of the bellows.