PSI - Issue 60

Sreerag M N et al. / Procedia Structural Integrity 60 (2024) 20–35 Sreerag M N/ Structural Integrity Procedia 00 (2023) 000 – 000

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f u        

Solving above non-linear equation for the unknown

f          b u

bf P P

(13)

Failure pressure, P bf is directly depending on the no-flaw burst pressure P b . Hence, P b is an important parameter for estimating the failure pressure in the presence of a defect. 3. Failure pressure estimation of cylindrical shells using Finite element Elastic plastic burst pressure of cylinders is usually found from empirical relations that are derived from various failure theories. Researchers like Von mises, Faupel, Soderberg, Turner, Nadai, Svensson, Tresca, Barlow, Christopher etc. had derived empirical methods of evaluating the burst pressure of a cylindrical shells. One of main drawn backs of using empirical relations is that they are not consistent for different materials and it cannot be used to find failure pressure for a cylinder having long seam or cirseam weld with mechanical properties different from the parent metal. Large diameter motor cases realised are rolled and welded construction and hence cirseam /long seam weld inherently becomes a part of fabrication process. Thus, in most cases using empirical relations to estimate failure pressure will not be good option and we will have to resort for finite element methods. Burst pressure can be estimated from finite element analysis finding the pressure corresponding to net section yielding. Burst pressure estimated with FEA will be closer to reality as it considers the geometric and material non linearity. The finite element models were meshed with 2D/3D elements with element type of PLANE183/SOLID185 in Ansys software. Number of elements in 2D/3D elements are max. 1 lakh/3.5 lakhs with element size of 1mmx1mm 1mmx5mmx5mm respectively. Applicable non-linear material properties are used in the weld and shell. Multilinear isotropic hardening material model is used for the analysis. Mesh convergence is verified comparing the hoop stress, meridional stress and radial dilation with the theoretical values. This meshing scheme is applied to all the models described in the paper. Table 1 shows the summary of no flaw failure pressure estimated for 3.2m diameter maraging steel motor.

Table 1: Elastic plastic burst pressure estimated empirical relations Empirical relation No flaw failure pressure (ksc) With PM property With R1 property Von-mises 97.50 88.45 Faupel (1956) 100.19 91.37 Soderberg (1941) 100.24 91.44 Turner (1910) 86.81 79.19 Nadai (1931) 100.24 91.44 Svensson (1958) 97.73 89.15 Tresca 84.84 76.97 Barlow 86.81 79.19 Christopher (2002) 99.64 90.91 FEM 97.37 88.83