PSI - Issue 60

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S. K. Pandey/ Structural Integrity Procedia 00 (2023) 000–000

S.K. Pandey et al. / Procedia Structural Integrity 60 (2024) 3–12

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ε ε 0 = σ σ 0 + α� σ σ 0 � n

(1)

2.1. Step 1: Selection and numbering of different sets of RO parameters Selection and numbering different sets of RO parameters is the key process to reduce the computation work in the exercise of unique RO parameter appraisal. In this section, an approach has been adopted for performing the selection and numbering of different sets of RO parameters (n, α) to reduce the number of points for study. The selection and numbering of points can be done in other fashion also and it doesn’t affect the result, but selection and numbering of points in the proper manner will lead the fast minimization of error and decrease the number of sets of data points for study and reduces the computation cost. If ‘n’ and ‘α’ are considered two mutual perpendicular coordinate axes, then each set of RO parameters corresponds to a point on n- α coordinate plane as in Fig.2.

Fig. 1. Schematic of error evaluation for different combinations of R-O parameter and evaluation of unique RO parameter values using optimization as presented later in Section 2.4

Fig. 2. Selection and numbering of RO parameter points

The horizontal axis and vertical axis are taken as n axis and α - axis respectively. For example, point number 19 represents the RO parameter (n’, α’). The (n,α) of smooth specimen is called here initial guess point and is considered here as point number 1 in n- α coordinate plane, if (n,α) of smooth specimen is not available then initial guess value can be taken from literature or design code for this material. The number of total sets of (n, α) may vary depending depend upon closeness of initial guess (n, α) and optimized (n, α). During the selection and numbering of different sets of RO parameters, for SS316LN, n = 2.5, α = 15 are selected for initial guess point for the temperature of 298K. The values of ‘n’ are range from 2.2 to 3.2 with an interval of 0.1, and the values of ‘α’ are ranging from 6 to 18 with an interval of 1. In this study, 85 sets of data have been used to increase the accuracy of result but even less number of data sets can also be used. Increasing the number of RO parameter sets increases the accuracy of unique RO parameters. Finite element analysis (discussed in next paragraph) for all five specimens (smooth, notch-5, notch-2.5, notch-1.25 and notch-0.5) with 85 sets of RO parameters have been carried out. Normalized-Errors have been calculated for all the sets of RO parameters. 2.2. Step 2: Evaluation of Error at each sets of (n, α) by FE analysis Elasto-plastic finite element analysis, with rate-independent isotropic plasticity model, has been carried out, using ABAQUS FEA code, for all five specimens with all 85 sets of RO parameters. The gauge length of specimen is 30 mm. The diameter of gauge region of prismatic smooth specimen is 5 mm. For the notched specimens, the minimum diameter in the notched region has also been kept as 5 mm in order to study the effect of notch on the load displacement behavior in the experiment. The half section of the specimens have been modelled (due to symmetry in