PSI - Issue 60

Rosy Sarkar et al. / Procedia Structural Integrity 60 (2024) 75–92 Rosy Sarkar/ Structural Integrity Procedia 00 (2019) 000 – 000

85 11

4.1.3 Ratcheting check using Efficiency Index Method (RCC MR code [RCCMRx RB (2012)]) As per RCC MR, Efficiency Index Diagram (EID) is used to determine the effective primary stress (P1 or P2). The effective primary stress is the equivalent uniaxial stress responsible for the same strain accumulation. The secondary ratio, which is the ratio of cyclic secondary stress range and primary stress, is first calculated, and the value of ν is estimated using EID . Effective stress intensity is the ratio of primary stress and ν. The limit of the effective stress is 1.3 * shape factor (1.5 for rectangular) * Sm (allowable stress intensity), and the elastoplastic plus creep strain is limited to 2 % at all conditions [RCCMRx RB (2012)]. Both the limits are checked, and the conditions for initiation of ratcheting at room temperature and 600 ℃ are given in Table 3 and Table 4, respectively.

Table 3 Initiation of ratcheting at room temperature as per Efficiency Index Diagram

Pressure (bars)

Displacement (mm)

PL + Pb (MPa)

Q (MPa)

P2= (PL+Pb)/v2 (MPa)

Limit< 1.3*1.5*Sm

Plastic strain (%)

7

127

23.5 50.7 67.7 84.5

3497.3 1621.8 1223.2 1686.9

286.8 286.7 287.8 286.8 287.2

286.65 286.65 286.65 286.65 286.65

0.23

15 20 25 30

59 44 34 28

0.232

0.24

0.233

101.3 0.23 The creep hold time is taken as 0 hours, and hence, the creep strain is equal to 0. The displacements initiating ratcheting, corresponding to the maximum stress limit and maximum strain limit at 600 ℃ ǡ are given in Table 4. Table 4 Initiation of ratcheting at 600 ℃ as per Efficiency Index Diagram Pressure (bars) Displacement (mm) PL + Pb (MPa) Q (MPa) P2= (PL+Pb)/v2 (MPa) Limit< 1.3*1.5*Sm Plastic strain + creep strain< 2% 813.8

7 7

57 63 39 43 32 36 25 28

23.71 23.71 33.84 33.84 40.57 40.57 50.68 50.68

1303 1438

175.8 184.7 175.6 184.1

185.25 185.25 185.25 185.25 185.25 185.25 185.25 185.25

2.1 3.2

10 10 12 12 15 15

911

2.08 3.16 2.01

1001

755 844 602

175

185.1 174.7

3.3

1.98 3.15

668.4

184

4.2 Elasto-Perfectly Plastic Analysis Many non-linear material models are available in the literature to simulate the cyclic accumulation of strain due to ratcheting [Suresh Kumar et al., (2012)]. This study assumes a simplified elastic-perfectly plastic and linear elastic material behavior. This assumption has been done to compare the codal procedures. For instance, there is Bree diagram in the ASME code, that has been developed assuming that the material has an elastic perfectly plastic stress strain diagram [Bree 1967 and 1968]. However, unlike elastoplastic analysis, it is an ideal approach and does not account for strain hardening. Hence, elasto-plastic analysis will be carried out as a part of future studies. The stress-strain diagram for elasto-perfectly plastic material is bilinear with two slopes. Upto flow stress, it follows the elastic path, and then, the stress-strain diagram is flat. Flow stress is the instantaneous value of stress required to continue the plastic deformation of a material. For computation purposes, the flow stress is considered as