PSI - Issue 57

Inge Lotsberg et al. / Procedia Structural Integrity 57 (2024) 569–580 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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A quadratic extrapolation of surface stresses from positions 0.4t, 0.9t and 1.4t is recommended at hot spots showing a steep stress gradient in DNV-RP-C203 (2019). Now the actual stress gradient is not very steep for the considered detail, but the method is included for completeness. A quadratic function is fitted through the stress points at 10, 20 and 30 mm. This gives the following stress distribution along the plate surface σ(y) = 0.00020y 2 - 0.01300y + 1.3545 where y is distance from the hot spot. This function passes through the stress points at 0.4t, 0.9t and 1.4t. Thus, at the hot spot the stress is equal to 1.355 for y = 0. Next the hot spot stress equal to 1.387 is derived from a linearization of stresses through the thickness from stresses listed in Table3. Analysis no 2: By following the same methodology as for analysis no 1 the hot spot stress for Method A is derived as 1.376. For Method B the calculated hot spot stress is equal to 1.457. It is observed that the calculated stress at a position 20 mm from the weld toe in Fig. 8 is less than at 30 mm from the weld toe. This makes a quadratic extrapolation of stresses difficult as shown in Fig. 8 when using stresses only at three positions to determine the hot spot stress. It is seen that a curve fitting to more stresses further away from the hot spot reduces the calculated hot pot stress to a value closer to the target value of 1.41 (when not using the low stress value at 20 mm). The integration of stresses through the thickness to derive the membrane stress and the bending stress is shown in Table 4. Δt in this table is difference between calculated stress points through the thickness and is equal to 2.5 mm. The resulting hot spot stress is the sum of the membrane stress and the bending stress and is equal to 1.341 (= 1.068+0.273).

Table 4. Calculation of membrane stress and bending stress through the plate thickness x σ(x) σ m ·Δt σ(x) - σ m t/2 - x σ b 1.25 1.589 0.199 1.474 8.75 0.484 3.75 1.150 0.144 1.035 6.25 0.243 6.25 1.001 0.125 0.886 3.75 0.125 8.75 0.992 0.124 0.877 1.25 0.041 11.25 0.980 0.123 0.865 -1.25 -0.041 13.75 0.967 0.121 0.852 -3.75 -0.120 16.25 0.946 0.118 0.831 -6.25 -0.195 18.75 0.919 0.115 0.804 -8.75 -0.264 σ m = 1.068 σ b = 0.273

Analysis no 3: By following the same methodology as foranalysis no 1 the hot spot stress for Method A is derived as 1.200. For Method B the calculated hot spot stress is equal to 1.319. It is noted that the stress at position 0.5t is reduced when using a refined mesh. The calculated stresses have not converged when using the recommended modeling to derive the hot spot stress. Thus, it is important to follow the recommendations of finite element modeling in addition to read out of stresses for derivation of hot spot stress. The low calculated stresses at position 0.5t may explain the low hot spot stresses for Method A and Method B. This shows that a finer element mesh at the hot spot region may not result in a more accurate hot spot stress. It may in fact result in non-conservative values as compared with that derived from a recommended finite element modeling. Thus, the derivation of hot spot stress is strongly related to the finite element modeling. It is observed from Table 2 that the calculated stress at a position 10 mm from the weld toe is less than at 15 mm from the weld toe. This makes a quadratic extrapolation of stresses difficult as shown in Figure 8 when using stresses only at three positions to determine the hot spot stress. It is seen that a curve fitting to more stresses further away from the hot spot reduces the calculated hot pot stress to a value closer to the target value of 1.41.