PSI - Issue 71

P.K. Sharma et al. / Procedia Structural Integrity 71 (2025) 66–73

71

4. Finite element modelling for determination of stress triaxiality values Finite element analysis was carried out to simulate the deformation behavior of notched specimen by providing the Norton’s creep rate equation parameters as the input. 1/4 th model of the notched specimen were prepared to take advantage of the symmetry (Fig. 6(a)). Very fine mesh were done near the notched region and the size of mesh is larger from far away zones as shown in Fig. 6(b,c). Mesh convergence study was carried out for all the specimens to fix the final mesh used for the study. The symmetry boundary conditions were given on 3 symmetric zones and pressure is applied at the top such that the net section stress at the notched minimum cross-section is same as that of the smooth specimen. Norton’s parameters at 900 °C were input to the model for evaluating the triaxiality.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0 1 2 3 4 5 6

Notched specimen 0.5 mm

Notched specimen 0.5 mm

1 mm 2 mm

1 mm 2 mm

Smooth specimen

Smooth specimen

Test Temperature - 800 0 C Stress = 70 MPa

Test Temperature - 900 0 C Stress = 50 MPa

Displacement (mm)

Displacement (mm)

0

2

4

6

8

0

2

4

6

8

Creep time (Hrs) Creep time (Hrs) Fig. 5: Effect of notch radius on displacement behavior of alloy 690 material tested at (a) 800 °C & 70 MPa stress (b) 900 °C & 50 MPa stress. (a) (b)

(c)

(a)

(b)

Fig. 6: Finite element modelling used for 1 mm notch radius specimen (a) Boundary conditions applied; (b) FE mesh used (c) zoomed view near notch of the specimen. The von-Mises and hydrostatic stress contour for 1 mm notched specimen at 900 °C is shown in Fig. 7. It can be observed that the maximum stresses occur at the notch minimum cross-section in the central plane of the specimen. Both the stresses reduce from the notch ends to the centre. The ratio of hydrostatic stress (σ m ) to the von-Mises stress (σ e ) were evaluated for all the specimen to evaluate the stress triaxiality (η) values as per the Eq. (2). The value of at different locations is given in Table 3. It can be observed that high stress triaxiality occurs for lower notch radius specimen i.e., 0.5 mm. The value of stress triaxiality changes from 0.33 to 0.89 from smooth specimen to specimen with notch radius of 0.5 mm respectively. = (2)

(b)

(a)

Fig. 7: Contour plot for 1 mm radius notched specimen after 10hrs of creep time (a) von-Mises stress (MPa) (b) Hydrostatic stress (MPa).