PSI - Issue 71

A. Syed et al. / Procedia Structural Integrity 71 (2025) 82–89

88

0.8

Temperature (°C) 25 300

0.7

0.6

0.5

Triaxiality (h)

0.4

0

2

4

6

8

10

Normalized distance (r s 0 / J )

(b)

(a)

Fig. 6: (a) Von-Mises stress (MPa) contour at J value of 100 N/mm (displacement – 10 mm) (b) Comparison of stress triaxiality from the crack tip distance at different temperature. 5. Determination of JR curve and its comparison at different temperature J-R curve is evaluated as per the procedure discussed in Syed et al. (2020). The plastic deformation energy is evaluated at different mandrel displacement by subtracting the frictional energy dissipation from the total energy. The amount of friction energy dissipation (F f ) is shown in Eq. (2) where ‘µ’ is the coefficient of friction taken from FE simulations, ‘θ’ is the conical mandrel angle, and ‘F’ is the load applied on the mandrel. J- integral is evaluated using the ‘η’ and ‘γ’ functions. J elastic is evaluated using the elastic stress intensity factor (k I ) as shown in Eq. (3). J plastic is evaluated using Eq. (4). = 2 ′ (3) ' ' ( 1) ( ) ( 1) ( ) ( 1) ( ) ( 1) ( 1) ( 1) ( 1) 1 2 i pl i pl i i i pl i pl i i i i A A a a J J b t b   − − − − − − −       − − = + −                   (4) where ‘A pl ’ is the plastic deformation energy, ‘a’ is the instantaneous crack length, ‘b’ is the remaining ligament length corresponding to the crack length ‘a’ . cos sin + 2 2    f F F  =      

(2)

2000

Test Temperature (°C) 25 300

1600

400 J-Integral (kJ/m 2 ) 800 1200

0

0.0

0.4

0.8

1.2

1.6

2.0

Crack growth (mm)

Fig. 7: Comparison of JR curve obtained after testing of clad tube specimen at different temperatures.

Comparison of the JR curve obtained at different temperature is shown in Fig. 7. It can be observed that the JR curve is higher at 300 °C as compared to 25 °C. For evaluating the crack initiation toughness, the value of JR corresponding to crack growth of 0.2 mm is noted. It was observed that the JR value is 105 kJ/m 2 and 182 kJ/m 2 for