PSI - Issue 60

A. Syed et al. / Procedia Structural Integrity 60 (2024) 195–202 A. Syed/ StructuralIntegrity Procedia 00 (2023) 000 – 000

198

4

along the longitudinal and radial directions respectively that leads to computationally effective as well as less errors in the solution. Mapped meshing has been done for the whole tube. 3.3. Boundary conditions applied to the model In order to model the ballooning of the clad tubes, internal pressure is applied at the inside surface of the tube as shown in Fig. 1(a). This pressure is varied from 5 bar to 70 bar to study the effect of internal pressure on the deformation behavior of the tubes. One end of the clad tube is restricted to move in axial direction due to the applied internal pressure. Axisymmetric boundary conditions have been applied to the model. Transient analysis has been carried out to determine the deformation of the fuel clad with time. Initial temperature input to the model is taken from the experiment (Sawarn et al. (2014, 2017)). Burst temperature is input to the model in the second load step. Temperature of the clad tube increases from the initial temperature to final burst temperature linearly. Linear variation of the temperature is assumed for the analysis because of the linear increase in temperature of the fuel clad tubes during experiment as shown in Fig. 1(b).

100 200 300 400 500 600 700 800 900 Temperature (deg.C)

0

10

20

30

40

50

Time (s)

(a)

(b)

Fig. 1: (a) Finite element mesh of clad tubes (b) Input temperature profile for the clad tube under 2.1 MPa internal pressure.

4. Results obtained from the FE analysis Transient analysis was carried out under different internal pressure (0.3 to 10 MPa) applied on the inside surface of the fuel clad. Deformation contour of the clad tube with internal pressure of 2.1 MPa and burst temperature of 828 ˚C is shown in Fig. 2. The maximum deformation of the clad tubes occurs near the centre of the tube due to slight reduction in the diameter of the tube at that location. Maximum deformation of the tube at the centre is around 2.14 mm and 1.7 mm at the ends of the tube. Ballooning of the clad tubes occurs due to the creep deformation of the tubes when it reaches temperature above 600 ˚C. Initially, the rate of creep deformation is low and then, it increases rapidly due to the exponential increase in creep strain with time. The rate of increase in the creep strain of the clad tubes depends on the rate of heating of tube during experiment. Rate of heating considered for the analysis is 15.067 ˚C/sec. The damage behavior of the tube is dependent on the value of stress triaxiality ( Rice and Tracey’s ) prevailing during operating conditions. Since stress triaxiality depends on the ratio of hydrostatic to von-Mises stresses, it is important to compute the values of von-Mises stress and hydrostatic stress values at different time duration. von Mises stress and hydrostatic stress contours for the clad tube with internal pressure of 2.1 MPa and burst temperature of 828 ˚C are obtained. Maximum von -Mises stress and hydrostatic stress occurs near the center of the tube as the deformation is maximum at that location.