PSI - Issue 60

A. Kumar et al. / Procedia Structural Integrity 60 (2024) 541–552 Akshay Kumar/ StructuralIntegrity Procedia 00 (2023) 000 – 000

546

6

MPa.

0.0 0.5 1.0 1.5 2.0

R1

R2

Resistance (K/W)

550

650

750

850

950

1050

1150

1250

Temperature (K)

Fig. 3: The resistance values R1 and R2 as a function of temperature

1000 1500

0 500

Heat transfer

550 coeff (W/m2-K)

650

750

850

950

1050

1150

1250

Temperature (K)

Fig. 4: Overall heat transfer coefficient (W/m 2 K) from PT to moderator as a function of temperature Structural Model for evaluation of diametrical creep Creep is more severe in materials that are subjected to heat for long periods, and generally increases as they near their melting point. The rate of deformation is a function of the material properties, exposure time, exposure temperature and the applied structural load. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function. The ballooning deformation of the PT is mainly due to uniform diametrical expansion and corresponding thinning of the tube, which can be captured using the steady state creep correlation (i.e., Norton’s creep law). The expression for creep in the steady state regime for the PT is given by Eq. 8. ̇ = exp(− ⁄ ) = material constant, = stress exponent, = applied stress, = activation energy of steady state creep, = universal gas constant, = absolute temperature (8) Shewfelt et.al. 1984 have developed creep equations that can be used to predict the transverse creep deformation of a pressure tube with varying internal pressures and experiencing temperature ramps. These correlations were developed based on uniaxial creep tests on Zr2.5 wt% Nb test specimens. The correlations are given in Eq. 9 and 10. For temperature range between 450°C and 500°C. For temperature range between 500°C and 700°C, ̇= 1.3×10 −5 σ 9 exp(−36600 ⁄ ) ̇= 1.3×10 −5 σ 9 exp(−36600 ⁄ ) + 5.7 × 10 7 σ 1.8 exp(−29000 ⁄ ) 2.2. Finite Element Analysis PT-CT problem is modeled using Finite Element (FE) software. The experiments on PT ballooning are reported by Nandan et al. 2012 for internal pressure values of 4 MPa and 6 MPa. They have reported the radial expansion and the time for PT to contact the CT at different axial and circumferential positions. In this paper we are presenting validation study for the case of 4 MPa internal pressure. FE Analysis was carried out in two parts: (a) Thermal analysis, (b) Structural analysis. With the help of thermal analysis, temperature distribution along the circumference of the pressure tube was calculated. This temperature profile act as an input data for structural analysis. The structural analysis was done to analyze the deformation of PT. Subsequently, the contact time between PT and CT was estimated. (9) (10)