PSI - Issue 5

Hyung-Kyu Kim et al. / Procedia Structural Integrity 5 (2017) 63–68 Hyung-Kyu Kim/ Structural Integrity Procedia 00 (2017) 000 – 000

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3. Uncertainty evaluation

Eq. (4) has been previously investigated for validation through experiments to design the outer tube thickness of a dual cooled annular fuel. The details can be consulted from Kim et al (2009). In that research, an important finding was that Eq. (4) was not conservative and overestimated the actual critical buckling pressure. Tubes collapsed at p = 3.824 MPa in the experiment although p cr = 4.518 MPa obtained from Eq. (4). The discrepancy is around 7.4%. Thus, it was thought that some uncertainties should be necessarily considered when Eq. (4) was actually applied. We attempted to find the uncertainties that could cause such an overestimation. To this end, we classified three different characteristics of the parameters in Eq. (4) such as the measurement uncertainties of E and ν , dimension uncertainties of t and r , and shape uncertainty of δ 1 . 3.1. Uncertainties of the mechanical properties It is general to use a material handbook or a common database to obtain the mechanical properties, E and ν . However, those include a measurement uncertainty. This uncertainty has been studied by Huh et al (2010). They evaluated the measurement uncertainty of the tensile properties to be ±1.66%. This implies that E can be as small as 98.34% of the listed value. Thus, the calculated value of p cr can be reduced to be 98.34% of the calculated result. On the other hand, the uncertainty of ν has not been studied in their work. This may be considered from the factor of (1 – ν 2 ) in Eq. (4) which is a general term to incorporate a plane strain condition. Because the range of ν of a metallic tube is assumed as 0.25-0.37, the discrepancy of (1 – ν 2 ) in that range is 8.6%. This implies the variation of p cr of Eq. (4) can be 8.6% if ν of the tube material has the value in the range of 0.25-0.37. But, in reality, it is expected that the variation will be much smaller than this because the variation of ν is not that large. 3.2. Uncertainties of the dimension This is attributed to the dimension tolerances of t and r . According to ASTM standards (2007, 2010), the allowable dimension tolerance depends on the sizes of t and r . For the present evaluation, a zirconium alloy (Zircaloy-4; E = 76.5 GPa, ν = 0.3 at 350ºC) tube of 5.1-16.5 mm in nominal outer diameter and 0.25-0.89 mm in nominal thickness was chosen as an example. In this case, the allowable tolerance of t is ±0.08 mm, and that of D (outer diameter) is ±0.05 mm. Calculation was carried out in two ways, i.e. by applying i) the minimum thicknesses and nominal outer diameters and ii) the maximum outer diameters and nominal thicknesses incorporating the maximum tolerances of each. Those were compared with the case of applying the nominal values of both thickness and diameter of the above mentioned ranges, whose result was referred to as p cr nom here. Consequently, a reciprocal of p cr / p cr nom gives the required safety factor to prevent the buckling failure accommodating the dimension tolerances.

Fig. 2. Critical buckling pressure and required safety factor corresponding to the variation of the thickness and outer diameter.