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Applicability Evaluation of Ramberg-Osgood Equation as New Cladding Plastic Material Model
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For the spent fuel modeling, the plastic model of the cladding used in FRAPCON uses the σ = K̃ format. Strength coefficient (K), strain hardening exponent (n), strain rate sensitivity constant (m) are derived as the function of temperature. The coefficient m related to the strain rate shows dependence on the strain rate only in the α-β phase transition section, 1,172.5~1,255 K. But this is the analysis range of the FRAPTRAN code, which is an accident condition nuclear fuel behavior evaluation code. It does not apply to evaluate spent fuel. This coefficient in FRAPCON is used as a constant value (0.015) below 750 K (476.85°C), and at a temperature above 750 K, it is assumed that it is linearly proportional to the temperature without considering the strain rate dependence, also. In order to confirm the effect of strain rate, multiple test data performed under various conditions are required. However, since the strain rate dependence is not critical and test specimen limitation in the case of spent fuel, it is needed to replace with a new plastic model that does not include the strain rate term. In the new plastic model, the basic form of the Ramberg-Osgood equation (RO equation) is the same as ε = + . If the new variable α is defined as α = /, this equation can be transformed into ε = + . The procedure for expressing the stress-strain curve of the cladding with the RO equation is as follows. First, convert the engineering stress-strain into true stress-strain. Second, using a data analysis program such as EXCEL or ORIGIN, obtain the slope of the linear trend-line on the linear part and use it as the elastic modulus. Third, using the 0.2% offset method, find the yield point and the yield stress. Finally, using the solver function of EXCEL, find the optimal values of α and that minimize the sum of errors. The applicability of the suggested RO equation was evaluated using the results of the Zircaloy-4 plate room temperature tensile test performed by the KAERI and the Zircaloy cladding uniaxial tensile test results presented in the PNNL report. Through this, the RO equation was able to express the tensile test results within the uncertainty range of ±0.005. In this paper, the RO equation is suggested as a new plastic model with limited test data due to the test specimen limitation of spent fuel and its applicability is confirmed.
