Ring Tensile Test (RTT) is mainly performed for comparing tensile strength and total strain between nuclear fuel cladding specimens under various initial conditions. Through RTT, the loaddisplacement (F-D) curve obtained from the uniaxial tensile test can also be obtained. However, the Young’s modulus estimated from the gradient of the straight portion is much lower than general value of materials. The reasons include tensile machine compliance, slack in the fixtures, or elastic deformation of the fixtures and the tooling. Another reason is that the bending of the test part in the ring is stretched with two pieces of tools. Although the absolute value of the Young’s modulus is smaller than the actual value, it is applicable to calculate the ratio of the Young’s moduli of different materials, that is, the relative value. The Young’s modulus, or slope of the linear section, varies slightly depending on which location data is used and how much data is included. In order to obtain a more accurate ratio of Young’s moduli between materials using the RTT results, a post-processing method for the ring tensile test results that can prevent such human errors is proposed as follows. First, the slope of the linear section is obtained using the displacement and load when the load increase is the largest and the displacement and load of the position that is 95% of the maximum load increase. To replace the section where the ring-shaped specimen is stretched at the beginning of the F-D curve, a straight line equal to the slope of the linear section is drawn to the displacement axis from the position of maximum load increase and moved to the origin to obtain the final F-D curve for a RTT. Lastly, the yield stress uses the stress at the point where the 0.2% offset straight line and the F-D curve meet as suggested in the ASTM E8/E8M-11 “Standard test methods for tensile testing of metallic materials”. RTT results post-processing method was coded using FORTRAN language so that it could be performed automatically. In addition, sensitivity analysis of the included data range on the Young’s modulus was performed by using the included data range as 90%, 85%, and 80% of the maximum load increase.

For the spent fuel modeling, the plastic model of the cladding used in FRAPCON uses the σ􀷥 = K􀟝̃􀯡 􁉂 􀰌􁈶 􀬵􀬴􀰷􀰯􁉃 􀯠 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.