## 2 Materials and Methods
### Assessment according to Elastic Analysis Criteria  
For the purpose of this work, the in-box LOCA is considered a design-basis accident, which should be assessed under Level-D criteria [14]. Hence, the failure is assessed with respect to two predominant modes that are thought to be relevant: the IPFL and the ILFED. The SDC-IC and RCC MRx recommend the following criteria to prevent IPFL failure mode [23; 24; 25].  
\[\overline{P_{L}+Q_{L}}\ \leq\ S_{em}\ (RCC-MRx)\ or\ \overline{P_{L}+Q_{L}}\ \leq\ S_{e}\ (SDC-IC)\]  
Figure 3: Static-structural analysis domain and boundary conditions.  
Figure 2: (a) HCPB BB cap region with highlighted symmetry section. (b) Symmetry section considered for simulation.  
where \(P_{L}\) and \(Q_{L}\) are the primary and secondary local membrane stress, respectively, and \(S_{em}\) or \(S_{e}\) is the allowable elastic stress limit for the material dependent on the temperature and neutron fluence. This limit is defined in different ways as per both the codes, and the Level-D limit is further derived using a lower safety factor. From [25], it can be seen that the limit values estimated according to SDC-IC are conservative compared to those according to RCC-MRx at temperatures above 350 \({}^{\circ}\)C, the usual operating temperature range of HCPB BB. This is due to the difference in the way of accounting for the uniform elongation of the material within the definition of the stress limits. In order to be conservative, the stress limit values according to SDC-IC criteria are used for the assessment of IPFL failure mode in this work. The SDC-IC defines the stress limit \(S_{e}\) as a function of the tensile strength (\(S_{u}\)), which is dependent on irradiation and temperature; as well as the uniform strain for uniform strain values greater than 2%. Since irradiated Eurofer97 has uniform strain values less than 2% in the expected operating temperature range of HCPB BB (350 \({}^{\circ}\)C to 600 \({}^{\circ}\)C), it is decided to ignore the dependence on it. Furthermore, since the limit values apply throughout the lifetime with a range of irradiation, the minimum tensile strength at unirradiated condition is used for the calculation of the stress limit \(S_{e}\). The Level-D criteria limit is estimated by multiplying the calculated \(S_{e}\) limit value with a safety factor of 2 to the as per the SDC-IC. In Figure 4, stress limits for Eurofer97 material are estimated and plotted.  
The criterion for ILFED failure mode as per the RCC-MRx includes the peak stresses while SDC-IC recommends an additional criterion without incorporating the peak stresses [23; 24].  
\[\overline{P_{L}+P_{B}+Q+F}\ \leq\ S_{et}\ (RCC-MRx)\ and\ \overline{P_{L}+P_{B}+Q}\ \leq\ S_{d}\ (SDC-IC)\]  
where the term \(\overline{P_{L}+P_{B}+Q+F}\) represents the total primary plus secondary stress including the peak stresses and the term \(\overline{P_{L}+P_{B}+Q}\) represents the total primary plus secondary stress excluding the peak stresses; \(S_{et}\) and \(S_{d}\) are the corresponding allowable total stress limits. Since the peak stresses in the FE solution can be affected by singularities and modelling approximations, it is decided to use the SDC-IC criteria without incorporating  
Figure 4: Stress limits with respect to temperature for Eurofer97 material.  
the peak stresses for the present work. Similar to the calculation IPFL stress limits, it is decided to ignore the dependence on failure strain and the stress triaxiality on stress limit \(S_{d}\) for uniform strain values greater than 2%, and the limit values are calculated using the minimum tensile strength at the unirradiated condition. Resulting stress limits are plotted in Figure 4. A safety factor value of 1.35 is used to multiply \(S_{d}\) limit to estimate the Level-D criteria limit as per SDC-IC.