# Comparative Theoretical Analysis of Halden Reactor Creep Tests on M5 Cladding Material
## 3 Experimental Results and Discussion
The only possible explanation found for this very large difference is that there can be phenomena in the rig that affect the diameter in opposite ways in the two tests. This may occur if corrosion and/or crud deposition on cladding occur during the rod in-pile operation. In fact, corrosion and crud (C&C in the following) in IFA-617 would cause a cladding diameter increase, which is opposite to creep, since this rig operates the rod at under-pressure conditions, whereas, in IFA-663, creep and C&C will contribute to diameter change in the same direction; i.e., they will both cause a diameter increase. Regarding C&C during the test, the HWR-658 report states that \"at each traverse, the gauges were effectively re-calibrated due to the presence of machined steps of known magnitude (approximately 50 \(\upmu\)m) on the end and mid-plugs. These calibration steps compensate for clad diameter changes arising from the growth of surface oxide layers\". However, one should note that, because corrosion would not affect the calibration step size, which remains at 50 \(\upmu\)m with or without corrosion, the step itself would not provide any correction for corrosion (or crud). Further, any C&C occurring in the unfueled zone of the rod (where the calibration steps are located), if existent at all, would be far lower than the C&C occurring in the fueled region due to the higher temperature (+40-50 \({}^{\circ}\)C) and the presence of surface boiling. \begin{table}
\begin{tabular}{c c c} \hline  & **IFA-617** & **IFA-663** \\ \hline \(\mathbf{\Phi}\) **(n/cm\({}^{2}\cdot\)s)** & \(2.9\times 10^{13}\) & \(2.8\times 10^{13}\) \\ \hline \(\mathbf{T}\) **(\({}^{\circ}\)C)** & \(375\) & \(359\) \\ \hline \(\mathbf{\sigma}\) **(MPa)** & \(-75\) & \(64\) \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the experimental conditions for tests IFA-617 and IFA-663 concerning the M5 cladding rod [8,9]. Unfortunately, the Halden reports [8; 9] do not provide any information about C&C aspects and their possible influence on \(\Delta\)D evolution vs. time. In order to address this point and reach practical conclusions, the following two equations with two unknowns (2) have been considered for the two tests:  
\[\left\{ \begin{array}{ll}-1.17\cdot\dot{D}_{\mathit{C}rep}+K\cdot\dot{D}_{ \mathit{C}\&C}=-1&[IFA617]\\ \dot{D}_{\mathit{C}rep}+\dot{D}_{\mathit{C}\&C}=7.7&[IFA663]\end{array} \right. \tag{2}\]  
In the above, \(\dot{D}_{\mathit{C}rep}\) and \(-1.17\cdot\dot{D}_{\mathit{C}rep}\) are the M5 creep rates in IFA-663 and IFA 617, respectively, while \(\dot{D}_{\mathit{C}\&C}\) is the corrosion + crud deposition rate during the test. The term K is the ratio of C&C deposition rate between the two experiments (i.e., IFA-617/IFA-663). By assuming \(K=1\), i.e., by assuming the same C&C deposition rate in the two tests, Equation (2) results in  
\[\begin{array}[]  
at the cladding surface in both rigs. Boiling may alter the local water chemistry and may cause accelerated corrosion (in fact, both HWRs report severe corrosion problems). Because of the very high temperature and because details of the water chemistry test condition are not reported, the extent of corrosion in the two tests may have been considerably larger as compared with the power reactor conditions. The above aspects regarding cladding corrosion also apply to crud deposition, especially concerning the effects of high surface temperature and surface boiling conditions. Hence, a C&C of about 3.7 \(\upmu\)m/1000 h may be on the high side as compared to power plants but not unrealistic for the conditions at which the two rigs were operated in the two mentioned experiments. The above results are based on the assumption that the C&C deposition rate is the same in the two tests (i.e., \(K\) = 1 in Equation (2)). A sensitivity assessment was conducted by varying parameter \(K\) up to \(\pm\)30%, i.e., from \(K\) = 0.7 to \(K\) = 1.3.