# Comparative Theoretical Analysis of Halden Reactor Creep Tests on M5 Cladding Material
## 3 Experimental Results and Discussion  
The best fit of the results shown in Figure 18 of the HWR-658 report, which depicts the details of the IFA-617 test, is presented in the plot of Figure 1. This shows that, after an initial phase of rapid diameter decrease (mentioned in both reports as 'primary creep'), a linear decline follows beyond a time of 500 h (reported as'secondary creep'). In the first 500 h period, a \(\Delta\)D of ca. \(-2.8\)\(\upmu\)m was detected, whereas, in the following phase, a linear trend was observed with a diameter change of \(-2.8\)\(\upmu\)m in a time-period of 2800 h.  
The models available in the previous versions of TRANSURANUS for M5 were not able to satisfactorily reproduce the experimental data described below, and this triggered interest in a more thorough examination of the experimental data and conditions. Regarding the IFA-663 test data [9], [PERSON] report HWR-755 mentions that some problems arose during the early phase of the experiment; hence, what can be considered reliable is the rate of diameter increase--i.e., the slope of the solid line in Figure 9 of the HWR-755 report--in the time interval between 3800 and 5600 full power hours. The M5 diameter change rate between these two points in time, as inferred from the data presented in that report, is 14 \(\upmu\)m/1800 h. As an additional note, the diameter increase rate as depicted in Figure 9 of the same report is similar for the three alloys studied, i.e., Zirlo, M5, and VVER (E110). However, the absolute \(\Delta\)D values for M5 and Zirlo are quite larger than for the VVER cladding (which was unfueled). The HWR-755 report does not address the reason for this behavior, which nevertheless does not interfere with the present analysis as this builds on the rate of \(\Delta\)D vs. time (and not on \(\Delta\)D absolute values). Figure 1: Diameter change vs. time for the M5 rod in IFA-617 experiment (data reproduced by estimate). The experimental diameter change rate was therefore \(-1\)\(\upmu\)m/1000 h in IFA-617 and 7.7 \(\upmu\)m/1000 h in IFA-663. Considering the experimental conditions in which the tests were conducted (see Table 1 below)--and in particular considering that IFA-617 was run at somewhat more demanding conditions than IFA-663--a slight correction is needed in order to make the results of the two tests directly comparable. The Franklin model (which strictly applies to Zr-4) has been used here for the purpose of completing the small correction mentioned above, which arises from the slight differences in fast neutron flux, average cladding temperature, and cladding stress in the two experiments. The Franklin model is as follows (Equation (1)):  
\[\frac{\Delta\mathrm{D}}{\mathrm{D}}=\mathrm{A}\cdot\mathrm{t}^{\mathrm{m}} \cdot\mathrm{Q}\mathrm{p}^{\mathrm{m}}\cdot\mathrm{q}_{\mathrm{0}}^{\mathrm{n} }\cdot\mathrm{e}^{(-\frac{\mathrm{Q}}{\mathrm{R}t})} \tag{1}\]  
where A = 1.11 \(\times\) 10\({}^{-13}\), m = 0.682, p = 0.550, n = 0.579, and Q/R = 1173. In the equation above, D is the initial diameter, \(\Delta\)D is the change in rod diameter (absolute value) at time t (hours), \(\varphi\) is the neutron flux (n/cm\({}^{2}\cdot\)s), \(\sigma_{\mathrm{0}}\) is the hoop stress (MPa), T is the temperature (K), and Q is the activation energy (cal/mole-K). The time factor is irrelevant in this particular context since the aim here is to assess how the test conditions (i.e., neutron flux, stress, and temperature) affect the diameter change rate. Applying Equation (1), one obtains the factors of 1.019, 1.096, and 1.047 for, respectively, the differences in neutron flux, hoop stress, and temperature between IFA-617 and IFA-663--the product of these factors being 1.17. This is the (rather small) scaling factor for the creep rates expected in the two tests. One should note that the absolute \(\Delta\)D rate as measured in the two IFA tests is, in the linear part, almost eight times larger in IFA-663 as compared with IFA-617.