Thermal creep in the fuel is usually described by an empirical relation­ship of the form

sth = Aone B/T,

where a is the stress, є is the strain, T is temperature and A, B and n are constants. Usually n = 1, B is about 4 x 104 K, and typical results for stoichiometric UO2 (x = 0) give A — 2 x 10-4 s-1 Pa-1. If the fuel is not stoichiometric it is harder, whereas mixed oxide is usually found to be softer.

The resulting relaxation time for thermal stress is shown in Figure 2.11. It is very short in the centre of the fuel, and over times of the order of seconds or more this part of the fuel can support only hydrostatic pressure. The outer part of the fuel on the other hand is quite rigid.

A second source of creep strain is due to the irradiation itself. The effect of a fission event is to melt the small volume of the fuel through which the fission fragments travel. Any shear stress in the melted region is transferred to the surrounding material causing it to strain a little. Then another fission event melts another region causing another additional strain, and so on. The result is a steady strain — rate proportional to stress and fission-rate density but only weakly dependent on temperature. Various experimental correlations have been proposed, typically of the form

Є f = A1 fa (2.7)

with A1 ~ 1.8 x 10-36 m3 Pa-1 ■ f is the fission-rate density in m-3 s-1, so with a in Pa equation 2.7 gives є in s-1.

The effect of irradiation creep is also shown in Figure 2.11. The relaxation time in the outer part of the fuel is substantially reduced but it is still hard on a timescale of days or weeks.

It is of course impossible to observe what happens to the fuel during irradiation but it is probably more or less as follows. After the fuel has swollen to touch the cladding the cladding exerts a compressive normal stress on its surface. The resulting stress distribution is shown in Figure 2.12. The fuel is incapable of exerting hoop stress in the central region, which is soft and stress-free because it is in contact with the central void. It is also incapable of exerting hoop stress at the outer edge where there are radial cracks. Thus the compressive surface stress is borne by a compressive hoop stress in a narrow ring of fuel just at the root of the cracks.

In steady operation the load-bearing ring moves slowly outwards as more of the fuel has time to relax the imposed stress and allow the cracks to close. But if there are changes in reactor power and therefore in the fuel temperature distribution the development is interrupted.

If the power rises, for example, the cracks reopen to some extent and the load-bearing ring is moved inwards.