Almost every fission event turns one atom (of uranium or plutonium) into two (of fission products). Some of these are gaseous or volatile (see section 2.3.5) and are mostly lost from the fuel, but the majority are solid and are retained either as interstitial atoms in the crystals or as inclusions of a distinct solid phase. Some of the gaseous fission products are retained as small bubbles within the crystals or on the grain boundaries.

Very roughly all atoms occupy about the same volume (of the order of 10-29 m3) in solid and liquid phases so the increase in the number of atoms means that the volume increases. Loss of some fission products from the fuel tends to mitigate the increase, but on the other hand retention of bubbles of gaseous fission products tends to enhance it. The net result is a fractional increase in the volume of the solid fuel of about 0.8 times the burnup.

This swelling is almost inexorable and if the fuel fits closely inside the cladding when it is new the cladding is forced to strain to accom­modate it. Thus for example 10% burnup would imply about 3% normal strain in the cladding in both the circumferential and (because friction between fuel and cladding does not allow relative motion) axial directions. As pointed out in section 3.3.4 the ductility of the irradiated cladding may be too low to accommodate so large a strain. Since the primary purpose of the cladding is to retain the radioactive fission products, if more than a very few fuel elements crack because of the swelling of the fuel inside them the design is unacceptable. The burnup has to be limited by design to a value at which trial irradiation has shown that no more than an acceptable number of cladding failures will occur.

It is usual to allow for the effects of fuel swelling by leaving space for the fuel to swell without straining the cladding. In some cases this has been done by manufacturing the fuel in the form of pellets with a central hole so that the increase in volume can be accommodated by filling or partially filling the hole. Alternatively and more usually the fuel is manufactured as porous pellets, the pores occupying some 10-20% of the overall volume, and the swelling is accommodated by filling the pores.

It is by no means certain, however, that either pores or a cent­ral void work in the manner intended to accommodate swelling. As explained in section 2.4.1 pores migrate during operation and a central void is often formed even when one is not present initially. In addition the fuel creeps (see section 2.4.3) so that there is a tendency for stress between fuel and cladding to be relieved by strain of the fuel as well as of the cladding, and irradiation-induced reduction of the density of the cladding (section 3.3.2) also helps to accommodate fuel swelling. In fact the picture is so confused that, although the strain of the clad­ding of an irradiated fuel element can be measured, it is not easy to predict.

A convenient parameter often used to characterise the space avail­able to accommodate the swelling of the fuel is the “smear density”. It is often defined as the ratio between the mass of fuel per unit length of the fuel element as manufactured and the mass of fuel it would contain if the cladding were completely filled with fuel at its maximum theoretical density (i. e. if there were no gap between the pellets and the cladding, and no porosity or central hole in the pellets). Oxide fuel elements are typically manufactured with 80% smear density.

Sometimes the term is used slightly differently, being defined as the average density the fuel would have if it were spread uniformly across the cross-section of the fuel element. Thus if the theoretical density of UO2 is 11000 kgm-3, a fuel element with 80% smear density according to the definition in the previous paragraph might alternatively be said to have a smear density of 8800 kgm-3.