Figure 4.61 gives schematic growth curves for Zircaloy illustrating several points. Note that L-textured (longitudinal, or in the original rolling direction) material grows, while T-textured (transverse to the rolling direction) mate­rial shrinks; when taking into account shrinkage of a component in the third direction (N, normal to the rolling direction), this behaviour results in approx­imately constant volume. The long direction (L) of a component is the most important: for instance the length of a fuel rod, channel box or GT. Note that cold worked (CW or SRA) material grows at a high and almost linear rate, while recrystallized (RXA) material grows in a 3-stage process, with the final high rate being called ‘breakaway’ growth. The various stages can be directly correlated to the irradiation-produced microstructure described earlier. For RXA Zircaloy, at low fluences where only <a> component loops exist, growth is small (~0.1%) and saturates. When <c> component loops begin to appear the growth rate increases and becomes nearly linear with fluence in the range 6-10 x 1025 n/m2, E >1 MeV. For L-texture material growth can reach 1% at 20 x 1025 n/m2. In initially cold worked (CW) or stress relieved material (SRA), <c> component dislocations occur as part of the deformation-induced struc­ture and more are formed during irradiation (Holt et al, 1996). The growth

rate is nearly linear with fluence and the magnitude is almost linear with the amount of initial CW. In heavily-worked material (typically 70-80% in a fuel rod) a growth of 2% can be reached by 20 x 1025 n/m2 (corresponding to a burnup of about 100 MWd/kgU). Figure 4.62 gives some values of irradia­tion growth for Zircaloy materials of different heat treatments, reflecting the amount of residual CW and dislocation density. An overview of factors affect­ing growth is given by Fidleris et al. (1987).

Texture

It can be argued (Hesketh et al, 1969; Alexander et al, 1977) that the magni­tude of growth strain in any given direction of a polycrystalline material can be related to the crystallographic texture and is proportional to a growth anisotropy factor Gd, given by

G=l-3fc, [4.1]

where fd is the resolved fraction of basal poles, fc, in the d-direction. The anisotropy factor depends on the assumptions that each grain behaves as an independent single crystal and that the volume change due to irradiation growth is zero.

At high burnup and high temperature (greater than about 360°C, 633K) and perhaps also in a heavily cold worked material, the familiar (1-3f) and

constant volume assumptions may not be valid. At low fluence the two assumptions are reasonable, but at high fluence the transverse strain is not zero (as would be predicted by the fx value) and the sum of the strains is strongly positive. It is also noted that cold worked material and recrystal­lized material have similar growth behaviour at high temperatures. It is fur­ther noted that the temperature of this irradiation is at the upper range (>378°C) expected for even a hot PWR.

For the high temperature data presented in Fig. 4.64, STEM studies revealed grain boundary cavities and occasional IG voids (Tucker et al. ,1984) which may explain the observed change of volume. Other studies have not reported cavities or voids at very high fluence at 290°C (363K) (Mahmood et al, 2000) or high fluence at 350°C (623K). Holt & Causey (2004) reported that for Zr-2.5Nb there is a small volume increase (0.05-0.1%) at low flu — ence, but at high fluence the volume change was close to zero.