At the end of August, researchers S.I. Golubov, A.V. Barashev and R.E. Stoller delivered to CASL an analysis of the effect of grain size on the radiation growth of multigrain, hexagonal close-packed (hcp) metals, taking into account the features of cascade damage due to neutron exposure. Irradiation growth occurs in zirconium-based alloys used for LWR fuel cladding. Experimental data suggests that irradiation growth deformation takes place via dislocation climb, formation of prismatic interstitial (and occasionally vacancy) dislocation loops, and vacancy loops on the basal planes.
In 2011, the ORNL-based team established a reaction-diffusion model for prediction of irradiation growth at an atomistic level, accounting for intra-cascade clustering of self-interstitial atoms (SIAs) with one-dimensional diffusion. The earlier model was useful in predicting the maximum possible strain rates due to irradiation growth, and provided insights into observations such as negative strain in the prismatic direction, co-existence of vacancy- and SIA-type prismatic loops, alignment of vacancy-type loops and voids along the basal planes, and also shed light on the role of cold work in radiation growth behavior. Building upon previously established models, the team has included considerations for polycrystalline materials and the absorption of mobile defects by grain boundaries. The work illustrates the relationship between grain shape, grain size, dislocation density, and radiation growth through demonstrations of three types of grains: a spherical grain, an elongated grain, and a flat grain.
In a general case, the sink strength of grain boundaries oriented in x, y and z directions can be approximated as:
kg is the grain boundary sink strength,
Rg is the grain radius,
ρ is the total dislocation density, and
εgi is SIA fraction clustered in cascades.
In the case of a spherical grain, Rgx=Rgy=Rgz=Rg, and the strain equations are given by:
As illustrated in Figure 8a, strain increases as grain size decreases. Thus, if the grain size is large enough, the radiation growth induced strain is the same as that for a single crystal. For low dislocation density, the effect of grain boundaries is visible at a grain radius of ~6 mm. When there is a high density of dislocations the effect is important at grain radii of ~1mm. In the case of very small grains (ρx,y,zRg2«5), the strain rates can reach quite large values on the order of 5x10-3 dpa-1 independent of the magnitude of dislocation densities.
For the case where the grains are elongated such that Rgx« Rgy, Rgz:
As illustrated in Figure 8b, for the non-basal elongated case, the strain rate in the prismatic direction reaches a maximum value of χ/2, which is about 10-2/dpa, negative in the x-direction and positive in y, whereas it is practically zero in the basal direction.
The situation is quite different in the case when a grain is elongated in a way that it has a small size in the basal direction, i.e. that Rgz« Rgx, Rgy:
In this case the strain rates in the prismatic directions also reach the maximum value of χ/2; however, both of them are positive. In addition, the strain rate in the basal direction is also reaches the maximum negative value of χ. The results of this case are illustrated in Figure 8c.
Figure 8 Calculated strain rates for various postulated grain aspect ratios for uniform distribution of prismatic dislocations (ρ) and ε=0.02. (a) spherical; (b) elongated in one prismatic direction; (c) elongated in both prismatic directions; (d) elongated in the basal direction.
Finally, the case where the grains are very flat (Rgx = Rgy = Ro << Rgz):