Effect of grain-structure topology in modelling aggregate irradiation creep behaviour of two-phase alloys

The two-phase alloy Zr–2.5Nb, a high-strength alloy for nuclear applications, has a grain structure in which the hcp α-phase is surrounded by the bcc β-phase. A satisfactory method for the macroscopic overall properties of this type of materials has yet to be developed. Based on the small volume fraction of the β-phase, some existent models of polycrystalline aggregates of Zr–2.5Nb argued to completely ignore the presence of the β-phase, and hope that errors cancel by fitting to experimental data. This may not introduce significant errors if the β-phase is randomly distributed, and if the deformation mechanisms are not an important part of the investigation. However, for highly correlated distributions of the two phases, the dependence of the overall polycrystalline properties in the topology of the distribution of the β-phase is intuitively feasible, or at least, the contrary has not been established. In this paper, we are interested in ascertaining the effect, if any, of the grain structure topology on the irradiation-induced deformation of this type of alloys. We compare the behaviours of three model polycrystalline aggregates with topologically different grain structures, one made up of “grains” in which the α-phase is embedded periodically in a β-phase, and another in which the β-phase is embedded periodically in the α-phase, and the third in which the β-phase is neglected. All have the same texture, and the first two have the same α:β volume ratio, and therefore cannot be distinguished within the existent models. The double interaction method (DIM) is introduced for the treatment of this type of quasi-periodic textured polycrystalline aggregates. In this method, the overall properties of the constituent grains with a periodic structure, are first calculated. The interaction direction derivation (IDD) method is used to consider the interactions among the “intra-granular” periodic elements. The overall properties of the textured polycrystalline aggregate can then be calculated, by considering the inter-granular interaction using the usual self-consistent method (SCM). It is found that, the β-phase may not be neglected in the usual self-consistent model treatment, unless the magnitudes of the creep compliances of the two phases are not very different.