## Appendix B Zircaloy-2 Constitutive Model  
The phenomenological model for the Zircaloy-2 alpha phase along with Zirconium hydrides was adopted from [49]. Herein, the primary slip system families considered are the basal \(\langle 11\bar{2}0\rangle\{0001\}\) systems (three variants), prismatic \(\langle 11\bar{2}0\rangle\{10\bar{1}0\}\) systems (three variants), and first-order pyramidal \(\big{<}c+a\big{>}\langle 11\bar{2}0\rangle\{11\bar{2}3\}\) systems (twelve variants). Twinning, for which this model is calibrated, is not commonly observed at room temperature, and is neglected. However, the slip resistance on the three HCP slip system families is noticeably different, leading to a rather anisotropic plastic response. This disparity is accounted for by using different material parameters for each family denoted by superscript \((A)\) while having the same slip relation for all systems denoted by superscript \((\alpha)\). The power-law slip rate equation takes a similar form to the one in the preceding section, i.e.,  
\[\dot{\gamma}^{(a)}=\dot{\gamma}^{(A)}_{0}\left|\frac{\tau^{(a)}}{\xi^{(a)}} \right|^{1/m^{(A)}}\text{sign}\Big{(}\tau^{(\alpha)}\Big{)}. \tag{10}\]  
While the reference strain rate \(\dot{\gamma}^{(A)}_{0}\) is again a constant, the drag stress \(\xi^{(\alpha)}\) evolves from an initial slip resistance value \(\xi_{0}{}^{(A)}\) by a different formula:  
\[\xi^{(\alpha)}=\sum_{\beta=1}^{n_{\text{slip}}}h^{(\alpha\beta)}\big{|}\dot{ \gamma}^{(\beta)}\big{|}=\sum_{\beta=1}^{n_{\text{slip}}}h^{(\beta)}\big{|} \dot{\gamma}^{(\beta)}\big{|}, \tag{11}\]  
where the self-hardening rate \(h^{(\alpha)}\) again evolves by a Vocc relation and the target saturation stress \(\xi^{(\alpha)}_{\text{s}}\) is a function of the applied strain rate:  
\[h^{(\alpha)}=h^{(A)}_{0}\left|1-\frac{\xi^{(\alpha)}}{\xi^{(\alpha)}_{\text{s }}}\right|^{r^{(A)}}\text{sign}\Bigg{(}1-\frac{\xi^{(\alpha)}}{\xi^{(\alpha)}_ {\text{s}}}\Bigg{)}, \tag{12}\]  
\[\xi^{(\alpha)}_{\text{s}}=\xi^{(A)}\Bigg{(}\frac{\dot{\gamma}^{(\alpha)}}{ \dot{\gamma}^{(A)}_{0}}\Bigg{)}^{n^{(A)}}, \tag{13}\]  
with the additional parameters \(h^{(A)}_{0}\) representing the initial hardening rate, \(\xi^{(\alpha)}_{\text{s}}\) the current saturation resistance of shear deformation, and \(\xi^{(A)}\) a scaling prefactor. Additional information on the implementation of the model and the treatment of slow strain rates can be found in [46]. The calibrated parameters for the Zircaloy-2 alpha phase are provided in Table 10, along with the six transversely-isotropic material moduli.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Property** & **Value** & **Units** \\ \hline \(C_{11}\) & 143,500 & MPa \\ \(C_{33}\) & 164,900 & MPa \\ \(C_{12}\) & 72,500 & MPa \\ \(C_{13}\) & 65,400 & MPa \\ \(C_{44}\) & 32,100 & MPa \\ \(C_{55}\) & 4200 & MPa \\ \(h_{0}\) (bas.) & \(-50.0\) & MPa \\ \(h_{0}\) (pri.) & \(-51.9125\) & MPa \\ \(h_{0}\) (pyr.) & \(-155.7375\) & MPa \\ \(\xi_{0}\) (bas.) & 58.0 & MPa \\ \(\xi_{0}\) (pri.) & 178.0 & MPa \\ \(\xi_{0}\) (pyr.) & 165.0 & MPa \\ \(\xi^{(\alpha)}\) (bas.) & 42.0 & MPa \\ \(\xi^{(\alpha)}\) (pri.) & 42.0 & MPa \\ \(\xi^{(\alpha)}\)(pyr.) & 42.0 & MPa \\ \(\dot{\gamma}_{0}\)(bas.) & \(3.5\times 10^{-4}\) & s\({}^{-1}\) \\ \(\dot{\gamma}_{0}\)(pri.) & \(3.5\times 10^{-4}\) & s\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 10: Zircaloy-2 alpha phase constitutive model parameters.  
The secondary hydride phase is modeled as an isotropic yet stronger elastoplastic material using a traditional J2 plasticity model with the tabulated yield stress provided in Table 10. As shown in a previous study [49], the initial yield stress of hydrides is about twice the average initial flow resistance of the alpha phase; as a result, stress concentrations are expected along phase boundaries, which is studied in the following numerical examples. It is important to note that lower levels of macroscale strain were applied during the simulations in this study, such that the local damage criterion from [49] is not activated.