**6. Conclusions**

A user material (UMAT) subroutine is updated to include the strain-gradient effects. Two different methods are used for determining GND densities. The performance of the two methods for simulating the formation of slip bands in a deformed α-zirconium specimen is investigated. Numerical results are compared with those measured with HR-EBSD. It is shown that:


The formation of the slip bands can also be simulated using higher-order straingradient crystal plasticity models. The incorporation of higher order terms to the CPFE model is in the scope of our future studies.

**Author Contributions:** Conceptualization, O.S. and H.A.; methodology, O.S. and H.A; formal analysis and investigation, O.S and H.A.; writing—original draft preparation, O.S.; writing—review and editing, H.A.; supervision, H.A.; funding acquisition, H.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by a Discovery Grant (#RGPIN/04969-2017) from the Natural Sciences and Engineering Research Council of Canada (NSERC).

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

