**1. Introduction**

Ultra-thin grain-oriented silicon steel (UTGO steel, thickness ≤ 0.10 mm) is an important magnetic material mainly used for manufacturing intermediate and high-frequency transformers [1–4], thanks to its ability to increase core power while reducing core loss and volume. Although the manufacturing route for grain-oriented silicon steel has been developed for decades, it is still difficult to produce ultra-thin products using a conventional process which is based on secondary recrystallization. The difficulty is due to acceleration of the inhibitor coarsening during recrystallization and poor control over Goss orientation under large rolling reduction [5–9]. At present, the most prevalent production method to prepare ultra-thin grain-oriented silicon steel is to use commercial grain-oriented silicon steel sheets as starting material, then cold-rolling the steel sheets to the desired thickness followed by annealing processes [4,10,11].

In recent years, many studies have reported the formation of deformation twinning in silicon steel. Shi et al. [12] and Xie et al. [13] discovered that deformation twinning occurred in Fe-6.5% Si alloy in a medium temperature tensile and compress test, and that this twinning promoted the plastic deformation of the alloy. Dunn et al. [14] demonstrated that both slip and twinning were activated during cold rolling in Fe-3.25 wt.% Si alloy, and {001}<110> oriented twins could be formed in Goss single crystal at an early deformation stage. Rusakov et al. [15] studied the features of twinning in cold-deformed Goss single crystal in an Fe-3% Si-0.5% Cu alloy and found that twins with near {001}<110> orientation were formed at 5% reduction and the twinning orientation did not change during the subsequent deformation. Dorner et al. [16] reported that the area fraction of {001}<110> oriented

**Citation:** Zhang, B.; Meng, L.; Ma, G.; Zhang, N.; Li, G.; Liu, K.; Zhong, S. Twinning Behavior in Cold-Rolling Ultra-Thin Grain-Oriented Silicon Steel. *Crystals* **2021**, *11*, 187. https://doi.org/10.3390/cryst11020187

Academic Editors: Ronald W. Armstrong and Wojciech Polkowski Received: 22 January 2021 Accepted: 12 February 2021 Published: 14 February 2021

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twins increased with an increase of deformation reduction and reached the maximum at 61% deformation reduction when studying the evolutions of crystallographic orientations of cold-rolled Goss single crystals in Fe-3% Si alloy. Even with extensive studies, there are still disputes on how the twins in BCC structured grain-oriented silicon steels are formed and evolved during cold rolling.

It is known that deformation twinning has a pronounced grain orientation dependence in FCC [17–19] and HCP [20,21] metals or alloys, and similar effects of initial grain orientation on deformation twinning are also reported in BCC structure [22,23]. Fu et al. [22] found that twins tend to occur in grains with a tensile orientation near the <001> corner and a compressive orientation near the <101>-<111> line, and this twinning activation is closely related to their corresponding Schmid factor, respectively. In the production of ultra-thin grain-oriented silicon steel, it is preferred that the starting material has a strong Goss texture, so that grains with exact Goss in a certain extent in the resultant UTGO steel will occupy the great majority of area. The deviation of grain orientation from the exact Goss will affect the subsequent orientation transition routes [23]. However, the effect of deviation degree on the twinning behavior remains unclear. In this study, the twinning behaviors during cold rolling ultra-thin grain-oriented silicon steel have been systematically analyzed, and special attention has been focused on the influence of initial Goss orientation deviation on the twinning behavior. The results will help to comprehensively understand the cold rolling process and to provide a theoretical basis for preparing ultra-thin grain-oriented silicon steel.
