**4. Conclusions**

In this work, the failure mechanism of symmetrical grain boundaries (GB) under external strain effects in body-centered cubic (bcc) iron are investigated via the molecular dynamics (MD) method. The local atomic structure evolution, energy state change, atomic displacements and free volumes were calculated for the above purpose. The following conclusions have been made:

(1) Full MD relaxations at high temperatures are necessary to obtain the lower energy states of GBs for further simulations under external strain.

(2) Two mechanisms are explored for the failure of symmetrical GBs under the external strain effect, including slip system activation, dislocation nucleation and dislocation network formation initially from the GB plane region induced by the external strain field or from the bcc-fcc phase interface induced by phase transformation under external strain effects.

(3) The change in free volume near the GB plane or bcc-fcc interface is not only related to the local structure change in the above two mechanisms, but can also lead to increases in the local stress concentration, providing a new explanation for the failure of GBs in BCC iron system.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/met12091448/s1, Figure S1: Schematic of grain boundary simulation model used in the present work. For stress-strain simulations, the external tensile strain field is applied on top and bottom surface of box, Figure S2: Atomic potential energy (**a**) and displacement distribution (**b**) of ∑3(112) GB at state with peak stress, Figure S3: Example of FCC lattice structure in fcc phase after phase transition, Figure S4: Snapshots (y-z plane) shows ∑ = 5(013) undergoes phase transition and green atom is fcc struc-ture blue atom is bcc. Then the GB happens to crack at 31 ps, region a, b and c are most obvious, Figure S5: Atomic potential energy (**a**) and displacement distribution (**b**) of ∑5(013) GB at state with peak stress, Figure S6: (**a**) The structure of ∑5(012) when slip system is activated with strain around 8%. The potential energy(b), stress(c) and atomic displacement distribution(d) at this state are shown respectively. Figure S7: (**a**) The structure of ∑3(111) when slip system is activated with strain around 14%. The potential energy, stress and atomic displacement distribution at this state are shown in (**b**), (**c**) and (**d**) respectively, Figure S8: Distribution of free volume near ∑3(111) GB region at (**a**) 0 ps and (**b**) at 28 ps (strain around 14%), Table S1: The peak tensile stresses of all cases studied in this work are listed in table.

**Author Contributions:** Conceptualization, N.G.; methodology, W.M. and N.G.; software, W.M.; validation, W.M.; formal analysis, W.M.; investigation, W.M.; resources, N.G.; data curation, W.M.; writing—original draft preparation, W.M.; writing—review and editing, Y.D., M.Y., Z.W., Y.L., N.G., L.D. and X.W.; visualization, W.M.; supervision, N.G.; project administration, N.G.; funding acquisition, N.G., X.W. and Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number (Project Nos. 12075141, 12175125 and 12105159).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are contained within the article.

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

#### **References**

