## 4 Conclusions  
In this work, studies were carried out on the dynamic deformation and fracture of thin-walled sections of steel gas pipelines with an external crack-like defect under the action of internal decreasing pressure. The research was performed on the basis of finite-element simulations using a cylindrical shell model executed by ANSYS-19.2 on the example of the thin-walled section of the gas pipeline \"Beineu-Bozoy-Shymkent\" in the Republic of Kazakhstan. The corresponding results showed that the operating pressure increment from the working to the critical one has a significant effect on crack propagation. Consequently, at the stage of modeling the displacements in conditions of working pressure, it was established that, within the time \(t=1.0\) ms, the crack expanded in the circumferential direction for 0.036 m. Further displacements occurred in the longitudinal direction, and the crack increased by 5.6 times. The maximum equivalent stresses were reached at time \(t=3.5\) ms, and with a value equal to 453 MPa. They increased 1.53 times with respect to their initial value. Within the time \(t=3.75\) ms, the growth of the equivalent stresses stopped due to gas decompression. At maximum pressure, similar results were qualitatively obtained. At that, the increment of the pressure from the operating (7.5 MPa) to the critical one (9.8 MPa) led to an increment of the crack length in the longitudinal direction by 0.3 times. The results of the stress-strain state and gas pipeline fracture in the tip zone at the operating pressure demonstrated that the distance between the crack walls reached 23 mm at the free edge within the time \(t=1.0\) ms. Conversely, within the times \(t=2.25\) ms and \(t=3.5\) ms, there were increments of two and three times respectively. The crack elongation in the longitudinal direction over time was instead equal to 5.8 times. In this case, within the time \(t=3.5\) ms, the equivalent stresses increased twice and, after that, the crack growth stopped due to gas decompression. Considerations on the crack growth in its tip area at the maximum pressure also showed that additional evaluations on the crack edge pressure resulted in an increment of 3.6% of the crack length value. The results were obtained for a temperature equal to +22 \({}^{\circ}\)C. The aforementioned developed models can be used for research on the dynamic deformation and fracture of steel gas pipelines subjected to temperatures ranging from \(-40\)\({}^{\circ}\)C up to +50 \({}^{\circ}\)C.  
**Author Contributions:** Conceptualization, N.Z., B.U. and U.I.; methodology, N.Z., U.I., M.B. and M.C.; investigation, N.Z.; data curation, N.Z., U.S., K.A. and U.I.; writing--original draft preparation, N.Z., U.I., M.C. and K.A.; writing--review and editing, N.Z. and U.I.; supervision, N.Z., M.B., A.U. and U.S.; project administration, N.Z., A.U., B.U. and M.C.; funding acquisition, N.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP19680589).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Acknowledgments:** The authors would like to thank the A. Pidhornyi Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine and the National Science and Technology Council (NSTC) of Taiwan for providing advisory assistance to this work.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.