## 1 Introduction
Due to the development of plastic strains, crack growth occurred. On the other hand, plastic strains were induced by the action of gas on the crack banks. As follows from the numerical modeling, the gas movement occurred at a velocity between 100 and 300 m/s. In [PERSON] et al. [44], existing analytical methods for calculating pipeline fractures were reviewed. The results of these calculations were compared with the findings from some experimental analyses of pipeline fractures. In [PERSON] [45], a review of analytical methods for calculating the gas pipeline fracture under the action of gas pressure was implemented. Methods for stopping thedevelopment of main cracks along gas pipelines were proposed. [PERSON] et al. [46] illustrated the research experience of the European Research Group on the strength of gas pipelines. Approaches for the analysis of the resistance of the plastic fracture were described. Specifically, a plastic fracture model based on a numerical analysis of the stress state was generated. In [PERSON] et al. [47], finite-element calculations together with experimental studies were applied to model the crack development, in which the velocity of crack propagation and gas decompression, which were in turn obtained after calculations, were considered. Their findings demonstrated that, under certain conditions, the rate of crack propagation was lower than that of gas decompression, which means that the simulated gas pipe can stop cracking by itself. Vice versa, the effects of the geometrical parameters and pipeline matrix variables on the crack propagation rate were analyzed by [PERSON] et al. [48]. In recent years, as commercial gas is still the only acceptable energy source used worldwide, the relevance of this field has also attracted increased interest from scholars. Thus, in [PERSON] et al. [49], an extended finite-element study of X42 and X52 grade gas pipelines according to API 5L [25] was carried out, where the gas pipelines were subjected to internal pressure only. Defects in the form of corrosion with depths of 55% and 60% of the wall thickness were simulated to investigate the effect of cracking. Consequently, it was observed that for shorter cracks, the fracture pressure decreased with increasing the initial crack depth. In situ experimental studies of cracks and defect propagations were instead investigated by [PERSON] et al. [50] and [PERSON] et al. [51]. Besides, a method for stopping cracks along gas pipelines by changing the configuration (flattening of the pipeline wall) of the pipe cross-section when a crack is approaching was proposed by [PERSON] and [PERSON] [52]. Thus far, the main causes of crack formation along pipelines were examined by [PERSON] et al. [53], [PERSON] et al. [54], [PERSON] et al. [55], [PERSON] et al. [56], and [PERSON] et al. [57]. Considering the aforementioned literature review, the task aimed at studying crack propagation in large-diameter gas pipelines requires further research since cost-effective and technically suitable methods for fracture localization were not proposed. In this regard, at this stage of the study, the main purpose of the work was to analyze the stress-strain state of the pipe section, taking into account the failures with an incipient crack and the failures in the crack tip zone on the example of the \"Beineu-Bozoy-Shymkent\" main gas pipeline [58]. In the future, it will give ideas about the mechanics of crack propagation formed on the surface of manistral gas pipelines. As a result, this will provide an initial understanding for the further application of the prestressing method for the localization of longitudinal propagation in gas pipelines, previously substantiated in the published works of the authors [59; 60; 61; 62; 63; 64]. Indeed, there is a need to study the issue of steel gas pipeline failures with further development of a method for their prevention, which is very actual at the national scale, as today the wear of gas pipelines in the Republic of Kazakhstan is more than 70% [65].