## 4 Conclusions  
This research presented a thorough investigation into the heating and hardening mechanisms of low-carbon cast 20 GL steel subjected to electrolytic plasma treatment. Utilizing numerical modeling and experimental temperature field analysis, the study demonstrated that even brief exposure durations could induce substantial temperatures at depths of up to several millimeters, facilitating thermal modification of the microstructure and enhancing microhardness.  
Figure 11: Microstructure of 20 GL steel: (**a**) initial structure; (**b**) at U = 150 V; (**c**) at U = 200 V; (**d**) at U = 250 V.  
A comparison between the numerical calculation results and experimental thermometry data indicated a strong correlation at 150 and 200 V. Discrepancies observed at 250 V can be attributed to a reduction in the quality of the thermocouple's thermal contact at temperatures exceeding 900 \({}^{\circ}\)C.  
The analysis of microhardness distribution as a function of depth revealed a distinct correlation between hardening and localized thermal effects. The peak hardness values are observed in regions where austenitization conditions and rapid cooling rates coincide. The study determined that achieving effective hardening in 20 GL cast steel necessitates cooling rates exceeding the critical threshold of approximately 50 \({}^{\circ}\)C/s. When rates are below this level, even upon reaching austenitization temperatures, the extent of hardening is limited, which is related to the inherent reduced hardenability of cast low-carbon steels.  
Microstructural analysis confirmed the formation of martensite and bainite in the surface layers of samples processed at 200 V and 250 V, indicating the presence of high-speed quenching conditions. This demonstrates the high efficiency of EPH as a method for locally strengthening difficult-to-quench cast steels under intensive cooling conditions.  
This investigation served as an initial examination of thermal phenomena during electrolytic plasma hardening for low-carbon 20 GL steel, offering an initial quantitative evaluation of heat flows, heating and cooling rates, and heating depth under varying processing conditions. Future research will involve more detailed structural analyses utilizing scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and phase analysis techniques. These future investigations aim to elucidate transformation mechanisms and formulate technological recommendations for employing EPH to enhance the wear resistance and extend the service life of cast steels in practical production environments.  
Conceptualization, B.R., R.K. ([PERSON]), Y.S. and R.K. ([PERSON]); methodology, B.R., R.K. ([PERSON]), A.M. and R.K. ([PERSON]); software, R.K. ([PERSON]) and A.M.; formal analysis, B.R. and A.M.; investigation, R.K. ([PERSON]), A.M. and N.K.; data curation, R.K. ([PERSON]) and N.K.; resources, R.K. ([PERSON]), Y.S. and R.K. ([PERSON]); supervision, B.R. and Y.S.; funding acquisition, Y.S.; writing--original draft preparation, R.K. ([PERSON]), A.M. and N.K.; writing--review and editing Y.S. and R.K. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, within the framework of the grant project AP19680287, \"Increasing the durability of steel parts of a freight car trolley by local electrolyte-plasma hardening\", in collaboration with Plasma Science LLP, Ust-Kamenogorsk, Kazakhstan.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Authors [PERSON] and [PERSON] were employed by the company Plasma Science LLP. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.