## 4 Conclusions  
A new combined process based on sequentially applied DB and LTGN to optimally improve the fatigue strength of 304 steel has been developed. The new process achieves a fatigue limit of 600 MPa, an improvement of 36.4% compared to untreated specimens. The major new findings concerning the correlation \"new process-surface integrity-fatigue behavior\" are as follows:  
* The approach generates a synergistic effect, as the obtained fatigue limit (600 MPa) is greater than that achieved by DB (540 MPa for smoothing or 580 MPa for single-pass hardening processes) or LTGN (580 MPa) alone. The synergistic effect is the result of the superimposition of two consecutive effects--strain hardening via DB and transformation hardening via LTGN--as a result of the formation of new solid phases with an increased volume of the crystal lattice. It is advisable to use smoothing DB (instead of hardening) in combination with LTGN, as lower roughness height parameters are obtained. * As the degree of plastic deformation of the surface layer (introduced by DB) increases, the content of the S-phase in the nitrogen-rich layer formed by LTGN decreases, with  
Figure 15: Fracture surface of the fatigue specimen (stress amplitude of 610 MPa; number of cycles to failure: 78,200), treated by hardening DB + LTGN: (**a**) general view; (**b**) mechanism of formation and growth of main macro crack. a resultant increased content of the \(\varepsilon\)-phase and a new (also hard) phase: stabilized nitrogen-bearing martensite. * It was found that axial residual stresses introduced into external cylindrical surfaces by LTGN are 2.43 times smaller compared to the hoop stresses, whose absolute value reaches 6.6 GPa. This trend is opposite to the typical nature of the distribution of the two types of residual stresses after the static SCW method. * The application of a combined process, including DB and subsequent LTGN, results in a much greater depth of zone with compressive residual stresses and significant surface axial and hoop residual stresses compared to turning and LTGN. At the same time, the hoop surface residual stresses decrease at the expense of the axial ones. These trends are more pronounced with an increase in the degree of preliminary plastic deformation. * The two combined processes (smoothing DB and LTGN and single-pass hardening DB and LTGN) were found to achieve the same fatigue limit of 600 MPa, an improvement of 3.45% compared to the turning and LTGN processes. However, the two combined processes increase the fatigue life more than 178 times compared to the turning and LTGN processes. The main reason for this improvement is the reduced residual stress distribution gradient and deeper compression zone obtained by these processes. * The formation of a fatigue macrocrack for all three groups of samples (turning + polishing + LTGN, smoothing DB + LTGN and single-pass hardening DB + LTGN) in the high-cycle fatigue field takes place at the boundary between the nitrogen-rich layer and the bulk material, which determines the similar mechanism of destruction of the three samples. Conceptualization, J.M. and G.D.; methodology, [PERSON] and G.D.; software, [PERSON] and G.D.; validation, [PERSON] and G.D.; formal analysis, J.M., G.D. and Y.A. ; investigation, A.A., V.D., Y.A., G.D. and J.M. ; resources, J.M. and G.D.; data curation, J.M. and G.D.; writing--original draft preparation, J.M. and G.D.; writing--review and editing, J.M. and G.D.; visualization, J.M., G.D., A.A. and V.D. ; supervision, J.M. ; project administration, J.M. and G.D.; funding acquisition, J.M. and G.D. All authors have read and agreed to the published version of the manuscript. This research was funded by the European Regional Development Fund within the OP. \"Science and Education for Smart Growth 2014-2020\" and the Project CoC \"Smart Mechatronics, Economics and Energy Saving Systems and Technologies\", No. BG05M2 OP001-1.002-0023. Not applicable. Data Availability StatementData are contained within the article. The authors declare no conflicts of interest.