## 1 Introduction  
Austenitic stainless steels (SS) are the most important class of SS in terms of relative share and application, accounting for 70% of the world's production of all types of SS. The present study focuses on AISI 304 chromium-nickel austenitic SS, which is used in many industrial areas as a structural component due to its high corrosion resistance, formability, machinability by cutting, and weldability. In addition, this steel is among the cheapest grades of austenitic SS, making it a favourite choice in industry. In the equilibrium state at room temperature, the structure of chromium-nickel austenitic SS consists of a primary austenitic matrix, secondary segregated carbides, and small amounts of \(\alpha\)-phase. The carbide phase is complex and contains (Cr,Fe)23C6 crystals [1]. Furthermore, the segregation of carbides from the austenite deteriorates the corrosion resistance of austenitic SS [2]. The influence of the \(\alpha\)-phase on the corrosion resistance depends on the nature of the aggressive environment. For example, the interaction between nitric acid and the \(\alpha\)-phase does not lower the chemical resistance of 304 SS, whereas interaction with sulphuric acid can deteriorate corrosion resistance. As the temperature increases, polymorphic conversion and dissolution of the carbide phase occur, transforming the \(\alpha\)-phase into the \(\gamma\)-phase. After quenching in water at 1050-1150 \({}^{\circ}\)C, a saturated solid solution of homogeneous austenite crystals becomes fixed [1]. As a general guideline, it is recommended to avoid the temperature range of 480-900 \({}^{\circ}\)C during heat treatment of austenitic SSs due to the risk of inter-crystalline corrosion [2]. The main disadvantages of chromium-nickel austenitic SSs, which can limit their application, are the low surface micro-hardness, which leads to low wear resistance; relatively low strength, including fatigue strength; and their propensity to incur inter-crystalline corrosion in the temperature range of 500-700 \({}^{\circ}\)C due to the release of chromium carbides at the boundaries of the austenitic grains. Notably, an effective means of improving the surface integrity (SI) of this steel is the so-called low-temperature surface treatment, which is performed with nitrogen- and carbon-containing media at temperatures below 500 \({}^{\circ}\)C, in which the mobility of chromium is low and the formation of precipitates is hindered. As a result, the wear resistance and fatigue strength significantly increase [3]. Besides changing the chemical composition of the surface layers, chromium-nickel austenitic SS can be processed to maximise the surface micro-hardness and strength, including fatigue strength, by surface cold working (SCW), especially when the nickel content is limited to 8-9 wt%. SCW is an effective approach for modifying the surface layer by inducing surface plastic deformation (SPD), during which the chemical composition does not change. SPD can contribute to significant improvements in SI, in addition to increased micro-hardness; significant residual compressive stresses, which reduce roughness; and a finer microstructure. At a higher degree of plastic deformation, the metastable austenite undergoes martensitic transformation. The strain-induced \(\alpha^{\prime}-\)martensitic phase possesses greater hardness and strength, but has a weaker the corrosion resistance. There are two types of SCW methods: dynamic and static. The advantage of dynamic methods, such as shot peening, laser peening, water cavitation peening, and surface mechanical attrition treatment (SMAT), is the ability to process complex surfaces. Chronologically, the dynamic methods predate the static methods. In 1871, [PERSON] developed the sandblast method, which is the predecessor of shot peening [4]. The static methods, known as burnishing methods, are suitable for processing rotating surfaces. One of the first patents for a static method was published in 1916 [5].