**1. Introduction**

Austenitic stainless steels, such as AISI 304 and AISI 316L, have wide usage in various types of parts, mechanisms and constructions in many different industries. For instance, they have wide application in chemical and food industries, pharmaceuticals, medicine, and automotive, aircraft, and maritime industries, etc. The parts used in these industrial and life care fields are subjected to many strict requirements, such as high corrosion and wear resistance, surface hardness and mechanical strength, and must have high integrity contact surfaces with little roughness asperity, etc., in order to achieve the intended operational characteristics. Often, the operational conditions of their work include cyclic loads, which could lead to fatigue failures, resulting in significant shortening of their operational lifetime. While in some cases machine parts destroyed due to fatigue from mechanical devices are relatively easy and not too costly to replace, in other cases, such as orthopedic prostheses [1], this is not an easy and simple task. Therefore, the fatigue durability of such prostheses is of great importance for the patient. Destruction of mechanical parts due to fatigue or wear, for example, when food processing machines are used, can lead to small particles (debris) getting into the food, thus endangering the health and even the lives of consumers. Even an auxiliary part's fatigue failure can cause severe operational issues, violation of the whole mechanism or even destruction of the entire device or machine.

There are many approaches developed over the years in order to minimize fatigue failures. They can be divided into two large areas: the first one is related to the design

**Citation:** Slavov, S.; Dimitrov, D.; Konsulova-Bakalova, M.; Vasileva, D. Impact of Ball Burnished Regular Reliefs on Fatigue Life of AISI 304 and 316L Austenitic Stainless Steels. *Materials* **2021**, *14*, 2529. https:// doi.org/10.3390/ma14102529

Academic Editors: Gilles Dessein, Stanislaw Legutko and J. Antonio Travieso-Rodriguez

Received: 5 April 2021 Accepted: 8 May 2021 Published: 13 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of the machine parts, and the second is related to the development of specific finishing processing technologies, which have led to improvement of fatigue strength.

Among the design approaches the most notable is "Infinite-life design" [2] which keeps all stresses below the limits of fatigue effects. This approach is used where safety and/or long life are more important than space and weight limitations. "Safe-life design" [3] allows fatigue cracks to occur during the operational period, but they never grow to a critical length. Some structures subjected to high stresses, such as aircraft wings and hulls, pressure vessels, and heavy duty bearings, employ this type of design. The designed "safe life" usually is about one-fourth of the predicted fatigue life. "Fail-safe design" allows cracks to occur, but they never lead to fatigue failure earlier than the scheduled maintenance. The maintenance process must detect, repair, or replace the damaged parts. This approach is employed mainly in the aircraft industry since the weight requirements are crucial and there are strict regulations for maintenance in comparison with other industries. "Damage-tolerant design" [4] includes fracture mechanics and takes into account the initial imperfections in the material structure. The approach is based on the assumption that imperfections (flaws, cracks, etc.) can exist in any structure, and these cracks propagate (and grow) during the usage period. This approach is commonly used in civil engineering, mechanical engineering, and aircraft engineering to manage the extension of cracks in structures by using the principles of fracture mechanics. In this approach, a corresponding specific maintenance program must provide detection and repair of accidental damage, corrosion, and fatigue failure before the structure residual strength is reduced below an allowable limit. Although the abovementioned fatigue-based design approaches have been implemented for a long time in engineering practice, it is still possible for fatigue failure situations to occur because of different shortcomings of design and omissions in implementation. There are many influencing factors which affect fatigue behavior [5], the most important of which are stress and strain concentrations; material properties and metallurgical factors; surface finish and directional properties; and type and nature of loading, etc.

Reduction of fatigue failures by using specific methods for parts production is the second strategic approach [6–10]. By choosing an appropriate processing method, the effect of various "defects"—caused by metallurgical factors, surface hardness, residual compressive or tensile stresses in the surface layer, surface roughness and topography, etc.—on fatigue endurance can also be significantly reduced. The surface roughness is of great importance among the technological factors because it is well known that fatigue failure usually originates on the surface of the part. There is evidence that, for steel, the higher the tensile strength, the more critical is the surface finish [11,12]. Because the surface condition has a significant effect on fatigue strength, some of the traditionally used finishing processes of machine parts, such as milling, turning, grinding, polishing, lapping, etc., cannot completely meet all requirements. The surface roughness after most of these processes has a typical topography with notches due to imperfections that occurred after removing the allowance. Residual tensile stresses and even cracks can occur after grinding, for example, due to intensive heating of the surface layer, which is usual for this finishing process [5,13,14].

A considerable increase of the fatigue strength can be achieved if finishing processes such as shot peening, deep rolling, ball burnishing (BB), etc., which are based on plastic deformation of the surface layer in a cold state, are applied [5,15,16]. After their application, compressive residual stresses are obtained in the surface layer, combined with the removal (or minimization of depth) of the notches from previous cutting operations [17]. Processes based on plastic deformation also increase the hardness of the surface layer, which favors wear resistance. When rolling or BB is applied to metastable austenitic stainless steels, such as the aforementioned AISI 304 and AISI 316L, the austenite (γ-phase) transforms into martensite (ε- and/or α'-) due to a recrystallization change caused by deformation energy, even at ambient temperature. On the other hand, a smooth surface topography with very little roughness (Ra criterion from 0.8 to 0.025 μm) can be achieved after rolling or BB is

applied as a finishing process [18,19]. This way, two of the abovementioned negative effects of the cutting finishing methods on fatigue resistance can be avoided.

Ball burnishing has several different varieties, depending on the purposes for which it is applied [20]. They are all related to the plastic deformation of the surface layer, but can differ in the way the deforming element moves along the parts' surface. When the goal is to achieve only surface smoothing, the classic BB schemes can be used [21], in which the trajectory of the deforming element is the same as that of the cutting tools in drilling, turning, and milling cutting operations. Recently, there has emerged more and more evidence that the BB process can be successfully implemented using computer numerical control (CNC) equipment, which allows application of different strategies and toolpaths [22–25]. Some authors [26] report improvements in BB tools that allow the simultaneous use of multiple deforming elements to increase the process productivity. Other authors [27] apply ultrasonic artificial vibrations to the deforming element in order to intensify the plastic deformation in the surface layer.

The BB process also can be applied in order to create a specific surface roughness (or so-called "regular reliefs") in addition to improving the other aspects of surface layer integrity [28]. Regular reliefs (RR) are formed by the traces of plastic deformation that are left on the surface as result of the passage of the deforming element, which is pressed with a certain deforming force. Here the deforming tool must perform a more complex trajectory (in contrast to the classical one), involving additional oscillation with a certain frequency and amplitude. As a result, this type of BB process is called "vibratory ball burnishing" (VBB) [28]. The RR obtained by vibratory ball burnishing can be five different types, according to the classification given in [28], the most interesting of which is the IV-th type, which covers all of the processed surface and forms a completely new surface roughness. Depending on the regime parameters of the VBB, the RR of the IV-th type can have specific rectangular or hexagonal cell patterns, which significantly increase the ability to retain lubricants and micro debris and stop them from wearing the surfaces burnished by this method, in comparison with smoothed ones [29–31]. Although the roughness of the RR is greater than that of the smoothed surfaces, they offer better contact conditions, such as reaching liquid friction at lower speeds [32], optimizing the contact spots, and increasing the wear resistance, while the other advantages of the BB process remain the same.

When VBB is adapted for implementation by using a CNC lathe or milling machine, the complex toolpath for obtaining RR can be achieved by interpolation between the machine axes [33]. In this case, the additional reciprocating movement (or the "vibration" component) of the ball tool is not needed, which significantly simplifies its construction. The preliminary mathematical modeling [34,35] of the tool path and the higher precision of the CNC equipment give opportunity to obtain full or partial RR with higher dimensional precision and repeatability of the cells. In the present work this variant of the BB process was used in order to obtain RR of the IV-th type on flat surface of the test parts subjected to fatigue failure tests. This type of RR is expected to have no worse fatigue-failure behavior than the smoothed surfaces after applying other (traditional) variations of the BB process. The results from earlier conducted experiments with AISI 304 steel [36] support this expectation, but the obtained experimental data concern only few of the BB process conditions, and the statistical analysis used to evaluate the significance of the regime parameters of the process can be improved by using the Bayesian approach [37].

Based on the investigated sources, the current work's main goal is to investigate the effect of RR of the IV-th type obtained by BB on the fatigue life of AISI 304 and AISI 316L austenitic steels. Secondly, it aims to study the effects of the main BB process regime and relief parameters and their interactions over fatigue life.

Finally, it aims to create a stochastic model for calculation of the probabilities of reaching a certain number of cycles until fatigue failure, for the possible combinations of "low" and "high" levels of the BB regime's parameters for both investigated steels.
