Experimental validation of ball burnishing numerical simulation on ball-end milled martensitic stainless-steel considering friction and the initial surface topography

Review Article Experimental validation of ball burnishing numerical simulation on ball-end milled martensitic stainless-steel considering friction and the initial surface topography Alejandra Torres a,b,* , Cyrus Amini c , Nuria Cuadrado a,d , J. Antonio Travieso-Rodriguez b , Jordi Llum a d , Montserrat Vilaseca a a Eurecat, Centre Tecnol ogic de Catalunya, Unit of Metallic and Ceramic Materials, Plac¸a de La Ci encia 2, 08243 Manresa, Spain b Department of Mechanical Engineering, Universitat Polit ecnica de Catalunya, Av. Eduard Maristany 10-14, 08019 Barcelona, Spain c Mechanical Engineering Department, University of Tabriz, 29 Bahman Blvd, Tabriz 5166616471, Iran d Department of Materials Science and Engineering, Universitat Polit ecnica de Catalunya, Av. Eduard Maristany 10- 14, 08019 Barcelona, Spain article info Article history: Received 25 October 2022 Accepted 3 December 2022 Available online 29 December 2022 Keywords: Numerical analysis Friction Ball burnishing Surface integrity Topography Roughness abstract Numerous simplified numerical models have been established to optimize the ball burnishing of steel surfaces. Nevertheless, their conceptualization has not considered the toolepart interaction, leading to an unsatisfactory process parameterization. As a solution, a structured numerical simulation has been defined that reproduces this interaction by several friction coefficient approximations. This study provides the tribological process inputs (friction and initial surface conditions) to this model, adapting it to a pre-textured martensitic precipitation hardening stainless-steel. Results show the versatility of the model to reproduce the surface integrity alterations. Hence, this consistent model configuration can be postulated as an economical and efficient approach to tackle ball burnishing parameterization according to the applicability of the manufactured steel parts. ©2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction Burnishing is an industrial procedure often used as a last machining operation [1e4] to improve surface integrity (roughness, residual stresses state, hardness, microstructure [4,5], reliability, and service performance [6]) of a final component avoiding extra machining costs [1,2,4]. This cold work process implies the displacement of a cylindrical or spherical indenter that can rotate on an irregular metal surface [1], resulting in a smooth surface [1,4,7,8]. The applied load is the most critical parameter affecting optimal surface *Corresponding author. E-mail address: [email protected] (A. Torres). Available online at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jmrt journal of materials research and technology 2023;22:3352e3361 https://doi.org/10.1016/j.jmrt.2022.12.100 2238-7854/©2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/). integrity [1,2,4,9]. Under the effect of this load, while peaks of roughness are displaced to the valleys (improving the surface finish) [1], an affected layer thickness [1,7] (up to 300 mmin depth on 15e5 PH martensitic stainless steel turned surfaces [1]) as well as a maximum compression state in the subsurface (at 100 mm depth [1]) are induced. In this manner, wear and fatigue resistance are increased owing to the strain hardening [1,3,8,10e12] and thereby, a new surface [3,8,13e15] and sub-surface stress state [1,3,7,11,16]. Studies quote a subtle influence by the speed [1,4,10], feed [1,10] and number of passes [1,17] on this final residual condition. With these precedents, several authors have worked on obtaining analytical and numerical models of surface finish and residual stress state from experimental data [4]. For instance, Li et al. [18] have defined constant coefficients to foresee the roughness behavior as a function of the yield strength. Zhang et al. [7] have established an empirical method to predict the roughness and residual state (from pressure, speed, and feed parameters) on 17e4 PH martensitic stainless-steel surfaces after burnishing with a qualitative fit for the latter one. Travieso et al. [12] and Aviles et al. [19] have developed a predictive analytical method of fatigue behavior of AISI 1038 and AISI 1045 burnished steel surfaces with significant adjustments. El-Tawel et al. [9] and Jerez-Mesa et al. [20] base their studies of the roughness imparted by burnishing (on brass and AISI 1038 steel surfaces, respectively) on the Taguchi technique. Garcı´a et al. [11] have measured the residual stresses by incremental hole drilling (IHD) procedure to set a FEM model in order to obtain the equations to calculate the strain release through IHD. In addition, numerous experimental studies have been customized according to specific surfaces. Thus, Loh et al. [16], Dzierwa et al. [21], Aviles et al. [19] and  Swirad et al. [22] have rated the effect of a defined burnishing configuration on the surface finish, while Chomienne et al. [1], Abrao et al. [15] and Luca et al. [8] have experimentally evaluated the burnishing parameters influence on residual stresses behavior. About finite element models (FEM), they are tailored to each particular condition, which makes it challenging for one model to be applicable in all cases [18]. In this regard, Rodriguez et al. [4] propose a 2D simulation in order to obtain the residual stresses values induced by hydrostatic ball burnishing on AISI1045 steel surface under a specific configuration, with quantitative discrepancies. Balland et al. [2] 3D model on 11SMn30 surfaces displays the flow of the ridge in agreement with the experimental outcomes obtained by Barquins et al. [23]. Rao et al. [24] models results are approaches to the experimental residual stresses values induced by burnishing on aluminum surfaces with variation less than 10%. Sayahi et al. [25] stablish a 2D and 3D finite element ball burnishing modelling to compare the numerical outputs with the experimental residual stresses acquired on Tie6Ale7Nb burnished surfaces demostrating a better adjusment of their 3D setting. The opposite is observed in the Yen et al. [10] burnishing models. Their 2D refined configuration on AlSl 52100 shows a better fit in terms of residual stresses than in 3D setting, while their 3D model displays a more representative material flow and deformation of the surface. In addition, based on simulation on AISI52100, Kermouche et al. [26] determine that the contact severity, the friction coefficient and the workpiece hardness as the key-parameters of process. Then, Maximov et al. [27] model approaches the tool motion to a series of planar movements on a modeled roughness surface, stablishing the flow stress and sliding friction coefficient numerically. In that sense, Amini et al. [3] trough their estructured 3D numerical model, have determined the friction influence of a ball burnishing configuration on an extruded AISI 1038 steel surface, regarding the initial finish as well, but including the initial residual tensor induced by the previous machining procedure. It shoul be noted that, the surface and subsurface integrity improvements after burnishing depend on the metal nature (steels, aluminum alloys, brass, and others), its microstructure [1,28] (that define the material mechanical properties) and its initial surface conditions (roughness, hardness and residual state) [29e33]. Thus, according to the martensitic percentage, TRIP steel AISI 301 LNS is affected by the process in different degrees. The higher contents involve reduced effects of texture generation and residual deep hardening [29]. Besides, after burnishing execution, steel textured surfaces (like Ck45 steel) can acquire a defined texture orientation independently of the former one [30]. Furthermore, by nanostructuring the microstructure in the subsurface on HRC55 20Cr4 steel trough burnishing, Kuznetsov et al. [34] determine the relevant influence of friction (as a function of load) in the final surface conditions. It is the friction that impose the intensity of the deformation-induced behavior. High friction causes a thinner layer of plastic deformation at the surface (maximum frictional shear stress concentration). Conversely, low friction extends the deformation to depth. In consequence, the main external parameters of the process such as applied load, lateral pass, ball material and ball diameter [1,2,4,7,9,10,16,20] must be configured in accordance with the metallic material of the machined component [1], considering the interactional effects, such as the friction coefficient [3,26,27] and the anisotropy imparted [3,10,17,21,30] (that is reduced as the load increases [17]), according to the functionality of the final component. This background highlights the complex requirements in process setup. In this regard, comprehensive considerations in terms of the tribo-contact between the microstructure of the target surface [1,28] and its interaction with the tool [3,20,26] must be assessed. Thus, despite the countless analytical, experimental and numerical studies dedicated to parameterize the process, none of them shows that even though belonging to the same metallic family, metals respond differently to the same plastic deformation mechanism depending on the initial surface conditions and their microstructure capability of interaction with the tool. In order to overcome this grueling assignment, burnishing process is approximated as a deformable solid mechanics problem settled by means of numerical modeling. Previous simplified simulations have tried to predict the influence of burnishing variables on the final surface quality, but each of them has been validated according to a given material [2,4,10,24e27] and without considering the toolepart interaction [4,9,24,26e28] (friction and roughness). In that sense, Amini et al. [3] eliminated these simplifications in their 3D ball burnishing numerical model on a pretextured AISI-1038 steel surface (experimentally settled in previous works [12,20]) with the Power-law model as plastic journal of materials research and technology 2023;22:3352e3361 3353 behavior [35]. Since the inertia effects during the process are negligible [3] and the constant feed rate did not elucidate significant influence on the final steel surfaces [1,4,10], the aforementioned numerical model has been configured based on the implicit static analysis in ANSYS software which has exploited the augmented Lagrangian method as contact algorithm [36] and the Coulomb-Mohr's frictional model without cohesion [37] to detect contact areas between the ball and the surface. Modeling the burnishing process under these assumptions, proves the great impact of friction on the final surface integrity. To extend the applicability of Amini et al. model [3] to other ferrous materials (skipping one of the aforementioned FEM limitations [18]), a ball burnishing process on a UNS S46500 milled martensitic precipitation hardening stainless-steel has been simulated and validated. Although this material is industrially relevant due to its wide use in aerospace application [38], it has not previously been studied,. In addition, in order to evaluate different tribo-contact scenarios as well as their numerical conceptualization accuracy, ball burnishing experiments have been performed under two loading conditions, 270 N and 470 N. These two load levels entail two different friction coefficients and therefore, a different final surface and subsurface quality (reproduced by the 3D FEM model with accuracy). Hence, the numerical model is able to emulate the deformation induced by the maximum residual tensor and its affectation spread in depth (as is stated experimentally [34]). Thus, on one hand, the surface roughness of the obtained samples has been evaluated by means of 3D optical profilometry, and on the other, residual stresses state has been established by X-ray diffraction technique (XRD). By doing so, the adaptability of ball burnishing numerical simulation with a martensitic stainless-steel component has been investigated, contributing to the search for a reliable and versatile numerical tool for the future steel ball burnishing execution. 2. Material and methods 2.1. Material The target material of this study was an UNS S46500 martensitic precipitation hardening stainless-steel used in the aerospace industry and processed under as-delivered conditions. 2.1.1. Chemical composition Chemical composition given in Table 1 was obtained by means of spark emission spectrometry employing a SPEC- TROMAXx LMF08 equipment (SPECTRO, Kleve eGermany). 2.1.2. Microstructural characterization Microstructural analysis was performed using Field Emission Scanning Electron Microscopy (FE-SEM) Ultra Zeiss (ZEISS, USA). In order to reveal the microstructure, the material was grinded and polished to mirror surface finish with 0.03 mm colloidal silica suspension, then it was etched with Kalling I reagent. Fig. 1 shows the microstructure, which mainly consists in martensite with intergranular precipitates. 2.1.3. Surface texturing Prior to ball-burnishing process, the surface was textured according to the milling operational parameters shown in Table 2. The milling procedure was performed by a CNC router milling machine (LAGUN, Spain). Four milled samples were measured to obtain the 2D roughness profiles (Fig. 2) according to the ISO 4287:1999 standard [39], since the model needs a two-dimensional signal for its initial development. After milling and burnishing, relevant industrial surface parameters (Sa,Sq) were obtained according to ISO-25178e2:2016 standard [40](Fig. 4), in order to provide the weighting of peaks and valleys with respect to a median plane and to determine the dispersion of this distribution. The topographic images were acquired by means of an InfiniteFocusSL -Alicona microscope (Bruker, Germany) and the results were obtained with Mountains image analysis software (Digital Surf, France). Once the 2D roughness profile was extruded to sweep the mesh into the model, a representative surface-weighted pattern of the whole surface was obtained and the numerical Sa and Sq parameters were compared with the experimental outcomes. Fig. 2 shows several irregularities in the experimental roughness profiles of the machined surfaces. Results are different to those obtained with ferritic microstructures by Amini et al. [3], which showed a regular roughness profile under the same milling conditions. This fact spawns another challenge for the numerical prediction of the texture after the tribological interaction induced by ball burnishing process on a less malleable microstructure. In this regard, maximum peaks and minimum valleys have been provided as an input to the numerical simulation. Table 1 eUNS S46500 Chemical composition (in wt %). %Fe %C %Ni %Cr %Mo %Al %Ti 74.40 ±0.02 0.01±6E-4 10.89 ±0.01 11.69 ±0.03 1.01±6E-3 0.05±6E-4 1.70 ±0.02 Fig. 1 eUNS S46500 microstructure. journal of materials research and technology 2023;22:3352e33613354 2.2. Burnishing process Ball burnishing process on the surface was performed by means of a CNC router milling machine. The burnishing tool protected by Spanish patent number 201730385 commercially known as Acoustomill [41] was used by adapting a 10 mm diameter hardmetal ball in the force transmission unit. The initial burnishing load and the number of passes were selected according to the referential conditions used in the preceding study settled by Amini et al. on ferritic milled surfaces [3]. A load increase was executed in order to evaluate the microstructural response of the tribological interaction, as well as the capability of the model to predict this answer. Unlike to the previous study, burnishing process was performed in the perpendicular direction to the milling finish, to evaluate the flexibility of the model. Operational parameters are summarized in Table 3. 2.3. Experimental methods 2.3.1. Mechanical properties Ultrasonic method was used to compute elastic properties by means of a Panametrics 5900 PR (Olympus, Japan) and an oscilloscope Hameg HM1508 (RS, UK) in 40.95 mm length. Plastic tensile properties were computed by means of conventional tensile tests [42] in the longitudinal orientation. Five specimens adapted to ISO 6892-1 standard requirements [42] with a width of 6 mm and a parallel length (Lc) of 34 mm were tested. Strain rate during the tests until the failure of the sample was 0.0067 s 1 .Table 4 shows the mechanical properties obtained for the target material. 2.3.2. Friction coefficient The first interaction between the tool and the rough surface is treated as the normal contact between a rigid sphere and an elastic half-space which is resolved with the classical theory of Hertz for non-adhesive contact [43]. This analytical model has demonstrated significant adjustments depending on the process configuration and the material to be deformed [44e46]. Based on this theory, through Eqs. (1) and (2), contact radius (a) and pressure in the centre of the contact region (p 0 ) were computed as a function of the normal force (F) and the indenter radius (R). a3¼3F$R4E*(1) p3 0¼6F$E*2p3$R2(2) where E*is the reduced elastic modulus, a parameter obtained from expression (3): 1E*¼1n2 1E1þ1n2 2E2(3) In Eq. (3),E 1 and E 2 are the Young's modulus and n 1 ,n 2 are the Poisson's coefficients of the interacting materials. Then, friction tests were performed conforming to the sequence for designing of laboratory friction and wear proposed by the Table 2 eMilling conditions. Tool Lateral pass width [mm] Depth of cut [mm] Feed rate [mm/min] Cutting speed [rpm] Ball mill UT coating ø 10 [mm] two teeth 0.30 0.20 600 2000 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 y [um] x [mm] Fig. 2 eMeasured roughness profile obtained through ball end milling (discontinuous line) and extruded surface profile (continuous line) applied as an input in the simulation of burnishing process. Fig. 3 eScheme of modeled surface, boundary conditions and the path traveled during ball burnishing [2]. journal of materials research and technology 2023;22:3352e3361 3355 American Society of Materials (ASM) [47]. A Micro-inden- tationeScratch Tester MHT (CSM Instruments, Germany) was used to investigate the friction coefficient (COF) during burnishing over milled surfaces. Linear scratch was performed on a length of 20 mm at 600 mm/min at room temperature in dry conditions with a tungsten carbide ball indenter of 2.5 mm diameter. The obtained contact pressures during ball-burnishing under the conditions listed in Sec. 2.2 for 270 N and 470 N were 2700 MPa and 3100 MPa, respectively. Three tests per surface were performed. 2.3.3. Residual stresses Residual stress measurements were conducted with a PAN- alytical emodel X'Pert-PRO-MRD equipment (UCDavis, USA) using a point detector assembled to a parallel plate collimator with 0.27angular opening with a pixel size of 255 mm255 mm and a planar graphite secondary monochromator. Reflection (211) of the bcc phase (martensite) was considered, according to the sin 2 J, mode U-tilt method, with a penetration depth up to 4 mm. 2.4. Numerical model Implicit static analysis was performed using ANSYS software. Ball burnishing was performed in x-axis direction, while the pattern of roughness (Fig. 2) was extruded along the z-axis. The burnished zone corresponds to an area of 0.9 mm 1.2 mm. Initial residual stress tensor induced by milling process was embedded at the depth of 4 mmasan initial input. It is worth to note that the initial stress tensor is anisotropic (see section 3.3). WC-Co ball was approximated as a non-deformed solid rigid due to its small deformation compared to that of workpiece. Finally, experimental COFs were introduced as an input in order to approximate the model with the real tribological interaction. Fig. 3 shows the model configuration. 3. Results 3.1. Friction coefficient (COF) Table 5 summarizes COF results obtained as an effect of the two pressure conditions stated in 2.3.2. The aforementioned burnishing parameters were applied on the martensitic milled surface. As a result of the 15% increase in the contact pressure, an increase of 15% rise in friction coefficient has been determined. This indicates the degree of dependency between the surface-ball contact and friction. 3.2. Macro-texture In order to validate the simulation, numerical parameters Sa and Sq have been compared with the average of three experimental measurements obtained on a surface equal to and corresponding to the simulated area (0.9 mm 1.2 mm). Despite the estimation of the initial roughness profile, results reveal that the numerical model can establish the performance of the target textured martensitic stainless-steel surface under the pressure stimulus transferred by the tool in terms of macro-texture. Significant adjustments are obtained in the peaks and valleys distribution with respect to a median plane (Sa) as well as its dispersion (Sq). Hence, Fig. 5 shows the topography evolution under the conditions stated in Table 3 while the nodal displacement in the Y direction (Uy) from the simulation has been displayed in Fig. 6. It is worth to note that Fig. 5 values scale has been adjusted to the surface conditions prior to the ball burnishing execution. Nevertheless, Figs. 5 and 6 are comparable. In this regard, when the burnishing load increases, valleys are deeper (around 4 mm) than the initial value in the roughness profile (1.4 mm), both experimentally and numerically. Simulation results enlighten the material displacement out of the 0.0 0.2 0.4 0.6 0.8 1.0 1.2 270 N 470 N Sa [μm] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 270 N 470 N Sq [μm] Experimental results Numerical results Milling Burnishing Milling Burnishing Fig. 4 eSurface amplitude descriptive parameters after machining processes. Table 3 eOperational parameters of burnishing. Applied load 270 [N], 470 [N] Lateral pass width 0.30 [mm] Feed rate 600 [mm/min] Vibration No Table 4 eMechanical properties of UNS S46500. E [GPa] ns 0.2 [MPa] UTS [MPa] n 198.8 ±0.4 0.294 ±2$10 4 1571 ±8 1656 ±5 0.029 ±0.002 journal of materials research and technology 2023;22:3352e33613356 burnished area. Regarding the peaks, experimental data shows maximum around 1.5 mm while the simulation displays it as 1.0 mm, approximately. When ball burnishing is performed at 270 N load, the surface is smoothed consistently. On the other hand, when the load increases, the overlapping of material provides an irregular finish. Results reveal the effect of tribological interaction on the final surface. 3.3. Residual stresses state Both parallel (Sx) and perpendicular (Sz) components of residual tensor to the burnishing direction at a depth of 4 mm were obtained by means of XRD for each condition. Comparison of experimental and numerical results for 270 N and 470 N is depicted in Fig. 7. The values shown under the experimental bars represent the increased percentage of the residual stress component after burnishing compared to that obtained after milling process. The adapted model started from an anisotropic surface configuration provided by the pre-machining process with the highest residual tensor component along the z-axis. Given that ball burnishing was performed in the perpendicular direction to this initial finishing (along the x-axis), results show that the greatest increase of the compressive residual stress component occurs in the parallel direction to the burnishing path (62% under 270 N load and 95% under 470 N load), with respect to the initial milling state. So, these burnishing configurations induce a greater effect in the direction in which the initial residual stress component is weaker (keeping the initial anisotropy trend), unlike the initial numerical model, where the original direction of ball-end milling did not influence the final residual stress on the ferritic surface [3]. Thus, it is worth noting the ability of the model to reproduce this performance through the appropriate mechanical and tribological characterization, where the self-hardening coefficient (n) plays a significant role in the microstructural differentiation. When the simulation was performed at 470 N load, only a slight mismatch appears in the parallel direction to the burnishing path with respect to the experimental values. Considering that the increase in contact pressure causes the displacement of peaks below the initial valleys (shallow decline), there will be an increase of the pile up, and therefore a larger divergence. Besides, the roughness profile has been extruded along the z-axis, so sharp peaks appear in x-direc- tion. Consequently, these peaks act as a hinder to prevent plastic deformation along the x-axis. As a result, a higher stress is witnessed than in experimental conditions. The impact assessment of the proposed load conditions shows that the effect of 470 N exceeded the milling valleys below 4 mm depth (Section 3.2). This implies a shift in the ball burnishing interaction, increasing the residual stress tensor perpendicular component to the burnishing path by 73% (more than twice the increase obtained at 270 N load). The lower friction coefficient obtained at 270 N load, leads to the fact that the small penetration of the ball into the deformed zones by the initial machining allows displacing part of the peaks towards the valleys, reinforcing the adjacent zone until constitutes a uniform surface as was observed in section 3.2.If this hypothesis is factual, the subsurface response should be different for both cases. In fact, simulation provides a first insight of the subsurface tensor behavior inside the characteristic range proposed by Chomienne et al. (300 mm) [1]by means of Fig. 8. Data revealed the variability of the final tensor as a function of the applied load. Under 270 N load, the component of the residual surface tensor in the perpendicular direction to the process tends to increase sub-superficially. On the other hand, it was observed that at 470 N, the residual tensor (both directions) gradually decreases up to 25 um in depth and then increases again.. Nevertheless, Sz component (at 54 mm and 86 mm, respectively) is around 1265 MPa, under both load conditions. Another aspect to consider is the isotropic state that the material reaches early (~50 mm) under the highest load. Consequently, high tribological interaction involves both, less anisotropic affectation in depth as well as a reduction tensor in the first microns in the subsurface. Table 5 eFriction coefficient (COF) at different contact pressures [4]. Contact Pressure [MPa] COF 2700 0.13 ±0.01 3100 0.15 ±0.01 Fig. 5 eExperimental surface conditions after machining processes. journal of materials research and technology 2023;22:3352e3361 3357 4. Discussion The current simulation is not limited to a specific steel. By introducing the mechanical and tribological properties of the material and eliminating the first simplification considered in other models [2,4,10,24,25,27]) by including the COF between the roughness and the hard ball, the simulation allows to predict the final surface integrity. Despite the irregularities in the roughness profile after milling process, its approximation to the maximum and minimum points (peaks and valleys), permitted to obtain fairly accurate numerical results in the final macro-texture. Model captured material overlapping adjacent to the burnishing direction (pile up) when ball burnishing proceeded at 470 N load. Otherwise, a uniform surface finishing was achieved at 270 N load. Thus, the effect of friction as well as the assertion of the applied load as a fundamental parameter on the surface integrity deterioration [1,2,4,9,34] are evidenced and validated. Regarding the new compression residual state [3,8,13e16], enhancements are not limited to the surface [1,3,7,11,16]. According to Chomienne et al. [1], simulation elucidates the bulk affectation of the process over martensitic microstructures (until 300 mm depth), which is also validate in this work. The maximum compression state up to 100 mm in depth [1]has validated as well. The 3D FEM model reflects that high applied burnishing loads (470 N) induces a maximum value of residual stress tensor at the surface (4 um) in response to the tribocontact (higher COF). Under 270 N load, the maximum value is reached within the 50 mm and a noticeable anisotropic residual stress tensor distribution is imposed. According with Capilla-Gonz alez et al. [17], as the load increases, the isotropy tendency increases. Simulation validates this statement while allows to exhibit the residual stress tensor distribution depending on the tribo-contact between the ball and the textured surface (because of the shift on the applied load). Therefore, an increase in load involves a bidirectional compression effect. Besides, unlike the ferritic steels [3,12,20], martensitic stainless steels replay in a different way to this plastic deformation mechanism as reported in the literature [1,7,11]. In fact, granted anisotropy is not independent of the initial tensor (on the contrary to the ball-burnishing on Fig. 6 eSurface topology after simulation. -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 Milling 270N 470N Sx [MPa] 62% 95% -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 Milling 270N 470N Sz [MPa] 37% 73% Milling Burnishing experimental results burnishing numerical results Fig. 7 eSx (left) and Sz (right) components of residual tensor at a depth of 4 mm after machining processes (% values represent the increase of residual stresses compared to the milling condition in each of the simulated processes). journal of materials research and technology 2023;22:3352e33613358 textured ferritic surface simulation [3]). Substantial improvements in the compression residual state have been obtained in the parallel direction to the burnishing route, although the anisotropic trend remains in the perpendicular direction (as was quoted by [3,10,17,21]). These results demonstrate the flexibility of the model. Therefore, it is worth emphasizing the great importance of supplying a real COF for a successful model adjustment, since the final numerical integrity is substantially dependent on the friction coefficient, as it was demonstrated also in the previous model for ferritic steels [3]. 5. Conclusion This paper demonstrates the applicability of the Amini et al. [3]structured 3D ball-burnishing numerical simulation (initially configured according to roughness, initial residual condition and friction during ball emilled AISI 1038 steel surfaces contact) adapted to the tribological interaction between the tool and a martensitic stainless-steel surface. Beyond the limitations dictated by a customized FEM configuration for each material, this work shows the versatility of the model because of: Numerical 3D roughness parameters as well as the final topography have a convincing agreement with the experimental values. The model limitation to introduce the experimental roughness profile was successfully overcome by approximating the average profile to a sinusoidal wave that considers maximum peaks and minimum valleys. It is noteworthy how after the 2D roughness profile extrusion into the model, a representative surfaceweighted pattern of the whole surface was obtained to finally achieve a numerical fit of the Sa and Sq parameters to the experimental outcomes after ball burnishing process. This simulation reproduced the detrimental effects of load and friction increase on the surface quality by a higher dispersion (Sq) in the arithmetical mean heigh (Sa) distribution (valleys reach the 4 mm depth when the initial values were around 1.4 mm). A cramped mismatch in terms of residual stress tensor in one of four directions, did not alter either its trend (anisotropy) or the final surface integrity. The increase in contact pressure involved a shallow slump causing a larger divergence. Additionally, the peaks of the roughness profile (restricted to maximum values of experimental peaks) extruded along the z-axis, constitute sharp elements that work as obstacles, obstructing the plastic deformation along the advance route. Nevertheless, despite the higher stress obtained numerically with respect to the experimental values in x-axis direction (a difference of about 200 MPa), the process parameterization can be validated quantitatively as a function of the component applicability (which defines the residual stress conditions) by means of this simulation. An approximation of the subsurface stress behavior (up to 300 mm in depth) to verify both the depth extent and the load affectation degree in the final isotropic state cited in previous works. When the process is performed under 270 N load, the surface finish is improved as the residual tensor increases continuously until 54 mm depth, keeping the anisotropy trend. Under 470 N, the surface residual tensor is higher but tends to shrink during the first microns. Furthermore, this strong interaction leads to a detrimental surface integrity and to an early isotropic state. However, subsurface behavior is out of the reach of the current study since it demands a detailed evaluation at the microstructural level. Nevertheless, considering the relevance of this material applications future experimental and numerical investigations on the microstructural behavior of this material under ball-burnishing should be done. The outstanding results in terms of the final surface integrity highlighting the relevance of including friction as a Residual tensor profile at 270 N load Residual tensor profile at 470 N load -1500 -1300 -1100 -900 -700 -500 -300 -100 100 0 50 100 150 200 250 300 RS [MPa] Depth [μm] SX SZ -1500 -1300 -1100 -900 -700 -500 -300 -100 100 0 50 100 150 200 250 300 RS [MPa] Depth [μm] SX SZ Fig. 8 eResidual stress state up to a depth of 300 mm after burnishing process obtained in the simulation. journal of materials research and technology 2023;22:3352e3361 3359 fundamental parameter in the numerical process conceptualization. Therefore, the model has been validated with regard to its versatility constituting a useful and economical tool to define the most efficient path for ball burnishing processes on steels not yet studied (such as the UNS S46500 stainless-steel) and that require an increase of the surface quality of the final components.. Author contributions Conceptualization, A.T., J.A.T.-R., M.V., J.L.,N.C.; methodology, A.T., M.V, J.A.T.-R, N.C., J.L.,; software, C.A., A.T., N.C.; validation, J.A.T.-R., N.C., J.L. and M.V.; formal analysis, A.T., N.C., J.A.T.-R., J.L.,M.V.; investigation, A.T., N.C.; J.A.T.-R., J.L.; resources, J.A.T.-R., J.L., C.A., N.C.,M.V.; data curation, A.T., N.C., J.A.T.; writingdoriginal draft preparation, A.T., C.A.; writingdreview and editing, A.T., N.C., J.A.T.-R., J.L., M.V., C.A.; visualization, A.T., C.A., N.C.; supervision, N.C., J.A.T.-R., J.L., M.V.; project administration, M.V.; funding acquisition, J.A.T.- R., J.L.,M.V. All authors have read and agreed to the published version of the manuscript. Funding This research was funded by Eurecat's“Vicente L opez" PhD grant program and by the Ministry of Science, Innovation and Universities of Spain, through grant RTI2018-101653-B-I00, which is greatly appreciated. Also, by the regional government of Catalonia and FEDER funds for regional development through grant 001-P-001822. Data availability statement The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. references [1] Chomienne V, Valiorgue F, Rech J, Verdu C. Influence of ball burnishing on residual stress profile of a 15-5PH stainless steel. CIRP J. Manuf. Sci. Technol 2016;13:90e6. [2] Balland P, Tabourot L, Degre F, Moreau V. Mechanics of the burnishing process. Precis Eng 2013;37(1):129e34. https:// doi.org/10.1016/j.precisioneng.2012.07.008. [3] Amini C, Jerez-Mesa R, Travieso-Rodriguez JA, Llum aJ, Estevez-Urra A. 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