# Fatigue enhancement and hardening effect through ultrasonic vibration-assisted ball-burnishing process on AISI 1045 steel

Eric Velázquez-corral, Jordi Llumà, Ramón Jerez-mesa, Vincent Wagner, Gilles Dessein, J Antonio Travieso-rodriguez

► To cite this version:

Eric Velázquez-corral, Jordi Llumà, Ramón Jerez-mesa, Vincent Wagner, Gilles Dessein, et al.. Fatigue enhancement and hardening effect through ultrasonic vibration-assisted ball-burnishing process on AISI 1045 steel. Fatigue and Fracture of Engineering Materials and Structures, 2023, 47 (1), pp.203 - 219. 10.1111/ffe.14180. hal-04360269

HAL Id: hal-04360269

https://ut3-toulouseinp.hal.science/hal-04360269v1

Submitted on 21 Dec 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Fatigue enhancement and hardening effect through ultrasonic vibration-assisted ball-burnishing process on AISI 1045 steel

Eric Velázquez-Corral<fnref n="1" /> ID
Vincent Wagner<fnref n="3" />

Jordi Llumà<fnref n="2" /> ID
Gilles Dessein<fnref n="3" />

Ramón Jerez-Mesa<fnref n="1" /> ID
J. Antonio Travieso-Rodriguez<fnref n="1" /> ID

## Correspondence

Ramón Jerez-Mesa, Department of Mechanical Engineering, Universitat Politécnica de Catalunya, Barcelona, Spain.

Email: ramon.jerez@upc.edu

## Funding information

Ministerio de Ciencia e Innovación, Grant/Award Number: PDC2022-133596-I00

## Abstract

This paper aims to present a study of the effects of ball burnishing with vibration assistance on the bending fatigue endurance of cylindrical specimens subjected to bending stress and obtain the best input parameters. The specimens were burnished through six different combinations of preload force, number of passes, and vibration assistance, finding that burnishing while applying a 90-N preload, five passes, and the addition of vibration assistance results in larger fatigue strength. In terms of roughness, it has been proved that vibration-assisted ball burnishing reduces the mean roughness up to 90%, while enhancing the skewness and kurtosis parameters. The softening effect while deforming, caused by the vibration assistance, helped to reconstruct the surface, obtaining higher depths of affectation and hardening. Fatigue strength was improved by a 6.54% by only adding vibration assistance to the ball-burnishing process.

## KEYWORDS

fatigue enhancement, fractographahy, hardening, microstructure, vibration-assisted ball burnishing

# 1 | INTRODUCTION

AISI 1045 steel is a widely used material in the automotive industry due to its good mechanical properties and low cost compared to other non-medium carbon steels. It is mainly used to manufacture shafts and cams, but during the last years, some technology has been developed to enhance its surface properties.<fnref n="1" />

The processes to enhance the superficial properties can be divided into cutting and non-cutting processes. Conventional cutting processes have converged into more sophisticated processes by adding new trends, like laser-assisted milling,<fnref n="2" /> nano-cutting fluids in turning,<fnref n="3" /> ultrasonic machining,⁴ or cryogenic machining⁵ that allowed enhancing the superficial properties of a non-treated material, improving the final roughness or hardness increase. However, these processes have shown a poor improvement in terms of fatigue life enhancement, compared to other finishing technologies such as shot or laser

<footnote n="1">¹Department of Mechanical Engineering, Universitat Politécnica de Catalunya, Barcelona, Spain</footnote>

<footnote n="2">²Department of Science and Materials Engineering, Universitat Politécnica de Catalunya, Barcelona, Spain</footnote>

<footnote n="3">³Laboratoire Génie de Production, École Nationale d'Ingénieurs de Tarbes, Tarbes, France</footnote>

<footnote>**Abbreviations:** BB, ball burnishing; M, machined; VA, vibration assistance; VABB, vibration-assisted ball burnishing.</footnote>
peening,⁶ deep rolling,⁷ or burnishing,⁸ which demonstrated a fatigue enhancement through an increase of the compressive residual stresses, roughness decrease, and hardness improvement.

In particular, the burnishing process consists of a cold deformation in which the outer asperities are compressed against the surface, filling the material valleys and reaching a smoother surface and hardening due to this strengthening induced. In summary, the main advantages of burnishing are roughness smothering,⁹,¹⁰ hardness increase,¹¹,¹² corrosion resistance,¹³⁻¹⁵ wear resistance,¹⁶,¹⁷ and fatigue life enhancement¹⁸,¹⁹ due to the effect of the compressive residual stresses.²⁰ Within the deforming processes, one of the most common and used is ball burnishing (BB). This process consists of a ball rolling over the surface and compressing the peaks against the valleys of a treated surface, creating a hardened and reconstructed layer at the surface.

Regarding roughness, it has been widely demonstrated that ball burnishing enhances the topography of a treated material, being the burnishing force the most influential parameter of the process.²¹,²² Recently, the importance of the roughness properties has been reported to achieve better results in terms of fatigue,²³ being the smoothest surfaces the optimal ones to enhance fatigue behavior. The ball-burnishing process induces a microstructure deformation, or restructuration, based on a grain-size refinement in a determined depth of affectation.¹⁴,²⁴ Typically, this depth is directly related to the compressive residual stresses and the increase of the hardness, deriving in a strengthening of the material.²⁵,²⁶ Specifically, for AISI 1045, the grain size reduction reported in cylindrical specimens was up to the 50% and an estimated depth of affectation of 0.2 mm, which contributed to an increase in the external hardness from 280 HBN to 326 HBN and induced a considerable amount of compressive residual stresses.²⁰ These results were translated to a direct fatigue improvement of 20% when the ball-burnishing process was applied. Travieso-Rodriguez et al²⁷ found that there exists a relation between the external hardness and the fatigue lifespan of ball-burnished AISI 1038 samples, obtaining better fatigue results when the hardness was enhanced.

During the last decade, a process combining conventional ball burnishing and ultrasonic vibration assistance called vibration-assisted ball burnishing (VABB) was introduced and used by several authors to enhance surface integrity and properties, such as external roughness and hardness.²⁸⁻³⁰ The vibration assistance consists of the relaxation of the quasi-static stress when a material is deformed, as it is during the ball burnishing, and therefore, it is easier to deform and obtain a higher depth of

affectation, enhancing the microstructure.³¹ Recently, Saffar et al³² analyzed the effect of the vibration assistance at 20 kHz on AL7075 alloy specimens and found a fatigue improvement of 32% compared to traditional ball burnishing, jointly with a 16% and 56% increase in superficial hardness and surface hardened depth, respectively.

This study aims to analyze and quantify the effect of the vibration assistance on AISI 1045 cylindrical specimens within a ball-burnishing process in terms of rotatory bending fatigue. First, S-N curves are obtained, and these results are matched with the microstructure reconstruction and the depth hardening for assisted and non-assisted ball-burnishing processes. As the main novelty, the effect of vibration assistance on rotatory bending fatigue specimens is studied. In addition, the crack growth and fracture mechanism will be analyzed.

## 2 | MATERIALS AND METHODS

### 2.1 | Fabrication and specifications

All specimens are manufactured from a cold-drawn bar of AISI 1045 steel provided by Ferros Gumà S.L. The 15-mm diameter bar is quenched and drawn, obtaining an initial hardness of 220–260 HV at the surface. The chemical composition is shown in Table 1.

The manufacturing process was executed in a 3-axis Pinacho SE 200 × 750 lathe with a FAGOR 8055 CNC module, obtaining the specimens specified in Figure 1 and following the ASTM E606/E606M-12 and DIN 50113 standards. The initial turning was performed using an ISO VNMG 160408-MM YG213 insert under lubrication conditions, using a cutting speed of 60 m/min and a feed of 0.10 mm/rev. For the finishing, it was used a DCMT 070204-PSF insert from Tungaloy, with a cutting speed of 120 m/min and a feed of 0.08 mm/rev with lubrication.

Once the machining is finished, the ball-burnishing (VABB or BB) operation is performed over the interest surface of the workpiece. The tool is based on a calibrated spring to calibrate the burnishing force applied. It also contains a piezoelectric-sonotrode module that gets excited at a frequency of 40 kHz, having a maximum amplitude of oscillation of 8 µm at the ball top. The balls used for this experiment are made of AISI 52100 chromium steel balls, with a hardness of 57-66 HRC; seven 2-mm diameter balls and one 10-mm diameter are used for the final setup. The bigger ball is responsible for deforming the peaks of the surface by rolling, while the small ones allow free rotation and lodging inside the tool cap of the 10-mm ball.
<table><caption>TABLE 1 Nominal chemical composition of AISI 1045 steel.</caption><thead><tr><th rowspan="2">Material</th><th colspan="8">Chemical composition by element in wt. (%)</th></tr><tr><th>C</th><th>Si, ≤</th><th>Mn</th><th>S, ≤</th><th>Cr, ≤</th><th>Ni</th><th>Mo</th><th>Cr + Mo + Ni, ≤</th></tr></thead><tbody><tr><td>AISI 1045</td><td>0.45</td><td>0.40</td><td>0.65</td><td>0.05</td><td>0.40</td><td>0.40</td><td>0.10</td><td>0.63</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>FIGURE 1 Ball-burnishing setup for the specimen's fabrication. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

## 2.2 | Preliminary design of experiments

A preliminary study with this tool was performed by Velázquez-Corral et al³³ on AISI 1045 fatigue samples, concluding that the combination of 90-N and five passes was optimal to enhance the fatigue lifespan and having a fair comparison between VABB and BB. However, the bibliography explains that the increase of the burnishing force derivates in a higher value of the compressive residual stresses, which benefits fatigue resistance.²⁰ For this reason, an initial full-factorial design of experiments (DoE) of high and low levels of burnishing force is suggested, considering the authors' previous experience. The DoE characteristics are shown in Table 2. The number of passes will be tested at three levels, while the vibration assistance will be activated (at 40 kHz) or deactivated (at 0 kHz).

## 2.3 | Rotatory bending fatigue

The fatigue specimens were tested in a rotatory bending machine, RFB-200-500. For the first stage, a total stress of 517 MPa was used for all the specimens, while for the second stage, the stress was modified by increasing or decreasing the weight held by the manual actuator with a pulley. The frequency of rotation was set to 1300 rpm for all specimens while controlling the temperature at the surface to not exceed 60°. During the second stage,

the stress values used to obtain the S-N curves were 596, 527, 497, 448, and 398 MPa, testing five samples of VABB and BB for each stress level. The stress values were calculated according to the Euler-Bernoulli equation shown in Equation (1):

$$S_{ap} = \frac{32FL}{\pi d^3} \qquad (1)$$

where $S_{ap}$ corresponds to the stress applied, $F$ is the force in weight applied in the pulley mechanism, $L$ is the beam distance from the pulley to the mobile chuck where the specimen is subjected, and $d$ is the diameter of the specimen tested (see Figure 2).

## 2.4 | Weibull statistics

Weibull statistics are commonly used in fatigue analysis to describe the distribution of the fatigue life of a material or component. Fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading, leading to failure under a stress level lower than its static strength.³⁴,³⁵ The Weibull distribution is a flexible distribution that can describe a range of failure mechanisms and is commonly used to model fatigue failure. The distribution has shape parameter ($\beta$) and scale parameter ($\alpha$). The shape parameter indicates the degree of scatter of the distribution, while the scale
<table><caption>TABLE 2 Factors, levels, and full-factorial array for the DoE.</caption><thead><tr><th rowspan="2">Factor</th><th rowspan="2">Symbol</th><th colspan="3">Level</th><th rowspan="2">Units</th></tr><tr><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>Force of burnishing</td><td>Fb</td><td>90</td><td>270</td><td>-</td><td>N</td></tr><tr><td>Number of passes</td><td>np</td><td>1</td><td>3</td><td>5</td><td>-</td></tr><tr><td>Frequency of the VA</td><td>f</td><td>0</td><td>40</td><td>-</td><td>kHz</td></tr><tr><th>Sample</th><th>Fb</th><th>np</th><th>f (kHz)</th><th>Nomenclature</th></tr><tr><td>1</td><td>90</td><td>1</td><td>0</td><td>90-1-0</td></tr><tr><td>2</td><td>90</td><td>1</td><td>40</td><td>90-1-40</td></tr><tr><td>3</td><td>90</td><td>3</td><td>0</td><td>90-3-0</td></tr><tr><td>4</td><td>90</td><td>3</td><td>40</td><td>90-3-40</td></tr><tr><td>5</td><td>90</td><td>5</td><td>0</td><td>90-5-0</td></tr><tr><td>6</td><td>90</td><td>5</td><td>40</td><td>90-5-40</td></tr><tr><td>7</td><td>270</td><td>1</td><td>0</td><td>270-1-0</td></tr><tr><td>8</td><td>270</td><td>1</td><td>40</td><td>270-1-40</td></tr><tr><td>9</td><td>270</td><td>3</td><td>0</td><td>270-3-0</td></tr><tr><td>10</td><td>270</td><td>3</td><td>40</td><td>270-3-40</td></tr><tr><td>11</td><td>270</td><td>5</td><td>0</td><td>270-5-0</td></tr><tr><td>12</td><td>270</td><td>5</td><td>40</td><td>270-5-40</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>FIGURE 2 RFB-200-500 setup for fatigue testing. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

parameter indicates the characteristic life of the distribution. The Weibull distribution can be used to estimate the probability of failure at a given stress level and to estimate the safe life of a component.³⁶,³⁷ By fitting experimental fatigue data to the Weibull distribution, the characteristic life and shape parameters can be determined.³⁸ These parameters can then be used to predict the failure probability of a component under a given stress level.

The probability density function (PDF) of the Weibull distribution is expressed as it is shown in Equation (2):

$$f(x) = \frac{\beta}{\alpha} \left(\frac{x}{\alpha}\right)^{\beta-1} e^{-\left(\frac{x}{\alpha}\right)^{\beta}} \quad (2)$$

The Weibull cumulative density function represents the probability that failure will occur before a given stress level and is expressed as it is shown in Equation (3). The probability of survival is defined in Equation (4).

$$P_f(x) = 1 - e^{-\left(\frac{x}{\alpha}\right)^{\beta}} \quad (3)$$

$$P_s(x) = 1 - P_f(x) = e^{-\left(\frac{x}{\alpha}\right)^{\beta}} \quad (4)$$

$P_f$ is defined as the failure probability, and $P_s$ is the survival probability; the independent variable represents the cycles to failure $N$. Both parameters from the Weibull distribution are determined by Equation (5):
$$ \ln\left(\ln\left(\frac{1}{1-P_f(x)}\right)\right) = \beta\ln(x) - \beta\ln(\alpha) \quad (5) $$

This expression is linear, so the shape parameter $\beta$ is determined by the previous equation. However, the failure probability has to be calculated in function of the fatigue results, and for that purpose, Equation (6) is proposed:

$$ P_f(x) = \frac{N_i - 0.3}{n + 0.4} \quad (6) $$

where $n$ represents the total number of samples within the same stress level and $N_i$ is the failure number sorted. The mean time to failure ($\mu$) represents the expected time of failure in a given system, and the variance ($\sigma^2$) represents the variability; they are expressed as Equations (7) and (8):

$$ \mu = \alpha\Gamma\left(1 + \frac{1}{\beta}\right) \quad (7) $$

$$ \sigma^2 = \alpha^2 \left[ \Gamma\left(1 + \frac{1}{\beta}\right) - \left(\Gamma\left(1 + \frac{1}{\beta}\right)\right)^2 \right] \quad (8) $$

Both parameters can be related by calculating the coefficient of variation (CV), defined as shown in Equation (9):

$$ CV = \frac{\sigma}{\mu} = \frac{\sqrt{\Gamma\left(1 + \frac{1}{\beta}\right) - \left(\Gamma\left(1 + \frac{1}{\beta}\right)\right)^2}}{\Gamma\left(1 + \frac{1}{\beta}\right)} \quad (9) $$

## 2.5 | Roughness acquisition

The topographical parameters analyzed for the prior surface in this investigation are the amplitude parameters specified in the standard ISO 25178, namely, Sa (represents the arithmetical deviation of the roughness profile of the sampling length), Sz (the sum of the most prominent peak height value and the most significant pit depth value), and Ssk and Sku (distribution of the material at different heights on the surface). Skewness, Ssk, is a measure of the asymmetry of the profile about the mean line. Negative skewness indicates that a more significant percentage of the profile is above the mean line, and a positive value indicates that a more significant percentage is below the mean line. The profiles with peaks removed or

deep scratches have negative skewness, whereas profiles with valleys filled in or high peaks have positive skewness. Kurtosis, Sku, values higher than 3 represent abrupt surfaces, while values lower than 3 represent smoother surfaces. The data filtering was done by eliminating the cylindrical surface, the atypical values, and a Gaussian noise filter.

## 2.6 | Scanning electron microscopy (SEM)

The microstructure analysis is done on a sectional cut surface of both burnished treated samples after mirror polishing and chemically etching the surfaces with Nytal for 10–15 s to reveal the grain boundaries. To see this effect, a JEOL JSM-7001F scanning electron microscopy (SEM) is used. The crack growth of the samples and the rupture mechanism will also be analyzed by looking at the resultant surface morphology.

## 2.7 | Microhardness measurements

To characterize the hardness of the fatigue specimens, an FFRI DM2D Vickers hardness testing machine was used to perform measurements at the cylindrical surface and along its sectional axis, according to the ASTM Standard E84, and applying 100 gf. Vickers hardness consists of a pyramidal diamond indenter applying a given load onto a target surface during 10 s, leaving a rhombical imprint measured through the average distance of both rhombical diagonals.

# 3 | RESULTS

## 3.1 | Preliminary fatigue results

The fatigue results of the first stage are shown in Figure 3.

As can be seen, there is an increasing trend in fatigue lifespan when the number of passes is increased and when the vibration assistance is activated, obtaining the best results when it is applied a high level of the number of passes and 40 kHz for the vibration assistance frequency. However, not a big difference between levels of burnishing force is appreciated, only noticing a slight improvement for the low level of force, but overlapping due to the standard deviation of the results obtained. However, the best results are obtained with 90-5-40 and 90-5-0. These results agree with other bibliographic references,³⁹⁻⁴¹ in which lower values of pressure
<figure><img src="image_4.png" /><figcaption>**FIGURE 3** Fatigue results in the first stage.</figcaption></figure>

resulted in higher fatigue values. This may be associated with the significant increase in surface defects, such as microcracks and surface spalls at higher ball-burnishing forces, which outweigh the beneficial effects of work hardening and residual compressive stresses. In addition, vibration assistance improves the fatigue results due to the possible hardening effect and increase of the residual stresses.²⁸

The analysis of variance compared the behavior of fatigue resistance by determining the mean effects plot of the factors and interactions between them and then compared to the experimental results shown in the previous section. Figure 4 shows the mean effects and interaction plots of fatigue results. First, the *p*-value analysis determines that the number of passes, the vibration assistance, the burnishing force, and the number of passes-vibration assistance interaction, in that order, are the most critical and significant parameters due to having a *p*-value lower than 5%. The number of passes reports a significant improvement when it is increased. The vibration assistance shows the VABB advantages against the BB in terms of fatigue resistance, mainly due to a possible hardening effect on the surface and the sublayers plus the increase of the compressive residual stresses and its affectation in-depth.²⁸ The interaction of the number of passes and the vibration assistance shows a correlation between the fatigue improvement and when higher levels are applied, as reported in the main effects plot. Regarding ball-burnishing implications, a positive and strong correlation exists between the two factors to increase the fatigue lifespan; increasing both factors results in better fatigue results. Once the results have been statistically analyzed, it can be concluded that the optimal combination to enhance the fatigue resistance within these input intervals is the 90-5-40 specimen. To evaluate the

contribution of the vibration assistance, both 90-5-40 and 90-5-0 combinations will be remanufactured and tested at different levels to obtain complete S-N curves in the second iteration shown in the following subsection.

First, the *p*-value analysis determines that the number of passes, the vibration assistance, the burnishing force, and the number of passes-vibration assistance interaction, in that order, are the most essential and significant parameters due to having a *p*-value lower than 5%. The number of passes reports a significant improvement when it is increased. The vibration assistance shows the VABB advantages against the BB regarding fatigue resistance. The burnishing force offers better results when the low level is applied. The interaction of the number of passes and the vibration assistance shows a correlation between the fatigue improvement and when higher levels are applied, as reported in the main effects plot. Once the results have been statistically analyzed, it can be concluded that the optimal combination to enhance the fatigue resistance within these input intervals is the 90-5-40 specimen. To evaluate the contribution of the vibration assistance, both 90-5-40 and 90-5-0 combinations will be remanufactured and tested at different levels to obtain complete S-N curves.

## 3.2 | Microstructure analysis

Figure 5 shows the cross-sectional microstructures from a BB and VABB virgin specimen (non-tested in fatigue). The superficial affectation of both partitions can be noticed due to the VABB and BB effect by reconstructing the surface due to the local plastic deformation. First, Figure 5A shows the final microstructure obtained after the BB process and exists a deformation in the direction
<figure><img src="image_5.png" /><figcaption>FIGURE 4 ANOVA results, taking the number of cycles to fatigue fracture as the output value, and the processing factors as the input values. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 5 Microstructure revealed after cross-sectioning and Nytal etching for (A) 90-5-0 (BB) specimen and (B) 90-5-40 (VABB) specimen. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
of the burnishing feed, but more importantly, there is a pearlite lamellae deformation resulting in a planar shape, which is characteristic of a ductile behavior deformation. The most noticeable is quite near the surface due to the significant effect of the process itself, as was expected, where a significant quantity of compressed pearlite lamellae can be observed. The end of the deformed zone has an estimated depth of affectation of 3–5 µm, which can be considered the final of the new microstructure evolution and, therefore, the apparition of a new coating due to the BB and, at the same time, the beginning of the bulky part of the material.

Second, the VABB specimen microstructure is represented in Figure 5B. As mentioned above, there is an evident deformation in the same direction as the burnishing feed due to the path of the ball rolling and compressing the peaks against the surface valleys. However, the first difference between processes is that the deformed zone is estimated in a more significant depth, around 8–9 µm, being higher than the conventional ball burnishing, and then measuring the exact contribution of the vibration assistance through this process, being the improvement almost twice of BB's affectation. This new microstructure can be considered as reconstruction and not only deformation because there are zones in which the direction of these lamellae is almost horizontal, and there is not so much space between them. It is also observed the presence of pearlite lamellae breakage close to the surface (see Figure 5B) when the VABB is applied. This pearlite lamellae breakage could be explained by the fact that the significant movement induced by the vibration assistance and the acoustoplasticity phenomenon activation are increasing the deformation rate. In addition, the presence of fragile fracture areas (see Figure 5B) may indicate the increase of the superficial hardness and the deeper affectation due to the major penetration of the vibration assistance. Both microstructures analyzed are compatible with a deformed dynamic nanocrystalline structure. However, adding the vibration assistance enhances the deformation provident from the conventional ball burnishing, thus having a complete reconstruction of the microstructure, which could be hardened, by comparing both specimens' “breaking” mechanism after the polishing.

## 3.3 | Topography analysis

The original roughness for all samples manufactured was 1.398 ± 0.574 µm, and the burnishing conditions applied are shown in Table 3. Both burnishing processes show an average roughness reduction higher than 80%, being VABB the best one and achieving a 90% of roughness

reduction. By comparing both processes, the main contribution of the VA is estimated to be a 7% improvement by itself, obtaining an average roughness of 0.125 µm. These results agree with the bibliography, pointing to a roughness reduction by ultrasonic assisting processes.²⁸,³⁰ The dynamic force superimposition to the static load can explain the roughness improvement. The tool motion by the vibratory effect acts on bulged edges. It deforms the surface asperities easily, combined with the softening effect during the acoustoplastic phenomena, resulting in a more uniform surface. This assumption can be corroborated by analyzing Figure 6. The 3D-colored map of BB and VABB specimens shows fewer height differences, especially observing the peaks marked as red between both specimens. The homogeneity is more visible visually and mathematically in the VABB specimen than in the BB specimen (see Table 3).

In terms of material distribution parameters, the stabilization to optimal Gaussian values (0 for $S_{sk}$ and 3 Gaussian) is evident when a burnishing process is applied. The initial topology is defined by a high, negatively skewed, and leptokurtic distribution, which converges closely to the Gaussian perfect value. In fact, by comparing the VABB and BB groups, the skewness distribution is enhanced by applying the VA. The initial high leptokurtic distribution for the kurtosis varies to platykurtic when the burnishing is applied, except for BB, which presents both distributions within the specimen sets.

## 3.4 | Fatigue results

The results of the intermediate iteration pointed to a burnishing force level of 90 N and five passes as the optimal conditions to enhance fatigue resistance. Under these conditions, it is executed more tests at different stress levels to complete all stress regimes of the S-N, while guaranteeing a higher repeatability to make accurate predictions in further statistical analysis. It was tested five stress levels (596, 527, 497, 448, and 398 MPa) and five repetitions for each level, resulting in 25 specimens for the VABB curve and 25 more for the BB curve. The resultant Wöhler curves are presented in Figure 7.

Results showed in Figure 7 evidence an improvement of the fatigue strength when the process is assisted, passing from 403 MPa in BB to 430 MPa in VABB, meaning a 6.54% improvement only by assisting the process when burnishing. These results verify also the consistency and acceptable variability at low and medium stress levels as it was expected. However, as near the fatigue strength is, more lifecycle dispersion is reported but within normal
<table><caption>TABLE 3 Roughness results.</caption><thead><tr><th>Group</th><th>Sa</th><th>ΔSa/Sa'</th><th>Sz</th><th>Ssk</th><th>Sku</th></tr></thead><tbody><tr><td>90-5-0 (BB)</td><td>0.227 ± 0.052</td><td>83%</td><td>1.254 ± 0.216</td><td>-0.396 ± 0.274</td><td>3.416 ± 0.874</td></tr><tr><td>90-5-40 (VABB)</td><td>0.125 ± 0.014</td><td>90%</td><td>0.627 ± 0.076</td><td>-0.118 ± 0.071</td><td>2.372 ± 0.144</td></tr><tr><td>M</td><td>1.398 ± 0.574</td><td>-</td><td>8.374 ± 3.071</td><td>-1.010 ± 0.326</td><td>4.297 ± 0.732</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>FIGURE 6 3D-height map of (A) 90-5-0 (BB) specimen and (B) 90-5-40 (VABB) specimen. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 7 S-N curves for 90-5-40 (VABB) and 90-5-0 (BB) specimens. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

ranges. In Equations (10) and (11), it is shown the Bas-quin approximation for both cases:

$$ \sigma_N^{BB} = 1369N^{-0.008747}; N = \left( \frac{1369}{\sigma_N^{BB}} \right)^{11.4325} \quad (10) $$

$$ \sigma_N^{VABB} = 1233N^{-0.07614}; N = \left( \frac{1233}{\sigma_N^{VABB}} \right)^{13.1337} \quad (11) $$

This improvement reported coincides with some other bibliographical references, which pointed to a fatigue resistance enhancement for vibration-assisted ball-burnished specimens.³² The explanation for these results can be synthesized in a more than possible hardening effect at the surface and subsurface layers. The microstructure images shown previously conclude that the depth of affectation is enhanced in VABB, and
significantly, a microstructure reconstruction is presented that could be compatible with the sublayer hardening effect through dynamic recrystallization. The superimposition of the dynamic component of the force results in a higher degree of plastic deformation, probably refining the grains, increasing the hardness, and inducing compressive residual stresses. Smoother roughness results reduce the possibility of superficial defects, which were also better on 90-5-40 specimens than 90-5-0. These improvements are limited to the tested conditions. However, the improvement of the vibration assistance under different conditions could lead to an eventual calculus of Marin's equation coefficient in further investigations for the VABB.

## 3.5 | Statistical analysis through Weibull

Weibull statistical analysis allows better exploitation of the fatigue results and evaluation of various structural elements' survival/reliability probability. The two-parameter Weibull distribution is commonly used to represent constant amplitude in fatigue life data, and it is used to model extreme values such as the lifetime in the fatigue test and the failure time. This is important due to the highly dispersed value obtained in the fatigue test (especially when the stress level tested is near the fatigue limit).

Applying the equations explained in previous sections, the cumulative probability distribution for each stress level of both processes is calculated and shown in Figure 8A. Looking at the results, all plot lines present good linearity, measured by the R-square, over 0.8–0.94, but there is one at 0.7, which is also considered good but is abnormal compared to the other set of samples. The 527 MPa stress level for VABB presents reduced linearity compared to other stress levels, mainly caused by the very low dispersion of a subset of samples (four of five samples were broken within the range of 86,000 to 89,000) and one last specimen at a considerable higher value, but still within the standard and accepted value after applying Chebyshev criterion. These demonstrated low variation between consecutive specimens and the stability of the process but made the linearization of the Weibull parameters due to the almost overlapping probability of failure calculus, having from 24% to 79.6% a small range of variation, and the last item survived a wider value. In case of not considering this sample, the reliability index of this function would be near 95%, meaning a reasonable Weibull distribution fitting.

Weibull parameters $\alpha$ and $\beta$ represent the scale and shape parameters. First, the scale seems accurate for all levels and is consistently higher for VABB than for BB,

which seems logical due to the higher fatigue results when assisting. The $\beta$ relates the dispersion of the values, and low values indicate a high dispersion, as it is usually seen at stress levels close to the fatigue strength. Results are shown in Table 4.

As seen in Table 4, the mean time to failure (MTTF) values are consistently higher when assisting, proving the enhancement of the fatigue resistance at all stress levels tested. However, the evolution of the coefficient of variation (CV), which relates the MMTF and the standard deviation (SD), presents differences between processes (see Figure 8B). For the VABB, there is a pretty stable value between the first four levels. However, it increases dramatically near the fatigue strength, which is expected due to this regime's high variability. On the other hand, BB shows a minimum during the second, while the highest is the fourth stress level. These values reinforce the idea that fatigue has to be treated as statistics and perform several runs to be able to detect upper and lower outlier values.

## 3.6 | Fractography

The BB and VABB specimens were examined to understand the effects of both processes on crack propagation after a rotatory bending fatigue test. The fracture sections show the typical features of carbide steels. They start at the external zone, where the burnishing process is performed, while finishing at the central zone of the specimen. Figure 9 represents two samples tested at the highest stress level (596 MPa), one being ball burnished and the other being vibration-assisted ball burnished. The life of the specimens was 9944 and 15,364 cycles, respectively. Both surfaces present a craggier fraction zone due to the high stress applied, showing cold-worked zones because of plastic deformations caused by compressive forces during ball burnishing and more accentuated in the VABB specimen.

The initiation of the fracture is caused by several initiation points nucleated near the treated surface (see Figure 9A,B), as it was expected for high-stress level testing.²⁰ This is due to the quick residual stress relaxation at the surface, deriving in crack nucleation near the treated zone. Due to the non-uniform flow of the material during the ball-burnishing process, some areas actuate as stress concentrators by having lower compressive residual stresses, then favoring the nucleation and propagation of the crack. An increase in the value and depth of the residual stresses will benefit the fatigue resistance, which could be enhanced by adding vibration assistance through a ball-burnishing process. Both specimens show similar behavior. However, a thin line over the two surfaces is
<figure><img src="image_9.png" /><figcaption>FIGURE 8 (A) Weibull plots for 90-5-40 (VABB) and 90-5-0 (BB) specimens, respectively. (B) Evolution of the CV in function of the MTTF.</figcaption></figure>

<table><caption>TABLE 4 Weibull results for 90-5-40 (VABB) and 90-5-0 (BB) fatigue specimens.</caption><thead><tr><th colspan="8">VABB</th></tr><tr><th>β</th><th>α</th><th>R<sup>2</sup></th><th>MTTF</th><th>CV</th><th>SD</th><th>S<sub>aq</sub> (MPa)</th></tr></thead><tbody><tr><td>4.50</td><td>12,382.14</td><td>0.84</td><td>11,299.68</td><td>0.25</td><td>2848.74</td><td>596</td></tr><tr><td>7.47</td><td>92,557.04</td><td>0.70</td><td>86,867.89</td><td>0.16</td><td>13,745.41</td><td>527</td></tr><tr><td>3.10</td><td>171,730.89</td><td>0.94</td><td>153,572.13</td><td>0.35</td><td>54,250.38</td><td>497</td></tr><tr><td>4.73</td><td>646,616.03</td><td>0.86</td><td>591,798.00</td><td>0.24</td><td>142,584.02</td><td>448</td></tr><tr><td>1.46</td><td>1,889,460.17</td><td>0.91</td><td>1,712,364.60</td><td>0.70</td><td>1,195,636.69</td><td>408</td></tr></tbody><thead><tr><th colspan="8">BB</th></tr><tr><th>β</th><th>α</th><th>R<sup>2</sup></th><th>MTTF</th><th>CV</th><th>SD</th><th>S<sub>aq</sub> (MPa)</th></tr></thead><tbody><tr><td>7.01</td><td>11,789.44</td><td>0.94</td><td>11,028.78</td><td>0.17</td><td>1851.61</td><td>596</td></tr><tr><td>12.46</td><td>71,133.17</td><td>0.93</td><td>68,260.73</td><td>0.10</td><td>6665.11</td><td>527</td></tr><tr><td>7.48</td><td>119,438.14</td><td>0.94</td><td>112,108.28</td><td>0.16</td><td>17,705.44</td><td>497</td></tr><tr><td>2.51</td><td>366,362.35</td><td>0.90</td><td>325,093.93</td><td>0.43</td><td>138,588.70</td><td>448</td></tr><tr><td>2.92</td><td>995,733.29</td><td>0.93</td><td>888,132.44</td><td>0.37</td><td>330,750.87</td><td>408</td></tr></tbody></table>
<figure><img src="image_10.png" /><figcaption>**FIGURE 9** Fatigue fractures of (A) 90-5-0 (BB) specimen broken at 9944 cycles and (B) 90-5-40 (VABB) broken at 15,364 cycles. Crack initiation detail of (C) BB specimen and (D) VABB specimen. Fragile fracture area of (E) BB specimen and (F) VABB specimen. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

appreciated (see Figure 9E,F). This “change of plane” reported has different depths, being 15–20 µm for the BB specimen and 60–65 µm for the VABB. The fracture mechanism of both specimens is compatible with fragile behavior, which the hardening of the surface could cause due to BB and VABB processes. However, this large difference in the depth could be explained by the fact that the vibration assistance enhances the mechanical work effectuated on the surface by the force superimposition of the dynamic load and the vibration assistance, then obtaining higher hardness values at major affectation

depths. The other option in case there is no such a big difference in hardness that could cause this uniform crack could be a change of mechanical behavior from compressive stress to tensile stress, coinciding with the “neutral axis” of stress.⁴² Also, if it is compared to the depth reported in the microstructural analysis, this difference is caused by the impossibility of seeing grain refinement or hardening effect on metallography. The more extensive lifespan reported by the VABB during the Wöhler analysis could be explained by the fact that the hardened coating generated during the deformation process is
wider than the conventional BB one, thus resisting a higher number of cycles at the same stress levels and reducing the crack propagation speed at the surface, actuating as a barrier.

The final of fracture is located at the center of both specimens, having similar behavior. This behavior is reported for both specimens because at bulk material there is no affectation from VABB or BB. Figure 10A,B shows the crack originated during the final shearing of the test, resulting in a ductile morphology characterized by the micro-dimples presence (Figure 10C).

## 3.7 | Micro-hardness results

The results in terms of depth are presented in Figure 11. Indeed, the VABB process has a more profound effect on the hardening phenomena than BB. As seen, superficial values (at 0.05 mm) show an initial difference. The BB curve decreases faster and converges into base material hardness value at an approximate

0.20–0.25 mm depth. At the same time, VABB hardness decreases more slowly and converges at nearly 0.3 mm of depth from the highest point. These results could confirm the fatigue resistance enhancement in terms of lifecycle. The hardened layer reduces crack propagation at the surface, and the more significant this layer, the more resistance to this growth. The brittle fracture mechanism can be explained by a larger hardened zone in VABB than BB and a hardness difference at similar depths to the unusual crack reported. However, the second hypothesis gains force because it demonstrates the positive effects of the VA in terms of hardening. However, the hardness profiles shown in Figure 11 do not experience an extremely abrupt decrease at some point, so this plan change could be partly explained by the mechanical behavior change explained before, plus the minor effect of hardening. To confirm this, in future investigations, the dislocation densities could be measured the dislocation densities in depth and have a complete view of the microstructure evolution in terms of depth.

<figure><img src="image_11.png" /><figcaption>FIGURE 10 (A) Crack originated during the exit at the center of the specimen. (B) Detail of the crack. (C) Resultant ductile morphology.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**FIGURE 11** Hardness profile in depth.
[Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

4 | DISCUSSION

Topologically, both surfaces are smoothed because the ball is rolling and smoothing out the bulged edges of the initial machining or the previous pass, so the probability of deforming the asperities is increased by augmenting the force and performing successive burnishing passes. Concerning the VA, the kinematic energy added to the process enhances the work-hardening but to a lower degree than the burnishing force,⁴³ explaining why VABB roughness values are better than BB when the same level of plastic deformation (burnishing force and several passes) is applied.

Microstructural results present pearlite-ferrite grain deformation due to the shearing of BB/VABB processes. An increase in the depth of affectation is reported when the VA is applied by a few microns, confirming that VA enhances the microstructure deforming rate and its homogeneity.⁴⁴,⁴⁵ Pearlite lamellae breakage instead of deformation, as seen in BB, indicates a higher deformation rate at more significant penetration depths. However, in BB, the lamellae are planar and stretched toward the burnishing, which shows a ductile behavior instead of the fragility present in the VABB sample. This microstructure found can be compatible with a highly deformed dynamic nanocrystalline structure, which is not present in the M sample, and therefore, this evolution is provoked by the ball-burnishing procedure and enhanced by the vibration assistance used in this experimentation. After this layer, the bulk microstructure appears, which is considered the end of the influenced layer in terms of dynamic recrystallization. This distance between the top surface and the end of the deformed layer is also directly dependent on deforming parameters, as the higher the deformation rate is, the depth of affectation may increase.⁴⁶

In the preliminary testing, there is an increasing trend in fatigue lifespan when the number of passes is

increased and when the vibration assistance is activated, obtaining the best results when it is applied a high level of the number of passes and 40 kHz for the vibration assistance frequency. However, not a big difference between levels of burnishing force is appreciated, only noticing a slight improvement for the low level of force, but overlapping due to the standard deviation of the results obtained. However, the best results are obtained with 90-5-40 and 90-5-0. These results agree with other bibliographic references,³⁹⁻⁴¹ in which lower pressure values resulted in higher fatigue values. This may be associated with the significant increase in surface defects such as microcracks and surface spalls at higher ball-burnishing forces that outweigh the beneficial effects of work hardening and residual compressive stresses. In addition, vibration assistance improves the fatigue results due to the possible hardening effect and increase of the residual stresses.²⁸ In the final iteration, it is found that fatigue strength is enhanced by 6.54% only by applying VA. After confirming it by applying Weibull statistics, the results are within the normal ranges. This analysis could be used for future industrial applications that require a prediction lifespan within specific safety ranges, depending on the application. The fractography study pointed out that a more significant superficial layer could contain compressive residual stresses and actuate as a crack propagation barrier, thus reducing the proliferation speed and enlarging the fatigue lifespan. This effect is mainly caused by the softening effect during the deformation process of the VA, favoring the higher degree of plastic strain induced at the surface, expressed as an increase of the residual stresses.²⁸ The accumulation of dislocation energy is enhanced in terms of depth, so the dynamic recrystallization is activated and derives in grain refinement, which increases the hardness of the coating and, especially, the depth effect.⁴³ This grain refinement was not visible at the metallography. However, the combination of this stress layer in the fractography picture with
the in-depth hardness profile points to a more than possible grain refinement in-depth, provoked by the plastic deformation of the ball pressure and enhanced by the vibration.

Overall, it is demonstrated that VABB enhances the main surface integrity factors and could potentially increase fatigue strength. However, further questions can be made regarding the effect of vibration assistance on other topological characteristics that could help to explain this phenomenology. First, a profile in-depth of residual stresses and the relaxation during the cycling could help to understand the fracture of the reported mechanism. In terms of microstructure, it would be necessary to perform an EBSD and TEM analysis at the surface to understand better the overall plastic deformation induced and deformed crystals reoriented and grains refined.

## 5 | CONCLUSIONS

Once all results have been shown, the main conclusions of this study are as follows:

* It is concluded that the VABB process provokes a more significant plastic deformation onto AISI 1045 cylindrical surfaces than BB. The complete reconstruction and fragile fracture areas point out an increase in the hardness by a possible grain size reduction. The hardness in-depth is also enhanced by means of the VA.

* The VABB process reduces up to 90% the mean average roughness, and the material distribution tends to be Gaussian, defined as perfect.

* The application of VA enhances the fatigue strength near 6.54%, meaning an increase of 27 MPa. Also, a Weibull model is obtained.

* The rupture mechanism found denotes that VABB creates a wider barrier to prevent crack propagation and nucleation than BB, explaining why VABB obtains better fatigue results than BB.

## AUTHOR CONTRIBUTIONS

**Methodology:** Eric Velázquez-Corral, Vincent Wagner, Ramón Jerez-Mesa, and Jordi Llumà. **Software:** Eric Velázquez-Corral, Vincent Wagner, and Jordi Llumà. **Validation:** Vincent Wagner, Ramón Jerez-Mesa, J. Antonio Travieso-Rodriguez, Jordi Llumà, and Gilles Dessein. **Formal analysis:** Eric Velázquez-Corral, Vincent Wagner, Jordi Llumà, and Gilles Dessein. **Investigation:** Eric Velázquez-Corral, J. Antonio Travieso-Rodriguez, and Jordi Llumà. **Resources:** Vincent Wagner, Ramón Jerez-Mesa, J. Antonio Travieso-Rodriguez, Jordi Llumà,

and Gilles Dessein. **Data curation:** Eric Velázquez-Corral and Jordi Llumà. **Writing—original draft preparation:** Eric Velázquez-Corral and Ramón Jerez-Mesa. **Writing—review and editing:** Eric Velázquez-Corral, Vincent Wagner, Ramón Jerez-Mesa, J. Antonio Travieso-Rodriguez, Jordi Llumà, and Gilles Dessein. **Visualization:** Eric Velázquez-Corral and Ramón Jerez-Mesa. **Supervision:** Vincent Wagner, Ramón Jerez-Mesa, J. Antonio Travieso-Rodriguez, Jordi Llumà, and Gilles Dessein. **Project administration:** Gilles Dessein. **Funding acquisition:** Ramón Jerez-Mesa, J. Antonio Travieso-Rodriguez, Jordi Llumà, and Gilles Dessein. All authors have read and agreed to the published version of the manuscript.

## ACKNOWLEDGMENTS

This research was funded by the Ministry of Science and Innovation of Spain, through grant PDC2022-133596-I00, which is greatly appreciated. We would like to thank bachelor's students Emilio Vega and Muhammad Zain for their help on executing some tests.

## CONFLICT OF INTEREST STATEMENT

The authors declare no potential conflict of interests.

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## ORCID

Eric Velázquez-Corral https://orcid.org/0000-0001-8037-7913

Jordi Llumà https://orcid.org/0000-0002-4982-206X

Ramón Jerez-Mesa https://orcid.org/0000-0002-5084-3108

J. Antonio Travieso-Rodriguez https://orcid.org/0000-0002-9273-5762

## REFERENCES

1. Alam MS, Das AK. Recent trends in surface cladding on AISI 1045 steel substrate: a review. *Funct Mater Appl Phys: FMAP-2021*. 2022;22:94.

2. Woo W-S, Lee C-M. A study of the machining characteristics of AISI 1045 steel and Inconel 718 with a cylindrical shape in laser-assisted milling. *Appl Therm Eng*. 2015;91:33-42.

3. Chan CY, Lee WB, Wang H. Enhancement of surface finish using water-miscible nano-cutting fluid in ultra-precision turning. *Int J Mach Tools Manuf*. 2013;73:62-70.

4. Sharma A, Babbar A, Jain V, Gupta D. Enhancement of surface roughness for brittle material during rotary ultrasonic machining. In: Matec web of conferences, Vol. 249 EDP Sciences; 2018:1006.

5. Pu Z, Outeiro JC, Batista AC, Dillon Jr OW, Puleo DA, Jawahir IS. Enhanced surface integrity of AZ31B Mg alloy by cryogenic machining towards improved functional
performance of machined components. *Int J Mach Tools Manuf.* 2012;56:17-27.

6. Gao YK. Improvement of fatigue property in 7050-T7451 aluminum alloy by laser peening and shot peening. *Mater Sci Eng A.* 2011;528(10-11):3823-3828.

7. Muñoz-Cubillos J, Coronado JJ, Rodríguez SA. Deep rolling effect on fatigue behavior of austenitic stainless steels. *Int J Fatigue*. 2017;95:120-131.

8. Dzionk S, Przybylski W, Ścibierski B. The possibilities of improving the fatigue durability of the ship propeller shaft by burnishing process. *Machines*. 2020;8(4):63.

9. Swirad S, Wdowik R. Determining the effect of ball burnishing parameters on surface roughness using the Taguchi method. *Procedia Manufacturing*. 2019;34:287-292.

10. Vaishya RO, Sharma V, Mishra V, et al. Mathematical modeling and experimental validation of surface roughness in ball burnishing process. *Coatings*. 2022;12(10):1506.

11. Basak H, Ozkan M, Toktas I. Experimental research and ann modeling on the impact of the ball burnishing process on the mechanical properties of 5083 Al-Mg material. *Kovové Materiály-Met Mater*. 2019;57(1).

12. Ramesh S, Kudva SA, Anne G, Manne B, Arya S. Optimization of ball-burnishing process parameters on surface roughness, micro hardness of Mg-Zn-Ca alloy and investigation of corrosion behavior. *Mater Res Express*. 2019;6(10):1065e8.

13. Cao C, Zhu J, Tanaka T, Pham DN. Investigation of corrosion resistance enhancement for biodegradable magnesium alloy by ball burnishing process. *Int J Autom Technol*. 2020;14(2): 175-183.

14. Ramesh S, Anne G, Kumar G, Jagadeesh C, Nayaka HS. Influence of ball burnishing process on equal channel angular pressed Mg-Zn-Si alloy on the evolution of microstructure and corrosion properties. *Silicon*. 2021;13:1549-1560.

15. Uddin M, Hall C, Santos V, Visalakshan R, Qian G, Vasilev K. Synergistic effect of deep ball burnishing and HA coating on surface integrity, corrosion and immune response of biodegradable AZ31B Mg alloys. *Mater Sci Eng: C*. 2021;118:111459.

16. Attabi S, Himour A, Laouar L, Motallebzadeh A. Effect of ball burnishing on surface roughness and wear of AISI 316L SS. *J Bio-and Tribo-Corros*. 2021;7:1-11.

17. Attabi S, Himour A, Laouar L, Motallebzadeh A. Mechanical and wear behaviors of 316L stainless steel after ball burnishing treatment. *J Mater Res Technol*. 2021;15:3255-3267.

18. Hua Y, Liu Z, Wang B, Hou X. Surface modification through combination of finish turning with low plasticity burnishing and its effect on fatigue performance for inconel 718. *Surf Coat Technol*. 2019;375:508-517.

19. 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(10): 2529.

20. Avilés R, Albizuri J, Rodríguez A, De Lacalle LL. Influence of low-plasticity ball burnishing on the high-cycle fatigue strength of medium carbon AISI 1045 steel. *Int J Fatigue*. 2013;55: 230-244.

21. de Oliveira DA, Martins AM, de Castro Magalhães F, Abrão AM. Characterization of the topography generated by low plasticity burnishing using advanced techniques. *Surf Coat Technol*. 2022;448:128891.

22. Dzierwa A, Markopoulos AP. Influence of ball-burnishing process on surface topography parameters and tribological properties of hardened steel. *Machines*. 2019;7(1):11.

23. Greitemeier D, Dalle Donne C, Syassen F, Eufinger J, Melz T. Effect of surface roughness on fatigue performance of additive manufactured Ti-6Al-4V. *Mater Sci Technol*. 2016;32(7): 629-634.

24. Silva-Álvarez DF, Márquez-Herrera A, Saldaña-Robles A, et al. Improving the surface integrity of the CoCrMo alloy by the ball burnishing technique. *J Mater Res Technol*. 2020;9(4):7592-7601.

25. Sova A, Courbon C, Valiorgue F, Rech J, Bertrand P. Effect of turning and ball burnishing on the microstructure and residual stress distribution in stainless steel cold spray deposits. *J Therm Spray Technol*. 2017;26:1922-1934.

26. Teimouri R, Skoczypiec S. Simulation of gradient grain size and hardness in ultrasonic burnishing process through multi-physics of contact mechanic and microstructure evolution. *Mech Mater*. 2022;174:104463.

27. Travieso-Rodríguez JA, Jerez-Mesa R, Gómez-Gras G, Llumà-Fuentes J, Casadesús-Farràs O, Madueño-Guerrero M. Hardening effect and fatigue behavior enhancement through ball burnishing on AISI 1038. *J Mater Res Technol*. 2019;8(6): 5639-5646.

28. Amini S, Bagheri A, Teimouri R. Ultrasonic-assisted ball burnishing of aluminum 6061 and AISI 1045 steel. *Mater Manuf Process*. 2018;33(11):1250-1259.

29. Ituarte IF, Salmi M, Papula S, et al. Surface modification of additively manufactured 18% nickel maraging steel by ultrasonic vibration-assisted ball burnishing. *J Manuf Sci Eng*. 2020; 142(7):71008.

30. Teimouri R, Amini S, Bami AB. Evaluation of optimized surface properties and residual stress in ultrasonic assisted ball burnishing of AA6061-T6. *Measurement*. 2018;116:129-139.

31. Liu Y, Wang L, Wang D. Finite element modeling of ultrasonic surface rolling process. *J Mater Process Technol*. 2011;211(12): 2106-2113.

32. Saffar S, Eslami H. Increasing the fatigue life and surface improvement of Al7075 alloy T6 by using ultrasonic ball burnishing process. *Int J Surf Sci Eng*. 2022;16(3):181-206.

33. Velázquez E, Marqués JA, Fernández I, Travieso JA, Jerez R, Llumà J. Preliminary study of the hardening effect and fatigue behaviour enhancement through vibration assisted ball burnishing on C45 steel. In: Iop Conference Series: Materials Science and Engineering, Vol. 1193 IOP Publishing; 2021:12029.

34. Danzer R, Supancic P, Pascual J, Lube T. Fracture statistics of ceramics-Weibull statistics and deviations from Weibull statistics. *Eng Fract Mech*. 2007;74(18):2919-2932.

35. Rinne H. *The Weibull Distribution: A Handbook*: CRC Press; 2008.

36. Sakin R, Ay I. Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites. *Mater Des*. 2008;29(6):1170-1181.

37. Schijve J. A normal distribution or a Weibull distribution for fatigue lives. *Fatigue Fract Eng Mater Struct*. 1993;16(8): 851-859.

38. Djeghader D, Redjel B. Weibull analysis of fatigue test in jute reinforced polyester composite material. *Compos Commun*. 2020;17:123-128.
39. Celik M, Caydas U, Akyuz M. The influence of roller burnishing process parameters on surface quality and fatigue life of AA 7075-t6 alloy. *Mater Werkst.* 2022;53(5):608-616.

40. Ibrahim AA. Fatigue life enhancement of carbon steel by ball burnishing process. *MEJ Mansoura Eng J.* 2020;33(2):1-9.

41. Zhang P, Lindemann J, Ding WJ, Leyens C. Effect of roller burnishing on fatigue properties of the hot-rolled Mg-12Gd-3Y magnesium alloy. *Mater Chem Phys.* 2010;124(1):835-840.

42. Kramer IR, Feng CR, Wu B. Dislocation-depth distribution in fatigued metals. *Mater Sci Eng.* 1986;80(1):37-48.

43. Teimouri R, Amini S. Analytical modeling of ultrasonic burnishing process: Evaluation of active forces. *Measurement.* 2019;131:654-663.

44. Zhang D, Li Y, Wang H, Cong W. Ultrasonic vibration-assisted laser directed energy deposition in-situ synthesis of NiTi alloys: effects on microstructure and mechanical properties. *J Manuf Process.* 2020;60:328-339.

45. Zhuang D-D, Du B, Zhang S-H, Tao W-W, Wang Q, Shen H-B. Effect and action mechanism of ultrasonic assistance on

microstructure and mechanical performance of laser cladding 316L stainless steel coating. *Surf Coat Technol.* 2022;433: 128122.

46. Gharbi F, Sghaier S, Al-Fadhalah KJ, Benameur T. Effect of ball burnishing process on the surface quality and microstructure properties of AISI 1010 steel plates. *J Mater Eng Perform.* 2011;20:903-910.

**How to cite this article:** Velázquez-Corral E, Llumà J, Jerez-Mesa R, Wagner V, Dessein G, Travieso-Rodriguez JA. Fatigue enhancement and hardening effect through ultrasonic vibration-assisted ball-burnishing process on AISI 1045 steel. *Fatigue Fract Eng Mater Struct.* 2024;47(1):203-219. doi:10.1111/ffe.14180