# Finite Element Simulation and Experimental Investigation of Nanostructuring Burnishing AISI 52100 Steel Using an Inclined Flat Cylindrical Tool

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## Abstract

**:**

## 1. Introduction

_{0.05}. It is obvious that this method of burnishing with different inclination angles of the indenter needs further investigation with the application of various methods, including numerical analysis and experiment.

- Development of numerical and finite element simulations of the burnishing process with the application of a cylindrical indenter with an adjustable inclination angle to the treated surface;
- Dynamometric studies of the process and establishment of the relationship of contact forces and the friction coefficient with the inclination angle of the indenter;
- Simulation and experimental study of the influence of the cylindrical indenter inclination angle and of burnishing force on the contact pressure and shear deformation;
- Establishment of microstructure change regularities, microhardness, and roughness depending on the inclination angle of the cylindrical indenter and its burnishing force.

## 2. Materials and Methods

#### 2.1. Material for Treatment and the Tool

#### 2.2. Mathematical and Finite Element Models

_{2}plastic flow theory is adopted, which demands determining the flow stress. One of the most common models of metal material mechanical processing is the Johnson–Cook model [16]. This model allows us to take into account not only strain hardening but also the dependence on the strain rate and thermal softening at a temperature increase. In the Johnson–Cook model, the equation for the yield stress has the following form:

^{−1}); ${T}^{*}=\left(T-{T}_{r}\right)/\left({T}_{m}-{T}_{r}\right)$ is homological temperature; T

_{r}is the specified temperature at which the model parameters are determined (usually a room temperature); T

_{m}is the melting point.

_{r}and T

_{m}are introduced. The values of the Johnson–Cook model parameters for AISI 52100 steel are presented in Table 1. There are parameter values from other authors’ articles that are accepted in this study. The parameters of the model differ significantly from different authors, as well as the stress–strain diagrams of AISI 52100 steel, which can be seen, for example, in Figure 6 in the article [17].

_{m}parameter was considered not as the melting point, but as a model parameter that allows us to more accurately describe experimental data using Formula (1).

_{2D}and in the three-dimensional one P

_{3D}will be as follows

_{2D}and S

_{3D}are the areas of the contact zones in the two–dimensional and three-dimensional cases, respectively.

_{c}is the width of the contact zone in meters in the three-dimensional case, and the corresponding width of the indenter contact (perpendicular to the plane of simulation) with the workpiece in the case of two-dimensional simulation;

_{c}is the length of the contact zone in meters, and the corresponding contact length of the indenter with the contacting bodies’ surface plane in the case of two-dimensional simulation in the formulation of a plane strain condition.

_{in}= 5 µm and the diameter of the cylindrical indenter d = 9 mm, it is possible to estimate the width of the contact zone along the direction perpendicular to the plane of simulation as follows

_{3D}more precisely through the circular segment area and the corresponding area of the cone plane section, then we can get the value for the coefficient k = 1.334. Thus, to match the forces, we have the values given in Table 2.

#### 2.3. Methods of Experimental Research

_{xy}at a distance x from the burnishing surface is determined by the inclination angle γ tangent to the influx boundary (Figure 5b).

_{x}, F

_{y}, F

_{z}are the contact forces acting in the direction of the coordinate axes.

## 3. Results

#### 3.1. Experimental Study of the Friction Coefficient and Cumulative Shear Deformation

_{y}) and feed (F

_{z}) (Figure 9).

_{y}and F

_{z}is observed at a small tilt angle of 0.5°, which causes the maximum friction coefficient μ = 0.33, calculated by Formula (9) (Figure 10). As the tilt angle increases, there is a gradual decrease in the friction coefficient, which reaches a minimum of µ = 0.26 at an angle of 2°. It is also important to note that during the entire track treatment, there are no trends in changes in contact forces, which characterizes the nanostructuring burnishing process as stationary.

#### 3.2. Numerical Results

#### 3.3. Investigation of the Influence of the Tilt Angle of the Cylindrical Indenter on the Microhardness, Microstructure, and Roughness of the Surface Layer

_{0.05}after nanostructuring treatment with a force of 250 N was carried out at five points of the burnishing tracks on each side of the split disc. The results of microhardness measurement depending on the indenter tilt angle are presented in Table 3 and Figure 17. The highest average value of microhardness 1508.2 HV

_{0.05}is reached at an angle of α = 2°, with the lowest 1152 HV

_{0.05}corresponding to the tilt angle of α = 0.5 °. An increase in the angle α of more than 2° leads to a decrease in microhardness. At an angle of α = 2.5°, the microhardness is 1412.4 HV

_{0.05}. The cause of the decrease in microhardness at an angle of α = 1.5° requires an in-depth additional study. The patterns of changes in microhardness in a thin surface layer generally correspond to the changes in stresses identified during finite element modeling of the process and the results of the experimental study of shear strain.

## 4. Discussion

_{0.05}, which proves the advantages of the proposed approach.

## 5. Conclusions

- FEM analysis indicates that the maximum values of contact pressure and plastic strain occur when the tilt angle is 2°. At a burnishing force of 250 N, the pressure reaches 3.5 GPa, the plastic strain is more than 1.2, and the temperature is 405 °C, which fully corresponds to the conditions of steel nanostructuring;
- Burnishing the planes of the split disk with a tool installed in a Kistler 9257BA dynamometer made it possible to establish that the friction coefficient decreases linearly from 0.33 to 0.26 as the tilt angle varies from 0.5° to 2.0°;
- 3D profilometry of the mating surfaces of the split disk enabled the determination of shear strains. True strains increase from 1.05 to 2.4 within the same range of tilt angle;
- The studies at an optimal burnishing force of 250 N and a feed rate of 0.04 mm/rev reveal that the minimum value of microhardness 1,152.6 HV
_{0.05}corresponds to an angle of 0.5°, while the maximum value of 1508.2 HV_{0.05}occurs at a tilt angle of 2°; - Transmission microscopy fully explains the achieved level of microhardness since the minimum size of nanocrystallites in the range of 15–30 nm occurs at indenter tilt angles of 2–2.5°;
- The surface roughness changes in the opposite direction to hardness, ranging from 120.3 to 161.8 nm at small tilt angles to 360.16 nm at an angle of 2.5°.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Temperature dependences of elastic properties and thermal coefficient of linear expansion (TCLE) of AISI 52100 steel.

Temperature, °C | Young’s Modulus E, GPa | Poison’s Ratio ν | Temperature, °C | TCLE α, 10^{−6}Degrees ^{−1} |
---|---|---|---|---|

22 | 201.33 | 0.277 | 22 | 11.5 |

200 | 178.58 | 0.269 | 204 | 12.6 |

400 | 162.72 | 0.255 | 398 | 13.7 |

600 | 103.42 | 0.342 | 704 | 14.9 |

800 | 86.87 | 0.396 | 804 | 15.3 |

1000 | 66.88 | 0.490 |

Temperature, °C | Density ρ, kg/m^{3} | Temperature, °C | Thermal Conductivity k, W/(m × °C) | Temperature, °C | Specific Heat c_{p}, J/(kg × °C) |
---|---|---|---|---|---|

0 | 7834 | 0 | 37.5 | 0 | 486 |

100 | 7809 | 100 | 40.5 | 100 | 519 |

200 | 7781 | 200 | 40.0 | 200 | 544 |

300 | 7749 | 300 | 38.0 | 300 | 578 |

400 | 7713 | 400 | 36.5 | 400 | 615 |

500 | 7675 | 500 | 34.5 | 500 | 662 |

600 | 7634 | 550 | 33.0 | 600 | 745 |

700 | 7592 | 600 | 32.0 | 700 | 2089 |

800 | 7565 | 650 | 30.0 | 750 | 649 |

900 | 7489 | 700 | 28.5 | 800 | 657 |

1000 | 7438 | 750 | 25.5 | 900 | 619 |

1100 | 7388 | 800 | 24.5 | 1000 | 636 |

1200 | 7340 | 850 | 25.0 | 1100 | 649 |

1270 | 7302 | 900 | 25.5 | 1200 | 665 |

1450 | 7026 | 1270 | 29.0 | 1270 | 672 |

1500 | 6995 | 1450 | 39.3 | 1450 | 765 |

1600 | 6934 | 1538 | 40.3 | 1480 | 777 |

1627 | 41.5 | 1510 | 791 | ||

1540 | 804 | ||||

1600 | 804 |

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**Figure 1.**The tool with a variable angle of cylindrical indenter inclination to the treated surface and with burnishing force adjustment.

**Figure 2.**Contact interaction diagram of a cylindrical indenter inclined to a plane surface during nanostructuring burnishing.

**Figure 5.**Experimental estimate of shear deformation in a split disc: (

**a**) diagram of the tool movement when burnishing the track on the disc surface; (

**b**) diagram to estimate shear deformation by the surface layer depth.

**Figure 6.**Diagram for determining contact and friction forces when processing a plane surface with a cylindrical indenter.

**Figure 7.**Nanostructuring burnishing of the split disc surfaces with a tool installed in a Kistler 9257BA dynamometer.

**Figure 9.**Dynamometry of reaction forces in contact with a cylindrical indenter: (

**a**) Tilt angle of 0.5°; (

**b**) Tilt angle of 2.0°.

**Figure 10.**Dependence of the reaction forces (

**a**) and friction coefficient (

**b**) on the tilt angle of the indenter.

**Figure 11.**Profilometry of the material influx of the split sample: (

**a**) tilt angle of 0.5°; (

**b**) tilt angle of 2.0°.

**Figure 14.**The dependences of (

**a**) the contact pressure and (

**b**) cumulative plastic strain on the burnishing force.

**Figure 15.**The dependences of (

**a**) the contact pressure and (

**b**) cumulative plastic strain on the tilt angle.

**Figure 18.**Images of the AISI 52100 steel upper layer microstructure: (

**a**) the initial heat-treated state; after nanostructuring burnishing at the tilt angle of the tool: (

**b**) tilt angle of 0.5°; (

**c**) tilt angle of 1°; (

**d**) tilt angle of 1.5°; (

**e**) tilt angle of 2°; (

**f**) tilt angle of 2.5°.

**Figure 19.**Example of a microprophile topography at different indenter tilt angles: (

**a**) tilt angle of 0.5°; (

**b**) tilt angle of 1°; (

**c**) tilt angle of 1.5°; (

**d**) tilt angle of 2°; (

**e**) tilt angle of 2.5°.

**Figure 20.**Change in the arithmetic mean deviation of the surface profile Ra depending on the tilt angle of the cylindrical indenter α.

Authors, Paper | A, MPa | B, MPa | n | C | m | T_{r}, °C | T_{m}, °C |
---|---|---|---|---|---|---|---|

Poulachon et al. [18] | 11.032 | 4783 | 0.0946 | 0 | 1 | 0 | 775 |

Guo et al. [19] and Ramesh et al. [20] | 688.17 | 150.82 | 0.3362 | 0.04279 | 2.7786 | 1370 | |

Shrot et al. [21] | 635.926 | 101.703 | 0.649 | 2.259 | 635.926 | ||

Guo et al. [22] and Bapat et al. [23] | 2482.24 | 1498.5 | 0.19 | 0.027 | 0.66 | ||

This paper | 322 | 994 | 0.34 | 0.043 | 0.597 | 20 | 6510 |

P_{3D}, N | P_{2D}, kN |
---|---|

100 | 354 |

150 | 531 |

200 | 708 |

250 | 885 |

No. | Tilt Angle | HV_{0.05} | Mean HV_{0.05} | SE of Mean | ||||
---|---|---|---|---|---|---|---|---|

1 | 0.5 | 1152 | 1127 | 1177 | 1104 | 1203 | 1152.6 | 17.54024 |

2 | 1 | 1481 | 1463 | 1301 | 1379 | 1412 | 1407.2 | 32.13783 |

3 | 1.5 | 1362 | 1286 | 1379 | 1331 | 1257 | 1323 | 22.85388 |

4 | 2 | 1446 | 1463 | 1596 | 1499 | 1537 | 1508.2 | 26.95812 |

5 | 2.5 | 1463 | 1446 | 1379 | 1395 | 1379 | 1412.4 | 17.63973 |

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**MDPI and ACS Style**

Kuznetsov, V.; Smolin, I.; Skorobogatov, A.; Akhmetov, A.
Finite Element Simulation and Experimental Investigation of Nanostructuring Burnishing AISI 52100 Steel Using an Inclined Flat Cylindrical Tool. *Appl. Sci.* **2023**, *13*, 5324.
https://doi.org/10.3390/app13095324

**AMA Style**

Kuznetsov V, Smolin I, Skorobogatov A, Akhmetov A.
Finite Element Simulation and Experimental Investigation of Nanostructuring Burnishing AISI 52100 Steel Using an Inclined Flat Cylindrical Tool. *Applied Sciences*. 2023; 13(9):5324.
https://doi.org/10.3390/app13095324

**Chicago/Turabian Style**

Kuznetsov, Victor, Igor Smolin, Andrey Skorobogatov, and Ayan Akhmetov.
2023. "Finite Element Simulation and Experimental Investigation of Nanostructuring Burnishing AISI 52100 Steel Using an Inclined Flat Cylindrical Tool" *Applied Sciences* 13, no. 9: 5324.
https://doi.org/10.3390/app13095324