# Bending Fatigue Behaviour and Fatigue Endurance Limit Prediction of 20Cr2Ni4A Gear Steel after the Ultrasonic Surface Rolling Process

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- It provides a reliable process and smooth surface. Once semi-finished samples are processed, the surface roughness can be greatly reduced and the residual stress can be introduced into the workpiece.
- (2)
- It provides a low force on the workpiece. The acting force is elastic and has no adverse effect on the machine tool.
- (3)
- As there is no high-temperature process, the gear material hardly undergoes structural transformation, and the original fine structure formed by heat treatment or forging can be maintained.
- (4)
- It provides uniform strengthening and stress control through the process parameters (static pressure, amplitude, step and processing speed, for example) and can control the strengthening layer depth. Moreover, there is a continuous transition between the reinforced layer and the matrix without stripping.

## 2. Materials and Methods

#### 2.1. Materials

^{−2}/s, to determine the tensile properties of steel. The tensile strength σ

_{b}of the 20Cr2Ni4A material is 1043 MPa, the yield strength σ

_{0.}

_{2}is 732 MPa, the elongation δ is 20%, the reduction in area ψ is 65%.

#### 2.2. Experimental Procedures

#### 2.2.1. Ultrasonic Surface Rolling Process

#### 2.2.2. Surface Roughness Test

^{#}sample shows the morphology of the sample without USRP treatment. The 1

^{#}, 2

^{#}and 3

^{#}samples show the morphologies after the USRP treatment. In comparison, it can be seen that the surface texture of the processed material tends to be uniform due to the friction reduction in the USRP. At the same time, the surface tool marks after milling are almost pressed due to the plastic flow of the metal. Moreover, as the static load level increases, the surface texture tends to be smoother, but it can be seen in Figure 3 that when the static load reaches 1963 N, the surface scratches become deep because the plastic deformation of the surface is too large due to the excessive static load, resulting in obvious machining cracks.

#### 2.2.3. Surface Microhardness Test

#### 2.2.4. Surface Residual Stress Test

#### 2.2.5. Crystal Structure Test

^{#}style was used as a control group, and the performance is compared for the 0

^{#}style (without USRP treatment) and the 2

^{#}style (standard USRP treatment), and 3

^{#}belongs to the USRP over processed group. From a macroscopic perspective, the style of the roughness, surface hardness and residual stress on the fatigue is severe, but from a microscopic perspective, is the same conclusion reached? Based on this question, this paper selects the standard 0

^{#}sample (without USRP treatment) and 2

^{#}sample (standard USRP treatment) to define the fatigue damage mechanism from a microscopic perspective. Transmission electron microscopy (TEM) was conducted on a Tecnai F20 instrument (American FEI Company, Hillsboro, OR, USA) and used to photograph the microscopic appearance of the surface layer treated by USRP. The XRD samples at the fracture were obtained by an MXP21VAHF X-ray diffractometer. The grain size and distribution of the sample were probed by an FEI quanta 650FEG thermal field emission scanning electron microscope and electron backscatter diffraction (EBSD).

#### 2.2.6. Three-Point Bending Fatigue Behaviour Test

^{#}, 2

^{#}, and 3

^{#}samples were selected for fatigue testing, and the corresponding S-N and P-S-N curves were obtained. Due to the large discreteness of the fatigue test, 30 samples were taken for a three-point bending fatigue test in each group to ensure the reliability of the data.

^{#}, 2

^{#}and 3

^{#}test groups prepared 18 samples for the experiment, respectively (2

^{#}samples are shown in Figure 4c). The cyclic characteristic coefficient is defined by the load ratio r = F

_{min}/F

_{max}= 0.5. The sinusoidal loading method was adopted, and the frequency is 79 Hz. Since the stress in the middle of the sample (S/2) is the greatest during the fatigue test, the surface treated by USRP is placed downward and within the span range to ensure the accurate measurement of the strengthening effect of USRP treatment.

## 3. Experimental Results

#### 3.1. Results of the Three-Point Bending Fatigue Performance

^{6}); when the life reaches high cycle fatigue (N > 10

^{6}), it obeys the Weibull distribution [22]. Therefore, assuming that the data at each group of stress levels conform to the two-parameter Weibull distribution, the distribution function equation is:

_{a}is the scale parameter, which is also the characteristic life of the material. The key to drawing the Weibull distribution curve is to use appropriate methods to estimate the values of the two N

_{a}and β parameters. The most widely used maximum likelihood estimation method is used to estimate the parameters of the Weibull curve. The two-parameter N

_{a}and β estimation equations are shown in Equations (2) and (3):

_{a}and β presented in Table 5 are obtained.

^{#}sample is smaller than that of both 2

^{#}and 3

^{#}. Among them, β is the slope of the Weibull curve, which is the shape parameter of the Weibull distribution. The larger the β value, the smaller the Weibull dispersion. This indicates that the data points of the 2

^{#}and 3

^{#}samples are more scattered, and the randomness of the fatigue failure is also large. This is related to USRP treatment. Increasing the static load reduces the surface roughness and increases the hardness and residual stress; however, in addition to the roughness, the other two parameters are randomly increased on the material surface, which causes the local stress state of the material to be unstable during the fatigue process and in turn causes the fatigue life to be excessively dispersed.

_{a}(as shown in Figure 5a–c), it is found that the life sequentially increases in the order of 0

^{#}, 2

^{#}, and then 3

^{#}. This is consistent with the expected effect. As the static load increases (the S value in Figure 5 corresponds to the stress value in GPa), the fatigue life increases. However, when the static load is too large, the surface properties of the material decrease. In contrast, a variety of fatigue crack sources are formed that are likely to cause fatigue cracking.

_{i}and fatigue life N

_{i}corresponding to different failure probabilities P need to be determined in conjunction with the Weibull distribution function. Based on the two-parameter Weibull distribution function, the bending fatigue life of the two process materials is calculated at three typical failure probabilities P (P

_{1}= 10%, P

_{2}= 50%, and P

_{3}= 90%). The calculation results are substituted into Equations (6) and (7), and the test results of the three models are presented in Table 6:

_{1}= 10%) is also the highest probability of survival. The bending fatigue limits of the 0

^{#}, 2

^{#}and 3

^{#}samples are 651.36, 918.88, and 904.21 MPa, respectively.

#### 3.2. Results of the Fatigue Fracture Morphologies

^{#}after 50 and 500 magnification times. It can be seen that crack initiation mainly occurs in the surface defects, and there are obvious inclusions on the surface. It shows that the 0

^{#}surface without USRP treatment has poor performance, and it is easy to form a fatigue crack source on the surface, which eventually leads to bending fatigue failure, and there is no obvious strengthening layer in Figure 7b. Figure 7c,d show the results of the fatigue fracture of sample 2

^{#}after 50 and 500 times. The shape of the fatigue fracture surface on sample 2

^{#}can be clearly divided. Moreover, the crack initiation site is not on the surface of the material but inside the material, and the final failure is caused by internal defects [24]. This is mainly because the surface properties of the 2

^{#}sample are optimized by the USRP. The surface properties have been significantly improved. Therefore, it is difficult to give priority to the formation of crack sources on the surface under the same stress loading, but at the secondary surface or the internal defects of the material. The fatigue performance of sample 2

^{#}is also better than that of sample 0

^{#}. Figure 7d shows that the strengthening layer is obvious, and its thickness is uniform. These USRP parameter settings are good, and its surface properties are the best. Figure 7e,f are the fatigue fractures of sample 3

^{#}. There are two crack initiation areas on the fracture for sample 3

^{#}, which are on the surface and inside of the material. This is related to the excessive static load parameter in the USRP, which leads to an uneven reinforcement layer, as shown in Figure 7f. The strengthening layer exists from 7.51 μm to 28.18 μm, the inclusion defects of the surface layer are also incorporated into the reinforcement layer, and then a large residual stress is introduced. The fatigue performance is relatively better than that for sample 0

^{#}without treatment.

## 4. Discussion

#### 4.1. Mechanism of the Surface Properties on the Fatigue Performance

#### 4.1.1. Effects of the Surface Mechanical Properties on the Fatigue Performance

#### 4.1.2. Effects of the Surface Morphology on the Fatigue Performance

^{#}is the largest, and that for sample 2

^{#}is the smallest. As the static load increases, the average surface roughness decreases first and then increases. When the static load is 1374 N, the minimum average surface roughness is 0.114 μm, which is approximately five times lower than that before strengthening, indicating a substantial reduction in the roughness of the material surface. When the static load is 1963 N, the static load is very large, which causes the surface plastic deformation to be too large, the surface roughness to increase, and the average surface roughness to slightly increase to 0.197 μm.

^{#}, and Figure 11b–d show the results for sample 2

^{#}. It can be seen from the figure that after the USRP treatment, the grain refinement and grain boundaries in the material increase due to the slippage, proliferation and entangling of the dislocations, which are caused by plastic deformation.

#### 4.2. Mechanism of the Cross-Sectional Structure on Fatigue Performance

#### 4.2.1. Effects of the Residual Stress on the Fatigue Performance

^{#}, 2

^{#}and 3

^{#}samples are 996.34, 1085.51 and 1073.19 MPa, respectively. It can be seen that the USRP treatment increases the material residual stress, and the existence of compressive stress and gradient in the residual compressive stress hinders the propagation of fatigue cracks and improves the fatigue strength of the material. However, excessive USRP treatment causes surface defects, a residual stress release, and an uneven distribution in the USRP treatment layer. This easily causes stress concentrations when subjected to bending loads that eventually form a fatigue source and decrease the fatigue life of the material.

#### 4.2.2. Effects of the Microhardness on the Fatigue Performance

^{#}and 3

^{#}materials increase significantly within a certain range. The thickness of the layer with an increased microhardness can reach more than 1000 μm and then reach the microhardness level before treatment. The reason is that with increasing depth, the plastic deformation degree is smaller, the grain size is larger and the residual austenite content is larger; that is, the effect of work hardening, fine grain strengthening and phase structure strengthening decreases layer by layer. The area closest to the surface is closer to the boundary, which is less constrained and more prone to deformation. At the same time, after the treatment, the surface of the sample recovers elastically, the density between the grains is reduced, and the maximum microhardness value never occurs. On the subsurface, this is consistent with the measured residual compressive stress distribution. The maximum microhardness value of sample 3

^{#}is 802 HV at a distance of 150 μm from the surface. This is because sample 3

^{#}undergoes an excessive USRP treatment, and the hardness increase is very obvious. The 2

^{#}sample is significantly improved, but it is 35 HV smaller than that of sample 3

^{#}.

#### 4.2.3. Effects of the Phase Structure on the Fatigue Performance

^{#}are too large, to accurately analyse the impact of the USRP treatment on fatigue performance, only samples 0

^{#}and 2

^{#}are selected for EBSD (Electron Backscattered Diffraction) analysis. The results are shown in Figure 15.

## 5. Conclusions

- (1)
- The 20Cr2Ni4A carburized gear steel herein has a high strain rate behaviour under the action of USRP. This behaviour significantly improves the bending fatigue performance of the steel. When the static load is 1374 N, the minimum surface roughness is 0.114 μm, and the maximum microhardness value and residual compressive stress value are 828 HV and 612 MPa, respectively. Compared with the samples without the USRP treatment, the surface roughness decreases by approximately 5 times, the surface microhardness increases by 27%, and the residual compressive stress on the surface increases by approximately 20 times. The fatigue strength of the material increases with decreasing surface roughness and increasing microhardness and residual compressive stress, and the optimal static load value is 1374 N.
- (2)
- The bending fatigue life of 20Cr2Ni4A carburized gear steel at 0, 1374, and 1963 N static load was tested, and the bending fatigue limit of the three samples was calculated by P-S-N curve fitting. The bending fatigue limits of samples 0
^{#}, 2^{#}, and 3^{#}are 651.36, 918.88, and 904.21 MPa, respectively. The fatigue fracture was analysed using SEM. It was found that the fatigue source in sample 0^{#}without the USRP treatment is on the sample surface; the fatigue source in sample 2^{#}after the standard USRP treatment is mostly on the subsurface or inside the sample during the fatigue process, and the gap between the fatigue stripes decreases. The fatigue source in sample 3^{#}with a large static load is generated unevenly on the surface, and the crack source is not singular in nature. - (3)
- According to the sample surface structure analysis of the influence of USRP treatment on the fatigue performance, USRP treatment significantly improved the surface roughness, increased surface hardness, introduced a lot of residual compressive stress, introduced a large number of dislocation multiplications, and further improved the fatigue performance. It was also found that excessive USRP treatment would lead to increased surface roughness. Although a large amount of residual compressive stress was introduced and surface hardness was improved, the fatigue performance was still reduced.
- (4)
- Combined with EBSD phase structure analysis and the change in gradient residual stress and microhardness, the section microstructure diagram of 20Cr2Ni4A steel after the USRP standard treatment process is drawn. The grain diagram is divided into five layers from the surface layer to the core, showing a symmetrical distribution. The grain size, residual stress and hardness of the gradient distribution inhibit the initiation and propagation of fatigue cracks, which is also the reason why the crack source takes place on the subsurface and the fatigue striation spacing decreases.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

USRP | Ultrasonic surface rolling process |

EBSD | Electron Backscatter Diffraction |

TEM | Transmission Electron Microscopy |

PH | Precipitation hardened |

SEM | Scanning electron microscopy |

UNSM | Ultrasonic Nano Surface Modification |

LSCM | Confocal laser scanning microscopy |

XRD | X-ray diffraction |

P-N | Predicted failure probability and Number of cycles |

P-S-N | Predicted failure probability and Stress and Number of cycles |

FWHM | Full width at half maximum |

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**Figure 4.**Three-point bending fatigue test device. (

**a**) Testing machine, (

**b**) three-point bending fixture, (

**c**) samples treated with URSP.

**Figure 5.**P-N curves of the three-point bending fatigue tests before and after USRP treatment. (

**a**) Sample 0

^{#}, (

**b**) sample 2

^{#}, and (

**c**) sample 3

^{#}.

**Figure 6.**P-S-N life curves from the three-point bending fatigue tests for (

**a**) sample 0

^{#}, (

**b**) sample 2

^{#}, and (

**c**) sample 3

^{#}.

**Figure 7.**SEM images of fatigue fractures for sample (

**a**) 0

^{#}at 50× magnification, (

**b**) 0

^{#}at 500× magnification, (

**c**) 2

^{#}at 50× magnification, (

**d**) 2

^{#}at 500× magnification, (

**e**) 3

^{#}at 50× magnification, (

**f**) 3

^{#}at 500× magnification.

**Figure 8.**SEM images of fatigue fractures after USRP: (

**a**) river pattern, (

**b**) extrusion surface, (

**c**) crack morphology, and (

**d**) fatigue pattern.

**Figure 11.**TEM images before and after USRP: (

**a**) 0

^{#}sample surface micromorphology, (

**b**) 2

^{#}sample surface micromorphology, (

**c**) 2

^{#}sample intercrystalline dislocations, (

**d**) 2

^{#}intercrystalline dislocations.

**Figure 15.**EBSD graphical results before and after the USRP treatment: (

**a**) EBSD tissue orientation of sample 0

^{#}, (

**b**) EBSD tissue orientation of sample 2

^{#}, (

**c**) grain orientation distribution of sample 0

^{#}, (

**d**) grain orientation distribution of sample 2

^{#}, (

**e**) surface retained austenite distribution of sample 0

^{#}, (

**f**) surface retained austenite distribution of sample 2

^{#}.

**Figure 16.**Schematic diagram of the microstructure of the carburized steel after USRP treatment: (

**a**) EBSD tissue orientation of the surface, (

**b**) 10 microns from the surface, (

**c**) 500 microns from the surface, (

**d**) 10,000 microns from the surface.

Element | Cr | Ni | Mn | Si | Al | S | O |
---|---|---|---|---|---|---|---|

Percentage composition | 1.25–1.65 | 3.25–3.65 | 0.30–0.60 | 0.15–0.35 | ≤0.01 | ≤0.005 | ≤0.0012 |

Heat Treatment Process | ||||
---|---|---|---|---|

Normalizing Temperature/°C | Carburizing Temperature/°C | High-Temperature Tempering/°C | Quenching Temperature/°C | Low-Temperature Tempering/°C |

950 | 920 | 640 | 800 | 150 |

Sample Number | Line Speed m/min | Step mm | Amplitude μm | Static Load N |
---|---|---|---|---|

0^{#} | 0 | 0 | 0 | 0 |

1^{#} | 2 | 0.08 | 20 | 785 |

2^{#} | 2 | 0.08 | 20 | 1374 |

3^{#} | 2 | 0.08 | 20 | 1963 |

Number | Mean Load (kN) | Alternating Load (kN) | Test Frequency (Hz) | Bending Stress Value (MPa) |
---|---|---|---|---|

1 | 35 | 11.6 | 79 | 1656 |

2 | 30 | 10 | 79 | 1422 |

3 | 28 | 9.3 | 79 | 1326 |

4 | 26 | 8.6 | 79 | 1230 |

**Table 5.**Weibull distribution function before and after the USRP treatment under different stress levels.

σ_{max} (MPa) | β | N_{a} | Fatigue Life Equivalent Value (10^{4} Cycle) | |||
---|---|---|---|---|---|---|

P_{1} = 10% | P_{2} = 50% | P_{3} = 90% | ||||

0^{#} | 1422 | 9.12 | 88,187 | 6.88 | 8.47 | 9.66 |

1326 | 2.54 | 312,447 | 12.87 | 27.04 | 43.41 | |

1230 | 4.34 | 804,220 | 47.88 | 73.91 | 97.46 | |

1073 | 3.07 | 1,764,083 | 84.82 | 156.57 | 231.41 | |

2^{#} | 1656 | 7.01 | 78,900 | 5.79 | 7.57 | 8.99 |

1422 | 3.09 | 141,436 | 6.83 | 12.56 | 18.53 | |

1326 | 3.15 | 581,996 | 28.45 | 51.80 | 75.87 | |

1230 | 3.84 | 2,886,819 | 160.70 | 262.41 | 358.68 | |

3^{#} | 1656 | 2.71 | 164,714 | 7.18 | 14.38 | 22.41 |

1422 | 1.75 | 469,887 | 13.02 | 38.12 | 75.61 | |

1326 | 3.03 | 817,778 | 38.93 | 72.47 | 107.67 | |

1230 | 2.50 | 1,311.653 | 53.28 | 113.26 | 183.16 |

Sample | Failure Probability (%) | m | C |
---|---|---|---|

0^{#} | 10 | 9.99 | 0.0296 |

50 | 10.87 | 0.3323 | |

90 | 11.72 | 0.0643 | |

2^{#} | 10 | 13.92 | 0.0096 |

50 | 13.69 | 0.1989 | |

90 | 13.69 | 0.7301 | |

3^{#} | 10 | 7.69 | 0.0006 |

50 | 7.08 | 0.2241 | |

90 | 7.06 | 1.4039 |

Sample | Surface Roughness Ra/μm | Average/μm | ||
---|---|---|---|---|

Area 1 | Area 2 | Area 3 | ||

0^{#} | 0.626 | 0.686 | 0.602 | 0.638 |

1^{#} | 0.118 | 0.115 | 0.130 | 0.121 |

2^{#} | 0.107 | 0.146 | 0.090 | 0.114 |

3^{#} | 0.185 | 0.233 | 0.173 | 0.197 |

Incident Angle (2θ/°) | a | b | c | |
---|---|---|---|---|

44.780 | 65.226 | 82.400 | ||

0^{#} | β_{1} | 0.458 | 0.554 | 0.599 |

β_{1}^{2} | 0.210 | 0.307 | 0.359 | |

2^{#} | β_{2} | 0.460 | 0.769 | 0.786 |

β_{2}^{2} | 0.212 | 0.591 | 0.618 | |

Relative variation ratio | Δ = 100% × (β_{2}^{2} − β_{1}^{2})/β_{1}^{2} | 7.62% | 92.51% | 72.14% |

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**MDPI and ACS Style**

Wang, Z.; Huang, Y.; Xing, Z.; Wang, H.; Shan, D.; Xie, F.; Li, J.
Bending Fatigue Behaviour and Fatigue Endurance Limit Prediction of 20Cr2Ni4A Gear Steel after the Ultrasonic Surface Rolling Process. *Materials* **2021**, *14*, 2516.
https://doi.org/10.3390/ma14102516

**AMA Style**

Wang Z, Huang Y, Xing Z, Wang H, Shan D, Xie F, Li J.
Bending Fatigue Behaviour and Fatigue Endurance Limit Prediction of 20Cr2Ni4A Gear Steel after the Ultrasonic Surface Rolling Process. *Materials*. 2021; 14(10):2516.
https://doi.org/10.3390/ma14102516

**Chicago/Turabian Style**

Wang, Zhiyuan, Yangfei Huang, Zhiguo Xing, Haidou Wang, Debin Shan, Fengkuan Xie, and Jiming Li.
2021. "Bending Fatigue Behaviour and Fatigue Endurance Limit Prediction of 20Cr2Ni4A Gear Steel after the Ultrasonic Surface Rolling Process" *Materials* 14, no. 10: 2516.
https://doi.org/10.3390/ma14102516