# Simulation of the Fatigue Crack Initiation in SAE 52100 Martensitic Hardened Bearing Steel during Rolling Contact

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## Abstract

**:**

## 1. Introduction

^{9}cycles without failure, while exposing it to a different lubricant combined with electrical charging (ECCF mode) led to spalling caused by WEC after 10

^{8}load cycles, proving the fact that fatigue may be severely driven by external factors rather than pure mechanical loading.

## 2. Material

## 3. Simulation

_{c}), and particularly the critical resolved shear stress (CRSS) for a dislocation along with a slip band in order to start to move, are material-related parameters. These material properties can be obtained experimentally. The segment length (d

_{s}) is a model parameter to discretize the slip bands and the average shear stress on the slip band ($\Delta \underset{\_}{\tau}$) is calculated by means of finite element method (FEM) simulations.

_{11}= C

_{22}= C

_{33}= E(1 −$\nu $)/(1 − $\nu $ − 2$\nu $

^{2}) = 282 GPa, C

_{12}= C

_{13}= C

_{23}= E$\nu $/(1 − $\nu $ − 2$\nu $

^{2}) = 121 GPa, and C

_{44}= C

_{55}= C

_{66}= G = 80 GPa is assigned to the micro-model. The comprehensive explanation regarding the employment of the TM formulation in FEM simulations of the crack initiation procedure is provided in the works of Mlikota et al. [24,25,26,27,28,29] and Božić et al. [30,31,32].

^{2}with a thickness of 0.01 μm. The generated microstructure consists of 236 grains as shown in Figure 9c. More detailed explanations regarding the sub-modelling technique employed in this work is discussed by Mlikota et al. [24,25].

^{−2}μm. Since the purpose of this numerical study was the comprehension of the effect of microstructural porosities on the fatigue behaviour of the bearing components, the position, size, and number of the voids is different from the experimental observations in order to reduce the computational time and effort. In this sense, the position of the artificial pores is considered on the grain boundaries which are the boundaries of the different sections in FEM platform. The actual number of porosities in the real microstructure is also expected to be higher, but here, in order just to get an impression about the influence of porosities on the fatigue performance of the component, 18 pores are implemented in the area with higher stress concentration. All the pores have more or less the same size in the numerical modelling.

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Test bench with axial cylindrical roller bearings. 1 housing, 2 thrust bearing 2, 3 spacer, 4 thrust bearing 1, 5 shaft, 6 clamping bolt, 7 bearing seat, 8 drain pipe, 9 cap, 10 bearing support with the screwed-on pilot pin, 11 lid cup of spring package, 12 lid, 13 auxiliary bearing. Both test bearings consist of a housing and a shaft washer. The two shaft washers (b) are mounted on the shaft and rotate during testing; the two housing washers (a) are embedded in the housing/support [8].

**Figure 2.**Geometry factor (Y) vs. $a$/$\rho $ showing the three stages of crack growth from a spherical pore [12].

**Figure 3.**Schematic description of conventional fatigue crack growth behavior [13].

**Figure 6.**SE (

**up**) and BSE (

**down**) images of the microstructure in the depth of 165 μm below the raceway. The porosities within the microstructure are signified by the yellow circles.

**Figure 7.**Experimental S-N diagram of SAE 52100 martensitic hardened steel [15].

**Figure 8.**Schematic of a slip band as a combination of two parallel layers of dislocations colliding with a free surface at a specific angle.

**Figure 9.**(

**a**) Macro-model or global model of the bearing and the loading condition. (

**b**) Cross-section of the macro-model in the contact area between the cylinders and the rings. (

**c**) Micro-model developed in the area with the highest stress concentration.

**Figure 10.**Microstructural models of SAE 52100 martensitic hardened steel, without pores (

**left**) and with pores (

**right**).

**Figure 11.**Comparison between fatigue crack initiation of the microstructures without voids (

**a**) and with voids (

**b**).

**Figure 12.**Damage initiation in the microstructural model of SAE 52100 martensitic hardened steel without voids in steps 1 (

**a**), 10 (

**b**), and 36 (

**c**).

**Figure 13.**Damage initiation in the microstructural model of SAE 52100 martensitic hardened steel with voids in steps 1 (

**a**), 10 (

**b**), and 38 (

**c**).

**Table 1.**Chemical composition of SAE 52100 martensitic hardened steel in wt % [18].

Element | C | Cr | Mn | Si | Ni | Cu | Mo | Al | S | P |
---|---|---|---|---|---|---|---|---|---|---|

Percentage | 1.01 | 1.57 | 0.44 | 0.25 | 0.06 | 0.04 | 0.03 | 0.03 | 0.005 | <0.01 |

E (GPa) | G (GPa) | ν | R_{m} (MPa) | CRSS (MPa) | W_{C} | Slip Band Length d (μm) |
---|---|---|---|---|---|---|

210 | 80 | 0.3 | 962 | 160 | 69 | 1 |

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**MDPI and ACS Style**

Dogahe, K.J.; Guski, V.; Mlikota, M.; Schmauder, S.; Holweger, W.; Spille, J.; Mayer, J.; Schwedt, A.; Görlach, B.; Wranik, J.
Simulation of the Fatigue Crack Initiation in SAE 52100 Martensitic Hardened Bearing Steel during Rolling Contact. *Lubricants* **2022**, *10*, 62.
https://doi.org/10.3390/lubricants10040062

**AMA Style**

Dogahe KJ, Guski V, Mlikota M, Schmauder S, Holweger W, Spille J, Mayer J, Schwedt A, Görlach B, Wranik J.
Simulation of the Fatigue Crack Initiation in SAE 52100 Martensitic Hardened Bearing Steel during Rolling Contact. *Lubricants*. 2022; 10(4):62.
https://doi.org/10.3390/lubricants10040062

**Chicago/Turabian Style**

Dogahe, Kiarash Jamali, Vinzenz Guski, Marijo Mlikota, Siegfried Schmauder, Walter Holweger, Joshua Spille, Joachim Mayer, Alexander Schwedt, Bernd Görlach, and Jürgen Wranik.
2022. "Simulation of the Fatigue Crack Initiation in SAE 52100 Martensitic Hardened Bearing Steel during Rolling Contact" *Lubricants* 10, no. 4: 62.
https://doi.org/10.3390/lubricants10040062