# Fretting Fatigue in Mechanical Joints: A Literature Review

^{*}

## Abstract

**:**

## 1. Introduction

- Wear of the surfaces;
- A considerable reduction in fatigue life.

#### 1.1. Contact Mechanics

- ${p}_{0}=\frac{2P}{\pi a}$
- ${a}^{2}=\frac{8PR\left(1-{\nu}^{2}\right)}{\pi E}$

- ${q}^{\prime}\left(x\right)=0$ if $a>\left|x\right|>c$
- ${q}^{\prime}{}^{\left(x\right)}=-\mu {p}_{0}\frac{c}{a}\sqrt{1-{\left(\frac{x}{c}\right)}^{2}}$ if $\left|x\right|<c$

**Figure 2.**Contact configuration of the Cattaneo–Mindlin problem, with normal and tangential contact load distribution.

#### 1.2. Fretting Damage in Structural Joints

## 2. Press Fitted Shaft-Hub Joints

- $SWT={\sigma}_{max}\xb7{\epsilon}_{a}$, where ${\sigma}_{max}$ is the maximum normal stress in one cycle on the critical plane and ${\epsilon}_{a}$ is the normal strain amplitude on the critical plane [50];
- $FS=\frac{\Delta \gamma}{2}\left(1+\alpha \xb7\frac{{\sigma}_{max}}{{\sigma}_{y}}\right)$, where $\Delta \gamma $ is the maximum shear strain range, ${\sigma}_{max}$ is the maximum normal stress in one cycle, ${\sigma}_{y}$ is the yield stress and $\alpha $ can be approximated to 0.5 [51].

#### Most Significant Results

- In fretting conditions, cracks develop near the edge of the contact area, corresponding to the peak contact stress. However, if fretting wear occurs, cracks have been reported to initiate at the inner surface of contact area because of peak stresses occurring at the edge of the wear scar. At the same time, fretting crack initiation at the contact edge is significantly reduced because of the cracks getting ground off;
- A stress relief groove and, possibly, a hub overlap, increases fretting fatigue life. Mixed results have been reported about the influence of the groove radius. More experimental results are needed in order to define the benefits or disadvantages of increasing or decreasing the groove radius;
- It was reported that no significant increase in fatigue strength under press fitting can be expected for high strength steels;
- Use of fretting fatigue criteria such as the SWT and the FS criterion was found to be useful to identify the crack nucleation location. More research is needed in order to assess the use of these parameters;
- Linear elastic fracture mechanics (LEFM) and TPP numerical routine proved to be efficient tools for the evaluation of the crack growth life.

## 3. Dovetail Joints

- Increasing the sheet loading increased the width, roughness and depth of the fretted region;
- For equal condition of loading and same material, fretting reduced fatigue life;
- For equal condition of loading and material, frequency did not affect the fretting phenomenon.

^{6}cycles.

^{6}cycles.

^{6}cycles.

**Figure 25.**A schematic drawing of the dovetail fixture developed by Conner and Nicholas [72].

- a rough correlation between the SWT parameter and contact damage appeared to exist;
- contact stress values appeared to be strongly dependent on the coefficient of friction;
- the stress gradient died out at approximately the same depth for all gradients. This is significant because if this occurs for a wide range of geometries and frictional values, the bulk contact stress can be used to determine the likelihood of crack growth, given that contact stresses will initiate a crack to that depth [75].

^{6}to 10

^{7}cycles, the stress intensity factor fields were shown to be different for each fixture; it was suggested to compute the fracture mechanics driving force for each fixture and to compare it with the stress intensity factor field threshold. In particular, fixture A and B were found to produce stress conditions where any crack that nucleated would continue to propagate and were, therefore, loads that could be related to a criterion for crack nucleation. Fixture C instead showed a stress intensity factor field that allowed for cracks to nucleate and arrest until the load required to exceed the long crack growth threshold was surpassed. Thus, the load causing failure in this case related to the threshold stress intensity factor range and not to a nucleation criterion. It can be concluded that the comparison between three fixtures highlights that a simple fracture mechanics model is not sufficient to explain all the experimental results [79].

- two load cells in order to be able to directly measure the contact forces applied to the specimen;
- the heating elements capable of simulating the temperature conditions in the attachment region of the turbine rotor.

_{mr}(constant when the blade is rotating at constant angular velocity), the aerodynamic force F

_{p}(resulting in axial and tangential force components, cyclic in nature at a constant angular velocity of the rotor) and the moments produced by the eccentricity of pressure with respect to CG (M

_{XG}, M

_{YG}, M

_{ZG}). The material taken into consideration was an aero engine Ti-alloy, with a Young Modulus of 110 GPa, Poisson’s ratio of 0.3 and density equal to 4500 kg/m

^{3}. They first carried out an analysis for both the geometries applying just the angular velocity in order to understand the skew effect of the dovetail interface. They then carried out an analysis for each different force acting on the dovetail, another analysis with the application of both centrifugal force and aerodynamic force, and, lastly, an analysis in which all the loads were applied at the same time. They concluded that the skew effect increases the peak contact pressure and slip by a factor of two compared to a straight dovetail slot. This happens because the skew angle generated an additional moment. The skew effect also tends to shift the pressure distribution peak to the lower contact edge, compared to the peak line contact loading obtained from a straight dovetail. The distributions of other contact variables were also found to be considerably different. On the loaded skewed geometry blade, the contact pressure, slip and surface stresses were found to be significantly higher.

- Summation approach: this approach considered the summation of the FFDP evaluated for two slip directions;
- Maximum principal-shear stress: this approach considered the use of maximum principal stress in place of ${\sigma}_{T}$ and the replacement of shear stress $\tau $ with maximum shear stress considering all the stress components. The formula would then become:

^{7}cycles.

- traditional SWT parameter ($SWT={\sigma}_{max}\xb7{\epsilon}_{a}$ where ${\sigma}_{max}$ is the maximum normal stress in one cycle on the critical plane and ${\epsilon}_{a}$ is the normal strain amplitude on the critical plane [50]);
- averaging SWT introducing a weight function since it was reported that crack initiation parameters (such as SWT) provided conservative life predictions in the case of high stress gradients. The averaged SWT parameter is expressed as follows:

#### Most Significant Results

- Different dovetail skew angles were not found to substantially influence fretting fatigue life;
- Coatings and shot-peening were found to be effective for raising the resistance to fretting fatigue crack initiation. More types of coatings should be tested in order to give better guidelines;
- Analytical studies indicate that smaller punch radiuses are expected to improve fretting fatigue behaviour, but it was highlighted that the effect of vanishing small radiuses is unknown and therefore that research on the matter is needed;
- The Ruiz criterion successfully located the initiation location, but it was highlighted that the parameters used by Ruiz do not have a direct physical interpretation and, therefore, are not generally suitable for quantitative analyses. Other parameters have been mathematically developed, although validation on different geometries is currently lacking;
- The use of the SWT criterion, especially in its weighted variant [86] and modified variant [91] were found to be able to successfully predict crack nucleation site on specimens. The modified variants also successfully predicted the fretting fatigue life of specimens. However, it was highlighted that these approaches must be further tested under different loading conditions in order to be fully validated;
- The TSR-CSR diagram was found to be a useful tool for the prediction of fretting fatigue failure, even though it is different for every material, and so it has to be retrieved for each material tested or used;
- The linear elastic fracture mechanics (LEFM) approach was also found to be generally a good tool for the evaluation and prediction of crack growth lives;

## 4. Bolted Joints

- Evaluation of the general response of the bolted joint when rotating bending and other remote loading conditions are applied (macroscopic response—level 1);
- Evaluation of the contact traction at the interface between the parts in contact (contact interactions and interface characterisation—level 2);
- Evaluation of the full stress field near the critical damage areas (stress field or local response—level 3).

#### Most Significant Results

- In fretting contact conditions, increasing the tightening torque is generally a good approach for improving fretting fatigue life. This is explicable with the consequent lowering of sliding happening in the contact area;
- It has also been highlighted that, for low tightening torques, fretting fatigue does not occur. This can be visually explained by means of fretting maps, like the one used by Benhamena et al. [100]. It has been found that for low contact loads, and regardless of high or even very low slipping, fretting fatigue might not occur. For more information about fretting maps, please refer to [108,114,115,116];
- Bonding the mating surfaces does improve fatigue life, but is a limitation affecting the disassembly of the joint;
- Use of fretting fatigue criteria such as the SWT, the FS and the Ruiz criterion was found to be useful to identify the crack nucleation location. More research is needed in order to assess the use of these parameters;
- Applying Ni-P coatings was proven to improve fretting fatigue life;
- Applying lubrication between the contact surfaces has been reported to have mixed results. The results may arise from different initial experimental conditions. More studies need to be carried out, in order to assess more clearly the advantages and disadvantages of the use of lubricants;
- The TSR-CSR diagram was found to be a useful tool for the prediction of fretting fatigue failure also for bolted joints.

## 5. Conclusions

- Under fretting conditions, cracks develop near the edge of the contact area, corresponding to the peak contact stress. However, if fretting wear occurs, cracks have been reported to initiate at the inner surface of contact area because of peak stresses occurring at the edge of the wear scar. At the same time, fretting crack initiation at the contact edge is significantly reduced because of the cracks getting ground off;
- Relative slip and contact pressure are fundamental parameters that directly influence, together with wear, the local stress–strain contact state. Therefore, evaluating the joint action of these parameters is important for predicting the macroscopic behavior of the joint, as different combinations can lead either to an improvement or a deterioration of fretting fatigue life;
- Multiaxial fatigue parameters used with the critical plane approach (as SWT and FS) appear to be helpful in locating fretting fatigue crack initiation location for all kind of joints. However, the total predicted life is strongly influenced by the choice of the initial crack length, which is arbitrary;
- The TSR-CSR diagram was found to be a useful tool for the prediction of fretting fatigue failure both in dovetail and bolted joints. Research for the application of this criterion on press-fitted shaft/hub joints is lacking, however, and is therefore needed. It must also be highlighted that the TSR-CSR diagram is different for each material and so it must be retrieved for any new, used or tested material;
- The application of the linear elastic fracture mechanics (LEFM) approach was also found to be optimal for the evaluation and prediction of crack growth lives for all the joints covered in this review;
- Coatings and shot-peening were found to be effective for raising the resistance to fretting fatigue crack initiation. More types of coatings should be tested, however, since the results refer to a very limited group of treatments; fretting maps are also very useful and easy to read tools that can give a visual and immediate description of the fretting regime (or lack of) occurring in the joint.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Contact configuration for Nowel–Hills solution with normal and tangential contact load distribution.

**Figure 5.**Schematics of the fretting fatigue test: (

**a**) schematics of the load applied to the shaft-hub coupling; (

**b**) relative slip measurement sensor; (

**c**) schematics of the shaft-hub and sensor assembly before and (

**d**) after applying the load [30].

**Figure 6.**Fretting fatigue testing machine [31].

**Figure 7.**(

**A**) Type A, (

**B**) type B, (

**C**) Type C, (

**D**) Type D and (

**E**) Type E shaft-hub specimens used by Nishioka and Hirakawa [34].

**Figure 8.**Effect of stress relief groove on fretting fatigue life of the axle. Reprinted with permission from Ref. [38]. Copyright 2022 Elsevier.

**Figure 11.**(

**a**) Specimen, (

**b**) general FEA model and (

**c**) crack growth FEA model used by Gutkin and Alfredsson Reprinted with permission from Ref. [23]. Copyright 2022 Elsevier.

**Figure 12.**Radial press-fit grip-ultimate number of cycles. Experimental results include both crack initiation and propagation life, whereas the numerical results only contain crack propagation to failure Reprinted with permission from Ref. [23]. Copyright 2022 Elsevier.

**Figure 15.**Evolution of the shaft-hub specimens designed by Croccolo et al. [48].

**Figure 17.**Schematics of the fretting fatigue apparatus. Reprinted with permission from Ref. [53]. Copyright 2022 Elsevier.

**Figure 19.**General arrangement of (

**a**) test piece and (

**b**) dovetail profile. Reprinted with permission from Ref. [59]. Copyright 2022 Springer Nature.

**Figure 20.**(

**a**) Representation of test configuration designed to simulate blade root loading condition and (

**b**) Test load train schematic. Reprinted with permission from Ref. [65]. Copyright 2022 Elsevier.

**Figure 21.**Geometry of the indenter. 2a is the length of the straight part of the punch, 2b is the contact length [66].

**Figure 22.**The contact problem for the radiused flat contact geometry (symmetrical contact): pressure distribution. Reprinted with permission from Ref. [67]. Copyright 2022 Elsevier.

**Figure 31.**Loads acting on the rotor: (

**a**) centrifugal and aerodynamic loads on the blade and (

**b**) 3D forces and moments at blade CG. Reprinted with permission from Ref. [81]. Copyright 2022, Elsevier.

**Figure 33.**(

**a**) Tangential stress range and compressive stress range with respect to load amplitude (

**b**) S-N curve for the fretting fatigue test of dovetail joint. Reprinted with permission from Ref. [83]. Copyright 2022 Elsevier.

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## Share and Cite

**MDPI and ACS Style**

Croccolo, D.; De Agostinis, M.; Fini, S.; Olmi, G.; Robusto, F.; Scapecchi, C.
Fretting Fatigue in Mechanical Joints: A Literature Review. *Lubricants* **2022**, *10*, 53.
https://doi.org/10.3390/lubricants10040053

**AMA Style**

Croccolo D, De Agostinis M, Fini S, Olmi G, Robusto F, Scapecchi C.
Fretting Fatigue in Mechanical Joints: A Literature Review. *Lubricants*. 2022; 10(4):53.
https://doi.org/10.3390/lubricants10040053

**Chicago/Turabian Style**

Croccolo, Dario, Massimiliano De Agostinis, Stefano Fini, Giorgio Olmi, Francesco Robusto, and Chiara Scapecchi.
2022. "Fretting Fatigue in Mechanical Joints: A Literature Review" *Lubricants* 10, no. 4: 53.
https://doi.org/10.3390/lubricants10040053