Failure Analysis of Dovetail Assemblies Under Fretting Load

8/13/2019 Failure Analysis of Dovetail Assemblies Under Fretting Load

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Review

Failure analysis of dovetail assemblies under fretting load

Da-Sheng Wei , Shan-Hu Yuan, Yan-Rong Wang

School of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China

a r t i c l e i n f o

Article history:

Received 12 January 2012Received in revised form 9 June 2012

Accepted 21 June 2012

Available online 31 August 2012

Keywords:

Dovetail assemblies

Contact

Fretting fatigue

Life prediction

High gradient stress

a b s t r a c t

Fretting wear and subsequent fatigue are the damage processes caused by micro slip under

high cycle fatigue (HCF) loading between contacting structural members. Fretting fatiguehas become recognized as a major failure mode in aircraft, which can reduce the life of a

structure by as much as 4060% under certain conditions. There are two keys to evaluating

the fretting fatigue life of dovetail assemblies: one is determining the high stress gradients

at the edge of the contact zone under complex loading by means of numerical methods,

especially the finite element method (FEM); the other is finding suitable parameters to cor-

relate with fretting fatigue life to improve predictive accuracy.

2012 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

2. Two keys in the analysis of fretting failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

2.1. Numerical calculation of fretting contact stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

2.2. Fretting fatigue test and life prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

2.2.1. Fretting fatigue specific parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

2.2.2. Multi axial fatigue parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

2.2.3. Methods based on fracture mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

3. Several important factors on fretting fatigue life and corresponding treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

3.1. Distinguishing the propagation life from the total life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

3.2. Effect of geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

3.3. Effect of loading ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

3.4. Effect of coefficient of friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

4. Study on fretting fatigue performance of dovetail in the fan of aero engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

1350-6307/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engfailanal.2012.06.007

Corresponding author.

E-mail address: [email protected](D.-S. Wei).

Engineering Failure Analysis 26 (2012) 381396

Contents lists available at SciVerse ScienceDirect

Engineering Failure Analysis

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http://dx.doi.org/10.1016/j.engfailanal.2012.06.007mailto:[email protected]://dx.doi.org/10.1016/j.engfailanal.2012.06.007http://www.sciencedirect.com/science/journal/13506307http://www.elsevier.com/locate/engfailanalhttp://www.elsevier.com/locate/engfailanalhttp://www.sciencedirect.com/science/journal/13506307http://dx.doi.org/10.1016/j.engfailanal.2012.06.007mailto:[email protected]://dx.doi.org/10.1016/j.engfailanal.2012.06.007


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1. Introduction

Dovetails, gears, and splines have been widely used in aero engines where fretting is an important failure mode due to

loading variation and vibration during long-time service[1,2]. Failure caused by fretting fatigue becomes a prominent issue

when service time continues beyond 4000 h. In some cases, micro slip at the edge of a contact zone can reduce the life by as

much as 4060%[3]. For example, failure due to fretting in compressor/fan dovetail assemblies manufactured from titanium

alloys are often observed. Many aero engine companies such as Rolls-Royce always focus on the solution to the fretting prob-

lem. In fact, fretting fatigue has been one of the cost sources relating to HCF [4]. With the increase of service time and reli-ability requirements of aero engine components, fretting fatigue should be paid more attention.

There are two key issues in the analysis of fretting fatigue: one is solving contact stress accurately; the other is carrying

out the fretting fatigue test and trying to find a suitable life prediction method. The high stress gradients at the edge of con-

tact zone are the basis of failure analysis of fretting fatigue, and it is a challenge to obtain the stresses accurately under com-

plex loading history. Fatigue has always been a difficult and widely studied field, and introducing fretting complicates it

further. Thus, it is necessary to develop a suitable method to predict fretting fatigue life to satisfy engineering requirements.

Several factors such as geometry, material elasticplastic behavior, load history, etc., affect fretting fatigue and make it

difficult to study. Therefore, researchers always focus on specific key factors affecting fretting fatigue life. Obtaining an accu-

rate solution for contact stresses, analyzing damage mechanisms of fretting fatigue, and finding other key factors are empha-

sized in modern research, especially under complex loading (vibrating load on blades and the low cycle fatigue (LCF) loads on

the whole rotor). Geometry is another important factor affecting contact stress and fretting behaviors. Reasonable structural

geometry is essential to reduce contact stress and inhibit fretting fatigue.

The concept of fretting was proposed in the 1920s, however as an engineering problem in aviation, fretting studies startedin the late 1970s and early 1980s. In the last 1015 years, fretting fatigue has been paid more attention and studied by means

of numerical simulation and experimental verification. Many engineering materials are chosen for fretting studies: carbon

steel was used in early investigations of the initiation mechanism of fretting cracks [5], while titanium alloys (TC5 [6], Ti-

17 [7]), especially Ti6Al4V [8], have been the primary concern in recent studies; Aluminum alloys (2024-T351 [9],

2X24-T351, 2X24-T39[10] and 7075-T6[11]), steel (NiCrMo-V[12]and AISI 52,100[13]) and nickel-base super alloys

(In718[14]) have also been studied. There may be as many as 50 factors [15]that can affect the fretting behavior of mate-

rials, in which contact pressure, coefficient of friction, slip amplitude, and cyclic axial stress are relatively important. There-

fore different emphasis is chosen in different studies such as processing technology, micro structure, geometry, loading

conditions and so on. Surface treatments such as shot-peen have been shown to improve the fretting performance, and

the fretting life will increase significantly due to residual compressive stress on the surface [16,17]. Except for shot-peen,

coating the contact surface helps to delay appearance of the wear [18], and Golden and Shepard [4], and Golden et al.

[19]used specimens with thin, hard, low-friction coatings (such as diamond-like carbon, DLC) with different surface treat-

ment to study fretting behaviors. This indicates that surface residual compressive stresses with different depths would lead

Fig. 1. HCF and LCF loading: (a) on dovetail assemblies[26]and (b) on fretting specimen [21].

382 D.-S. Wei et al. / Engineering Failure Analysis 26 (2012) 381396


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to different lifetimes. Swalla et al. [20]studied the microstructure of Ti6Al4V alloy by using EBSD (element backscatter

diffraction) and EDX (energy dispersive X-ray) to experiment with new fretting fatigue damage parameters. Geometry

has great influence on contact stress, for example, the contact length and rounded radii in rounded flat-on-flat, or the radii

in cylinder-on-flat, would change the pressure distribution on the contact surface[21,22]. For the contact of cylinder-on-flat,

size effects are an important research avenue, and there is a critical contact width, a0, which is dominated by the range of

micro slip; tests with contact width great than the critical contact width had relatively short fatigue lives [23]. McVeigh et al.

[24]used the quasi-analytical formula and FEM solution to study the effect of wear on the distribution of contact stress, and

it showed that the contact interface was no longer in ideal, smooth condition after wear, which will lead to the fluctuation of

contact stress along the interface. McVeigh and Farris [25]and Szolwinski et al. [26]studied the effects of HCF loading on

fretting fatigue; the former focused on the FE solution of fretting contact stresses under complex loading, which was in good

agreement with the Mindlins solution, and the latter focused on studying the effect of HCF loading on fretting fatigue life; it

was similar to Namjoshis study in[27]. In summary, it is clear that the calculation of contact stresses and prediction of fret-

ting life are two keys in fretting failure analysis, which are also the emphasis in the following section.

2. Two keys in the analysis of fretting failure

2.1. Numerical calculation of fretting contact stresses

Contact mechanics is an important branch of computational mechanics, and obtaining contact stress on an interface is the

basis of fretting life prediction. It is quite difficult to determine the contact stresses accurately between a blade and disk be-cause of the complex geometry and loading. The dovetail assemblies are always subject to centrifugal forces (LCF loading P)

and vibrational loads (HCF loading DQ) shown inFig. 1a. According to the loading, fretting specimens with a contact pad are

designed and used widely in many studies. Fig. 1b shows the loading on the specimen: r0 is bulk stress,P is pressure, Qisfretting load which is usually perpendicular to the load P. Different fretting states can been obtained by changing the ratio of

Q/P, which will clearly effect on the shear stress in the contact zone[21,28].

Analytical and quasi-analytical formulas based on the Hertzian solution were used to calculate contact stresses [24,26,29]

and form the code of CAPRI [30], which was developed for the new edition of CAFDEM[31]to analyze contact stresses be-

tween different materials. For some non-conforming contact, solutions from the quasi-analytical formula were always ver-

ified by FEM [32]. FEM is an effective and feasible way to obtain the fretting stress and strain under complex loading

conditions that require the introduction of elasticplasticity[33]. Currently, general FEM programs have been wildly used

in contact analysis of dovetail or fretting specimens such as ANSYS[34]and ABAQUS[11,15,25,35]. The boundary element

method (BEM) has also been applied for contact stress analysis. For example, the BEM program of BEASY is used to study the

contact between a rail and the wheels of a train[36]. BEM appears advantageous in analysis of crack propagation due toadaptive mesh division. Fadag et al. [15]calculated the crack propagation life of a fretting specimen by using BEM program

FRANC2D.

Fig. 2. FE model of fretting specimen for calculation of contact stress.

D.-S. Wei et al. / Engineering Failure Analysis 26 (2012) 381396 383


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The fretting fatigue specimen was used in previous studies[9,25,29], which calculated that the dangerous point was con-

tact point b shown inFig. 1b on the contact face. In these simulations, the effect of the vibrational load Qon fretting contact

stresses was controlled by the ratio ofQ/lP[21,26]. For conditions requiring complex calculations, FEM is often used toestablish the numerical model. For example, complex boundary conditions were considered in FEM models established

by Lykins et al.[35]and Fadag et al.[15]: the former focused on crack initiation by using a cylindrical fretting pad, while

the latter focused on crack propagation by using a flat pad with a rounded edge.Fig. 2shows these force boundary condi-

tions, which were pressure P, fretting loadQ, and bulk stressr on the fretting specimen. The mesh division is key in contactanalysis by means of FEM, especially when the contact appears between a 90wedge pad or a flat one with rounded edge as

the fretting specimen. These shapes lead to an obvious stress concentration for which the numerical solution is dependent on

the density of FE mesh. When solving engineering problems using FEM, the mesh density plays a critical role that can affect

the results: Wang et al.[3739]investigated the effect of mesh density on impellers stresses and utilized suitable number of

elements to stabilize them; Shokrieh and Rafiee [40]also showed that the stress and tip deflection of a wind turbine are

strongly dependent on the number of elements; Gonzlez-Herrera and Zapatero[41]showed that the minimum element size

around the crack tip presents a great effect on the value of crack closure stress of the compact tension specimen. Therefore, a

convergence analysis must be performed on the FE model, especially in the contact analysis between blade and disk, and a

suitable number of elements can be obtained by increasing the mesh density in a step-by step manner.

Fig. 3. FE Mesh of dovetail: (a) the coarse mesh used in early study [34]and (b) the fine mesh in recent study [42].



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It could be estimated that a 3D mesh with approximately 1,00,000 elements would be needed in order to resolve the local

contact field between sphere and plane[11]. Thus it is necessary to determine the suitable mesh density to obtain accurate

contact stresses: McVeigh et al.[24]refined the mesh with approximately 700 elements along a contact length of 3 mm to

get the peak stress, which had error to within 4% of the analytical solution. Fadag et al. [15]mentioned in the analysis of

crack propagation of a fretting specimen that mesh size should be at most one tenth of the initial crack length.

Furthermore, dovetail specimens are used to study fretting behavior. Though the fretting specimen reflects the fretting

behavior similar to dovetail assemblies and its testing is easy to be carried out, its geometry and loading appear to be quite

different compared to dovetail assemblies subjected to the working loads of an aero engine. Therefore dovetail specimen cal-

culations have also started to be given sufficient attention. Fig. 3shows FE models to be improved to get high-precision solu-

tions. Fig. 3a and b shows the coarse mesh used in early contact stress analysis and the fine mesh in recent research,

respectively. Sinclair studied the contact stress of dovetail assemblies in literatures [4244], which indicated that there

was a high stress gradient at the edge of blade/disk contact zone, and the solution precision of the mesh density should

be paid close attention when using numerical methods such as FEM. It is obvious that low solution precision of fretting con-

tact stresses would lead to low precision of life prediction. Sinclair used two-dimension models of dovetails to calculate the

contact stress using ANSYS and found that mesh density would affect the numerical solution of high stress gradients. Fur-

thermore, he established three-dimension models to investigate the effects of the configuration of the contact surface (with

and without crowing) on contact stress, and found that a contact profile with crowing would improve stress distribution in

contact zone [45,46]. It is clear that Sinclair had not incorporated vibrational loads into the analysis of contact stress, which is

a key factor in fretting fatigue. Based on Sinclairs studies, Wei et al.[47]tried to calculate the elasticplastic contact stress

and suggest the minimum mesh quantity to be used in the contact zone according to the analysis of convergence. Hammo-

uda et al. [48]also carried out the elasticplastic analysis to obtain the cyclic curve of shear stressstrain.

The evaluation of a blade/disk structure was carried out under a real working load. The contact problem shows obvious

nonlinearities (e.g., material nonlinearity, geometric nonlinearity, etc.), which results in expensive calculation cost using

FEM. In the case of a global model of a contacting blade/disk with fine element size, it is very time consuming to achieve

a good level of convergence for contact results [49]. There is no doubt that a mesh fine enough to achieve an accurate contact

solution would result in long computation time. So a sub-model [45,46,49]and a multi scale method[50]were used not only

to maintain accuracy, but also to improve computational efficiency. Another approach is to equate the three-dimensional

contact problem to a two-dimensional one by means of geometry and loading equivalence [51].

2.2. Fretting fatigue test and life prediction

It is well known that experiments are the basis for studying the fretting fatigue life of materials and structures. Fig. 4

shows a typical fretting fatigue experimental setup. This system allows variation of the axial load on the fretting specimen,

and the normal and tangential loads on fretting pads controlled by lateral and longitudinal springs, respectively [35]. The

shapes of the fretting specimens were adopted in fretting tests as follows: sphere pad/flat [52,53]; cylinder pad/flat

[9,15,25,52,54,55]; 90wedge pad/flat[55]; flat pad with rounded edge/flat[15,55].

As mentioned previously, the dovetail specimen has been used in fretting fatigue tests to substitute the typical fretting

fatigue specimen. Golden and Calcaterra[57]used dovetail specimens with different contact angles (Fig. 5a shows a dovetail

specimen with contact angle of 45) to study fretting fatigue life, and the results indicated that fretting fatigue life of a dove-

tail specimen will decrease with the increase of contact angle. Conner and Nicholas [58]used a similar specimens shown in

Fig. 5b to study the effect of surface treatment on fretting fatigue. These two studies lead to the following observations:

firstly, using a contact pad lead to a shorter contact length, which may reduce the fretting fatigue life and cause differences

between the test and the actual structure; secondly, the vibration load was not introduced. Rajasekaran and Nowell [59]and

Golden[60]designed different loading systems to achieve a combination of low-frequency large-amplitude cycles, and high-

Fig. 4. Typical fretting fatigue experimental setup and loading on specimen[35,56].



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frequency low-amplitude cycles, respectively. Additionally, except for the typical fretting and dovetail specimens, a C-spec-

imen was created by Golden[31,61]to analyze the nature of fretting cracks in contact pads and measure the threshold load.

Similar to conventional fatigue, fretting fatigue data are the basis of fretting fatigue life prediction. Based on the calcu-

lated parameters and experiment data, the methods of fretting fatigue life prediction can be classified into three groups.

2.2.1. Fretting fatigue specific parameters

Fretting is a damage process caused by wear, corrosion, and fatigue, which is driven by micro slip at the contact surfaceunder cyclic fretting contact stress [29], so micro slip is an important fretting parameter. The typical length of fretting con-

tact is from 0.1 mm to 1.1 mm [62,63], and the micro slip is generally between 0.5 lm and 100 lm, such as the empirical

values of 550 lm in[62], 25100 lm in[29], 1050 lm in[11]and 0.550 lm in[52]. Based on micro slip and fretting

contact stress, Ciavarella and Demelio[64]summarized several parameters of fretting fatigue damage as follows:

(1) Slip amplitude d: d is the relative tangential displacement of contacting particles during the cycle, which is similar to

the strain amplitude in conventional fatigue. The parameter was only used in some early studies[63].

(2) Frictional energy dissipation parameter Q. The Parameter Q, which is also called F1 or fretting wear parameter [64], is

given as

QsdlrNd 1

where s is the shear force,dis the relative tangential displacement, lis the coefficient of friction, and rNis the normal stress.

Fig. 5. The dovetail specimens: (a) From Golden Calcaterra [57]and (b) From Conner and Nicholas[58].



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(3) Ruizs parameter G. Parameter G, which is also called F2 or fretting fatigue (FF) parameter, introduced by Ruiz et al.[65],

empirically takes into account the evidence that cracks are more likely to develop in regions of tension rather than

compression[64]. It can be described as

G QrTsdrNlrNdrT 2

whererTis the shear stress. When rT> 0, cracks initiated on the contact surface tend to propagate into the interior.

2.2.2. Multi axial fatigue parameterUnder some conditions, fretting fatigue can be considered as fatigue with local stress concentrations. Then based on the

calculated fretting stresses at positions with high stress gradients, multi axial fatigue parameters can be used in life predic-

tion, which had already been performed in some studies[35,66].

(1) SmithWatsonTopper (SWT) parameter. Coffin[67]and Manson[68]proposed the relationship between the plastic

strain range and fatigue life. The total strain-life equation is

D2

r0fE

2Nfb

0f2Nfc

3

Then the mean stress correction was introduced by Smith, et al. [69]to develop the SWT relationship

rmax

D

2 r

0f

2

E 2N

f2

b r0

f

0

f2N

fbc 4

The multi axial SWT equation can be established by using the maximum normal stress on the critical planern,maxinsteadof maximum tension stressrmaxin the left hand side of Eq.(4). Szolwinsk and Farris[29]evaluated the fretting life of a spec-imen with a cylinder pad by introducing the maximum axial fretting stress into the SWT equation [9]

rmax rxfret r0 2p0ffiffiffiffiffiffiffiffiffiffiffiffiffilQ=P

p r0 5

whererx is the maximum axial stress on the fretting pad, r0is the maximum cyclic axial stress on the specimen, p0is themaximum of Hertzian contact pressure, and l is the coefficient of friction.

(1) FatemiSocie (FS) parameter. Fatemi and Socie[70]suggested a parameter combining the shear strain amplitude and

maximum normal stress on the critical plane. The life equation is

ctkrn;maxSys0fG2N

fb0 c0f2Nfc0 6

wherectis the shear strain amplitude, andrn,max is the maximum normal stress on the critical plane. The following param-eters were used to correlate observed fretting lives in Lykinss et al. study [35]: the strain-life relationship, the maximum

strain corrected for strain ratio effects, the maximum principal strain corrected for principal strain ratio effects, the SWT

parameter, the SWT critical plane parameter, the FS critical plane parameter, and the Ruiz parameter. The results indicated

that the maximum strain amplitude at the contact interface was an important parameter in predicting the life of fretting

fatigue crack initiation. In addition to this, Lykins et al.[56]and Lee and Mall[71]experimented with the shear strain ampli-

tude on the critical plane as a fretting parameter.

(1) Equivalent stress parameter. The advantage of the equivalent stress parameter is that it avoids the need to find a critical

plane on which fretting initiation occurs. Golden and Grandt[31]used the parameter to correlate the fretting fatigue

initiation life and give the stress-life diagram of fretting fatigue, which was similar to the SNcurve. The equivalentstress parameter can be written as

req 0:5Drpsuw

rmax1w 7

2.2.3. Methods based on fracture mechanics

There is a high stress gradient at the edge of the contact zone of the fretting specimen, especially for a specimen with a

90wedge pad or a flat pad with a rounded edge. The elastic peak stress with a high gradient can be equivalent to a singular

one at the crack tip of the double-edged cracked plate specimen as shown in Fig. 6[72,73]. Surseh gave the derivation of the

equivalence in[74]. The fracture mechanics method has already been used to predict the fretting fatigue life, which leads to

the crack analogy method (CAM). Naboulsi[55]obtained the crack analogy fatigue (CAF) parameter-life curve, which is sim-

ilar to SNcurve and can be used to evaluate the fretting life. He then [75]developed the modified crack analogy method

(MCAM) by introducing a geometry correction. Lindley [76] and Nicholas et al. [77] gave the fretting S

N

curve, but it

was difficult to apply because of the lack of experimental data.



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Due to the analogy, the propagation life can be used as the approximate value of the fretting fatigue life. The fretting fa-

tigue crack growth process can be divided into two stages shown in Fig. 7 [52,72,78]: for stage I, a surface crack initiates

under the influence of contact loads at an angleU, which then grows until it reaches a critical distance, lc. For stageII, a mode

Icrack which is primarily governed by the uniform cyclic stress grows until it reaches a critical distance, hc.

NIrepresents the propagation life in stage I, andNIIrepresents the propagation life in stage II, then the total lifeNcan be

calculated as follows:

NIZ Ic0

dl

CIDKImI 8

Fig. 6. The analogy between contact bodies and cracked body: (a) a two-dimensional contact between 90 wedge pad and substrate [72]and (b) double-

edge cracked plate specimen[72].

Fig. 7. Two stages crack growth.



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NII

Z hccsin/

dl

CIIDKIImII

9

N NINII 10

The crack initiation angle U and the critical distance lc are key factors in (8) and (9)since they can be obtained by cal-

culating the stresses around the crack tip and the stress intensity factor (SIF)[52,72]. It is clear that the stress state of contact

between a 90wedge pad and substrate is similar to the singular stress around the crack tip. For the contact between a spec-

imen and a flat pad with a rounded edge, methods based on stress gradients have been used in [7981]and lead to the notchanalogy method[82]. This is used as the mean stress along the critical depth to correlate the fretting life. Giummarra and

Brockenbrough[10]has given the expression of mean stress as follows:

Drx 1

z

Z z0

Drxdz 11

Another approach is using the small crack propagation life as the approximation of the fretting fatigue life. Pre-cracks can

be set at the position of peak stress to represent a defect on the contact surface [83], and then the small crack propagation

law is used to calculate the propagation life. The following formula has been used in many studies [7,15,30]to calculate the

propagation life of a small crack.

da

dN eB

KeffKth

P

In KeffKth

Q" #

In KcKeff

D

12

Limited by the experimental technology, the combined experiment-numerical approach was used to calculate the fretting

life[56]and to predict the path of crack propagation[84]. With the advancement of testing technology, researchers continue

to try to find micro-damage parameters [85,86].

3. Several important factors on fretting fatigue life and corresponding treatment

3.1. Distinguishing the propagation life from the total life

Life prediction methods (such as the multi axial fatigue prediction method) as mentioned previously only aim to deter-

mine initiation life, while the observed fretting life in testing consists of two parts: initiation life and propagation life. This is

unlike the test data from a smooth bar specimen, in which propagation life can be neglected. In Lykins et al. study[35], the

average crack propagation life based on the striation measurements was determined to be 11% of the total life, whereas the

calculated value based on the Paris law was estimated to be 8% of the total life. Szolwinskis calculation in [9,29]indicatedthat the crack propagation life was 515% of the total life. Several methods can be used to distinguish the propagation life

from the total life, i.e. to determine initial crack size of fretting crack propagation, which are listed as follows:

(1) Szolwinski chose 1 mm as the depth of a semi-circular crack. In the study, it was shown that for a crack length of 1 mm

and a half width contact size, it can be assumed that the applied remote stresses, not the contact stresses, dominate

the propagation of the crack[29]. It is interesting that Szolwinski used the specimen width as the final crack size to

calculate the propagation life in[29], while only using the half specimen width in[9], but this has almost no effect on

the results. Hutson[87]suggested that the long crack propagation law can be used for calculation when the initial

crack size is larger than 50 lm.

Fig. 8. Plot of normal pressure, ap(x)/P, for a range of values ofb/a[24].



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(2) The initial crack size can be determined according to measurements taken during testing. Lykins et al. [35]determined

that crack initiation life in proportion to total life is about 90% based on striation measurements. In a subsequent study

[56], Lykins et al. used an initial crack length of 380 lm, which is equivalent to the typical capability of using the non-

destructive technique (NDT), which is able to detect a 760 380 lm semicircular crack.

(3) The initial crack size also can be determined by the threshold of small crack propagation. The small crack or El Haddad

parameter[88]had been used in fretting crack growth by Garcia and Grandt [7], Fadag et al.[15]and Nicholas et al.

[77], which was defined as

l0 1

pKIeffthYre

213

The corresponding small crack corrected threshold fatigue stress range is [7]

Fig. 9. FE meshes and stress solutions: (a) coarse mesh and (b) fine mesh and (c) contact stress distribution.



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Drth DKIeffthffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffipll0

p 14wherere is the fatigue limit, Y is geometric correction factor, KIeffth is the effective long crack SIF threshold which was ex-pressed in terms of ratio of SIF[15]. Whenl>l0, it is deemed a long crack, and is otherwise a short crack. For the C-specimens

designed by Golden and Grandt in[31], a value of approximately 25 lm forl0was calculated. In other words, for cracks smal-

ler thanl0, the material behavior is controlled by stress, and above l0, linear elastic fracture mechanics (LEFM) can be used to

predict crack growth[10,31].

3.2. Effect of geometry

A lot of researches have already proved that the geometry of the fretting pad, such as a sphere, cylinder, 90wedge, or

rounded flat edge will obviously affect the distribution of contact stress and fretting fatigue life. Similarly, the geometry

of a fretting specimen, such as its thickness and a dog-bone shape, is also an important factor[89]. According to the loading

analysis inFig. 1b, the distribution of contact stress with different ratios ofb/a (stick length/contact length) are shown in

Fig. 8. It should be noted that asb/a? 0, the pressure profile approaches the Hertzian distribution[24]; as b/a? 1, this rep-

resents the pressure coming from the contact between the 90wedge and the substrate; when 0


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max;R max1 Rm

15

The similar correction is used in calculating the propagation life[15,77,30]

DKIeff KImax1 RLm

16

Additionally, fretting usually appears under combined LCF and HCF loading. The damage cumulation method can be used

to investigate how combined loading affects fretting fatigue life [26]. Studies of[91]Naboulsi and Mall and[92]Jin and Lee

indicated that linear damage cumulation would lead to a convenient calculation, while non-linear cumulation would lead to

a more accurate result.

3.4. Effect of coefficient of friction

Fretting stress states have been found to depend highly on the assumed coefficient of friction, l, which is very difficult tomeasure in any type of experimental setup. For example, for the dovetail fixture in [19], it is only possible to measure the

value once per test, and then only the static value can be determined. An assumed coefficient of friction was often used in

calculation: the fretting fatigue life of 2024-T3 aluminium and SAE 1015 steel are calculated by using SWT parameter in[29],

and it is obvious that different coefficients of friction (l= 0.5,0.7, 0.9) result in different calculated life. Szolwinski pointedout that the value of the coefficient of friction is usually between 0.6 and 0.75 under fretting conditions, who then adopted

l= 0.65 in the study of 2024-T351 aluminium in [9],l = 0.4 for Ti6Al4V in[24]andl= 0.45 for Ti6Al4V in[26]. Datsy-shyn and Kadyra[6] and Ciavarella and Demelio [64]also used different coefficients of friction to calculate the SIF under

fretting loading. These studies indicate that the coefficient of friction is a key factor in fretting analysis which is still difficult

to determine accurately.

4. Study on fretting fatigue performance of dovetail in the fan of aero engine

Studies indicate that there is an obvious difference between the working conditions of a blade/disk and the testing con-

ditions of a fretting fatigue specimen. Therefore simulations of the fretting behavior of dovetail assemblies under working

conditions were carried out in order to study fretting behaviors, which are listed as follows:

Fig. 12. Stress distribution of fir tree attachment: (a) peak stress between different contact pairs and (b) analysis of convergence.



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Firstly, elasticplastic stress analysis of a dovetail subjected to centrifugal force was accomplished by using a coarse mesh

(shown inFig. 9a) and a fine mesh (shown inFig. 9b)[47,93].Fig. 9c shows that high stress gradients occur near the edges

of the contact zone of the dovetail (points A and B). It indicates that stresses converge at Mesh No. 4 according to the

trend of the numerical solution shown in Fig. 10. It should be noted that when the relative error between two peak con-

tact stresses is less than 5% using different mesh densities, it can be concluded that the stress solution is converging.

Secondly, the stress distribution of a fir tree attachment was studied under centrifugal and thermal loading by using the

FE mesh shown in Fig. 11[94]. Fig. 12a describes the stress distribution along different contact pairs.Fig. 12b give the

relationship between solution and mesh density: for a dovetail attachment, about 450 elements along the contact zone

should lead to numerical convergence, while for fir tree attachment, about 1000 elements are needed.

Fig. 13. Different profiles of contact surface: (a) arc/line and (b) interior arc/arc and (c) exterior arc/arc.



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Thirdly, the effects of critical geometrical parameters on the distribution of contact stresses were studied. These were the

contact angle h, contact length L, fillet radius R at the edge of contact zone[95], and the contact surface profile[93]. Dif-

ferent profiles, such as arc/line, interior arc/arc and exterior arc/arc shown in Fig. 13ac, respectively, would lead to the

different pressure distribution profiles inFig. 14. It indicates that arc/line and arc/arc contact profiles would remove the

high stress gradient at the edge of contact zone, and arc/arc would further reduce the contact stress.

Fourthly, based on the contact stresses and SIFs of dovetail assemblies, a fracture mechanics approach is adopted to judge

the crack initiation direction and the growth path[47,96]. Pre-cracks were set at point B shown in Fig. 15a to calculate the

SIFs. Then the curve of SIFs-angle shown inFig. 15b was used to determine the crack initiation direction. The minimum

strain energy density criterion was used to judge the direction of crack propagation and the crack growth law was used to

calculate the growth life.

Fig. 14. The stress distributions on contact surface with different profiles.

Fig. 15. Model of crack initiation of dovetail: (a) FE model of cracked body and (b) SIFs as function of angle.



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5. Conclusion

The fretting fatigue is not only a fundamental scientific problem but also an engineering one. This is not a new question,

but it is not well solved because of the many factors affecting it. Calculation of contact stress and fretting fatigue life predic-

tion are the two key studies. Many studies have already revealed the fretting failure mechanism and adopted some tech-

niques to restrain fretting from occurring. There are however still some deficiencies: cyclic elasticplasticity of materials

and vibrational loads should be taken into account for the calculation of the contact stress. It is useful to study the fretting

behaviors of different contact profiles, such as arc/line, arc/arc, etc. In addition to this and similar to conventional fatigue,fretting fatigue life prediction is always a critical issue in HCF, and finding suitable life parameters is undergoing continuous

research.

Acknowledgements

This work is supported by the National Natural Science Foundation of China with No. 51105023 and also supported by the

Fundamental Research Funds for the Central Universities.

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Failure Analysis of Dovetail Assemblies Under Fretting Load