Investigation of crack initiation path in AA7050-T7451 under fretting conditions

Journal Pre-proof Investigation of crack initiation path in AA7050-T7451 under fretting conditions G.M.J. Almeida, G.C.V. Pessoa, R.A. Cardoso, F.C. Castro, J.A. Araújo PII:

S0301-679X(19)30617-6

DOI:

https://doi.org/10.1016/j.triboint.2019.106103

Reference:

JTRI 106103

To appear in:

Tribology International

Received Date: 31 July 2019 Revised Date:

26 November 2019

Accepted Date: 3 December 2019

Please cite this article as: Almeida GMJ, Pessoa GCV, Cardoso RA, Castro FC, Araújo JA, Investigation of crack initiation path in AA7050-T7451 under fretting conditions, Tribology International (2020), doi: https://doi.org/10.1016/j.triboint.2019.106103. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Investigation of crack initiation path in AA7050-T7451 under fretting conditions G.M.J. Almeidaa,*, G.C.V. Pessoaa, R.A. Cardosob, F.C. Castroa, J.A. Araújoa *

Corresponding author. E-mail address: [email protected] (G. Almeida)

a

Department of Mechanical Engineering, University of Brasilia, 70910-900 Brasilia, DF, Brazil

b

Department of Mechanical Engineering, Federal University of Rio Grande do Norte, 59078-970 Natal, RN, Brazil Abstract Early crack orientation in 7050-T7451 aluminum alloy was investigated under fretting conditions. New tests were performed in the partial slip regime to observe the influence of the tangential load amplitude, mean bulk stress, and pad radius on the crack orientation. Three critical plane fatigue parameters were combined with different stress averaging methods to estimate the crack initiation direction. The normal stress-based Smith–Watson–Topper parameter provided better crack orientation estimates than the shear stress-based parameters. The experimental observations indicated a small increase in the early crack angle when the tangential load amplitude was raised.

Keywords: Fretting, Crack orientation, Critical plane, 7050-T7451 aluminum alloy

Nomenclature P

normal load per unit length

Q

tangential load per unit length

Qa

tangential load amplitude

Fb

bulk load

p0

peak contact pressure

R

pad radius

t

time

x

coordinate parallel to contact surface

y

coordinate normal to contact surface

a

semi-width of the contact

θ

material plane orientation

λ

rotation angle of a rectangular hull

a1 (λ ) , a2 (λ ) semi-sides of a λ-oriented rectangular hull E

Young’s modulus

ν

Poisson’s ratio

σuts

ultimate tensile strength

σy

yield stress

ΔK th

threshold stress intensity factor range

Δσ−1

uniaxial fatigue limit range

f

coefficient of friction

κ

material constant of the Modified Wöhler Curve Method

K

material constant of the Fatemi-Socie parameter

L

critical distance

σm

mean bulk stress

σn

normal stress

σn

average normal stress

σn , a

normal stress amplitude

σn , a

average normal stress amplitude

σn ,max

maximum normal stress

σn ,max

average maximum normal stress shear stress

τ

τ

average shear stress

τa

shear stress amplitude

τa

average shear stress amplitude

τ a ,MRH

Ψ

shear stress amplitude defined by the Maximum Rectangular Hull (MRH) method shear stress path

1. Introduction Fretting is a complex tribological process associated with the minute relative motion of one contacting surface over another. In addition, fretting fatigue is an accumulative damage process in which the initiation and propagation of cracks occur in the presence of fretting and cyclic stresses in the bulk of the component. The fretting fatigue phenomenon can be observed in many components, such as the dovetail connections between blade and disc in aircraft engines [2, 1] and the clamp region of electrical conductor wires [4, 3]. The fretting damage can lead to premature crack initiation and if associated with fatigue loading the life of these parts can be considerable reduced [5]. Over the years, in an attempt to understand the failure mechanisms involved in fretting fatigue problems, critical plane approaches became vastly used by its capability to predict both life and crack initiation direction. This type of approach considers that cracks initiate in the material plane where a certain combination of stress and strain quantities is the most severe. Examples of critical plane models include those proposed in Refs. [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Lykins et al. [16] carried out fretting fatigue tests and utilized fractography techniques to investigate the crack initiation in a Ti-6Al-4V alloy. Two critical plane parameters (the Smith–Watson–Topper and the maximum shear stress range) were studied and the results suggested that the fretting fatigue crack initiation in this titanium alloy is governed by shear stresses.

Namjoshi et al. [17], also studying the fretting fatigue crack initiation behaviour of the Ti-6Al-4V conducted an experimental and analytical investigation and similarly concluded that the crack initiation mechanism in this titanium alloy seems to be ruled by shear stresses on the critical plane. Hojjati-Talemi et al. [18] performed fretting fatigue tests on the 2024-T3 aluminum alloy and defined the crack initiation direction. Further, using the maximum tangential stress, the maximum energy release rate and the zero K II proportional criteria, the authors modelled the crack propagation trajectory and compared results with experimental observations. However, due to the fact that the fretting fatigue problem involves non-proportional loading, a considerable discrepancy was observed in the results. Recently, Vázquez et al. [20, 19] also used the Smith-Watson-Topper (SWT) and Fatemi-Socie (FS) critical plane criteria in order to investigate the crack initiation process on fretting fatigue tests performed on the 7075-T651 aluminum alloy. For this material, the normal stress-based SWT parameter provided better estimations when compared with the FS, a shear stress based criterion. Fretting conditions induce high stress gradients near the contacting surfaces, which makes hot-spot approaches generally not well suited for dealing with such problems. Thus, in this work, averaging methods are used in an attempt to find an effective stress that represents more properly the stress state in the presence of stress gradients. The stress averaging methods considered are the Center of the Structural Volume [21], the Critical Plane Search on each Point [22, 19], and the Critical Direction [23]. The main purpose of this study is to evaluate the accuracy of the aforementioned stress averaging methods, when associated with critical plane fatigue criteria, in estimating the initial direction of fretting cracks. The evaluation was based on a series of fretting tests conducted on 7050-T7451 aluminum alloy in the partial slip regime. The experimental program was designed to observe the influence of the tangential load amplitude, the mean bulk stress, and the pad radius on the initial crack direction. The experimental results used were partially reported in a previous work [24]. New test data and a more detailed description of the early crack directions were included in the present study.

2. Fatigue Damage Parameters 2.1. Smith–Watson–Topper parameter Smith, Watson, and Topper [25] proposed a stress-strain fatigue parameter that takes the mean stress effect into account. Combining this parameter with a critical plane approach, Socie [26, 8] extended the SWT parameter to multiaxial fatigue conditions. Considering a linear elastic material behavior, a stress-based version of this parameter can be written as

SWT = σn,a σn ,max

(1)

where σn , a is the normal stress amplitude and σn ,max is the maximum normal stress in a loading cycle. The critical plane is defined as the material plane where the fatigue parameter given by Eq. (1) is maximum.

2.2. Fatemi–Socie parameter Fatemi and Socie [9] developed a fatigue parameter for multiaxial loading conditions. When the stress-strain relation is elastic, the Fatemi–Socie parameter can be written as

⎛ σ ⎟⎞ FS = τ a ⎜⎜⎜1 + K n ,max ⎟⎟ (2) σ y ⎟⎠ ⎜⎝ where τ a and σn ,max are the shear stress amplitude and the maximum normal stress at the critical plane, respectively. The sensitivity of the material to the maximum normal stress is embodied in the constant K, and σ y is the yield stress of the material. In the original model formulated by Fatemi and

Socie [9], the critical plane was defined as the material plane which experiences the maximum value of the shear strain amplitude, or the shear stress amplitude when the strain is purely elastic. In this work, however, the critical plane is defined as the one where the fatigue parameter (Eq. 2) reaches its maximum.

2.3. Modified Wöhler Curve Method The Modified Wöhler Curve Method (MWCM) [11] is commonly used for estimating fatigue limit under multiaxial loading conditions. The MWCM parameter can be defined as

MWCM = τ a + κ

σn ,max τa

(3)

where τ a and σn ,max are the shear stress amplitude and the maximum normal stress, respectively, at the critical plane and κ is a material constant. According to this method, the critical plane is defined as the material plane where the maximum value of shear stress amplitude is found. In cases where more than one plane have the same value of maximum shear stress amplitude, the critical plane is defined as the one which has the highest value of maximum normal stress σn ,max .

2.4. Definition for the shear stress amplitude There are many ways to define the shear stress amplitude τ a on a material plane, for instance, using the Chord Method [27], Minimum Circumscribed Circle [28], Minimum Frobenius Norm Method [29], Maximum Rectangular Hull (MRH) [30], and the Momentum of Inertia Method [31]. In this work, the MRH method is used due its simple implementation and low computational cost, and to the fact that it provides accurate results for synchronous and asynchronous combined loadings [33, 34, 32]. This method defines the shear stress amplitude as the hypotenuse of the semi-sides of the biggest rectangle that can circumscribe the shear stress loading path Ψ observed at the material plane Δ , as shown in Fig. 1. The semi-widths of the rectangle circumscribing the load path Ψ can be calculated as

ai (λ ) =

1⎡ τi (λ, t ) − min τ i (λ, t )⎤⎥ , i = 1, 2. ⎢⎣ max t t ⎦ 2

(4)

where the angle λ defines the orientation of the rectangle. For each λ angle between the interval 0D ≤ λ < 90D , a value of τ a can be evaluate as

τ a (λ ) = a12 (λ ) + a22 (λ )

(5)

The shear stress amplitude is then defined by maximizing Eq. (5), i.e.

τ a ,MRH = Dmax D τ a (λ ) 0 ≤λ<90

(6)

Figure 1: Schematic of the Maximum Rectangular Hull (MRH) method on a material plane Δ .

3. Critical Plane Averaging Methods 3.1. Method 1 – Center of the Structural Volume It is possible through the Theory of Critical Distance (TCD) to estimate with a good accuracy the fatigue damage in notched components [36, 35]. Since Giannakopoulos et al. work [37], where the similarity between the stress field of notched elements and components subjected to fretting conditions was noticed, the TCD has been used in order to evaluate fretting fatigue problems [38, 39, 23, 22, 40, 41]. The TCD aims to estimate the fatigue limit of components containing stress raisers such as notches and cracks. The approach consists in evaluating an effective stress that can appropriately characterize

the fatigue damage process inside a specified volume surrounding the stress raiser. This volume, in general is associated with the material characteristic length L, a material property proposed by Taylor [42] that can be defined as 2

1 ⎛ ΔK ⎞ L = ⎜⎜ th ⎟⎟⎟ π ⎜⎝ Δσ−1 ⎟⎠

(7)

where ΔK th is the threshold stress intensity factor range and Δσ−1 the uniaxial fatigue limit range, in this case, both for a load ratio equal to −1 . For 2D analysis, the TCD can be expressed in simplified versions by substituting the material volume above mentioned by the Point, Line or Area Method [42]. Susmel [21] assumed that the critical distance parameter can also be thought as the diameter of the structural volume depicted in Fig. 2. In this case, application of critical plane criteria at L / 2 (Point Method) would provide us the representative information concerning fatigue damage and likely direction of crack initiation. Figure 2: Illustration of the Center of the Structural Volume Method.

3.2. Method 2 – Critical Plane Search at each Point As the fretting problem involves high stress gradients, the stress state can considerably change even for points close to each other. The same is true for the orientation of the critical plane. In order to take into account this high stress gradient effect, the critical plane can be determined considering different points as shown in Fig. 3. The application of the Method 2 consists in the following steps. First, one needs to choose a point on the contact surface where the stress state is the most severe. In the contact configuration here analyzed, this point is located at the trailing edge of the contact zone ( x / a = −1, y / a = 0 , where a is the contact semi-width). Determining the critical plane at this point, one can determine the angle θ1 which here is faced as the direction where the crack is expected to initiate. The next step consists in propagating this virtual crack by the distance L / α , where α is a numerical constant that controls the discretization level of the simulated crack path. Hence, the previous steps can be applied successively in order to determine the directions ( θ1 , θ2 , …, θn ). The process is terminated when the crack reaches a depth from the contact surface equal to L. In this work, α = 10 was chosen after performing a convergence study. Figure 3: Illustration of the Critical Plane Search at each Point Method.

3.3. Method 3 – Critical Direction This averaging method firstly proposed by Cardoso et al. [23] also intends to consider the high stress gradient effect. In this method, a 2L length line oriented by an angle θ with respect to an axis perpendicular to the contact surface is discretized in many material points, as shown in Fig. 4. For a given time instant t, the normal and shear stresses are computed along a line defined by r ≤ 2 L with an orientation θ. The average values of the normal stress σn and the shear stress τ along this line can be defined, respectively, as

σn (θ , t ) =

1 2L σn (r , θ , t ) dr 2L ∫ 0

(8)

and

τ (θ , t ) =

1 2L τ (r , θ , t ) dr 2L ∫ 0

(9)

For a complete loading cycle, it is possible to determine the average values of the maximum normal stress, σn ,max (θ ) , the normal stress amplitude, σa (θ ) , and the shear stress amplitude, τ a (θ ) , for each θ direction, by using the following expressions:

σn ,max (θ ) = max σn (θ, t ) 0≤t
(10)

σa (θ ) = max σn (θ , t ) − min σn (θ, t ) 0≤t
0≤t
(11)

and

τ a (θ ) =

1⎡ τ (θ , t ) − min τ (θ , t )⎤⎥ (12) ⎢ max 0≤t
These average stress quantities can be used in any of the multiaxial fatigue criteria (SWT, FS, MWCM) presented in Section 2. Very recently, the Critical Direction Method was combined with the Carpinteri-Spagnoli critical plane criterion [10] and promising predictions of fretting crack initiation direction were obtained [24]. Figure 4: Illustration of the Critical Direction Method.

4. Experimental work 4.1. Material and specimens Fretting tests on 7050-T7451 aluminum alloy were used in this study. The results of these tests were partially reported in a previous work [24]. Here, new test data and a more detailed description of the observed early crack directions were included. The AA7050-T7451 has been used in aerospace applications due to its attractive combination of low density and high mechanical strength. Common applications are in internal fuselage structures, spars and ribs [43]. The mechanical properties of the material are listed in Table 2. Table 2: Monotonic and cyclic properties of 7050-T7451 aluminum alloy. Young’s Modulus, E

71.7 GPa

Poisson’s ration, ν

0.33

Yield stress, σ y

469 MPa

Ultimate tensile strength, σuts

524 MPa

Fatigue limit range, Δσ−1

292 MPa

Threshold stress intensity factor range, ΔK th

5.5 MPa m

Critical distance, L

113 μm

Samples of the material were subjected to Keller’s chemical etching (2.5 ml HNO3 + 1.5 ml HCl + 1 ml HF + 99 ml H 2O ) in order to reveal the grains boundaries and orientations. With the aid of a confocal laser microscope, two distinct regions were observed as shown in Fig. 5, where L, T and S are the longitudinal (rolling), long transverse and short transverse directions, respectively. The recrystallized region is characterized by the big grains while the non-recrystallized region is characterized by the small ones. The average size of the small grains was 8 μm. Figure 5: Microstructure of AA7050-T7451. (a) L ×T plane, (b) L × S plane and (c) T × S plane. Flat dog-bone specimens and cylindrical pads both made of AA7050-T7451 were used in the fretting tests. The specimens have a square cross section of 13× 13 mm. Two sizes of cylindrical pads were

considered in this work: a smaller one with a radius of 30 mm and a larger one with a radius of 70 mm. The superficial roughness of all the specimens and pads were measured using a confocal laser microscope before running the tests. Table 3 shows the minimum, maximum and the average roughness values of all the specimens and pads utilized in this work. Table 3: Roughness of the pads and specimens before the tests. Roughness

Ra (μm) Min. Max. Average

Specimens

0.24

0.41

0.33

Pads

0.26

0.45

0.32

4.2. Fretting device layout The fretting apparatus was mounted on a customized MTS 322 Test Frame. A schematic view of this machine and a detailed list of its components is shown in Fig. 6. The actuators labeled as 1 and 3 are responsible for applying the tangential and fatigue loads, respectively. The normal static load is applied by an external manual hydraulic system. The fretting apparatus is connected to both the fretting actuator and the external hydraulic system which is in charge of applying the normal load. One side of the specimen is in contact with the cylindrical pad whereas the other is supported by a bearing. The alignment between pads and the specimens was verified by using a pressure measurement film [44, 45, 18]. Figure 6: Layout of the two-actuator fretting fatigue machine.

4.3. Fretting tests The tests were designed to evaluate the influence of the following parameters on crack initiation direction: tangential load amplitude, contact geometry (pad radius) and mean bulk load. Table 4 summarizes the tests conditions. In configurations 1 to 3, the tangential load amplitude was increased while all other parameters were held the same. Tests 2 and 4 aimed to investigate the influence of the pad radius. These tests were designed so that the pad radii were different while the ratio Qa / P , the peak pressure p0 , and the mean bulk load ( σm ) were kept constant. Note that, under such conditions, the main difference among the tests is the stress gradient beneath the contact. In order to evaluate the effect of the mean bulk load on crack initiation direction, two set of tests were considered. In one of them, tests 4 to 6, a pad radius of 30 mm was considered and only the mean bulk load varied. In the other set of tests (2, 7 and 8) the pad radius was 70 mm. Table 4: Loading and geometry configurations of fretting experiments. Load config.

(N/mm)

P (N/mm)

C1

240

800

C2

320

C3

R (mm)

a (mm)

p0

σm

(MPa)

(MPa)

0.3

70

1.34

380

0

800

0.4

70

1.34

380

0

400

800

0.5

70

1.34

380

0

C4

136.4

341

0.4

30

0.57

380

0

C5

136.4

341

0.4

30

0.57

380

25

C6

136.4

341

0.4

30

0.57

380

50

C7

320

800

0.4

70

1.34

380

25

C8

320

800

0.4

70

1.34

380

50

Qa

Qa / P

For all tests carried out, the loading history (Fig. 7) was as follows. Firstly, the bulk load Fb was applied monotonically to the specimen and held constant. Then, the pads were clamped against the specimen by a constant normal load P. Finally, the oscillatory tangential load Q (t ) was prescribed on the pad. Figure 7: (a) Schematic of the experimental fretting fatigue configuration and (b) loading history.

5. Results 5.1. Experimental results Figure 8 shows a scheme of the post-test procedure conducted to identify and measure the fretting crack orientations. After running 106 cycles at 10 Hz, each test was stopped. Then, the contact zone of the specimen as well as the region beneath it were isolated by performing transverse cuts represented by the horizontal dotted lines. Next, this sample was transversely cut at its center along the contact width (vertical dotted line) and embedded into a phenolic resin, as illustrated in Fig. 8. To reveal the microstructure and the cracks, the samples were sanded, polished, chemically etched in Keller’s solution for 12 seconds and then washed in tap water. All images and crack direction measurements were obtained using a confocal laser microscope. The observed fretting cracks are shown in Fig. 9 for three selected tests. For the sake of clarity, tests were named according to the following rule: Cm Tn, where m and n refer to the loading configuration and test numbers, respectively. Figure 8: Schematic of the post-test procedure to identify and measure the fretting crack angles. Figure 9: Selected experimental fretting cracks images. (a) C2 T3; (b) C3 T1 and (c) C4 T1. Three different methodologies were considered for estimating the initial direction of fretting cracks (Methods 1, 2 and 3 described in Section 3). Note that the definition of early crack initiation will depend on the method being adopted but, in any case, the initial crack length is related to the critical distance L. For Methods 1 and 2, the early crack length is about 100 μm, while for Method 3 it is about 200 μm. Aiming to be consistent with the methods used in this work, three different procedures to measure the direction of crack initiation were used, as illustrated in Fig. 10. For the Method 1 (Center of the Structural Volume), Fig. 10(a), the crack initiation direction is defined by moving away from the crack initiation location following its path up to the vertical depth L / 2 . The same is valid for the Method 2 (Critical Plane Search on each Point), however in this case, the crack path is followed up to the depth L, Fig. 10(b). On the other hand, for the Method 3 (Critical Direction), the crack initiation direction is defined by the line which starts at the crack initiation point and ends at the intersection between the crack and a semi-circle of radius 2 L centered at the crack initiation spot, Fig. 10(c). Positive angles are defined in counter-clockwise direction. When multiple cracks were observed, only the longest one was considered. Table 5 summarizes the experimental crack directions obtained according to each methodology addressed in this study. Between two and three tests were carried out for each load configuration. Average values of crack initiation direction were computed to be further compared with numerical estimates. Figure 10: Experimental measurement methodologies illustrated in the test C4 T2: (a) Method 1, (b) Method 2 and (c) Method 3. Table 5: Crack angles at L, L / 2 and 2 L from the contact surface. Crack Angle, θ ( D ) Test C1 T1

L/2 7.3

2L

L 14.0

Average Crack Angle ( D )

12.8

L/2

L

2L

24.4 ± 24.2 22.9 ± 12.5 21.4 ± 12.2

C1 T2

41.5

31.7

30.0

C2 T1

24.8

25.0

28.0

C2 T2

36.6

36.6

36.6

C2 T3

37.5

24.0

24.0

C3 T1

32.5

23.1

25.7

C3 T2

37.0

37.0

37.0

C4 T1

39.9

41.1

29.7

C4 T2

24.2

23.9

22.0

C5 T1

31.3

31.3

31.3

C5 T2

31.7

31.7

31.7

C6 T1

36.3

36.3

36.3

C6 T2

33.7

32.5

24.4

C7 T1

54.4

39.8

40.7

C7 T2

17.3

18.3

16.7

C7 T3

42.5

41.1

39.7

C8 T1

55.6

50.8

46.5

C8 T2

42.6

32.5

27.9

33.0 ± 7.1

28.5 ± 7.0

29.5 ± 6.4

34.8 ± 3.2

30.1 ± 9.8

31.4 ± 8.0

32.1 ± 11.1 32.5 ± 12.2

25.9 ± 5.4

31.5 ± 0.3

31.5 ± 0.3

31.5 ± 0.3

35.0 ± 1.8

34.4 ± 2.7

30.4 ± 8.4

38.1 ± 18.9 33.1 ± 12.8 32.4 ± 13.6

49.1 ± 9.2

41.7 ± 12.9 37.2 ± 13.2

5.2. Comparison of predictions with test data The cylinder/plane contact configuration and the loading conditions investigated allowed the use of analytical solutions to obtain the surface and sub-surface stress distributions. The normal traction can be calculated according to the solution developed by Hertz [46], and the shear traction distribution can be obtained from the solution due to Mindlin and Cattaneo [48, 47]. The stress field beneath the contact was obtained from the Muskelishvili potential [49]. For more details on the stress analysis of the fretting contact problem, the reader is referred to Ref. [50]. Table 6 shows the early crack angles estimated by combining the SWT, FS and MWCM parameters with each of the averaging stress methods. Comparing the estimated angles with the observed values listed in Table 5, it can be argued that the SWT parameter yields more appropriate crack angles than the shear-based parameters, since it correctly predicts crack directions inward the contact region (i.e., positive crack angles). Further developments are still needed to improve the accuracy between the estimated and observed crack angles. For instance, the use of different multiaxial fatigue criteria (e.g., [12]) may provide better estimates. The observed crack angles listed in Table 5 are also showed in graphical form in Figs. 11 to 13. To help the identification of trends in the crack angle with respect to a variation of an experimental parameter, the configurations were grouped by each of the parameters varied: tangential load amplitude, pad radius, and mean bulk stress. Note that, for the same configuration, the mean value and standard deviation of the observed crack angle may vary according to the stress averaging method considered. This is because of the different crack initiation lengths adopted by these methods. From the experimental observations, it can be seen that the crack angle slightly increases as the tangential load Qa is raised (test configurations 1 to 3). From the test sets intended to investigate the influence of increasing the mean bulk load (test configurations 4 to 6 and 2, 7 and 8), it is noted that in neither of them a significant variation of the crack initiation angle with respect to the mean bulk load was observed. Therefore, the orientation of early fretting cracks do not seem not be dependent on the mean bulk load, at least for the testing conditions investigated. From the limited tests performed to assess

the effect of the pad radius on the early crack angle (test configurations 2 and 4), no significant variation of the crack angle was observed. Figures 11 to 13 also compare the observed crack angles with the estimates provided by Methods 1 to 3, respectively. From a qualitative point of view, the performance of the normal stress-based SWT parameter is superior than those obtained using the shear-based parameters, since the correct crack direction is predicted despite the averaging method considered. This observation is in accordance with a similar analysis performed by Vàzquez et al. [19] for fretting fatigue tests on 7075-T651 aluminum alloy. These results suggest that the crack initiation process in aluminum alloys under fretting conditions is related to the normal stresses within the process zone beneath the contact. The size of this process zone is on the order of the critical distance L. It is also seen from Figs. 11 and 12 that the shear stress-based models (FS parameter and MWCM) provided similar crack angles. However, cracks were predicted to propagate outward the contact region, a result that it is not in agreement with the experimental observations (see, e.g., Fig. 9). On the other hand, it can be seen from Fig. 13 that the MWCM associated with the Critical Direction Method can predict crack propagation inward the contact region. It should be noted again that the SWT parameter provided crack directions inward the contact region regardless the stress averaging method used. Table 6: Estimates of fretting crack angle based on different fatigue parameters and stress averaging procedures. Crack Angle ( D ) Method 1

Method 2

MWCM SWT

FS

Method 3

Config.

FS

MWCM SWT

FS

MWCM SWT

C1

-30

-32

6

-25

-28

5

-34

66

1

C2

-30

-34

6

-25

-29

5

-33

63

5

C3

-31

-35

6

-26

-30

5

-33

61

6

C4

-26

-28

6

-22

-24

3

-32

75

-4

C5

-26

-28

7

-21

-24

4

-32

75

-1

C6

-26

-28

7

-21

-24

5

-31

75

0

C7

-30

-34

6

-25

-29

5

-33

63

5

C8

-30

-34

6

-25

-29

5

-32

63

5

Figure 11: Observed crack orientations versus predictions based on Method 1 (Center of the Structural Volume). The range bars represent the standard deviations of the observed crack angles (refer to Table 5). Figure 12: Observed crack orientations versus predictions based on Method 2 (Critical Plane Search on each Point).The range bars represent the standard deviations of the observed crack angles (refer to Table 5). Figure 13: Observed crack orientations versus predictions based on Method 3 (Critical Direction). The range bars represent the standard deviations of the observed crack angles (refer to Table 5).

6. Conclusions New fretting tests on 7050-T7451 aluminum alloy were performed to observe the influence of the tangential load amplitude, bulk stress, and pad radius on the early crack direction. Also, a detailed description of the crack angles within the process zone beneath the contact surface was provided. The Modified Wöhler Curve Method, Fatemi–Socie and Smith–Watson–Topper criteria were combined

with three different stress averaging methods in order to simulate the initial direction of the fretting crack. The main findings of the paper can be summarized as follows: (1) Among all the experimental parameters investigated, the tangential load amplitude was the only one which seemed to affect the angle of crack initiation. A slight increase of such an angle was detected with the increase of the tangential load. (2) The SWT criterion yielded more appropriate crack angles than the shear-based criteria, since it correctly predicted crack directions inward the contact region. It thus seems that the crack initiation process in AA7050-T7451 is related to the normal stresses within a process zone beneath the contact. The size of the process zone is on the order of the critical distance L. (3) The shear stress-based criteria (FS parameter and MWCM) combined with the Center of the Structural Volume and the Critical Plane Search on each Point Methods provided similar early crack angles. However, the estimated crack directions were outward the contact region, a result which is not in agreement with the experimental observations. When associated with the Critical Direction Method, the MWCM was able to predict crack directions inward the contact region. Further developments considering different multiaxial fatigue criteria may provide more accurate estimates of the initial direction of fretting cracks.

7. Acknowledgements This work was financially supported by Centrais Elétricas do Norte do Brasil S/A (Eletronorte), INTESA as part of the ANEEL Research and Development Program in Brazil and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. These supports are gratefully acknowledged. J.A. Araújo and F.C. Castro also would like to thank the support provided by CNPq (Contracts 305302/2017-5 and 308126/2016-5).

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Paper highligths: • • • •

Fretting crack initiation path was evaluated for AA7050-T7451. Critical Plane multiaxial fatigue criteria were used to estimate crack angle. The SWT parameter was more accurate predicting early crack orientation. Early fretting crack angles seem to increase when tangential load is raised.