Application of a total life prediction model for fretting fatigue in Ti–6Al–4V

International Journalof Fatigue

International Journal of Fatigue 29 (2007) 1311–1318

www.elsevier.com/locate/ijfatigue

Application of a total life prediction model for fretting fatigue in Ti–6Al–4V D.B. Garcia b

a,*

, A.F. Grandt

b

a Southwest Research InstituteÒ, 6220 Culebra Road, San Antonio, TX 78238-5166, United States School of Aeronautics and Astronautics, Purdue University, 315 N. Grant Street, West Lafayette, IN 47907-1282, United States

Received 5 December 2005; received in revised form 26 September 2006; accepted 8 October 2006 Available online 28 November 2006

Abstract A method for predicting the total fretting fatigue life is applied for Ti–6Al–4V dog-bone fretting fatigue specimens. The total life model incorporates a dual mechanism approach of including the crack initiation life and propagation life while simultaneously determining an associated initial flaw size. This technique adds autonomy to existing fretting fatigue models by releasing the dependence on estimating an initiation flaw size. The model is exercised on two sets of Ti–6Al–4V fretting fatigue experiments and compared to existing results and life prediction methods. The variable initiation crack length model predicts the experimental data and proves to be a new advancement in total fretting fatigue life prediction. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Ti–6Al–4V; Fretting; Initiation; Propagation; Life prediction

1. Introduction Fretting fatigue is often recognized for reduction in expected component life because of large cyclic stresses resulting from two materials being clamped together and oscillated relative to one another. Peak stresses at the edges of contact act to quickly nucleate cracks, while remotely applied loads combined with contact stresses propagate the cracks to failure. The rapid nucleation and steady propagation makes a dual mechanism total life prediction model appealing. Fatigue crack nucleation life can be obtained by correlating a multiaxial fretting stress field to a strain-life based fatigue damage parameter. The life determined from the model is assumed to correspond to a crack size and geometry dictated by observation or engineering judgement. Propagation life is the estimation of the remaining life of a component assuming an initial flaw and applying linear elastic fracture mechanics (LEFM). The *

Corresponding author. Tel.: +1 210 522 3112; fax: +1 210 522 6965. E-mail address: [email protected] (D.B. Garcia).

0142-1123/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2006.10.007

resulting lives calculated from the two methods are then added together to predict the total fretting fatigue life. The dual mechanism total life approach for fretting fatigue has been implemented by Szolwinski and Farris, and Golden and Grandt while making several improvements along the way [1,2]. Szolwinski and Farris incorporated a Smith–Watson– Topper parameter acting on a critical plane to calculate the initiation life at the surface of Al-2024-T351 fretting fatigue specimens with cylindrical contact pads [1]. A nucleated crack was defined through observation as 1 mm (0.04 in.) deep with a 1.5 mm (0.06 in.) half-width. Propagation life was estimated by using the stress intensity factor for a semi-elliptic surface flaw in a plate under tension while neglecting the influence from the contact stresses on the propagation life. Szolwinski and Farris then used the propagation life prediction subtracted from the experimentally observed lives to compare their initiation criteria [1]. The next evolution in the dual life mechanism approach was developed by Golden and Grandt and Murthy et al. for Ti–6Al–4V fretting fatigue specimens [2,3]. They

D.B. Garcia, A.F. Grandt / International Journal of Fatigue 29 (2007) 1311–1318

estimated initiation life with a stress invariant life parameter coupled with a weakest link statistical model [2,3]. The propagation model, developed by Golden and Grandt, implements a weight function for a semi-elliptical surface flaw to calculate the stress intensity factor [2]. The versatility of the weight function allows for the non-uniform fretting fatigue stress field to be incorporated, but still requires an initial flaw size assumption. Golden determined the initial crack depth to be 25.4 lm (0.001 in.) deep, which corresponds to the El Haddad short crack parameter for Ti– 6Al–4V [2,4]. The crack aspect ratio of depth divided by half-width, a/c, was determined through observation of contact pads to be a/c = 0.2 [4]. The Golden and Grandt life prediction results compared well with the experimental fretting fatigue results for Ti– 6Al–4V, but was shown to be overly conservative at lives close to and greater than one million cycles [2]. This conservative behavior in combination with the initial flaw size assumptions provided the motivation for the work discussed in this document. The objective of the research was to attempt to make the fretting fatigue life prediction model more autonomous by removing the requirement for an estimated initial flaw size, and still maintain confidence in the results. This problem was approached by implementing the existing fretting fatigue life prediction techniques discussed by Murthy et al. and Golden and Grandt in combination with a new variable initial crack size total fretting fatigue life prediction model introduced by Navarro et al. [2,3,5,6]. Two separate fretting fatigue experimental data sets were obtained from the Purdue University Fretting Fatigue Group [7,8] and analyzed for this study. The analysis consists of predicting the total fretting fatigue life of Ti– 6Al–4V dog-bone specimens by implementing a new variable initial crack size life prediction model. The results are then compared to the predictions from previous models.

Ni1(ah1)…Nin(ahn)

ah

One accepted approach for predicting total fretting fatigue life consists of separately calculating the initiation life and then estimating an initial flaw size to determine the remaining crack propagation life. A total fretting fatigue life prediction method was introduced by Navarro et al. that avoided the initial flaw size estimation that was required of the other approaches [5,6]. The model is based on total life prediction of notched members by relating the growth rates of strain-life and LEFM fatigue models [9]. Although initiation and propagation are different phenomena, the consequence is the same; the failure of the specimen. A more rigorous explanation can be found in the literature [5,6,9], but highlights are provided here for application to this research. During fretting fatigue, either crack initiation or propagation will be the dominant growth mechanism at some time during the life of the specimen. The variable initiation length model provides a method of determining which mechanism is dominating life and the corresponding initial crack length for propagation calculations. This approach is based on the optimization of a total life curve that is created by the summation of an initiation life curve and propagation life curve as shown in Eq. (1). N T ðah Þ ¼ N i ðah Þ þ N p ðah Þ

K

Np1, …Npn

Np (x) Propagation lives

da/dN

Pad

Hypothetical crack position

Dog-Bone

ð1Þ

The first step in developing the total life curve is to specify a potential or hypothetical crack path, ah, like the one in Fig. 1. The initiation life curve is created by calculating the initiation lives, Ni1, Ni2, . . . Nin, for the given stress state and associated damage parameter at a series of positions, x = ah1, ah2, . . . ahn, along the hypothetical crack path beginning at the surface of the specimen (x = 0) and continuing into the depth of the specimen to an arbitrary depth x = ahn. The propagation life curve is created by implementing a LEFM analysis to calculate the remaining

Ni (x) Initiation lives

σeq

2. Variable initiation length model

NT (x) Total lives

1312

Initial Flaw Size

Hypothetical crack lengthh Hy

Initial flaw size

Fig. 1. Schematic showing the variable initiation length process.

D.B. Garcia, A.F. Grandt / International Journal of Fatigue 29 (2007) 1311–1318

Dog-Bone

R76.2

73.15 20.32

15.24 Contact Pads

1313

10˚

406.4

9.65

R3.048 3.048

38.1 Fig. 2. Schematic showing fretting fatigue specimen geometries and configurations.

life, Np1, Np2, . . . Npn, at initial crack sizes starting just below the surface and continuing to the same arbitrary depth as the initiation life curve. The procedure for calculating initiation and propagation are shown in Fig. 1. Now, the initiation life curve and propagation life curves are functions of a hypothetical crack path, and can be summed to form the total life curve, NT(x). The total life of the specimen and non-arbitrary initial crack size can now be determined from the total life curve [5,6]. The minimum value of the total life curve corresponds to the position in the specimen where the hypothetical growth rate from the initiation life curve is equal to the growth rate from the propagation life curve. The conceptual growth rates for the initiation life curve and propagation life curve are defined as dNi/dx and dNp/dx, respectively. Navarro explains this concept from the growth rate perspective in full detail [5,6]. The semi-arbitrary initial flaw size estimation is no longer necessary because the model predicts its size. Navarro showed that this new approach works for fretting fatigue with spherical contact of Al 7075-T6 [5,6]. The current work discusses the method as it applies to fretting fatigue in Ti–6Al–4V with nominally flat indenters. 3. Fretting fatigue stress field The fretting fatigue stress fields used for this analysis were associated with experiments that consisted of dogbone specimens being cyclically loaded while two nominally flat contact pads simultaneously applied a normal and shear load. For these experiments, the contact pads were flat (approximately 3.05 mm) with rounded edges (3.05 mm radius), and were tapered at 10° from the flat. A schematic of the specimen geometries can be seen in Fig. 2. It should be noted that the dog-bone specimens will propagate a fretting fatigue crack until failure and are used for the life prediction modeling. The contact pads witness the same contact stresses as the dog-bones, but do not have

the remotely applied cyclic bulk load to propagate the cracks to failure. The experiments discussed in this project were tested in the condition known as partial slip, which is where the contacting interfaces are actually stuck together with the exception of a small band or racetrack surrounding the contact. This type of contact should not be confused with gross sliding. The geometry of the contacting surfaces and the coefficient of friction combined with the relative displacements lead to large localized stresses surrounding the stick region [3]. Due to the highly localized stresses, fretting fatigue crack initiation sites can be accurately predicted with analytic tools [1,3,7,10]. The resulting loads from the experiments combined with the pad geometry are used to determine the corresponding stress field for each dog-bone specimen with the help of the software package CAPRI, developed at Purdue University [1,3,7,10]. More information on the CAPRI software can be found in the literature [1,3,7,10], but a brief overview is provided here. CAPRI calculates the tractions of arbitrary indenter geometries as they come into contact with an elastic half space. The program provides the contact pressure and shear tractions which can then be used to determine the subsurface stresses. Contact pad geometries are usually prescribed as flat with rounded edges or cylindrical, but the CAPRI software also allows for indenter geometries taken from numerical smoothing of surface measurements. The pad profiles used for this research came from a moving average fitting technique, while the profiles used in the Golden and Grandt and Murthy et al. [2,3] work came from a polynomial fitting technique of surface measurements. It should be noted that different profiles provide different stresses and different stress gradients, so consistency within the individual project was maintained. The program provides the contact pressure and shear tractions which can then be used to determine the subsurface stresses. An example of the tangential stress profile parallel to the contact face obtained through CAPRI analysis for a fret-

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D.B. Garcia, A.F. Grandt / International Journal of Fatigue 29 (2007) 1311–1318 1500

DogBone Contact Pad

Contact Pad

ΔQ

ΔQ

P

P Max Stress

Δσ

Tangential Stress σxx (MPa)

1000

500

0

-500 σxx max σxx min

-1000

0

0.2

0.4

0.6

Depth Into Specimen (mm)

Fig. 3. Tangential stress profiles into the depth of specimen associated with crack opening and closing stresses into the specimen depth.

ting fatigue experiment performed by the Purdue fretting fatigue group is shown in Fig. 3. The Ti–6Al–4V specimen was tested with a remote cyclic bulk stress range of 287.5 MPa (41.7 ksi) at a load ratio of R = 0.03. The contact pads applied a normal load of P = 1668 N/mm (9525 lb/in) with a shear load range of DQ = 1230 N/mm (7022 lb/in). It can be seen in Fig. 3 that the near surface maximum stress is very high and decays to the bulk stress within about 76.2 lm (0.003 in.), but the minimum stress decays at a much slower rate. 4. Initiation model The fatigue crack initiation model implemented in this analysis consists of a multiaxial fatigue parameter combined with a stressed area or weakest link approach. Eq. (2) is the equivalent stress damage parameter, and has shown promising results for analyzing smooth and notched specimens in fatigue for Ti–6Al–4V [2,3]. Other multiaxial damage models like Findley, Socie, and SWT, may also be used, but the advantage of the equivalent stress parameter is that it avoids the need to find a critical plane on which initiation occurs [11,12]. w

req ¼ 0:5ðDrpsu Þ ðrmax Þ

ð1wÞ

ð2Þ

imum points in the fretting fatigue cycle, and is given by Eq. (3) [12]. 1 h Drpsu ¼ pffiffiffi ðDrxx  Dryy Þ2 þ ðDryy  Drzz Þ2 2 12 2 þðDrzz  Drxx Þ þ 6ðDr2xy þ Dr2yz þ Dr2zx Þ ð3Þ The maximum stress term from Eq. (2) is given by Eq. (4) and the mean stress term is given by Eq. (5). Because fretting stresses can reach very large values in an elastic solution, a first order approximation to account for plasticity is implemented, which is discussed in the work by Perez specifically for fretting fatigue [13]. Perez found that plastic shakedown was occurring during the fretting cycles and suggested that some approximation for plasticity would be beneficial. The maximum stress is capped at the cyclic yield stress, which corresponds to 758 MPa (110 ksi) for Ti–6Al–4V. The summed stress values from Eq. (5) are the stress components based on the maximum and minimum points in the fatigue cycle. The Modified Manson– McKnight coefficient, b, is given in Eq. (6), and primarily used to control the sign of the mean stress term [12]. Eq. (6) represents the sum of the individual principal stresses at the maximum and minimum stress points in the fretting fatigue cycle.

rmax ¼ rmean þ 0:5Drpsu qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b 2 2 2 rmean ¼ pffiffiffi ðRrxx  Rryy Þ þ ðRryy  Rrzz Þ þ ðRrzz  Rrxx Þ þ 6ðRr2xy þ Rr2yz þ Rr2zx Þ 2 2 ðRr1 þ Rr3 Þ b¼ ðRr1  Rr3 Þ The coefficient, w, is a fitting parameter that was determined experimentally to be w = 0.433 for Ti–6Al–4V [12]. The pseudo stress, Drpsu, is an alternating stress defined by each stress component based on the maximum and min-

ð4Þ ð5Þ ð6Þ

Once the equivalent stress is calculated for the fretting fatigue cycle, a weakest link approach is implemented that was originally developed to relate notched fatigue specimens to smooth bar fatigue data. Further in-depth discussion can

D.B. Garcia, A.F. Grandt / International Journal of Fatigue 29 (2007) 1311–1318

be found in the literature [11,12,14], but the following equations are necessary for the initiation calculation. The premise behind the model is that the initiation site on a notched specimen is less likely to exist than on a large smooth bar specimen for a given stress state. Eq. (7) implies that the probabilities of failure for the two specimen types are the same, and the data is fit to capture that relationship. The Fs term corresponds to the stressed area term, which is given in Eq. (8). The DA term is given by the incremental area of each position of stress over the given contact size. The Fs1 term is the stressed area coefficient of the baseline smooth bar experiments and is given as Fs1 = 0.161 for Ti–6Al–4V[12]. The alpha, a, coefficient is a shape factor for a Weibull distribution determined through experiments to be a = 35 [3,12]. The final governing equation for cycles to initiation for Ti–6Al–4V is given in Eq. (9) where the equivalent stress is in MPa, and the equation was obtained from curve fitting experimental data.  1a F s2 Dreq;1 ¼ Dreq;2 ð7Þ F s1 a  n   X ri;j F sj ¼  ð8Þ DAi;j rmax;j i¼1 req ¼52; 476ðN f Þ

0:6471

þ 450:85ðN f Þ

0:03582

ð9Þ

5. Propagation model The crack propagation model is based on incremental growth dictated by the fatigue crack growth relationship and stress intensity factor solutions derived from a weight function. The solution method and procedure used in this project were originally developed by Golden and incorporate the Shen and Glinka weight function with the Newman and Raju reference stress intensity factor solutions for a semi-elliptical surface crack in a plate [14–17]. The stress intensity factor solution given in Eq. (10), is related to the integral of the stress, r, acting perpendicular to the potential crack and multiplied by a weighting function mA(x,a) or mB(x,a) for the depth point and surface point respectively. The general form of the weight function was found by Shen and Glinka for two dimensional cracks to be given by Eqs. (11) and (12) for depth and surface points as shown in Fig. 4 [17]. The weight function derivations and further explanation can be found in [2,14]. Z a K¼ rðxÞmðx; aÞdx ð10Þ

1315

This weight function requires that the stress varies in only one dimension, and that the existence of the crack does not influence the stress field. These assumptions also require that the crack propagate in Mode I. Fretting fatigue cracks in Ti–6Al–4V have been shown to form at arbitrary angles dependent upon the contact geometry and applied loads, but they quickly change direction and end relatively normal to the contact face. Because of the nature of the maximum and minimum values of the fretting fatigue stress field, it is possible to obtain very large DK values and stress ratios less than R = 1. The large DK influence is addressed in the propagation software by limiting the stress ratio to R = 1. It is recognized that a negative stress ratio would imply a negative Mode I Kmin value and the stress intensity factor only has meaning for positive K values, but the negative Mode I stress ratio is allowed in this work because the crack propagation data used was originally analyzed with negative stress ratios up to R = 1 [18,19]. In order to implement a crack propagation prediction technique for fretting, a method that accounts for variable stress ratios must be considered. For previous work with this alloy, an effective stress intensity factor crack propagation model was developed [18,19]. This model is not a crack closure model and does not include intrinsic qualities like closure or crack propagation resistance. The model is a fitting technique that includes load ratio influences. The equation for the effective stress intensity factor is given by Eq. (13), which is a function of the maximum stress intensity factor, Kmax, stress ratio, R, and fitting parameter, m. The crack propagation is dictated by Eq. (14). Table 1 gives the values for the constants Kth, B, P, Q, D, and Kc employed here for Ti–6Al–4V [18,19]. m

m1

K eff ¼ K max ð1  RÞ ¼ DKð1  RÞ  P "  Q #  D da K eff Kc B K eff ¼e ln ln dN K th K th K eff

ð13Þ ð14Þ

Table 1 Crack propagation coefficients for Ti–6Al–4V [18,19] p p Kth (ksi in) B P Q D Kc(ksi in)

m+

m

3.83

0.72

0.275

-18.1

3.71

0.235

-0.006

60

0

h 2 x 1=2 mA ðx; a; a=c; a=tÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 þ M 1A ð1  Þ a 2pða  xÞ x x 3=2 i þM 2A ð1  Þ þ M 3A ð1  Þ ð11Þ a a h 2 x 1=2 mB ðx; a; a=c; a=tÞ ¼ pffiffiffiffiffi  1 þ M 1B ð Þ a px x x 3=2 i þM 2B ð Þ þ M 3B ð Þ ð12Þ a a

A B

2c

W

x a

y

t

Fig. 4. Schematic showing the location of the stress intensity factor calculation.

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D.B. Garcia, A.F. Grandt / International Journal of Fatigue 29 (2007) 1311–1318

In addition to the crack propagation data for Ti–6Al–4V, a short crack parameter was also implemented into the analysis. This short crack parameter is based on the El Haddad short crack correction, which is determined from the long crack threshold and endurance limit for Ti–6Al–4V. This parameter was used by Golden [14] in previous Ti–6Al– 4V fretting fatigue life prediction work and the same as the one discussed by Navarro[5,6]. The value for the short crack parameter was estimated to be a0 = 25.4 mm (0.001 in.) for Ti–6Al–4V. 6. Experimental data The fretting fatigue experimental data was obtained from previous experiments performed by Farris et al. [7,8]. Two separate data sets of Titanium experiments were obtained. The first set consisted of Ti–6Al–4V dog-bone specimens with Ti–6Al–4V contact pads [7]. The second set of Titanium experiments consisted of Ti–6Al–4V dogbone specimens with Ti-17 contact pads [8]. The equivalent stress parameter versus fatigue life data determined from the experiments is given in Fig. 5 [20]. The fact that the smooth specimen baseline data do not correspond to the fretting fatigue results is a consequence of the severe fretting stress gradients that result In early crack formation at the specimen surface, followed by longer periods of crack growth, and in some cases, arrest. Thus, it is obvious from these results that a total fatigue life analysis is required for fretting tests (i.e., the equivalent stress nucleation model cannot be used alone). 7. Results and discussion Because the variable initiation crack length method discussed in Section 2 was originally developed for through cracks modified with an elliptic crack correction, it was val-

idated on existing crack propagation data to see if it works for elliptical surface cracks and the weight function [20]. These data came from bare Ti–6Al–4V fretting fatigue experiments that were analyzed by Golden [14]. The results obtained by Golden were in good agreement and his model predicted the total life well except for the higher life regime. The high life experiments were under predicted by Golden’s model. This would result in conservative life estimates, but may end up being too conservative for practical use. In order to incorporate the Navarro method into a two dimensional crack solution, an initial aspect ratio of a/ c = 0.2 was assumed. This is the same assumption implemented in the prior methods and comes from the fact that the observed aspect ratio of the fretting cracks formed in the contact pads varies from 0.1 < a/c < 0.4 [21]. Fig. 6 is a representation of the variable initiation length derivation for the same fretting fatigue specimen discussed in the fretting fatigue stress field section. If the variable initiation length method is applied to the Ti–6Al–4V data, the total life predictions compare better. The best result is that an initial flaw size was determined by the analysis, not the user. This removes one of the assumptions that are made to get accurate fretting fatigue crack propagation results. The life prediction comparison is shown in Fig. 7. The data represented include the total life predictions from the Navarro method compared to the previous research method in which an initial flaw size is assumed [20]. The plot shows that the previous technique will not capture the higher cycles, but incorporating the Navarro solution method will help capture the larger lives. The first analysis consisted of determining the total lives of the experiments of the Ti–6Al–4V dog-bone specimens and contact pads. By observing the life predictions, it can be seen that there is generally good agreement in the predicted lives versus the experimental lives. Even the higher cycle regime shows good agreement. There was not much difference in the two life prediction models. The second

800

600

Estimated Cycles, N

Equivalent Stress (MPa)

140000

400

200

0 3 10

105

Minimum of Total Life Curve Determines Initial Flaw Size

100000 80000 60000 40000

Baseline Ti64-Ti17, R=0.0 Ti64-Ti64, R=0.0 Ti64-Ti64, R=0.5

104

120000

Initiation Life Curve, Ni Propagation Life Curve, Np Total Life Curve, NT

20000

106

107

Total Life (N) Fig. 5. Equivalent stress values for Titanium fretting fatigue experiments and baseline smooth bar Ti–6Al–4V equation [20].

0 0.00

0.05

0.10

0.15

0.20

Initial Crack Depth, a (mm) Fig. 6. Depiction of variable initiation length method for an actual experiment.

D.B. Garcia, A.F. Grandt / International Journal of Fatigue 29 (2007) 1311–1318

Estimated Initial FLaw Sizes, ai, (mm)

Predicted Fretting Fatigue Lives, Nf

107 Navarro Variable Initial Flaw 25μm Initial Flaw Predicted=Experimental 6

10

105

4

10

0.10

1317

Ti64-Ti64, R=0 Ti64-Ti64, R=0.5 Ti64-Ti17, R=0

0.08

0.06

0.04

0.02

0.00 104

105

106

107

Total Predicted Fretting Fatigue Lives, NT 103 103

104

105

10 6

107

Fig. 9. Initial flaw sizes determined through variable initiation length method for Ti–6Al–4V.

Experimental Fretting Fatigue Lives, Nf Fig. 7. Comparison of predicted and experimental fretting fatigue lives for Ti–6Al–4V experiments.

8. Conclusions

Predicted Fretting Fatigue Lives, Nf

10

7

106

10

The conclusions regarding Ti–6Al–4V dog-bone specimens and Ti-17 contact pads that were either shot peened or bare are given below:

Variable Initial Flaw 25.4μm Initial Flaw Predicted=Experimental

1. A variable initiation length parameter provided by the Navarro analysis allows for more autonomy in predicting the total fretting fatigue life of a specimen. The new method removes the need for an initial flaw size assumption. 2. The variable initiation length total life prediction method can be implemented successfully for fretting fatigue when using surface flaws and the weigh function stress intensity factor approach.

5

104

103 3 10

10

4

10

5

10

6

10

7

Acknowledgements

Experimental Fretting Fatigue Lives, Nf Fig. 8. Predicted and experimental fretting fatigue lives for Ti64–Ti17 fretting fatigue comparisons.

analysis used Ti–6Al–4V dog-bone specimens with Ti-17 contact pads, and these results are shown in Fig. 8. Just to emphasize the Navarro method, the initial crack size is plotted versus total life for the various experiments in Fig. 9. No obvious trend emerges, but it can be seen that the Navarro nucleation crack size occurs at a position less than 0.06 mm (0.0024 in.) except for three specimens, which are still below 0.1 mm (.04 in.) [20]. The previous location is the point at which nucleation no longer dominates the life of the specimen, and propagation is taking over. This is to be expected because of the decreasing stress field. It still shows that propagation life is the dominant factor for the total life of the specimen and begins to dominate very near the surface.

This work was supported, in part, under Air Force Contract No. F33,615-01-2-5225, with Dr. Jeffrey R. Calcaterra, AFRL/MLLMN, Project Monitor. The material for this project was provided by General Electric Aircraft Engines (GEAE), Cincinnati, Ohio, with direction from Dr. Robert VanStone. Fretting fatigue specimens and results were obtained from experiments performed by Dr. T.N. Farris at Purdue University. References [1] Szolwinski MP, Farris TN. Mechanics of fretting fatigue crack formation. Wear 1996;198:93–107. [2] Golden PJ, Grandt Jr AF. Fracture mechanics based fretting fatigue life predictions in Ti–6Al–4V. Eng Fract Mech 2004;71:2229–43. [3] Murthy H, Farris TN, Slavik DC. Fretting fatigue of Ti–6Al–4V subjected to blade/disk contact loading developments in fracture mechanics for the new century. In: 50th anniversary of Japan society of materials science, 2001. p. 41–8.

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[4] Golden PJ, Bartha BB, Grandt AF, Nicholas T. Measurement of the fatigue crack propagation threshold of fretting induced cracks in Ti– 6Al–4V. Int J Fatigue 2004;26(3):281–8. [5] Navarro C, Dominguez J. Initiation criteria in fretting fatigue with spherical contact. Int J Fatigue 2004;26:1253–62. [6] Navarro C, Garcia M, Dominguez J. A procedure for estimating the total life in fretting fatigue. Fatigue Fract Eng Mater Struct 2003;26:459–568. [7] Farris TN. Communication regarding Ti–6Al–4V and Ti-17 fretting fatigue experiments, Purdue University. [8] Farris TN, Murthy H, Perez-Ruberte E, Rajeev PT. Experimental characterization of fretting fatigue of engine alloys. In: Proceeding of the 6th annual national turbine engine conference. Jacksonville: FL; 2001. [9] Socie DF, Morrow J, Chen WC. A procedure for estimating the total fatigue life of notched and cracked members. J Eng Fract Mech 1979;11:851–9. [10] McVeigh PA, Harish G, Farris TN, Szolwinski MP. Modeling interfacial conditions in nominally flat contacts for application to fretting fatigue of turbine engine components. Int J Fatigue 1999;21:S157. S156. [11] Slavik DC, Dunyak T, Griffiths J, Kurath P. Crack initiation modeling in Ti–6Al–4V for smooth and notched geometries. In: Proceeding of the 5th annual turbine engine high cycle fatigue conference, Chandler: AZ; 2000. [12] Slavik DC, Farris TN, Murthy H, McClain RD. Fatigue crack initiation modeling for application with stress gradients in smooth

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[19]

[20]

[21]

and notched geometries. In: Proceedings of the 6th annual national turbine engine high cycle fatigue conference, Jacksonville: FL; 2001. Perez E, elasto-plastic finite element analysis of contacts with applications to fretting fatigue, Thesis MS, Purdue University, August 2001. Golden PJ. High cycle fatigue of fretting induced cracks, PhD Dissertation, Purdue University, December 2001. Newman Jr JC, Raju IS. An empirical stress-intensity factor equation for the surface crack. Eng Fract Mech 1981;15(1–2):185–92. Raju IS, Newman Jr JC. Stress–intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates. Eng Fract Mech 1979;11:817–29. Shen G, Glinka G. Weight functions for a surface semi-elliptical crack in a finite thickness plate. Theor Appl Fract Mech 1991;15:247–55. HCF, High cycle fatigue (HCF) science and technology program 1999 annual report. AFRL-PR-WP-TR-2000-2004, Universal Technology Corporation, January, 2000. HCF, High cycle fatigue (HCF) science and technology program 2002 annual report. In: Tom M, Bartsch, editor, AFRL-PR-WP-TR-20002004, Universal Technology Corporation, Universal Technology Corporation, January, 2002. Garcia DB. Crack propagation analysis of surface enhanced titanium alloys with fretting induced damage. PhD Dissertation, Purdue University, May 2005. Garcia DB, Grandt AF. Fractographic investigation of fretting fatigue cracks in Ti–6Al–4V. Eng Failure Anal 2005;12(4):537–48.