TOWARD DEVELOPING A PROBABILISTIC METHODOLOGY FOR PREDICTING HIGH-CYCLE FRETTING FATIGUE IN AERO-ENGINES

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1 Proceedings of ASME Turbo Expo 2010 Power for Land, Sea, &Air June 14-18, 2010, Glasgow, Scotland, UK GT TOWARD DEVELOPING A PROBABILISTIC METHODOLOGY FOR PREDICTING HIGH-CYCLE FRETTING FATIGUE IN AERO-ENGINES Kwai S. Chan Michael P. Enright Harold R. Simmons Southwest Research Institute San Antonio, TX 78238, USA Patrick J. Golden Air Force Research Laboratory Wright-Patterson AFB, OH 45433, USA Ramesh Chandra Alan C. Pentz NAVAIR Patuxent River, MD 20670, USA Abstract This paper reports the results of an investigation focused on identifying the necessary steps required to develop a probabilistic fracture mechanics-based methodology for treating high-cycle fretting fatigue in military engine disks. The current methodology based on finite-element method (FEM) modeling, analytical contact stress analysis, and probabilistic fracture mechanics for analyzing low-cycle fretting fatigue is highlighted first. Incorporation of highfrequency vibratory stress cycles into a composite mission profile containing mostly low-cycle stresses requires the use of the Campbell diagram and the need to identify the mode shape, frequency, and forcing function for blade excitation induced by stator wake, flutter or rotating stall. Forced response computation methods for addressing these phenomena in the literature are reviewed to assess their applicability for integration with a contact stress analysis and a probabilistic fracture mechanics life-prediction code. This overview identifies (1) a promising path for combining vibratory stress computation, FEM structural modeling, contact stress analysis, and probabilistic fracture mechanics for treating high-cycle fretting fatigue at the attachment region of engine disks, and (2) a new approach for treating high-cycle fretting fatigue due to vibratory stresses separately from low-cycle fretting fatigue at various positions of a fan-speed profile. 1 Introduction Premature cracking has been observed in several engine disks in military aircraft. Available data suggests that fretting fatigue may be a strong contributor to the premature formation of fatigue cracks in these engine disks. To better assess the risk of disk failure, a probabilistic fatigue crack growth (FCG) methodology has been previously developed for treating fretting fatigue by considering the stress variability [1], inspection intervals [2], material variability [2], and risk mitigation by locally-induced residual stresses [3,4]. The methodology is based on an integration of a global finite element analysis of the disk-blade assembly [5] and associated contact stresses [6, 7], small-crack fretting fatigue modeling [7], and risk assessment using the DARWIN (Design Assessment of Reliability with Inspection) probabilistic fracture mechanics code [8]. The methodology has been demonstrated for an actual military engine disk under real life loading conditions. The influence of inspection and residual stress on potential risk reduction has been investigated for simulated mission profiles typical of those associated with low-cycle fatigue (LCF). The contribution of high-cycle vibratory stresses to the risk of engine failure has not been considered in the previous studies [1-4]. 1 Copyright 2010 by ASME

2 High-cycle fatigue (HCF) has been identified as one of the costliest in-service damages in military aircraft engines [9, 10]. HCF of turbine blades and disks can pose a significant engine risk because fatigue failure can result from resonant vibratory stresses sustained over a relatively short time. A common approach to mitigate HCF risk is to avoid dangerous resonant vibration modes (first bending and torsion modes, etc) and instabilities (flutter and rotating stall) in the operating range [11-14]. However, it might be impossible to avoid resonance for all flight conditions. Thus, substantial efforts have been spent in recent years to develop computational methods for analysis and prediction of the resonance forced response of bladed disks. In particular, computational methods and lifeprediction tools have been developed as part of the High-Cycle Fatigue Program at the Air Force Research Laboratory [6, 7, 15-17]. Some of these tools are relevant and may be applied to assess of the risk of HCF in engine disks that may contain LCF-induced fatigue cracks. In this article, pertinent computational methods in the literature are summarized to establish a framework for developing a probabilistic lifeprediction methodology for assessing fatigue crack growth due to high-cycle vibratory stresses in engine disks. 2 Current Treatment of Fretting Fatigue Crack Growth The current methodology developed by the authors [1-4] for treating fretting fatigue crack growth relies on the use of a simplified mission to compute the global contact forces at the blade/disk interface using a 3D finite-element analysis approach. Fig. 1 illustrates a typical fan speed profile based on the composite mission associated with actual engine usage histories [1]. The finite-element results were used to predict the contact normal force, P, shear force, Q, and contact moment, M, all per unit thickness, via the method developed by Gean and Farris [18]. In general, the blade force is proportional to the square of the rotor speed, Ω [18]: 2 [ t ( P cosθ + Q sin )] Ω F = θ (1) blade i i where P i and Q i are the P and Q values for individual zones that are subdivided to model the attachment region of a disk. The sum of the radial components of P and Q times their slice thickness t must equal the total radial force applied by the blade, as shown in Eq. (1). An example prediction of Q versus P obtained via this method is shown in Fig. 2, which depicts the relationship among contact forces P and Q for the typical fan speed profile shown in Fig. 1. i NL-Fan Speed (% Max) Fig. 1. Q (N/mm) Fig Time (s) Typical fan speed profile based on the composite mission associated with actual engine usage histories. Points indicate load steps. From Chandra et al. [1] Slide Out Slide In µ = P (N/mm) 3000 incr speed decr speed Representative P and Q history for the typical fan speed profile shown in Fig. 1. From Chandra et al. [1]. In Fig. 2, the dashed lines indicate the bounds imposed by the coefficient of friction µ. When Q = µp, the contact is called sliding or gross slip. When Q < µp, the contact is referred to as partial slip. The slope α of the Q versus P curve during partial slip is a characteristic of the component [18]. In previous studies [1-4], contact stresses were obtained directly from the contact forces and moments using the numerical solution of the singular integral equations (SIE) that characterizes the contact interface using the CAPRI software [6] or the Worst Case Fret WCF model [7]. The CAPRI SIE solver was developed to calculate contact stresses for a random shaped indenter pressing into a flat plate with a shear force applied using a Fourier Transform technique [6]. The WCF model [7] was developed to treat the propagation and arrest of small cracks under the influence of the fretting stress field in the presence of a remotely applied bulk stress. The WCF model considers a flat pad with round edges of radius, r, Copyright 2010 by ASME

3 fretting on a half plane. The flat pad is subjected to a normal load P, and a shear force Q. A bulk stress S is applied in the half plane. The contact stress field for the flat pad can be obtained for a given set of P and Q values. The input parameters to both models included the Young s modulus (E = 107 GPa), Poisson s ratio (ν = 0.33), coefficient of friction (µ = 0.7), pad radius (4.955 mm), and the length of the flat pad (6.466 mm). The normal (P) and tangential (Q) forces on the contact surfaces as well as the bulk stresses (S) in the disk were obtained from the finite-element analyses of the blade/disk assembly. The pressure and tangential loads for individual steps of a mission as given by FEM analyses were utilized to compute the contact stresses at the trailing edge of contact for various depths beneath the contact surface. The contact stresses were then summed with the bulk stress to obtain the total stress profile along a specified direction. For illustration, the computed total stress profiles for the first zone on the high pressure side (Hi01) at load step 1 and step 2 of the mission in Fig. 2 are presented in Fig. 3 [1]. Load step 1 resulted in a tensile stress at the trailing edge of contact, while step 2 resulted in a compressive stress. The difference between step 1 and step 2 gives the maximum stress range of the fretting fatigue cycle. The stress ranges associated with load steps 1 and 2 are shown as a function of distance from the contact surface in Fig. 3 [1], which also shows the bulk stress range and the threshold stress range for a large-crack fatigue crack growth threshold of 2 MPa(m) 1/2. The bulk stress range is less than the threshold stress for crack growth when the crack depth is less than 200 µm. Thus, a microcrack less than 200 µm in depth would not grow if the bulk stress acted alone. In contrast, the total stress ranges computed by AFRL using CAPRI [6] and by SwRI using WCF [7], which were in agreement, were higher than the threshold stress range and a micro crack could propagate as a large crack. The growth for fatigue crack under the contact stress field was then treated by probabilistic fracture mechanics via the DARWIN code [8]. The stress ranges shown in Fig. 3 correspond to the contact stresses within one LCF loading cycle. Since they exceed those defined by the large-crack FCG threshold, there is sufficient driving force for a crack to propagate during this loading cycle. Another important observation that can be deduced from Fig. 3 is that there is a sufficient margin between the FCG threshold boundary (dashed line) and the bulk stress (dotteddashed line) that the crack may or may not grow when highcycle vibratory stresses are induced during portions of this LCF loading cycle. The non-propagation region is highlighted as blue in Fig. 3, which represents the triangle region between the dashed line and the dotted-dashed line for crack depth less than 200 µm. In this region, HCF loads that are induced during portions of the LCF cycle may be limited by the growth of small cracks, depending on whether or not the HCF stress ranges exceed the threshold stress boundary. For crack depth greater than 200 µm, the threshold stress is exceeded by the bulk stresses alone. Under this circumstance, HCF loads, if activated by resonance, act in concert with the LCF contact and bulk stresses to propagate the crack to greater length and maybe to the critical length for fracture, depending on the duration of the resonance. Stress Range, MPa Growth Above Dashed Line π K σ = th 2(1.12) πa No GrowthBelow Dashed line Depth, µm Hi01_0001/Hi01_0002 AFRL SwRI Bulk Stress Large Crack K th (semi-circular crack) Fig. 3. Computed stress ranges for high pressure slice 1 corresponding to load steps 1 and 2 compared to the bulk stress range and the threshold stress ranges for a large-crack growth threshold, K th, of 2 MPa (m) 1/2. From Chandra et al. [1]. 3 High-Cycle Vibratory Stresses High-cycle vibratory stresses in compressors or turbine blades are the result of excitation forces induced by aerodynamic phenomena such as stator wakes, flutter, and rotating stall [11-14]. Integral order forced vibration can occur in fans, compressors, and turbine blades when a periodic aerodynamic pulsation acts on a given blade row at a frequency near the resonant frequency of the system [11-14, 19, 20]. The aerodynamic forcing function associated with blade passing frequency, known as blade passing forced response [11-14], is caused by non-uniform upstream pressure field due to periodic obstacles such as stator vanes and struts, while low order harmonics, e.g., those arising from non uniform flow due to non-symmetric intake duct geometries, give rise to lowengine order forced response [11-14, 19, 20]. Dynamic analyses of the bladed disk are typically performed to measure or to compute for the excitation mode shapes and frequencies for various rotational speeds [11-14, 19, 20]. These results are then displayed in a frequency versus speed or Campbell diagram by plotting the natural frequencies of the bladed disk and the excitation frequencies as a function of rotor speed, as shown in Fig. 4 [11]. Thus, the rotor speeds at which significant forced vibration may occur can be discerned from the Campbell diagram as the crossing point between the excitation and the natural frequencies that signifies the resonant frequency of a particular mode shape. In general, blade resonance in the first modes (first bending and first torsion modes etc.) are avoided in the operating range during 3 Copyright 2010 by ASME

4 the design stage and blade passing frequencies are designed to lie outside the engine operation range [11-14]. In cases where not all of the resonance modes are completely removed from the operating range, the associated response level must be assessed by accurate forced response stress computation and/or by engine testing [11]. The transient response of blades during the run-ups or run downs of the aero-engine must be included in the consideration of high-cycle vibratory stresses [11,12]. Amplitude (mm) Max mistuned response Tuned response Min mistuned response Each dot is the max response on the frequency range Frequency, Hz Speed, RPM Fig. 4. A Campbell diagram is utilized to identify resonance frequencies in the operating range. From Seinturier [11]. In a bladed disk, the dynamic response of individual blades can differ because of small variations in dimensions and geometry due to manufacturing tolerances, mounting clearance, and material properties [11, 15]. These small variations of blade characteristics lead to frequency scatter (i.e., mistuning) that can reach standard deviations that are one to two percent of the mean vibration values. This small scatter is sufficient to break the cyclic symmetry of the structure. In a mistuned bladed disk, each blade response differs from each other without a constant phase angle between each sector of the bladed disk. The vibration energy can be localized on only few sectors, generating important resonant responses on a small number of blades [11]. A typical response of a mistuned blade disk, presented as the amplification of the tuned response, is illustrated in Fig. 5 [11]. There are large variations in the blade-to-blade response. The maximum response on one blade is a factor of 1.5 times the tuned response value, while the minimum is about one-half of the tuned response for the example shown: maximum response values of up to 3 times the tuned response have been experienced for other cases. The frequency where excitation occurs may also be widespread. Fig. 5. Frequency (Hz) Forced response of a mistuned blade. From Seinturier [11]. Flutter is an aero-elastic instability in which the aerodynamic forces induced by blade vibration energy feed into the structure and the stresses escalate with each additional cycle of vibration until the energy input is balanced by the energy absorbed by damping [12]. In most cases, flutter cannot be stopped once it is initiated except by changing engine conditions. An important feature of flutter is that it is nonintegral and does not lie on the engine order line, as illustrated in Fig. 6 [12]. Different types of flutter have been identified for various pressure ratios and mass flows. Depicted in a compressor stability map, some of these flutter regions occur near the stall line [12]. For example, two large first bending mode flutter zones were reported in the design of a low aspect ratio fan disk: one zone extended from 65 to 80% of corrected speed and the other extended from 82 to 92% of corrected speed [16]. The flutter boundaries were identified from experimental vibratory stress data as the locations where the alternating stress was above the noise and below a specified stress value [16]. Fig. 6. Frequency Stress Campbell diagram from engine test data with the stress response associated with resonance and flutter. From Srinivasan [12]. 4 Copyright 2010 by ASME

5 4 Forced Response Computations In the design stage, forced response computations are performed to determine if the dynamic stresses are acceptable or not, and to assess the potential danger of excitation at crossings. The governing equation to be solved is given by [11, 12]: [ M ] X ( t) + [ C] X ( t) + [ K ] X ( t) = F( t) (2) where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix of the structure, and F(t) is the unsteady force vector. X(t), X (t), and X (t) are the displacement, velocity, and acceleration functions of time of the structure, respectively. Modal analyses provide the mass and stiffness terms, while the damping and unsteady force terms must be evaluated by forced response computations. Forced response computations are strongly connected to mechanical damping, aero-elastic damping, and various coupling techniques for treating fluid-solid interaction [11]. In weak coupling, both the fluid and structure behavior are linear. In intermediate coupling, the structure is elastic but the fluid is nonlinear. In multi-physics coupling, the structure and the fluid are both nonlinear. Some of these forced response computational processes, which are summarized in several review papers [11-14], require predictions of the structural response (frequency and mode shape) using a FEM code, analyses of steady and unsteady fluid flow by CFD modeling, and coupling of the unsteady harmonics results from CFD in FEM structural modeling to compute the blade stresses. For certain applications, simplified methods are also available for estimating stator wake-induced vibratory stresses in fan blades [20]. The procedure involves estimating the blade excitation forcing function for blades passing through stator wakes [20]. A wake-induced pulsation profile is then simulated on the basis of the velocity profile for the entire rotation. Fourier analysis of the pulsation profile is performed to produce integral order excitations. Information on the blade resonance frequency and mode shape are obtained by modal analyses using finite-element analysis or impulse testing in the laboratory. The frequency response and the order related pulsation are combined in a Campbell diagram to compute the blade vibratory stresses at the excitation frequencies. Once computed, the dynamic stresses are combined with the static (or mean) stresses in a Goodman diagram to determine whether or not the dynamic stresses exceed the HCF endurance limit [11, 20]. The Goodman relation is known to break down and give over-prediction of the HCF limit for some Ti-alloys such as Ti-6Al-4V [22, 23]. It is uncertain whether or not the Goodman relation applies to other Ti-alloys with a microstructure similar to that of Ti-6Al-4V [23]. The Goodman approach is certainly not conservative for engine disks that are subjected to fretting fatigue loads and contain LCF-induced cracks. The presence of cracks in an engine disk necessitates the use of a fatigue crack growth approach for risk assessment. In the reminder of this paper, the forced response function and the high-cycle vibratory stresses in the blades are assumed to be known and available for the HCF crack growth analysis. 5 High-Cycle Fretting Fatigue at the Attachment Region Once the high-cycle vibratory forces on a blade are known, they need to be incorporated into a FEM structural analysis to compute the global contact loads, P and Q, due to the LCF and HCF loading. Fig. 7 shows schematically a representation of the dovetail geometry of the attachment region of a disk with a vibrating blade. The main LCF load is the radial load, R(t), applied to the blade. Excitation is assumed to induce a highcycle vibratory force, G HCF (t), in the tangential direction. A vibratory force, R HCF (t), in the radial direction is assumed here, but it may be negligibly small. Fig. 7. Dovetail geometry subjected to radial load R(t) and R HCF(t) and G HCF(t) due to high-cycle flowinduced vibration. Modified from Gean and Farris [18]. Applying the Gean and Farris analysis [18] leads to the P and Q expressions given by P Q R(t) + R HCF(t) 1 = P m + P HCF 2 G HCF(t) max (3) 1 = Q m + Q HCF 2 max (4) where the mean values of P and Q (P m and Q m ) are functions of R(t), the LCF load on the blade. The vibratory values of P and Q ( P HCF and Q HCF ) are contributed by the vibratory loads acting on the blade and are functions of both R HCF (t) and G HCF (t). In addition, the minimum values of P and Q (P min and Q min ) are given by Eqs. (3) and (4), but the + sign is replaced with the sign. Since the blade passing frequency is expected to occur at a percentage of the maximum engine 5 Copyright 2010 by ASME

6 speed, the HCF vibratory forces are expected to oscillate at the (P m, Q m ) point in a P-Q plot, as shown in Fig. 8, during an engine run-up or rundown event. Flutter-induced vibrations may occur at different engine speeds and thus may reside along different lines in the P-Q diagram. Once the Ps and Qs are computed from the Gean and Farris type analysis [18], the contact stresses at the attachment region can be computed via one of two analytical codes based on the singular-integralequations approach, the CAPRI code [6] or the Worst Case Fret model [7]. incr speed Fig. 8. Q HCF and P HCF due to resonance decr speed Q and P history for a typical fan speed profile with P HCF(t) and Q HCF(t) due to high-frequency forced vibrations. The existence of a no-growth region in Fig. 3 implies that not all values of ( P HCF, Q HCF ) in a P-Q diagram would lead to HCF crack growth. The values of P HCF and Q HCF that lead to FCG can be estimated from the threshold results shown in Fig. 3. During partial slip, Q HCF oscillates at a relatively constant value of P m. The ratio of Q HCF / Q LCF required to cause HCF crack growth can be computed as the ratio of the threshold stress range to the contact stress range induced during an LCF cycle. The result is presented in Fig. 9 for a representative engine disk, which shows the value of Q HCF / Q LCF as a function of crack depth for a case that corresponded to the maximum engine speed. Fig. 9 shows that the Q HCF / Q LCF ratio is about 0.43 for a 10 µm crack and then decreases with crack length to a minimum value of 0.26 at about 2500 µm crack depth. Beyond this point, the driving force for FCG comes mainly from the bulk stress and the contact stress becomes increasingly negative (compressive). For continual crack growth, the high-cycle vibratory stresses must induce Q HCF / Q LCF values that exceed the threshold boundary shown in Fig. 9. In contrast, HCF stress cycles that are below the threshold boundary would not cause crack growth until an LCF load cycle extends the crack to increase the Q HCF / Q LCF value above the threshold boundary. This finding suggests that it may be feasible to identify HCF stress ranges that lead to crack growth or no growth on the basis of the P HCF and Q HCF values. Fig. 9. Computed values of Q HCF/ Q LCF above which HCF crack growth occurs as a function of crack depth for the LCF load cycle presented in Fig Crack Growth Modeling Once the contact stress and bulk stress are computed, the FCG life can be predicted for the combined LCF and HCF load histories. For the deterministic fracture mechanics assessment, the disk blade attachment region can be modeled as a rectangular plate with a semicircular surface crack placed along the edge of contact. The stress intensity factors can be computed using a weight-function-based surface crack stress intensity factor solution that includes a correction for small crack effects by adding the small-crack parameter, a o, [24] to the actual crack depth, where a o is the small-crack parameter. The crack path can be taken to be at a 20 angle from the normal to the attachment surface where the interior stress ranges are highest [2]. This particular crack angle also corresponds to the observed crack growth direction in fretting fatigue experiments and in failed disks reported in the literature [2]. Crack growth rate values have been obtained using a NASGRO model [25] fit to the material data. The NASGRO equation describes all three regions of the largecrack FCG curve and is given by da dn (1 f ) K = C 1 R n Kth 1 K Kc 1 Kmax where C and n are empirical constants for the power-law region. The parameter p is an empirical constant describing the large-crack threshold region, K th, and the parameter q describes the fast fracture region where the maximum K, K max, approaches the critical stress intensity at fracture, K C. The parameter f is the ratio of K op /K max, where K op is the stress intensity factor at which the crack tip is fully open. The presence of a compressive residual increases K op and thus reduces the effective K, which is the difference between K max q p (5) 6 Copyright 2010 by ASME

7 and K op. The value of f is computed in NASGRO using the Newman crack closure model [26]. Fracture Risk Assessment Information regarding a number of random variables is typically required to perform a probabilistic fracture assessment. These variables can be categorized into six primary groups related to the size and location of the initial crack, variability associated with applied stress values and crack growth life models, and uncertainty in the frequency and quality of non-destructive inspection [8]. For treating HCF crack growth, additional information on the excitation frequency, duration, the stress amplitudes, and the engine speed or speeds at which excitation occurs must be known. It is expected that some of the pertinent data may not available to characterize these variables, but must be estimated. However, previous depot inspections revealed premature cracking in some disks [1, 2, 4]. Because of uncertainties, many of these variables such as excitation frequencies, time duration, vibratory stress level, crack depth, and some materials properties might need to be treated as random variables. Using total stress values from the FEM and contact stress modeling, crack area versus flight hour values can be computed for various zones in a bladed disk using the DARWIN probabilistic fracture mechanics software [8, 27]. The procedure or path for performing HCF crack growth for risk assessment of a bladed disk under combined LCF and HCF load histories is summarized in Fig. 10. Figure 10(a) illustrates the steps required to generate the pertinent LCF and HCF stress histories at the blade/disk interface. These stress histories are then incorporated into the DARWIN [8, 27] probabilistic fracture mechanics code for risk assessments. It is anticipated that the average of the nominal crack area versus flight hour values can be predicted using essentially the same procedure developed earlier for treating LCF crack growth. It is anticipated that the stress variability can be adjusted so that the predicted probability of fracture, P c, can be matched with the observed value. 7 Concluding Remarks This overview paper provides an assessment of various pertinent information required to treat high-cycle fretting fatigue in military engine disks. This overview identifies a promising path for combining vibratory stress computation, FEM structural modeling, contact stress analysis, and probabilistic fracture mechanics for treating high-cycle fretting fatigue at the attachment region of engine disks. The approach requires incorporating the resonant frequency, vibratory stress profile, and duration at the appropriate engine speed and treats high-cycle fretting fatigue due to vibratory stresses separately from low-cycle fretting fatigue at various positions of a fanspeed profile. Fig. 10. (a) (b) (a) Analysis procedures for incorporating highcycle vibratory stresses into the current fretting fatigue methodology for treating combined LCF and HCF crack growth, and (b) Probabilistic framework in DARWIN for assessing the risk of fretting fatigue fracture in engine disks due to LCF and HCF loads in a military mission profile. 7 Copyright 2010 by ASME

8 Acknowledgements This work was supported by NAVAIR under Agreement EDO- 08-SA References [1] Chandra R, Golden PJ, Enright MP, Chan KS. Fretting fatigue-based risk assessment of gas turbine engine disks. 49 th AIAA Structures, Structural Dynamics, and Materials Conference, Paper AIAA , April 7-10, 2008, Schaumburg, IL. [2] Enright MP, Chan KS, Moody JP, Golden PJ, Chandra R, Pentz AC. Probabilistic fretting fatigue assessment of aircraft engine disks. Proceedings of ASME Turbo Expo 2009, Power for Land, Sea, and Air, Paper GT , June 8-12, 2009, Orlando, FL. [3] Chan KS, Enright MP, Moody JP, Golden PJ, Chandra R, Pentz AC, 2010, Residual stress profiles for mitigating fretting fatigue in gas turbine engine disks. International Journal of Fatigue, (In Press). [4] Enright MP, Chan KS, Moody JP, Golden P, Chandra R, Pentz A. Influence of random residual stress on fretting fatigue risk of engine disks. AIAA Journal, AIAA (In Press). Also published in Proceedings, 50 th AIAA Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, May 4-9, 2009, Paper AIAA [5] Golden PJ, Calcaterra, J, 2006, A fracture mechanics life prediction methodology applied to dovetail fretting, Tribology International, Vol. 39, pp [6] McVeigh PA, Harish G, Farris TN, Szolwinski MP, 1999, Modeling interfacial conditions in nominally flat contacts for application to fretting fatigue of turbine engine components, International Journal of Fatigue, Vol. 21, pp. S [7] Chan KS, Lee Y-D, Davidson DL, Hudak SJ, 2001, A fracture mechanics approach to high cycle fretting fatigue based on the worst case fret concept, International Journal of Fracture, Vol. 112, pp [8] Wu YT, Enright MP, Millwater HR, 2002, Probabilistic methods for design assessment of reliability with inspection, AIAA Journal, Vol. 40, No. 5, pp [9] Nicholas T, 1999, Critical issues in high cycle fatigue, International Journal of Fatigue, Vol. 21, pp. S221-S231. [10] Cowles BA, 1996, High cycle fatigue in aircraft gas turbines an industry perspective, International Journal of Fracture, Vol. 80, pp [11] Seinturier E, 2007, Forced response computation for bladed disks industrial practices and advanced methods, Proceeding of 12th IFToMM World Congress, Besançon, France, June 18-21, pp [12] Srinivasan AV, 1997, Flutter and resonant vibration characteristics of engine blades, Journal of Engineering for Gas Turbines and Power, Vol. 119, pp [13] Brϑard C, Vahdati M, Sayma AI, Imregun M, 2002, An integrated time-domain aeroelasticity model for the prediction of fan forced response due to inlet distortion, ASME Journal of Engineering for Gas Turbines and Power, Vol. 124, pp [14] Manwaring SR, Rabe DC, Lorence CB, Wadia AR, 1997, Inlet Distortion Generated Forced Response of a Low- Aspect-Ratio Transonic Fan, ASME Journal of Turbomachinery, Vol. 119, pp [15] Kenyon JA, Griffin JH, 2002, Maximum mistuned forced response demonstrated on experimental bladed disk 7 th National Turbine Engine High Cycle Fatigue Conference. May 14-17, 2002, Palm Beach, Florida. [16] Sanders AJ, Rabe D, Fost R, 2002, An experimental investigation of stall flutter in an advanced design lowaspect ratio fan blisk, 7 th National Turbine Engine High Cycle Fatigue Conference, May 14-17, 2002, Palm Beach, Florida. [17] Calcaterra J, Naboulsi S, 2005, Design methodology to investigate contact fatigue damage in turbine engine hardware, International Journal of Fatigue, Vol. 27, 2005, pp [18] Gean MC, Farris TN, 2005, Finite element analysis of the mechanics of blade/disk contacts, 46th AIAA Structures, Structural Dynamics, and Materials Conference, Austin, TX, April [19] Fleeter S, Zhou C, Houstis EN, Rice JR, 1999, Fatigue life prediction of turbomachine blading, CSD TR #99-030, School of Mechanical Engineering and Department of Computer Sciences, Purdue University, West Lafayette, Indiana. [20] Simmons HR, Brun K, Cheruvu S, 2006, Aerodynamics instability effects on compressor blade failure: a root cause failure analysis, Paper GT , 51st ASME International Gas Turbine & Aeroengine Technical Congress, Barcelona, Spain, May [21] Goodman J, 1930, Mechanics applied to engineering. 9 th ed, New York, NY: Longmans, Green & Co., Inc., pp [22] Nicholas T, Zuiker JR, 1996, On the use of the Goodman diagram for high cycle fatigue design, International Journal of Fracture, Vol. 80, pp [23] Chan KS, 2010, Changes in fatigue life mechanisms due to soft grains and hard particles. International Journal of Fatigue, Vol. 32, pp [24] El Haddad MH, Smith KN, Topper TH, 1979, Fatigue crack propagation of short cracks. ASME J Eng Mat Tech, Vol. 101, pp [25] NASGRO Fracture Mechanics and Fatigue Crack Growth Analysis Software, v5.0, NASA-JSC and Southwest Research Institute, [26] Newman Jr, JC, 1984, A crack-opening stress equation for fatigue crack growth. Int. J. Fracture, Vol. 24, pp. R131-R135. [27] DARWIN User s Guide, 2008, Southwest Research Institute, San Antonio, TX. 8 Copyright 2010 by ASME