High-cycle fatigue (HCF) is one of the prime causes of turbine engine failure in military aircraft [1]. It can result in essentially unpredictable failures due to the growth of fatigue cracks in blade and disks under ultrahigh frequency loading, where the cracking initiates from small defects often associated with microstructural damage caused by fretting or foreign object impacts [2]. To prevent HCF failures, methodologies are required that identify the microstructural damage which can lead to such failures. This paper is focused on the critical levels of damage in a Ti-6Al-4V alloy, typically used in the front, low-temperature stages of the engine.

During HCF, engine components experience high frequency (~1-2 kHz) vibrational loads due to resonant airflow dynamics, often superimposed on a high mean stress [2,3]. Because of the high frequencies, HCF-critical turbine components must be operated below the fatigue-crack propagation threshold (DK_TH) such that crack propagation cannot occur within ~10⁹ cycles. Although an extensive database [4,5] exists for such thresholds, it has been derived mainly from test geometries containing large (> few mm) cracks, often under loading conditions that may not be representative of turbine-engine HCF. Furthermore, except under specific loading conditions, e.g., at very high mean loads, such tests are not necessarily relevant to the HCF problem, where the critical flaw sizes are much smaller, i.e., < 500 mm [6]. Since small cracks can grow at velocities faster than corresponding large cracks (at the same applied driving force) and can propagate below the large-crack DK_TH threshold, design against HCF failure must be based on the notion of a practical small-crack threshold, measured under the representative conditions [7].

The main reasons why small cracks behave differently from large cracks are when crack sizes become comparable to i) microstructural size scales, where biased sampling of the micro-structure leads to accelerated crack advance along "weak" paths (continuum limitation), ii) the extent of local plasticity ahead of the crack tip, where the assumption of small-scale yielding implicit in the use of K is not strictly valid (linear-elastic fracture mechanics limitation), and iii) the extent of crack-tip shielding behind the crack tip, where the reduced role of shielding leads to a higher local driving force than for the equivalent large crack at the same applied D K (similitude limitation) [8]. Of these cases, the latter is most important in the present case as cyclic plastic-zone sizes will generally not exceed a few micrometers, and the crack sizes relevant to the HCF problem are invariably larger than the characteristic microstructural dimensions.

In the present work, the near-threshold crack-growth rate behavior of large (>5 mm) cracks, naturally-initiated small (~45–1000 mm) cracks, and small (<500 m m) surface cracks initiated from sites of simulated foreign object damage (FOD), are compared in a single microstructure of Ti-6Al-4V, tested at high frequencies (~50-1500 Hz) and load ratios (R ~ 0.1-0.95). Specifically, we examine whether "worst-case" threshold values, measured for large cracks, can have any utility as a practical lower bound for the onset of small-crack growth under HCF conditions.

A Ti-6Al-4V alloy (6.30Al, 4.17V, 0.19Fe, 0.19O, 0.13N, bal. Ti (wt%)) was supplied as 20 mm thick forged plates from Teledyne Titanium after solution treating 1 hr at 925°C and vacuum annealing for 2 hr at 700°C. The microstructure consisted of a bimodal distribution of ~60 vol% primary-a and ~40 vol% lamellar colonies of a+b, with a UTS of 970 MPa, a yield strength of 930 MPa and a Young’s modulus of 116 GPa [9]. To minimize residual stresses, all samples were subsequently low-stress machined and chemical milled to remove ~30–100 mm of material.

Large-crack propagation studies were conducted on compact-tension C(T) specimens (L-T orientation; 8 mm thick, 25 mm wide) at R ratios (ratio of minimum to maximum loads) varying from 0.10 to 0.95 in a lab air environment (22° C, ~45% relative humidity). Crack lengths were monitored in situ using back-face strain compliance and verified periodically by optical inspection. Crack closure was also monitored using back-face strain compliance; specifically, the (global) closure stress intensity, K_cl, was approximated from the closure load, measured at the point of first deviation from linearity in the elastic compliance curve upon unloading. Based on such measurements, an effective (near-tip) stress-intensity range, DK_eff = K_max – K_cl, was determined. To approach the threshold, both constant and variable R testing was employed. Under both conditions, loads were shed with the normalized K-gradient of -0.08 mm^-1. With variable R testing, the threshold was approached under constant-K_max/increasing-K_min conditions to minimize the effect of closure [10,11]. At 50-200 Hz (sine wave), tests were conducted on servo-hydraulic testing machines operating under automated closed-loop K control, with the fatigue thresholds, DK_TH and K_max,TH, defined as the minimum values of these parameters at a propagation rate of 10^-10 m/cycle. Corresponding fatigue tests at 1000 Hz were performed under K control on a newly developed MTS servohydraulic test frame using a voice-coil servovalve.

In addition, the growth rates of small surface cracks initiated from sites of simulated FOD were examined at an applied maximum stress of 500 MPa (R = 0.1, 20 Hz) using cylindrical tensile specimens containing a rectangular gauge section. The damage was obtained by firing 3.2 mm diameter, chrome-hardened steel spheres, using compressed gas, onto the flat specimen surface. Impacts with an incident path orthogonal to the sample surface were performed at velocities of ~200 to 300 m/s, representing typical in-service impact velocities on blades. Stress intensities characterizing the small cracks were computed from the Newman-Raju surface crack solution [12], assuming a half-surface length to depth ratio of unity (from fractographic observations).

Effect of load ratio: The effect of load ratio on the fatigue-crack growth rates of large (>5 mm) cracks in Ti-6Al-4V at 50 Hz indicates (as expected) that higher load ratios induce lower DK_TH thresholds and faster growth rates at a given applied DK (Fig. 1). A two-parameter fit of the Paris regime yields a growth law (in units of m/cycle, MPaÖ m) of da/dN = 5.2 x 10^-12 DK^2.5 K_max^0.67. The role of load ratio is commonly attributed to crack closure, which in Ti alloys is mainly associated with roughness-induced closure [13-15]. Based on compliance measurements, no closure was detected above R = 0.5; however, at R = 0.1-0.3, K_cl values were roughly constant at ~2.0 MPaÖ m. Characterizing in terms of DK_eff reduces the disparity in growth rates with varying R, implying that an important origin of the load ratio effect is indeed crack closure [see 16]. However, above R ~ 0.5 where closure is presumed to be minimal, DK_TH values continue to decrease with increasing R. This indicates that alternative K_max-controlled mechanisms may cause the load ratio effect at very high R. One such mechanism may be near-tip closure, which cannot be resolved using compliance methods, yet has been detected in microscopy studies.

The measured variation of DK_TH and K_max,TH values with R are compared with the Schmidt and Paris model [17] in Fig. 2. This model is based on the notion that K_cl and the effective DK threshold, DK_eff,TH, are constant and independent of R; it predicts that measured DK_TH and K_max,th thresholds will be load-ratio independent, respectively, above and below a transition R where K_min = K_cl. The present constant-R results are consistent with this model, and the transition R, above which closure is ineffective (K_min > K_cl), is observed at K_min = K_cl » 2-3 MPaÖ m, consistent with the experimentally measured value of K_cl.

Effect of frequency: The role of frequency is shown in Fig. 3 where growth rates at 50 and 1000-1500 Hz are compared. High frequency results are not statistically distinguishable from the low frequency data. Additional tests at 200 Hz and 20,000 Hz (the latter using ultrasonic fatigue [18]) confirmed the lack of a frequency effect on ambient-temperature growth-rate behavior in Ti-6Al-4V. Such frequency-independent growth rates for Ti alloys tested in air have been reported for 0.1–50 Hz [19]; the current work extends this observation to beyond 1000 Hz.

Effect of loading sequence: In order to measure "lower-bound" thresholds, at very high R where closure is minimal, variable-R testing was performed at 1000 Hz using constant-K_max/increasing-K_min loading sequences (Fig. 4). Here, compared to DK_TH of 2.4 MPaÖ m at R = 0.8, at a constant K_max of 26.5 MPaÖ m, a final load ratio of R = 0.92 was achieved yielding a threshold of 2.2 MPaÖ m; with a constant K_max of 36.5 MPaÖ m, a threshold of DK_TH = 1.9 MPaÖ m was achieved with a final R of 0.95. Note that the closure is minimal as the high R results in large minimum crack-tip opening displacements (~ 8 mm at R = 0.95). The DK_TH threshold of 1.9 MPaÖ m, measured under constant-K_max cycling at R = 0.95, is taken to be a "worst-case" threshold in this alloy. It is to be compared with results on naturally-initiated small cracks in this microstructure, where small-crack growth is not observed below DK = 2.9 MPaÖ m (R = 0.1) [20].

Small-crack behavior: Naturally-initiated small cracks (a ~ 45–1000 mm) have been measured in this microstructure using cylindrical tensile samples [20]. Results at R = 0.1 (at a maximum stress of 550 MPa at 85 Hz) are compared in Fig. 5 with the present large-crack data. Although small-crack growth rates generally exceed those of the large cracks at the same applied DK, no small crack growth is seen below DK ~ 2.9 MPaÖ m. This value is ~50% larger than the "worst-case" DK_TH of 1.9 MPaÖ m, measured with large cracks in this alloy using constant-K_max cycling.

Small-crack growth from simulated foreign object damage sites was also examined. The effect of the damage, which was in the form of craters several millimeters in diameter [21], was to markedly reduce the fatigue life from that obtained with an undamaged sample. Specifically, fatigue lives were reduced by over 2 orders of magnitude following 200 - 300 m/s impacts, with cracks tending to initiate at the bottom of the indent for the lower velocity impacts and at the crater rim for the higher velocity impacts. The growth rates of small cracks originating from such FOD sites are also compared in Fig. 5 with growth-rate data for large and naturally-initiated small cracks in this alloy. Both the naturally-initiated and FOD-initiated small-crack velocities were within the same scatter band, initially up to an order of magnitude faster than corresponding large-crack results. However, FOD-initiated cracks were not observed in the Ti-6Al-4V below a DK of ~2.9 MPaÖ m; i.e., well above the "worst-case" DK_TH threshold.

Effect of environment: A comparison of crack growth in this alloy at high frequencies (1-1.5 kHz) in room temperature air and vacuum (~10^-6 torr) is shown in Fig. 6 at R = 0.6-0.8. Although threshold values are essentially unchanged (DK_TH ~ 2.6 MPaÖ m in air vs. 2.7 MPaÖ m in vacuo), crack-growth rates are some 3 orders of magnitude faster in air than in vacuo. In view of the lack of a frequency effect on growth rates between 50 and 20,000 Hz, the magnitude of the disparity in growth rates in air and vacuum is quite surprising. The origin of the apparent environmental contribution to crack growth is unclear, but may be associated with the role of oxygen in limiting the degree of slip reversibility at the crack tip [22,23]. Due to the lack of a frequency effect at ~20 to 20,000 Hz, the environmental mechanism responsible for faster growth rates in air must be fast; indeed, the rate of oxidation of Ti-5Al-2.5Sn in the presence of small amounts of water vapor (10^-6 torr) has been shown to be extremely rapid [22]. Applying the oxidation reaction kinetics in [28] to the equilibrium partial pressure of water vapor at 25°C, a clean surface of the Ti alloy would be ~90% covered in oxide in 2.6 ´  10^-7 seconds. Thus, if slip-step oxidation were responsible for the faster growth rates in air, one would not expect to see a frequency effect until frequencies exceed ~4 MHz, consistent with the observed results.

Lower-bound threshold concept: The problem of turbine engine HCF requires that design must be based on the notion of a threshold for no crack growth under conditions of high mean loads, ultrahigh frequencies and small crack sizes. Since the measurement of small-crack thresholds is experimentally tedious, the approach used here has been to simulate the mechanistic origins of the small-crack effect using "worst-case" large cracks, i.e., the measurement of thresholds under conditions which simulate the similitude limitation of small cracks by minimizing closure. The present results show that with constant-K_max cycling at 1 kHz, a "worst-case" threshold can be defined in Ti-6Al-4V at DK_TH = 1.9 MPaÖ m (R ~ 0.95). Although D K_TH ® 0 as R ® 1 [24], the current value at R = 0.95 is defined as K_max ® K_Ic in the absence of global closure and below the stress intensities for the growth of naturally-initiated small cracks and small cracks emanating from sites of foreign object damage. Consequently, it is believed that the "worst-case" threshold concept can be used as a practical lower bound for the stress intensity required for the onset of small-crack growth under HCF conditions.

Based on an investigation into the high-cycle fatigue of a Ti-6Al-4V turbine engine alloy tested in air and vacuum at room temperatures, the following conclusions can be made:

1. Room temperature fatigue-crack growth (~10^-12 to 10^-6 m/cycle) and threshold DK_TH values were found to be frequency-independent over the range 50 to 1,500 Hz. Comparison to prior results strongly suggest that such behavior extends out to 20,000 Hz (<10^-10 m/cycle).
2. A "worst-case" fatigue threshold, measured for large cracks at R = 0.95 under constant-K_max conditions, was found to be 1.9 MPaÖ m for this alloy. This should be compared with measurements on naturally-initiated small cracks and FOD-initiated small cracks in the same microstructure, where small-crack growth was not reported below DK ~ 2.9 MPaÖ m.
3. Foreign object damage, simulated by hardened steel spheres impacted at 200-300 m/s on a flat surface, provides sites for fatigue crack initiation. At applied stresses ~10% below the 10⁷-cycle fatigue strength, crack-initiation lives were many orders of magnitude shorter than in un-impacted samples. Subsequent small-crack growth from the FOD sites occurred at rates considerably faster than large cracks subjected to the same applied DK level. No crack growth from FOD sites was observed at DK values below 2.9 MPaÖ m.
4. Fatigue-crack growth rates in vacuo (~10^-12 to 10^-9 m/cycle) were ~3 orders of magnitude slower than corresponding rates in room air; DK_TH values, conversely, were unchanged.
5. The "worst-case" fatigue threshold of 1.9 MPaÖ m, measured for large cracks at R = 0.95, was found to provide a practical lower bound to describe the onset of growth of small cracks initiated naturally or from sites of foreign object damage, under HCF conditions in this alloy.

Acknowledgments: Supported by the Air Force Office of Scientific Research by the Multidisciplinary University Research Initiative on High Cycle Fatigue to the University of California under Grant No. F49620-96-1-0478. We thank the Hertz Foundation (for supporting B.L.B.), Drs. G. Lütjering, J. A. Hines and J. O. Peters for their small-crack data, Dr. D.L. Davidson for his in vacuo data, and Dr. A.W. Thompson for helpful discussion.