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 stress intensity) 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].

Small cracks appear to behave differently from large cracks 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), or 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 tested under both constant-R and constant-K_max conditions is evaluated. Large crack behavior is compared to propagation behavior of naturally-initiated small (~45–1000 mm) cracks, and small (<500 m m) surface cracks initiated from sites of simulated foreign object damage (FOD), (all evaluated in the same Ti-6Al-4V microstructure). 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. The high load ratio large-crack tests are believed to eliminate the crack closure mechanism, thereby simulating the behavior of small cracks that are larger than microstructural dimensions but do not have a developed wake.

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 machining stresses, all samples were subsequently low-stress ground and chemically 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 0.96 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, P_cl, 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-R and constant-K_max loading regimens were employed. Under both conditions, loads were shed with the normalized K-gradient of -0.08 mm^-1 as suggested in ASTM E647. The constant-K_max tests were used to achieve threshold values at very high load ratios to minimize the effects of closure and represent worst-case in-service load ratios [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.

Effect of frequency: A comparison of fatigue crack growth behavior at 50 Hz and 1000 Hz is shown in Fig. 1. Cursory experiments at 200 Hz lie within the scatter of the 50 Hz and 1000 Hz data indicating that near-threshold behavior is essentially frequency independent in the range of 50 Hz – 1000 Hz. The apparent lack of a significant frequency effect on near-threshold behavior has also been observed at 1.5 kHz [12], and 20,000 Hz [13] on the same material (Fig. 2). Such frequency-independent growth rates for Ti alloys tested in air have also been reported for 0.1–50 Hz [14,15]; the current work extends this observation to beyond 1000 Hz. This result is particularly interesting in light of the significant accelerating effect of ambient air on fatigue crack growth when compared to behavior in vacuum. Davidson has shown that growth rates in vacuum (10^-6 torr) are ~2 orders of magnitude slower than in air at an equivalent D K, although the non-propagation threshold remains roughly the same. This apparent discrepancy may be due to a environmental mechanism that is not rate-limited in the regime of 50-20,000 Hz. One suggested mechanism involves slip-step oxidation [16]: in air, as the loading cycle is applied, a freshly exposed slip-step oxidizes rapidly thereby preventing slip reversal during unloading. Based on the kinetic calculations of Gao, Simmons, and Wei [17], a freshly exposed slip-step would take ~1 minute to oxidize in a vacuum of 10^-6 torr whereas in air the same oxidation process occurs in ~100 ns. For this reason, the behavior observed in vacuum would not be seen in air at any frequency < 10 MHz!

Effect of load ratio: Constant-R fatigue crack propagation is shown in Fig. 3 at four load ratios: R = 0.1, 0.3, 0.5, and 0.8 (50 Hz). These results are compared to constant-K_max fatigue crack propagation at four K_max values: K_max = 26.5, 36.5, 46.5, and 56.5 MPaÖ m (1000 Hz). As expected, higher load ratios induce lower DK_th thresholds and faster growth rates at a given applied DK. The role of load ratio is commonly attributed to crack closure, which in Ti alloys is mainly associated with roughness-induced closure [18-20]. 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. The measured variation of DK_th and K_max,th values with R are compared in Figs. 5a and 5b. As originally suggested by Schmidt and Paris [21], if the load required to induce closure is independent of load ratio; and, if the variation in threshold with load ratio is simply due to the presence of closure, one would expect a transition in behavior from a K_max-invariant threshold at low R to a D K-invariant threshold at high R. The transition would be expected to occur at the load ratio where K_min,th = K_cl. The present results are consistent with this analysis and provide an indirect verification that K_cl ~ 2 MPaÖ m. This closure level is further supported by the observation that R = 0.3 and R = 0.5 growth-rate data merge at D K > 4.7 MPaÖ m (where the R = 0.3 behavior is closure-free since K_min,R=0.3 > 2 MPaÖ m). Perhaps the most convincing presentation of this transition from a closure-influenced- to a closure-free-threshold is shown in a plot of D K_th versus K_max,th (Fig. 5c, which is simply a coordinate transformation of Figs. 5a and 5b).

Correcting for closure by characterizing growth in terms of DK_eff collapses the low load ratio data (R < 0.5) onto a single curve, Fig. 6 [see also 22]. However, above R ~ 0.5 where closure is presumed to be eliminated, DK_TH values continue to decrease with increasing R. This is observable in the D K_th-K_max,th behavior as well (Fig. 5c): in the region where threshold is K_max-controlled, D K_th is not invariant and continues to drop with increasing K_max. This indicates that above R ~ 0.5, alternative K_max-controlled mechanisms may cause the load ratio effect. This mechanism is most likely related to the Marci effect observed in Ti-6Al-2Sn-4Zr-6Mo as well as other alloys [23] where, above a certain K_max condition, crack growth rates no longer diminish as DK is shed, and cracks can propagate at all applied DK levels.

There have been several proposed explanations for this observed K_max influence on thresholds at very high load ratios. These are described briefly below:
 

• Room temperature creep crack growth. Significant room temperature creep has been observed in Ti-6Al-4V when the applied stress is > ~80% of the yield strength and has been used to analyze the effect of load ratio on S/N behavior [24].

• Near-tip closure. Recent in situ SEM studies on the mechanisms for fatigue crack propagation in Ti-6Al-4V [12] have indicated that even at very high load ratios (R~0.8), there may be significant crack wake interference (closure) up to ~100 m m behind the crack tip. While this near-tip closure would not be detectable by standard closure measurements (i.e. compliance-based measurements), it could significantly shield the crack-tip from fully unloading.

• Stress-assisted hydride formation. Several independent studies have concluded that under sufficient triaxial stress, internal hydrogen can precipitate as metal hydrides (specifically, TiH₂) at a /b [25] or a/a [26] interfaces leading to brittle fracture along the interface. This phenomena has been used to explain both sustained load cracking [27,28] where crack advance is observed under monotonic load and accelerated fatigue crack growth at high load ratios [25,29]. Pao, Feng and Gill [25] have shown that, at a constant load ratio (R = 0.9), the near-threshold fatigue behavior is dependent on the internal hydrogen content, with threshold values dropping from 2.7 MPaÖ m (at 40 ppm H) to 2.0 MPaÖ m (at 1000 ppm H) Fig. 7. The influence of internal hydrogen content on fatigue crack propagation is distinctly similar to the influence of K_max.

Worst-case 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. To verify this "worst case" approach, the high load-ratio fatigue crack propagation data are compared to fatigue behavior from naturally initiated small cracks (~45–1000 mm) and small cracks (<500 m m) emanating from sites of foreign object damage; in both cases crack growth is not observed below DK ~ 2.9 MPaÖ m, Fig. 9 (details described in [30]). 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). 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:

• 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 1,000 Hz. Comparison to recent studies at 1500 Hz and 20,000 Hz as well as literature in the range of 0.1–50 Hz suggests that near-threshold behavior is frequency independent over 5 orders of magnitude.
• Fatigue-crack growth rates in vacuo (~10^-12 to 10^-9 m/cycle) were ~2 orders of magnitude slower than corresponding rates in room air; DK_TH values, conversely, were unchanged. The apparent change in growth mechanism may be attributable to a mechanism such as slip-step oxidation where the rate of the reaction is faster than the cycle time over the range of frequencies studied.
• The influence of load ratio is only partially explained by the closure mechanism. An additional mechanism causes thresholds to decrease below the "closure-free" threshold as R or, K_max) is increased. Observations of sustained load cracking indicate that this mechanism is most likely related to stress-induced hydride formation.
• 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. The long-crack K_max method is considered to provide a practical lower bound to design against the onset of growth of small cracks (when the small cracks are larger than microstructural dimensions).

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.