166 Effects of Damage on HCF Properties process. The proposed answer to this question is based on the concept of a weakest link theory where the location of the fatigue failure initiation point is a random variable in space. However, in precracking of the material in the case of C-shaped specimens, and particularly in the case of notched specimens, the process finds the location of the weakest link and initiates the crack in that location. Threshold testing then samples locations in a larger region, but the weakest link has already been identified. Thus, the crack continues to propagate at the precrack location once the threshold stress is reached. Further evidence of the relatively small effect of a short crack on the FLS can be found in the work of Lanning et al. [8] where prior LCF loading was followed by step testing to establish the HCF limit stress corresponding to a life of 10 6 cycles. Results for the FLS corresponding to 10 6 cycles as a function of the number of LCF cycles are shown in Figure 4.17 for specimens with small notches having k t =27. The full LCF life was 10,000 cycles at the stress used in the precracking, 609MPa. Many specimens were heat tinted after LCF loading so the final fracture surfaces could be examined for any cracks formed during the initial LCF loading. One crack was found which was formed in a small notch specimen after 2500 LCF cycles, at 25% of LCF life. The crack had a depth of approximately 25m, and a width of about 250m. This crack corresponds to the lower of the two data points in Figure 4.17, at 2500 LCF cycles. Since a crack was not observed in the specimen with the data point at a higher HCF fatigue limit, which is only greater by 10MPa, it appears that a crack of this size may not be significantly detrimental to the HCF limit stress. Note, however, that a crack with lesser depth, perhaps only half of that found, would not be easily detectable using the heat-tinting method. 0 200 400 600 800 1000 0 500 1000 1500 2000 2500 3000 10 6 HCF limit stress (MPa) Initial LCF cycles R HCF = 0.8 Ti-6Al-4V, f = 50 Hz K t = 2.7, small notch 10 initial LCF cycles 10 4 LCF strength @ R = 0.1 Figure 4.17. HCF limit stress at 10 6 cycles versus number of initial LCF loading cycles for stress relieved small notch specimen, R LCF =01 and R HCF =08 (from [8]). LCF–HCF Interactions 167 Similar data obtained from other tests on notched specimens [8] are presented in Figure 4.18. In these cases, preloading in LCF often involved testing at stress levels that produced plastic deformation near the notch root. The plastic strain field was normally larger than that obtained under pure HCF with no preload, so the comparison of data from LCF–HCF tests with pure HCF tests is much more complicated than in the smooth bar case. In the case of specimens tested at R = 08, the high peak stresses under HCF combined with the plastic deformation occurring under the prior LCF makes the comparisons even more difficult. It should be noted that in at least two cases of this type of LCF–HCF loading, a crack was found on the fracture surface which indicated that the LCF produced initial cracking which resulted in a reduction of subsequent HCF strength [8]. The effect of precracking is discussed below. Nonetheless, the reduction of fatigue strength due to LCF in notched specimens does not appear to be very significant until at least 25% of LCF life has been expended. As pointed out above, this is based on average life so that with scatter and a factor of safety, it is not reasonable to expect that a material would be subjected to 25% of average life in service. In one of the earliest studies of load-history effects, Kommers [21] pointed out that for small specimens of steel with diameters of about 0.3 in. (7.6 mm) there is no evidence of cracks being formed for large cycle ratios of 0.9 at stresses above the endurance limit. Cycle ratio is defined as the ratio of the number of cycles applied at a given overstress (stress above the endurance limit) to the number of cycles necessary to cause failure at that overstress. It was concluded that a crack is formed only a short time before failure although the author noted that other test results show that this is not true for large specimens. In addition to studying the effect of prior loading history where the stresses were below the HCF fatigue limit, a brief study was made at AFRL/ML of the effect of prior 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 R = 0.1 R = 0.8 σ f /σ end N /N f Ti-6Al-4V plate k t = 2.7 Figure 4.18. Fatigue strength of notched specimens subjected to prior LCF [8]. 168 Effects of Damage on HCF Properties LCF where stresses are above the HCF fatigue limit [22]. Contrary to the thoughts of Kommers [21], this latter work was conducted under the common belief that cracks initiate under LCF at a smaller fraction of life than under HCF. Consequently, the subsequent HCF life may be shortened after LCF cycling because, if cracks are present, the life to initiation may be drastically reduced. If, however, the LCF and HCF are conducted at different values of R, then the LCF loading may be at peak stresses below the HCF fatigue limit and any cracks may be below the fatigue crack growth threshold. The case of different values of R for LCF and HCF was investigated. The effect of prior LCF at R =−1 on the subsequent HCF fatigue limit at R = 05 was evaluated using the step-loading technique. Specimens were subjected to a predetermined number of LCF cycles and tested subsequently under HCF. The LCF life is approximately 10 5 cycles at R =−1 with a maximum stress of 600MPa at 1 Hz. The results showing the fatigue limit corresponding to 10 7 cycles as a function of prior LCF cycles are presented in Figure 4.19. The data show two things. First, there does not appear to be any significant degradation of HCF fatigue limit due to prior LCF cycling, even up to 75% of life. Second, there does not appear to be a trend in the limited data obtained with the number of steps in the step-loading technique as shown in Figure 4.19. Another important study of the influence of prior loading cycles at high stress levels on the fatigue limit was conducted by Walls et al. [23]. They noted that many questions have been raised about use of the Haigh diagram for assessing design margins for components subjected to combined LCF and HCF, and they suggested the exploration of the use of fracture mechanics as an alternative. In particular, they emphasized that such an approach needs to be validated under realistic operating conditions on real components. To accomplish this, they subjected two single-crystal blades to two different types of 550 600 650 700 0 20406080100 3 steps 4 steps 7 steps Maximum stress (MPa) Percent LCF life Ti-6Al-4V plate 70 Hz R = 0.5 Figure 4.19. Fatigue limit against % LCF life. LCF–HCF Interactions 169 vibratory loading modes typically found in engine-operating environments. In the first case, the HCF loading was a high-amplitude, non-resonant vibration (NRV). The high amplitude was well above that observed under normal operating conditions and was chosen so that it would propagate a 0.75 mm initial flaw. In the second case, the blade was subjected to alternately applied NRV and a resonant vibratory mode. In this case, the NRV amplitude was lowered to a level typical of engine operation while the resonant mode was large enough to produce crack propagation from some pre-flaw. In both cases, several large amplitude cycles were interspersed between the applied HCF cycles to represent the LCF driver in a typical mission from major throttle excursions such as takeoff and landing. While details of the complete loading history such as number of HCF cycles and values of R are not available, the following table (Table 4.2) gives some of the basic information of the loading history, where p–p denotes peak to peak amplitude. The loading conditions were put into a fracture mechanics model that did not consider any load interactions such as overload effects. The material was represented by a crack growth curve and a threshold stress intensity below which no crack propagation takes place. Appropriate K solutions for the blade geometry based on observed crack shapes from fracture surfaces were used. For blade #1, loaded in HCF only by the NRV stresses, the model predicted 4 complete missions from the initial flaw to final fracture. This compared favorably with 3–5 arrest marks on the fracture surface of a blade subjected to that mission. The fracture surface information was enhanced by the nature of the fracture mode in the material used, which changed based on the K range applied to the blade. This made it possible to distinguish between LCF and HCF loading conditions. For blade #2 subjected to the combined NRV and resonant vibration modes, the fracture surfaces for each individual block of HCF loading were distinguishable due to the different amplitudes of the individual blocks as shown in Table 4.2. The loading block information was put into the fracture mechanics model and resulted in a prediction of 103 complete missions. This compared favorably to the 95 missions evaluated from the fractography. The model was further used to predict the crack size at which the NRV first started to propagate based on threshold data. Crack growth from the NRV mode was predicted to commence at a crack length of 5.5 mm. The fractography, which showed that early propagation was due only to the resonant mode, indicated that NRV-driven crack propagation started at a crack length of 5.1 mm. Table 4.2. Summary of LCF–HCF loading conditions Loading mode Blade #1 Blade #2 Non-resonant 350 MPa p–p 175 MPa p–p Resonant None 295 MPa p–p LCF 0–875 MPa 0–875 MPa 170 Effects of Damage on HCF Properties The results of these two experiments and the corresponding fracture mechanics compu- tations led the authors to conclude that HCF life can be reasonably well predicted under a realistic mission spectrum involving both LCF and HCF. The ability to predict the onset of HCF based on the threshold stress intensity factor was also noted. It should be pointed out that the specific missions investigated for the components selected did not appear to involve any load interactions. Further, the starting flaw sizes were large enough so that small crack effects did not have to be considered. 4.2.1. Studies of naturally initiated LCF cracks Damage due to LCF cracks can alter the HCF resistance of a material by changing the criterion for crack nucleation and subsequent propagation from one governed by stress (endurance limit) to one governed by fracture mechanics (crack growth threshold). Studies investigating the interaction of naturally initiated LCF cracks and HCF threshold do not appear to have been conducted prior to the USAF HCF program. However, there had been studies that addressed major/minor cycle interaction, lower-bound HCF threshold, and crack growth of both long cracks and artificially induced small cracks including history effects. Akita et al. [24] demonstrated in Ti-6Al-4V with C(T) specimens that repeated loading blocks containing a single overload caused the da/dN crack growth curve to shift down, thereby producing an increase in the threshold level. Traditional methods for managing HCF have relied heavily on the Haigh (Goodman) diagram approach. The Haigh diagram approach requires smooth bar fatigue data over a range of stresses and stress ratios in order to define a material’s fatigue endurance limit. The endurance limit, defined as the stress range below which failure does not occur within a specified lifetime, is then used to specify allowable design stresses. The shortcoming of this approach is that it does not account for any type of defect such as that caused by FOD, fretting fatigue, or cracking due to LCF or combined loading. In the next sections, the effects of loading history on the crack propagation characteristics of a material, particularly the threshold for HCF crack propagation, are discussed. 4.3. CRACK-PROPAGATION THRESHOLDS As shown above, the fatigue crack-growth threshold, a fracture mechanics concept, can be used to determine a stress level below which a crack of a given size will not grow. Threshold can be used to determine an allowable stress as a function of crack size and is seen as a viable alternative design parameter to the allowable design stress as determined from the Goodman diagram approach. As with the Goodman diagram approach, threshold is a material specific quantity and must be determined under a variety of conditions. The experimental method by which a threshold is determined and the applicability of LCF–HCF Interactions 171 that value of threshold to different methods of creating a crack are issues that have not been completely resolved within the technical community. Some examples are presented below. The subject of crack-growth thresholds is presented in greater detail in Chapter 8. Sheldon et al. used artificially created surface cracks in a so-called K b specimen geometry to study the effect of specimen geometry and shed rate in Ti-6Al-4V [25]. They found that increased shed rates could be used to arrive at valid thresholds. However, they also noted that the choice of the starting value of K max had an effect on the allowable shed rate that could be used and still measure valid thresholds. As K max was increased, the absolute value of the gradient needed to be decreased in order to distance the crack tip stress field from the plastic wake. Sheldon et al. also found that specimen thickness ranging from 2.54 to 6.35 mm did not influence the measured threshold at R = 01 and R =08. This study showed that both specimen geometry and load history could influence the value of the material threshold. This is just one indication that the threshold may not be an inherent material property. In another investigation, Lenets and Nicholas [26] used two different methods for determining the fatigue crack-growth threshold in titanium alloy IMI 834. The first test method used a transition from no-growth to growth while the second used a growth to no-growth approach. This is analagous to increasing K or decreasing K in standard threshold testing. A consistent difference between the two thresholds for each test method was found. Increasing K applied to the initially dormant crack produced higher fatigue crack-growth thresholds as compared to the situation when decreasing K values were applied to a growing crack. Lenets and Nicholas concluded that this difference in measured thresholds was attributed to the crack tip shielding associated with residual stresses in front of the crack tip caused by the two different loading histories. These two cited studies, along with results from numerous other investigations, indicate that loading history is an important consideration when determining a threshold for crack propagation and that a single number for a material threshold may not be a valid consideration. The subject is discussed in further detail in Chapter 8. Loading-history effects are also crucial elements in the study of LCF–HCF interactions in establishing allowable limits for HCF loading. Most of the work in this area has been associated with combined cyclic fatigue (CCF), that is HCF, generally at high R, which is accompanied by periodic underloads to zero or near-zero stress. Several studies have shown that superimposed HCF cycling adversely affects the LCF life of steel [27, 28] and superalloys [29]. Some of the first work in crack growth under combined LCF–HCF was conducted on Inconel 718 at 650 C [30]. The data showed that crack-growth rate at this temperature was dominated by time-dependent behavior for the LCF cycles and cycle- dependent behavior for HCF. The minor (HCF) cycles had a threshold stress intensity, dependent on stress ratio, below which they had no effect on LCF growth rates, and above which the HCF growth dominated. 172 Effects of Damage on HCF Properties Guedou and Rongvaux [31] were among the first to examine the effect of superimposed HCF on the LCF life. In Ti-6Al-4V at 20 C and Inconel 718 at 550 C, they examined both initiation life (to a crack depth of 50 m) and crack propagation life. They found that superimposing HCF cycles (R = 060 0 80, and 0.85) on LCF cycles significantly reduced both the initiation and propagation life relative to those measured for LCF-only loading. In agreement with Ouyang et al. [29], the crack propagation life was reduced significantly more than initiation life. Perhaps the greatest amount of research on combined HCF and LCF loading has been conducted by Powell et al. [32–35] who have examined the crack-growth rate of titanium alloys and other materials under combined HCF and LCF loading. Details of some of these investigations are presented later in this chapter. The earliest investigations [32, 33] were conducted on Ti-6Al-4V and demonstrated the existence of an onset stress intensity, K onset , below which HCF had no effect on LCF growth rate and above which it dominated the growth rate under combined loading. The linear summation of growth rates obtained from LCF and HCF loadings alone was shown to predict the combined behavior for this material. Thus, K onset was essentially equivalent to K th for HCF alone, provided that the ratio of number of HCF to LCF cycles was large enough so that HCF growth rates per block exceeded those due to LCF alone. This condition has led to the requirement for using very high frequency testing apparatus in order to perform these types of tests in a reasonable time. Subsequent work shows Ti-6Al-4V [34] to be less sensitive to load-history effects than nickel-base superalloys. Later work in Ti-6Al- 4V [35] showed the effects of multiple LCF underloads and overloads combined with high stress ratio HCF loading on crack growth. The linear summation model showed that the introduction of overloads caused the fatigue-crack-growth curves to shift to lower values of K HCF , when compared with multiple underloads. In the following section, further details are presented on thresholds obtained under LCF–HCF load spectra and studies of history effects in determining such thresholds. 4.3.1. Overloads and load-history effects While a considerable amount of work has been done to study the effect of transient load cycles on crack-growth rate, only a very small portion of that work has addressed the question of determining a threshold for subsequent crack growth. Most of the published literature on underloads and overloads in crack-growth modeling deals with spectrum loading and the retardation or acceleration of growth rates. The work on overloads has concentrated on retardation effects, the slowing down of crack growth for some number of cycles after the overload before the crack resumes its steady-state growth rate. The term “delay cycles,” the number of cycles it takes before steady state resumes, is commonly used in describing the retardation phenomenon. A schematic of the growth rate behavior under constant amplitude loading, after an overload, is shown in Figure 4.20. P max refers LCF–HCF Interactions 173 Time P P max P ss da /dN A 0 B Figure 4.20. Schematic of overload applied to constant amplitude fatigue cycling and the corresponding effect on crack-growth rate; (A) retardation, (B) arrest. to the peak load of the overload cycle, while P ss refers to the maximum load of the steady- state cycles. Note that minimum loads or stress ratios have to be specified to completely define the loading condition. The usual situation studied is denoted by “A” in the figure, indicating a temporary retardation of growth rate until steady-state growth conditions are resumed. ∗ One subset of this type of study is when the number of delay cycles becomes large enough to consider that subsequent crack growth has been completely arrested, denoted schematically by “B” in Figure 4.20. In this case, the threshold for crack growth following an overload which, in turn, follows the same amplitude steady state crack growth, can be determined. The overload ratio, defined as OLR = P max /P ss from Figure 4.20, is a common terminology used when describing overload effects. No systematic study of the influence of OLR on the threshold for crack propagation after single or multiple overloads seems to have been conducted. Some of the earliest work on transient loading involved the study of the number of delay cycles after a single peak overload. Probst and Hillberry [36], in conducting a study of crack ∗ In some cases, an acceleration of crack growth rate occurs immediately after or during the overload cycle. Part of this can be attributed to the overload cycle itself. This is not shown in the figure nor discussed in this book. 174 Effects of Damage on HCF Properties retardation under the simple spectrum depicted in Figure 4.20, employed a “zeroing-in” technique to determine the size of the plastic zone required to arrest a crack at any partic- ular fatigue stress intensity level. Their tests involved testing under constant K conditions and their results on overload crack retardation were attributed to some combination of crack blunting, development of residual compressive stresses ahead of the crack tip, and crack closure. Replacing P max by K 0 and P ss by K fmax in Figure 4.20, they observed that the bound- ary between total arrest and continued crack propagation after the overload was described by a straight line, K fmax =0435K 0 , for a wide variety of test conditions using 2024-T3 Al as the test material. They modeled the phenomenon using the concept of an effective K that is reduced fromthe applied K bya quantity that can be considered equivalentto a crack closure load. The quantity was related to the overload plastic zone size. This type of modeling has seen considerable use over the years. In the same time period, Gallagher and coworkers [37, 38] investigated load-interaction models to predict crack growth under different types of overloads resulting from spectrum loading. They modeled the instantaneous crack-growth rate following an overload and showed it was possible to generalize the stress intensity to account for the overload- generated arrest or threshold condition using an overload shut-off ratio. The modeling made use of the concept of plastic zone size and was able to account for the effect in materials with different yield strengths. Since the focus of their work was on the explanation of the retardation phenomenon, the experiments also covered the limiting condition of complete retardation. The overload shut-off ratio was the experimentally determined overload ratio above which crack arrest occurred. Similar type work was conducted by Alzos et al. [39] where, instead of a single overload, they applied a single transient load that combines an overload with an underload, the latter often referred to also as a negative overload. In Figure 4.20, the minimum load for the single overload cycle would go below the minimum load of the steady-state cycling. They found the growth/arrest boundary corresponding to a subsequent crack-growth rate of da/dN =10 −8 mm/cycle which was the limit of resolution in their experiments. Most of the emphasis in their work, like in much of the research in this area, was on delay in crack growth, and very little of the work addressed complete crack arrest. One of the more significant studies of the effects of prior loading on the subsequent threshold for crack propagation was that of Hopkins et al. [40] who used an increasing-load step test at constant R to determine the overload modified long crack threshold, K ∗ th .In both a nickel-base alloy and Ti-6Al-4V, they found that for high values of prior overloads that K ∗ th increased exponentially with the magnitude of the prior applied overload. (Log K ∗ th was found to be linear with K maxOL ) It was also found that the K ∗ th /overload data could be extrapolated to obtain the basic threshold at low stress ratios where valid precracking is impractical for this type of test. Other findings of significance were the effect of frequency on the overload modified threshold and the effect of the number of overload cycles. In both the titanium alloy at room temperature and the nickel-base LCF–HCF Interactions 175 superalloy at elevated temperature, their data showed higher thresholds at 1000 Hz than at 30 Hz. Also, when 50 overload cycles were used instead of one, the threshold was 20% higher in the titanium at R =05, but unchanged in titanium at R =0 9 and nickel at R = 0785. The authors, after examining all of the data, concluded that crack closure as well as residual compressive stresses that develop at the crack tip due to the overload contribute to in the threshold due to overloads. Closure, however, was not considered to be a factor in tests at high R. These approach and other methods like them provide models that work well in describ- ing crack retardation regions where crack growth is retarded. However, these approaches require experimentally determined inputs such as the overload shut-off ratio and a baseline K th to successfully correlate such data. After observing that little work dealing directly with the determination of load- interaction effects on threshold, and even less with small cracks, was available, Moshier and co-workers conducted a series of investigations on load-history effects on the HCF threshold [4, 6, 9]. They studied load-history effects on the crack-growth threshold in notch specimens with LCF precracks on both medium size cracks [9], and later with very small cracks [4]. The experiments were conducted primarily on forged Ti-6Al-4V plate material. Double-notch-tension test specimens having the dimensions shown in Figure 4.21 were used. Stress concentration factors and notch depths of the two notches were chosen so that failure could be confined to the more severe notch having an elastic stress concentration factor, k t , based on net section stress, of 2.25. The use of equal depth for the two notches produced essentially no bending in the specimen whether fixed or pinned grips were used. To study the load-history effects on the HCF threshold, the loading schematic of Figure 4.22 was used. The cracks were developed by precracking which, for these inves- tigations, was referred to as LCF. In the earliest investigation [9], precracking was conducted at stress ratios of −10 and 0.1. Following the step-loading procedure as shown in Figure 4.22, load was increased until crack growth was detected. K th was defined as the value of K where propagation begins from a no-growth state. The K th determined in the studies by Moshier et al. represents the onset of crack propagation. This quantity is identical to that referred to in the terminology K onset used by Powell et al. (see [32], for example) or K ∗ th used by Hopkins et al. [40] as an “overload modified threshold” determined from increasing-load step testing on precracked test specimens. All of the data were obtained at either R = 01orR = 05, whereas the LCF cracks were generated at R =01orR =−10. The term “overload” or “underload effect” was used in this investigation as described later. The data for the HCF threshold after a LCF crack was initiated are plotted in a Kitagawa type diagram in Figures 4.23 and 4.24 for HCF values of R =01 and R =05, respectively. In each of the figures, a curve is drawn representing the long crack threshold of K max = 51MPa √ m for R = 01 (Figure 4.23) and K max =58 MPa √ m for R =05 (Figure 4.24). The curves represent the best bilinear fit of a/c measurements from fracture surfaces for the starting LCF-generated crack. . combined LCF and HCF, and they suggested the exploration of the use of fracture mechanics as an alternative. In particular, they emphasized that such an approach needs to be validated under realistic. an increase in the threshold level. Traditional methods for managing HCF have relied heavily on the Haigh (Goodman) diagram approach. The Haigh diagram approach requires smooth bar fatigue data. which a crack of a given size will not grow. Threshold can be used to determine an allowable stress as a function of crack size and is seen as a viable alternative design parameter to the allowable