High Cycle Fatigue: A Mechanics of Materials Perspective part 23 pdf

206 Effects of Damage on HCF Properties the LCF cycles can be considered to be an underload on the baseline HCF cycles. On top of this simple spectrum, a single overload is added to the baseline LCF cycle. Defining the overload ratio as OLR =K max /K ss , experiments were carried out to see when the onset of HCF activity occurred. The results, based on the use of a number of values of OLR, are presented in Figure 4.51. The curves shown are the best fit to the actual data points which are not shown for clarity. OLR = 1 represents the case where there is no overload in the baseline LCF–HCF cycle. The pure LCF curve is also shown. The results show that as OLR increases, the retardation effect of the single overload diminishes the growth rate until the minor cycles have almost no influence on the baseline LCF cycle at a value of OLR = 2.0. This work, conducted on Ti-6Al-4V, also shows that the apparent onset of HCF activity is delayed by the overload cycle. In this case, there is both an underload in the baseline combined cycle as well as a superimposed overload. While the behavior of the baseline cycle defined by OLR = 1.0 is predictable with linear summation of the LCF and HCF cycles, the additional effect of the overload is both to reduce the minor cycle contribution to the growth rate and to reduce the threshold where minor cycle activity begins. The natural conclusion arising from these studies is that growth rates and thresholds from constant amplitude loading cannot always be used directly in spectrum loading without consideration of interaction effects. Both retardation and acceleration effects have been noted in various studies, with overloads usually observed to retard crack-growth rates while underloads are found to accelerate the growth rates. While these observations are common, the exceptions prove that a single rule cannot be applied in all cases. In [52], HCF and LCF tests were used to establish baseline material properties, and simple mission tests were used to assess additional failure modes that may exist if 10 –1 10 –2 10 –3 10 –4 10 –5 10 –6 8 9 10 20 30 40 50 OLR = 1.0 OLR = 1.15 OLR = 1.3 OLR = 1.45 OLR = 1.75 OLR = 2.0 LCF only da /dBlock (mm/block) Ti-6Al-4V n = 1000 ΔK LCF (MPa m) Figure 4.51. Fatigue crack growth for various overload ratios, R HCF =07, 1000 minor cycles per block. LCF–HCF Interactions 207 LCF–HCF interactions are important. This was explored with mission tests at 75  F with Ti-6Al-4V and were based on the following criteria: (a) tests that avoid specimen ratcheting failure modes (typically high stress, high R) that are not representative of component failures, (b) LCF stresses that are in the main regime of design interest for turbine engines (average N f ∼10000 cycles), (c) HCF stresses that are in the regime of design interest (R>05 and HCF > 10 7 cycles), (d) mission histories that include LCF + periodic HCF cycles until mission failure, and (e) tests that can be run economically in the laboratory. A double-edge V-notch specimen geometry was used to avoid ratcheting for load-control testing and loads were selected to keep the fatigue lives in the regime of design interest. Baseline notch LCF tests at R = 01 were run to identify stresses for an LCF failure of ∼10000 cycles while baseline notch HCF tests were used to identify the value of R for an average HCF failures of ∼10 7 cycles. All interaction tests were missions or blocks of cycles that were repeated until failure. Missions included an LCF load-up R =01+10000–100000 repeated HCF cycles R =07–09 +anLCF unload reversal R =01 for each mission. The baseline and mission test conditions for the notch geometry are given in Table 4.3. Stresses are reported in units of ksi. The first group of mission tests was used to assess the HCF capability when minimal LCF damage is present. This was evaluated with 10,000–100,000 HCF cycles/mission with an HCF cycle from 56 to 80 ksi (R = 07). These conditions were intentionally selected to avoid significant predicted LCF damage. The number of HCF cycles to failure for these mission tests is compared to the number of cycles to failure for HCF alone with probability plots shown in Figure 4.52. Given the similarity of these distributions Table 4.3. Baseline and LCF–HCF mission tests LCF LCF HCF HCF HCF/mission Freq Expt HCF Expt missions Pred life S min S max S min S max (Hz) cycles with Fs 9 90 NA NA LCF 0.5 NA 9963 11365 8 80 NA NA LCF 0.5 NA 10766 16489 8 80 NA NA LCF 0.5 NA 10821 16489 NA NA 56 80 HCF 1k 234894301 234894301 6370632 NA NA 56 80 HCF 1k 11694364 11694364 6370632 NA NA 56 80 HCF 1k 2613654 2613654 6370632 8805680 10000 0.5/1k 16400000 1640 613 8805680 10000 0.5/1k 71682975 7168 613 8 80 56 80 100000 0.5/1k 14298296 142 63 8 80 56 80 100000 0.5/1k 9312872 93 63 8 80 56 80 100000 0.5/1k 405933382 4059 63 8807280 10000 0.5/1k 142814 527 14281 16222 8806580 10000 0.5/1k 94130587 9413 16222 208 Effects of Damage on HCF Properties HCF + LCF HCF 1.00E5 1.00E6 1.00E7 1.00E + 08 1.00E + 09 99 95 90 80 70 60 50 40 30 20 10 5 1 HCF cycles to failure Percent Figure 4.52. Capability of notched HCF tests compared to the HCF capability of LCF–HCF mission tests when HCF damage dominates. for the small set of data presented, a significant LCF–HCF interaction does not seem to be present for cases when HCF damage dominates. The second group of tests was run to assess if LCF failure modes are influenced when minimal predicted HCF damage exists. Minimal HCF damage was evaluated with mission tests that included an LCF load-up reversal R = 01 +10 000 repeated HCF cycles (S max =80 ksiS min =72 for R =09 or 65ksi for R =082). The HCF parameters were selected near the minimum allowable stress for a 10 7 HCF limit so that HCF could be ignored as a contributing factor, assuming no LCF–HCF interactions. The number of LCF cycles to failure for the notch mission tests as compared to N f for the notch specimens with LCF alone is shown in Figure 4.53. The values for predicted N f used an average smooth specimen S equiv fatigue curve with the modified Manson-McKnight fatigue parameter. The local stresses from the notch were obtained from elastic-plastic analysis and notch life was predicted with the local notch stresses and notch gradients using the effective stressed area, Fs approach described in Appendix E. (see Chapter 5 for a detailed discussion of notch fatigue). The tests are seen to be well predicted within the 2X scatter bands that are representative of a reasonably accurate LCF life method. Neglecting LCF–HCF interactions is shown here to be a reasonable assumption for these mission tests where the predicted HCF damage is minimal. From the viewpoint of design, it appears that one can use an HCF limit based on minimum properties such that HCF can be ignored as a failure mode in the type of mission used here that contains HCF and LCF conditions. LCF–HCF Interactions 209 Ti-6Al-4V notches with LCF + Min allowable HCF (predictions with smooth specimen curve plus Fs) 1,000 1,000 10,000 10,000 100,000 100,000 Observed LCF to failure Predicted LCF to failure LCF Only LCF + min HCF Figure 4.53. Notched LCF tests compared to the LCF of LCF–HCF mission tests with minimal HCF damage. REFERENCES 1. Nicholas, T., “Step Loading, Coaxing and Small Crack Thresholds in Ti-6Al-4V under High Cycle Fatigue”, Fatigue – David L. Davidson Symposium, K.S. Chan, P.K. Liaw, R.S. Bellows, T.C. Zogas and W.O. Soboyejo, eds. TMS (The Minerals, Metals & Materials Society), Warrendale, PA, 2002, pp. 91–106. 2. Kitagawa, H. and Takahashi, S., “Applicability of Fracture Mechanics to Very Small Cracks or the Cracks in the Early Stage”, Proc. of Second International Conference on Mechanical Behaviour of Materials, Boston, MA, 1976, pp. 627–631. 3. 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Diskson, eds, 3, EMAS, Warley UK, 1993, pp. 1575–1580. 25. Sheldon, J.W., Bain, K.R., and Donald, K.J., “Investigation of the Effects of Shed-Rate, Initial K max , and Geometric Constraint on K th in Ti-6Al-4V at Room Temperature”, Int. J. Fatigue, 21, 1999, pp. 733–741. 26. Lenets, Y.N. and Nicholas, T., “Load History Dependence of Fatigue Crack Thresholds for Ti-Alloy”, Engineering Fracture Mechanics, 60, 1998, pp. 187–203. LCF–HCF Interactions 211 27. Makhutov, N., Romanov, A., and Gadenin, M., “High-Temperature Low-Cycle Fatigue Resis- tance Under Superimposed Stresses at Two Frequencies”, Fatigue Engng Mater. Struct., 1, 1979, pp. 281–285. 28. Zaitsev, G.Z. and Faradzhov, R.M., Metallovedenie i Termicheskaya Obrabotka, 2, 1970, pp. 44–46. 29. 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Chapter 5 Notch Fatigue 5.1. INTRODUCTION A notch in a component can be considered to be a defect since it produces a local stress concentration or stress raiser that can ultimately be the location of an HCF failure. Thus, it is important to understand the effect of a notch on the FLS and to be able to predict the strength without having to conduct extensive experiments for each notch geometry. An alternate reason for understanding and modeling notch behavior is that it represents a condition where there are stress gradients in going from maximum stress at the notch root to lower stress at locations beneath the notch. Stress gradients also arise in fretting fatigue, discussed later in Chapter 6. Additionally, FOD, discussed later in Chapter 7, often produces some type of geometric discontinuity. To be able to predict the effect of the discontinuity or damage to stresses induced by vibratory HCF loading requires an understanding of notch effects in fatigue. For these reasons, we present an overview of notch fatigue as related, primarily, to the fatigue limit or threshold for crack propagation. 5.2. STRESS CONCENTRATION FACTOR In notch fatigue, the primary aim is to be able to predict the fatigue behavior of a material or component with a stress concentration from smooth bar data. The majority of fatigue data available is in either the LCF regime or corresponds to fatigue lives below the endurance limit, if such a limit exists at all. The first aspect of addressing notch fatigue strength is to define the severity of the notch or stress concentration. To do this, the elastic stress concentration factor, k t , is used. ∗ Here, k t is defined as the ratio of the peak stress at the root of a notch to the average stress over the net cross section: k t = peak stress at notch root average stress over the net cross section ∗ The symbol used for the elastic stress concentration factor throughout the literature is either K t or k t . The former definition was commonly used before fracture mechanics was developed, when K was introduced as the stress intensity factor. However, K t is still widely used. In this book, the term k t will be used wherever possible for consistency. Note, however, that many drawings made early in the preparation of this manuscript or taken from the literature will still show K t as the stress concentration factor. For this inconsistency and possible confusion, the author expresses his sincere apologies. 213 214 Effects of Damage on HCF Properties Values of k t can be found in tables or handbooks and have been obtained from closed- form elastic solutions for simple geometries, photoelasticity experiments in the early days, and finite element calculations in the more recent literature. The value of k t is a measure of the severity of the notch or discontinuity and is used to predict fatigue lives in many engineering applications. There are numerous cases in components with complex geometries where k t cannot be defined as stated above because there is no well-defined “net-section.” An example of such a geometry would be at the root of a notch in a dovetail attachment region where the cross section has a continuing variable geometry. In such a case, the net-section stress is hard to define because a section is difficult to be identified uniquely. Similarly, a notch in a complex 3-d geometry has an undefined value of k t when the cross-section stresses, wherever the cross section is defined, are highly variable in all directions. Even if k t is formally defined, it may have no meaning for engineering and design purposes for HCF applications. In Figure 5.1, three geometries are shown schematically under far-field uniform tensile loading. In (a), a mild notch is depicted, and the stress at the notch tip is slightly higher than the net-section stress over the width, w. Note that if the gross cross section width =d is used (incorrectly), then a large stress concentration factor will result with resulting misleading approximations for the fatigue strength. All calculations for k t are based on linear elastic material behavior and are independent of material and depend only on geometry. In (b) and (c), two identical notch radii are shown, but the two do not have the same value of k t . In (b), the average stress is more influenced by the local notch field than in (c) which is closer to that of an infinite body. The stress concentrations are w d (a) (c) (b) d d Figure 5.1. Three geometries illustrating the definition of k t . Notch Fatigue 215 different, therefore, and this demonstrates that both the notch geometry and the overall geometry are important in determining k t . 5.3. WHAT IS K t ? There are a number of industrial applications where accounting for damage is necessary, even though the amount and severity of such damage is hard to quantify. In cases such as those with FOD, discussed later in Chapter 7, a knockdown factor in the form of an equivalent value of k t is often used. While the design procedure may quote k t = 3, for example, as the guideline, the intent seems to be to reduce the fatigue limit by a factor of 3 in this example, so the guideline should be k f =3 instead. ∗ The fatigue notch factor, k f , is defined and discussed later in Section 5.4. The ambiguous meaning of quoting a value of k t to represent damage is illustrated in a simple example here. Not only is k t not unique in terms of the geometry it represents, but for a given geometry the value of k t also depends on the loading condition. In this example, a rectangular plate with a U-shaped notch is loaded in tension or bending, as shown in Figure 5.2. With the nomenclature and loading as depicted in the figure, values of k t are presented for several r/d ratios for tension as well as bending loading in Figure 5.3. For a fixed value of k t , any of a number of values of r/d can be used to produce that value. Further, for a fixed geometry with specified values of D/d and r/d, the value of k t is different under axial load than under pure bending. Thus, the specification of a value of k t to represent a damage state is rather ambiguous and, as mentioned above, is a misuse of the term when a fatigue notch factor, k f , is probably what was intended. M r d/2 d/2 D d P M P Figure 5.2. Nomenclature for plate with U-shaped notch under tension and bending. ∗ In recognition of the intent to reduce fatigue strength for FOD damage in ENSIP in preliminary design, k t =3 was introduced in the original document. The latest versions of ENSIP now use k f =3 as the guideline. . Kitagawa, H. and Takahashi, S., “Applicability of Fracture Mechanics to Very Small Cracks or the Cracks in the Early Stage”, Proc. of Second International Conference on Mechanical Behaviour of Materials, . International Conference on the Mechanical Behaviour of Materials, Geneva, Switzerland, 25–29 May 2003 (on CD-ROM). 12. Maxwell, D.C. and Nicholas, T., A Rapid Method for Generation of a Haigh Diagram for. of Engineering for Gas Turbines and Power – Transactions ASME, 119, 1997, pp. 143–146. 24. Akita, K., Misawa, H., Tobe, S. and Kodama, S., “Fatigue Crack Propagation Behavior of Ti-6Al-4V Alloy under