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186 Effects of Damage on HCF Properties A load-history-free material threshold is equivalent to precracking at threshold. This load-history independent threshold can be calculated from the model by setting K pc equal to the K th . This assumes that the load-history-free threshold would be measured if the LCF cracking could occur at threshold. This substitution gives: K th = 1−R th K eff 1− −R th (4.30) Experimentally, the history-free threshold is measured using stress-relief-annealed spec- imens. K thresholds calculated from the model [Equation (4.22)] are 43MPa √ m for R = 01 and 2.89 MPa √ m for R = 05 for Ti-6-4 and 337MPa √ m for R = 01 for Ti-17. These compare favorably with the experimentally measured thresholds of 4.23 and 28 MPa √ m for Ti-6-4 at R =01 and R =05, respectively, and 346MPa √ matR =01 for Ti-17. To further investigate the load-history effect on threshold outlined above from the work of Moshier et al. [4, 6], Golden and Nicholas [43] followed the same procedure but pre- cracked at an even lower stress ratio of R =−30. They examined LCF–HCF interactions at negative values of R under both smooth bar conditions, where LCF generated cracks are difficult to detect and may not even exist, and under notch fatigue, where cracks were deliberately introduced and detected. Their investigation explored the nature of the crack initiation, threshold crack propagation, and any associated load-history effects when a specimen is initially subjected to loading at negative stress ratios. Two types of experi- ments were conducted. In the first series of tests, smooth bars were loaded at R =−35in order to see if this would initiate cracks which might affect the subsequent threshold at a higher value of R. In the second series of tests, LCF cracks were deliberately introduced with loading at R =−3 and the subsequent threshold was determined experimentally. The effect of loading history was assessed for both test procedures using Ti-6Al-4V as the test material. The smooth bar specimens were tested under three conditions: (1) a baseline condition with no preloading; (2) preloaded and then heat tinted prior to threshold step test; and (3) preloaded, heat tinted and stress relieved prior to threshold step test. The 10 7 cycle fatigue strength for each of these three test conditions are reported in Figure 4.31 for R = 01 and R =05 step tests. These tests were conducted on specimens subjected to prior LCF at a value of R =−35 at a stress level of 240 MPa, which is below the observed failure stress of 265 MPa at that value of R. If it is postulated that cracks nucleate due to some function of total stress or strain range, but will only continue to propagate when subjected to a positive stress range that produces a positive crack driving force, K, then cracks should be found before the HCF testing begins. After subjecting the specimens to 10 7 cycles at R =−35, the specimens were then tested in HCF until failure at either R =01 or R =05 using the step-loading procedure. Some of the specimens were stress relieved after the initial loading at R =−35 in order to remove any history effects on a crack LCF–HCF Interactions 187 500 550 600 650 700 750 800 R = 0.1 Baseline R = 0.1 R = 0.1 SR R = 0.5 Baseline R = 0.5 R = 0.5 SR Fatigue strength (MPa) Ti-6Al-4V 10 7 cycles, 70 Hz Preload @ R = –3.5 240 MPa, 10 7 cycles Figure 4.31. Fatigue limit stress for specimens subjected to preloads at R =−35. that may have formed. The results are summarized in Figure 4.31 where baseline tests are compared with preload tests with and without stress relief (SR) for both values of R. Note that the peak stress levels applied in the HCF tests are considerably higher than the peak stress used in the preloading (240 MPa). Using an expanded stress scale emphasizes the possibility that a minor reduction in HCF strength may have been obtained due to preloading at R =−35, but the magnitude of any such reduction is not very significant. The results show that the pre-loading reduces the 10 7 cycle fatigue strength of the Ti-6Al-4V material by approximately 5%. Given the small difference in fatigue strength and the small number of specimens, this difference is not very significant in a statistical sense. Also, the stress relief did not seem to have a consistent or significant effect on the results. Examination of the fracture surfaces of these specimens showed no obvious heat tint markings. A threshold stress analysis, however, reveals that the calculated a 0 for this material and geometry would be approximately 60 m. A Kitagawa diagram was drawn for these test conditions (circular bar) as described earlier in the work by Morrissey et al. [15] (see Figure 4.11). The small reduction of strength observed from these tests would indicate cracks approximately 10m deep, which is typically too small to detect using the optical microscope. An SEM examination of the fracture surface revealed some possible initial flaws. Examples are shown in Figure 4.32. Here the lines indicate the possible initial crack boundaries. These markings were considered an upper bound to the crack sizes that may have been present after preloading. This was found to be consistent with a Kitagawa diagram analysis. Such features were not observed in baseline specimens which received no stressing at negative R. In the notched specimens, the precrack test phase was run until cracks were generated and observed with an infrared damage detection system. Therefore, nearly all specimens had a measurable heat tinted crack on the fracture surface and several had multiple cracks. 188 Effects of Damage on HCF Properties 02-A10 (R HCF = 0.5) 02-A17 (R HCF = 0.1) 20μm 20μm Figure 4.32. Fracture surfaces of specimens subjected to preload at R =−35. The threshold stress and crack depths were plotted on a Kitagawa diagram. All of the data for the notch specimens precracked in LCF at R =−3 and R =−1 followed or fell slightly below the short crack and/or LEFM R = 01 threshold predictions. The SR did not seem to have a consistent or significant effect on the results. To compare the results from the smooth bar tests and the precracked notched specimens, a normalized Kitagawa diagram was introduced. Crack length on the x-axis is normalized with respect to a 0 while stress on the y-axis is normalized with respect to the FLS for the specific geometry and value of R. This diagram can be used to compare results from two (or more) entirely separate geometries. Such a plot is shown as Figure 4.33 where the smooth (circular) bar and the notched specimen are represented by their respective long crack (solid) and El Haddad short crack corrected (dashed) curves for R = 01. Curves for the two geometries for R =05 lay nearly on top of the R =0 1 curves in both cases and are not plotted. Nearly identical normalized curves on a Kitagawa diagram at different stress ratios were also observed and documented in Golden [44] for arch-shaped specimens from a fretting fatigue study. In Figure 4.33, for R =01, maximum endurance limit stresses used were 310 MPa, and 570 MPa, for the notched and smooth specimens, respectively. The long crack K th used in the analysis was 4.6 MPa √ m. For the notched specimen, a 0 =25 m for a surface crack with a/c =06 and a 0 =15 m for a through crack while for the smooth specimen a 0 = 58m. Experimental data points from the notched tests at R = 0.1 are also shown on the curve. Horizontal and vertical dashed lines represent the predicted a/a 0 crack sizes for 95 and 80% of fatigue strength which covers and even exceeds the range of the data shown in Figure 4.31 for specimens preloaded at R =−35. This leads to predicted LCF–HCF Interactions 189 σ th /σ end 0.2 0.4 0.6 0.8 1 3 0.1 1 10 R = –3 R = –3, SRA R = –1 R = 0.1 a /a 0 Notched Round bar 0.12 0.57 Figure 4.33. Normalized Kitagawa diagram showing curves for circular bar and notched specimens. crack sizes in the smooth bars of approximately 7–35 m. As noted above, no indications of such cracks were observed and, further, no load history effects were observed in the notched specimens precracked at R =−3 since the data follow the predicted short crack corrected threshold line in the Kitagawa plot. Another plot that can be used to represent these data is the measured threshold stress intensity factor, K max threshold, versus the applied K max precrack. K max precrack is the stress intensity factor of the final crack size during precracking with the precracking stress applied while K max threshold was calculated using the same crack size but with the threshold stress applied. The plot, shown in Figure 4.34, contains all of the data collected in [43] that have threshold values measured at R = 01. LCF precracking R values are labeled in the legend. Several curves are added to this plot that represent the predicted or measured threshold behavior for long cracks with and without load-history effects and also for short cracks. The horizontal line is simply the long crack threshold K max = 51MPa √ m while the endurance stress, end , is the boundary for growth or no growth for material with very short cracks in which failure is controlled by stress rather than LEFM. This boundary was calculated using Equations (4.31) and (4.32) where pc is the R =−3 precrack maximum stress of 150 MPa and end is the R =01 endurance stress of 310 MPa. The short crack threshold curve is a transition between the endurance stress and LEFM criteria much like that used in the Kitagawa diagram. Here K pc was calculated by Equation (4.31) and the small-crack threshold stress intensity factor, K thsc , was calculated according to Equation (4.33). Finally, Equation (4.34) is plotted showing the effect of tension overload on the threshold. This line was fit to R = 01 fatigue crack-growth threshold tests performed by Moshier et al. [6] where the crack-growth 190 Effects of Damage on HCF Properties 0 2 4 6 8 10 0 5 10 15 20 25 LCF R = –3 LCF R = –3, SRA LCF R = 0.1 LCF R = –1 Predicted short crack threshold σ end R = 0.1 Overload fit Maximum K pc (MPa m) Maximum K th (MPa m) 5.1 MPa m Long crack threshold Figure 4.34. Summary of calculated R = 01K max threshold of cracks measured in precracked notched spec- imens. The precracking K max for the endurance stress and short crack threshold predictions are based on the R =−3 precracking stress of 150 MPa. thresholds were measured after different levels of R =01 precracking. K pc = pc √ a Ya (4.31) K thend = end √ a YaK thend = end √ a Ya (4.32) K thsc = thlc a a +a 0 Ya Y a +a 0 (4.33) K th =0303K pc +333 (4.34) The results plotted in Figure 4.34 are very consistent with the predictive curves. Starting from the lower precracking K max , the R =−3 precracked data all seem to have R =01 thresholds that match the short crack curve very well. In the K max precrack range of 5−10 MPa √ m, the data precracked at R =−3 and R =−1 seem to follow the long crack R =01 threshold as expected with some scatter. Two points from this study precracked at R = 01 seemed to follow the load history fit quite well, which was consistent with similar notch data generated by Moshier et al. [4]. What is interesting to note is the data point precracked at R =−3 and K max =12MPa √ m that has an R =01 threshold much lower than predicted using the K max overload fit and much lower than the data precracked at R =01 with the same precracking K max . Although this result was from only one test, it could only be due to the compression portion of the cycle during the precracking. This result is also consistent with the R =−1 precracking data presented by Moshier et al. [4]. LCF–HCF Interactions 191 The authors conclude that at higher levels of precracking, the compressive “overload” (sometimes referred to as an underload) has the effect of eliminating or canceling the effect of the tensile “overload” load-history effect. At lower levels of precracking K max where a tensile “overload” load-history effect was not expected, the compressive precracking appeared to have very little effect. The question then arises, could it be possible that the negative stress ratio precracking had an undetected “underload” effect on the crack-growth threshold of many of the tests that didn’t appear to show an effect? Single or multiple underload cycles have been shown to accelerate crack growth for a short period of crack extension in constant amplitude crack-growth tests [45]. During threshold step tests it is possible that stress levels are encountered that grow the crack at a K less than the threshold level (either long crack or short crack) due to the “underload” load history. The crack, then, could grow a short distance out of the reduced K th effect and then arrest until the next step increase in stress. This sequence could repeat until a stress is reached that grows the crack to failure. In the analysis, only this final stress would be considered, therefore, the “true” reduced crack-growth threshold stress would not be known and could be lower than has been measured. This scenario, however, is speculative and current experimental procedures and available data cannot prove or disprove this possibility. Another consideration in the determination of thresholds for HCF crack propagation is crack length. Ritchie points out the importance of the small fatigue crack phenomenon when determining HCF thresholds [46]. Any number of variables including crack size and geometry, mode mixity, applied loading spectra and residual stress may affect the HCF threshold. Ritchie et al. [47] propose a high stress ratio, large-crack-growth test to determine a lower bound HCF threshold. The long-crack lower bound threshold was presented as a way of describing the onset of small crack growth from natural crack initiation and FOD sites. Frequencies of 50 to 1 kHz were used to study large-crack propagation in Ti-6Al-4V using C(T) specimens. The high stress ratio, large crack- growth test is used to simulate the closure-free small-crack behavior and determine a lower bound long crack threshold of 19MPa √ m. Comparisons were done with closure corrected lower stress ratio, long crack-growth threshold tests to verify the determined lower bound long-crack threshold. The comparisons, however, indicated that the higher stress ratio threshold was less than the closure corrected lower stress ratio test due to an additional mechanism such as room temperature creep or slip-step oxidation. Although an additional mechanism caused the measured higher stress level threshold to be less, it is in any event still a conservative estimate and thus a lower-bound threshold for Ti-6Al-4V. Additionally, Boyce and Ritchie found that thresholds for Ti-6Al-4V were frequency independent over the range of 50–1000 Hz. Campbell et al. [48] investigated mixed-mode crack-growth thresholds using through cracks in Ti-6Al-4V plate material. They determined that a slight increase in mode I threshold results when the crack kinking 192 Effects of Damage on HCF Properties direction increases from 0 to 30 degrees as compared to the pure mode I case. Crack kinking angles greater than 30 degrees produced lower mode I thresholds. When combined LCF and HCF loading, which is sometimes referred to as combined cycle fatigue (CCF), is present, crack-growth rate behavior has been seen to follow two different patterns as depicted in Figure 4.35. In A, the more common behavior, LCF growth rates follow the rate for LCF alone below the HCF threshold. The transition to an accelerated growth rate occurs when the threshold for pure HCF alone is reached as the crack extends. At that point, if the number of HCF cycles per block is high enough, an accelerated growth rate is observed. The stress intensity at which this occurs is often called K onset . For this type of behavior, a linear summation model seems adequate for describing the behavior. The model can be expressed as da dN Block = da dN LCF + n da dN HCF (4.35) where the block, or CCF crack-growth rate, is given as the sum of the contribution of one LCF cycle and n HCF cycles, where n is the number of HCF cycles per block. If one considers that crack-growth rate data are normally plotted on logarithmic scales, the model essentially predicts that either LCF or HCF alone determine the observed growth rate, depending on which one is larger. This, in turn, is a function of n, the number of HCF cycles per block, and the value of K with respect to the HCF threshold. A second type of behavior, depicted as B in Figure 4.35, is similar to that shown as A, but the crack-growth rate at values of K below the HCF threshold is observed to occur at an elevated rate compared to that for LCF alone. The reasons for this behavior do not appear to be very well understood according to published results, but such behavior can be non-conservative from a design viewpoint because the threshold for HCF could be reached in a shorter period of time than that predicted by a simple linear summation log da /dBlock log ΔK HCF only LCF only LCF + HCF log da /dBlock log ΔK HCF only LCF only LCF + HCF A B Figure 4.35. Schematic of two types of behavior observed in combined LCF–HCF. LCF–HCF Interactions 193 approach to combined LCF–HCF growth rates. Note that the schematic of Figure 4.35 depicts the behavior in a manner that is usually used for presenting such data, namely on log–log plots. What appears to be an elevated growth rate for low values of K for the block loading could easily be more than a factor of two or three, perhaps even higher. No systematic study of the materials for which this accelerated growth rate occurs below the HCF threshold under CCF has been conducted. 4.4. DESIGN CONSIDERATIONS Damage tolerant design, when applied to LCF alone, is based on inspection size capability for cracks, crack-growth-rate computations, and the determination of proper inspection intervals to locate cracks before they reach a critical size. In an aeroengine, the LCF cycles are related to the number of flights and are fairly well determined by usage. For a component experiencing both LCF and superimposed vibratory (HCF) loading, the HCF contribution to the growth rate must also be considered. In particular, for high frequency vibrations where the number of HCF cycles can be large, reaching the threshold for HCF can be the governing criterion for failure because the crack-growth rate under the combined LCF–HCF loading may accelerate far beyond that for LCF alone. Predicting the onset of the HCF activity thus becomes an important aspect for design and component lifing [49]. Wanhill [50], for example, has pointed out the importance of the use of K th for design. He considers that clearly, the most significant application of fatigue thresholds includes the case of combined LCF–HCF loading where the LCF grows the crack until the threshold for HCF is reached. Whether or not the threshold value obtained from long cracks, K th , can be used to asses the onset of accelerated growth under combined LCF–HCF loading, has yet to be determined for most materials and loading conditions. These conditions involve various combinations of R for the major and minor cycles as well as the number of HCF cycles per LCF “block.” Crack growth under the conjoint action of HCF and LCF was studied by Powell et al. [51]. The objective was to see when the HCF accelerated the steady-state LCF growth rate and how this was related to the threshold for HCF. Two titanium alloys were studied, Ti-6Al-4V and Ti-5331S, the latter also known as IMI829. Using corner-cracked specimens, the crack-growth behavior under pure LCF at R = 01 with superimposed HCF at R = 09(Q = 012, see below) is illustrated in Figures 4.36 and 4.37 for the two alloys. In these experiments, conducted at room temperature, there were 10,000 HCF cycles for each LCF cycle (denoted as n = 10,000). The plot shows that the threshold for HCF is easy to determine for the Ti-6-4 alloy by locating the intersection of the LCF only and combined LCF–HCF curves. The lack of correlation of LCF only and LCF–HCF curves in Ti-5331S that occurs well below the threshold for HCF alone makes it difficult to determine the point of intersection from Figure 4.37. The Ti-6-4 alloy 194 Effects of Damage on HCF Properties 10 –1 10 –2 10 –3 10 –4 10 –5 10 100 LCF only LCF–HCF da /dBlock (mm/block) Ti-6Al-4V n = 10,000 ΔK total (MPa m) Figure 4.36. Fatigue-crack-growth rates under pure LCF and combined LCF–HCF in Ti-6Al-4V at room temperature. ΔK total (MPa m) 10 –1 10 –2 10 –3 10 –4 10 –5 10 100 LCF only LCF–HCF da /dBlock (mm/block) Ti-5331S n = 10,000 Figure 4.37. Fatigue-crack-growth rates under pure LCF and combined LCF–HCF in Ti-5331S at room temperature. follows the common behavior denoted as type A in Figure 4.35 while the Ti-5331S follows the unusual behavior depicted as B in Figure 4.35. The authors tried to explain the anomalous behavior below threshold, where the HCF seems to accelerate the LCF growth rate, by a combination of a short-crack effect and the development of crack closure. It was noted that the grain size of the Ti-5331S was approximately 0.6 mm, whereas the Ti-6-4 had a grain size of only 0.025 mm. The accelerated growth rate in Ti-5331S was observed at low values of K when the crack length was of the order of less than 3 grain LCF–HCF Interactions 195 diameters. Whatever the explanation, the accelerated LCF growth rate below threshold is an important factor to take into account when determining how many LCF cycles can be sustained before the HCF threshold is reached. In this particular case, the LCF growth rate under combined cycling is a factor of 2–4 above that for LCF alone, thereby decreasing the number of cycles or time it takes to reach the HCF threshold by the same factors. This clearly has to be taken into account when applying a damage tolerant design approach for HCF under combined LCF–HCF loading. Experiments similar to the ones at room temperature, described above, were also conducted on Ti-5331S at 550 C. The results are presented in Figure 4.38 where the growth rate per block is compared with the predictions of the linear summation model. The data show that either the HCF threshold is reduced, or that LCF growth is accelerated below the steady-state HCF threshold. The linear summation is carried out for both the average behavior and the worst case, the latter taking into account the scatter obtained in both the LCF and HCF testing. Here is another example where there appears to be an interaction between LCF and HCF in the threshold region for HCF when the two are combined into a simple spectrum. Beyond the threshold, the data appear to follow the average behavior as predicted by the linear summation model. ΔK total (MPa m) 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 1 10 100 Test 1 Test 2 Linear sum, worst case Linear sum, average da /dBlock (mm/block) Ti-5331S 550¡C n = 10,000 Figure 4.38. Combined LCF–HCF growth rates and model predictions in Ti-5331S at 550 C. . however, reveals that the calculated a 0 for this material and geometry would be approximately 60 m. A Kitagawa diagram was drawn for these test conditions (circular bar) as described earlier in. What appears to be an elevated growth rate for low values of K for the block loading could easily be more than a factor of two or three, perhaps even higher. No systematic study of the materials. LCF at a value of R =−35 at a stress level of 240 MPa, which is below the observed failure stress of 265 MPa at that value of R. If it is postulated that cracks nucleate due to some function of
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