High Cycle Fatigue: A Mechanics of Materials Perspective part 38 pptx

356 Effects of Damage on HCF Properties nothing changes during the SR process other than the removal of residual stresses. This finding is consistent with that discussed in the previous section for impact on leading edge geometries. Of greater significance is the observation that ballistic impacts to the same depth as pendulum or quasi-static indentations are more severe in terms of the resulting fatigue limit strength reduction. This is especially true for the deeper indents corresponding to ballistic impacts at 300 m/s. In the work of Peters et al. [2], the impacts at 300 m/s produced small amounts of cracking at the crater whereas the impacts at 200 m/s produced no observable cracks. This shows that low velocity (pendulum) or quasi-static indentation does not produce the same amount of damage as ballistic impact for this material under the specific impact conditions (depth of indent) described, particularly at higher velocities. Results for the tests in torsion are summarized in Table 7.3. Here, only ballistic impacts were evaluated at R =0 for both AR and SR samples, and R =−1 for AR only. The SR samples show a reduction in k f which is equivalent to an increase in  FLS . This is attributed to the implied existence of tensile residual stresses in the failure region. The value of k t in Table 7.1 for a deep notch in tension indicates that fracture would be expected at the bottom of the notch. This is confirmed by the observed location of initiation near the notch bottom as shown in Figure 7.29(a). On the other hand, torsion tests of a specimen Table 7.3. Experimental values of k f for ballistic notches under torsion Notch type R =0 R =−1 AR shallow 131 1.62 AR deep 200 2.00 SR shallow 101 – SR deep 147 – 200 µm (a) (b) 600 µm Figure 7.29. Fractographs showing initiation sites in (a) tension, (b) torsion. Foreign Object Damage 357 with a shallow notch would be expected to produce a failure near the surface because of the higher value of k t as listed in Table 7.1. The fractograph, Figure 7.29(b), confirms such a finding. In both cases illustrated, the specimen was subjected to SR, so only microstructural damage or hardening could account for fracture initiating at any other location. In one extreme case initiation occurred near the surface of a deep notch from high velocity (312 m/s) ballistic impact. While initiation would be expected to occur at the bottom according to k t analysis for tension fatigue loading, damage in this case was sufficient in the form of local tearing to reduce the fatigue strength below that of most of the other specimens. This resulted in fracture initiating near the location of extensive damage at the surface. The difference in  FLS between AR and SR in the tension and torsion cases for ballistic impact seems to indicate that the tensile residual stresses are somewhat higher near the surface than at the bottom although scatter in test results makes this observation some- what tenuous. In both the tension and torsion cases, for ballistic impact at 300 m/s which produces the deeper crater, the debit in fatigue strength is greater than that expected due solely to the stress concentration factor, indicating some type of microstructural dam- age near the failure location whether it be at the bottom, for tension tests, or near the surface, for torsion tests. Finally, for the shallow indents produced by ballistic impact at 200m/s, there is no apparent reduction in fatigue strength under torsion testing after SR, even though the value of k t is 1.32 at the failure location. This implies that some type of strengthening mechanism is present that retards fatigue failure, most likely delay- ing fatigue initiation. In a study of deep rolling and other surface treatments in this same alloy, Nalla et al. [19] identified a strengthening mechanism in the form of an induced work hardening near-surface layer that improves the fatigue resistance of the material. Figure 7.30 shows high resolution SEM images of a region at the deformed surface where a different microstructure can be seen over the first several microns from the free surface. This region of intense plastic deformation seems to have a retarding effect on fatigue crack initiation as deduced from the experimental data, particularly from the SR specimens. All of the data obtained in tension at R = 01 and torsion at R = 0 are summarized in Figure 7.31 where hollow symbols represent the SR specimens and solid symbols are for specimens that were not stress relieved and are designated AR. The data are plotted as a function of k t for the various notches, where it should be noted that k t is different for the same geometry notch when tested in tension or torsion as discussed earlier. This figure illustrates the trend of SR specimens to have higher strengths than AR specimens, even higher than would be expected from a k t analysis. For reference purposes, the line representing 1/k t is shown. Ideally, a line showing theoretical values of 1/k f , which would be somewhat higher, should be shown. However, for the notch geometry and loading conditions used here, there is no model for values of k f . 358 Effects of Damage on HCF Properties X-section of impact site Specimen: 04-424, Ti-6-4 Orientation imaging microscopy (OIM) image Image Quality (IQ) image Backscattered electron image (BEI) 5 µm 6 µm Figure 7.30. SEM images of region near impacted surface. 0 0.2 0.4 0.6 0.8 1 1 1.2 1.4 1.6 1.8 2 Ballistic SR Ballistic AR Pendulum SR Pendulum AR Quasi-static SR Quasi-static AR 1/k t 1/k f k t Figure 7.31. Fatigue limit strength for all tension R = 01 and torsion R = 0 tests. Figure 7.31 shows that the ballistically impacted specimens show degradation in strength beyond that predicted simply by k t . The results are in agreement with those shown in the previous section for 2.0 mm ball indents on leading edges where damage under ballistic impact was greater than from quasi-static or pendulum indents. The observations discussed above indicate that FOD, even under carefully controlled laboratory conditions, involves a number of mechanisms that contribute to the fatigue Foreign Object Damage 359 strength of a material. Normal impacts on flat plates under ballistic and slower velocity conditions that produce craters of a given depth produce damage involving a number of mechanisms. The fatigue strength, that is a reflection of the damage severity, is also a function of loading conditions under axial or torsion stress states. Residual stresses are deduced to be tensile in most cases while some type of strengthening mechanism from the indenting exists that is not removed by stress relief annealing. The result of plastic deformation near the surface seems to have a beneficial retardation effect on crack initiation. For the deeper of the impacts discussed here, the impact damage from ballistic or lower velocity conditions reduces the fatigue strength beyond that predicted from the geometry of the resultant crater as characterized by the equivalent elastic stress concentration factor. However, quasi-static and low velocity pendulum indents produce different damage mechanisms than equivalent depth craters from ballistic impacts even though the fatigue strengths may be similar. These results, combined with observations of damage in leading edge specimens in the previous section, indicate that simulating FOD using quasi-static or low velocity methods may not produce identical results to true FOD in terms of either fatigue strength or damage mechanisms. 7.9.2. Other laboratory FOD simulations This section illustrates several methods for analyzing FOD data obtained from several specimen geometries using different techniques based primarily on concepts developed for notches as described earlier in Chapter 5. In the HCF program of the US Air Force [8], the fatigue properties of specimens subjected to well-controlled laboratory FOD simulations were deduced based on the geometry of the notch produced. An extensive experimental investigation was conducted where the fatigue limit strength of a material subjected to real or simulated FOD was characterized. All tests were run on Ti-17 material at room temperature using two different test specimen geometries to simulate the leading edge of an airfoil. The axial specimen geometry, similar to the one shown earlier in Figure 7.16 (see also Appendix G), was machined with a 12-mil root radius that simulates a blunt tip airfoil leading edge geometry. The bending specimen geometry is shown in Figure 7.32. This specimen is tested under 4-point bending to simulate the stress gradients in an airfoil. The use of this specimen is described in more detail in Appendix G. The edge of this specimen was machined with 7-mil and 14-mil root radii to simulate a sharp and blunt tip airfoil geometry, respectively. The FOD to the leading edge was simulated on the axial and bending specimens with a steel chisel indentor fired from a solenoid gun described earlier in this chapter (see also Appendix G). The FOD indentor had a nominal root radius of 5 mil with a 60  included angle. Several depths of penetration were obtained at a 30  impact angle using different energy levels on the solenoid gun. At a depth of ∼10mil, the onset of shear cracks in the material being extruded was observed. The FOD at ∼20 mil produced more extensive 360 Effects of Damage on HCF Properties 0.2 6.00 1.0 2.0 0.6 Sharp tip 0.25 0.007R 0.014R 0.032 Blunt tip 0.014R 0.014R 0.090 0.25 Figure 7.32. Bend bar simulating sharp and blunt airfoil leading edge. All dimensions in inches. damage as expected. Numerous shear cracks were observed on the flanks of the FOD in the extruded material, but no tears or cracks were observed at the root of the FOD notches. The FOD depth was determined with a line normal to the FOD as a notch depth profile. The FOD impact angle was determined from a line normal to the FOD impact with respect to a line tangent to the specimen leading edge face. An example of deep FOD in a sharp tip bend specimen is given in Figure 7.33. Lines to obtain the FOD impact angle and depth are shown schematically in the figure. Fatigue tests on the axial specimens were predominately run at R =−1 under step testing to 10 7 cycles. Three different FOD impact angles were evaluated for the axial tests in the “as-FODed” and “FODed + stress relief (SR)” conditions. Tests with FOD + SR were used for comparison to assess the role of residual stresses in the analysis. The SR condition was obtained on the Ti-17 material in a vacuum furnace for 8 hours at 1130  F after the FOD impact. The Ti-17 bending tests were run under step loading to 10 6 cycles. Bending tests were run at one nominal impact angle for both the sharp and the blunt tip leading edge geometries. Tests were run for the geometries in the as-FODed and FODed + SR conditions. The results are presented as k f as a function of geometry, impact angle, stress relief, and FOD depth. To account for different values of R, k f is defined as S equiv for the smooth specimen data normalized by S equiv at the specimen failure stress calculated for the notched specimen. Several methods were used to predict allowable HCF limits for specimens with FOD. Crack initiation methods were used, where baseline HCF capability for Ti-17 was obtained Foreign Object Damage 361 D θ D: FOD depth θ: FOD angle Figure 7.33. Fractography for deep FOD in the sharp tip geometry. from the best-fit curve to the smooth specimen data using equivalent stress to consolidate data obtained at different values of R. The first prediction ignored the FOD notch stress concentration and damage, and was based solely on the calculated maximum stress at the notch location. This approach is easy to implement, but is inaccurate for FOD tests as shown in Figure 7.34. The term S un-notched refers to the local stress at the location of the FOD, uncorrected for the notch effect or any stress gradient due to the notch. In this and subsequent plots, S curve refers to the baseline smooth bar data. This result is generally non-conservative as expected. This method of data analysis simply shows the debit in fatigue strength at the notch location. By definition, k f is the reciprocal of the y-axis value that appears to range from slightly over one to as high as five. The next approach utilized the calculated local peak stresses with the smooth specimen fatigue curve. For this approach, stress components are obtained from the measured notch geometry with maximum and minimum load cases at the interpolated loads with 3D elastic-plastic stress analysis. This approach is generally conservative (Figure 7.35) as expected. There does not seem to be any trend with stress relieved specimens compared to those without SR, indicating that residual stresses are neither compressive nor tensile consistently. Rather, they appear to be scattered and probably depend on the specific conditions at each impact site and the specific failure initiation location. 362 Effects of Damage on HCF Properties 0 0.5 1 1.5 2 2.5 3 3.5 4 0 5 10 15 20 25 30 Un-notched predictions S un-notched /S curve FOD depth (mil) Conservative Axial S, as-FODed Axial S, with SR Bending S, as-FODed Bending S, with SR Figure 7.34. Prediction of the HCF capability of specimens with FOD using the unnotched stresses. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 5 10 15 20 25 30 Peak local stress predictions Axial S, as-FODed Axial S, with SR Bending S, as-FODed Bending S, with SR Peak S equivalent /S curve FOD depth (mil) Conservative Figure 7.35. Prediction of the HCF capability of specimens with FOD from the peak concentrated stress. Machined notch data for the same material are shown in terms of equivalent peak local stress as a function of fatigue life in Figure 7.36. In the plot, the RFL model (see Chapter 2) was used to represent the smooth bar data. Data for specimens with very small notches are shown along with those that were obtained for machined U- and V-notches. The local stress approach with smooth specimen fatigue curves under-predicts the HCF capability of specimens for small notches. On the other hand, the V-notch data are over- predicted based on the local stress at the notch tip. The notch data and the smooth bar Foreign Object Damage 363 40 50 60 70 80 90 10 3 10 4 10 5 10 6 10 7 10 8 Local stress approach (w = 0.445) Median RFL Fit 90% RFL Fit 10% RFL Fit Smooth bar failure Smooth bar run-out Small notch V-Notch U-Notch S equiv (Ksi) N f (cycles) Figure 7.36. Smooth and notched bar fatigue results with the peak local stress approach. data would match on this plot if k f =k t . As seen, the small notch data exhibit a size effect that would produce higher strengths as the notch size became smaller. The V-notch data indicate that the notch may be sharper at the tip than measured. Local stress approaches were modified with notch fatigue stress concentration q–k f  and feature stress (Fs) approaches. Both methods try to account for stress gradients at the notch root by recognizing that fatigue in that location is not governed solely by the peak stress. The first notch method evaluated is a q–k f approach, alternately referred to simply as the q approach. This approach is used to predict FOD capability from the combination of k t and an equation for k f . Note that this approach is essentially an empirical approach using the fatigue notch factor, k f , applied to notch geometries. It is summarized by the following three equations:  equivqadj =k f  equiv unnotched  (7.4) q = k f −1 k t −1 (7.5) q = 1  1+ a   (7.6) where  equiv unnotched is calculated at the critical location without the notch present, k t = notch concentrated stress/unnotched stress,  is the notch root radius, and “a” is a material constant. Equation (7.6) is the empirical equation for k f , shown earlier as Equation (7.3). k t can be difficult to define for 3D component geometries, but the approach is well suited 364 Effects of Damage on HCF Properties 40 50 60 70 80 90 10 3 10 4 10 5 10 6 10 7 10 8 Notch methods approach (w = 0.445) Median RFL Fit 90% RFL Fit 10% RFL Fit Smooth bar failure Smooth bar run-out Small notch with Fs Small notch with q Fs Adj. S equiv (ksi) N f (cycles) Figure 7.37. Small notch correlation with Fs and q–k f approaches as compared to smooth specimen fatigue curves. to small FOD or machined notches where the local stress can be referenced to the stresses in the unnotched geometry. For this approach, the material constant a =18 mil was found to best correlate small machined notch test data as shown in Figure 7.37. The Fs approach or equivalent stressed surface area takes into account the stress distribution about the peak stress at a notch root. This approach is described in Appendix E. Both the q and the Fs approaches do a credible job of consolidating small notch data with smooth bar data as shown in Figure 7.37. Since the two approaches produced almost equivalent results, the q approach was used to consolidate the FOD test results because it is much simpler to apply than the Fs approach described in Appendix E. The results of the axial and bend specimen FOD tests for the various impact angles (in the axial tests) and the different tip radii (for the bend tests), modified using the q approach, are presented in Figures 7.38 through 7.42. In all cases, the notch geometry was measured as described above. The predictions for a constant notch root radius of 4.4 mil are represented with solid black lines for the different geometries and impact angles. Significant scatter exists in the FOD test results, but calculated k f with the q approach generally provides a reasonable prediction of the mean HCF behavior of specimens with FOD for different impact angles and FOD depths. For reference purposes, the k t values are also shown in the plots. Results are summarized for tests in the “as-FODed” and “as-FODed + stress relief (SR)” conditions in Figures 7.43 and 7.44. The predictions are best with a reduction in test scatter when the stress relief cycle is employed after FOD to reduce residual stresses (Figure 7.44). Foreign Object Damage 365 1 2 3 4 5 6 7 0 5 10 15 20 25 Axial specimens (R = –1, 10° impact angle) Pred K t K t Correlation K f as FODed K f with SR Pred K f with q K t or K f FOD depth (mil) Conservative Figure 7.38. Predicted and experimental k f for FOD tests in the axial specimen geometry with a 10  impact angle. 1 2 3 4 5 6 7 Axial specimens (R = –1, 30° impact angle) Pred K t K t Correlation K f as FODed K f as FODed (R = 0.5) K f with SR Pred K f with q K t or K f 0 5 10 15 20 25 FOD depth (mil) Figure 7.39. Predicted and experimental k f for FOD tests in the axial specimen geometry with a 30  impact angle. Results with both the q and Fs approaches for the axial and bend specimens are similar as summarized in Figures 7.45 and 7.46. For the axial specimens, the SR samples appear to have less scatter and consolidate better with smooth bar data than those without SR. While the authors of this report [8] propose implementation of these approaches for design applications, it should be noted that the indentor geometry and notch conditions covered only a limited range of FOD variables. As noted in the previous notch section, extending . approach, the material constant a =18 mil was found to best correlate small machined notch test data as shown in Figure 7.37. The Fs approach or equivalent stressed surface area takes into account. the HCF capability of specimens with FOD from the peak concentrated stress. Machined notch data for the same material are shown in terms of equivalent peak local stress as a function of fatigue. stress distribution about the peak stress at a notch root. This approach is described in Appendix E. Both the q and the Fs approaches do a credible job of consolidating small notch data with smooth bar data as