High Cycle Fatigue: A Mechanics of Materials Perspective part 36 doc

336 Effects of Damage on HCF Properties 7.8. SCOPE OF THE FOD PROBLEM As noted in Appendix G, FOD can even be of a size that can barely be detected by the unaided eye. A majority of FOD involves damage sizes that are less than 2 mm (0.080") in depth. There have been instances in service usage where concerns over HCF failures originating at extremely small FOD sites have led to frequent inspections of leading edges of fan blades using both a finger nail inspection or running dental floss up and down to find small FOD nicks or dents. More important, it is not yet known whether HCF failures which emanate from very small FOD are due to the degradation of material properties or are, instead, due to excessive vibratory stress amplitudes which just happen to choose the FOD location as the origin site based primarily on statistics of there being a very slight reduction in material capability at that site. Fan and compressor blades at the front end of jet engines are the components that receive the majority of damage, particularly at the leading edge of the airfoil. Due to the high frequency vibratory stresses that can be present in the fan and compressor sections associated with normal engine operation, it is not uncommon for fatigue cracking to initiate from FOD sites and grow catastrophically within minutes to hours of engine running time. The HCF caused by steady state or transient vibrations of the component is one of the leading causes of in-service failures of blades that have been subjected to FOD. It is important, therefore, to know the fatigue strength of materials and airfoil geometries that have been damaged by foreign objects of various types, sizes, velocities, and incident impact angles. Evaluation of FOD resistance of materials and structural components has been con- ducted in a highly empirical manner over the years. Engine companies generally subject individual components such as fan and compressor blades to simple vibratory loading to determine fatigue resistance. FOD is then introduced at anticipated critical locations and the damaged component is tested to determine the debit in fatigue resistance due to FOD. For laboratory specimens, there is little reported work on the introduction of FOD and subsequent evaluation of the fatigue resistance, particularly under HCF conditions. Some of the relevant research is described later in this section. For either real compo- nents or laboratory test samples, the method used for inflicting real or simulated FOD is extremely important. “Real” FOD can be produced by shooting typical objects ingested into an engine at velocities and incident angles expected under operational conditions. Other simulations of FOD can be achieved by machining a notch in the material of a size to match real FOD observed from field experience, by using quasi-static indentation of a chisel with a appropriate radius to the proper depth, by pendulum or drop weight impacts at various angles to the leading edge including a side impact chisel, or any other method such as a solenoid gun to produce the required geometry of notch. It has not yet been established that any of the simulation methods produce conditions identical to those of real FOD from ballistic impacts in terms of residual stress fields or material damage Foreign Object Damage 337 ahead of the notch. In fact, it is shown below that ballistic impacts and quasi-static chisel indents that produce nearly similar size craters in a leading edge do not produce the same HCF resistance under axial fatigue loading. Current design practice establishes allowable vibratory stresses on a pristine material through the use of a constant-life Haigh diagram that presents material data as alternating stress as a function of mean stress for either run-out conditions (infinite life) or a fixed number of cycles, typically 10 7 or higher (see Chapter 2). For FOD, the allowable vibratory stress is reduced by some percentage to account for the possibility of FOD in non-critical areas. For critical areas such as the leading and trailing edges of a blade, a notch severity corresponding to the worst case expected damage is assumed in the form of an equivalent stress concentration factor, k t , with perhaps a maximum notch depth associated with it. Such assumptions are usually based on field experience with similar geometries and usage in engines. The notch sensitivity can be further refined by converting from a stress concentration factor to a fatigue notch factor, k f (see previous section on notches), using empirical relations that have been developed for a number of materials and notch geometries, or by using actual notch fatigue test data on the material under consideration [6]. While the literature on notch fatigue is extensive (see Chapter 5), including both LCF and HCF, its extension to the solution of FOD problems is not direct or even applicable in many cases. There are several aspects of FOD that make it more complicated than a problem dealing solely with a notch induced by an impacting object. First, the impacting object causes material or microstructural damage ahead of the ensuing notch that, in turn, may reduce the fatigue properties of that material. Second, the impact event usually involves plastic deformation that leads to a state of residual stress in the notch vicinity. These residual stresses must be taken into account in any analytical modeling of the fatigue behavior of a sample subjected to FOD. Third, cracks or tears may be produced during the impact event which changes the problem from one of notch fatigue to that of determination of the threshold stress intensity for subsequent crack propagation due to HCF loading. Finally, the geometry of the damage produced by FOD on a typical geometry of a fan or compressor blade from impacts at various angles to the leading edge can be quite complicated and not easily described solely by conventional methods that utilize parameters such as depth and radius of notch. It is not surprising, therefore, to find little in the way of systematic investigations on the effects of FOD on the fatigue properties of materials. Furthermore, most investigations focus on the reduction of fatigue life due to FOD and subsequent loading at a given mean and vibratory stress level. Nicholas et al. [7] conducted a series of impact experiments on titanium leading edges and compared results with those on machined notches. The projectiles and velocities used in that investigation produced much higher levels of damage than are of interest in the present discussion. Further, the emphasis for comparison was on fatigue life, generally in the LCF regime. For HCF design, what is needed is a description of the reduction 338 Effects of Damage on HCF Properties of the FLS defined as the maximum stress that will not lead to fatigue failure for a predetermined (large) number of cycles. In other words, HCF design for FOD must be able to establish the allowable combination of steady-state and vibratory stress levels for a component. 7.8.1. Laboratory simulation methods Simulation methods for inducing damage representative of real FOD are intended to be easier to conduct than real ballistic impact. Different methods being used are discussed in Appendix G. Here we discuss the three methods that have been most widely used in recent investigations of FOD and its effect on the fatigue strength of materials and simple components. These methods were used in the recent US Air Force HCF program [8]. 7.8.1.1. Solenoid gun This is the current baseline used by General Electric Aircraft Engines Co. where they have developed extensive experience in producing simulated FOD. It was selected over the ballistic method which is very erratic and difficult to control. The solenoid gun provides a very controlled input energy to the specimen and produces the typical nick depths (0.005"–0.025") experienced in service. The main problem with the solenoid gun is that the impact energy is controlled, not the notch depth. As a result, the notch depth will vary depending on the dimensions of the leading edge region. The mass of the solenoid is relatively heavy; therefore, impact velocities are relatively low for low energy impacts. The velocity for low energy impact on a sharp-tip specimen (described later) is less than 10 ft/s. Therefore, the description of this method as a “dynamic” simulation is questionable. The advantage of the solenoid gun is its ease of use and repeatability of impact velocity. The terminology “gun” in “solenoid gun” is somewhat misleading if one thinks of a gun as a method of launching projectiles at high velocities. 7.8.1.2. Pendulum The pendulum systems also impact with a controlled energy level and at relatively low velocity. A 5 foot pendulum arm gives a 9 ft/s impact which is roughly the same impact velocity as that of the solenoid gun at the lowest power setting. The pendulum system also needs some type of catch system to prevent multiple impacts. One advantage of the pendulum system is that the energy at impact is simple to calculate. Unfortunately, where that energy goes to during the impact event is largely unknown even though it has been studied extensively. The pendulum system does not seem to offer anything over the solenoid gun, both being fairly low velocity methods of inducing damage with a mass much larger than that used in a ballistic impact experiment. On the other hand, the pendulum is a test device that is commonly found in many mechanical testing laboratories. Foreign Object Damage 339 7.8.1.3. Quasi-static A quasi-static method involves loading a specimen into a servo-hydraulic or screw-driven test frame and pushing on the specimen with an indentor. The cross-head is lowered until the indentor just touches the specimen, and then the FOD nick is controlled by cross-head displacement or maximum load. Since cross-head displacement is not the same as nick depth due to compliance in the load train and variability in establishing the exact point where contact starts, this makes overall control of the depth somewhat difficult. In addition, it is necessary to calibrate the relationship between cross-head displacement and nick depth for each specimen configuration and notch depth (similar to what has to be done for the solenoid gun or pendulum method). The advantage of the quasi-static method is that if cross-head displacement is controlled, this may provide a more controlled nick depth than controlling with impact energy like with the solenoid gun or pendulum methods. In addition, the quasi-static method can provide continuous load versus displacement information which may be useful in terms of determining net energy input into the target and its fixture. On the positive side is that for any reasonable size test machine and fixture, the energy available to deform the specimen is essentially unlimited. 7.8.2. Simulations using a leading edge geometry Foreign object damage is a common occurrence in blades and vanes of turbine engines and is most common on the leading edges of those components. FOD can be in the form of a crater or tear in the impacted component and can reduce the fatigue capability of the material at the location of the impact. The degradation of the fatigue strength can be attributed to three primary factors: a stress concentration due to a notch-like geometry, the generation of residual stresses during the formation of the crater, and microstructural damage which can range from microcracking through the formation of shear bands to the transformation of the microstructure [2, 9]. At certain levels of severity of the impact conditions, the formation of cracks during the impact event can occur, necessitating consideration of the threshold for crack propagation of initially very small cracks from a notch-like geometry [10]. In addition, changes in the geometry of the airfoil leading edge and residual stresses due to plastic deformation may produce local stress ratios at the notch tip which are, in general, different than the far-field applied stress ratio and may even drive the initiation location from surface to sub-surface [3]. Of the factors affecting the fatigue strength, the stress concentration is easiest to handle by using theoretical or empirical notch fatigue factors applied to measured deformation profiles. In many engineering and design applications, the geometry of the notch is simulated in the laboratory using quasi-static methods as opposed to resorting to ballistic impact. There are certainly questions related to this procedure if the damage produced differs 340 Effects of Damage on HCF Properties from that which occurs in the real event even though the notch geometry produced is identical [3]. In studying FOD on leading edges, the geometry and orientation of the blade or vane has to be considered. For a rotating blade, the angle of incidence (see Figure 7.16c) between an ingested particle and the blade can be estimated by considering the relative vector velocities of the angular velocity of the blade, dependent on radial location and rotational speed, and the forward velocity of the engine. In addition, the twist of the blade provides the angle between the rotational direction and the angle of the leading edge of Gage Section 38.1 25 R. 25.4 25 R. 17.3 111 A A 5.08 1.78 3.81 12.2 0.38 R. (a) (b) (c) θ Figure 7.16. Leading edge (LE) specimen. All dimensions in mm (a) Overall dimensions (b) Section A-A (c) Schematic showing orientation of impacting sphere. Foreign Object Damage 341 the blade with respect to that direction. Typical angles of incidence range between 0 and 60  and impact velocities can be in the several hundred m/s regime. Laboratory simulations conducted by Ruschau et al. [11] used a representative velocity of 300 m/s and incident angles covering 0–60  on two different leading edge geometries on the axially loaded leading edge specimen shown in Figure 7.16. Further, the fatigue strength was evaluated using step loading at stress ratios of both R =01 and R =05. To study the influence of impact angle, results were obtained on Ti-6Al-4V bar stock samples for a range of FOD impact angles for a cyclic life of 10 6 cycles. The data are presented in Figure 7.17 and are normalized with the smooth bar fatigue strength at the same life for each value of R. Results show little debit in fatigue life for the 0  impact angles, while a large loss in fatigue strength is noted for the other impact angles examined. The greatest loss in fatigue strength occurred with the 30  samples for both values of R examined. The lowest fatigue strengths for the 30  samples are similar to reference data of Haritos et al. [6] for the same titanium alloy tested with a machined notch of k t =27. Some of the difference in fatigue strength between 0  and higher angle impacts may be attributed to the residual stress state produced during the impact event. The states of residual stress and plastic deformation that result from the dynamic impact have been evaluated analytically for a hard spherical ball striking a simulated leading edge. Details are presented later in Section 7.14 and in Appendix G. Those results show that for an ideal normal 0   impact at the center of the leading edge sample, a compressive residual stress field is created in a region surrounding the FOD notch, with a residual tensile stress field existing some distance interior of the impact site. Such a residual stress state would thus reduce the elastic stress concentration created by the FOD notch, and, if the tensile 0.4 0.5 0.6 0.7 0.8 0.9 1 030456015 R = 0.1 R = 0.5 Normalized stress Angle of incidence, θ (degrees) Ti-6Al-4V bar 10 6 cycles 30 Hz Figure 7.17. Normalized fatigue strength for various foreign object impact angles. 342 Effects of Damage on HCF Properties region is sufficient in magnitude, would lead to fatigue initiation in the interior region of the sample, as observed in [12]. For the case of non-normal impact angles, analysis (see Appendix G) shows that while a large compression stress region is created from the impact, a small tensile stress field is created near the surface at the entrance side of the damage site. This tensile stress region at the surface would offset any beneficial influence from the compressive stress field, hence the fatigue strength of a non-normal FOD impact would be reduced to some extent [11]. However, since it is difficult to hit the exact center of the leading edge sample, particularly with angled impacts, such a tensile stress region would be expected to vary significantly in size and magnitude with slight differences in impact location, thus leading to a large variability in fatigue behavior [11]. The large degree of scatter in fatigue results makes it difficult to demonstrate any trend of decreasing fatigue strength with increasing impact angle. However, as seen in Figure 7.17, impacts other than 0  can be deduced to produce more damage in terms of tensile residual stresses that can greatly reduce the fatigue strength. This explanation of the variability in fatigue strengths is from the standpoint of the residual stress field alone. Such a scenario assumes an ideal, “clean” damage crater with no cracking, tears, nicks, of other type of damage acting in conjunction with the FOD notch. This is not generally the case, and is discussed further in later sections. Further tests were performed to examine the influence of leading edge thickness on fatigue strength, but were limited to 0  and 30  impact angles only [11]. The fatigue strength was determined for a cyclic life of 10 7 cycles at a test frequency of 350 Hz. The results of samples with leading edge radii of 0.38 and 0.127 mm, using Ti-6Al-4V forged plate, showed similar fatigue behavior in the 0  and 30  impacts. This differed from the forged bar data which demonstrated a larger debit in fatigue performance resulting from the simulated FOD at a 30  impact angle over the 0  impact. Even with a large amount of scatter in the data, the 0  data showed a larger debit in fatigue strength than expected. While the 0  impact should produce a compressive residual stress field behind the impact crater, thereby providing higher fatigue strength over a 30  impact, the impact sites for several specimens were slightly off-center and produced damage that appeared similar to that observed in samples impacted at 30  . Thus, off-centered 0  impacts can cause some residual tensile stresses in the FOD notch vicinity similar to the 30  impacts, thus explaining the lower than expected results for 0  . Of particular importance in the results of the study of the influence of the leading edge thickness was the observation that while the samples with the 0.127 mm edge radius were much thinner and thus more prone to deeper FOD impacts, fatigue strength losses were, in general, similar to the thicker leading edge sample results. There was no apparent influence of sample edge radius (or thickness) on the degree of fatigue strength losses for the type of FOD investigated. In that study [11], only 1 mm glass spheres at a single velocity of 305 m/s were used. Different impact parameters (e.g., FOD material, size, Foreign Object Damage 343 shape, velocity, etc.) may have an influence on the trends reported. In general, off-angle impacts were found to be more detrimental than head-on 0   impacts. Fatigue strength losses, some as high as 50%, showed little or no correlation with leading edge thickness or depth of notch. Mall et al. [3] simulated FOD with a quasi-static indentor against a flat plate whose width was 1.27 mm as shown in Figure 7.18. The use of this simple geometry allowed them to conduct elastic-plastic FEM analysis to study the deformation profiles and to compute residual stresses. Chisel indentors of hardened steel were loaded against the edge of a flat plate under displacement control to achieve various depths of damage. The indentors had a tip diameter of either 1, 2, or 5 mm. The fatigue strength of the damaged specimen that was indented twice, once on each opposing edge (for symmetry), was obtained in tension–tension fatigue at 350 Hz at values of R = 01 and 0.5. The results are shown in Figure 7.19 as a function of the permanent depth of the indent. These are not small indents compared to the ones used in the previous studies cited. In this case, extensive plastic deformation was observed which was verified with the finite element calculations that showed permanent strains in excess of 15% in some cases. For damage depths in excess of 2000 m, the authors observed damage in the form of shear cracks along with plastic deformation. For depths less than 2000 m, on the other hand, there R 45° R = 0.5, 1.0, 2.5 mm 50 6 12 0.127 Figure 7.18. Specimen and impactor geometry used in [3]. Dimensions are in mm. 344 Effects of Damage on HCF Properties 0 100 200 300 400 500 600 700 0 500 1000 1500 2000 2500 3000 Ti-6Al-4V plate 10 7 cycles 1 mm chisel, R = 0.5 1 mm chisel, R = 0.1 2 mm chisel, R = 0.5 2 mm chisel, R = 0.1 5 mm chisel, R = 0.5 5 mm chisel, R = 0.1 Undamaged, R = 0.5 Undamaged, R = 0.1 Fatigue strength (MPa) Damage depth (µm) Figure 7.19. Fatigue strength versus damage depth [3]. was no evidence of damage other than the plastic deformation in the vicinity of the indent. The shear cracking in the case of deeper indents is reflected in the fatigue strengths which were approximately 200 MPa, as shown in Figure 7.19, which is approximately one-third that of the undamaged material. The fatigue strength appears to level off as depths beyond 2000 m are reached. For this particular scenario, a value of k f =3 appears to represent the worst-case data reasonably well. 7.8.3. Role of residual stresses These results of leading-edge impact studies, including analytical modeling, point out the important role of residual stresses in altering the fatigue strength of material subjected to FOD. To study the influence of residual stresses, stress relief annealing has been used in titanium specimens [13, 14]. By annealing, residual stresses are effectively elimi- nated while preserving the microstructural and mechanical characteristics of the material. Whether or not this applies to material that has been subjected to very large local strains, such as at the tip of a notch produced by an impact event, has not been ascertained. Damage induced by FOD in a leading edge geometry was studied in a series of experiments involving variations of impact energy, size of impactors, and various methods of inducing damage, ranging from quasi-static to ballistic impact [12]. The specimen geometry was that shown above in Figure 7.16. Samples were ballistically impacted with steel spheres of nominal diameters of 0.5, 1.33, and 2.0 mm at velocities ranging from approximately 60 to 500 m/s. The impact conditions were chosen to obtain similar kinetic energy impacts from different size projectiles. The samples were shot on each leading edge, two shots per sample, in the center of the gage section at an impact angle Foreign Object Damage 345 of 30  relative to the centerline of the test sample cross section. The nomenclature for the definition of impact angle is furnished in Figure 7.16(c). Because of the use of two impacts on each sample, each data point generated represents the behavior of the worst of two nominally identical impact conditions. For comparison with the ballistic impact specimens, quasi-static indents were imparted using a testing machine under displacement control to produce notches that were geo- metrically similar to those obtained under ballistic impact. This was accomplished using a steel indentor geometry with the same radius as the ballistically impacting spheres and accounting for the elastic rebound in the quasi-static indentation. The radius of the ballistically impacted crater was nominally the same as the radius of the impacting sphere [9, 14]. A third method of imparting damage was through the use of a pendulum fitted with chisel indentors whose radii were identical to the three impacting spheres. A single mass at two different incident velocities was chosen to produce similar values of depth of penetration to those of the sphere impacts. The incoming and rebound velocities of the pendulum were recorded for subsequent energy calculations. All of the impacted and indented specimens were fatigue tested using the step-loading procedure with load steps of 10%. The initial load block was taken well below the anticipated fatigue strength of the damaged specimen. 7.8.4. Energy considerations The depth of crater was examined as a function of the energy for each of the three impact methods and the results are presented in Figure 7.20. For the quasi-static indents, the energy is obtained from the load-displacement records by taking the area bounded by the loading–unloading curve for each specimen. This represents the net energy absorbed in the specimen and is not influenced by any (elastic) compliance of the specimen under the end supports used during the indentation process. A straight line in the figure is an approximation to the quasi-static indent data obtained using a chisel indentor whose radius was 0.67 mm (half the diameter of the 1.33 mm sphere). The two clusters of quasi- static data points represent attempts to produce two different values of the permanent displacement with the same indentor. The same indentor geometry was used for the pendulum impacts. The energy absorbed is calculated from the net kinetic energy used to produce the deformations, the vector sum of the input, and rebound kinetic energy as measured in the experiments. The two clusters of pendulum data points represent two different input velocities used to produce two nominally different depths. The data follow the quasi-static data quite closely. The remaining data in Figure 7.20 represent those from the ballistic impact experiments. These data represent impacts with all three sphere diameters and, in addition, several different velocities chosen to duplicate the kinetic energy of a different size sphere. . undamaged material. The fatigue strength appears to level off as depths beyond 2000 m are reached. For this particular scenario, a value of k f =3 appears to represent the worst-case data reasonably. plastic deformation that leads to a state of residual stress in the notch vicinity. These residual stresses must be taken into account in any analytical modeling of the fatigue behavior of a sample. and can reduce the fatigue capability of the material at the location of the impact. The degradation of the fatigue strength can be attributed to three primary factors: a stress concentration