366 Effects of Damage on HCF Properties 1 2 3 4 5 6 7 0 5 10 15 20 25 Axial specimens (R = –1, 50° 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) Figure 7.40. Predicted and experimental k f for FOD tests in the axial specimen geometry with a 50  impact angle. 1 2 3 4 5 6 7 0 5 10 15 20 25 Sharp tip LE bend specimen (R = –1) Predicted 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) ~20° Impact angle Figure 7.41. Predicted and experimental k f for FOD tests for a bending specimen with the sharp tip geometry. approaches such as the one based on q or k f to a wider range of notch geometries can lead to errors. For FOD, as will be shown later, changes in the residual stress states, and material damage, as severity of the impact increases, make it even more difficult to extend the approaches described herein. Foreign Object Damage 367 1 2 3 4 5 6 7 0 5 10 15 20 25 Blunt tip LE bend specimen (R = –1) Predicted 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) Run-outs included ~20° Impact Angle Figure 7.42. Predicted and experimental k f for FOD tests for a bending specimen with the blunt tip geometry 0 0.5 1 1.5 2 2.5 3 0 5 1015202530 Predictions with q approach (no SR) Bend specimen, as FODed Axial specimen, as FODed S with q /S curve FOD depth (mil) Conservative Figure 7.43. Predicted HCF capability vs the baseline fatigue behavior for as-FODed tests. 7.10. ANALYTICAL MODELING OF FOD Appendix G describes, in detail, both experimental and analytical simulation methods for the prediction and modeling of FOD. It describes some of the procedures that can be used to measure and predict the effects of FOD and gives current state-of-the-art examples of techniques and methodologies that are in use and/or are being developed. In this section, some analytical procedures and findings are described which relate to hard body FOD. More extensive studies and observations are contained within the Appendix. 368 Effects of Damage on HCF Properties 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 Predictions with q approach (with SR) Bend specimen, FOD + SR Axial specimen, FOD + SR S with q /S curve FOD depth (mil) Conservative Figure 7.44. Predicted HCF capability vs the baseline fatigue behavior for as-FODed tests with a stress relief cycle to minimize residual stresses. 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 Predictions for axial specimens S (Fs) with SR S (q) with SR S (Fs) as FODed S (q ) as FODed S method /S curve FOD depth (mil) Figure 7.45. Similar predicted HCF capability with q and Fs approaches for axial specimens with FOD. While experimental observations of FOD show wide variability with little or no change in impact conditions, analytical modeling should be expected to provide more consistency. This is true only if the actual conditions occurring during FOD are modeled accurately. This is not always the case, either analytically or experimentally. In particular, the role of centrifugal loading can be important in an impact event. In [8], analytical modeling studies of leading edge FOD impact events were conducted to determine the effects of various parameters on leading edge damage, residual stress distribution, and predicted Foreign Object Damage 369 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 Predictions for bending specimens S(Fs) with SR S(q ) with SR S(Fs) as FODed S(q ) as FODed S method /S curve FOD depth (mil) Figure 7.46. Similar predicted HCF capability with q and Fs approaches for bending specimens with FOD. HCF capability. The parameters investigated were impact velocity, impact angle, blade centrifugal loads, projectile geometry, and imperfect impact. MSC/DYTRAN was used for analysis of the high-speed impact events. Existing DYTRAN finite element models of the specimen shown in Figure 7.16, referred to earlier, were utilized for the analysis. The specimen finite element model geometry and a close-up of a steel ball projectile can be found in Appendix G. The dynamic analysis modeling included strain-rate-dependent material properties and material failure. The material failure model was based on the Von Mises yield function. Material strain-rate dependency was included. The chosen material failure model allowed for failure of the element by definition of an effective plastic strain at failure. The high- strain-rate effective plastic strain at failure utilized in this analysis was 35%. The single effective-plastic-strain variable utilized does not distinguish between different material failure modes such as tension, compression, shear, and mixed modes. A more accurate failure model would provide a better residual stress state and deformation of the FOD site location. An HCF–LCF cycles-to-failure model based upon a Walker methodology was developed and used to investigate parameter influences on predicted fatigue life to failure. The Walker strain is defined as  Walker =  max E   eq E  max  m (7.7) where  max is the maximum stress, m is the Walker strain exponent, and  eq is the equivalent strain range. The ability of this formulation to consolidate fatigue data at different values of R is illustrated in Figure 7.47 which shows data from smooth bar as well as notched specimens and lines indicating the degree of scatter. 370 Effects of Damage on HCF Properties 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.E + 03 1.E + 04 1.E + 05 1.E + 06 1.E + 07 1.E + 08 1.E + 09 Life-cycles Walker Strain% LCF Typ –2.19 σ –3 σ 2.19 σ HCF Circ notch Flat notch Figure 7.47. Ti-6Al-4V RT consolidated HCF and LCF results. One of the analytical studies performed was an investigation of blade preload effects (due to centrifugal load) on the residual stress distribution around the FOD site. Residual stress distributions and predicted cycles to failure were investigated and compared. Spec- imens were impacted at different angles and impact velocities while experiencing 0 ksi, 20 ksi, and 40 ksi static stress fields simulating the blade centrifugal load. A 1.33 mm diameter steel ball with a 1000 ft/s velocity was used. The study indicated that as blade preload increased, higher compressive and tensile residual stresses would be produced at the FOD site. Although the influence of preload on predicted fatigue life was not clearly observed, it might be attributed to a relatively coarse mesh density, and the use of a simple material failure model. It was observed, however, that including residual stress reduced the predicted fatigue life to failure by more than a few orders of magnitude as indicated in Figure 7.48, which also shows that increasing the impact angle reduces Blade preload effects 0–20 ksi – 0 Cycle 10,000 1,00,000 10,00,000 1,00,00,000 10,00,00,000 1,00,00,00,000 10,00,00,00,000 0 5 10 15 20 25 30 35 40 Blade preload nominal (ksi) Fatigue life to failure 0° with residual 0° without residual 30° with residual 30° without residual 60° with residual 60° without residual Averaged with residual Averaged without residual Figure 7.48. Predicted fatigue life of preloaded blade cycled to 20 -ksi nominal stress. Foreign Object Damage 371 the predicted fatigue life. More variance exists in the “without residual stress” predicted fatigue life results. Model mesh density might affect the variance. After impact, the finite element model is faceted at the local FOD. Local facets produce sharp angles that are stress risers. Including the residual stress reduces the predicted fatigue life and smoothes out the curves. Figure 7.49 illustrates that as the cyclic stress increases to 0–40–0 ksi, residual stress due to impact has less effect on the predicted life. Comparing Figures 7.48 and 7.49 suggests that residual stress is more critical in the HCF regime than the LCF regime. Figure 7.49 shows that as impact angle increases, fatigue life decreases. One interpretation of this analysis is that performing experiments on FOD in blades under laboratory environments, absent of centrifugal loading, may produce results that are not representative of real engine conditions and could be misleading. Similarly, reproducing the correct impact angle, particularly for low angles, can influence the fatigue life of the specimen. 7.10.1. Perturbation study As shown in Appendix G, FOD test results can exhibit a great deal of scatter in both the fatigue life of specimens and the nature of the damage when impacted under nominally identical conditions. It has proven to be very difficult to reproduce exactly the same FOD from one test specimen to the next. To study this analytically, an impact site perturbation Blade preload effects with angle of impact 0–40 ksi – 0 Cycle 1,000 10,000 1,00,000 10,00,000 0 102030405060 Impact angle degrees Fatigue life to failure 0 ksi Preload with residual 0 ksi Preload without residual 20 ksi Preload with residual 20 ksi Preload without residual 40 ksi Preload with residual 40 ksi Preload without residual Figure 7.49. Predicted fatigue life of preloaded blade cycled to 40 ksi nominal stress. 372 Effects of Damage on HCF Properties R +Y +X R/4 R/2 3R/4 R Steel ball Ball location is perturbed by a factor of R in the +X direction Velocity vector * Not drawn to scale Blade specimen R Figure 7.50. Perturbation study definition for the 0  impact angle study. study was performed [8]. Similar to the study in the previous section, the effect on fatigue life for the 0  impact angle of the blunt edge radius (0.381 mm/0.015") blade specimen was addressed. Here, a 1.33 mm ball with a velocity of 1000 ft/s was investigated by offsetting the vector of the incoming ball by amounts ranging from 0.25 to 1.0 times the radius of the leading edge as shown in Figure 7.50. It was found that increased impact site offset in the +X direction (down) produced increased tensile residual stress on the top side of the blade. The effect of the offset in fatigue life is summarized in Figure 7.51 which illustrates that with increased impact site offset there is a reduction in fatigue life. For the X = 0 location, the case of 0–20 ksi produces a fatigue life is calculated to be 3,370,000 cycles, while increasing the offset to Impact site perturbation study 0° angle impact, 1000 ft /s Blunt edge specimen 1.E + 04 1.E + 05 1.E + 06 1.E + 07 1.E + 08 1.E + 09 1.E + 10 0 0.0025 0.005 0.0075 0.01 0.0125 0.015 Impact site offset from zero (inches) Fatigue life to failure 0–20 ksi cycles to failure with residual stress 0–40 ksi cycles to failure with residual stress 0–20 ksi cycles to failure without residual stress 0–40 ksi cycles to failure without residual stress Figure 7.51. 0  Impact site offset study on fatigue life. Foreign Object Damage 373 Blade specimen R +Y +X +R/4 Velocity vector * Not drawn to scale –R/4 +R/2 –R/2 30° Steel ball Ball location is perturbed by a factor of R in the ±Y direction Figure 7.52. Perturbation study definition for the 30  impact angle study. X = R, fatigue life decreases by a factor of 2.9 to 1,180,000 cycles. The 0  perturbation study suggests that a good deal of fatigue life variation could be observed due to imperfect impacts. Another study looked at the effect of impact offset when the incoming angle of the projectile was 30  as shown in Figure 7.52. Five impact cases were investigated with the blunt edge specimen. It was observed that as Y goes from −R/2to+R/2 the depth of the FOD site increases. The −R/2 and −R/4 impacts removed elements through the thickness of the blade tip. For Y =0 and greater, some elements remained on the exit side of the impact, and there were more elements removed at the entrance side. The compressive stress distribution was found to be driven from a more interior distribution for Y =−R/2 toward a surface distribution for Y =+R/2. Figure 7.53 compares the fatigue life results for this perturbation study. For the 0–20 ksi cyclic case with residual stresses, the calculated maximum number of cycles to failure was 9,80,000 cycles at the Y =−R/4 location. The minimum of 2,00,000 cycles occurred at the Y = 0 location. There is a factor of 4.9 between the maximum and the minimum calculated fatigue life. These results demonstrate that there can be a significant difference in predicted fatigue life given an imperfect impact. The 0  impact angle perturbation study of the blunt edge specimen shows a 2.9 factor between the maximum and the minimum calculated fatigue life values. For the 0  impact, fatigue life decreased as offset increased. For the 30  impact of the blunt edge specimen, a 4.9 factor between the maximum and the minimum fatigue life was observed. The two impact site perturbation studies performed here suggest there is a variation in fatigue life due to imperfect impacts. Further analysis would need to be done to more accurately address the actual magnitude of the variation. 374 Effects of Damage on HCF Properties Impact site perturbation study 30° angle impact, 1000 ft/s Blunt edge specimen 1.E + 03 1.E + 04 1.E + 05 1.E + 06 1.E + 07 1.E + 08 1.E + 09 1.E + 10 –0.0075 –0.005 –0.0025 0 0.0025 0.005 0.0075 Impact site offset from zero (inches) Fatigue life to failure 0 –20 ksi cycles to failure with residual stress 0 – 40 ksi cycles to failure with residual stress 0 –20 ksi cycles to failure without residual stress 0 – 40 ksi cycles to failure without residual stress Figure 7.53. 30  Impact site offset study on fatigue life. 7.11. SUMMARY COMMENTS The nature of the FOD problem that involves objects impacting static or rotating com- ponents, as well as some of the research findings summarized in this chapter, clearly distinguish FOD as the most difficult subject to deal with from an HCF (materials) design and analysis perspective. While extensive FOD occurs on a regular basis, fortunately only a small percent of damaged components actually fail from HCF. Thus, the combination of damage and vibratory stress is what must be assessed to establish the potential for a combined FOD/HCF failure to occur. Adding to the complexity of the problem, as pointed out in this chapter, is the very wide variety of damage modes that may occur. This variability is due not only to the type of impacting object that causes the damage, covering a range in sizes, shapes, and materials, but also to the geometry of the com- ponent being impacted. For the latter, the susceptibility of the component to vibratory stress is an important aspect for design against FOD/HCF failure. Another consideration is the consequence of a component failure, for example, whether a blade is contained within the engine housing and how much potential damage such a blade or piece of blade might cause downstream in the engine. Most of all, however, is the question of what objects cause FOD. The word “foreign” in FOD is very appropriate because it is rare when the foreign object can be identified. Only the damage remains after the event and, in extreme cases, no evidence remains at all when catastrophic failure occurs. One organization is currently using steel cubes to simulate FOD, one is 3.2 mm on a side and one is 4.8 mm on a side. While these cubes, when specifically oriented, produce damage that is very similar to what is observed in the field or provide a worst case scenario, it is obvious that steel cubes are not the real objects being ingested into engines in the Foreign Object Damage 375 field. Although standard size birds have been identified for bird ingestion simulations and engine qualification, no hard objects have been identified to produce FOD similar to what is encountered in the field beyond the steel cubes mentioned above. Will there ever be a “standard” sand particle or stone with which to evaluate the FOD tolerance of an engine or an engine component? It is this author’s opinion that some sort of standardization should be developed for the purpose of at least comparing the FOD tolerance of different designs or FOD tolerance enhancements. One aspect of FOD that has not been addressed in this book is the subject of FOD repair. Current methods involve either replacing the component when damage is severe or blending out the damaged region by grinding or filing. Blend limits and specifications depend not only on the extent of the damage but also upon the location of the damage such as radial position along the leading edge of a blade. As noted in this chapter, residual stresses can be produced during the FOD event. The extent and magnitude of such stresses have not been quantified to any great extent, so blending may or may not eliminate all residual stresses or, worse, may expose detrimental (tensile) residual stress fields. Concurrently, microstructural damage may occur beyond the crater in the form of shear bands, internal cracking, or other. Such damage may not be detectable or visible on a component. Current repair specifications are highly empirical and do not consider the extremely complex nature of the damage imparted to a material during an FOD event as noted in this chapter. Simulations of FOD events may not produce the actual damage encountered in service because the impacting object is not known or the method of imparting damage (quasi-static for example) may not produce the same damage as a ballistic impact. Finally, the very complex nature of the FOD event lends its treatment to statistical methods where the probabilities of the event itself as well as the vibratory loading and the material capability should all be considered. This subject is discussed in Chapter 8. REFERENCES 1. Martinez, C.M., “Effects of Ballistic Impact Damage on Fatigue Crack Initiation in Ti-6Al-4V Simulated Engine Blades”, M.S. Thesis, School of Engineering, University of Dayton, Dayton, OH, April, 2000. 2. Peters, J.O., Roder, O., Boyce, B.L., Thomson, A.W., and Ritchie, R.O., “Role of Foreign Object Damage on Thresholds for High-Cycle Fatigue in Ti-6Al-4V”, Metallurgical and Materials Transactions, 31A, 2000, pp. 1571–1583. 3. Mall, S., Hamrick, J.L., II, and Nicholas, T., “High Cycle Fatigue Behavior of Ti-6Al-4V with Simulated Foreign Object Damage”, Mech. of Mat., 33, 2001, pp. 679–692. 4. Franklin, J. and Kleinakis, E., “FOD Data Mining and Investigation”, Chapter 2 in Ref. [4]. 5. “Best Practices for the Mitigation and Control of Foreign Object Damage–Induced High Cycle Fatigue in Gas Turbine Engine Compression System Airfoils”, Work performed by RTO AVT Task Group-094, NATO RTO Technical Report TR-AVT-094, December 2004. . modeled accurately. This is not always the case, either analytically or experimentally. In particular, the role of centrifugal loading can be important in an impact event. In [8], analytical modeling studies. wide variety of damage modes that may occur. This variability is due not only to the type of impacting object that causes the damage, covering a range in sizes, shapes, and materials, but also. Metallurgical and Materials Transactions, 3 1A, 2000, pp. 1571–1583. 3. Mall, S., Hamrick, J.L., II, and Nicholas, T., High Cycle Fatigue Behavior of Ti-6Al-4V with Simulated Foreign Object Damage”,