High Cycle Fatigue: A Mechanics of Materials Perspective part 58 pdf

556 Appendix F 0.7 0.8 0.9 1 1.1 1.2 1.3 012345 R = 51 mm Flat & R = 3 mm P max /P 0 max b/a Figure F.5. Ratio of peak pressure P max to peak pressure P 0 max for increasing thickness to contact length ratio for two pad geometries. the correct contact length, a, stick zone size, c, pressure eccentricity, e, stick zone eccentricity, e c , the normal rigid-body displacement,  v , the tangential rigid body displacement,  u , and the pad profile rotation angle  m . The peak pressure P max was also calculated for increasing specimen thickness to study the thickness effect on the pressure distribution. A normal load of 12 × 10 6 N/m was applied to a pad geometry of 51 mm radius pad as well as a 3-mm flat and edge radius pad for increasing thickness. The peak pressure was obtained for each specimen thickness and pad geometry and normalized with the peak pressure P 0 max obtained from the half-space solution. Figure F.5 shows that the CARTEL solution (finite thickness) approaches the CAPRI solution (half-space) for a thickness where the thickness to contact length ratio b/a is greater than 5. The half-contact length that was used for the two pad geometries was a = 11mm for the cylindrical pad and a =17 mm for the flat pad. REFERENCES 1. Hills, D.A., Nowell, D., and Sackfield A., Mechanics of Elastic Contacts, Kluwer Academic Publishers, 1992. 2. Murthy, H., Harish, G., and Farris, T.N., “Efficient Modeling of Fretting of Blade/Disk Contacts Including Load History Effects”, ASME Journal of Tribology, 126, 2004, pp. 56–64. 3. Ciavarella, M., Hills, D.A., and Monno, G., “The Influence of Rounded Edges on Indentation by a Flat Punch”, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 212(4), 1998, pp. 319–328. 4. Jager, J., “Half-planes Without Coupling Under Contact Loading”, Archive of Applied Mechanics, 67, 1997, pp. 247–259. 5. Goryacheva, I.G., Murthy, H., and Farris T.N., “Contact Problem with Partial Slip for the Inclined Punch with Rounded Edges”, Int. J. Fatigue, 24, 2002, pp. 1191–1201. Appendix F 557 6. Barber, J.R., Elasticity, Kluwer Academic Publishers, Netherlands, 1992. 7. Mindlin, R.D., “Compliance of Elastic Bodies in Contact”, J. Appl. Mech., 16(3), 1949, pp. 259–268. 8. Farris, T.N., “Mechanics of Fretting Fatigue Tests of Contacting Dissimilar Elastic Bodies”, STLE Tribol. Trans., 35, 1992, pp. 346–352. 9. Hills, D.A. and Nowell, D., Mechanics of Fretting Fatigue, Kluwer Academic Publishers, 1994. 10. Johnson, K.L., Contact Mechanics, Cambridge University Press, Cambridge, 1985. 11. Nowell, D.A. and Sackfield, A., Mechanics of Elastic Contacts, Butterworth-Heinemann, Oxford, 1993. 12. Rajeev, P. and Farris, T., “Numerical Analysis of Fretting Contacts of Dissimilar Isotropic and Anisotropic Materials”, J. Strain Analysis, 37(6), 2002, pp. 503–517. 13. Szolwinski, M.P. and Farris, T.N., “Mechanics of Fretting Fatigue Crack Formation”, Wear, 198, 1996, pp. 193–107. 14. Westergaard, H.M., “Bearing Pressures and Cracks”, Journal of Applied Mechanics, June, 1939, pp. A49–A53. 15. Filon, L.N.G., “On an Approximate Solution for the Bending of a Beam of Rectangular Cross-Section under any System of Load, with Special Reference to Points of Concentrated or Discontinuous Loading”, Philosophical Transactions, 201, 1903, pp. 63–155. 16. Sneddon, I.N. (1951), Fourier Transforms, McGraw-Hill, New York, 1951. 17. Bentall, R.H. and Johnson, K.L., “An Elastic Strip in Plane Rolling Contact”, Int J. Mech. Sci., 10, 1968, pp. 637–663. Appendix G ∗ Experimental and Analytical Simulation of FOD ∗ Jeffrey Calcaterra INTRODUCTION Foreign Object Damage (FOD), as described in Chapter 7, is one of the most difficult problems facing designers and maintainers of modern gas turbine engines. One of the main reasons for the difficulty is the uncertainty associated with FOD events. To simulate and model, an FOD event and the resulting damage requires replicating, analytically or numerically, the results of impacts of objects onto structural components or specimens that represent structural component materials and geometries. This, in turn, requires detailed knowledge of the event that actually took place. In most cases, the evidence after an FOD field event is the damaged component. The event itself is surmised from the inspection of the damage and comparing it with damage produced under controlled simulated conditions, even though what is being simulated is not completely known. The uncertainties about FOD events center around the wide variety of hard-body FOD sources, ranging from very small impactors such as sand and small rocks, up to large impactors such as tools and bolts. Further, similar types of impactors can cause a wide range of damage. They can impact the leading edge, trailing edge, or somewhere on the body of the blade. They can also dent, crater, nick, or tear the blade. Not only does FOD cause a wide range of damage sizes, but even similarly shaped damage can cause significantly different post-impact responses. An example of this is shown in Figure G.1. In this figure, laboratory specimens are shown that were damaged under carefully controlled conditions. The specimens had the same geometry, both were impacted at the same location using 1 mm glass spheres at a velocity of 300 m/s and the resulting damage was geometrically similar. Even more disparate results can be seen in Figure G.2 where nominally identical impacts under laboratory conditions resulted in different damage mechanisms. Both of these specimens were impacted with 1.0-mm-diameter glass spheres. In one case (Figure G.2a), the material was deformed while in the second case (Figure G.2b), the impact caused chipping and what the authors [2] designate as “loss of material” for obvious reasons. Despite attempts to make the damage on both of these sets of specimens identical, the residual fatigue strengths of these specimens were widely disparate. The uncertainty in ∗ This document was prepared by Dr. Jeffrey Calcaterra of the US Air Force Research Laboratory, Materials Directorate and is based primarily on a document originally prepared for NATO RTO [1]. 558 Appendix G 559 Figure G.1. Comparison of impact surfaces on simulated airfoil leading edges from 1 mm glass spheres at a velocity of 300 m/s. 200 μm (b) (a) 200 μm Figure G.2. Head-on view of a 30  ballistic impact FOD site for a 0.38-mm leading edge radius sample exhibiting (a) little or no loss of material and (b) a larger loss of materials. the laboratory is only magnified in service, where the FOD impactor can be sand, rocks, pieces of a carrier deck, etc., and can strike the blade at a wide range of impact angles and velocities. In short, there is not one typical type of FOD. The purpose of this appendix is to describe experimental and analytical simulation methods for the prediction and modeling of FOD. It sets out to describe 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. Because of the uncertainty associated with FOD, simulating typical cases in order to develop design methodologies poses a significant challenge. The first step necessary to develop an FOD simulation method is to survey field experience and determine which types of impacts account for the most FOD occurrences. The second step is to determine how to best simulate these impacts. This step includes both numerical and experimental methods. The final step is to develop life prediction methodologies that account for 560 Appendix G the relevant impact parameters and provide the most accurate prediction of post-impact capability. The sections of this appendix mirror these steps. CHARACTERIZATION OF FIELD EXPERIENCE Previous studies conducted by the United States Air Force [3] have indicated that there were very few pertinent data available from engine companies concerning the distribution of FOD sizes, shapes, and occurrence rates. As a result, the USAF initiated a field inspection campaign in order to collect such data. The first phase of the study involved inspecting complete fan and compressor modules from a number of engines. The study looked at over 75 stages and included data from approximately 5000 blades [3]. The FOD location relative to the blade span is summarized in Figure G.3. As an example of the information presented in Figure G.3, approximately 12% of the damage to Stage 14 blades took place between 45 and 55% of the distance from root to tip. For each stage, the majority of the FOD occurs beyond 80% span. As the blade steady stresses are low towards the tip, the effects of centripetal stiffening are expected Stage 16 10 1 4 7 13 of FOD % % Span 0% 10% 40% 70% 100% 80% 60% 50% 30% 20% 90% 70%–80% 50%–60% 40%–50% 20%–30% 10%–20% 30%–40% 0%–10% 60%–70% Figure G.3. Percentage of FOD located along the span relative to the blade tip. Appendix G 561 0 6 4 10 8 12 14 16 18 0 0.2 0.4 0.5 0.3 0.1 0.05 0.25 0.45 0.15 0.35 20 2 100% 90% 80% 60% 70% 20% 0% 10% 30% 40% 50% FOD depth (in.) Frequency Figure G.4. Histogram and cumulative distribution function for FOD depth. The data shown are measured on a line normal to the leading edge to the deepest part of the damage along the chord of the blade. Viewing angle was not recorded. to be low, as well as is the ratio of minimum to maximum stress (R) in the vicinity of most FOD events. The cumulative distribution of FOD depths is displayed in Figure G.4. The measured FOD depth ranged from 0.002 in. to 0.5 in. (0.05 to 13 mm) with an average depth of approximately 0.060 in. (1.5 mm). Although this study provided a wealth of infor- mation concerning average and extreme FOD values, it collected little data concerning the geometry and damage characterization of in-service FOD. Due to this shortfall, the USAF initiated a second FOD study. The objective of this effort was to define the range of FOD geometries that could occur in service. To meet this objective, the USAF provided examples of “typical” FOD based on their experience in inspecting and overhauling turbine engines. A total of 51 Ti-8-1-1 blades from either 1st, 2nd or 3rd stage fans from turbojet fighter engines were provided for evaluation. These 51 blades had been identified as having FOD during a previous inspection; of these blades 31 contained a total of 42 discrete FOD sites. The remaining blades were severely damaged (e.g., see Figure G.5) and therefore were not further characterized. The USAF study found the discrete FOD consisted of dents, tears, and notches, as can be seen by the examples in Figures G.6 through G.9. Damage was primarily to the leading edge of the blades – specifically, 40 leading edge FOD and two trailing edge FOD sites were observed. In two cases, the leading edge damage consisted of FOD that had been previously blended and returned to service. Additional details on the FOD geometry can be found in [3]. In addition to the USAF study, the information from a UK Ministry of Defence (MOD) study on FOD is included here. Examination of several Pegasus fan blades from Harrier aircraft indicates that FOD is only found on the pressure surface (except in the case of 562 Appendix G Figure G.5. Examples of severely damaged blades (excluded from study). stall). Common damage seen on all blades consists of small impact sites mostly smaller than 1 mm diameter. The density and severity of these impact sites increases noticeably from root to tip, which corresponds to the USAF study [3], Figure G.3. Figure G.10 is an example of pressure surface FOD damage. The leading edge is to the right and hence the object would be traveling from right to left and has impacted at an acute angle. It appears that the impact has completely stopped the progress of the particle, although glancing impact craters are also frequently found. Figure G.11 shows FOD sites observed on a set of fan blades from a Tornado RB199 engine that had experienced major surge due to the FOD. The whole set of blades in the fan each displayed severe damage to the leading edge corner and several have tears and notches further down the blades. FOD geometry distributions In order to determine a typical FOD geometry measurements of depth and root radius were made from photographic enlargements (4X to 10X). The distribution of measured FOD depths is shown in Figure G.12. These data are shown along with a larger data set Appendix G 563 Figure G.6. 0.059 in. dent with no cracking in leading edge of 2nd stage fan blade. Figure G.7. 0.028 in. tear in 2nd stage fan blade. 564 Appendix G Figure G.8. Two notches in leading edge of 2nd stage fan blade. The smaller notch is 0.015 in. deep while the second is 0.059 in. deep. Microscopic examination of the deformation ridge indicates that impact occurred at an oblique angle. Figure G.9. 0.090 in. deep notch in leading edge of 2nd stage blade. Again microscopic examination of the deformation ridge provides clues about the impact angle. Appendix G 565 Figure G.10. FOD impact site on Pegasus fan blade. previously obtained by Pratt and Whitney and the USAF in an extensive field survey of FOD damage [4]. All data in Figure G.12 are from 1st, 2nd, and 3rd stage fan blades of the same engine. As can be seen in Figure G.12 the two distributions are of very similar form, resembling either typical log normal or Weibull probability density functions. These results indicate that the sample population of this small study is representative of the FOD likely to be found in service for low-bypass engine fan blades. It is important to recognize that FOD depth distributions are fundamentally different from crack size distributions used in classical damage tolerance analyses. The difference is due to the fact that cracks progress in a slow stable fashion throughout the life of the component, whereas FOD of any given depth can be introduced at any time in the component life, regardless of when the last inspection occurred. Thus, in developing an improved HCF design methodology, it appears that FOD depths beyond the blend limits also need to be evaluated to ensure that a blade will survive in operation until the next inspection. The distribution of measured FOD root radii is shown in Figure G.13. As can be seen, this distribution is relatively uniform in comparison to the FOD depth distribu- tion in Figure G.12. This difference in distribution shape indicates that there is minimal correlation between notch depth and root radius. An overall index of the severity of the FOD can be obtained by combining the measured FOD root radii of Figure G.13 with the FOD depths of Figure G.12 to determine the distribution of elastic stress . distribution. A normal load of 12 × 10 6 N/m was applied to a pad geometry of 51 mm radius pad as well as a 3-mm flat and edge radius pad for increasing thickness. The peak pressure was obtained for each. material and (b) a larger loss of materials. the laboratory is only magnified in service, where the FOD impactor can be sand, rocks, pieces of a carrier deck, etc., and can strike the blade at a. Butterworth-Heinemann, Oxford, 1993. 12. Rajeev, P. and Farris, T., “Numerical Analysis of Fretting Contacts of Dissimilar Isotropic and Anisotropic Materials , J. Strain Analysis, 37(6), 2002,