16 Introduction and Background as a knowledge of the vibratory loading, is a viable and reliable method for designing for pure HCF. The failures encountered also indicate that the problem is typically not one of long-life degradation or a high number of accumulated cycles, but rather one of shorter life including infant mortality and conditions which were not anticipated in design or detected in developmental engine testing. The problem appears to be the synergistic combination of HCF with other modes of initial or service-induced damage, something that is not addressed in a Goodman diagram. As noted earlier, the HCF problem in turbine engines provides an example of how HCF capability can be degraded by service usage which also has to be considered in a robust design process. Although the examples cited in this book come largely from experience with turbine engines, the problem and approaches are felt to be quite generic and applicable to other applications where HCF is a design consideration. A final aspect of HCF design has to be related to the statistical distribution of fatigue strengths. There are a number of scenarios surrounding field failures where analysis indicates that failures should not have taken place under the assumed circumstances. On the one hand, the circumstances may not have been properly categorized and vibratory loading, for example, may have been greater than that determined from detailed analysis or actual component or engine testing. On the other hand, the fatigue strength could be shown to be adequate to prevent failure. Under both circumstances, there is little known about the tail end of the distribution function that describes either the applied loading or the material capability. In an attempt to shed some light on this subject, specifically in regard to material capability, some aspects of the statistics of fatigue limit strength are presented in Chapter 3. 1.6. DAMAGE TOLERANCE Before discussing damage tolerance, the distinction between durability and damage tol- erance should be established. From the original version of ENSIP [5], the following definitions are established. Section 3.1.3 defines damage tolerance as “the ability of the engine to resist failure due to the presence of flaws, cracks or other damage for a spec- ified period of unrepaired usage.” Section 3.1.7 defines durability as “the ability of the engine to resist cracking (including vibration, corrosion and hydrogen induced crack- ing), corrosion, deterioration, thermal degradation, delamination, wear and the effects of foreign and domestic object damage for a specified period of time.” It is Noteworthy that damage tolerance is applied to critical structural components whose failure would cause major damage or total failure. Durability, on the other hand, eliminates the task of excessive and unscheduled maintenance involving part replacement or added inspections. The remainder of this section is concerned with the concept of damage tolerance and its potential application to HCF. Introduction 17 While damage tolerance as applied to LCF has a limited role in HCF, the concepts and philosophical aspects are important to grasp in understanding how HCF problems can be addressed. Damage tolerance is a design philosophy that was adapted by the US Air Force for both airframe structures in the 1970s and for turbine engines in the 1980s. It evolved from experience with field failures attributable to either initial or service-induced damage or flaws that were not accounted for initial design. It involves the assumption of the existence of initial defects (flaws) in critical structural components combined with inspection methods to assure flaws of a size larger than those assumed do not exist when the structure enters service. For a comprehensive discussion of all of the aspects of damage tolerance as well as the associated nondestructive evaluation techniques, the reader is referred to the book by Grandt [7]. It is the intent of this section only to provide an overview of some of the concepts involved in damage tolerant design and how they relate to problems in HCF. The Air Force defines damage tolerance in engines in the latest version of ENSIP [4] in the same manner as in the original version [5] as cited above, namely “the ability of the engine to resist failure due to the presence of flaws, cracks, or other damage. ” Among the other guidance provided in ENSIP, the scope of the applicability of damage tolerance is established as: Damage tolerance requirements should not, in general, be applied to components in which structural cracking will result in a maintenance burden but not cause inability to sustain flight or complete the mission; i.e., durability-critical parts. However, damage tolerance require- ments should be applied to durability-critical parts to: (1) identify components sensitive to manufacturing variables and pre-damage which could cause noneconomical maintenance (e.g., blades), or (2) aid in the establishment of economic repair time or other maintenance actions. Damage tolerance is the only one method used in design to assure structural integrity. Other methods include safe-life design or fail-safe design (see [7], for example). One of the reasons that damage tolerance is not used universally for critical structural components is the maintenance burden and associated cost for the required inspections. Nonetheless, the requirement by the US Air Force provides details on how to achieve a damage tolerant design. In ENSIP [4] it states Damage tolerance will be achieved by proper material selection and control, control of stress levels, use of fracture-resistant design concepts, manufacturing and processing con- trols, and the use of reliable inspection methods. The design objective will be to qualify components as in-service noninspectable to eliminate the need for depot inspections prior to achievement of one design lifetime. As a minimum, components will be qualified as depot- or base-level inspectable structure for the minimum interval. Damage tolerance can be achieved by performing crack growth evaluation as an integral part of detail design of fracture-critical engine components. Initial flaws (sharp cracks) should be assumed in highly-stressed locations such as edges, fillets, holes, and blade slots. Imbedded defects 18 Introduction and Background (sharp cracks) should also be assumed at large volume locations such as live rim and bore. Growth of these assumed initial flaws as a function of imposed stress cycles should be calculated. Total growth period from initial flaw size to component failure (i.e., the safety limit) is thus derived. Trade studies on: (1) inspection methods and assumed initial flaw size, (2) stress levels, (3) material choice, and (4) structural geometry can be made until the safety limit is sufficiently large such that the need for in-service inspection is eliminated or minimized. Damage tolerance design procedures which account for distribution of variables that affect growth of imbedded defects are permitted (e.g., probability of imbedded defects associated with the specific material and manufacturing processes). Specific requirements on initial flaw sizes, residual strength, critical stress intensities, inspection intervals, damage growth limits, and verification are contained elsewhere in this document. Damage tolerance requirements may be applied to durability-critical parts to: (1) identify components sensitive to manufacturing variables and pre-damage which could cause non-economical maintenance (e.g., blades), or (2) aid in the establishment of economic repair time or other maintenance actions. The concepts embodied within a damage tolerant approach to structural integrity can be illustrated with the aid of several figures. In Figure 1.2, the traditional design approach to LCF is illustrated schematically and shows that fatigue life, being a statistical variable in life for a given stress level, has to be treated with enough of a factor of safety (or uncertainty) to account for a worst case scenario in terms of material capability. The shape of the S–N curves depicted in Figure 1.2 has no physical meaning and is used merely to illustrate the concept of having both an average and a design curve. Since these curves are different, the resultant design allowables can then severely underestimate the average behavior of the material. Because of the conservative nature of this design Applied Stress Number of Cycles to Crack Initiation Average Design Allowable Distribution Of Lives Figure 1.2. Schematic of S–N curve with illustration of scatter. Introduction 19 approach, the US Air Force implemented a program called “Retirement for Cause (RFC)” on some of their engines that had not been designed using damage tolerance procedures. RFC was actually an early application of damage tolerance to an existing design. The RFC approach allowed the Air Force to keep in service components that had reached their design life (see Figure 1.2) but had not developed any signs of fatigue cracking. Since only a small fraction of components would be expected to show signs of failure at the design lifetime because of the conservatism in the design, inspection procedures coupled with crack growth analyses based on fracture mechanics were implemented on the remaining components. The procedure is shown schematically in Figure 1.3, which incorporates the fundamental philosophy of damage tolerant design. If the inspection capability to reliably detect a flaw of a given size is available, then all inspected parts will have flaws no larger than those shown as “inspection capability” in the figure. The worst case, shown as curve “A,” would then have the crack growth behavior shown and would fail after two inspection intervals if the interval was chosen as half of the predicted crack growth life as shown. The interval could be chosen as one-third to be more conservative. For the worst case, A, the crack would be found at the first inspection and the part removed from service. All remaining parts where no crack was found could be kept in service for another inspection interval and the new worst case component would follow curve “C” as shown. The procedure could be repeated for curve “D” as many times as practical. Note that as the life increases, the probability of a crack developing increases as the average life is approached (see Figure 1.2). Note also that an average part, denoted by curve “B,” would be retired when a crack above the inspection limit was detected and that, in the example Crack Length Number of Cycles Inspection limit Critical crack size Inspection interval A B C D Figure 1.3. Schematic of crack growth in damage tolerant design. 20 Introduction and Background cited, there would be two inspections available to find the crack if it was missed at the first inspection. ∗ The applicability of damage tolerance to HCF, discussed in Chapter 8, is severely limited because of the rapid growth of cracks under HCF where large numbers of cycles can be accumulated in a short period of time. This would require unacceptably short inspection periods, some of which could be shorter than a single mission. Another aspect of damage tolerance applied to HCF is illustrated in Figure 1.4 where, as an example, a single event such as FOD can cause a level of damage that is severe compared to an inspection level and can occur at any time. It is the possibility of such damage occurring and the concurrent rapid rate of crack growth under HCF that precludes the applicability of damage tolerance to HCF in many cases as discussed below. 1.6.1. Application to HCF A damage tolerant design approach for HCF must take into account both potential initial (manufacturing) and service-induced damage in order to be successful. Further, the margin of safety must be determined for any operating condition in order to know how close to the “edge of the cliff” one is operating. The types of damage that must be addressed, if relevant, include fretting, galling, FOD, combined LCF–HCF, corrosion pitting, thermomechanical fatigue, creep, and their combinations. It is of interest to note the limited scope of requirements, especially details, for HCF that were contained within the original ENSIP [5], the document which governs the design and development of US D N Design life Actual life Critical damage state Remove from service or inspect LCF FOD Figure 1.4. Schematic of damage accumulation applicable to HCF. ∗ Figures 1.2 and 1.3, and many variations thereof, were used numerous times as an illustration of how a damage tolerant approach could save costs in not having to replace engine components when they reached their design lifetimes. These schematic plots were created and used by Dr Walter Reimann of the Air Force Materials Laboratory many times to champion the Retirement for Cause (RFC) program that was eventually adopted by the US Air Force and produced cost savings approaching a billion dollars. Introduction 21 Air Force engines. The following sections are extracted from that original version of ENSIP and deal specifically with, or are applicable to, HCF: Section 4.6.2 defines initial flaw size: “Initial flaws shall be assumed to exist as a result of material, manufacturing and processing operations. Assumed initial flaw sizes shall be based on the intrinsic material defect distribution, manufacturing process and the NDI methods to be used during manufacture of the component.” Section 4.7.4 addresses HCF design requirements: “Engine components shall be capable of withstanding combined steady and high cycle fatigue stresses, including vibratory stresses that occur at sustained power conditions, for the required design service life.” Section 5.7.4 requires: “The HCF life of engine components shall be evaluated by analysis and measurement of vibratory stresses during the engine tests. ” Appendix Section 5.6b “Certain levels of vibratory stress, e.g., 10 ksi, should be assumed to exist on each fracture critical part to identify sensitive components.” Appendix Section 4.7.4 “it is recommended that vibratory or high cycle stress be restricted to a value of 40% of that allowed by the minimum value material property allowable due to the sensitivity of high cycle stresses to damping variabil- ity, part to part resonance variation, unknown excitations, etc. An alternative design approach to achieve margin is to limit the steady stress such that a significant level of vibratory stress (e.g., 30 ksi peak-peak) will not exceed the minimum value material allowable.” It is important to recognize that ENSIP was written and implemented at a time when LCF failures were the major concern of the US Air Force. While ENSIP was establishing a damage tolerant approach to LCF, it was also recognized that HCF is another problem of great concern, but no approach as detailed as that developed for LCF was suggested for addressing HCF design at that time. It is of interest, therefore, to examine a more recent approach to HCF through the use of a Goodman diagram in the light of the requirements and intent specified in the ENSIP document. ∗ The approach to HCF in a more recent version of ENSIP is documented in Appendix B. It can be seen from the above requirements and specifications that HCF design does not address some of the aspects of field service–induced damage and does not present any methodology for doing so. The requirements, like a 40% allowable of ∗ Subsequent to the original ENSIP document in 1984 [5], several revisions have taken place. Many of these revisions deal with HCF and are the result of the Air Force National Turbine Engine High Cycle Fatigue program. Appendix C presents some of the sections that were revised or added to deal specifically with HCF issues. 22 Introduction and Background the Goodman vibratory stress or an absolute limit on allowable alternating stress, are based on experience and may have little applicability to newer designs, materials, or operating conditions. In particular, one can note that the guidelines proposed in the original ENSIP become less conservative at higher mean stresses because the frac- tional approach is based on lower vibratory stress allowables at high mean stress (see Chapter 2) or an absolute vibratory level which eventually intersects the Goodman allow- able if mean stress is allowed to increase. What is not specified or accounted for in design is any in-service damage including that caused by loading such as LCF. Most components that are subjected to HCF are not designed based on HCF considerations alone. In general, they are checked for tolerance to HCF, or an allowable vibratory stress level is specified. What governs the design, for example LCF, is addressed sep- arately and then the HCF resistance is evaluated by itself. There does not appear to be any systematic approach to designing for the combination of HCF and another dam- age mechanism. If interactions occur, the synergism might cause failure even though failure is not predicted by any one mode individually. This is particularly true for combined LCF–HCF loading which is discussed below and in Chapter 4 in greater detail. One of the key parameters which must be considered in damage tolerant design for HCF is mean stress. Mean stress, resulting primarily from the rotational speed of an engine in the form of centrifugal loading, has a very significant influence on the fatigue limit of a material. For example, Greenfield and Suhr [8] show data for a low alloy steel which has a tensile strength of 840 MPa and a yield strength of 700 MPa. For this material, which exhibits a true run-out stress, the increase in mean stress from zero up to 775 MPa reduces the fatigue strength by greater than a factor of four. They observe that, for design purposes, “a reduction in the level of mean stress may be regarded as almost as important as a reduction in the level of fatigue stress in reducing the risks of failure by fatigue.” Similarly, in fracture mechanics, the threshold stress intensity, which is the value below which cracks will not propagate at a very low chosen value of growth rate (10 −10 m/cycle in some standards), is a decreasing function of stress ratio or mean stress. Under combined LCF–HCF loading, for example, it has been shown that the threshold at which HCF influences the growth rate under LCF, denoted by K onset , is not a material constant, but rather it is a function of stress ratio, R [9]. In one specific example, the value of K onset was found to decrease by over a factor of two in Ti-6Al-4V when R increases from 0.1 to 0.7 whereas it remains nearly constant for R>07 [9] (HCF crack growth thresholds are discussed in Chapter 8). From the preceding, it appears that a margin of safety which is either a fixed fraction of the allowable alternating or vibratory stress or a fixed value of vibratory stress, independent of mean stress, becomes smaller as mean stresses become higher. This is true whether a total life criterion, such as the Goodman diagram, or a damage tolerant approach based on an initial flaw size is being used. Given this observation, in an Air Force review of root causes of HCF failures, Introduction 23 it was not surprising to find that designers from the major engine companies identified components with high mean stresses to be the most likely candidates for potential HCF problems. 1.7. CURRENT STATUS The Goodman diagram is still considered to be an acceptable design tool for HCF provided it is applied correctly. Two aspects which may not yet be handled adequately are the presence of initial damage and the accumulation of service-induced damage. Initial damage, such as rogue flaws or inclusions, for example, would have to be found in laboratory or component testing and taken into account in establishment of the minimum design allowables. An alternate approach would be to characterize initial damage in terms of an expected statistical distribution of defects, a process now employed for internal defects in LCF design. One could question how many organizations or laboratories use data from a specimen or component which was clearly defective as part of their database, even though the defect is discovered only after performing the test! It is this situation, where defects appear only occasionally, that has led the USAF to adapt the damage tolerant approach to engine structures because defects are not always found in baseline testing for LCF. Good statistics on the presence of defects from specimen testing would require an inordinate number of tests. Thus, the assumption of the presence of initial damage is a logical approach to avoid potential failure due to the occasional defect. ∗ A similar approach based on damage tolerant concepts could also be warranted for HCF. The second aspect, service-induced damage, is not addressed in a Goodman diagram. Illustrative calculations for combined LCF–HCF clearly indicate that service life and safe design space under pure HCF is affected by the superimposed presence of LCF loading, and a potential methodology for considering this damage is presented in Chapter 4. It remains to be seen if a similar approach can be developed for constructing a damage tolerant Goodman diagram for other types of field-induced damage such as fretting, FOD, corrosion pitting, and others. Certainly this would appear to be a more rational approach than limiting allowable vibratory stresses to some percentage of the Goodman diagram or ∗ It should be noted that in LCF design, the assumption of initial flaws in a damage tolerant design did not add weight to components. In the latest version of ENSIP [4], referring to historical experience with engines designed using damage tolerance, it states: “These design configurations have shown that damage tolerance requirements can be met with small or modest increases in overall engine weight, will have little impact on engine performance, and will provide greatly-improved engine durability while weapon system life cycle cost is significantly reduced.” In pure LCF design assuming no initial flaws, the use of design allowables based on extensive testing which provides data representing the lower bound on a distribution curve, similar lives are predicted. In other words, the lower bound on the LCF database reflects the existence of the same type of flaws that are assumed in damage tolerant design. It was cases where the occasional flaws or defects were not discovered in specimen testing that led to problems when such flaws appeared in component hardware. 24 Introduction and Background some absolute magnitude. For both cases where the Goodman diagram does not handle design adequately, the requirement in the 1984 ENSIP document [5] defining initial flaw size should be noted again. Section 4.6.2 of that document states that initial flaw size can be based on inherent material defect distribution. This indicates that perhaps inspection for initial or in-service damage may not be necessary but, rather, calculations or statistical data on damage accumulation could be substituted in an HCF design life methodology. In these summary observations, it should be noted that a Goodman diagram is a total life diagram even though most of the life under HCF is attributed to the initiation phase. Initiation, or nucleation, in fatigue is defined in various manners in the technical literature. One of the more common engineering definitions is the time (number of cycles) it takes for a crack to form and grow to a detectable or observable size. Dependent upon the inspection capability, this crack size can become large and initiation can then become a dominant portion of the entire fatigue life. The second part of total life is the crack propagation portion which can be determined using fracture mechanics principles (which are not addressed to any significant extent in this book). If crack initiation is defined as the formation of a crack-like defect at the microstructural level, then crack-propagation life can become a larger fraction of total life. This latter interpretation of crack initiation is more commonly referred to a crack nucleation. In this book, we lean more toward an engineering definition for initiation and find, in general, that very long-life fatigue tests have a minimal fraction of their lives associated with crack propagation. For this reason, the Goodman diagram is often used interchangeably as a total or infinite life criterion as well as an initiation criterion. The fraction of life that is initiation to a specific crack size, however, may differ with change in mean stress. Crack propagation life from the defined initiation crack size to failure would have to be subtracted from total life to come up with a true initiation diagram. The addition of fracture mechanics principles to the construction and use of Goodman diagrams, discussed in Chapter 8, would help separate the initiation and propagation stages in the plot and provide a better indication of the inherent damage tolerance of the material to HCF. This is shown clearly in the calculations for HCF loading only where there are regions where a crack will not grow if initiated (damage tolerant) and other regions where the crack will grow at stresses below those needed for initiation (damage intolerant). It is possible that a true initiation diagram combined with a superimposed fracture mechanics–based plot will give better insight into the stress states where such behavior can be expected. Analyses, such as that by Barenblatt [10] which deals with crack propagation within the grain and between grains in a material, can then be interpreted better from a design point of view when they demonstrate the potential for cracks to initiate but subsequently either slow down or arrest, a phenomenon commonly associated with small crack behavior [11, 12]. It is possible, for example, that the propensity for this phenomenon to occur may be constrained to certain combinations of mean and alternating stresses, based on the information contained in a combination of a Goodman diagram and fracture mechanics–based analysis. Introduction 25 From the analysis of the conditions under which initiation and propagation under HCF, LCF, or combined HCF/LCF can occur, it appears that a very important design consideration for any component is a realistic estimate of the number of LCF as well as HCF cycles to which it will be subjected in service. This could result in drastic changes in the allowable design space, for example, if the component is potentially subjected to some type of steady state or resonant vibratory loading as opposed to transient vibratory conditions which may only produce a limited number of HCF cycles per mission or per LCF cycle. Any component designed for anything other than HCF alone will generally undergo some degree of damage from that design consideration (e.g., LCF, TMF, creep). Even though the condition on which design is based will not cause component failure during the design life, some degree of subcritical damage or degradation may occur and that, in turn, can result in less resistance to HCF. Thus, the Goodman diagram may not be a valid indicator of HCF resistance if these other damage modes exist. Further, the HCF resistance will decay with life and this decay should be taken into account by combining the effects of HCF with any other mechanism which is the basis for design. The use of a damage tolerant Goodman diagram, therefore, is recommended. 1.8. FIELD EXPERIENCE In HCF, as in other modes of failure, field experience tends to improve our knowledge base. “Lessons learned” are often the basis of new approaches, and many of these are documented in guide specifications such as ENSIP. On the other hand, I have had experience in several investigations where closure cannot be reached on the root cause or exact scenario under which an HCF failure occurred. We still have much to learn about HCF material behavior and design. ∗ I can recall many meetings where, as a group of technical experts, we went through a systematic analysis of the conditions leading to an HCF failure and can prove, through existing data, knowledge, and analysis, that a failure could not have occurred. Only the failed parts in our hands were able to convince us of our inability to completely describe the event accurately. Eventually, we arrive at an unlikely ∗ In a recent revision, dated 22 September 2004, to ENSIP [4], under VERIFICATION LESSONS LEARNED (A.5.13.3.2), the following appears: “The most significant lessons learned for this requirement is that, for almost every field failure experienced by the USAF over the last decade, the test data showed the failure should not have occurred. This experience conclusively demonstrates that a deterministic approach to verification of HCF capability cannot succeed. One statistical study by a major engine manufacturer estimated that a deterministic process (analysis and testing) could at best discover less than forty percent of the HCF failures that would occur over the life of the program.” The document goes on to recommend that a new approach must recognize “the stochastic nature of the material strength, the component behavior and the operational usage.” The statistical aspect of HCF design is discussed briefly in Chapter 8. . LCF FOD Figure 1 .4. Schematic of damage accumulation applicable to HCF. ∗ Figures 1.2 and 1.3, and many variations thereof, were used numerous times as an illustration of how a damage tolerant approach could. minimum interval. Damage tolerance can be achieved by performing crack growth evaluation as an integral part of detail design of fracture-critical engine components. Initial flaws (sharp cracks) should. aspect of damage tolerance applied to HCF is illustrated in Figure 1 .4 where, as an example, a single event such as FOD can cause a level of damage that is severe compared to an inspection level and