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A modified constant-life Haigh diagram has been formulated to account for plasticity occurring at stress concentrations under cyclic loading at sufficiently high stress ratios. The notch plasticity is assumed to occur within a range of elastic stress concentration factors, kt, and cycles to failure, Nf, such that plastic straining occurs only during the first cycle of constant-amplitude cycling and straining remains elastic thereafter. This condition is expected to occur in high cycle fatigue at stress concentrations of moderate kt loaded at high stress ratio. The validity of the model is assessed by means of fatigue data from Ti–6Al–4V notched specimens having a range of kt. The model, purposely kept simple for ease of use as a design tool, is found to capture trends in the fatigue data not predicted using traditional straight-line models on a mean stress versus alternating stress constant-life plot.

A new approach, which uses the Findley critical plane damage parameter along with the stress gradient at the notch, was developed for predicting notched HCF life. The proposed approach and methodology for HCF notch analysis accounts for: (i) the multiaxial stress state at the notch, (ii) the notch size effect, and (iii) the effect of fatigue stress ratio. Two fatigue failure criteria based on the critical distance method were used to define a notch gradient parameter, GF. It was shown that GF is invariant with notch geometry and fatigue stress ratio. This invariance of GF was used to successfully and consistently analyze and predict notched HCF life of the titanium alloy Ti–6Al–4V for: (i) different notch geometries, and (ii) different fatigue stress ratios. For a notch under a general 2-dimensional stress state subjected to constant amplitude fatigue loading, the current approach can be performed in closed-form. Closed-form equations were developed for the fatigue notch factor Kf, and the Findley gradient factor, GF, as a function of the critical distance, ac, the notch radius, ρ, the stress concentration factor Kt, and the stress ratio, R. The proposed approach can be applied equally well using either finite element analysis or the closed-form analysis. A relationship was also established between GF and the notch sensitivity of a material. A new Findley notch sensitivity parameter, QF, given by (2-GF) was proposed as a convenient and a more robust measure of the notch sensitivity than the classical notch sensitivity parameter, q, which can vary with the applied fatigue stress ratio.

A new vibration-based fatigue testing methodology for assessing high-cycle turbine engine material fatigue strength at various stress ratios is presented. The idea is to accumulate fatigue energy on a base-excited plate specimen at high frequency resonant modes and to complete a fatigue test in a much more efficient way at very low cost. The methodology consists of (1) a geometrical design procedure, incorporating a finite-element model to characterize the shape of the specimen for ensuring the required stress state/pattern; (2) a vibration feedback empirical procedure for achieving the high-cycle fatigue experiments with variable-amplitude loading; and finally (3) a pre-strain procedure for achieving various uniaxial stress ratios. The performance of the methodology is demonstrated with experimental results for mild steel, 6061-T6 aluminum, and Ti-6Al-4V plate specimens subjected to a fully reversed bending, uniaxial stress state.

Fretting fatigue, or contact fatigue, is defined as damage resulting from small magnitude (0.5–50 microns) displacement between contacting bodies where at least one of the bodies has an applied bulk stress. Of particular importance at the present time is the occurrence of contact fatigue in the blade to disk attachments in aero-engines. Appraisal of the various fretting fatigue life prediction methods currently available suggests that those based on computation of “stress at a point” or a function of stress at a point are not always sufficiently accurate. Further, stresses averaged over a critical volume have problems associated with that approach. Thus, the applicability and limits of a fracture mechanics-based life prediction methodology are explored in the present paper. Results from this modeling approach are compared to experimentally determined fretting fatigue life on various contact geometries, including sphere/flat, cylinder/flat, flat-on-flat and the more realistic dovetail configuration relating to blade-disk attachments.

A novel testing methodology has been developed to determine the fatigue limit strength of structural materials at high frequencies. The procedure involves the use of a base-excited plate specimen driven into a high frequency resonant mode which allows completion of a fatigue test in a few hours. The use of a step-testing method allows determination of the fatigue limit strength of the material corresponding to a very large number of cycles, 10 6 or 10 7 in this case. The methodology consists of a topological design procedure, incorporating a finite element model, to produce the shape of the specimen necessary to achieve the required stress state/pattern, and a forced vibration-based fatigue procedure for conducting the high cycle fatigue experiments with variable-amplitude loading. The successful application of the methodology is demonstrated by the experimental results from steel, 6061-T6 aluminum, and Ti-6Al-4V plate specimens subjected to fully reversed uniaxial and biaxial bending stress states. Results are compared with existing data produced using traditional fatigue test machines.

A fracture mechanics methodology was evaluated for a fretting fatigue geometry in which one end of a specimen clamped between fretting pads was loaded in axial fatigue. In previous work, results from experiments on Ti–6Al–4V pads and specimens were evaluated using finite element analyses where stress intensity factors were calculated assuming a single-edge tension, Mode I crack to form. In the present work, mixed-mode behavior was considered and a more realistic crack geometry was incorporated. KI and KII were calculated from stress fields determined from the finite element analysis using a weight function method and assuming a single-edge Mode I/Mode II inclined crack. A correction was then applied based on empirical crack aspect ratio data. KI and KII were analyzed for several experimentally determined combinations of contact pad geometry, specimen thickness, and loading conditions used to obtain a range of normal and shear forces, each corresponding to a fatigue life of 107 cycles. The fracture mechanics methodology was used to determine the conditions for propagation or non-propagation of cracks that initiate in the edge of contact region based on a mixed-mode driving force and a short crack corrected threshold. The coefficient of friction was also varied in the analyses. The fracture mechanics approach appears to be a better method for determining the threshold for fretting fatigue than a stress analysis because thresholds for K are better known than criteria for crack initiation in a gradient stress field.

Fretting fatigue damage can reduce the service life of engineering components in contact. The attachment between blades and disks in the fan and compressor stages of gas turbine engines is often a dovetail geometry. As a result, normal and tangential cyclic contact loads are present. Results of fretting fatigue tests using a new dovetail fixture are detailed here. Dovetail specimens and three types of contact pads were all machined out of Ti−6A1−4V. Two types of palliatives are also examined: aluminum bronze coatings and low-plasticity burnishing. While the palliatives were effective in increasing the fatigue life, the three pad geometries produced essentially the same fatigue life.

The ingestion of debris into jet engines creates nicks and dents on the leading edges of blades and vanes. This is commonly known as foreign object damage (FOD). Such damage, which can often result in premature failure, was simulated in the laboratory using diamond cross-section axial fatigue samples that were impacted with 1 mm diameter glass beads at 305 m s −1 at either 0 or 30° angle of incidence. The samples had either a thin leading edge (LE) with a radius of 0.127 mm or a thick LE with a radius of 0.381 mm. Fatigue strength of impacted specimens showed degradation of 10–50% due to LE damage, regardless of the depth of the damage zone. FOD related impact notch depth, loss of material (LOM), shear, folds, embedded shattered glass, and microstructural damage were characterized by SEM. Fatigue strength degradation was found to be higher for the 30° impacts than for the 0° impacts. No clear correlation between notch depth or LE thickness and fatigue strength was found.

This study investigated the high cycle fatigue (HCF) behavior of a titanium alloy, Ti–6Al–4V, after being subjected to simulated foreign object damage (FOD). For this purpose, rectangular specimens were damaged to various depths by steel indenters of different diameters under quasi-static loading to simulate damage found in turbine engine airfoils during service. The fatigue strength of these specimens for 10 7 cycles was measured. Finite element analysis was used to compute the deformation and stress state created by the simulated FOD and to explain the relationship between damage and fatigue strength. The examination of damage mechanisms on the fracture surface near FOD showed a region of either macro bands (in the X-shape) of intense plasticity (i.e. intensely deformed material) having strain levels of 15–20%, shear bands, or shear stress-induced cracks depending upon the indentation depth and indenter diameter. The depth from the specimen edge up to the center of these X-shaped macro bands on the fracture surface had a simple empirical relationship with the reduction in fatigue strength. The residual stresses, introduced from the FOD, caused the effective stress ratio or mean stress in the vicinity of FOD to be different than that applied to the specimen. These modified stress states provided the explanation for reduction in the fatigue strength of the material with FOD.

The role of residual stresses in the high cycle fatigue (HCF) strength of Ti–6Al–4V subjected to foreign object damage (FOD) was evaluated on simulated airfoil and rectangular geometries. Both real and simulated impacts were conducted using spherical projectiles launched at 300 m/s and quasi-static chisel indentation, respectively. The spheres used were 1 mm diameter glass beads while the quasi-static indentor had a radius of 1 mm. The airfoil specimens had leading edge (LE) radii of either 0.13 or 0.38 mm and were indented at 30° to the airfoil LE. The rectangular plates were 1.25 mm thick and were indented quasi-statically at 0°. All specimens subjected to FOD were subsequently tested in uniaxial HCF at a frequency of 350 Hz using a step loading procedure to determine the fatigue limit corresponding to 107 cycles. Before the HCF testing, half of the specimens were stress relief annealed to remove residual stresses. Results indicate that stress relief generally improves the fatigue limit stress, indicating that tensile residual stresses are present after both quasi-static or dynamic indentation. For the dynamic impacts, the craters formed have less influence on the fatigue strengths than that predicted from conventional notch fatigue analysis.

High cycle fatigue (HCF) failures in materials used in rotating components of gas turbine engines have often been found to be attributable to fatigue loading on materials which have sustained damage from other sources. Damage can be present in the form of initial material or manufacturing defects, or can develop during service operation. Three major sources of in-service damage have been identified which can alter the HCF resistance individually or in conjunction with one another: low cycle fatigue (LCF), foreign object damage (FOD), and fretting. Methodologies for treating such damage in establishing material allowables are considered. Some recent results on the effects of damage on the Haigh (Goodman) diagram and a discussion of the life management aspects of HCF are presented.

Step testing provides a method for generating an endurance stress for a particular stress ratio with a single specimen as well as a method of generating endurance limits for one-of-a-kind specimens, e.g. specimens that may have been subjected to pre-test damage that cannot be accurately reproduced. The objective of this paper was to determine the statistical validity of the step test method for specimens excised from Ti–6Al–4V forgings. Room temperature endurance limits and constant-life Haigh (modified-Goodman) diagrams for smooth Ti–6Al–4V specimens generated by both the step method and conventional method (using S–N curves) are analyzed and statistically compared. Using lognormal-based statistical methods, the endurance stress at prescribed reliability limits and a confidence level (50%) is determined for the 10 7 cycle life. It appears that step testing yields results that are within the statistical limits of conventional S–N curve results and therefore is a valid method for generating endurance limits and therefore Haigh diagrams for Ti–6Al–4V specimens. Some questions are raised regarding the validity of the step method when a large number of steps are used.

Fatigue crack growth thresholds for Ti-alloy IMI 834 were determined at Kmax values equal to 6, 10 and 25 MPa m , using two different load patterns, both including an abrupt change in ΔK. Increasing ΔK applied to the initially dormant crack resulted in higher fatigue crack growth thresholds as compared to the situation when an initially growing crack was arrested by decreasing ΔK values. The discrepancy can be attributed to the crack tip shielding associated with residual stresses in front of the crack rather than with fracture surface contact behind the crack tip. Practical merits of the two experimental techniques are discussed.

An investigation has been conducted to evaluate the effects of cyclic frequency and hold times on crack growth in a representative α 2 titanium aluminide, Ti24Al11Nb at 49 °C. Fatigue crack propagation experiments conducted over a wide range of frequencies from 0.01 to 100 Hz indicate a strong dependence of d a /d N upon cyclic loading frequency Superposition of hold time at maximum load has a deceleration effect of the growth rate per cycle whereas superposition of a hold time at minimum load results in a higher crack growth rate which is attributed to enhanced environmental degradation. It is postulated that the hold time at maximum load results in an interaction of the environmental effect with a retardation effect due to the crack tip blunting as a consequence of creep under maximum applied load. The frequency and hold time behavior is rationalized in terms of a complex interaction between fatigue, blunting owing to creep and environmental degradation through a simple model which considers the interaction effects.

Sustained load crack growth in IN100 at 732°C (1350°F) is studied using two specimen geometries, a standard compact tension specimen, and a radially crack ring loaded in tension. The effects of specimen thickness on the growth rate are investigated covering a range from 5.6 mm to 18.3 mm (0.22 to 0.72 in.) in thickness. Only the thinnest specimens show a crack growth rate which is lower than that obtained from all of the other thickness specimens. Stress-intensity factor, net section stress, and the C*-integral were investigated as possible crack growth rate correlating parameters. The concept of an "effective" crack length determined from specimen compliance measurements is introduced as a measure of crack length for severely tunneled crack front geometries. Neither net section stress nor C* is found to be acceptable as a crack growth parameter based on data from both test geometries. Although K provides fair correlation, the phenomenology of creep crack growth prevents its description adequately with only a single parameter. In particular, the crack growth rate is observed to decrease from an initially higher value to a "steady state" rate for constant values for any of the correlating parameters investigated.

Effects of temperature, frequency, and cycles with superimposed hold times are evaluated in Ti-1100 in order to study the complex creep-fatigue-environment interactions in this material. Crack growth rate tests conducted at cyclic loading frequency of 1.0 Hz show that raising the temperature from 593 to 650 C has only a slightly detrimental effect on crack growth rate, although these temperatures produce growth rates significantly higher than at room temperature. From constant {Delta}K tests, the effects of temperature at constant frequency show a minimum crack growth rate at 250 C. From the minimum crack growth rate at 250 C, the crack growth rate increases linearly with temperature. Increases in frequency at constant temperatures of 593 and 650 C produce a continuous decrease in growth rate in going from 0.001 to 1.0 Hz, although the behavior is primarily cycle dependent in this region. Tests at 1.0 Hz with superimposed hold times from 1 to 1,000 s are used to evaluate creep-fatigue-environment interactions. Hold times at maximum load are found to initially decrease and then increase the cyclic crack growth rate with increasing duration. This is attributed to crack-tip blunting during short hold times and environmental degradation at long hold times. Hold timesmore » at minimum load show no change in growth rates, indicating that there is no net environmental degradation to the bulk material beyond that experienced during the baseline 1 Hz cycling.« less

Experimental crack growth rates were determined in Inconel 718 middle cracked tension [M(T)] specimens at 649°C under conditons of high frequency (10 to 100 Hz) and high load ratio, R. Under these conditions, the materialexperiences cycle-dependent crack growth as well as time-dependent crack growth. At very high R values approaching unity, the observed growth rates are lower than those obtained under sustained load at the same mean load in the absence of the superimposed cyclic loading. Tests on compact tension [C(T)] specimens at lower frequencies were used to demonstrate the existence of three regions of behavior-cycle-dependent, mixed mode, and time-dependent. A linear cumulative damage model was used to predict the growth rates due to combined cycle-dependent and time-dependent mechanisms. The model was developed from 427°C data for the cyclic term and sustained load crack growth data for the time-dependent term. Although the model cannot predict the synergistic effect at high R, it provides a reasonable representation of much of the data. The authors conclude that the use of low-temperature data for the cyclic term is inadequate for representing the threshold values and growth rates at low AK values at the higher temperature.

The high cycle fatigue (HCF) resistance of Ti-6Al-4V for gas turbine engine applications is studied when the material is first subjected to low cycle fatigue (LCF). The high cycle fatigue (HCF) threshold is determined after small LCF surface cracks are formed in notch tension specimens. LCF loading at two stress ratios, R = 0.1 and R -1.0, is used to initiate the LCF cracks, which are detected using direct current potential difference (DCPD). The surface crack sizes are measured under load using a static loading fixture and a scanning electron microscope (SEM). In addition to the SEM surface measurements, heat tinting is used to mark the crack profiles before HCF testing so that fractography can be used after failure to measure the 2D crack geometry. The LCF surface-cracked specimens are tested at room temperature in lab air at 600 Hz using a step-loading procedure at two stress ratios, R = 0.1 and R = 0.5. The LCF loading history is found to affect the HCF threshold compared to what is predicted from long crack threshold values obtained from other crack geometries. Variations in HCF crack growth thresholds obtained on specimens with LCF crack sizes from 25 to 175 μm are attributed to overload and underload effects from the LCF precracking.

Factors of safety are applied in structural design to account for both variability and uncertainty. In high-cycle fatigue (HCF), the variability in the fatigue strength of a material is accounted for by considering the statistical variation and employing a −2σ or −3σ (for a normal distribution), or some other factor to account for the lowest value of a material variable within some statistical limits. These allowable values can then be plotted on a Haigh diagram or incorporated into some other design tool. The ignorance associated with not knowing the value of the applied load, such as from stresses due to some vibratory condition, can also be accounted for by further reducing the allowable stresses due to expected values of the applied loads. In addition to the alternating stress, the maximum allowable stress is also shown as a function of mean stress on this Haigh diagram. While the values shown are nominal, not statistically minimum values, these are considered material allowables for the sake of illustration in this chapter.

Foreign object damage (FOD) involves the damage caused by objects ingested into turbine engines. These events typically take place upon takeoff and landing. Ingested objects, which involve a range of soft and hard materials of all sizes and shapes, cause damage when they strike rotating blades, static vanes, or other parts of the engine where they cause a reduction in strength of the component. Such events are difficult to prevent although methods, such as the use of screens is unsuccessfully attempted at times in the past. A greater concern arises when the component that is damaged is also undergoing some type of forced or resonant vibration that can lead to high-cycle fatigue (HCF) in the damaged area. The problem of FOD is somewhat related to fatigue of notches, but is much more complicated because it involves additional aspects. The severity of a notch, from a geometric point of view, is characterized by a stress concentration factor, k t , which, under FOD, can vary significantly in service. Different types of damages are illustrated in this chapter involving a wide variation in geometry and corresponding values of k t . Robust engineering methods are needed to predict the influence of these geometric variables on HCF threshold stresses.

Of primary concern in high cycle fatigue (HCF) design is the material capability, after it is subjected to service conditions that may degrade capability over time and cycles. Low cycle fatigue (LCF) loading, while accounts for in design and not leading to failure during the design life, may degrade the capability of the material regarding its HCF resistance. One other form of potential damage, which is due to transient stresses above the fatigue limit during HCF loading, must also be considered. A practical problem arises when, in designing against HCF, the occurrence of stress transients above the endurance limits (FLS) becomes a possibility. Both stress transients above the FLS and prior or combined loading, under conditions where part of the loading is above the HCF limit, constitute conditions that are referred to as LCF–HCF loading. The LCF portion of the loading is designated as such irrespective of the frequency of loading and is not necessarily restricted to true LCF conditions that normally involve strain-control testing, a low number of cycles to failure, and inelastic deformation in a typical load-displacement loop. It is simply used to designate loading conditions that are different from the HCF conditions being evaluated.

Turbine engine components undergoing high frequency resonances, reciprocating automotive engines traveling hundreds of thousands of miles at several thousand rpm, railroad wheels making contact with the rails on every revolution over hundreds of thousands of miles, bridges carrying thousands of moving axle loads every day, and rotating machine components that operate on a continuous basis, are just some of the examples where materials can be subjected to large numbers of cycles. These large numbers of cycles may take many years to accumulate in service, whereas in design, data are needed in a much shorter period. The field of gigacycle fatigue has seen great interest in recent years and is discussed in detail in this chapter. Regarding the testing technique, piezoelectric test devices have been developed, which operate with an axial specimen in a longitudinal first mode resonance condition at the driving frequency of 20 kHz. The frequency of the driving force is extended to 30 kHz using the same excitement principle. It should also be noted that these types of tests are not pure resonance tests but, rather, are forced vibrations of lightly damped systems, conducted at or near the resonant frequencies of the test article. The analysis that leads to interpretation of the experimentally observed quantities, such as peak displacements is quite complicated, and the ability to maintain the test at a resonant frequency under constant conditions is very difficult.

Publisher Summary A notch in a component can be considered to be a defect, since it produces a local stress concentration or stress raiser that can ultimately be the location of a high-cycle fatigue (HCF) failure. In notch fatigue, the primary aim is to be able to predict the fatigue behavior of a material or component with a stress concentration from smooth bar data. Thus, it is important to understand the effect of a notch on the endurance limits (FLS) and to be able to predict the strength without having to conduct extensive experiments for each notch geometry. An alternate reason for understanding and modeling notch behavior is that it represents a condition where there are stress gradients in going from maximum stress at the notch root to lower stress at locations beneath the notch. Stress gradients also arise in fretting fatigue. To be able to predict the effect of the discontinuity or damage to stresses induced by vibratory HCF loading, requires an understanding of notch effects in fatigue. This chapter presents an overview of notch fatigue as related, primarily, to the fatigue limit or threshold for crack propagation.

A new vibration-based multiaxial fatigue testing methodology for assessing high cycle turbine engine material fatigue strength at various stress ratios is presented. The idea is to accumulate fatigue energy on a base-excited plate specimen at high frequency resonant modes and to complete a fatigue test in a much more efficient way at very low cost. The methodology consists of: (1) a topological design procedure, incorporating a finite element model, to characterize the shape of the specimens for ensuring the required stress state/pattern, (2) a vibration feedback empirical procedure for achieving the high cycle fatigue experiments with variable-amplitude loading, and finally (3) a yielding procedure for achieving various uniaxial stress ratios. The performance of the methodology is demonstrated by the experimental results from mild steel, 6061-T6 aluminum, and Ti-6Al-4V plate specimens subjected to fully reversed bending for both uniaxial and biaxial stress states. Results are compared with those produced using traditional fatigue test machines.Copyright © 2003 by ASME

A framework for the probabilistic analysis of high cycle fatigue is developed. The framework will be useful to U.S. Air Force and aeroengine manufacturers in the design of high cycle fatigue in disk or compressor components fabricated from Ti-6Al-4V under a range of loading conditions that might be encountered during service. The main idea of the framework is to characterize vibratory stresses from random input variables (uncertainties such as initial crack size, crack location, loading, material properties, and manufacturing variability). The characteristics of such vibratory stresses will be portrayed graphically as histograms, or probability density function (PDF). The outcome of the probability measures associated with all the values of a random variable exceeding the material capability is achieved by a failure function g(X) defined by the difference between the vibratory stress and Goodman line or surface such that the probability of HCF failure is P(f) = P(g(X

Impact damage on titanium leading-edge configurations was investigated through a series of hard-particle impact tests. Fatigue tests were used to assess the severity of damage in terms of an equivalent elastic-stress-concentration factor. The concept of geometric scaling was investigated by using various leading-edge thicknesses and projectile sizes in the impact tests. Observations of the type of damage and the use of a critical velocity concept tended to validate the scaling concepts.

Life predictions of turbine engine structural components utilize fracture mechanics principles to determine fatigue crack growth rates. Fatigue cracks grow under conditions of variable temperature, frequency, hold time, stress ratio and stress level. At elevated temperatures, time-dependent material behavior can play a significant role in the material behavior. Cumulative-damage models must account for all these variables as well as interaction effects. The earliest modeling involved interaction schemes and, primarily, time-independent material behavior. More recent work has focused on time-dependence and creep-fatigue interaction effects. A review of current modeling concepts is presented.

Creep crack growth in a nickel base superalloy at elevated temperatures was analyzed through a hybrid experimental-numerical (HEN) procedure. This HEN procedure consisted of simultaneous use of creep crack growth test displacement data from center cracked plate specimens of IN-100 at 732°C and a theoretical finite element model of the test specimen. A method for getting creep crack growth behavior solely from high resolution displacement measurements, in conjunction with a cracked specimen model which utilizes realistic constitutive relationships, has been developed. The constitutive law, in the form of the Bodner-Partom material model, was especially tailored to the nickel base superalloy studied which displays time-dependent nonlinear inelastic behavior at elevated temperatures. It has been demonstrated that the technique can be applied where crack extension is very small and could not otherwise be resolved by conventional experimental crack measuring techniques. This method provides realistic monotonically increasing crack growth values. The predictions agreed to within 10% of post-test measurements.

Stress-strain curves in tension obtained on a large number of structural materials at strain rates up to 1000/s are presented. A modified split Hopkinson bar apparatus used for high strain rate tensile testing is described. Data are compared with other published results. The flow stress of all the materials tested is seen to increase to some extent over the range in strain rates from 0.001 to 1000/s.