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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 critical evaluation of the statistics of the fatigue strength distribution as determined by the staircase (or up-and-down) method is presented. The effects of test parameters (namely, step size and sample size) were analyzed using numerical simulation to determine the accuracy of fatigue strength standard deviation calculations using traditional staircase statistics, resulting in a quantification of standard deviation bias as a function of step size and sample size. A non-linear correction was formulated to mitigate this standard deviation bias inherent in small-sample tests. In addition, the simulation was used to investigate the effectiveness of a bootstrapping algorithm on standard deviation estimates. The bootstrapping algorithm was found to significantly reduce the potential of large standard deviation errors in small-sample tests. Together, the use of the non-linear correction factor and the bootstrapping algorithm may allow an improved method to estimate the statistics of a material’s fatigue strength distribution using a small-sample staircase test strategy. 2006 Elsevier Ltd. All rights reserved.

The objective of this research was to investigate the high cycle fatigue behavior of a titanium alloy using an ultrasonic fatigue system. Fatigue testing from 10 6 to 10 9 cycles under fully reversed cycling ( R = −1) was performed to determine the ultra-high cycle fatigue behavior of Ti–6Al–4V. The staircase test method was employed to obtain accurate values of the mean fatigue limit stress corresponding to fixed numbers of cycles up to 10 9 . These results were compared to similar data generated on conventional servohydraulic test systems and electromagnetic shaker systems to determine if there are any frequency effects. In addition, specimens were tested with and without cooling air to determine the effects of temperature on the fatigue behavior. Results indicate that the fatigue strength determined from ultrasonic testing was consistent with conventional testing. In addition, the temperature rise in this material during ultrasonic testing is insignificant and has no apparent effect on the endurance limit.

The objective of this work was to compare the fretting fatigue performance of Ti-6Al-4V dovetail specimens on Ti-6Al-4V pads having various contact angles typical of engine hardware; 35°, 45° and 55° dovetail angles were considered. The dovetail fixtures were instrumented with strain gages so that the local normal and shear contact forces could be calculated. The contact force hysteresis loops were recorded showing the stick-slip history. At R = 0.1, gross slip was observed for several thousand cycles followed by partial slip after the average coefficient of friction increased. At R = 0.5, gross slip was present only during the first half cycle. During partial slip, the slope of the shear versus normal force was a function of the dovetail angle. The local contact loads, therefore, differed for the same remotely applied force. Despite this, the fretting fatigue life depended primarily on the remotely applied load not dovetail angle.

A critical distance method for predicting the fatigue limit stresses of notched specimens was implemented for notched specimens with a wide range of notch dimensions. Circumferentially notched cylindrical specimens (kt=1.97–4.07) taken from Ti–6Al–4V forged plate were cycled to failure (R=0.1 and 0.5) using a step loading method for estimating the 106 cycle fatigue limit stresses. These experimental data were used in combination with finite element solutions for all specimen geometries to determine a ‘critical distance’, a quantity or parameter determined from the stress distribution surrounding the notch in combination with fatigue limit stress data from unnotched specimens. A unique parameter was not found for all of the specimen geometries. However, predictions for the fatigue limit stresses of the larger notch geometries may be made with some amount of accuracy using a single value of the critical distance parameter, while reasonable predictions for the specimens with the smallest notch dimensions may be made upon the recognition of an apparent size effect.

The objective of this research was to investigate the fatigue strength of Ti–6Al–4V using an ultrasonic fatigue system. Fatigue testing up to 10 9 cycles under fully reversed loading was performed to determine the ultra-high cycle fatigue behavior of Ti–6Al–4V. Endurance limit results were compared to similar data generated on conventional servohydraulic test systems and electromagnetic shaker systems to determine if there are any frequency effects. Fatigue specimens were tested with and without cooling air to determine the effects of increased specimen temperature caused by internal damping due to cycling at a very high frequency. An infrared camera was also used to record specimen temperatures at various load levels. Results indicate that the effects of frequency, including internal heating, on the very high cycle fatigue behavior of Ti–6Al–4V are negligible under fully reversed loading conditions.

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 unique fatigue specimen was designed from the used fretting pads of Ti–6Al–4V fretting fatigue experiments. Many of these pads contained cracks that initiated and then arrested during the original fretting experiments. Heat tinting was used to mark the crack surface, and stress relief was applied to some specimens to remove load-history effects. The specimens were subjected to high cycle fatigue step testing and the threshold stresses were measured. The measured fretting crack sizes were used to calculate the crack propagation threshold, ΔKth. The results were analyzed for short crack and load history effects. Crack size effects were readily explained with a simple short crack model. No load history effects were noted for these fretting induced cracks.

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.

Notch size effects on the high cycle fatigue (HCF) limit stress of Ni-base superalloy Udimet 720 were investigated on cylindrical specimens with three notch sizes of the same stress concentration factor Kt=2.74. The HCF limit stress corresponding to a life of 106 cycles was experimentally determined at a stress ratio of 0.1 and a frequency of 25 Hz at room temperature. The stresses were calculated using finite element analysis (FEA) and the specimens analyzed using scanning electron microscopy (SEM). Test results show that at the same Kt value, notch size can slightly affect the HCF limit stress of U720 when notch root plasticity occurs. FEA and SEM results reveal that the notch size effects are influenced by a complicated combination of the stress and plastic strain fields at the notch tip, the nominal stress, and the effects of prior plastic deformation on fatigue crack initiation.

Effects of prior low cycle fatigue (LCF) cycling on the subsequent high cycle fatigue (HCF) limit stress corresponding to a life of 10 7 cycles are investigated for Ti-6Al-4V at room temperature. Tests are conducted at 420 Hz on an electrodynamic shaker-based system at several different LCF maximum loads and under subsequent HCF at R =0.1, 0.5 and 0.8 using a step loading procedure. Under these load combinations, which include the possibility of overload or underload effects if cracks form, there is no statistically significant effect of the prior LCF on the subsequent HCF limit stress. While LCF loading at a high stress of 900 MPa is seen to result in strain ratcheting, no distinct features on the fracture surface and different mechanisms of crack propagation from those obtained at lower maximum loads were observed. LCF loading up to 50% of expected life did not produce any indications of crack formation from either the stress limit data or the fracture surfaces.

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 effects and mechanisms of low cycle fatigue (LCF) on subsequent high cycle fatigue (HCF) limit were investigated in nickel-base superalloy Udimet 720 at room temperature at a stress ratio of 0.1 and frequencies of 1 and 25 Hz for LCF and HCF, respectively. The HCF limits were determined after various fractions of LCF life consumption. Results show that small fractions of LCF life consumption significantly reduce the subsequent HCF limit, and the reduction is attributed to a combination of LCF damage and the plastic deformation induced during the LCF process. Microstructural characterization indicates that both LCF and plastic deformation reduce the HCF limit by activating the slip systems in the FCC structure of the material, creating favorable sites for easy subsequent HCF damage.

The effect of initial plastic strain on the high cycle fatigue (HCF) lives of smooth cylindrical Ti–6Al–4V specimens is investigated. Specimens were monotonically, quasi-statically loaded under strain control in tension to produce plastic strains from 1% to 5% and under load control in compression to produce 9.5% plastic strain. A step-loading technique was then employed to establish the 106 or 107 cycle fatigue limit stress under load control conditions for stress ratios of R=0.1, 0.5 and 0.8 at frequencies of either f=50 or 400 Hz. Results are compared with baseline fatigue limit stresses for Ti–6Al–4V without prior plastic strain. Initial plastic prestrain in both tension and compression resulted in a small reduction in the fatigue limit at R=0.1, while a lesser reduction was exhibited at higher stress ratios in terms of maximum stress.

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.

Combined low-cycle fatigue/high-cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V-notched cylindrical Ti-6Al-4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10 7 cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10 6 cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity-induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.

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.

Previous research has shown that Ti–6Al–4V exhibits pronounced stress ratio effects under high cycle fatigue (HCF) loading. At high stress ratios ( R >0.7), a transition of failure mode occurs from traditional surface fatigue crack initiation and growth to bulk-dominated damage initiation and coalescence of multiple microcracks consistent with a ductile tensile test. At these high stress ratios, ratchetting was shown to occur (Int. J. Fatigue 21 (1999) 679; Mech. Time-Dependent Mater. 2 (1999) 195), leading to progressive strain accumulation until final failure. This study explores the microstructural origins of this stress ratio transition in HCF using computational micromechanics. The material being studied is a two-phase Ti–6Al–4V plate forging, consisting of a duplex microstructure with a hexagonal close-packed (hcp) α-phase and lamellar grains with layers of body-centered cubic (bcc) β-phase and secondary hcp α-phase. Crystallographic slip is the dominant mode of plastic deformation in this material. A 2-D crystal plasticity model that incorporates nonlinear kinematic and isotropic hardening at the slip system level is implemented into the finite element method to simulate the cyclic plasticity behavior. The finite element model is used to qualitatively understand the distribution of microplasticity in this alloy under various loading conditions. For typical HCF stress amplitudes, it is shown that microstructure scale ratchetting becomes dominant at R =0.8, but is insignificant at R =0.1 and 0.5. Reversed cyclic microplasticity is insignificant at all three stress ratios. The effects of phase morphology and orientation distribution are shown to affect the microscale plastic strain distribution in terms of the location and magnitudes of the plastic shear bands that form within clusters or chains of primary α grains. The results of the finite element modeling are also considered in light of previous experimental results.

Thin plate samples of Ti–6Al–4V contacted on both sides with pads of the same material were used to simulate contact conditions in real structures subjected to fretting fatigue. Laboratory tests on specimens of varying thicknesses were used to determine the stresses that correspond to a fatigue life of 107 cycles using a step-loading procedure. For the specific apparatus used in this study, changes in thickness produced changes in the ratio of shear load to clamping load for a specific fretting pad geometry. Specimen thicknesses of 1, 2, and 4 mm, and stress ratios of R=0.1 and 0.5 were investigated for two different contact pad lengths. Fatigue limit stresses in the specimen were found to be relatively insensitive to the average clamping or shear stress. Finite element analyses of the test geometry were used to provide details of the stress distribution in the contact region for the flat-on-flat geometry with blending radius. Results show that stress and displacement fields for a variety of test conditions corresponding to a fatigue life of 107 cycles vary widely and do not provide any clear indication of the existence of a simple parameter equivalent to a uniaxial fatigue limit stress. The stress and displacement fields are also shown to be very sensitive to the coefficient of friction used in the analysis.

Load history effects on room temperature fatigue-crack-growth threshold measurement are evaluated for titanium alloys Ti–6Al–4V and Ti-17. Baseline thresholds are determined by the use of a conventional load-shedding technique. Load history is synthesized by precracking at Δ K levels with K max greater than the subsequently measured threshold. Threshold for the latter is defined as the first notice of crack propagation under increasing Δ K , constant R , step loading. An empirical overload model is developed to account for precracking history on the threshold. Stress relief annealing after precracking and prior to threshold measurement is demonstrated to eliminate load history effects on rising Δ K , constant R , step loading threshold measurement, and to be comparable to that made using load shedding, but with considerable time saving.

The high cycle fatigue (HCF) notch size effect is investigated for Ti-6Al-4V flat dogbone specimens with two notch sizes, each having an elastic stress concentration factor of K t =2.72. Points were generated on a constant life Haigh diagram using a step-loading technique. The notch size effect is compared with previous results obtained from circumferentially notched cylindrical specimens in terms of the biaxial state of stress at the notch root and von Mises effective stress. Within the range of dimensions tested, there is limited dependence of the fatigue limit upon the notch root radius. Stresses at the notch root and the fatigue notch factor are examined as a function of uniaxial stress, effective stress, notch plasticity, and notch root radius.

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.

The fatigue nucleation and crack growth rate (FCGR) characteristics of Laser Shocked Peened (LSP) titanium 6Al–4V were examined and compared with unprocessed material. While crack initiation behavior of smooth (Kt=1.0) LSP processed samples is similar to baseline material, a marked improvement is observed in the notched (Kt>1) fatigue strength of LSP processed samples over unprocessed samples. Similar trends were noted for specimens that had been subjected to simulated foreign object damage (FOD) and subsequently fatigue tested. The FCGR resistance of LSP processed samples tested at low stress ratios (R) is likewise shown to be significantly greater than for unprocessed, baseline material and is due to the large residual compressive stresses, which reduce the locally applied stress. Advantages in FCGR resistance diminish at higher R. Differences in growth rate behavior are accounted for by using the effective stress intensity range, ΔKeff. The rationale of using ΔKeff is further demonstrated through fractographic investigations.

The high cycle fatigue (HCF) behavior of Ti–6Al–4V is investigated for cylindrical specimens having three sizes of geometrically similar circumferential V-notches, each with an elastic stress concentration factor, K t , of approximately 2.78. A step loading technique for obtaining a point on a constant life (10 6 cycles) Haigh diagram from a single test specimen was implemented. Tests were performed at stress ratios of R =0.1, 0.5, and 0.8 for specimens machined from two different product forms of Ti–6Al–4V, bar and plate forgings. Results indicate that while there is a definite notch size effect in the Ti–6Al–4V bar within the range of notch sizes tested, little or no such effect exists in the plate.

Experiments were conducted to determine the effects of test frequency on the high cycle fatigue (HCF) behavior of Ti-6Al-4V. Specimens were tested at a range of frequencies for three different stress ratios (0.1, 0.5, and 0.8). Results indicate a frequency dependence that varies with stress ratio (R). At low R, the fatigue strength increases with increasing frequency. As R is increased, this trend continues until a transition zone is reached. Above this transition the frequency effect seems to vanish at the lower frequencies, but it is still apparent at high frequency. In addition, the material exhibits ductile behavior above the transition point. The ductile behavior is characterized by void nucleation and growth and the apparent lack of fatigue crack initiation and growth that is evident at low stress ratios. Scanning electron microscopy is used to examine the failure mechanisms and transition regions. Several possible explanations are presented to explain the observed frequency and stress ratio effects. Strain accumulation at high R is observed and is attributed to cyclic strain ratchetting.