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Fatigue crack growth and thresholds at ultrasonic frequencies
International Journalof Fatigue
International Journal of Fatigue 28 (2006) 1456–1464
www.elsevier.com/locate/ijfatigue
Fatigue crack growth and thresholds at ultrasonic frequencies Stefanie Stanzl-Tschegg
*
Institute of Physics and Materials Science, BOKU, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria Received 28 December 2004; received in revised form 6 May 2005; accepted 3 June 2005 Available online 5 May 2006
Abstract The existence of a threshold of fatigue crack growth is treated for the aluminium alloy 7075-OA as well as Ti–6Al–4V. Results are reported on the influence of environment (vacuum and ambient air) and load ratio (R = 1 to +0.8) on fatigue crack growth in the nearthreshold regime. The main results are: in vacuum, crack growth still takes place at lower rates than 1010 m/cycle, and thus thresholds – if at all – are below approximately 5 · 1012 m/cycle. No frequency influence on crack propagation is present for loading frequencies of 20 Hz and 20 kHz. In ambient air environment, thresholds are identical at 20 kHz and 20 Hz cycling frequency, but crack growth is slower at ultrasonic frequency in humid air than at 20 Hz. Time governing processes, like surface diffusion of water vapour to the crack tip, water vapour adsorption and formation of a mono-layer at the crack tip as well as diffusion of hydrogen in front of the crack tip are discussed. The influence of load ratio is shown and discussed. 2006 Elsevier Ltd. All rights reserved. Keywords: Fatigue crack growth; Fatigue threshold; Ultrasonic fatigue; Very high cycle fatigue; Air humidity; Corrosion fatigue; Strain rate; Load ratio; 7075; Ti–6Al–4V
1. Introduction Similar to the question about the existence of a fatigue limit, the basic question arises on the existence of a threshold value for propagation of an already existing crack or defect in metallic materials. Both questions relate to the mechanisms of deformation at very low cyclic loads (i.e., below a ‘‘fatigue limit’’ or a ‘‘threshold stress intensity’’) at very high numbers of cycles. Investigations on the mechanisms of crack initiation and propagation in this regime have been performed and reported, among others, by Sakai [1], Mughrabi [2], Murakami [3] and Tanaka [4] at the International Very High Cycle Fatigue (VHCF) Conferences in Paris 1999 and Vienna 2001. Measurement in the VHCF (108–1011 cycles) regime is most time consuming or not at all possible with conventional fatigue testing machines, which operate at frequencies of some Hz up to utmost 1000 Hz so that the question on the existence or non-existence of a fatigue or threshold limit could not be *
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answered comprehensively until now. Therefore, development of the ultrasound fatigue testing technique has been promoted, and results on fatigue crack propagation features in the VHCF regime, that could not been obtained with conventional equipment, have been reported [5,6]. As shown in numerous investigations, ultrasonic fatigue testing is an efficient method to reduce testing times by a factor up to 1000 compared to conventional testing procedures. Specimens are vibrating in resonance, if adequate specimen designs allow adjustment to the resonance frequency of the ultrasonic system. Increasing the cycling frequency by three orders of magnitude and using adequately designed specimens to fulfil resonance criteria raises questions of comparability of ultrasonic data and data measured with conventional methods, and there especially the question on the role of the environment is important. It could be shown that fatigue crack growth in Al alloys – besides other metallic materials, like 13% chromium steel, grey cast irons and mild steel [5] – is not influenced by the cycling frequency in the crack growth regime below 107 m/cycle, if the experiments are performed in inert environment. After variation of the loading frequency by
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three decades and testing at three different load ratios it could be concluded that no (intrinsic) strain rate influence on near threshold fatigue crack growth exists in most of the studied materials [7]. Face-centred cubic [8] crystal systems are known to be relatively insensitive to rates of plastic deformation [13]. Additionally, the plastic deformation is small, if cycling is near threshold. If the crack tip plastic deformation is larger and growth rates are in the Paris regime, however, frequency influences on crack growth of several fcc metals are reported in the literature [9–11]. As another important result, crack growth rates being orders of magnitude below one lattice space per cycle, have been detected. This has been measured unambiguously in 1980 already [6], though accuracy of measurement at this time was not as good as today owing to less accurate electronic control devices. It could be shown that in bcc (verylow carbon iron, cast iron with globular graphite, 13% chromium steel) as well as fcc metallic materials (copper, steel 304) mean fatigue crack growth rates as low as 5 · 1013 m/cycle exist. In these studies, the experiments were carried out in inert silicone oil, and in addition the influence of corrosive environment was investigated. Ambient air, the environment usually present, is a corrosive medium for aluminium alloys, and chemical processes are caused by atmospheric moisture. Environmental influences result in time dependent processes, so that correlated influences by the frequency of fatigue loading have to be expected. Results on the environmental influence on crack propagation in the VHCF regime, with numbers of cycles up to more than 1010 will be reported in the following, reviewing more recent investigations [7–9] on an aluminium and a titanium alloy, considering that crack propagation in the VHCF regime is essentially determined not only by material inherent properties (chemical composition, yield strength, etc.) and loading conditions (load ratio) but also to a large degree on the surrounding environment. The experiments, reported in this study, were obtained at R = 1 with overaged 7075 alloy as representative for homogeneous slip aluminium alloys, as well as Ti–6Al– 4V alloy. Testing was performed at two frequencies (20 or 50 Hz and 20 kHz), and in addition the influence of the R-ratio was studied. Experiments at 20 Hz and 20 kHz were performed in ambient air and in vacuum to separate the different influences of load ratio, strain rate, air humidity and slip properties on near threshold fatigue crack growth. 2. Material and experimental procedure Results are presented for the wrought and overaged 7075 (7075-OA) as well as the Titanium alloy Ti–6Al–4V. The chemical composition of the 7075 alloy was (in wt%): Zn 7.2, Mg 2.8, Cu 1.7, Cr 0.06, Fe 0.3, Si 0.1, Mn 0.06, Ti 0.05, Ga 0.01, Zr 0.1. The alloy was solution annealed at 470 C, quenched and overaged by tempering at 107 C (8 h) plus 163 C (65 h). The resulting static properties are: Rm = 464 MPa, Rp0.2 = 524 MPa, A5 = 10.8%
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(with Rm = ultimate tensile stress, Rp0.2 = yield stress and A5 = tensile strain). The Ti–6Al–4V alloy was received as plate in solution-treated and overaged (STOA) condition. The chemical composition of Ti–6Al–4V was (in wt%): Al 6.30, V 4.17, Fe 0.19, O 0.19, N 0.013, H 0.0035, Ti balance. The alloy was solution-heat treated (1 h at 925 C) and vacuum annealed (2 h, 700 C). It consists of a bimodal distribution of approximately 60% primary a phase and approximately 40% lamellar colonies of a + b. Static strength properties of Ti–6Al–4Vp are: Rm = 970 MPa, Rp0.2 = 930 MPa, KIC = 67 MPa m and E = 116 GPa [7]. Specimens of the aluminium alloy were machined from rolled sheets of 20 mm thickness as standard middle tension (M(T) specimens [10]) for the servo-hydraulic tests. The thickness was 5 mm and centre notches were introduced using a saw and razor blades. The specimens were machined adequately to perform crack growth experiments in TL-direction (7075). Tube specimens were used in ultrasonic tests with length axis oriented in T-direction. A hole was drilled and a notch was introduced by spark erosion (with mineral oil as protective liquid) into the wall centre to cause crack initiation there (using spark erosion in order to avoid residual stresses introduced by mechanical notching). The cracks grew along the circumference of the tube in the plane of maximum normal stress with the crack front normal to the surface of the tube. The notch was positioned such that the crack growth direction at a crack length of 6 mm (without notch) was in TL-direction (7075). The specimen thickness was between 2 and 5mm and no pronounced effect of thickness could be detected [7]. The same specimen shape was used for the Ti–6Al– 4V [8]. Fatigue crack growth was investigated at load ratios R = 1, R = +0.05 and R = +0.5. Ultrasonic equipment appropriate to perform fatigue experiments at mean loads other than zero is described in detail in [5,15]. The experiments were performed in ambient air of 18–22 C and 40–60% relative humidity and alternatively in vacuum of maximum 3 · 103 Pa. Testing was performed with servohydraulic equipment at 20 Hz and with ultrasonic equipment at 20 kHz. In servo-hydraulic tests, specimens were cycled continuously, and in the ultrasonic experiments with pulses consisting of 1000 cycles and periodic pauses of 25– 100 ms to avoid rise of temperature. The maximum temperature of the specimens in servo-hydraulic tests was 30 C and 25 C in the ultrasonic experiments [9]. Fatigue crack growth is measured at the surface of the specimens using an optical microscope. Crack growth rates were determined as mean growth rates over crack length increments of 0.15–0.20 mm in servo-hydraulic as well as ultrasonic experiments. If fatigue cracks propagate first and stop then, the crack length increments during 1.5 · 106 cycles in servo-hydraulic tests, or 2 · 107 cycles in ultrasonic tests are used to calculate the mean growth rate. The stress intensity factor range, DK, was lowered until no crack growth could be observed within these
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numbers of cycles. With the optical resolution of 20 lm (in servo-hydraulic tests) and 7 lm (in ultrasonic tests), limiting hypothetical growth rates of 1.3 · 1011 m/cycle and 3.5 · 1013 m/cycle, respectively, serve to characterise arrest of fatigue crack growth. In servo-hydraulic experiments, a limiting growth rate of 1010 m/cycle was used to define a threshold according to the recommendations of ASTM [10], whereas in ultrasonic experiments threshold stress intensities were additionally determined at 3.5 · 1013 m/cycle. 3. Results The stress intensity factor range, DK, as well as Kmax has been used to present the fatigue crack growth data. DK was calculated according to DK ¼ K max K min ; where Kmax is the maximum stress intensity and Kmin is the minimum stress intensity of a cycle. For fully reversed loading (R = 1) this means, that DK = 2Kmax. This presentation was used in these studies instead of only counting the positive part of a load cycle at R = 1, i.e., DK = Kmax which is suggested by ASTM [10]. The two ways of presentation (DK or Kmax) will be discussed. 3.1. Influence of mean load and environment on fatigue crack growth and thresholds 3.1.1. (Da/DN vs. DK or Kmax) curves of 7075-OA, R = 1, +0.05, +0.5, vacuum Fig. 1 shows the FCGR’s and thresholds of the homogeneous slip 7075–OA alloy, obtained in vacuum and plotted vs. DK in Fig. 1a and vs. Kmax in Fig. 1b. The experiments were performed in vacuum at load ratios R = 1, +0.05 and +0.5 at ultrasonic testing frequency [7]. Arrows indi-
cate measurements with no visible crack growth within 2 · 107 cycles, resulting in threshold crack growth rates of 3.5 · 1013 m/cycle. Following results are obvious: The threshold values increase and the fatigue crack growth rates decrease with decreasing R-ratio, if plotted vs. DK. If Da/DN is plotted vs. Kmax instead of DK, the sequence of the curves is reversed, i.e., the threshold values increase and the fatigue crack growth rates decrease with increasing R-ratio. Crack propagation takes place at such low rates as 1011–1012 m/cycle, which is by a factor of 10–100 below a mean crack propagation rate of one lattice space per cycle. The correlating threshold values are at least 22% lower at a crack growth rate of 3.5 · 1013 than at 1010 m/cycle, which means that there is well pronounced cracking still in this VHCF crack growth regime. In addition, it has been shown [7] that an influence of testing frequency is absent, i.e., the curves of 20 Hz and 20 kHz measurement are almost identical. The fatigue crack growth rates in vacuum do not differ more than by a factor of 2, which is similar to the scatter of the results. This means that no strain rate influences were found in the inert environment. 3.1.2. (Da/DN vs. DK or Kmax) curves of 7075-OA, R = 1, +0.05, +0.5, ambient air Results of measurements in ambient air of 18–22 C and 40–60% relative humidity are shown in Fig. 2. Comparing fatigue crack propagation in ambient air with that in vacuum, a pronounced influence of air humidity is obvious. The threshold stress intensities at 3.5 · 1013 m/cycle in ambient air, for example, are approximately 60–70% lower than in vacuum, and threshold stress intensities at 1010 m/cycle are 45–55% lower than in the inert environment. 10-6
10-8 10-9 10-10 10-11 10-12
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7075-OA Vacuum
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b
1
2
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Maximum Stress Intensity Factor, K
7
10
, (MPam 1/2)
max
Fig. 1. Influence of mean load on fatigue crack growth of 2075-OA in vacuum. Testing frequency: 20 kHz, R-ratios = 1, +0.05 and +0.5, vacuum of 103 Pa. Plot vs. DK (a) and plot vs. Kmax (b).
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7075-OA Ambient Air
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Crack Growth Rate, a/ N, (m / Cycle)
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Maximum Stress Intensity Factor, K
10
, (MPam 1/2)
max
Fig. 2. Influence of mean load on fatigue crack growth of 7075-OA in ambient air of 18–22C and 40–60% RH. Testing frequency: 20 kHz, R-ratios = 1, +0.05 and +0.5. Plot vs. DK (a) and plot vs. Kmax (b).
3.2. Influence of loading frequency on fatigue crack growth and thresholds of 7075-OA alloy in inert and corrosive environment at different mean loads Fig. 3 shows the FCGR curves for 7075-OA measured at a loading frequency of 20 Hz with servo-hydraulic equipment and at 20 kHz ultrasonic frequency in ambient air at a mean load of zero (R = 1). In addition, the curve, obtained in vacuum with ultrasonic equipment, is presented. Surprisingly, the threshold stress intensities, Kth,max (and likewise DKth [7]) at 1010 m/cycle measured with servohydraulic and with ultrasonic equipment are similar within the ranges of scatter in ambient air. Above threshold, however, a significant difference of growth rates determined at the two different testing frequencies is obvious. Mean growth rates in the range of 1010–108 m/cycle are found for R = 1 loading p and maximum stress intensities between 2.5 and 7 MPa m at ultrasonic frequency, whereas cycling at 20 Hz results in
10-6 Crack Growth Rate, a/ N, (m / Cycle)
The crack propagation curves measured in ambient air show a change of slope as the stress intensity approaches the threshold. Fatigue cracks grow with minimum mean growth rates of approximately 5 · 1011 m/cycle, or they remain arrested. These low growth rates are obtained by taking the mean value of actually measured crack propagation rates and arrests at a constant cyclic stress intensity. The values of the threshold stress intensities at 1010 m/ cycle at 3.5 · 1013 m/cycle in ambient air differ by approximately 10% only, which is less than in vacuum. If the Da/DN results are plotted vs. Kmax instead of DK (Fig. 2b),the sequence of the threshold values at different load ratios is reversed like in vacuum. At crack rates above threshold, in the range of 1010–108 m/cycle, however, the curves coincide for the three R-ratios.
7075-OA R=-1
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20 Hz, Ambient Air 20 kHz, Ambient Air 20 kHz, Vacuum
10-13 10-14
1
2
3
5
Maximum Stress Intensity Factor, K
7
10
, (MPam 1/2)
max
Fig. 3. Influence of testing frequency (20 kHz – open symbols and 20 Hz – closed symbols) on FCGR’s in ambient air at R = 1 in 7075-OA.
approximately a factor 10–50 higher growth rates. This shows that the corrosive influence of ambient air at the ultrasonic frequency is smaller than at conventional testing frequencies at stress intensities above threshold. 3.3. Fracture morphology The influence of environment on the fracture surface appearance is documented in Fig. 4. It shows the border of a fracture surface of a 7075-OA specimen, which was cycled at R = 1 at ultrasonic frequency in ambient air first, with decreasing cyclic stress intensity until the threshold was reached. The left side of Fig. 4 shows the resulting fracture surface. Mainly transcrystalline fracture features with a low portion of plastic deformation are visible and in addition some intergranular brittle fracture features
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Fig. 4. Fracture surface of alloy 7075-OA after near-threshold loading at 20 kHz ultrasonic frequency at R = 1 in ambient air (left side) and in vacuum (right side). Crack growth direction from left to right.
(elongated grains in L direction), which cause a slightly rougher fracture. After evacuating the vacuum chamber, loading was continued in vacuum at a near threshold cyclic stress intensity causing crack growth rates of 1011–1010 m/cycle. The correlating fracture surface is visible at the right side of Fig. 4 showing ductile transcrystalline fracture features. No essential influence by the load ratio could be observed [7]. 3.4. (Da/DN vs. DK or Kmax) curves of Ti–6Al–4V, tested in ambient air Fatigue crack growth in Ti–6Al–4V alloy at load ratios R = 1, +0.1 and +0.8 in ambient air, measured at 20 kHz and 50 Hz is shown in Fig. 5. The 50 Hz data were determined by Boyce and Ritchie [16] with material of the same lot as used for the ultrasonic measurements [12].
Identical thresholds are detected with ultrasonic 20 kHz equipment and by servo-hydraulic 50 Hz measurement. Higher fatigue crack growth rates, however, between 1010 and 108 m/cycle are found at ultrasonic frequency at the investigated R-ratios of +0.1 and +0.8. In order to analyse the load ratio influence, the Da/DN data are plotted vs. the positive part of a load cycle, Kmax, instead of the amplitude of loading, DK, for a loading frequency of 20 kHz in Fig. 6. Coinciding fatigue crack growth curves above approximately 3 · 1010 m/cycle are obtained with this, but a lower threshold stress intensity, Kmax,th at R = 1 than at R = +0.1 results. For R = +0.8, the curve is shifted at whole towards higher Kmax values. Fig. 7 shows the variation of the cyclic (DKth) as well as the maximum values (Kth,max) of the stress intensity thresh-
10-7 Crack Growth Rate, a/ N, (m / Cycle)
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Ti6Al4V 20 kHz Ambient Air
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R=0.1
R=0.8
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2
20 1/2
, (MPam )
max
Fig. 6. Fatigue crack growth in Ti–6Al–4V at 20 kHz loading frequency in ambient air at R-ratios = 1, +0.1 and +0.8. Plot vs. Kmax.
Crack Growth Rate, a/ N, (m / Cycle)
10-7 Ti6Al4V Ambient Air
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20 kHz
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50 Hz 7
10
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Stress Intensity Factor Range, K, (MPam ) Fig. 5. Influence of loading frequency (20 kHz – open symbols, 50 Hz – closed symbols [12]) on fatigue crack growth in Ti–6Al–4V in ambient air at R-ratios = 1, +0.1 and +0.8.
Fig. 7. Variation of DK and Kmax thresholds of Ti–6Al–4V with load ratio. Testing frequency: 20 kHz; ambient air.
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olds for different positive mean loads. With increasing R values, decreasing cyclic stress intensities are necessary to propagate a fatigue crack, and at R-ratios above +0.5 the needed tensile portions are rather high in order to obtain crack growth. 4. Discussion Strain rate (frequency) effects, load ratio and environmental influences on fatigue crack growth in 7075 OA and Ti–6Al–4V are discussed in the following. 4.1. Vacuum-crack growth rates below 1010 m/cycle Most interesting is the non-existence of a crack growth threshold value in the range of one lattice space per cycle (several 1010 m/cycle), which would be the physically meaningful value being expected. Performing threshold measurements at ultrasonic frequencies allows to reach lower threshold crack growth rates, e.g., 5 · 1013 m/cycle. This non-existence of thresholds in the range of several 1010 m/cycle has been detected for numerous other materials, as reported earlier [17]. The non-existence of a threshold at approximately 1010 m/cycle and its shift into the range of 1011–1013 m/cycle leads to cyclic stress intensity thresholds being approximately 25% lower than assumed before, which is of high practical relevance. 4.2. Influence of ambient air environment
*
mechanisms
Crack growth rates increase and threshold stress intensities decrease in Aluminium alloys reported in this and former papers [7,12,13], if cycled in ambient air instead of vacuum, since moisture acts as a corrosive environment. Moisture decreases the cyclic plastic strain that a crack tip can endure. Water vapour of ambient air is transported to the crack tip by diffusion where chemical processes with newly created fracture surfaces lead to the formation of hydroxide, hydrated oxides and the release of hydrogen [18]. Loading frequency and partial pressure of water vapour control the surface reaction at the crack tip. Embrittling is explained by hydrogen adsorption at the surface or in the first few atomic layers, where it facilitates dislocation nucleation [19]. Diffusion of hydrogen ahead of the crack tip [20,21] is reported, which is supported by dragging by mobile dislocations [22]. The influence of humidity on fatigue crack propagation in aluminium alloys does not only depend on chemical composition, grain size, load ratio and yield strength, but also on their slip properties [23,24]. In 7075, under- or peak-ageing favours planar slip and crystallographic (stage I-like [24]) fatigue crack propagation at low stress intensities in inert environment whereas over-ageing promotes homogeneous slip and stage II crack propagation. The homogeneous slip material was found to be less susceptible to embrittling by air humidity than the same material heat-treated to promote planar slip [23,24].
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Diffusion of water molecules as well as surface reaction kinetics are time dependent processes, and it may be assumed therefore that the loading frequency influences the material response. Experiments with wrought aluminium 2024-T3 [25], 7075-T6 [26] and cast aluminium AlSi9Cu3 [27] showed that air humidity influences fatigue crack growth at ultrasonic frequencies at a load-ratio of R = 1, if growth rates are small, i.e., below approximately 2 · 109 m/cycle. Similarly, influences of air humidity or aqueous environment on ultrasonic fatigue crack growth were detected in austenitic and ferritic steels, copper [28] and in magnesium alloys [27] at very low growth rates and cyclic stress intensities close to the threshold. 4.3. Ambient air – no frequency influence on threshold values It is interesting to note that identical thresholds are obtained with loading frequencies of 20 Hz and 20 kHz for the aluminium alloy 7075 [7] and Ti–6Al-4, though humidity has a pronounced influence on fatigue crack growth. Threshold stress intensities of 7075 OA at R = 1, R = +0.05 and R = +0.5 at 1010 m/cycle are 58–79% of the respective values measured in vacuum, and the threshold stress intensity values at 5 · 1013 m/cycles are 54–78% of those in vacuum. The threshold stress intensities are lower at 5 · 1013 m/cycles than at 1010 m/cycles in air as well as in vacuum, but the difference between these two values is larger in vacuum than in air, since slow crack propagation instead of crack arrest is more pronounced in vacuum than in air in the crack growth regime below one atomic distance per cycle. Minimum mean growth rates in ambient air are approximately 5 · 1011 m/cycle, whereas cracks may still propagate at mean growth rates of 5 · 1012 m/cycle in vacuum. 4.4. Ambient air – crack growth in the regime above threshold – frequency influence Above threshold, however, slower fatigue crack growth rates at 20 kHz than at 20 Hz are observed in all materials tested until now besides the Ti–6Al–4V alloy. This effect is most pronounced at a load ratio R = 1 and becomes smaller at higher load ratios. The frequency influence in humid air may be attributed to shorter duration of a cycle at ultrasonic frequency in comparison to a lower frequency. One time governing process for the environment to become effective, is adsorption, i.e., the possibility to build-up a gas mono-layer at the crack tip [24,29,32]. Another time governing process is bulk diffusion of hydrogen together with the interaction with dislocations, assuming that hydrogen enters the material at the crack tip. Third, surface diffusion of water vapour to the crack tip could be a time limiting process [29]. Estimations of the upper limit of growth rates that allow environmental reactions at the crack tip at the ultrasonic frequency with a crack opening time of 2.5 · 105 s are treated in the following. It will be shown that this is approximately 1 · 109 m/
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cycle, if surface coverage by water vapour molecules is postulated and is approximately in the same range, if bulk diffusion of hydrogen (without dislocation interaction) is considered at the ultrasonic loading frequency of 20 kHz. Surface diffusion of water vapour, however, is estimated to be fast enough to not act as a time limiting process. (i) In order to estimate the time ts needed to generate a gas mono-layer at the crack tip (crack front) by adsorption, the Langmuir equation may be used. The relative humidity of ambient air at 20 C was 40–60% in the experiments of this work, so that the partial pressure of water vapour was 1200 Pa. This results in a time ts needed to form a water vapour mono-layer of ts 10 ls: The crack opening or exposure time tE may be written as tE ¼ d=2ðDa=DN Þ f ; where d is the lattice constant. A mono-layer can be built up only, if tE P ts : For d = 4 · 1010 m (aluminium) and f = 20 kHz an upper limit of the crack growth rate, below which a monolayer can be formed, Da/DN = d/2f Æ ts will be Da=DN 109 m=cycle: This is an approximation only as it is not known how high the sticking probability has to be to cause an environmental influence, i.e., if the mono-layer has to be built up completely; it has been assumed 0.3 in this study. The influence of the load ratio may be attributed to the longer time a crack is open during a load cycle at higher load ratio [6]. At 20 Hz, full surface coverage may be expected irrespective of load ratio at 1010 m/cycles, whereas at ultrasonic frequency the longer crack opening time at high load ratio is necessary to obtain a similar surface coverage at the same crack growth rate. (ii) If transport of hydrogen into the crack front volume by diffusion is assumed, the time t being needed by a molecule to pass a specified distance, could be grain boundary diffusion or bulk diffusion or diffusion determined by dislocation dragging. As a very rough and first approach, bulk diffusion without dislocation interaction has been considered as time governing process [29]. The bulk diffusion coefficient of hydrogen at room temperature was assumed be between DB ¼ 2 1013 and 1014 m2 =s according to [18]. The crack tip exposure time tE during one cycle is given by one half of the inverse frequency (at best the crack is open during the tensile part) tE ¼ 1=2f ¼ 2:5 105 s: Assuming this time to be available for diffusion of the molecules, a distance
x 7 1010 –3 109 m will be covered by them during one cycle. This means that an influence by hydrogen by bulk diffusion may be expected for crack growth rates, which are lower than (0.7– 3) · 109 m/cycle at a loading frequency of 20 kHz, which is by a factor of 2–7 above the threshold regime. If hydrogen diffusion by dislocation dragging rather than bulk diffusion of hydrogen is considered as the relevant mechanism at the crack tip, a diffusion coefficient of 1013 m2/s has been assumed for hydrogen in a-iron [21,22] as the needed time to attain a critical hydrogen concentration for metal embrittlement in front of the crack tip. An approach to calculate the critical crack growth rates to account for dislocation assisted hydrogen transport, should be considered. (iii) If the critical time for water vapour migration to the crack tip is estimated, surface diffusion may be considered as the rate controlling process. Literature values for diffusion constants are differing very much, but it may be assumed that surface diffusion constants are by orders of magnitude higher than the reported bulk diffusion constants between 1014 and 2 · 1013 m2/s. Therefore, the needed crack tip exposure time tE has to be at least 10 times lower than for bulk diffusion of hydrogen, and thus the critical crack growth rate could be at least 10 times higher (i.e., higher than approximately 108 m/cycle) in order to obtain water vapour influence. Therefore, this process is considered as a non-rate controlling mechanism, so that no limitation by the high ultrasonic frequency as to this environmental influence should be expected. Additional mechanisms are acting, like capillary sucking and pumping effects as well as discontinuous crack propagation, which probably change (raise) the critical crack growth rate, at which environmental effects would still become effective and thus could explain the experimental results showing that ambient air affects ultrasonic crack growth at such high growth rates as 2 · 108 m/cycle. Pumping of the environment into the crack tip region is effective by movement of the already formed fracture surfaces due to the tension-compression type of loading. Crack propagation in the threshold regime is discontinuous rather than a cycle by cycle process [6,30–32] taking place in specified areas only, while the crack is arrested in other parts of the crack front. It may be assumed therefore that water vapour reaches the crack tip during these arrest periods, so that actually higher mean crack growth rates than 109 m/cycle are sufficient to obtain an environmental interaction. These results are also in accordance with results of Henaff et al. [14], who studied fatigue crack growth at frequencies of 0.2–200 Hz at different low water vapour pressures. They showed, for example, that a water vapour pressure of 103 Pa is sufficient to obtain environmental effects at 10 Hz if growth rates are below 108 m/cycle. Performing ultrasonic experiments in ambient air, a load cycle is approximately a factor 1000 shorter, the water vapour pressure of 1200 Pa, however, is approximately a factor
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106 higher than the conditions studied by Henaff et al., so that the observed environmental interactions below 108 m/cycle are plausible. Experiments on 2024-T3 in dried air as surrounding environment at ultrasonic fatigue loading leads to a crack growth curve positioned between the vacuum and ambient air curves, showing lower crack growth rates than in humid air above approximately 109 m/cycle, but identical thresholds below 5 · 1012 m/ cycle [25] and thus confirm the above mentioned estimation. To summarise, the results of the above treated estimations of limiting crack growth rates plus additional effects, like capillary sucking and pumping effects as well as discontinuous crack propagation, demonstrate that an environmental influence may be expected at crack growth rates below some 108 m/cycle. It may be concluded that the environmental influence is fully pronounced at crack growth rates below at least approximately 109 m/cycle at a loading frequency of 20 kHz, so that the observed identical threshold values at 20 Hz and 20 kHz are plausible and not surprising.
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result is probably more pronounced crack tip blunting at this high R-ratio. Plotting the DKth and Kmax,th values vs. R [33] demonstrates that fatigue cracking is mainly controlled by the maximum values at low mean values up to approximately R = +0.6 and controlled mainly by the stress intensity ranges at higher R-values (Fig. 7). The same is true for the aluminium alloys, and there even at the negative load ratio of R = 1. Most important, no influence of frequency is detected in the threshold regime, as shown in Fig. 5 for the Ti–6Al–4V alloy. The higher growth rates above threshold in ultrasonic experiments, compared with cycling at 50 Hz, can neither be explained with environmental influences, nor with strain rate effects. Geometric influences as well as possible slight differences of the loading conditions (flat specimens with thickness 10 mm and crack lengths more than 10 mm in the 50 Hz experiments, tubular specimens with a wall thickness of 2 mm and crack lengths between 1.5 and 7.5 mm at 20 kHz) may have contributed to the observed difference of growth rates. 5. Conclusions
4.5. Influence of load ratio and testing frequency Comparing the plots of Da/DN vs. Kmax and, respectively, DK, leads to a reversed sequence of the curves, i.e., the threshold values of Kmax increase and the fatigue crack growth rates decrease with increasing R-ratio (Figs. 1 and 2) for the aluminium alloy 7075-OA being tested in vacuum as well as in ambient air. This result is similar to that on 13% Cr steel [17] (studied in ambient air), though the (Da/DN vs. Kmax) curves of this material are closer together. The decrease and, respectively, increase of the threshold values of DK and Kmax with load ratio is not only observed for positive R-ratios but also for 1. The curves remain separated in the plot vs. Kmax like in the plot vs. DK in the whole tested crack growth range including the Paris regime, if the experiments are performed in vacuum (Fig. 1), whereas in ambient air, the curves coincide above the threshold regime, at crack growth rates between approximately 1010 and 108 m/cycle (7075-OA) (Fig. 2). This means that above threshold, obviously the tensile part of loading only is responsible for environmentally assisted fatigue crack propagation rates. Plotting the Da/DN curves of Ti–6Al–4V alloy vs. Kmax instead of DK leads to coinciding Da/DN values in a similar way, but only for the R-ratios R = 1 and +0.05 (up to R = +0.5, which is not shown in Fig. 6) at crack growth rates above threshold. A lower Kmax threshold, however, results for R = 1 than for R = 0.05. This means that the tensile part of cyclic loading controls crack propagation beyond the threshold regime, whereas in the threshold regime the compressive part of cycling at R = 1 is in addition effective, causing additional damage, probably by reducing the fracture surface roughness [8]. For R = +0.8 the whole curve is shifted towards higher Kmax values in comparison with the R = 1 curve. The reason for this
The ultrasonic fatigue testing technique allows extensive investigations of fatigue crack growth in the VHCF regime. Main results are: 1. In inert environment (vacuum), the dependence of crack growth on the cyclic stress intensity is similar at cyclic frequencies of 20 kHz and 20 (or 50) Hz in the investigated crack growth regime below approximately 108 m/cycle (7075-OA) and several 1010 m/cycle (Ti– 6Al–4V). This indicates that no intrinsic frequency, i.e., strain rate influence on thresholds and near threshold fatigue crack growth exists in the alloy aluminium 7075 and Ti–6Al–4V. 2. In inert environment, crack propagation is possible at such low growth rates as 3.5 · 1013 m/cycle, which means that thresholds for crack propagation (and respective DKth values) are lower than conventionally determined ‘‘threshold’’ values (in the range of several 1010 m/cycle). In this regime of very low crack growth rates, crack propagation is discontinuous. 3. Pronounced influence of air humidity on near-threshold fatigue crack growth is obvious at 20 kHz ultrasonic fatigue loading. Under fully reversed loading conditions, higher crack growth rates are observed in humid environment than in vacuum, and the slope of the Da/DNcurve is essentially smaller than in vacuum for the 7075-OA alloy. 4. The threshold stress intensities of the 7075-OA alloy, cycled in ambient air at R = 1, R = 0.05 and R = +0.5 at 1010 m/cycle are 54–78% of the respective values measured in vacuum. Under the influence of water vapour, eventual intercrystalline brittle fracturing is observed, whereas a smooth transcrystalline fracture mode is typical for vacuum.
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5. In ambient air, the threshold stress intensities of the aluminium alloy and the Ti–6Al–4V alloy are identical at 20 Hz and 20 kHz. At higher stress intensities, fatigue cracks propagate by a factor of 5–50 faster if cycled at 20 Hz instead of 20 kHz in 7075-OA. 6. Calculations, roughly estimating the rate controlling processes of water vapour and hydrogen diffusion as well as generation of a water vapour layer at the crack tip due to adsorption, prove that an environmental influence is fully effective even at the high ultrasonic frequency of 20 kHz at fatigue crack growth rates below approximately 109 m/cycle. 7. The compressive part of a load cycle leads to additional fatigue damage in the Ti–6Al–4V alloy. A possible mechanism is degradation of fracture surface asperities and resulting reduction of surface roughness. Acknowledgements Part of this work was performed as thesis by Dr. B. Holper within a project of ONR, USA and Dr. A.K. Vasudevan. Their financial support is gratefully acknowledged. In addition, cooperation with Prof. H. Mayer and helpful discussion with Prof. J. Petit is gratefully acknowledged. References [1] Sakai T, Sato Y, Oguma N. Characteristic S–N properties of highcarbon–chromium-bearing steel under axial loading in long-life fatigue. Fat Fract Eng Mater Struct 2002;25:765–73. [2] Mughrabi H. Mechanisms of fatigue failure in ultralong life regime. Fat Fract Eng Mater Struct 2002;25:755–64. [3] Murakami Y, Yokoyama NN, Nagata J. Mechanism of fatigue failure in ultralong life regime. Fat Fract Eng Mater Struct 2002;25:735–46. [4] Tanaka K, Akiniwa Y. Fatigue crack propagation behaviour derived from S–N data in very high cycle regime. Fat Fract Eng Mater Struct 2002;25:775H–84H. [5] Stanzl-Tschegg S, High-cycle crack growth in the Paris- and threshold regime at ultrasonic frequencies. In: Soboyejo WO, Srivatsan, editors. High cycle fatigue of structural materials, TMSASM symposium proceedings in honor of P. Paris. TMS, Warrendale; 1997. p. 211. [6] Stanzl S, Tschegg E. Measurement of fatigue crack propagation threshold and of growth rates below 1012 m/cycle by a time saving method. Metal Sci 1980;14(4):143–97. [7] Holper B, Mayer H, Vasudevan AK, Stanzl-Tschegg SE. Near threshold fatigue crack growth in aluminium alloys at low and ultrasonic frequency: Influences of specimen thickness, strain rate, slip behaviour and air humidity. Int J Fatigue 2003;25:397–411. [8] Laird C, Charsley P. Strain rate sensitivity effects in cyclic deformation and fatigue fracture ultrasonic fatigue, The Metallurgical Society of AIME, PA; 1982. p. 187. [9] Taylor D, Knott JF. The effect of frequency on fatigue crack propagation rate. Proceedings of the 6th international conference on fracture, vol. 3. Oxford: Pergamon Press; 1984. [10] Shih YS, Chen JJ. The frequency effect on the fatigue crack growth rate of 304 stainless steel. Nucl Eng Design 1999;191:225–30. [11] Baik YM, Kim KS. The combined affect of frequency and load level on fatigue crack growth in stainless steel 304. Int J Fatigue 2001;23:417–25.
[12] Mayer H, Holper B, Zettl B, Stanzl-Tschegg SE. Slow fatigue crack growth in 2024-T3 and Ti–6Al–4V at low and ultrasonic frequency. Z Metallkd 2003;94(5):539–46. [13] Holper B, Mayer H, Vasudevan AK, Stanzl-Tschegg SE. Near threshold fatigue crack growth at positive load ratio in aluminium alloys at low and ultrasonic frequency; influences of strain rate, slip behaviour and air humidity. Int J Fatigue 2004;26:27–38. [14] ASTM. ASTM Designation E647-00: Standard Test Method for Measurement of Fatigue Crack Growth Rates; 2000. [15] Stanzl SE, Czegley M, Mayer HR, Tschegg EK. Fatigue crack growth under combined mode I and mode II loading. Fracture mechanics, perspectives and directions, ASTM STP 1989;1020:479–96. [16] Boyce BL, Ritchie RO. Effect of load ratio and maximum stress intensity on fatigue threshold in Ti–6Al–4V. Eng Fract Mech 2001;68:129. [17] Stanzl SE, Tschegg EK. Fatigue crack growth and threshold behaviour at ultrasonic frequencies. Fracture mechanics, ASTM STP 1983;791(II):3–18. [18] Ricker RE, Duquette DJ. The role of hydrogen in corrosion fatigue of high purity Al–Zn–Mg exposed to water vapor. Metall Trans A 1988;19A:1775–83. [19] Lynch SP. Environmentally assisted cracking: overview of evidence for an adsorption-induced localised-slip process. Acta Metall Mater 1988;36(10):2639–61. [20] Wei RP. Rate controlling processes and crack growth response. In: Bernstein IM, Thompson AW, Bernstein IM, editors. Hydrogen effects in metals. Thompson (AW): TMS; 1980. p. 677. [21] Holroyd NJH, Hardie D. Factors controlling crack velocity in 7000 series aluminium alloys during fatigue in an aggressive environment. Corros Sci 1983;23(6):527–46. [22] Tien JK, Nair S, Bates RC, Buck O. Dislocation sweeping model for hydrogen assisted subcritical crack growth. Scripta Metall Mater 1980;14:591–4. [23] Suresh S, Vasudevan AK, Bretz PE. Mechanism of slow fatigue crack growth in high strength aluminium alloys: role of microstructure and environment. Metall Trans A 1984;15:369–79. [24] Petit J, Fouquet J, Henaff G. Influence of ambient atmosphere on fatigue crack growth behaviour of metals. In: Carpinteri A, editor. Handbook of fatigue crack propagation in metallic structures. Amsterdam: Elsevier; 1994. [25] Stanzl-Tschegg SE, Mayer HR, Tschegg EK. The influence of air humidity ion near-threshold fatigue crack growth of 2024-T3 aluminium alloy. Mater Sci Eng A 1991;147:45–54. [26] Mayer H, Papakyriacou M, Pippan R, Stanzl-Tschegg S. Influence of loading frequency on the high cycle fatigue properties of AlZnMgCu1.5 aluminium alloy. Mater Sci Eng A 2001;314:51–7. [27] Papakyriacou M, Mayer H, Fuchs U, Stanzl-Tschegg SE, Wei RP. Influence of atmospheric moisture on slow fatigue crack growth at ultrasonic frequency in aluminium and magnesium alloys. Fatigue Fract Eng Mater Struct 2002;25(8/9):795–804. [28] Stanzl S, Tschegg E. Influence of environment on fatigue crack growth in the threshold region. Acta Metall 1981;29:21–32. [29] Stanzl SE, Tschegg EK. Effect of environment on near-threshold fatigue crack growth at ultrasonic frequencies. In: Ultrasonic fatigue. Pennsylvania, USA: The Metallurgical Society of AIME; 1982. p. 553. [30] Davidson DL, Lankford J. The effect of water vapor on fatigue crack tip mechanics in 7075-T651 aluminium alloy. Fatigue Fract Eng Mater Struct 1983;6:241. [31] McEvily AJ, Gonzalez-Velazquez JL. Fatigue crack tip deformation process as influenced by the environment. Metall Trans A 1992;23:2211. [32] Henaff G, Marchal K, Petit J. On fatigue crack propagation enhancement by a gaseous atmosphere: experimental and theoretical aspects. Acta Metall 1995;43:2931. [33] Vasudevan AK, Sadananda K, Louat N. A review of crack closure, fatigue crack threshold and related phenomena. Mater Sci Eng 1994;188:1.
International Journal of Fatigue 28 (2006) 1456–1464
www.elsevier.com/locate/ijfatigue
Fatigue crack growth and thresholds at ultrasonic frequencies Stefanie Stanzl-Tschegg
*
Institute of Physics and Materials Science, BOKU, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria Received 28 December 2004; received in revised form 6 May 2005; accepted 3 June 2005 Available online 5 May 2006
Abstract The existence of a threshold of fatigue crack growth is treated for the aluminium alloy 7075-OA as well as Ti–6Al–4V. Results are reported on the influence of environment (vacuum and ambient air) and load ratio (R = 1 to +0.8) on fatigue crack growth in the nearthreshold regime. The main results are: in vacuum, crack growth still takes place at lower rates than 1010 m/cycle, and thus thresholds – if at all – are below approximately 5 · 1012 m/cycle. No frequency influence on crack propagation is present for loading frequencies of 20 Hz and 20 kHz. In ambient air environment, thresholds are identical at 20 kHz and 20 Hz cycling frequency, but crack growth is slower at ultrasonic frequency in humid air than at 20 Hz. Time governing processes, like surface diffusion of water vapour to the crack tip, water vapour adsorption and formation of a mono-layer at the crack tip as well as diffusion of hydrogen in front of the crack tip are discussed. The influence of load ratio is shown and discussed. 2006 Elsevier Ltd. All rights reserved. Keywords: Fatigue crack growth; Fatigue threshold; Ultrasonic fatigue; Very high cycle fatigue; Air humidity; Corrosion fatigue; Strain rate; Load ratio; 7075; Ti–6Al–4V
1. Introduction Similar to the question about the existence of a fatigue limit, the basic question arises on the existence of a threshold value for propagation of an already existing crack or defect in metallic materials. Both questions relate to the mechanisms of deformation at very low cyclic loads (i.e., below a ‘‘fatigue limit’’ or a ‘‘threshold stress intensity’’) at very high numbers of cycles. Investigations on the mechanisms of crack initiation and propagation in this regime have been performed and reported, among others, by Sakai [1], Mughrabi [2], Murakami [3] and Tanaka [4] at the International Very High Cycle Fatigue (VHCF) Conferences in Paris 1999 and Vienna 2001. Measurement in the VHCF (108–1011 cycles) regime is most time consuming or not at all possible with conventional fatigue testing machines, which operate at frequencies of some Hz up to utmost 1000 Hz so that the question on the existence or non-existence of a fatigue or threshold limit could not be *
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0142-1123/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2005.06.058
answered comprehensively until now. Therefore, development of the ultrasound fatigue testing technique has been promoted, and results on fatigue crack propagation features in the VHCF regime, that could not been obtained with conventional equipment, have been reported [5,6]. As shown in numerous investigations, ultrasonic fatigue testing is an efficient method to reduce testing times by a factor up to 1000 compared to conventional testing procedures. Specimens are vibrating in resonance, if adequate specimen designs allow adjustment to the resonance frequency of the ultrasonic system. Increasing the cycling frequency by three orders of magnitude and using adequately designed specimens to fulfil resonance criteria raises questions of comparability of ultrasonic data and data measured with conventional methods, and there especially the question on the role of the environment is important. It could be shown that fatigue crack growth in Al alloys – besides other metallic materials, like 13% chromium steel, grey cast irons and mild steel [5] – is not influenced by the cycling frequency in the crack growth regime below 107 m/cycle, if the experiments are performed in inert environment. After variation of the loading frequency by
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three decades and testing at three different load ratios it could be concluded that no (intrinsic) strain rate influence on near threshold fatigue crack growth exists in most of the studied materials [7]. Face-centred cubic [8] crystal systems are known to be relatively insensitive to rates of plastic deformation [13]. Additionally, the plastic deformation is small, if cycling is near threshold. If the crack tip plastic deformation is larger and growth rates are in the Paris regime, however, frequency influences on crack growth of several fcc metals are reported in the literature [9–11]. As another important result, crack growth rates being orders of magnitude below one lattice space per cycle, have been detected. This has been measured unambiguously in 1980 already [6], though accuracy of measurement at this time was not as good as today owing to less accurate electronic control devices. It could be shown that in bcc (verylow carbon iron, cast iron with globular graphite, 13% chromium steel) as well as fcc metallic materials (copper, steel 304) mean fatigue crack growth rates as low as 5 · 1013 m/cycle exist. In these studies, the experiments were carried out in inert silicone oil, and in addition the influence of corrosive environment was investigated. Ambient air, the environment usually present, is a corrosive medium for aluminium alloys, and chemical processes are caused by atmospheric moisture. Environmental influences result in time dependent processes, so that correlated influences by the frequency of fatigue loading have to be expected. Results on the environmental influence on crack propagation in the VHCF regime, with numbers of cycles up to more than 1010 will be reported in the following, reviewing more recent investigations [7–9] on an aluminium and a titanium alloy, considering that crack propagation in the VHCF regime is essentially determined not only by material inherent properties (chemical composition, yield strength, etc.) and loading conditions (load ratio) but also to a large degree on the surrounding environment. The experiments, reported in this study, were obtained at R = 1 with overaged 7075 alloy as representative for homogeneous slip aluminium alloys, as well as Ti–6Al– 4V alloy. Testing was performed at two frequencies (20 or 50 Hz and 20 kHz), and in addition the influence of the R-ratio was studied. Experiments at 20 Hz and 20 kHz were performed in ambient air and in vacuum to separate the different influences of load ratio, strain rate, air humidity and slip properties on near threshold fatigue crack growth. 2. Material and experimental procedure Results are presented for the wrought and overaged 7075 (7075-OA) as well as the Titanium alloy Ti–6Al–4V. The chemical composition of the 7075 alloy was (in wt%): Zn 7.2, Mg 2.8, Cu 1.7, Cr 0.06, Fe 0.3, Si 0.1, Mn 0.06, Ti 0.05, Ga 0.01, Zr 0.1. The alloy was solution annealed at 470 C, quenched and overaged by tempering at 107 C (8 h) plus 163 C (65 h). The resulting static properties are: Rm = 464 MPa, Rp0.2 = 524 MPa, A5 = 10.8%
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(with Rm = ultimate tensile stress, Rp0.2 = yield stress and A5 = tensile strain). The Ti–6Al–4V alloy was received as plate in solution-treated and overaged (STOA) condition. The chemical composition of Ti–6Al–4V was (in wt%): Al 6.30, V 4.17, Fe 0.19, O 0.19, N 0.013, H 0.0035, Ti balance. The alloy was solution-heat treated (1 h at 925 C) and vacuum annealed (2 h, 700 C). It consists of a bimodal distribution of approximately 60% primary a phase and approximately 40% lamellar colonies of a + b. Static strength properties of Ti–6Al–4Vp are: Rm = 970 MPa, Rp0.2 = 930 MPa, KIC = 67 MPa m and E = 116 GPa [7]. Specimens of the aluminium alloy were machined from rolled sheets of 20 mm thickness as standard middle tension (M(T) specimens [10]) for the servo-hydraulic tests. The thickness was 5 mm and centre notches were introduced using a saw and razor blades. The specimens were machined adequately to perform crack growth experiments in TL-direction (7075). Tube specimens were used in ultrasonic tests with length axis oriented in T-direction. A hole was drilled and a notch was introduced by spark erosion (with mineral oil as protective liquid) into the wall centre to cause crack initiation there (using spark erosion in order to avoid residual stresses introduced by mechanical notching). The cracks grew along the circumference of the tube in the plane of maximum normal stress with the crack front normal to the surface of the tube. The notch was positioned such that the crack growth direction at a crack length of 6 mm (without notch) was in TL-direction (7075). The specimen thickness was between 2 and 5mm and no pronounced effect of thickness could be detected [7]. The same specimen shape was used for the Ti–6Al– 4V [8]. Fatigue crack growth was investigated at load ratios R = 1, R = +0.05 and R = +0.5. Ultrasonic equipment appropriate to perform fatigue experiments at mean loads other than zero is described in detail in [5,15]. The experiments were performed in ambient air of 18–22 C and 40–60% relative humidity and alternatively in vacuum of maximum 3 · 103 Pa. Testing was performed with servohydraulic equipment at 20 Hz and with ultrasonic equipment at 20 kHz. In servo-hydraulic tests, specimens were cycled continuously, and in the ultrasonic experiments with pulses consisting of 1000 cycles and periodic pauses of 25– 100 ms to avoid rise of temperature. The maximum temperature of the specimens in servo-hydraulic tests was 30 C and 25 C in the ultrasonic experiments [9]. Fatigue crack growth is measured at the surface of the specimens using an optical microscope. Crack growth rates were determined as mean growth rates over crack length increments of 0.15–0.20 mm in servo-hydraulic as well as ultrasonic experiments. If fatigue cracks propagate first and stop then, the crack length increments during 1.5 · 106 cycles in servo-hydraulic tests, or 2 · 107 cycles in ultrasonic tests are used to calculate the mean growth rate. The stress intensity factor range, DK, was lowered until no crack growth could be observed within these
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numbers of cycles. With the optical resolution of 20 lm (in servo-hydraulic tests) and 7 lm (in ultrasonic tests), limiting hypothetical growth rates of 1.3 · 1011 m/cycle and 3.5 · 1013 m/cycle, respectively, serve to characterise arrest of fatigue crack growth. In servo-hydraulic experiments, a limiting growth rate of 1010 m/cycle was used to define a threshold according to the recommendations of ASTM [10], whereas in ultrasonic experiments threshold stress intensities were additionally determined at 3.5 · 1013 m/cycle. 3. Results The stress intensity factor range, DK, as well as Kmax has been used to present the fatigue crack growth data. DK was calculated according to DK ¼ K max K min ; where Kmax is the maximum stress intensity and Kmin is the minimum stress intensity of a cycle. For fully reversed loading (R = 1) this means, that DK = 2Kmax. This presentation was used in these studies instead of only counting the positive part of a load cycle at R = 1, i.e., DK = Kmax which is suggested by ASTM [10]. The two ways of presentation (DK or Kmax) will be discussed. 3.1. Influence of mean load and environment on fatigue crack growth and thresholds 3.1.1. (Da/DN vs. DK or Kmax) curves of 7075-OA, R = 1, +0.05, +0.5, vacuum Fig. 1 shows the FCGR’s and thresholds of the homogeneous slip 7075–OA alloy, obtained in vacuum and plotted vs. DK in Fig. 1a and vs. Kmax in Fig. 1b. The experiments were performed in vacuum at load ratios R = 1, +0.05 and +0.5 at ultrasonic testing frequency [7]. Arrows indi-
cate measurements with no visible crack growth within 2 · 107 cycles, resulting in threshold crack growth rates of 3.5 · 1013 m/cycle. Following results are obvious: The threshold values increase and the fatigue crack growth rates decrease with decreasing R-ratio, if plotted vs. DK. If Da/DN is plotted vs. Kmax instead of DK, the sequence of the curves is reversed, i.e., the threshold values increase and the fatigue crack growth rates decrease with increasing R-ratio. Crack propagation takes place at such low rates as 1011–1012 m/cycle, which is by a factor of 10–100 below a mean crack propagation rate of one lattice space per cycle. The correlating threshold values are at least 22% lower at a crack growth rate of 3.5 · 1013 than at 1010 m/cycle, which means that there is well pronounced cracking still in this VHCF crack growth regime. In addition, it has been shown [7] that an influence of testing frequency is absent, i.e., the curves of 20 Hz and 20 kHz measurement are almost identical. The fatigue crack growth rates in vacuum do not differ more than by a factor of 2, which is similar to the scatter of the results. This means that no strain rate influences were found in the inert environment. 3.1.2. (Da/DN vs. DK or Kmax) curves of 7075-OA, R = 1, +0.05, +0.5, ambient air Results of measurements in ambient air of 18–22 C and 40–60% relative humidity are shown in Fig. 2. Comparing fatigue crack propagation in ambient air with that in vacuum, a pronounced influence of air humidity is obvious. The threshold stress intensities at 3.5 · 1013 m/cycle in ambient air, for example, are approximately 60–70% lower than in vacuum, and threshold stress intensities at 1010 m/cycle are 45–55% lower than in the inert environment. 10-6
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Fig. 1. Influence of mean load on fatigue crack growth of 2075-OA in vacuum. Testing frequency: 20 kHz, R-ratios = 1, +0.05 and +0.5, vacuum of 103 Pa. Plot vs. DK (a) and plot vs. Kmax (b).
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Fig. 2. Influence of mean load on fatigue crack growth of 7075-OA in ambient air of 18–22C and 40–60% RH. Testing frequency: 20 kHz, R-ratios = 1, +0.05 and +0.5. Plot vs. DK (a) and plot vs. Kmax (b).
3.2. Influence of loading frequency on fatigue crack growth and thresholds of 7075-OA alloy in inert and corrosive environment at different mean loads Fig. 3 shows the FCGR curves for 7075-OA measured at a loading frequency of 20 Hz with servo-hydraulic equipment and at 20 kHz ultrasonic frequency in ambient air at a mean load of zero (R = 1). In addition, the curve, obtained in vacuum with ultrasonic equipment, is presented. Surprisingly, the threshold stress intensities, Kth,max (and likewise DKth [7]) at 1010 m/cycle measured with servohydraulic and with ultrasonic equipment are similar within the ranges of scatter in ambient air. Above threshold, however, a significant difference of growth rates determined at the two different testing frequencies is obvious. Mean growth rates in the range of 1010–108 m/cycle are found for R = 1 loading p and maximum stress intensities between 2.5 and 7 MPa m at ultrasonic frequency, whereas cycling at 20 Hz results in
10-6 Crack Growth Rate, a/ N, (m / Cycle)
The crack propagation curves measured in ambient air show a change of slope as the stress intensity approaches the threshold. Fatigue cracks grow with minimum mean growth rates of approximately 5 · 1011 m/cycle, or they remain arrested. These low growth rates are obtained by taking the mean value of actually measured crack propagation rates and arrests at a constant cyclic stress intensity. The values of the threshold stress intensities at 1010 m/ cycle at 3.5 · 1013 m/cycle in ambient air differ by approximately 10% only, which is less than in vacuum. If the Da/DN results are plotted vs. Kmax instead of DK (Fig. 2b),the sequence of the threshold values at different load ratios is reversed like in vacuum. At crack rates above threshold, in the range of 1010–108 m/cycle, however, the curves coincide for the three R-ratios.
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Fig. 3. Influence of testing frequency (20 kHz – open symbols and 20 Hz – closed symbols) on FCGR’s in ambient air at R = 1 in 7075-OA.
approximately a factor 10–50 higher growth rates. This shows that the corrosive influence of ambient air at the ultrasonic frequency is smaller than at conventional testing frequencies at stress intensities above threshold. 3.3. Fracture morphology The influence of environment on the fracture surface appearance is documented in Fig. 4. It shows the border of a fracture surface of a 7075-OA specimen, which was cycled at R = 1 at ultrasonic frequency in ambient air first, with decreasing cyclic stress intensity until the threshold was reached. The left side of Fig. 4 shows the resulting fracture surface. Mainly transcrystalline fracture features with a low portion of plastic deformation are visible and in addition some intergranular brittle fracture features
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Fig. 4. Fracture surface of alloy 7075-OA after near-threshold loading at 20 kHz ultrasonic frequency at R = 1 in ambient air (left side) and in vacuum (right side). Crack growth direction from left to right.
(elongated grains in L direction), which cause a slightly rougher fracture. After evacuating the vacuum chamber, loading was continued in vacuum at a near threshold cyclic stress intensity causing crack growth rates of 1011–1010 m/cycle. The correlating fracture surface is visible at the right side of Fig. 4 showing ductile transcrystalline fracture features. No essential influence by the load ratio could be observed [7]. 3.4. (Da/DN vs. DK or Kmax) curves of Ti–6Al–4V, tested in ambient air Fatigue crack growth in Ti–6Al–4V alloy at load ratios R = 1, +0.1 and +0.8 in ambient air, measured at 20 kHz and 50 Hz is shown in Fig. 5. The 50 Hz data were determined by Boyce and Ritchie [16] with material of the same lot as used for the ultrasonic measurements [12].
Identical thresholds are detected with ultrasonic 20 kHz equipment and by servo-hydraulic 50 Hz measurement. Higher fatigue crack growth rates, however, between 1010 and 108 m/cycle are found at ultrasonic frequency at the investigated R-ratios of +0.1 and +0.8. In order to analyse the load ratio influence, the Da/DN data are plotted vs. the positive part of a load cycle, Kmax, instead of the amplitude of loading, DK, for a loading frequency of 20 kHz in Fig. 6. Coinciding fatigue crack growth curves above approximately 3 · 1010 m/cycle are obtained with this, but a lower threshold stress intensity, Kmax,th at R = 1 than at R = +0.1 results. For R = +0.8, the curve is shifted at whole towards higher Kmax values. Fig. 7 shows the variation of the cyclic (DKth) as well as the maximum values (Kth,max) of the stress intensity thresh-
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R=-1
R=0.1
R=0.8
-14
10
1
5 7 3 Maximum Stress Intensity Factor, K
10
2
20 1/2
, (MPam )
max
Fig. 6. Fatigue crack growth in Ti–6Al–4V at 20 kHz loading frequency in ambient air at R-ratios = 1, +0.1 and +0.8. Plot vs. Kmax.
Crack Growth Rate, a/ N, (m / Cycle)
10-7 Ti6Al4V Ambient Air
10-8 10-9 10-10 10-11 10-12
20 kHz
10-13 R=0.8
10-14
1
2
R=0.1 R=-1
3
5
50 Hz 7
10
20 1/2
Stress Intensity Factor Range, K, (MPam ) Fig. 5. Influence of loading frequency (20 kHz – open symbols, 50 Hz – closed symbols [12]) on fatigue crack growth in Ti–6Al–4V in ambient air at R-ratios = 1, +0.1 and +0.8.
Fig. 7. Variation of DK and Kmax thresholds of Ti–6Al–4V with load ratio. Testing frequency: 20 kHz; ambient air.
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olds for different positive mean loads. With increasing R values, decreasing cyclic stress intensities are necessary to propagate a fatigue crack, and at R-ratios above +0.5 the needed tensile portions are rather high in order to obtain crack growth. 4. Discussion Strain rate (frequency) effects, load ratio and environmental influences on fatigue crack growth in 7075 OA and Ti–6Al–4V are discussed in the following. 4.1. Vacuum-crack growth rates below 1010 m/cycle Most interesting is the non-existence of a crack growth threshold value in the range of one lattice space per cycle (several 1010 m/cycle), which would be the physically meaningful value being expected. Performing threshold measurements at ultrasonic frequencies allows to reach lower threshold crack growth rates, e.g., 5 · 1013 m/cycle. This non-existence of thresholds in the range of several 1010 m/cycle has been detected for numerous other materials, as reported earlier [17]. The non-existence of a threshold at approximately 1010 m/cycle and its shift into the range of 1011–1013 m/cycle leads to cyclic stress intensity thresholds being approximately 25% lower than assumed before, which is of high practical relevance. 4.2. Influence of ambient air environment
*
mechanisms
Crack growth rates increase and threshold stress intensities decrease in Aluminium alloys reported in this and former papers [7,12,13], if cycled in ambient air instead of vacuum, since moisture acts as a corrosive environment. Moisture decreases the cyclic plastic strain that a crack tip can endure. Water vapour of ambient air is transported to the crack tip by diffusion where chemical processes with newly created fracture surfaces lead to the formation of hydroxide, hydrated oxides and the release of hydrogen [18]. Loading frequency and partial pressure of water vapour control the surface reaction at the crack tip. Embrittling is explained by hydrogen adsorption at the surface or in the first few atomic layers, where it facilitates dislocation nucleation [19]. Diffusion of hydrogen ahead of the crack tip [20,21] is reported, which is supported by dragging by mobile dislocations [22]. The influence of humidity on fatigue crack propagation in aluminium alloys does not only depend on chemical composition, grain size, load ratio and yield strength, but also on their slip properties [23,24]. In 7075, under- or peak-ageing favours planar slip and crystallographic (stage I-like [24]) fatigue crack propagation at low stress intensities in inert environment whereas over-ageing promotes homogeneous slip and stage II crack propagation. The homogeneous slip material was found to be less susceptible to embrittling by air humidity than the same material heat-treated to promote planar slip [23,24].
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Diffusion of water molecules as well as surface reaction kinetics are time dependent processes, and it may be assumed therefore that the loading frequency influences the material response. Experiments with wrought aluminium 2024-T3 [25], 7075-T6 [26] and cast aluminium AlSi9Cu3 [27] showed that air humidity influences fatigue crack growth at ultrasonic frequencies at a load-ratio of R = 1, if growth rates are small, i.e., below approximately 2 · 109 m/cycle. Similarly, influences of air humidity or aqueous environment on ultrasonic fatigue crack growth were detected in austenitic and ferritic steels, copper [28] and in magnesium alloys [27] at very low growth rates and cyclic stress intensities close to the threshold. 4.3. Ambient air – no frequency influence on threshold values It is interesting to note that identical thresholds are obtained with loading frequencies of 20 Hz and 20 kHz for the aluminium alloy 7075 [7] and Ti–6Al-4, though humidity has a pronounced influence on fatigue crack growth. Threshold stress intensities of 7075 OA at R = 1, R = +0.05 and R = +0.5 at 1010 m/cycle are 58–79% of the respective values measured in vacuum, and the threshold stress intensity values at 5 · 1013 m/cycles are 54–78% of those in vacuum. The threshold stress intensities are lower at 5 · 1013 m/cycles than at 1010 m/cycles in air as well as in vacuum, but the difference between these two values is larger in vacuum than in air, since slow crack propagation instead of crack arrest is more pronounced in vacuum than in air in the crack growth regime below one atomic distance per cycle. Minimum mean growth rates in ambient air are approximately 5 · 1011 m/cycle, whereas cracks may still propagate at mean growth rates of 5 · 1012 m/cycle in vacuum. 4.4. Ambient air – crack growth in the regime above threshold – frequency influence Above threshold, however, slower fatigue crack growth rates at 20 kHz than at 20 Hz are observed in all materials tested until now besides the Ti–6Al–4V alloy. This effect is most pronounced at a load ratio R = 1 and becomes smaller at higher load ratios. The frequency influence in humid air may be attributed to shorter duration of a cycle at ultrasonic frequency in comparison to a lower frequency. One time governing process for the environment to become effective, is adsorption, i.e., the possibility to build-up a gas mono-layer at the crack tip [24,29,32]. Another time governing process is bulk diffusion of hydrogen together with the interaction with dislocations, assuming that hydrogen enters the material at the crack tip. Third, surface diffusion of water vapour to the crack tip could be a time limiting process [29]. Estimations of the upper limit of growth rates that allow environmental reactions at the crack tip at the ultrasonic frequency with a crack opening time of 2.5 · 105 s are treated in the following. It will be shown that this is approximately 1 · 109 m/
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cycle, if surface coverage by water vapour molecules is postulated and is approximately in the same range, if bulk diffusion of hydrogen (without dislocation interaction) is considered at the ultrasonic loading frequency of 20 kHz. Surface diffusion of water vapour, however, is estimated to be fast enough to not act as a time limiting process. (i) In order to estimate the time ts needed to generate a gas mono-layer at the crack tip (crack front) by adsorption, the Langmuir equation may be used. The relative humidity of ambient air at 20 C was 40–60% in the experiments of this work, so that the partial pressure of water vapour was 1200 Pa. This results in a time ts needed to form a water vapour mono-layer of ts 10 ls: The crack opening or exposure time tE may be written as tE ¼ d=2ðDa=DN Þ f ; where d is the lattice constant. A mono-layer can be built up only, if tE P ts : For d = 4 · 1010 m (aluminium) and f = 20 kHz an upper limit of the crack growth rate, below which a monolayer can be formed, Da/DN = d/2f Æ ts will be Da=DN 109 m=cycle: This is an approximation only as it is not known how high the sticking probability has to be to cause an environmental influence, i.e., if the mono-layer has to be built up completely; it has been assumed 0.3 in this study. The influence of the load ratio may be attributed to the longer time a crack is open during a load cycle at higher load ratio [6]. At 20 Hz, full surface coverage may be expected irrespective of load ratio at 1010 m/cycles, whereas at ultrasonic frequency the longer crack opening time at high load ratio is necessary to obtain a similar surface coverage at the same crack growth rate. (ii) If transport of hydrogen into the crack front volume by diffusion is assumed, the time t being needed by a molecule to pass a specified distance, could be grain boundary diffusion or bulk diffusion or diffusion determined by dislocation dragging. As a very rough and first approach, bulk diffusion without dislocation interaction has been considered as time governing process [29]. The bulk diffusion coefficient of hydrogen at room temperature was assumed be between DB ¼ 2 1013 and 1014 m2 =s according to [18]. The crack tip exposure time tE during one cycle is given by one half of the inverse frequency (at best the crack is open during the tensile part) tE ¼ 1=2f ¼ 2:5 105 s: Assuming this time to be available for diffusion of the molecules, a distance
x 7 1010 –3 109 m will be covered by them during one cycle. This means that an influence by hydrogen by bulk diffusion may be expected for crack growth rates, which are lower than (0.7– 3) · 109 m/cycle at a loading frequency of 20 kHz, which is by a factor of 2–7 above the threshold regime. If hydrogen diffusion by dislocation dragging rather than bulk diffusion of hydrogen is considered as the relevant mechanism at the crack tip, a diffusion coefficient of 1013 m2/s has been assumed for hydrogen in a-iron [21,22] as the needed time to attain a critical hydrogen concentration for metal embrittlement in front of the crack tip. An approach to calculate the critical crack growth rates to account for dislocation assisted hydrogen transport, should be considered. (iii) If the critical time for water vapour migration to the crack tip is estimated, surface diffusion may be considered as the rate controlling process. Literature values for diffusion constants are differing very much, but it may be assumed that surface diffusion constants are by orders of magnitude higher than the reported bulk diffusion constants between 1014 and 2 · 1013 m2/s. Therefore, the needed crack tip exposure time tE has to be at least 10 times lower than for bulk diffusion of hydrogen, and thus the critical crack growth rate could be at least 10 times higher (i.e., higher than approximately 108 m/cycle) in order to obtain water vapour influence. Therefore, this process is considered as a non-rate controlling mechanism, so that no limitation by the high ultrasonic frequency as to this environmental influence should be expected. Additional mechanisms are acting, like capillary sucking and pumping effects as well as discontinuous crack propagation, which probably change (raise) the critical crack growth rate, at which environmental effects would still become effective and thus could explain the experimental results showing that ambient air affects ultrasonic crack growth at such high growth rates as 2 · 108 m/cycle. Pumping of the environment into the crack tip region is effective by movement of the already formed fracture surfaces due to the tension-compression type of loading. Crack propagation in the threshold regime is discontinuous rather than a cycle by cycle process [6,30–32] taking place in specified areas only, while the crack is arrested in other parts of the crack front. It may be assumed therefore that water vapour reaches the crack tip during these arrest periods, so that actually higher mean crack growth rates than 109 m/cycle are sufficient to obtain an environmental interaction. These results are also in accordance with results of Henaff et al. [14], who studied fatigue crack growth at frequencies of 0.2–200 Hz at different low water vapour pressures. They showed, for example, that a water vapour pressure of 103 Pa is sufficient to obtain environmental effects at 10 Hz if growth rates are below 108 m/cycle. Performing ultrasonic experiments in ambient air, a load cycle is approximately a factor 1000 shorter, the water vapour pressure of 1200 Pa, however, is approximately a factor
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106 higher than the conditions studied by Henaff et al., so that the observed environmental interactions below 108 m/cycle are plausible. Experiments on 2024-T3 in dried air as surrounding environment at ultrasonic fatigue loading leads to a crack growth curve positioned between the vacuum and ambient air curves, showing lower crack growth rates than in humid air above approximately 109 m/cycle, but identical thresholds below 5 · 1012 m/ cycle [25] and thus confirm the above mentioned estimation. To summarise, the results of the above treated estimations of limiting crack growth rates plus additional effects, like capillary sucking and pumping effects as well as discontinuous crack propagation, demonstrate that an environmental influence may be expected at crack growth rates below some 108 m/cycle. It may be concluded that the environmental influence is fully pronounced at crack growth rates below at least approximately 109 m/cycle at a loading frequency of 20 kHz, so that the observed identical threshold values at 20 Hz and 20 kHz are plausible and not surprising.
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result is probably more pronounced crack tip blunting at this high R-ratio. Plotting the DKth and Kmax,th values vs. R [33] demonstrates that fatigue cracking is mainly controlled by the maximum values at low mean values up to approximately R = +0.6 and controlled mainly by the stress intensity ranges at higher R-values (Fig. 7). The same is true for the aluminium alloys, and there even at the negative load ratio of R = 1. Most important, no influence of frequency is detected in the threshold regime, as shown in Fig. 5 for the Ti–6Al–4V alloy. The higher growth rates above threshold in ultrasonic experiments, compared with cycling at 50 Hz, can neither be explained with environmental influences, nor with strain rate effects. Geometric influences as well as possible slight differences of the loading conditions (flat specimens with thickness 10 mm and crack lengths more than 10 mm in the 50 Hz experiments, tubular specimens with a wall thickness of 2 mm and crack lengths between 1.5 and 7.5 mm at 20 kHz) may have contributed to the observed difference of growth rates. 5. Conclusions
4.5. Influence of load ratio and testing frequency Comparing the plots of Da/DN vs. Kmax and, respectively, DK, leads to a reversed sequence of the curves, i.e., the threshold values of Kmax increase and the fatigue crack growth rates decrease with increasing R-ratio (Figs. 1 and 2) for the aluminium alloy 7075-OA being tested in vacuum as well as in ambient air. This result is similar to that on 13% Cr steel [17] (studied in ambient air), though the (Da/DN vs. Kmax) curves of this material are closer together. The decrease and, respectively, increase of the threshold values of DK and Kmax with load ratio is not only observed for positive R-ratios but also for 1. The curves remain separated in the plot vs. Kmax like in the plot vs. DK in the whole tested crack growth range including the Paris regime, if the experiments are performed in vacuum (Fig. 1), whereas in ambient air, the curves coincide above the threshold regime, at crack growth rates between approximately 1010 and 108 m/cycle (7075-OA) (Fig. 2). This means that above threshold, obviously the tensile part of loading only is responsible for environmentally assisted fatigue crack propagation rates. Plotting the Da/DN curves of Ti–6Al–4V alloy vs. Kmax instead of DK leads to coinciding Da/DN values in a similar way, but only for the R-ratios R = 1 and +0.05 (up to R = +0.5, which is not shown in Fig. 6) at crack growth rates above threshold. A lower Kmax threshold, however, results for R = 1 than for R = 0.05. This means that the tensile part of cyclic loading controls crack propagation beyond the threshold regime, whereas in the threshold regime the compressive part of cycling at R = 1 is in addition effective, causing additional damage, probably by reducing the fracture surface roughness [8]. For R = +0.8 the whole curve is shifted towards higher Kmax values in comparison with the R = 1 curve. The reason for this
The ultrasonic fatigue testing technique allows extensive investigations of fatigue crack growth in the VHCF regime. Main results are: 1. In inert environment (vacuum), the dependence of crack growth on the cyclic stress intensity is similar at cyclic frequencies of 20 kHz and 20 (or 50) Hz in the investigated crack growth regime below approximately 108 m/cycle (7075-OA) and several 1010 m/cycle (Ti– 6Al–4V). This indicates that no intrinsic frequency, i.e., strain rate influence on thresholds and near threshold fatigue crack growth exists in the alloy aluminium 7075 and Ti–6Al–4V. 2. In inert environment, crack propagation is possible at such low growth rates as 3.5 · 1013 m/cycle, which means that thresholds for crack propagation (and respective DKth values) are lower than conventionally determined ‘‘threshold’’ values (in the range of several 1010 m/cycle). In this regime of very low crack growth rates, crack propagation is discontinuous. 3. Pronounced influence of air humidity on near-threshold fatigue crack growth is obvious at 20 kHz ultrasonic fatigue loading. Under fully reversed loading conditions, higher crack growth rates are observed in humid environment than in vacuum, and the slope of the Da/DNcurve is essentially smaller than in vacuum for the 7075-OA alloy. 4. The threshold stress intensities of the 7075-OA alloy, cycled in ambient air at R = 1, R = 0.05 and R = +0.5 at 1010 m/cycle are 54–78% of the respective values measured in vacuum. Under the influence of water vapour, eventual intercrystalline brittle fracturing is observed, whereas a smooth transcrystalline fracture mode is typical for vacuum.
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5. In ambient air, the threshold stress intensities of the aluminium alloy and the Ti–6Al–4V alloy are identical at 20 Hz and 20 kHz. At higher stress intensities, fatigue cracks propagate by a factor of 5–50 faster if cycled at 20 Hz instead of 20 kHz in 7075-OA. 6. Calculations, roughly estimating the rate controlling processes of water vapour and hydrogen diffusion as well as generation of a water vapour layer at the crack tip due to adsorption, prove that an environmental influence is fully effective even at the high ultrasonic frequency of 20 kHz at fatigue crack growth rates below approximately 109 m/cycle. 7. The compressive part of a load cycle leads to additional fatigue damage in the Ti–6Al–4V alloy. A possible mechanism is degradation of fracture surface asperities and resulting reduction of surface roughness. Acknowledgements Part of this work was performed as thesis by Dr. B. Holper within a project of ONR, USA and Dr. A.K. Vasudevan. Their financial support is gratefully acknowledged. In addition, cooperation with Prof. H. Mayer and helpful discussion with Prof. J. Petit is gratefully acknowledged. References [1] Sakai T, Sato Y, Oguma N. Characteristic S–N properties of highcarbon–chromium-bearing steel under axial loading in long-life fatigue. Fat Fract Eng Mater Struct 2002;25:765–73. [2] Mughrabi H. Mechanisms of fatigue failure in ultralong life regime. Fat Fract Eng Mater Struct 2002;25:755–64. [3] Murakami Y, Yokoyama NN, Nagata J. Mechanism of fatigue failure in ultralong life regime. Fat Fract Eng Mater Struct 2002;25:735–46. [4] Tanaka K, Akiniwa Y. Fatigue crack propagation behaviour derived from S–N data in very high cycle regime. Fat Fract Eng Mater Struct 2002;25:775H–84H. [5] Stanzl-Tschegg S, High-cycle crack growth in the Paris- and threshold regime at ultrasonic frequencies. In: Soboyejo WO, Srivatsan, editors. High cycle fatigue of structural materials, TMSASM symposium proceedings in honor of P. Paris. TMS, Warrendale; 1997. p. 211. [6] Stanzl S, Tschegg E. Measurement of fatigue crack propagation threshold and of growth rates below 1012 m/cycle by a time saving method. Metal Sci 1980;14(4):143–97. [7] Holper B, Mayer H, Vasudevan AK, Stanzl-Tschegg SE. Near threshold fatigue crack growth in aluminium alloys at low and ultrasonic frequency: Influences of specimen thickness, strain rate, slip behaviour and air humidity. Int J Fatigue 2003;25:397–411. [8] Laird C, Charsley P. Strain rate sensitivity effects in cyclic deformation and fatigue fracture ultrasonic fatigue, The Metallurgical Society of AIME, PA; 1982. p. 187. [9] Taylor D, Knott JF. The effect of frequency on fatigue crack propagation rate. Proceedings of the 6th international conference on fracture, vol. 3. Oxford: Pergamon Press; 1984. [10] Shih YS, Chen JJ. The frequency effect on the fatigue crack growth rate of 304 stainless steel. Nucl Eng Design 1999;191:225–30. [11] Baik YM, Kim KS. The combined affect of frequency and load level on fatigue crack growth in stainless steel 304. Int J Fatigue 2001;23:417–25.
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