Cycle-dependent Crack Growth Research Articles

A phase-field model for fatigue crack growth

A phase-field model is presented for the study of fatigue crack growth. A crack growth viscosity parameter is introduced into the standard phase-field model for brittle fracture to account for rate- or cycle-dependent crack growth phenomena. A modified J-integral is developed to demonstrate how the phase-field approach can be used to generate Paris-law type crack growth rates. In order to model more general crack growth versus applied loading behaviors that are not a single simple Paris-law, steady-state finite element calculations are performed to calibrate fits of the phase-field model to measured crack growth rates found in da/dN versus ΔK curves. Transient time- or cycle-dependent calculations are performed and compared to experimental measurements on samples where crack turning is induced by the presence of a hole in the vicinity of the crack. A three-dimensional example with turning of the crack front is also computed illustrating the capabilities of the phase-field approach for complex crack paths.

Thermomechanical fatigue crack growth in a single crystal nickel base superalloy

Thermomechanical fatigue crack growth in a single crystal nickel base superalloy was studied. Tests were performed on single edge notched specimens, using in phase and out of phase thermomechanical fatigue cycling with temperature ranges of 100–750 °C and 100–850 °C and hold times at maximum temperature ranging from 10 s to 6 h. Isothermal testing at 100 °C, 750 °C and 850 °C was also performed using the same test setup. A compliance-based method is proposed to experimentally evaluate the crack opening stress and thereby estimate the effective stress intensity factor range ΔKeff for both isothermal and nonisothermal conditions. For in phase thermomechanical fatigue, the crack growth rate is increased if a hold time is applied at the maximum temperature. By using the compliance-based crack opening evaluation, this increase in crack growth rate was explained by an increase in the effective stress intensity factor range which accelerated the cycle dependent crack growth. No significant difference in crack growth rate vs ΔKeff was observed between in phase thermomechanical fatigue tests and isothermal tests at the maximum temperature. For out of phase thermomechanical fatigue, the crack growth rate was insensitive to the maximum temperature and also to the length of hold time at maximum temperature. The crack growth rate vs ΔKeff during out of phase thermomechanical fatigue was significantly higher than during isothermal fatigue at the minimum temperature, even though the advancement of the crack presumably occurs at the same temperature. Dissolution of γ′ precipitates and recrystallization at the crack tip during out of phase thermomechanical fatigue is suggested as a likely explanation for this difference in crack growth rate.

A frequency dependent embrittling effect of high pressure hydrogen in a 17-4 PH martensitic stainless steel

The effects of hydrogen on tensile and fatigue-life properties of 17-4PH H1150 steel have been investigated by using a smooth, round-bar specimen for tensile tests and circumferentially-notched specimen for fatigue-life tests. The specimens were precharged by an exposure to 35-100 MPa hydrogen gas at 270°C for 200 h. For the 100 MPa hydrogen exposure, the steel showed a significant degradation in ductility loss, translated by a relative reduction in area, RRA, of 0.31. The fatigue-life test of the present notch specimen (stress concentration factor of 6.6) reflects the fatigue crack growth (FCG) for long cracks. The fatigue limit of the non-charged and H-charged notched specimens, defined by the threshold of non-propagation for long cracks, was not affected by hydrogen. At a higher stress amplitude, the H-charged specimen showed a significant FCG acceleration ratio compared to the non-charged specimen. Although, an upper bound of the FCG acceleration seemed to exist, this ratio was approximately 100. The fracture surface of the H-charged specimen was covered with quasi-cleavage (QC) at a lower stress amplitude and with a mixture of QC and intergranular (IG) facets at higher stress amplitudes. It has been suggested that a cycle-dependent crack growth accompanied by QC occurs at a lower stress amplitude, whereas a mixture of cycle-dependent crack growth (accompanied by QC) and time-dependent crack growth (accompanied by IG) occurs otherwise. This mixture justifies the 100 times FCG acceleration ratio in spite of the existence of the upper bound.

Mechanistic modelling of time-dependent fatigue crack growth in Ni-based superalloys

Advanced Ni-based superalloys for aero-engine disk applications can experience multiple damage mechanisms that include oxidation, creep and stress corrosion in additional to cycle-dependent fatigue crack initiation and growth. Interactions of these various damage mechanisms can lead to the occurrence of frequency, temperature, heat dwell and environmental effects on the fatigue crack growth response and service life of Ni-based superalloys. In this overview paper, the development of a set of generic microstructure-based fatigue crack growth models for treating concurrent time-dependent and cycle-dependent damage mechanisms at the microstructural levels is summarised. Key features of the mechanistic models are highlighted and utilised to assess the variability of time-dependent fatigue crack growth response in the threshold and power-law regimes due to variations in microstructure such as grain size, and γ′ size. This methodology provides a pathway for evaluating microstructural effects on multiple damage modes and extending the service lives of hot-section components.

Mitigating time-dependent crack growth in Ni-base superalloy components

Advanced Ni-based gas turbine disks are expected to operate at higher service temperatures in aggressive environments for longer time durations. Exposures of Ni-base alloys to these aggressive environments can lead to cycle-dependent and time-dependent crack growth in superalloy components for advanced turbopropulsion systems. In this article, the effects of tertiary γ′ on the crack-tip stress relaxation process, oxide fracture and time-dependent crack growth kinetics are treated in a micromechanical model which is then incorporated into the DARWIN® probabilistic life-prediction code. Using the enhanced risk analysis tool and material constants calibrated to powder-metallurgy (PM) disk alloy ME3, the effects of grain size and tertiary γ′ size on combined time-dependent and cycle-dependent crack growth in a PM Ni-alloy disk is demonstrated for a generic rotor design and a realistic mission profile using DARWIN. The results of this investigation are utilized to assess the effects of controlling grain size and γ′ size on the risk of disk fracture and to identify possible means for mitigating time-dependent crack growth (TDCG) in hot-section components.

Development of a Probabilistic Methodology for Predicting Hot Corrosion Fatigue Crack Growth Life of Gas Turbine Engine Disks

Advanced Ni-based gas turbine disks are expected to operate at higher service temperatures in aggressive environments for longer time durations. Exposures of Ni-based alloys to alkaline-metal salts and sulfur compounds at elevated temperatures can lead to hot corrosion fatigue crack growth in engine disks. Type II hot corrosion involves the formation and growth of corrosion pits in Ni-based alloys at a temperature range of 650 °C to 750 °C. Once formed, these corrosion pits can serve as stress concentration sites where fatigue cracks can initiate and propagate to failure under subsequent cyclic loading. In this paper, a probabilistic methodology is developed for predicting the corrosion fatigue crack growth life of gas turbine engine disks made from a powder-metallurgy Ni-based superalloy (ME3). The key features of the approach include: (1) a pit growth model that describes the depth and width of corrosion pits as a function of exposure time, (2) a cycle-dependent crack growth model for treating fatigue, and (3) a time-dependent crack growth model for treating corrosion. This set of deterministic models is implemented into a probabilistic life-prediction code called DARWIN. Application of this approach is demonstrated for predicting corrosion fatigue crack growth life in a gas turbine disk based on the ME3 properties from the literature. The results of this study are used to assess the conditions that control the transition of a corrosion pit to a fatigue crack and to identify the pertinent material parameters influencing corrosion fatigue life and disk reliability.

A Microstructure-Based Time-Dependent Crack Growth Model for Life and Reliability Prediction of Turbopropulsion Systems

The objective of this investigation was to develop an innovative methodology for life and reliability prediction of hot-section components in advanced turbopropulsion systems. A set of generic microstructure-based time-dependent crack growth (TDCG) models was developed and used to assess the sources of material variability due to microstructure and material parameters such as grain size, activation energy, and crack growth threshold for TDCG. A comparison of model predictions and experimental data obtained in air and in vacuum suggests that oxidation is responsible for higher crack growth rates at high temperatures, low frequencies, and long dwell times, but oxidation can also induce higher crack growth thresholds (ΔKth or Kth) under certain conditions. Using the enhanced risk analysis tool and material constants calibrated to IN 718 data, the effect of TDCG on the risk of fracture in turboengine components was demonstrated for a generic rotor design and a realistic mission profile using the DARWIN® probabilistic life-prediction code. The results of this investigation confirmed that TDCG and cycle-dependent crack growth in IN 718 can be treated by a simple summation of the crack increments over a mission. For the temperatures considered, TDCG in IN 718 can be considered as a K-controlled or a diffusion-controlled oxidation-induced degradation process. This methodology provides a pathway for evaluating microstructural effects on multiple damage modes in hot-section components.

Transient Crack Growth Behavior Under Cycle/Time-Dependent Step Loading for Pb-Containing and Pb-Free Solders

In the present study, fatigue crack growth tests of Pb-containing [Sn-37Pb (wt.%)] and Pb-free [Sn-3.0Ag-0.5Cu (wt.%)] solders were performed under cycle/time-dependent step loading at a constant J-integral range (ΔJ). The C* parameter was also estimated for discussing time-dependent crack growth behavior. The experimental results indicated that acceleration of the crack growth rate at the beginning of the second loading step was induced when the C* value for the first loading step was high, regardless of time- or cycle-dependent crack growth and for both Sn-37Pb and Sn-3.0Ag-0.5Cu solders. The length of the acceleration region of the crack growth rate for both solders was in good agreement with the creep damage zone size estimated by the creep zone model proposed by Riedel and Rice.

Grain size effects in a Ni-based turbine disc alloy in the time and cycle dependent crack growth regimes

The fatigue crack growth (FCG) behaviour in a Ni-based turbine disc alloy with two grain sized variants, in a low solvus high refractory (LSHR) superalloy has been investigated under a range of temperatures (650–725°C) and environments (air and vacuum) with trapezoidal waveforms of 1:1:1:1 and 1:20:1:1 durations at an R=0.1. The results indicate that a coarse grained structure possesses better FCG resistance due to the enhanced slip reversibility promoted by planar slip as well as the reduction in grain boundary area. The fatigue performance of the LSHR superalloy is significantly degraded by the synergistic oxidation effect brought about by high temperature, oxidising environment and dwell at the peak load, associated with increasingly intergranular fracture features and secondary grain boundary cracking. Secondary cracks are observed to be blocked or deflected around primary γ′, carbides and borides, and their occurrence closely relates to the roughness of the fracture surface, FCG rate and grain boundary oxidation. The apparent activation energy technique provides a further insight into the underlying mechanism of the FCG under oxidation–creep–fatigue testing conditions, and confirms that oxidation fatigue is the dominant process contributing to the intergranular failure process. At high enough crack growth rates, at lower temperatures, cycle dependent crack growth processes can outstrip crack-tip oxidation processes.

Life Prediction for Turbopropulsion Systems Under Dwell Fatigue Conditions

The objective of this investigation was to develop an innovative methodology for life and reliability prediction of hot-section components in advanced turbopropulsion systems. A set of three generic time-dependent crack growth models was implemented and integrated into the Darwin® probabilistic life-prediction code. Using the enhanced risk analysis tool and material constants calibrated to IN 718 data, the effect of time-dependent crack growth on the risk of fracture in a turboengine component was demonstrated for a generic rotor design and a realistic mission profile. The results of this investigation confirmed that time-dependent crack growth and cycle-dependent crack growth in IN 718 can be treated by a simple summation of the crack increments over a mission. For the temperatures considered, time-dependent crack growth in IN 718 can be considered as a K-controlled environmentally-induced degradation process. Software implementation of the generic time-dependent crack growth models in Darwin provides a pathway for potential evaluation of the effects of multiple damage modes on the risk of component fracture at high service temperatures.

Crack growth in a new nickel-based superalloy at elevated temperature

Crack growth at elevated temperature has been examined in a new fine-grained nickel-based superalloy under triangular, fast-slow, slow-fast, dwell and sustained loading conditions at 650 and 725∘C. The effect of loading waveform seems to be minimal for base frequencies over 0.01 Hz with a mixture of time and cycle dependent crack growth observed for all but the fast-slow waveform, where the crack growth remained cycle-dependent and the crack growth rate mostly constant. For base frequencies less than 0.01 Hz, crack growth under dwell load clearly accelerated and the crack growth rates were comparable with those under sustained load. Creep contribution was found to be negligible while crack tip constraint may be relevant to the out-of-plane crack growth observed under predominantly sustained load conditions.

Aspects of in vitro fatigue in human cortical bone: time and cycle dependent crack growth

Although fatigue damage in bone induced by cyclic loading has been recognized as a problem of clinical significance, few fracture mechanics based studies have investigated how incipient cracks grow by fatigue in this material. In the present study, in vitro cyclic fatigue experiments were performed in order to quantify fatigue-crack growth behavior in human cortical bone. Crack-growth rates spanning five orders of magnitude were obtained for the extension of macroscopic cracks in the proximal-distal direction; growth-rate data could be well characterized by the linear-elastic stress-intensity range, using a simple (Paris) power law with exponents ranging from 4.4 to 9.5. Mechanistically, to discern whether such behavior results from “true” cyclic fatigue damage or is simply associated with a succession of quasi-static fracture events, cyclic crack-growth rates were compared to those measured under sustained (non-cyclic) loading. Measured fatigue-crack growth rates were found to exceed those “predicted” from the sustained load data at low growth rates (∼3×10−10 to 5×10−7 m/cycle), suggesting that a “true” cyclic fatigue mechanism, such as alternating blunting and re-sharpening of the crack tip, is active in bone. Conversely, at higher growth rates (∼5×10−7 to 3×10−5 m/cycle), the crack-growth data under sustained loads integrated over the loading cycle reasonably predicts the cyclic fatigue data, indicating that quasi-static fracture mechanisms predominate. The results are discussed in light of the occurrence of fatigue-related stress fractures in cortical bone.

Creep, fatigue and oxidation in crack growth in advanced nickel base superalloys

This paper presents some of our recent results from an ongoing collaborative research programme on creep-fatigue behaviour of two advanced nickel base superalloys for turbine disc applications. The role of creep, fatigue and oxidation in crack growth has been investigated at 650°C under typical loading waveforms at selected loading frequencies. Load-line deflections were monitored in selected tests under static and long dwell loading conditions. Scanning electron microscopy was adopted to identify the fracture mode and to facilitate the evaluation of oxidation. The results show that mixed time and cycle dependent crack growth seems to be the predominant crack growth mode in the two PM nickel alloys studied. Whilst limited creep may be present at the crack tip, particularly under static and long dwell loading conditions, oxidation appears to be the predominant mechanism for crack growth under the test conditions examined.

Fatigue crack growth behavior of 95Pb–5Sn solder under various stress ratios and frequencies

Fatigue crack growth tests of 95Pb–5Sn solder have been carried out at frequencies from 0.01 to 10 Hz and at stress ratios from 0.1 to 0.7. It was found that the stress ratio had no influence on fatigue crack growth behavior under the frequency of 10 Hz due to cycle-dependent crack growth without crack closure. The fracture manner was changing from transgranular to intergranular with decreasing frequency. Fatigue crack growth under the frequency of 0.01 Hz was predominantly intergranular and time-dependent, while that under frequencies of 1 and 0.1 Hz was of mixed type but still cycle-dependent. Dynamic recrystallization occurred during fatigue crack growth tests; the initial grain size was about 50 to 100 μm and that after testing was about 10 to 15 μm. This phenomenon will have a significant influence on the intergranular crack growth behavior.

Environmentally assisted crack growth in a Ni–18Cr–18Fe ternary alloy at elevated temperatures

Fatigue crack growth experiments were conducted on a Ni–18Cr–18Fe ternary alloy under trapezoidal loading, in high-purity argon and oxygen at 873, 923 and 973 K, as a part of a broader study to elucidate the mechanism and rate controlling process for crack growth in nickel-base superalloys. The data were analyzed in terms of a new superposition model which facilitates the decomposition of data into the time-dependent and cycle-dependent contributions, as well as the respective mechanical and environmental components. The results demonstrated the effectiveness of the model, and showed that oxygen only affected cycle-dependent (or fatigue) crack growth, increasing the growth rates by about 2X. The time-dependent (or sustained-load) crack growth was principally associated with grain boundary cavitation and controlled by creep at these temperatures, with an apparent activation energy of 210±10 kJ mol−1. These results suggest that the pressure mechanism proposed by Bricknell and Woodford for oxygen enhanced crack growth in nickel-base superalloys did not operate at these temperatures. The near absence of environmental sensitivity in this Nb-free, Ni–Cr–Fe ternary alloy suggested the internal oxidation of Ni, Cr and Fe was not a significant contributor to the enhancement of crack growth. The results, instead, provided complementary support for the embrittling role of Nb that had been proposed by Gao et al.

Effect of temperature on small fatigue crack growth in nickel-base superalloys : Okazaki, M., Nohmi, S. and Yamada, H. J. Soc. Mater. Sci., Jpn. (1995) 44 (498), 348–354

This paper presents some of our recent results from an ongoing collaborative research programme on creep-fatigue behaviour of two advanced nickel base superalloys for turbine disc applications. The role of creep, fatigue and oxidation in crack growth has been investigated at 650°C under typical loading waveforms at selected loading frequencies. Load-line deflections were monitored in selected tests under static and long dwell loading conditions. Scanning electron microscopy was adopted to identify the fracture mode and to facilitate the evaluation of oxidation.The results show that mixed time and cycle dependent crack growth seems to be the predominant crack growth mode in the two PM nickel alloys studied. Whilst limited creep may be present at the crack tip, particularly under static and long dwell loading conditions, oxidation appears to be the predominant mechanism for crack growth under the test conditions examined.

クリープ温度領域における疲労き裂伝ぱとその下限界

An experimental study was made on fatigue crack growth in SUS304 stainless steel at 650°C for stress ratios R in the range of -0.2≤R≤0.4. The behaviors of near-threshold fatigue crack growth and the associated crack closure in this range were compared with those obtained previously for R≤-0.4 and 0.5≤R. The crack closure was observed for -0.2≤R≤0.4 under the creep-fatigue conditions employed. The R value had a significant effect on the relationship between the cycle-dependent crack growth rate da/dN and stress intensity range ΔK as well as on the value of fatigue crack growth threshold ΔKth for -0.2≤R≤0.4. When the J-integral range ΔJf, eff, in which the effect of crack closure was taken into account, was used instead of ΔK, the R dependence was eliminated, and the da/dN-ΔJf, eff relationship and the threshold value (ΔJf, eff)th were consistent with those obtained under 0.5≤R and R≤-0.4.To investigate the character of the fatigue crack growth threshold in the creep regime, crack growth experiments were made using two-step varying loads, in which high load-range blocks were introduced periodically in sub-threshold low load-range sequences. To exclude the effect of crack closure, high stress ratios were employed. It was found that, when the number of load excursions in the high load-range block used in the experiments was small, the threshold was extinguished: cracks grew even under load-ranges lower than the threshold value obtained under constant-amplitude loading conditions. A modified Miner's rule was found to give a reasonable estimate of the crack growth rate under two-step varying loading conditions.

Dynamic recrystallization during high temperature fatigue

Fatigue crack growth tests of 95Pb–5Sn solder have been carried out at frequencies from 0.01 to 10 Hz and at stress ratios from 0.1 to 0.7. It was found that the stress ratio had no influence on fatigue crack growth behavior under the frequency of 10 Hz due to cycle-dependent crack growth without crack closure. The fracture manner was changing from transgranular to intergranular with decreasing frequency. Fatigue crack growth under the frequency of 0.01 Hz was predominantly intergranular and time-dependent, while that under frequencies of 1 and 0.1 Hz was of mixed type but still cycle-dependent. Dynamic recrystallization occurred during fatigue crack growth tests; the initial grain size was about 50 to 100 μm and that after testing was about 10 to 15 μm. This phenomenon will have a significant influence on the intergranular crack growth behavior.

クリープ条件下の疲労き裂伝ぱ下限界挙動とき裂開閉口

The fatigue crack growth behavior of SUS 304 stainless steel at 650°C was investigated under low stress ratios R on the basis of the non-linear fracture mechanics. Emphasis was placed upon the near-threshold fatigue crack growth behavior and crack closure under creep conditions. It was found that in the very low da/dN region and the high da/dN region the relation between the cycle-dependent crack growth rate da/dN and stress intensity factor range ΔK obtained for -1≤R<0.2 deviated from the same correlation obtained under 0.5≤R. The values of fatigue threshold ΔKth for low R were much greater than those obtained for high R. Such a strong R dependence of the crack growth behavior found in the low R region was eliminated by the use of J-integral range ΔJf, eff, in which the effect of crack closure as well as that of material non-linearity were taken into account. The near-threshold crack growth behavior was found to be very sensitive to the loading history including frequency. This was rationalized in terms of the effect of oxide-induced crack closure enhanced by fretting as well as that of time-dependent creep deformation.

クリープ条件下の疲労き裂伝ぱにおける特異な下限界特性とフラクトグラフィ

Fatigue crack growth in SUS 304 stainless steel was investigated at 650°C under trapezoidal and sinusoidal stress waves. Special attention was placed upon the interrelation between the high-temperature fatigue crack growth behavior and fractographs. At high and intermediate crack growth rates, ΔJf (J integral range)-controlled cycle-dependent crack growth mode and J' (modified J integral)-controlled time-dependent crack growth mode were observed, which yielded transgranular and intergranular cracking, respectively. At low crack growth rates, a threshold of ΔJf was found to exist, below which the transgranular cycle-dependent crack growth mode vanished and the intergranular time-dependent crack growth mode emerged. This generated false fatigue thresholds, the levels of which were lower than the true one and arbitrary depending on the condition of stress cycling. In ΔJf (or stress intensity range ΔK) decreasing tests, fracture mode changed from transgranular to intergranular, in accordance with the transition from the cycle-dependent crack growth to the time-dependent one, which occurred when ΔJf crossed the true threshold.