Effects of stress ratio and temperature on fatigue crack growth in a Ti–6Al–4V alloy

Fatigue thresholds and fatigue crack growth (FCG) rates in corner notched specimens of a forged Ti–6Al–4V aero-engine disk material were investigated at room temperature and 350 °C. The threshold stress intensity range, ΔK_th, was determined by a method involving a step change in stress ratio (the ‘jump in’ method). It was found that for three high stress ratios (R=0.7–0.9), where crack closure effects are widely accepted to be negligible, there were similar ΔK_th values at room temperature and 350 °C under the same R. For a given temperature, ΔK_th was observed to decrease from 3.1 to 2.1 MPam with R increasing from 0.7 to 0.9. The fatigue crack growth rate was influenced by increasing temperature. For high stress ratios, FCG rate at 350 °C was higher than that at room temperature under the same ΔK. For a low stress ratio (R=0.01), higher temperature led to higher FCG rates in the near-threshold regime, but showed almost no effect at higher ΔK. The influence of stress ratio and temperature on threshold and FCG rates was analysed in terms of a K_max effect and the implication of this effect, or related mechanisms, are discussed. In light of this, an equation incorporating the effects of the K_max and fatigue threshold, is proposed to describe FCG rates in the near-threshold and Paris regimes for both temperatures. The predictions compare favourably with experimental data.     

On assumptions associated with ΔKeff and their implications on FCG predictions

In this paper, an assessment of commonly used assumptions associated with ΔK_eff and their implications on FCG predictions in light of existing experimental and numerical data is presented. In particular, the following assumptions are examined: (1). ΔK_eff fully describes cyclic stresses and strains at the crack-tip vicinity. (2). K_op can be determined experimentally or numerically with certain accuracy. (3). Overload alters K_op but not K_max and associated σ_max at the crack-tip ‘process zone’. (4). Contact of crack faces curtails the crack driving force in terms of ΔK_eff.The analysis indicates that there is insufficient support to justify the above assumptions. In contrary, the analysis demonstrates that a two-parameter fatigue crack driving force in terms of ΔK and K_max, which accounts for both applied and the internal stresses should be used in FCG analyses and predictions.     

Analysis of vacuum fatigue crack growth results and its implications

Conventionally, the reduction of ΔK_th with load ratio R has been interpreted in terms of crack closure arising from plasticity, oxide or crack surface roughness. Since, plane-strain conditions exist near-threshold, plasticity-induced closure is absent. Therefore, to account for R-ratio effects near-threshold, the oxide and roughness closure mechanisms have been proposed. Further analysis has shown that these other two closure effects also are small, when the results taken in vacuum were included. The present analysis shows that there is a unique relation of the oxide thickness with a threshold K_max, rather than with a threshold ΔK. This threshold K_max (K*_max,th) depends on environment. When the applied K_max<K*_max,th, the crack is stationary in the presence of the oxide formation and grows only when the applied K_max>K*_max,th. Thus, the oxide thickness—K_max relation seems to have a bearing on the criterion for crack growth in the presence of the environment. Oxide formation passivates the crack surfaces and retards the environmental damage ahead of the crack-tip. Examples from CrMo and NiCrMo steels support this viewpoint and suggest that there is a pressing need for quantifying the crack-tip environmental effects and fatigue thresholds.     

Micromechanisms of fatigue crack growth in a forged Inconel 718 nickel-based superalloy

The micromechanisms of fatigue crack propagation in a forged, polycrystalline IN 718 nickel-based superalloy are evaluated. Fracture modes under cyclic loading were established by scanning electron microscopy analysis. The results of the fractographic analysis are presented on a fracture mechanism map that shows the dependence of fracture modes on the maximum stress intensity factor, K_max, and the stress intensity factor range, ΔK. Plastic deformation associated with fatigue crack growth was studied using transmission electron microscopy. The effects of ΔK and K_max on the mechanisms of fatigue crack growth in this alloy are discussed within the context of a two-parameter crack growth law. Possible extensions to the Paris law are also proposed for crack growth in the near-threshold and high ΔK regimes.     

Classification of environmentally assisted fatigue crack growth behavior

Fatigue crack growth is represented using fracture mechanics parameters, ΔK and K_max. Environmental effects that depend on time and stress affect the fatigue behavior predominantly through K_max parameter. The superimposed effects of environment and stress are seemingly complex. We have developed a methodology for classifying and separating the effects of environment on fatigue crack growth. A “crack growth trajectory map” is constructed from the behavior of ΔK versus K_max for various constant crack growth rate curves. A “pure fatigue” behavior is defined, in terms of environment-free behavior, such as in high vacuum. Deviation from this “pure fatigue” reference of the trajectory map is associated with either monotonic mode of fracture or to the superimposed environmental effects on crack growth. Using such an approach, called “Unified Damage Approach”, we classify the environmental effects in almost all materials into only five types. Each of these types shows the combination of time and stress affecting the crack tip driving force, and thus ΔK and K_max. The trajectory map depicts the changing material resistance due to the changing crack growth mechanisms with increasing crack growth rate, as reflected in terms of the applied stress intensities, ΔK and K_max. Thus the trajectory map provides a useful tool to separate the contributions from pure fatigue and superimposed monotonic modes and the governing crack growth mechanisms as a function of load-ratio, crack growth rate and environment. Understanding and quantification of the governing mechanisms would help in developing a more fundamental and reliable life prediction method.     

Analyses of the fatigue crack propagation process and stress ratio effects using the two parameter method

In situ SEM observations (Zhang JZ. A shear band decohesion model for small fatigue crack growth in an ultra-fine grain aluminium alloy. Eng Fract Mech 2000;65:665–81; Zhang JZ, Meng ZX. Direct high resolution in-site SEM observations of very small fatigue crack growth in the ultra fine grain aluminium alloy IN 9052. Script Mater 2004;50:825–28; Halliday MD, Poole P, Bowen P. New perspective on slip band decohesion as unifying fracture event during fatigue crack growth in both small and long cracks. Mater Sci Technol 1999;15:382–90) have revealed that fatigue crack propagation in aluminium alloys is caused by the shear band decohesion around the crack tip. The formation and cracking of the shear band is mainly caused by the plasticity generated in the loading part of a load cycle. This shear band decohesion process has been observed to occur in a continuous way over the time period during the loading part of a cycle. Based on this observation, in this study, a new parameter has been introduced to describe fatigue crack propagation rate. This new parameter, da/dS, defines the fatigue crack propagation rate with the change of the applied stress at any moment of a stress cycle. The relationship between this new parameter and the conventional da/dN parameter which describes fatigue crack propagation rate per stress cycle is given.Using this new parameter, it is proven that two loading parameters are necessary in order to accurately describe fatigue crack propagation rate per stress cycle, da/dN. An analysis is performed and a general fatigue crack propagation model is developed. This model has the ability to describe the four general type of fatigue crack propagation behaviours summarised by Vasudevan and Sadananda (Vasudevan AK, Sadananda K. Fatigue crack growth in advanced materials. In: Fatigue 96, Proceedings of the sixth international conference on fatigue and fatigue threshold, vol. 1. Oxford: Pergamon Press; 1996. p. 473–8).     

Fretting fatigue crack analysis in Ti–6Al–4V

A study was conducted to verify the efficacy of a fracture mechanics methodology to model the crack growth behavior of fretting fatigue-nucleated cracks obtained under test conditions similar to those found in turbine engine blade attachments. Experiments were performed to produce cracked samples, and fretting fatigue crack propagation lives were calculated for each sample. Cracks were generated at 10⁶ cycles (10%-of-life) under applied stress conditions previously identified as the fretting fatigue limit conditions for a 10⁷ cycle fatigue life. Resulting cracks, ranging in size from 30 to 1200 μm, were identified and measured using scanning electron microscopy. Uniaxial fatigue limit stresses were determined experimentally for the fretting fatigue-cracked samples, using a step loading technique, for R=0.5 at 300 Hz. Fracture surfaces were inspected to characterize the fretting fatigue crack front indicated by heat tinting. The shape and size of the crack front were then used in calculating ΔKth values for each crack. The resulting uniaxial fatigue limit and ΔKth values compared favorably with the baseline fatigue strength (660 MPa) for this material and the ΔKth value (2.9 MPa√m) for naturally initiated cracks tested at R=0.5 on a Kitagawa diagram.Crack propagation lives were calculated using stress results of FEM analysis of the contact conditions and a weight function method for determination of ΔK. Resulting lives were compared with the nine million-cycle propagation life that would have been expected in the experiments, if the contact conditions had not been removed. Scatter in the experimental results for fatigue limit stresses and fatigue lives had to be considered as part of an explanation why the fatigue life calculations were unable to match the experiments that were modeled. Analytical life prediction results for the case where propagation life is observed to be very short experimentally were most accurate when using a coefficient of friction, μ=1.0, rather than for the calculations using μ=0.3     

Analysis of high temperature fatigue crack growth behavior

High temperature fatigue crack growth has been examined in the light of the new concepts developed by the authors. We observe that the high temperature crack growth behavior can be explained using the two intrinsic parameters ΔK and K_max, without invoking crack closure concepts. The two-parameter requirement implies that two driving forces are required simultaneously to cause fatigue cracks to grow. This results in two thresholds that must be exceeded to initiate the growth. Of the two, the cyclic threshold part is related to the cyclic plasticity, while the static threshold is related to the breaking of the crack tip bonds. It is experimentally observed that the latter is relatively more sensitive to temperature, crack tip environment and slip mode. With increasing test temperature, the cycle-dependent damage process becomes more time-dependent, with the effect that crack growth is dominated by K_max. Thus, in all such fracture processes, whether it is an overload fracture or subcritical crack growth involving stress corrosion, sustained load, creep, fatigue or combinations thereof, K_max (or an equivalent non-linear parameter such as J_max) remains as one essential driving force contributing to the final material separation. Under fatigue conditions, cyclic amplitude ΔK (or an equivalent non-linear parameter like ΔJ) becomes the second necessary driving force needed to induce the characteristic cyclic damage for crack growth. Cyclic damage then reduces the role of K_max required for crack growth at the expense of ΔK.     

A genetic algorithm for unified approach-based predictive modeling of fatigue crack growth

This paper presents a framework to derive models of fatigue crack growth in real-life applications based on the unified approach.The unified approach enunciates that two parameters-namely, the stress intensity amplitude ΔK and the peak stress intensity K_max-drive fatigue crack growth. It captures and explicates the various fatigue phenomena coherently. However, its application for damage prediction is still in its infancy. Mathematical models that are consistent with the approach and the various observed characteristics under various environments are imperative for fatigue damage life prediction. These models will reduce cumbersome experimentation that is usually needed for the fatigue crack growth analysis. The framework presented in this paper consists of using the unified approach to design the structure of a model that relates fatigue crack growth with the specified microstructure, applied stress and environmental conditions. The fatigue growth model is derived by parametrizing, using a genetic algorithm, these structural relationships from the known experimental data. This model can quantitatively estimate crack growth rate under the given combination of microstructure, applied stress and environmental conditions. The initial research on modeling fatigue crack growth dynamics in Al-5052 under vacuum and air has revealed that the models resulting from the framework can capture the actual crack growth pattern to within 12% accuracy, and that an automatic rendering of ΔK^* vs. trajectories is possible for a given material and environmental conditions.     

Analysis of crack propagation using ΔK and Kmax

In this investigation a general relationship between fatigue crack growth rate, da/dN, and a two-parameter ΔK and K_max driving force is derived using fundamental fatigue (ε–N curve) properties. A power-law relationship between ΔK and K_max is obtained by relating the crack growth rate to the fatigue life of the ‘process zone’. Theoretically, there are four different regions on a log–log plot depending on the particular combinations of ΔK and K_max. The actual analysis of experimental data indicates only two different regions namely, ΔK and K_max dominated, corresponding to high and low load ratios, respectively. A new way of representing the da/dN data in terms of ΔK and K_max by means of the crack propagation (CP) table is proposed. Finally, the application of the CP table for predicting crack growth rate under constant amplitude loading is explained and discussed.     

Crack-closure behavior of 2324-T39 aluminum alloy near-threshold conditions for high load ratio and constant Kmax tests

Fatigue-crack-growth rate tests were conducted on compact specimens made of 2324-T39 aluminum alloy to study the behavior over a wide range in load ratios (0.1  R  0.95) and a constant K_max test condition. Previous research had indicated that high R (> 0.7) and constant K_max test conditions near threshold were suspected to be crack-closure free and that any differences were attributed to K_max effects. During the tests, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local strain records on all tests, except R = 0.95. In addition, a back-face strain gage was used to monitor crack lengths and also to measure crack-opening loads from remote strain records. From local gages, significant amounts of crack closure were measured at the high-R conditions and crack-opening loads were increasing as the threshold condition was approached. Crack-closure-free data, ΔK_eff (= U ΔK) against rate, were calculated. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R even in the threshold regime, if crack-opening loads were measured from local strain gages and not from remote gages. At low R, all three major shielding mechanisms (plasticity, roughness, and fretting debris) are suspected to cause crack closure. But at high R and K_max tests, roughness and fretting debris are suspected to cause crack closure above the minimum load.     

Generation and analysis of FCG data using a single specimen and Kmax–ΔK testing matrix

A custom method to generate fatigue crack growth (FCG) data requires testing of multiple specimens at different load ratios, R, and the application of a load shedding procedure from pre-cracking level to threshold. In this paper, a novel method of testing has been investigated which utilizing a single specimen and a testing matrix in terms of K_max and ΔK values corresponding to predetermined R-ratios for which FCG data are recorded. Automatic K-controlled tests on 2324-T39 Al alloy were conducted using both increasing and decreasing ΔK procedures while K_max was kept constant. Results show that the increasing ΔK procedure gives less scatter than decreasing ΔK procedure. Also, fatigue crack growth curves near the threshold region obtained from increasing ΔK are above the curves obtained from decreasing ΔK procedure. These differences are explained by means of interaction between cyclic plastic zones and their effect on fatigue damage. The procedure with increasing ΔK demonstrated minimal interaction effects and hence it is recommended for efficient FCG data generation. The proposed procedure reduces testing time, the overall scatter associated with multiple samples and eliminates possible uncertainty linked to the load shedding procedure and its effects on threshold.     

Macromechanics study of stable fatigue crack growth in Al–Cu–Li–Mg–Ag alloy

This study was made on a fresh variety of Al–Li base alloy to investigate the role of ageing precipitates and microstructure dimensions in the fatigue crack growth resistance. The fatigue crack growth rate was measured in three different states of the material (i.e. base metal in T8 condition, friction stir weld and laser beam weld in full‐aged condition). Metallurgical analysis showed that the base metal in T8 temper is precipitation hardened by an equivalent amount of δ′ (AL₃Li), T₁ (AI₂CuLi) and θ′ (AI₂Cu) precipitates. The friction stir weld retained the morphology of strengthening precipitate; however, coarsening of Cu containing precipitates has occurred. On the other hand, laser beam weld showed a different type of CuAl phase morphology, which is characteristic of cast metal. The results of fatigue tests confirmed that fatigue crack growth resistance largely depends on microstructural features, specifically the strengthening phases. The fatigue crack resistance was in the order of base metal > laser beam weldment > friction stir weldment. The CuAl phase played a vital role in the crack closure of the laser beam weldment, thus enhancing the fatigue life as compared with the friction stir weldment, which was evident from the plot between log of da/dN (crack growth in each cycle) and log of ΔK (stress intensity range).     

The effect of silicon content on long crack fatigue behaviour of aluminium–silicon piston alloys at elevated temperature

The microstructure of aluminium piston alloys comprises primary and eutectic silicon together with numerous intermetallics. Previous research has shown that primary silicon strongly influences both fatigue crack initiation and subsequent propagation behaviour, however, the detailed effects of varying silicon volume fraction and morphology have not been fully addressed. Therefore, the fatigue properties of a number of candidate piston alloys with varying volume fractions of silicon have been studied. Long crack fatigue tests have been performed at room and elevated temperature typical of the gudgeon pin boss (200 °C) using a test frequency of 15 Hz (a typical engine frequency at engine idle condition).Microstructural characterisation using image analysis approaches combined with optical profilometry has been used to assess the fracture surfaces of test samples. The role of primary Si in enhancing crack growth rates at high ΔK levels, whilst affording improvements in crack growth rates at lower ΔK levels due to local crack deflections and shielding, has been confirmed. In the absence of primary Si (lower Si content alloys) the low ΔK level crack growth behaviour is dominated by matrix properties (intra-dendritic crack growth pre-dominates) whilst the high ΔK level crack growth behaviour is inter-dendritic and occurs along the weak path of the eutectic Si and/or intermetallic network.     

Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite—Part II: In situ self-healing

Successful arrest and retardation of fatigue cracks is achieved with an in situ self-healing epoxy matrix composite that incorporates microencapsulated dicyclopentadiene (DCPD) healing agent and Grubbs’ first generation Ru catalyst. Healing agent is released into the crack plane by the propagating crack, where it polymerizes to form a polymer wedge, generating a crack tip shielding mechanism. Due to the complex kinetics of healing a growing crack, the resulting in situ retardation and arrest of fatigue cracks exhibit a strong dependence on the applied range of cyclic stress intensity ΔK_I. Significant crack arrest and life-extension result when the in situ healing rate is faster than the crack growth rate. In loading cases where the crack grows too rapidly (maximum applied stress intensity factor is a significant percentage of the mode-I fracture toughness value), a carefully timed rest period can be used to prolong fatigue life up to 118%. At moderate ΔK_I, in situ healing extends fatigue life by as much as 213%. Further improvements in fatigue life-extension are achieved by employing a rest period, which leads to permanent arrest at this moderate ΔK_I. At lower values of applied stress intensity factor, self-healing yields complete arrest of fatigue cracks providing infinite fatigue life-extension.     

High cycle fatigue behaviour of microsphere Al2O3–Al particulate metal matrix composites

The high-cycle stress-life (S–N) curve and fatigue crack growth threshold (ΔK_th) behaviour of COMRAL-85^TM, a 6061 aluminium–magnesium–silicon alloy reinforced with 20 vol.% Al₂O₃-based polycrystalline ceramic microspheres, and manufactured by a liquid metallurgy route, have been investigated for a stress ratio of R = −1 (fully reversed loading). Fatigue testing was conducted on both smooth round bar (S–N) specimens and notched round bar (fatigue threshold) specimens. Unreinforced Al 6061-T6 also processed by a liquid metallurgy route and six powder metallurgy processed composites with particle volume fractions ranging between 5% and 30% were also studied. S–N data revealed that the powder metallurgy processed composites generally gave longer fatigue lives than the matrix alloy, whereas COMRAL-85^TM exhibited a reduced fatigue life. The fatigue threshold results were very similar for all the composites, being lower than for Al 6061-T6. Fatigue failure mechanisms were determined from examination of the fracture surfaces and the crack profiles.     

Predicting fatigue transverse crack growth in cross-ply carbon–epoxy laminates from quasi static strength tests by using iso-damage curves

Cross-ply laminates made of carbon/epoxy IM7/977-2 system are investigated. The fatigue study is confined to ambient temperature conditions and zero loading ratio. Damage is characterized by the transverse crack density ρ in the central 90°-layer. The family of experimental fatigue cracking curves (ρ versus N, where N is the number of cycles, for each tensile test maximum stress amplitude) can be replaced with a set of “iso-damage curves”, i.e. contour curves of constant ρ in the σ–log (N) plane. The iso-damage curves approximately constitute a fan of straight lines that intersect at a common point (σ_e, log (N_s)), where N_s is a very large number of cycles beyond which no more crack appears, and σ_e is some fatigue limit.Our aim is to propose a simple method to predict fatigue cracking at an arbitrary maximum stress level loading by using data stemming from a constant strain rate test. This method essentially rests upon the construction of the above “iso-damage” curves, using very simple assumptions.     

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size ( ) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

where C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.