Prediction of short fatigue crack growth of Ti‐6Al‐4V

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.     

AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH-THICKNESS AND SURFACE FATIGUE CRACKS

Abstract— The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through-thickness physically-short (50–400 μm) cracks, and naturally-occurring microstructurally-small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–^12–10–⁶m/cycle). Results are compared with those predicted numerically using an elastic-plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through-thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near-threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Vorhersagemodell für die Wachstumsraten kurzer Risse auf der Basis von Kmax‐konstant‐Versuchen an M(T)‐Proben

Prediction model for the growth rates of short cracks based on K_max‐constant tests with M(T) specimens The fatigue crack growth behaviour of short corner cracks in the Aluminium alloys Al 6013‐T6 and Al 2524‐T351 was investigated. The aim was to determine the crack growth rates of small corner cracks at stress ratios of R = 0.1, R = 0.7 and R = 0.8 and to develop a method to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T)‐specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The pre‐cracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a Focussed Ion Beam. The results of the fatigue crack growth tests with short corner cracks were compared with long fatigue crack growth test data. The short cracks grew at ΔK‐values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK‐values and the same stress ratios. A model was developed on the basis of K_max‐constant tests with long cracks that gives a good and conservative prediction of the short crack growth rates.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

Fatigue crack growth in a fillet welded joint

Existing theories for the growth of cracks at weld toes have proved difficult to verify because of a lack of experimental proof at short crack depths and slow growth rates. Arbitrary initial defect sizes have been employed in life calculations coupled with approximate two-dimensional stress analyses. In this study, the fatigue performance of a stress relieved fillet weld is determined by both theory and experiment. Crack growth results for shallow (less than 1 mm depth) elliptical cracks at weld toes are used to test an elastic expression for stress intensity using a correction factor from a three-dimensional stress analysis. No evidence of higher than expected growth rates, observed by others for very short cracks and cracks in notch plastic zones, is apparent. Integration of a growth law that includes the threshold stress intensity factor provides fatigue life predictions for various stress ratios and from experimentally measured defect depths. Needle peening the weld toe improves the fatigue life by retarding crack growth up to 1 mm below the weld toe.     

Near-threshold fatigue propagation of physically through-thickness short and long cracks in a low alloy steel

In this paper, the near-threshold fatigue behavior of physically through-thickness short cracks and of long cracks in a low alloy steel is investigated by experiments in ambient air. Physically through-thickness short fatigue cracks are created by gradually removing the plastic wake of long cracks in compact tension specimens. The crack closure is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. Based on the experimental results, the nominal threshold SIF range is shown to be dependent on the crack length and the characteristic of the crack wake which is strongly dependent on the loading history. The effective threshold SIF range and the relation between the crack propagation rate and the effective SIF range after the crack closure correction are shown to be independent on crack length and loading history. The shielding effect of the crack closure is shown to be related to the wake length and load history. The effective threshold SIF range and the relationship between the crack growth rate and the effective SIF range appear to be unique for this material in ambient air. These properties can be considered as specific fatigue properties of the couple material/ambient air environment.     

Effect of notch geometry on short fatigue crack growth in 8090 Al–Li alloy

The short-crack propagation behaviour of 8090 Al–Li alloy under different ageing conditions has been investigated. The effect of notch geometry on short fatigue crack growth was also studied. The results show that the geometrical configuration of the notch significantly affects the growth behaviour of the short crack, the growth rates of notched short cracks being much higher than those of long cracks at the same stress intensity factor range ΔK level. The orientations of the specimens had a stronger effect on the growth rate of long cracks than on that of short cracks. This revised version was published online in November 2006 with corrections to the Cover Date.     

INFLUENCE OF CONTACT LOADING ON FRETTING FATIGUE BEHAVIOUR

Abstract— Fretting induced cracking is commonly observed in industrial components that are in contact and are subjected to small oscillatory movements between them. Fretting causes a considerable reduction in fatigue strength. In this paper recent knowledge on the short and long crack growth behaviour is applied to estimate crack propagation and fatigue life in fretting. The model is based on mode I stress intensity factors with a threshold modified for short cracks. The predicted results are compared with experiments and the influence of the contact pressure is examined. A good correlation between predictions and experimental results are obtained for crack growth rates as well as fatigue lives in terms of number of cycles to failure. It is seen that the increase of fatigue life observed for contact pressures above a certain level can be predicted by the crack growth model.     

Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth

Based on the proposed concept of the fatigue threshold stress intensity factor ranges, a model has been developed that describes the kinetics of physically small fatigue crack and long fatigue crack growth. The model allows the calculation of the crack growth rate under the regular fully-reversed uniaxial loading from the data on the static characteristics of mechanical properties and the microstructure of the initial material. The crack depth at which the cyclic plastic zone size ahead of the crack tip will exceed the grain size should be considered as a criterion of the small-to-long crack transition. Under high-cycle fatigue conditions physically small fatigue crack growth will be divided into two phases of growth: the first phase is when the crack propagates along the slip planes of individual grains, and the second one is when the crack changes the mechanism of growth and propagates in the plane perpendicular to the loading direction. The model validity has been tested using the experimental data on the growth of the long cracks in specimens of titanium alloy VT3-1 in seven microstructural states and the small cracks in specimens of titanium alloy Ti–6Al–4V and aluminum alloy 2024-T3. Good agreement between the calculated and experimental results is obtained.     

Prediction of non propagating cracks

An explanation for non propagating fatigue cracks is presented based on the criterion that once the value of a particular strain intensity factor reduces to the threshold value for the material the crack should stop. Predicted lengths of these cracks based on solutions for the intensity factor are in good agreement with the experimental data. Intensity factor trends for cracks in notches are shown to vary from an initial decrease to a minimum value followed by an increase and eventual convergence with the trend for the equivalent long crack for sharp notches to the blunt notch curves that continuously increased during their approach to the long crack trend. The type of trend exhibited by a given notch depends both on notch geometry and notch size. In blunt notches the maximum value of the threshold stress for crack propagation is at initiation. However, for sharp notches the peak value of the threshold stress vs crack length curves shifts to a finite length. Stresses above the initiation level but below this peak stress level result in fatigue cracks which start but do not propagate to failure. Predicted values of the fatigue limit stresses for a variety of sizes in a circular and an elliptical notch are in good agreement with experimental results.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

ON THE TRANSITION FROM NEAR-THRESHOLD TO INTERMEDIATE GROWTH RATES IN FATIGUE

Abstract— Evidence is presented that the cyclic stress intensity threshold for fatigue crack growth in A1 2219-T851 is associated with a critical maximum value of stress intensity, K _c. This relationship is discovered by measuring the local value of stress intensity at the crack tip which is less than the applied stress intensity because of fatigue induced compressive residual stresses in the plastic zone. Crack growth rates and values of the crack tip residual stress are measured as functions of load ratio. For local stress intensities greater than K _c, the growth rate follows a power-law relationship, increasing monotonically with δ K . For local stress intensities below K _c, growth rates are also sensitive to the cyclic stress range, δσ. If the stress range is small, a threshold to growth, typical of long cracks, is seen. When the cracks are short and δσ exceeds a critical value, growth rates are a complex function of both δσ and δ K . This behavior is attributed to the effect of δσ on the propagation of the crack front past obstacles such as grain boundaries.     

Short fatigue crack growth from a blunt notch in plate specimens

Short crack growth behavior from a notch including crack closure and load ratio effects was investigated. Experiments and analyses were carried out using four-point bending specimens made of SAE 1045 steel, using a blunt notch keyhole specimen geometry. The lower the load ratio, the more notch effect on short crack growth behavior was observed. Short cracks in the notch affected zone had higher growth rates than long cracks. After the crack grew out of the notch effect field, short crack growth rates merged with the long crack growth rates. Several parameters were used to correlate the short crack growth rates including stress intensity factor range, effective stress intensity factor range, and stress intensity factor range based on notch root stress.     

Crack initiation under far-field cyclic compression and the study of short fatigue cracks

A procedure involving crack initiation under far-field cyclic compression is used to study the fatigue behavior of small flaws which are ˜0.3–0.5 mm in length and are amenable to linear elastic fracture mechanics (LEFM) characterization. This technique enables the determination of the threshold stress intensity range at which crack growth begins for small flaws and provides insight into some closure characteristics. Cracks were propagated in notched specimens of a bainitic steel subjected to fully compressive remote cyclic loads, until complete crack arrest occurred after growth over a distance of only a fraction of a mm at a progressively decreasing velocity. Following this, physically small flaws were obtained by machining away the notch. For the loads examined, the results indicate that the extent of damage left at the tip of the crack grown (and arrested) under remote compression is not large enough to affect subsequent tensile fatigue crack growth, when closure effects are not significant (e.g. at high load ratios). At high load ratios, the growth of small linear elastic cracks is identical to that of corresponding long flaws subjected to the same stress intensity range, which corroborates the similitude concept implicit in the nominal use of LEFM. At low load ratios, however, short tensile cracks propagate substantially faster than the longer flaws and exhibit lower threshold stress intensity range levels. Such apparent differences in their growth rates seem to arise, to a large extent, from the differences in their closure behavior, as indicated clearly from various aspects of the compression method. Global measurements of closure, with their inherent uncertainties, however, cannot account completely for the anomalous behavior of short flaws and for the effect of load ratio on short crack growth. Closure of short flaws begins to develop after growth over a minimum distance of about 0.5 mm in this steel. The significance and limitations of the compression technique are discussed and possible mechanisms responsible for the differences between long and short fatigue cracks are outlined.     

Fatigue propagation of short and long cracks in gaseous hydrogen environment in 3.5NiCrMoV steel

Turbo generators for nuclear plants are mostly equipped with hydrogen cooling systems. Current practice of characterizing the growth of fatigue cracks on the basis of fracture mechanics primarily relies on fatigue tests for long cracks which are typically of several millimeters in length. However, in view of extended life for the plants, the damage tolerance evaluation of such fatigue-critical engineering components requires understanding of the propagation of cracks of significantly smaller dimensions. Then the near threshold of short cracks is investigated and compared to the behavior of long crack by experiments under 4 bar hydrogen atmosphere. The short crack fatigue propagation in hydrogen atmosphere is shown similar to that in air, growing faster than the long crack and at ΔK ranging below the long crack threshold; this effect is related to a reduced crack closure shielding. The propagation behavior of long crack under hydrogen atmosphere is shown similar to that obtained in air in the low rate range, i.e. when the maximum of the stress intensity factor K_max is lower than a critical level of about 16 MPa m^1/2 with higher crack growth rate than in high vacuum. This environment effect is related to the presence of residual water vapor in both gases. For higher K_max, much faster growth rates under hydrogen atmosphere in comparison to air and vacuum are observed and related to hydrogen assisted intergranular propagation combining fatigue and sustained loading damage. The results are discussed on the basis of micrographic observations supporting the involved mechanisms.     

An investigation of crack closure and the propagation of semi-elliptical fatigue cracks in Q1N (HY80) pressure vessel steel

The results of an experimental investigation of the effect of crack closure on the propagation of semi-elliptical fatigue cracks are presented. Load-shedding fatigue threshold tests were carried out at stress ratios of 0.2, 0.35, 0.5 and 0.7. Crack closure was measured at the surface and depth positions using backface strain gauges, near-tip gauges, and a clip gauge. Differences between the surface and depth growth behaviour are explained by considerations of the effects of the transition from plane stress conditions at the surface to plane strain conditions at the depth. The effects of stress ratios are attributed largely to differences in the crack opening displacement, which result in asperities coming into contact to induce roughness-induced crack closure.     

Plastic strain distribution at the tip of a fatigue crack. application to fatigue crack closure in the threshold regime

The fatigue crack growth rate behaviour of a Co-33 wt pct Ni alloy was investigated at room temperature down to the threshold regime using CT specimens for two load ratios 0.1 and 0.3. Cyclic equivalent plastic strain distributions along an axis normal to the crack plane were experimentally determined over the whole range of crack growth rates using two techniques microhardness and a quantitative metallographic technique applied to twins, both calibrated on low cycle fatigue specimens. These experimental values were compared with theoretical curves as obtained from the monotonic plane strain finite element analysis of Tracey and adapted to cyclic loading according to the procedure proposed by Rice. A good agreement was found in stage II crack growth in the vicinity of the crack tip but a discrepancy was observed in the low crack growth rate regime, indicative of crack closure. It was possible to determine the effective amplitude of the stress intensity factor which accounts for this discrepancy and an intrinsic crack growth law was obtained which obeys Paris equation and which applies in the whole crack growth rate range independently of the load ratio.     

A predictive fatigue life model for anodized 7050 aluminium alloy

The objective of this study is to predict fatigue life of anodized 7050 aluminum alloy specimens. In the case of anodized 7050-T7451 alloy, fractographic observations of fatigue tested specimens showed that pickling pits were the predominant sites for crack nucleation and subsequent failure. It has been shown that fatigue failure was favored by the presence of multiple cracks. From these experimental results, a fatigue life predictive model has been developed including multi-site crack consideration, coalescence between neighboring cracks, a short crack growth stage and a long crack propagation stage. In this model, all pickling pits are considered as potential initial flaws from which short cracks could nucleate if stress conditions allow. This model is built from experimental topography measurements of pickled surfaces which allowed to detect the pits and to characterize their sizes (depth, length, width). From depth crack propagation point of view, the pickling pits are considered as stress concentrator during the only short crack growth stage. From surface crack propagation point of view, machining roughness is equally considered as stress concentrator and its influence is taken into account during the all propagation stage. The predictive model results have been compared to experimental fatigue data obtained for anodized 7050-T7451 specimens. Predictions and experimental results are in good agreement.     

Effect of stress ratio on fatigue crack growth in TiAl intermetallics at room and elevated temperatures

The fatigue crack growth behavior of γ-based titanium aluminides (TiAl) with a fine duplex structure and lamellar structure has been investigated by scanning electron microscope (SEM) in situ observation in vacuum at 750°C and room temperature. For the duplex structured material the fatigue crack growth rates are dominated by the maximum stress intensity, particularly at 750°C. The threshold stress intensity range for fatigue crack growth at 750°C is lower than that at room temperature for any corresponding stress ratio. The fatigue crack growth rate at 750°C is affected by creep deformation in front of the crack tip. The severe crack blunting occurs when the stress ratio is 0.5. For the lamellar structured material the scatter of fatigue crack growth data is very large. Small cracks propagate at the stress intensity range below the threshold for long fatigue crack growth. The effects of microstructure on fatigue crack growth are discussed.