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.     

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.     

On the through-thickness crack with a curve front in center-cracked tension specimens

Three-dimensional finite element analyses are performed on through-thickness cracks with slightly wavy front in center-cracked plates. Considering there is an inherent relationship between the crack shape and the corresponding stress intensity factor (SIF) distribution of a crack, the curved configuration of the crack is determined using a heuristically derived iterative procedure if the SIF distribution function is known. Several simple SIF distribution functions, for instance the constant SIF distribution along the crack front, are assumed to determine the crack shape. Under the assumption that the rate of fatigue crack growth depends on the SIF range or the effective SIF range, possible effects of plate thickness, crack length and crack closure level gradient on the behaviour of crack tunneling are investigated. The stability of the curved shape of a through-thickness crack in fatigue is also discussed, i.e. whether a crack can maintain its shape satisfying the conditions of constant SIF distribution or other distribution along the crack front during fatigue growth. This study will be useful for a better understanding of the behaviour of crack tunneling and help to evaluate the validity of the two-dimensional linear elastic fracture mechanics in cracked plates.     

AN ASSESSMENT OF CRACK CLOSURE AND THE EXTENT OF THE SHORT CRACK REGIME IN Q1N (HY80) STEEL

Abstract— The paper addresses some aspects of the differences in fatigue crack growth rate behaviour and threshold values obtained for long through-cracks, short through-cracks and surface cracks. Attention is focused on plasticity induced closure in the wake behind the growing crack tip. For long cracks at high K _max, closure is found to depend in a linear manner on K _max, i.e. K _op, increases with the size of the monotonic plastic zone. Closure increases at low δ K and this is primarily a consequence of the load shedding procedure. If short through-cracks are prepared by machining specimens containing long cracks, a substantial part of the plastic wake is removed and this can produce marked effects on the closure contribution during subsequent growth. The length of crack "closed" in a long crack threshold test was found to be of the order of 1 mm. Cracks less than this length exhibited "short crack" behaviour: greater than this length, they behaved as "long cracks", with plastic wake effects apparently fully operative. Small surface cracks exhibit "long crack" behaviour at lengths as short as 0.2 mm and reasons for this are discussed.     

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.     

THE EFFECT OF ENVIRONMENT ON CRACK CLOSURE AND FATIGUE THRESHOLD*

Abstract— The threshold value for fatigue crack growth of a medium carbon steel was increased when the test-environment was changed from air to an aggressive H₂S-containing brine. This increase in fatique threshold was shown to be caused by corrosion product-induced crack closure. Further, the fatigue threshold and crack closure level were shown to be dependent on the growth rate history in approaching threshold. The differences in fatigue crack growth rate and fatigue threshold resulting from test procedure and growth rate history were significantly reduced by employing the effective stress intensity concept.     

A SIMPLIFIED LABORATORY APPROACH FOR THE PREDICTION OF SHORT CRACK BEHAVIOR IN ENGINEERING STRUCTURES

Abstract— Conventionally determined fatigue threshold information (ASTM E647) can lead to non-conservative estimates of fatigue lifetimes when these data are utilized in damage tolerant design assessments. The non-conservative nature of such data can be attributed primarily to the development of excessively large amounts of crack closure at low R -ratios, particularly at near threshold stress intensity factor levels. These high closure levels attenuate the effective stress intensity condition prevailing at the crack tip and confound attempts to predict the behavior of short cracks that exhibit limited crack closure. A modified test procedure, involving constant maximum stress intensity factor ( K ^c_max) test conditions, is described which identifies fatigue crack propagation (FCP) threshold behavior in the absence of detectable amounts of crack closure. These data have been generated with conventional long crack specimens for several aluminum, iron, and nickel-based alloys and which are shown to closely simulate the FCP response of short cracks in these engineering materials. As such, the modified threshold test procedure, incorporating constant K _max loading conditions, represents a valuable tool in the prediction of the cyclic lifetime of engineering components. The stress-cyclic lifetime (S-N) curve for aluminum butt-welded beams was computed based on K ^c_max data and found to be in excellent agreement with actual test results.     

Propagation of physically short cracks in a bainitic high strength bearing steel due to fatigue load

Physically short cracks in a bainitic high strength bearing steel were fatigue loaded. The rapid propagation rate of early open short cracks agreed with that of long closure free cracks. After some rapid growth, the short cracks entered a transition period to the rate of growth limited long cracks. Potential drop showed that the short cracks were open to the tip throughout the growth sequence, which excluded crack face closure in the wake as the growth limiting mechanism in this material. Instead the short crack effect was related to residual stresses and other mechanisms at the crack tip. Crack manufacturing procedures were determined for straight long and short start cracks in the present material. LEFM with effective material parameters and limit compensation predicted the short crack lives.     

In situ investigation of small fatigue crack growth in poly-crystal and single-crystal aluminium alloys

Abstract   In situ scanning electron microscope observations of short crack growth in both a poly-crystal and a single-crystal alloy revealed that fatigue cracks may grow in a shear decohesion mode over a length that is several times the grain size, far beyond the conventional stage I regime. In the poly-crystal aluminium alloy 2024-T351, fatigue cracks were found to continue to grow along one shear band even after two mutually perpendicular shear bands had formed at the crack tip. For the single-crystal alloy specimen with the loading axis being nearly perpendicular to its main shear plane, mode I fatigue cracks were found to grow along the shear band. These two types of fatigue crack growth pose a significant challenge to the existing fatigue crack growth correlating parameters that are based on crack-tip opening displacement. In particular, it has been found that the cyclic crack-tip opening displacement, which accounts for both large-scale yielding and the lack of plasticity-induced crack closure, is unable to unify the growth rates of short and long cracks in aluminium 2024-T351, suggesting a possible dependence of crack growth threshold on crack length.     

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.     

Behaviour of short cracks in alloy 800HT under biaxial fatigue

Biaxial in phase fatigue tests were carried out on thin walled tube specimens of alloy 800HT at ambient temperature. The loading modes included tension, torsion, and combined tension—torsion with a tensile/shear plastic strain range ratio Δ?p/Δγp = 3^1/2. The influence of effective strain amplitudes and biaxiality on the initial growth of fatigue cracks was investigated using the replica technique. The results indicated that the loading conditions strongly affected the growth rates of short cracks. In torsion the cracks grew significantly more slowly than under axial or biaxial loading. A mean tensile stress perpendicular to the shear crack promoted its growth and reduced the fatigue life. The growth of the cracks could be described by the ΔJ integral for axial and biaxial loading; the integration predicted the fatigue life under axial and biaxial loading correctly. However, significantly conservative lifetime predictions were obtained for pure torsional loading since ΔJ does not include crack closure and crack surface rubbing.

MST/3234     

Mechanical properties of Al–Li alloys Part 2 Fatigue crack propagation

Abstract

Mechanisms influencing the ambient temperature mechanical properties of commercial Al–Li alloys 2090, 2091, 8090, and 8091 are examined, with specific emphasis on the role of microstructure. In Part 2, results on fatigue crack propagation behaviour are presented for both ‘long’ (≥ 5 mm) and ‘microstructurally small’ (~1–1000 μm) cracks and compared with behaviour in traditional high strength aluminium alloys. In general, it is found that the growth rates of long fatigue cracks in Al–Li alloys are up to two to three orders of magnitude lower than in traditional 7000 and 2000 series alloys, when compared at an equivalent stress intensity range ?K. By contrast, corresponding growth rates of microstructurally small fatigue cracks were up to two to three orders of magnitude higher than the long crack results. Such observations are attributed to the prominent role of crack tip shielding in Al–Li alloys resulting from the tortuous and deflected nature of the crack paths which results in a reduced crack tip ‘driving force’ from crack deflection and, more importantly, from the consequent crack closure induced by the wedging of fracture surface asperities. Since microstructurally small cracks are unable to develop the same level of shielding from crack closure by virtue of their limited wake, small crack growth rates are significantly accelerated. Unlike fracture toughness behaviour, artificial aging of commercial Al–Li alloys to peak strength has a mixed influence on the (long crack) resistance. Although behaviour at higher growth rates is relatively unaffected, in 2091 nominal threshold ?K_TH values are increased by 17%, whereas in 8090 and 8091 they are decreased by 16–17%. However, all alloys show reduced effective fatigue thresholds at peak strength after correcting for crack closure.

MST/926b     

A review of some aspects of fatigue crack growth under variable amplitute loading

The literature on some aspects of the influence of variable amplitude loading on fatigue crack growth has been reviewed. In particular the importance of residual stresses, fatigue crack closure, microstruture, geometry and environment on the fatigue crack growth of long, through-thickness cracks following overloads, underloads and overload-underload combinations in Mode 1 opening have been identified. Other behaviour, including the influence of temperature, frequency and the effects of mixed-mode loading, is beyond the scope of this review. Areas of work requiring further investigation have been proposed.     

Long fatigue life critical crack lengths*

A model based on surface strain redistribution and crack closure is presented for prediction of the endurance or fatigue limit stress by determining the threshold stress and critical length of short cracks that develop under microstructural control. The threshold stress first decreases with crack size to a local minimum then increases to a local maximum corresponding to the fatigue limit stress. This occurs at the critical crack length corresponding to about four grain diameters. The model is capable of determining the threshold stress range and depth of propagating and non‐propagating surface cracks as a function of stress ratio, material and grain size. The microstructure is shown to be particularly significant in the very long life regime (N_f ≈ 10⁹ cycles). When the surface cracks become non‐propagating, internally initiated cracks continue growing slowly, eventually reaching the critical crack length with failure occurring after a very high number of cycles (10⁷ < N_f < 10⁹ cycles).     

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.     

Analytical prediction of short to long fatigue crack growth rate using small- and large-scale yielding fracture mechanics

Modifications are introduced to account for the differences in crack growth behavior of long and short cracks, that permit the use of the stress intensity factor. These modifications stem from the principles of fracture mechanics for small- and large-scale yielding. Short cracks can grow well below the long crack fatigue threshold range, because the short crack fatigue threshold range is smaller than that for long cracks as it is dependent on the stress level, and the plastic constraint factor. Analytical expressions are developed for these relationships, and for the fatigue crack growth rates in plane stress and plane strain, for short semi-elliptical cracks including those emanating from notches. Microstructural features are not considered. A linear approximation is used for the gradual transition from plane stress to plane strain. The model is formulated using only the readily available material properties. It is then validated using published experimental data for fatigue crack propagation rates for positive and negative stress ratios down to –2. There is reasonable agreement between the model predictions and the published experimental data for short cracks (from 0.1 to 2 mm) and long cracks.     

Evaluation of fibre bridging stress of short fatigue cracks in SCS-6/Ti-15-3 composite

Single‐edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X‐ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging.     

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.     

A MODEL FOR THE FATIGUE LIMIT AND SHORT CRACK BEHAVIOUR RELATED TO SURFACE STRAIN REDISTRIBUTION

A model based on surface strain redistribution and the reduced closure stress of short cracks is shown to successfully predict the fatigue limit and short crack growth behaviour for aluminium alloy 2024-T351. Using this approach, the length of non-propagating cracks can be anticipated. The local stress intensity range may be resolved into two components (first the linear elastic fracture mechanics component and the second is due to surface strain concentration). Consequently, the local stress intensity range of aluminium alloy 2024-T351 is a maximum at a depth of approximately half a grain diameter and a minimum at a depth slightly in excess of three grain diameters. The reduced closure stress for short cracks coupled with the increased applied stress intensity caused by surface strain redistribution accounts for the variation of the effective stress intensity parameter as a function of crack depth. This parameter is a maximum for the smallest possible crack (3 μm) and decreases as crack length increases.