Experimental study of I + III mixed mode fatigue crack transformation propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the mode transformation process. It is found that with the crack growth, I + III mixed mode changes to Mode I. Crack mode transformation is governed by the Mode III component and the transformation rate is a function of the relative magnitude of the Mode III stress intensity factor. However, even in the process of the crack mode transformation the fatigue crack propagation is controlled by the Mode I deformation.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

The effect of steady torsion on fatigue crack growth in shafts

Most of catastrophic mechanical failures in power rotor shafts occur under cyclic bending combined with steady torsion: Mode I (ΔK_I) combined with Mode III (K_III). An analysis of the influence of steady torsion loading on fatigue crack growth rates in shafts is presented for short as well as long cracks. Long cracks growth tests have been carried out on cylindrical specimens in DIN Ck45k steel for two types of testing: rotary or alternating bending combined with steady torsion in order to simulate real conditions on power rotor shafts. The growth and shape evolution of semi-elliptical surface cracks, starting from the cylindrical specimen surface, has been measured for several loading conditions and both testing types. Short crack growth tests have been carried out on specimens of the same material DIN Ck45k, under alternating bending combined with steady torsion. The short crack growth rates obtained are compared with long crack growth rates. Results have shown a significant reduction of the crack growth rates when a steady torsion Mode III is superimposed to cyclic Mode I. A 3D Finite Element analysis has also shown that Stress Intensity Factor values at the corner crack surface depend on the steady torsion value and the direction of the applied torque.     

Sustained Mode I and Mode II fatigue crack growth in flat plates

This study was conducted to contribute to the understanding of fatigue crack growth under mixed mode loading. This was accomplished by developing and analyzing a flat plate specimen capable of maintaining crack growth on a plane oblique to the direction of the applied load. Several specimens were built and exposed to controlled fatigue loading in the laboratory. These specimens were then modeled using finite elements to determine the stress intensity factors (SIF). For the “Mode I/Mode II” specimens developed, the crack was forced to grow in a direction other than perpendicular to the load. The resulting crack front did not remain straight and flat, but stabilized into a curved or warped shape. Based on finite element analyses of these curved specimen cracks, it is concluded that the SIR were predominantly Mode I, with the Mode II and III SIR being negligible.     

The effect of crack surface interaction on the stress intensity factor in Mode III crack growth in round shafts

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor.The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

Development and growth of offset fingerlike cracks

The phenomenon of fingerlike crack growth was observed during fatigue crack growth in Polyvinylchloride, in which there was superimposed Mode III and Mode I crack tip loading. The resulting fracture surface markings were similar to the “river lines” on metal, or “lances” on glass fracture surfaces.A two-dimensional elastic stress analysis was made that could predict successfully the crack growth paths leading to the finger like cracks linking up. However, the reasons for the formation of these cracks are imperfectly understood.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

Mixed mode fatigue crack propagation in a ferritic–perlitic cold drawn tube

Previous work by the authors has shown that torsional fatigue tests on cold drawn tube specimens with a longitudinal micronotch present both Mode III ahead of the crack tip (throughout the tube thickness) and Mode I at the defect edges. The co-planar Mode III propagation was prevalent and is followed by Mode II crack propagation along the cold drawn direction.In this work, this behaviour is further investigated by a new series of experimental tests together with a finite element analysis. The mechanisms behind this competition between Mode I and Mode III cracks are analysed and some fractographies were performed on run-outs, broken and interrupted tests.Indeed, pure Mode I and pure Mode II crack propagation rates along with mixed mode crack propagation rates are analysed. Finally, the conditions in order to get Mode I crack growth or shear driven propagation are discussed.     

Fatigue crack growth analysis using 2-D weight function

A method for crack growth analysis of planar cracks under arbitrary Mode I loading is presented in the paper. The method is based on the point-load (2-D) weight function used for the calculation of stress intensity factors. An algorithm for the analysis of fatigue crack growth of planar cracks, and validation results supporting the entire methodology is also discussed. Application examples of the proposed method for crack growth analysis under arbitrary Mode I stress fields are presented as well.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes

Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and “S” shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens.     

THE BEHAVIOUR OF FATIGUE CRACKS SUBJECT TO APPLIED BIAXIAL STRESS: A REVIEW OF EXPERIMENTAL EVIDENCE

Abstract— Experimental studies aimed at understanding the fatigue process in metals and polymers have usually been performed under uniaxial stress. Only in the last two decades or so has much experimentation been carried out on fatigue crack propagation under biaxial stress. This paper reviews the available published data. Crack propagation behaviour under biaxial stress is dictated by 3 parameters: stress biaxiality itself, which is defined here as the ratio of the in-plane principal stresses, crack angle with respect to the applied principal stress directions and stress intensity factor range. Depending on the first two parameters, cracks may grow in Mode I, Mode II or Mixed-Mode. Crack growth data have been presented using these three divisions. Two short sections have been included on initiation and cyclic stress/strain behaviour under biaxial stress to emphasise the fact that crack growth cannot be fully understood without knowing something of them. The accumulated data do not lead to adequate conclusions on either the qualitative or quantitative behaviour of cracks subject to cyclic in-plane biaxial stress. Reasons for the confusion and even contradiction of independent results are put forward and some discussion given to the possible directions of future experimental work.     

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.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

THE EFFECTS OF STRESS RATIO ON THE GROWTH BEHAVIOUR OF SMALL FATIGUE CRACKS IN AN ALUMINUM ALLOY 7075-T6 (WITH SPECIAL INTEREST IN STAGE I CRACK GROWTH)

Abstract— The growth behaviour of small fatigue cracks has been investigated on aluminum alloy 7075-T6 at stress ratios R of 0, −1 and −2. The effects of stress ratio are discussed with special interest in the stage I region of small crack growth. Cracks which initiated at R =−1 and −2, grew by a stage I mechanism up to a certain depth followed by stage II crack growth. The stage I to stage II transition occurred under a constant maximum stress intensity factor which was approximately consistent with the threshold effective stress intensity range, λ K _eff,th, for large cracks. At R = 0, on the other hand, stage I crack growth was not observed because of crack initiation at inclusions. Small cracks grew more rapidly than large cracks subjected to the same nominal stress intensity ranges at all the stress ratios, and they grew below the threshold stress intensity range, λ K _th, for large cracks. Stage I cracks, in particular, showed much higher growth rates than large cracks and grew even below λ K _eff,th. It is suggested that stage II crack growth rates should be characterized in terms of an effective stress intensity range, while a micromechanics approach will be necessary to evaluate stage I crack growth rates.     

The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading

As part of a programme to investigate the mixed mode fatigue crack growth threshold behaviour of mild steel, tests were carried out on three-point bend specimens with spark machined initial slits inclined to give mixed Mode I and III displacements. Overall the expected tendency to Mode I crack growth showed as an initial directional discontinuity followed by a smooth rotation of the crack front until it was almost perpendicular to the specimen sides. At a smaller scale, initial crack growth was by the formation of Mode I branch cracks which developed into a ‘twist’ fracture surface consisting of narrow Mode I facets separated by cliffs. The facets eventually grew out and the fracture surface became smooth. The result in the initiation it was necessary to distinguish between the threshold conditions which result in the initiation of crack growth, specimen failure and crack arrest. An envelope based on Mode I branch crack growth provides a reasonable lower bound to the results for crack initiation and specimen failure. The crack arrest threshold results and some of the crack growth threshold results could not be analysed in detail because of lack of appropriate stress intensity factors.     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

Small-crack growth and fatigue life predictions for high-strength aluminium alloys. Part II: crack closure and fatigue analyses

Small-crack effects were investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad aluminium alloys. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue and small-crack tests were conducted on single-edge-notch tension (SENT) specimens and large-crack tests were conducted on middle-crack tension specimens under constant-amplitude and Mini-TWIST spectrum loading. A pronounced small-crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite-element and weight-function methods were used to determine stress intensity factors, and to develop equations for surface and corner cracks at the notch in the SENT specimen. (Part I was on the experimental and fracture mechanics analyses and was published in Fatigue Fract. Engng Mater. Struct. 21 , 1289–1306, 1998.) This part focuses on a crack closure and fatigue analysis of the data presented in Part I. A plasticity-induced crack-closure model was used to correlate large-crack growth rate data to develop the baseline effective stress intensity factor range (Δ K _eff ) against rate relations for each material, ignoring the large-crack threshold. The model was then used with the Δ K _eff rate relation and the stress intensity factors for surface or corner cracks to make fatigue life predictions. The initial defect sizes chosen in the fatigue analyses were similar to those that initiated failure in the specimens. Predicted small-crack growth rates and fatigue lives agreed well with experiments.