ESTIMATION OF TORSIONAL FATIGUE STRENGTH OF MEDIUM CARBON STEEL BARS WITH A CIRCUMFERENTIAL CRACK BY THE CYCLIC RESISTANCE-CURVE METHOD

Near-threshold fatigue crack propagation tests were performed on circumferentially precracked round bars of a medium carbon steel under torsional loading. The crack propagation rate decreased with crack extension, because of the shear contact of crack faces. The crack propagation rate without the influence of crack-surface contact was determined by extrapolating to zero crack extension the relationship between the crack propagation rate and crack extension. The applied stress intensity factor range was divided into two parts: one was the effective value responsible for crack growth and the other was the value corresponding to crack-tip shielding. The resistance-curve method was used to predict the fatigue limit for crack initiation and fracture. The R -curve was constructed using the experimentally determined threshold value of the stress intensity range, which was the sum of the threshold effective stress intensity range and the threshold shielding stress intensity range. The threshold effective stress intensity range was constant. The R -curve was independent of the precrack length and specimen dimensions. The predicted values agreed well with the experimental results.     

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.     

Determination of the length dependence of the threshold for fatigue crack propagation

A rising load amplitude crack growth test on specimens pre-cracked in cyclic compression is presented as a procedure to determine the length dependence of the threshold of fatigue crack propagation described by the R(resistance)-curve for the threshold of stress intensity factor range. The experimental results show that the residual stress field in front of the pre-crack can significantly influence the R-curve.In order to measure the material specific R-curve which is not affected by the pre-cracking condition it is important to use the smallest possible load amplitude. To achieve this goal, a very small notch root radius is essential. It is shown that at notches machined by razor blade polishing technique the load amplitude for pre-cracking can be reduced to values where the load history does not influence the R-curve for the threshold of stress intensity range.     

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.     

EFFECTS OF CRACK CLOSURE AND MEAN STRESS ON THE THRESHOLD STRESS INTENSITY FACTOR FOR FATIGUE OF AN ALUMINIUM CASTING ALLOY,

Abstract— Observations have been made of the threshold fatigue properties of an Al-Mg-Si casting alloy. First, it has been shown that there exists a critical value of the stress ratio, R , below which the threshold stress intensity factor decreases with increasing R but above which it is constant. Second, measurements of the cyclic crack opening displacement have been used to examine crack closure effects and to deduce the effective cyclic stress intensity factor. The two sets of data are compared with existing models for threshold phenomena.     

Fatigue thresholds of holed components under in-phase and out-of-phase torsional and axial loadings

The resistance-curve ( R -curve) method was applied to the prediction of the fatigue thresholds of notched components under in-phase and out-of-phase combinations of cyclic torsion and axial loadings. The prediction was compared with the experimental data obtained from thin-walled tubular specimen of medium-carbon steel with a hole. The stress was completely reversed and the mean stress was zero. The crack nucleated at the position of the maximum range of the circumferential stress on the periphery of a hole, and propagated almost straight for all cases examined. The experimental data of the thresholds for crack initiation and fracture agreed well with the predictions for in-phase and for out-of-phase loadings with 45° phase difference. For out-of-phase loading with 90°, the threshold for fracture was close to the crack initiation limit, because of the reduction of crack closure due to crack face rubbing by mode II shear cycling.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

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.     

Resistance-curve method for predicting propagation threshold of short fatigue cracks at notches

A new resistance-curve method was proposed for predicting the growth threshold of short fatigue cracks near the notch root. The resistance curve was constructed in terms of the experimentally determined threshold value of the maximum stress intensity factor which was the sum of the threshold effective stress intensity range ΔK_effth and the opening stress intensity factor K_opth The ΔK_effth value was constant, irrespective of crack length or notch geometry. The relation between K_opth and crack length was independent of notch geometry. The predicted effects of the notch-root radius and the notch depth on the propagation threshold of short fatigue cracks were compared with the experimental data obtained using center-notched specimens with various notch-root radii and single-edge notched specimens with various notch depths. Excellent agreement was obtained between predictions and experiments.     

THE INFLUENCE OF AGEING AT INTERMEDIATE TEMPERATURES ON THE MECHANICAL BEHAVIOUR OF A DUPLEX STAINLESS STEEL: Part II. FATIGUE LIFE AND FATIGUE CRACK GROWTH

Abstract— The mechanical behaviour of AISI 329 steel has been investigated for ageing times up to 20,000 h at temperatures of 475, 425, 375, 325 and 275°C. The study has concentrated on the changes in the response to cyclic strains, in the low-and the high-cycle fatigue regimes, and in the resistance to fatigue crack propagation as a function of temperature and time of ageing.
It is shown that ageing increases the fatigue resistance in the high-cycle fatigue regime, but the opposite occurs in the low-cycle fatigue regime. Ageing increases the LEFM threshold stress intensity factor range for fatigue crack propagation which reaches high values in these alloys, and is influenced by the fatigue load ratio. Crack closure contributes to the LEFM threshold stress intensity factor range for crack propagation only in the annealed condition of the AISI 329 steel.     

EARLY DEVELOPMENT OF FATIGUE CRACKING AT MANUAL FILLET WELDS

Abstract— An experimental study within the Canadian Offshore Corrosion Fatigue Research Programme was performed on the early development of fatigue cracking along the wavy toe of manual fillet welds between structural steel plates. Stress relieved and as-welded cruciform joints were tested under R = −1 and R = 0 loading at different stress amplitudes. The depth and the opening level of cracks as small as 10–20 μm were monitored using miniature strain gauges installed along the toe apex, in combination with beach marking. Most of the "initiation life" (25% to 50% of total life), conventionally defined by a crack depth of 0.5 mm, is consumed in short crack propagation. Three types of short crack development for different combinations of local mean stress and stress range are identified and analyzed. Growth rates in as-welded specimens are faster than in stress relieved specimens, which results in shorter "initiation lives". This is associated with a higher effective stress range, particularly under R = - 1 loading where cracks are open over nearly the full stress range. The V-notch stress intensity factor is a promising parameter to rationalize the crack "initiation life". It takes into account the thickness effect experimentally observed. Under R = - 1 loading of as-welded joints, using R = 0 data and taking the whole stress range gives a reasonably conservative approximation of the crack "initiation life".     

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.     

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.     

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.     

The effect of single overloads in tension and compression on the fatigue crack propagation behaviour of short cracks

The crack propagation behaviour in cast quenched and tempered steel after one overload cycle in tension as well as in compression on short cracks is investigated in deep notched specimens. The overload cycle exhibits a significant influence on the fatigue life endurance, due to the formation of an overload plastic zones in front of the crack tip. The crack propagation after overload cycles is investigated by inspection of the fatigue threshold R-curve and fatigue crack propagation rate. Tension overload increased the long crack threshold and reduced the R-curve effect, whereas overloads in compression reduced the crack growth resistance and shifted the threshold value to larger crack extension. A simple FE simulation was also performed to investigate the variation in the contribution of plasticity induced crack closure during crack propagation after the overload. Macroscopic mechanistic and dislocation models are introduced to explain the results obtained.     

The effect of notch plasticity on the behaviour of fatigue cracks emanating from edge-notches in high-strength β-titanium alloys

The present paper is aimed at investigating the behaviour of fatigue cracks emanating from edge-notches for two different microstructures of the Ti-6246 alloy, produced by two specific thermo-mechanical treatments and defined as β-annealed and β-processed, respectively. Pulsating four point bending tests were performed on double-edge-notched specimens. The initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 88 and 58% of the 0.2% material’s yield stress. Plastic deformation at the notch tip initially produced a local stress redistribution followed by elastic shake down due to the high cyclic strain hardening rates exhibited by both microstructures, as confirmed by finite element modelling. Crack closure effects, measured by an extensometric technique, and variations in crack aspect ratio were considered in the ΔK calculation. The obtained crack growth rate data were compared with those of long cracks measured on standard C(T) specimens as well as of microcracks measured on round, unnotched S-N type of specimens to evaluate the intrinsic fatigue crack propagation resistance of the two microstructures. The contribution of notch plasticization to crack closure was estimated by finite element modelling.     

PROPAGATION AND CLOSURE OF SHORT FATIGUE CRACKS AT NOTCHES UNDER COMPRESSIVE MEAN STRESSES

Abstract— Single-edge-notched specimens of a low-carbon steel were fatigued under cyclic in-plane bending with compressive mean stresses. The development of crack closure with crack growth was studied both experimentally and theoretically. The relation between the crack opening stress and the crack length was a function of the minimum (compressive) applied stress, irrespective of the maximum stress. The effective stress intensity range was a unique parameter in correlating the crack growth rate, even if the crack was embedded in the compressive plastic zone. Under a constant minimum stress, the length of nonpropagating cracks became longer with increasing maximum applied stress. A theoretical model was proposed for predicting the crack opening stress on the basis of the compressive stress distribution at the minimum applied stress. The predicted value agreed fairly well with the experimental result. The model gave upper bounds of the crack growth rate and the length of nonpropagating fatigue cracks within the plastic zone.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

Fatigue crack propagation rates and threshold stress intensity factors for welded joints of HT80 steel at several stress ratios

Fatigue crack propagation rates and threshold stress intensity factors were measured for welded joints and base metal by using 200 mm wide centre-cracked specimens. The fatigue crack propagation properties of welded joints were similar in spite of the different zones in which the cracks propagated (ie, in the heat-affected zone and in the weld metal) and the different welding process used (submerged arc welding and gas metal arc welding). They were, however, inferior to those of the base metal. It was revealed by observation of the crack closure that the fatigue cracks were fully open during the whole range of loading, due to the tensile residual stress distribution in the middle part of the welded joints. This observation also explains the lack of a stress ratio effect on the fatigue crack propagation properties of welded joints, and their inferiority to those of the base metal.     

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.