STATISTICAL INVESTIGATION OF THE BEHAVIOUR OF SMALL CRACKS AND FATIGUE LIFE IN CARBON STEELS WITH DIFFERENT FERRITE GRAIN SIZES

Abstract— In order to study the relation between the scatter characteristics of small crack growth behaviour and fatigue life, rotatory bending fatigue tests of smooth specimens were carried out using 0.21% carbon steels of different ferrite grain sizes. Fifteen to eighteen specimens were fatigued at each stress amplitude, and the initiation and propagation behaviour of the cracks which led to the final fractures were examined for all the specimens. The physical basis of scatter in fatigue life was investigated, based on the successive observation of fatigue damage on the surface using the plastic replica technique, followed by an analysis of the data assuming a Weibull distribution. A statistical investigation of the physical basis of scatter in relation to the ferrite grain size was performed, i.e. the distributions for crack initiation life, crack propagation life, fatigue life and growth rate of small cracks. Finally, the fluctuation of crack growth rate was studied in relation to the application of a crack growth law for microstructurally small cracks.     

HIGH CYCLE FATIGUE AND THRESHOLD BEHAVIOUR OF POWDER METALLURGICAL Mo AND Mo-ALLOYS

Abstract A detailed characterization of the room temperature fatigue properties of powder metallurgical Mo, Mo–W and Ti–Zr–Mo (TZM) alloys is presented. In particular the factors affecting fatigue crack nucleation and growth behaviour are described. Fatigue tests were carried out by conventional rotating-bending and compared with results from a time-saving 20 kHz resonance push-pull test method. Fatigue strength data were determined by a statistical evaluation of test results from a sufficiently large number of specimens. The results show an increase in fatigue strength with alloying additions. Fatigue cracks were observed nucleating at highly localized slip bands at the specimen surface with the fatigue crack zones comprising only a small fraction of the total specimen cross-section. Fatigue crack growth rates at low stress intensities and threshold stress intensity values for crack growth were determined for a stress ratio of R =– 1 using a 20 kHz resonance test method. These latter values were found to be sensitively dependent on microstructure, composition and processing history.     

FATIGUE GROWTH OF PHYSICALLY SMALL INCLINED CRACKS

The growth of physically small, self initiated, inclined corner and through-the-width cracks is investigated in a carbon steel under tension fatigue (R= 0.05). A preliminary procedure involving crack initiation under far-field cyclic compression is used. This precracking method is adopted to minimize the effect of residual damage at the tip of the crack grown (and arrested) under cyclic compression. Thus, the subsequent tensile fatigue crack propagates through a region with no (or very small) residual stress or damage. Experiments indicate that the early growth rate of the inclined corner cracks is discontinuous with a few decelerations. During the intermittent propagation period the corner cracks only extend into the thickness (depth) of the specimen and do not propagate along the width direction. However, after reaching a certain aspect ratio, the inclined flaws grow in a steady (continuous) manner in both the thickness and width directions. Through-the-width cracks, both inclined and perpendicular to loading direction, do not show the discontinuous growth pattern typical of the inclined corner cracks, but exhibit only one minimum in the crack growth rate behaviour.     

The characterization of fatigue crack growth behaviour by constant ΔK control testing

Essential to the assessment of the fatigue integrity of critical components is the prediction of their crack propagation lives. This requires the effective and efficient characterization of the fatigue crack growth behaviour of the material when using a small number of specimens. A test facility, able to control the range of applied load (Δ P ) and range of stress intensity factor (Δ K ), has been used to determine the fatigue crack growth rates in corner notched specimens of Udimet 720 for stress ratios of 0.5, 0.1 and −1.0. Initially, the results were analysed in terms of the three-point secant data reduction method. Subsequently, the benefits to be gained by the use of alternative methods involving regression analysis have been examined. The effectiveness of the procedures has been assessed in terms of the extent to which they reduce the width of the scatter band representing the fatigue crack growth behaviour and the accuracy with which the experimental observed fatigue lives are predicted. On this basis, the results from the Δ K controlled tests were superior to those obtained under Δ P control, when analysed by similar data reduction methods. In addition, the results from Δ K tests were improved when the secant method was replaced by a linear regression method, which allowed the sample interval to be reduced and more levels of constant Δ K to be examined in a single specimen.     

SCATTER IN SMALL CRACK PROPAGATION AND FATIGUE BEHAVIOUR IN CARBON STEELS

In order to investigate the physical basis of scatter in fatigue behaviour, rotatory bending of smooth fatigue specimens was carried out using two steels with different microstructures (ferrite/pearlite and tempered martensite). Fifteen or sixteen specimens were fatigued at each stress, and the initiation and propagation behaviour of a crack which led to the final fracture were examined for all the specimens. The emphasis was to investigate the scatter characteristics of fatigue behaviour based on the scatter of small crack propagation data. The data were analysed by assuming the Weibull distribution, and a statistical investigation of the physical basis of scatter was performed, i.e. the distributions for fatigue life, crack propagation life and growth rate of small cracks were established and the relation between the scatter in those distributions was studied.     

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.     

INITIATION AND PROPAGATION OF SHORT FATIGUE CRACKS IN A WELD METAL

Abstract— Fatigue tests were performed using a purpose designed triangular shaped specimen to investigate the initiation and propagation of short fatigue cracks in a weld metal. It was observed that short fatigue cracks evolved from slip bands and were predominantly within ferrite grains. As the test progressed, the short crack density increased with minor changes in crack length. The growth of short cracks, in the early stage resulted mainly from coalescence with other existing cracks. The mechanism of short crack behaviour is discussed.     

The evolution of short fatigue crack lengths and crack density: two approaches

The density and size of short cracks on the surface of 1Cr18Ni9Ti stainless steel smooth specimens during low cycle fatigue are investigated using a replica technique. The density and size data are analysed from two different observation policies, i.e. Policy I pays attention to the whole specimen test piece and Policy II is related to an ‘effective short fatigue crack criterion’, which pays attention to the dominant crack (DC) initiation zone and the zones ahead of the DC tips. The results reveal that both the crack density and crack size evolution exhibit a specific character during the microstructural short crack (MSC) and physical short crack (PSC) stages. The Policy I‐based observations exhibit an increasing density and little scatter of the density data. The increasing density violates the general test observation of decreasing collective crack effects in the PSC stage. The little scatter is too small to reflect the intrinsic scatter of fatigue properties. Both the crack density and crack size evolution from this policy show little relationship with the intrinsic localization of fatigue damage. However, Policy II‐based observations show an increasing crack density and an increasing density scatter in the MSC stage. The density and scatter reach their maximum values at the transition point between the MSC and PSC stages. Then, they decrease with fatigue cycling in the PSC stage and tend to their saturation values when the DC size is above about 500 μm. This behaviour shows a good agreement with the general test observations of decreasing collective crack effects and growth rate scatter in the PSC stage. Further, both approaches exhibit an evolutionary positively skewed crack size distribution, and an increasing difference between the average crack length and the DC length in the PSC stage, indicative of decreasing collective crack effects. A three‐parameter Weibull distribution (3‐PWD) is appropriately used to describe the crack sizes and a 6.5 to 7.6 μm value of location parameter of the distribution is obtained to reflect a minimum value for the initial cracks. It is worth noting that Policy I‐based observations show an increasing positively skewed crack size distribution, an increasing scatter of the size data and a decreasing shape parameter of the 3‐PWD. This represents an increasing collective crack effect and an increasing irregularity of interactive cracks, which violates the general test observations. In contrast, Policy II‐based observations exhibit a decreasing positively skewed size distribution shape and an increasing (from <1 gradually to >1) shape parameter of the 3‐PWD that is in agreement with the general test observations. The increasing shape parameter indicates that the collective crack effects act as an evolutionary process from an initial non‐ordered (chaotic) random state gradually to an independent random state at the transition point between the MSC and PSC stages and then, to a loading history‐dependent random state. This behaviour is in accordance with the evolutionary DC growth behaviour. Therefore, the evolutionary short crack behaviour associated with the intrinsic localization of fatigue damage should be appropriately revealed from the ‘effective short fatigue crack criterion’‐based observations.     

Fatigue growth of small corner cracks in aluminum 6061-T651

Results of an experimental investigation of the fatigue growth of small corner cracks emanating from small flaws are presented. A three-point bending state of loading was used and, by virtue of the orientation of the square cross-section of the specimen, the maximum tensile stress was developed at the middle of the gage section and on a corner edge. A growth-arrest behavior was observed and increases in crack length during growth periods were of the order of the transverse grain size, so it is inferred that grain boundaries act as barriers to continuing growth.     

THE GROWTH OF SMALL CORROSION FATIGUE CRACKS IN ALLOY 2024

Abstract— The corrosion fatigue crack growth characteristics of small surface and corner cracks in aluminium alloy 2024 is established. The damaging effect of salt water on the early stages of small crack growth is characterized by: (1) crack initiation at constituent particle pits, (2) intergranular microcracking for a≤100μm, and (3) transgranular small crack growth for a≥100μm. In aqueous 1% NaCl and at a constant anodic potential of −700 mV_SCE, small cracks exhibit a factor of three increase in fatigue crack growth rates compared to laboratory air. Small cracks exhibit accelerated corrosion fatigue crack growth rates at low levels of Δ K (< 1 MPa√m) below the long crack Δ K _th value. When exposed to Paris regime levels of crack tip stress intensity, small corrosion fatigue cracks exhibit growth rates similar to that observed for long cracks. Similar small and long crack growth behavior at various levels of R suggest that crack closure effects influence the corrosion fatigue crack growth rates of small cracks for a≥100 μm. Contrary to the corrosion fatigue characteristics of small cracks in high strength steels, no pronounced chemical crack length effect is observed for alloy 2024 exposed to salt water.     

THE EFFECT OF CRACK LENGTH ON FATIGUE THRESHOLD

This paper puts forward a new method for analysing the behaviour of very short fatigue cracks. A probability function is introduced into the definition of the growth threshold, which rationalises the scatter in experimental data produced using an aluminium bronze alloy. This probability function can be visualised in terms of the microstructure of the material.
It is shown that, in this material as in mild steels, fatigue crack initiation is not the critical stage. Initiation occurs relatively easily, but the cracks so formed may grow to only a few grain diameters in length before being arrested; thus it is the behaviour of cracks of this length which is critical in determining the fatigue strength of the material.
These observations, when combined with the probability functions, allow estimation of the probability of failure of a component or structure in service with greater confidence than the methods used at present.     

Simulation des Mikrorisswachstums unter Schwingbeanspruchung. Teil 1: Modell und Simulationsergebnisse,Mikrorisswachstum, Streuung,Einfluss von Beanspruchungsart und ‐höhe,Risskeimdichte und Korngröße

Simulation of fatigue microcrack growth. Part 1: Modelling and results of simulation, microcrack growth, scatter, effect of load condition, density of microcrack seeds and grain size Presented is a simulation of microcrack growth under alternating stresses. Microstructural barriers and the state of stress play a dominant role in the early stages of crack growth of metals. The polycristalline metal was modeled as an aggregat of hexagonal grains with a different crystallographic orientation of each grain. The effect of grain bounderies on stage I crack growth is considered in the model. The mode of shear crack growth is analyzed on the basis of microstructural crack growth within the first few grains, where the crack growth decelerates as the crack tip gets closer to the grain boundery. Normal stress crack growth has been considered for those cracks which are longer than microstructurelly short cracks, so‐called physically small cracks. Furthermore the transition from stage I to stage II growth is considered. The model is applied for thinwalled tubular specimens of the ferritic steel AlSI 1015 and the aluminium alloy Al Mg Si 1 subjected to tension and torsion as well as combined tension‐torsion loading. Also different load sequences are investigated. The microstructural crack pattern and crack distribution can sucessfully simulated with the model. The crack growth behaviour and the effect of lifetime until a crack length of 500 μm ist presented for numerous parameters.     

A NOTE ON MODELLING SHORT FATIGUE CRACK BEHAVIOUR

Based upon experimental short fatigue crack growth data and adopting the Brown–Hobson model, new crack growth equations have been derived in an attempt to describe more precisely short fatigue crack growth behaviour that separates the physically small crack regime from the long crack regime. An empirical model for physically small crack growth was developed by employing elastic–plastic fracture mechanics parameters.
By considering the proposed approach to short fatigue crack modelling, a new second 'microstructural' threshold condition has been established using only short fatigue crack growth data. In the case of fatigue in an aggressive environment it is suggested that three transition (threshold) conditions can be identified representing: (i) a stress-assisted pitting/pit-to-crack transition; (ii) a microstructurally short shear crack/physically small tensile crack transition; and (iii) a physically small crack/long crack transition.
A comparison of this approach with that of existing models has been made, and predictions of total fatigue lifetime using the model have been presented. A reasonable agreement has been observed between predicted and experimental crack growth rates.     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.     

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.     

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.     

An examination of small fatigue crack morphology

Test results for the growth of a small corner crack under cyclic loading are presented. The number of grains that are crossed by the crack front ranges from about three to ten during the crack advance. Crack path profile measurements on the adjacent corner faces are presented. Also, a microscopic examination of the crack path morphology of a polished and etched surface that is adjacent to the corner reveals the presence of complex branching mechanisms, and localized regions of intensive damage. Examination of sub-surfaces reveals that though branching and localized damage are present, they diminish with increasing depth of the subsurface. It is concluded that during early growth, the crack surface deviates substantially from an idealized planar surface model, and that Modes I, II, and III are all operative.     

The influence of microstructure on fatigue crack propagation in polyoxymethylene

An analysis of the influence of crystalline microstructure on fatigue crack propagation in poly-oxymethylene is presented. A series of test specimens containing a variety of diverse micro-structures was prepared through controlled thermal treatments of plaques from four different lots of polyoxymethylene. Extensive characterization of the crystalline microstructure was carried out in order to permit a direct comparison between the fatigue behaviour and crystalline microstructure. The degree of crystallinity and tie molecule density were both found to have a significant affect on fatigue crack propagation rate while average spherulite size did not appear to influence fatigue behaviour. Additionally, the fatigue fracture surfaces of many of the test specimens were examined. Three distinct surface topographies were observed and found to correlate with different stages of crack growth. In the region near the end of fatigue crack propagation, closely spaced surface markings that resemble fatigue striations were observed.     

Microstructural influence on the scatter in the fatigue life of steel reinforcement bars

Fatigue damage accumulation and failure of steel reinforcement bars (rebars) is a stochastic process. Scatter can be influenced by the sensitivity of the short crack growth to the microstructural features, especially near the fatigue limit. This work investigates the scatter inherent to the microscopic conditions near the fatigue limit of ferrite–pearlite and martensite microstructures found in the outer layer of rebars. An adapted Navarro–De Los Rios model within a Monte-Carlo framework is used to simulate the short crack growth in material grains. Grain size variation, grain orientation factor and multiple phases i.e., ferrite–pearlite and martensite were considered in the model. The results are compared with the scatter found in fatigue tests on hot-rolled-cold worked (HR-CW) as well as quenched and tempered (QST) rebars. It is shown that microstructural effects explains part of the observed scatter in the fatigue tests.     

A RELIABILITY-BASED MODEL TO PREDICT SCATTER IN FATIGUE CRACK NUCLEATION LIFE

This paper investigates the scatter inherent in the early stages of fatigue life. A probabilistic fatigue model is proposed which relates the microstructural heterogeneity to the scatter in crack nucleation life. The crack nucleation life is defined as the number of cycles necessary to develop a crack with a length equal to the grain size. The model assumes homogeneity at the level of the grain size. A fracture mechanics-based microstructural model is used to describe the response of the grains. The primitive random variables which drive crack nucleation are identified and recent developments recorded in the literature are used to describe their statistical characteristics. First order reliability methods are used to predict the statistical distribution of fatigue crack nucleation life. Comparisons are made with trends in experimental observations.