FRACTOGRAPHIC ANALYSIS OF FATIGUE CRACK GROWTH IN ENGINE COMPRESSOR DISKS OF Ti-6Al-3Mo-2Cr TITANIUM ALLOY

Abstract—Fractographic features related to fatigue crack growth in a Ti-6Al-3Mo alloy are studied using compressor disks tested on a hydraulic test bed and which simulate operational multiaxial cyclic loading conditions. The hold-time of a cycle results in the formation of a fracture relief which reflects mainly the two-phase (α+β) lamellar structure of the titanium alloy and a fragmentary fatigue striation formation. Correlation between the number of fatigue striations on the fracture surface and the number of applied blocks of loading (imitating the service conditions of compressor disks) has been obtained. The hold-time duration of the cycle does not affect the crack growth rate and the formation of the fracture relief in this material. An analytic expression is suggested to describe the relationship between fatigue striation spacing, δ, and the stress intensity factor K ^c_I as applied to quarter-ellipse-shaped cracks; it is of the form δ= C[ f (τ, FCi)K^c _I]⁴, where f (τ, FCi ) accounts for the hold-time, τ, and the programmed loading together with their influence on the fatigue crack growth behaviour. The particular threshold value of stress intensity factor ( K ^c_I) is established at 20 MPa m. The work indicates that the role of τ manifests itself via a considerable acceleration of crack growth.     

A CRACK CLOSURE STUDY TO PREDICT THE THRESHOLD BEHAVIOUR OF SMALL CRACKS

Abstract— The small crack problem is addressed within the applicability of Linear Elastic Fracture Mechanics as the result of crack closure phenomenon. The variation of crack closure stress intensity factory K _op as a function of crack length, a , was determined in two materials, namely a A508 steel and a 2024A1 alloy. These results were obtained on two-dimensional small cracks ( a ≫ 0.1 mm) which were machined from long fatigue cracks. These measurements of K _op in addition to data published in the literature on a nodular cast iron and a 9Cr–1Mo steel yield to a unique characteristic function: K _op/ K _o= 1 –exp(– ka ) in which k is the only parameter to characterize the small crack effect. A prediction of the threshold behaviour of small and long cracks on A508 steel is made using the results of crack closure measurements.     

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.     

DYNAMIC FATIGUE AND COMPUTER SIMULATION OF THE BEHAVIOUR OF Y2O3-ZrO2 CERAMICS

Abstract— There is a critical stress rate K _c for each of the three ZrO₂ ceramics tested. Fracture is controlled by the materials polycrystal fracture toughness, K ^c_p, if the stress rate is less than K _c. Otherwise, fracture is controlled by the single crystal fracture toughness, K ^c_s. The crack growth parameters determined by dynamic fatigue experiments can only represent macrocrack growth behaviour although the fracture of specimens in experiments originates from small surface flaws.     

MECHANISMS OF CYCLIC FATIGUE-CRACK PROPAGATION IN A FINE-GRAINED ALUMINA CERAMIC: THE ROLE OF CRACK CLOSURE

Abstract— Cyclic fatigue-crack growth and resistance-curve behavior have been studied in a fine-grained (∼ 1 μm), high-purity alumina. Specific emphasis is given to the mechanisms associated with crack growth that are controlled by the maximum ( K _max) and the alternating (Δ K ), stress intensities and to the role of crack-face interference (crack closure), which is known to be an important crack-tip shielding mechanism in metal fatigue. Significant levels of subcritical crack growth were detected above a threshold stress intensity of ∼60% of the fracture toughness ( K _c) in the alumina, with growth rates displaying a far larger dependence on K _max compared to Δ K. The role of crack closure was examined using constant- K _max experiments, where the minimum stress intensity ( K _min) was maintained either above or below the stress intensity for crack closure ( K _cl). Where K _min< K _cl, growth rates were found to exhibit a lower dependence on Δ K , which was rationalized in terms of the frictional wear model for crack growth in grain-bridging ceramics. It is concluded that crack closure, as conventionally defined, has little relevance as a crack-tip shielding mechanism during fatigue-crack growth in grain-bridging ceramics, due to the low dependence of growth rates on Δ K compared to K _max.     

ON THE OVERLOAD INDUCED FATIGUE CRACK PROPAGATION BEHAVIOR IN ALUMINUM AND STEEL ALLOYS

The overload induced fatigue crack propagation behavior of several aluminum and steel alloys was examined as a function of the baseline stress intensity factor range (δ K _b). In order to gain a clearer understanding of the parameters which influence the cyclic delay phenomenon, under both plane strain and plane stress conditions, tests were conducted at δ K _b values ranging from the near threshold regime to high δ K levels approaching fast fracture. Large amounts of overload induced cyclic delay (˜100,000 cycles) were observed at both high and low δ K levels (provided the plastic zone size/thickness ratio and plastic zone size/grain size ratio approached unity, respectively) with significantly less delay occurring at intermediate δ K values. All alloys examined exhibited this type of delay behavior which can be described by a "U-shaped" plot. The delay phenomenon at high δ K _b levels under plane stress conditions was attributed to increased crack closure associated with large tensile displacements in the wake of the advancing crack. At low δ K _b levels increasing cyclic delay was attributed to an increased effective overload ratio as δ K approached δ K _th.     

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

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

EVALUATION OF FATIGUE CRACK PROPAGATION PROPERTIES UNDER RANDOM LOADING AVOIDING CRACK CLOSURE

Abstract— Fatigue crack propagation rates and the fatigue threshold of HT80 steel were measured by maintaining the maximum load during the whole period of random loading in order to prevent fatigue crack closure. The random loading pattern involved 62 level block loadings in which the waveform was approximated to the Rayleigh distribution of peaks. The fatigue crack propagation rates under random loading were well predicted from those obtained from constant amplitude loading and assuming a linear cumulative damage law. That is, da/dn = C {Δ K ^m_eq−Δ K ^m_th} where the equivalent stress intensity factor, Δ K _eq={= n _iΔ K ^m_i/d n _i}^{1/ m} , where n_i = 0 for Δ K _i≤Δ K _th, or n_i = n_i for Δ K_i > Δ K _th.     

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.     

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.     

THE INFLUENCE OF STRENGTH AND STRESS RATIO ON SHORT-CRACK THRESHOLDS AND NON-PROPAGATING FATIGUE CRACKS

Quantitative predictions of the influence of yield strength and stress ratio, R , on the physically small crack fatigue threshold stress intensity, Δ K _0(s), are presented. It is shown that at R = 0 to -1, although the threshold stress Δ₀ increases, the threshold stress intensity, Δ K _0(s), decreases with increasing yield strength. Moreover, a lower bound value, Δ K _0(s)(min) is shown to have a constant value, irrespective of the strength and stress ratio. For a given strength, Δ K _0(s), decreases with increasing R in the range -1 R 0.6 and attains a constant low value for R > 0.6. Predicted values of Δ K _0(s) are in good agreement with experimental data for steels. The formation and length of non-propagating fatigue cracks, a _np, are also discussed. The methods suggested for estimating Δ K _0(s) and a _np may be found useful in design procedures.     

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.     

CLOSURE AND GROWTH OF MODE I CRACKS IN BIAXIAL FATIGUE

Abstract— —The closure behavior of mode I fatigue cracks under biaxial loading is studied with an elastic-plastic plane stress finite element model. Biaxial stresses are shown to have a significant impact on crack closure behavior at higher maximum stresses. In general, normalized crack opening stresses are highest for equibiaxial loading and lowest for pure shear loading. The differences are apparently negligible for maximum applied stresses less than about 0.4 σ₀. Experimental crack growth data are quantitatively consistent with these trends. Correlations of the experimental data with a simple Δ K _eff were successful as first-order engineering estimates. Changes in forward and reversed plastic zone sizes with biaxiality are not entirely consistent with trends in crack growth rates.     

THE EFFECT OF STRESS RATIO ON THE FATIGUE THRESHOLD CONDITION OF PHYSICALLY SMALL CRACKS

An approach is proposed to predict the intrinsic threshold of physically small cracks without invoking crack closure considerations. The basic assumption invoked is that a Δ K representation is valid for short cracks, hence the lower-bound threshold value, ΔK_0(s)(min) for short cracks can be numerically equated with the lower-bound threshold value of long cracks, ΔK*_{0(l)(min), s} of the same material. Several experimental observations provide a basis for this rationalization. The approach allows a quantitative prediction of stress ratio and crack length dependence of Δ K _0(S) which provides good agreement with experimental data for several low-strength steels and aluminium alloys. This alternative procedure may be found useful in design applications.     

A multiparameter approach to the prediction of fatigue crack growth in metallic materials

A multiparameter approach is proposed for the characterization of fatigue crack growth in metallic materials. The model assesses the combined effects of identifiable multiple variables that can contribute to fatigue crack growth. Mathematical expressions are presented for the determination of fatigue crack growth rates, d a /d N , as functions of multiple variables, including stress intensity factor range, Δ K , stress ratio, R , crack closure stress intensity factor, K _cl , the maximum stress intensity factor K _max , nominal specimen thickness, t , frequency, Ω , and temperature, T . A generalized empirical methodology is proposed for the estimation of fatigue crack growth rates as a function of these variables. The validity of the methodology is then verified by making appropriate comparisons between predicted and measured fatigue crack growth data obtained from experiments on Ti–6Al–4V. The effects of stress ratio and specimen thickness on fatigue crack growth rates are then rationalized by crack closure considerations. The multiparameter model is also shown to provide a good fit to experimental data obtained for HY-80 steel, Inconel 718 polycrystal and Inconel 718 single crystal. Finally, the implications of the results are discussed for the prediction of fatigue crack growth and fatigue life.     

THE INFLUENCE OF TEST VARIABLES ON THE FATIGUE CRACK GROWTH THRESHOLD

Abstract— A microcomputer controlled fatigue crack growth and threshold testing system has been used to investigate the influence of test variables on the measured values of Δ K _th, the threshold for fatigue crack growth, using a C-Mn steel. The work has examined: (1) the influence of crack length and test management; (2) the basic material scatter from repeated testing; (3) the effect of unloading rate C where C = (1/Δ/ K )(d Δ K /d a ); (4) the effect of step unloading; (5) the influence of minimum stress intensity factor, K _min . Comparisons have been made between the results of this computer controlled work and those published previously but made using a manual load shedding technique. The results of Δ K _th and fatigue crack growth rates are in general agreement with previous data and confirm the K _min dependence of Δ K _th and d a /d n. The value of Δ K _th is shown to be generally independent of the other test variables for a wide range of conditions and is reproducible with a low degree of scatter.     

Application of the shadow optical method to fatigue and crack closure studies

In this paper it will be shown that crack closure and related crack shielding mechanisms can be studied successfully by applying the shadow optical method, also known as the method of caustics. It is shown that at least one mechanism - plasticity induced crack closure - can be identified and determined from measurements of the transverse diameter of the caustic in the crack tip region. For given fatigue conditions at which crack closure occurs, several experiments have been performed to investigate the effectiveness of the crack opening in a typical fatigue cycle.
Two different methods of closure determination have been used. A comparison is made between one of the most currently used methods of back face strain (BFS) compliance measurement and the shadow optical method (SOM). The underlying features of these two experimental techniques provide the key to finding the extent of the load in the fatigue cycles over which the crack is actually open. This redefines the value of K_min and the meaning of ΔK. The driving force, ΔK_eff is shown to be reduced in or near the fatigue threshold of the alloy, because crack closure is most effective in this part of fatigue loading. The introduction of SOM to fatigue crack closure provides a suitable alternative for finding the effective part of the stress intensity range between the minimum and maximum loads. Conclusions drawn from this work were that in addition to determining that part of the fatigue cycle over which the crack is actually open, the shadow optical method allowed an accurate interpretation of the entire fatigue cycle between K_max and K_min     

FINITE ELEMENT ANALYSIS OF SPECIMEN GEOMETRY EFFECTS ON FATIGUE CRACK CLOSURE

Abstract— Elastic-plastic finite element analysis is used to study fatigue crack closure at three different crack length to width ratios for three plane stress specimen geometries: center-cracked plate, single-edge-cracked plate (tension), and single-edge-cracked plate (bend). The maximum stress to flow stress ratio, S_max/σ_O, which successfully describes closure results in many center-cracked plate configurations, does not correlate the effect of different geometries on the normalized opening stress, S _open/ S _max. Crack opening stresses for different geometries and crack lengths are successfully correlated by a normalized stress intensity parameter, K _max/ K ₀, where K ₀=σ₀φa. The quality of the correlation is very high at small K _max/ K ₀, and gradually deteriorates as K _max/ K ₀ increases beyond the small-scale yielding regime.     

FATIGUE CRACK GROWTH OF SILICON NITRIDE WITH CRACK WEDGING BY FINE FRAGMENTS

Abstract— Fatigue crack growth tests of silicon nitride Si₃N₄ were carried out under four-point bending using square bar specimens at room temperature. A pre-crack was introduced by a bridge indentation method. Decreasing K -type tests at stress ratios of R = 0.1 and 0.6 and also under static load were first carried out, and after observing the cessation of crack growth, K -increasing tests were performed except for the case of a static load. Crack closure was observed on most specimens by the elastic compliance method. Furthermore, SEM observations of the crack paths were made to see what was happening during crack growth. The threshold and the region of steady crack growth were observed more clearly under cyclic loading, and an effect of load cycling certainly existed which became more evident when the maximum stress intensity factor K _max approached the threshold. A wedge effect, caused by fine fragments on the crack surface, played an important role in crack closure behaviour of each specimen, and it is suggested that the crack growth rate is controlled by both the effective stress intensity range Δ K _eff and the effective mean stress intensity factor K _m,eff at least as a first approximation.     

Mixed-mode crack opening displacement measurements for small fatigue cracks growing in Astroloy at 20 °C

Crack opening displacements were measured for small fatigue cracks in Astroloy being grown with uniaxial stress application under high-cycle fatigue conditions. Four cracks were investigated including one that grew from 27 to 74 μm in three increments. Most of the cracks grew at an angle to the loading axis and all opened bimodally. Crack opening scaled with distance from the crack tip similar to an elastic crack, which allowed the calculation of a local stress intensity factor for both mode I and mode II. The proportion of mode II stress intensity factor was relatively large, varying as 0.06 < Δ K _II /Δ K _I < 0.42, with an average of ~0.3. Thus, uniaxial loading remote to the cracks resulted in a bimodal opening response on the scale of the cracks.