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.     

The preferred fatigue crack propagation mode in a M250 maraging steel loaded in shear

Macroscopic torsional fatigue cracks are shown to propagate in shear, in plain tubular specimens, in the M250 maraging steel, for stress ranges from 90% down to 40% of the yield stress. This cannot be explained in terms of microcrack coalescence for the smallest stress range, for which microcracks are scarce. The kinetics and mechanisms of mode II fatigue crack growth are thus investigated, using precracked CTS or tubular specimens. For a high Δ K _II , slowly decelerating mode II propagation takes place for a distance that increases with Δ K _II before branching occurs. Friction stresses along the crack flanks shield the applied load and explain this deceleration. An inverse analytical procedure is used to derive the effective stress intensity factor, allowance being made for friction effects, from displacement profiles measured from microgrids using a scanning electron microscope. The measured crack growth rates correlate much better with the effective stress intensity factor than with the nominal Δ K _II value. The crack paths observed in torsion are discussed in terms of maximum crack velocity.     

Very high cycle fatigue behaviour of 2000-MPa ultra-high-strength spring steel with bainite–martensite duplex microstructure

The very high cycle fatigue and fatigue crack growth (FCG) behaviours of 2000-MPa ultra-high-strength spring steel with different bainite–martensite duplex microstructures (designated as B-M1 and B-M2) obtained through isothermal quenching and fully martensite (designated as M) for comparison were studied in this paper by using ultrasonic fatigue testing and compact-tension specimens. It was found that for the B-M1 sample with well-controlled thin and uniformly distributed bainite, the fatigue crack threshold Δ K _th is higher and FCG rate da / dN at an early stage is lower than those of the M sample. Therefore, the former has rather longer fatigue life at high stress amplitude, though both have almost identical fatigue strength. However, the fatigue properties of bainite–martensite duplex microstructure are significantly deteriorated with the formation of large bainite. Furthermore, like that of the M sample, the S–N curves of the B-M1 and B-M2 samples also display continuous declining type and fish-eye marks were always observed on the fracture surface in the case of internal fractures, which were mainly induced by inclusion. A granular bright facet (GBF) was observed in the vicinity around the inclusion. For each of the three samples, the stress intensity factor range at the boundary of inclusion (Δ K_inc ) decreases with increasing the number of cycles to failure ( N _f), while the stress intensity factor range at the front of GBF(Δ K _GBF) is almost constant with N _f and equals to its Δ K _th. This indicates that Δ K _GBF might be the threshold value governing the beginning of stable crack propagation.     

A GENERALIZED CONCEPT OF A FATIGUE THRESHOLD

Abstract— The conditions for non-propagating LEFM type fatigue cracks were investigated on an Inconel, 617 Alloy in the range of K _max between 10 and 50 MPa m^1/2 under four different types of fatigue loading conditions. In all tests, K _max was held constant during the fatigue cycling prior to determining the non-propagation condition. It was found that with decreasing range of applied K the fatigue tolerance range Δ K _{eff, th} increases. Furthermore, there is slight increase of Δ K _eff,th with decreasing K _max of approximately 20–30% when K _max is decreased from 50 to 10 MPa m^1/2. The results of the four types of tests are considered in respect to the damage in the near-region of the crack front, i.e. increasing K _max increases the damage zone and therefore decreases the fatigue tolerance range Δ K _eff,th.     

On the mechanism of fatigue failure in the superlong life regime (N>107 cycles). Part II: influence of hydrogen trapped by inclusions

High cycle fatigue fracture surfaces of specimens in which failure was initiated at a subsurface inclusion were investigated by atomic force microscopy and by scanning electron microscopy. The surface roughness R _a increased with radial distance from the fracture origin (inclusion) under constant amplitude tension–compression fatigue, and the approximate relationship: R _a ≅ C Δ K ²_I holds. At the border of a fish-eye there is a stretched zone. Dimple patterns and intergranular fracture morphologies are present outside the border of the fish-eye. The height of the stretch zone is approximately a constant value around the periphery of the fish-eye. If we assume that a fatigue crack grows cycle-by-cycle from the edge of the optically dark area (ODA) outside the inclusion at the fracture origin to the border of the fish-eye, we can correlate the crack growth rate d a/ d N , stress intensity factor range Δ K _I and R _a for SCM435 steel by the equation
   
and by d a/ d N proportional to the parameter R _a .
Integrating the crack growth rate equation, the crack propagation period N _p2 consumed from the edge of the ODA to the border of the fish-eye can be estimated for the specimens which failed at N _f > 10⁷. Values of N _p2 were estimated to be ∼1.0 × 10⁶ for the specimens which failed at N _f ≅ 5 × 10⁸. It follows that the fatigue life in the regime of N _f >10⁷ is mostly spent in crack initiation and discrete crack growth inside the ODA.     

A TEST METHOD FOR MODE II FATIGUE CRACK GROWTH RELATING TO A MODEL FOR ROLLING CONTACT FATIGUE

Abstract— From fractographic observations of specimens that have failed due to rolling contact fatigue, it has been concluded that the first stage of damage is the formation of mode II fatigue cracks parallel to the contact surface due to the cyclic shear stress component of the contact stress. Although these initial subsurface cracks, in both metals and ceramics, are produced in a direction parallel to the cyclic shear stress, cracks eventually grow in a direction close to the plane of the maximum tensile stress if we apply a simple mode II loading to them. The difference between crack growth in simple mode II loading and crack growth due to rolling contact fatigue is, we suppose, whether or not there is a superimposed compressive stress. Based on this hypothesis, we developed an apparatus to obtain the intrinsic characteristics of mode II fatigue crack growth, and developed a simplified model of subsurface crack growth due to rolling contact fatigue.
Some results in terms of da/dN versus ΔK_II relations have been obtained using this apparatus on specimens of steel and aluminum alloys. Fractographs of the mode II fatigue fracture surfaces of the various materials are also provided.     

THE RELATION BETWEEN CRACK BLUNTING AND FATIGUE CRACK GROWTH RATES

Abstract— Previous work has shown that the inclusion of the strain energy released by crack blunting leads to an energy minimum for fatigue crack growth that can be used to predict stage II fatigue crack growth. The present work assumes a polynomial relation between crack blunting and crack extension to derive an expression for the rate of fatigue crack growth that is dependent upon only the applied Δ K , E , σ_ys, K _c, and the exponent p in the relation between crack blunting and crack extension. This expression is thought to be generally valid since it accurately predicts fatigue crack growth rates for a wide variety of titanium, nickel, aluminium and steel alloys. A unique characteristic of the model is its ability (for long crack, slow crack growth) to account for the different slope for different materials in the Paris Law region of the d a /d N vs. δ K curve. The model specifically shows that this slope, m , is dependent solely upon the exponent, p , in the relation between crack blunting and crack extension.     

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 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.     

NON-ISOTHERMAL FATIGUE CRACK GROWTH IN HASTELLOY-X

Abstract— Non-isothermal fatigue crack growth tests were performed on Hastelloy-X single edge notch specimens in which strain and temperature were varied simultaneously. Conditions were selected to include nominally elastic and nominally plastic conditions and temperatures up to 925°C. The crack growth rates were first reported as a function of the strain intensity factor (δ K _ε) derived from a crack compliance analysis. Out-of-phase (ε_max at T _max) cycling showed faster crack growth rates than isothermal or in-phase (ε_max at T _max) cycling under elastic straining. Under fully plastic cycling, the opposite results was observed, i.e. crack growth rates under isothermal cycling are faster than under TMF cycling. On a δ K _ε-basis, a strain range effect was observed. All the results were rationalized using a corrected stress-intensity factor (δ K _eff) computed from the actual load, the closing bending moment caused by the increase compliance with crack length, and with the effective opening stress. Each mode of fracture was found to be characterized by a unique crack growth rate vs δ K _eff curve. On a δ K _eff-basis, the isothermal crack growth rates at T _min and T _max provide an upper and a lower bound for the TMFCG rates. The effectiveness of δ K _eff to correlate crack growth rates under fully plastic cycling is discussed in detail.     

DETERMINATION OF KI AND KII FOR CURVILINEAR CRACKS UNDER A NON-UNIFORM BIAXIAL STRESS FIELD

Abstract— Any structural element subjected to a static or alternating biaxial load with variable or random amplitudes may suffer from damage that can be described by fracture mechanics parameters. Brittle fracture conditions, fatigue crack growth rate and direction, as well as corresponding safety margins, are the most important unknowns which have to be predicted.
A method is presented for estimating stress intensity factors K _I and K _II for a curvilinear crack subjected to a non-uniform biaxial stress field. The method is based on the assumption of an equivalent arc crack, determined separately for each of the real crack tips. The K _I and K _II values are estimated by means of a modified weight function, called a unitary weight function, evaluated here for the arc crack by using the boundary element method (BEM). According to the principle of superposition any form of non-uniform stress field may be considered. Accuracy of the method and associated problems of curvilinear crack analysis are also discussed.     

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.     

An experimental and theoretical approach for an estimation of ΔKth

The existence of a fatigue threshold value may affect the design process when a damage-tolerant design is considered that uses non-destructive techniques for evaluating the shape and dimensions of the defects inside materials. Obviously it should be possible to estimate the stress field surrounding these defects and this is not generally a problem with modern numerical methods.
Many factors are involved in determining the growth rate of a fatigue crack. Some of these are highly significant and it is possible to obtain the coefficients of a correlation function. Some others are not well defined and the only effect is to expand the scatter of experimental data.
Consider the sigmoidal curve we obtain when plotting the crack growth rate versus the applied Δ K _I . A very difficult parameter to measure but very useful for fatigue design is the Δ K _Ith value, because below this value a crack may be forming, hence, here Δ K _Ith is defined by the transition between a normal (e.g. 10⁻¹⁰ m/cycle) and a very low range of crack growth rate (<10⁻¹⁰ m/cycle).
The Δ K _Ith value is very difficult to obtain by experimental methods because the growth rate is of the order or less than the atomic lattice span (3 × 10⁻¹⁰ m/cycle), but we can correlate the transition value with the cyclic crack tip plastic zone size and other structural parameters of metallic materials.
The aim of this work is to offer a contribution about the parameters which influence Δ K _Ith in stainless steels and welded joints based on the crack tip plastic zone radius.     

A MODEL OF FATIGUE CRACK GROWTH AFTER AN OVERLOAD IN D16T Al-ALLOY SUBJECTED TO BIAXIAL CYCLIC LOADS AT VARIOUS R-RATIOS

Abstract— Fatigue crack growth after a biaxial overload has been investigated. The crack retardation parameters, N _D, and, a _D, do not have monotonous dependencies on the biaxial stress ratio, λ, because the shear stress, τ_III, acting in the perpendicular direction of the specimen face, influenced the values of these parameters.
It has been found that the plastic zone size parameters, r _ab, and Δ, do not increase monotonously with increasing λ ratio. The plastic zone size in the crack growth direction, r _ho= a _D13, was calculated on the basis of newly proposed relations.
Crack growth after an overload was simulated on the basis of the equivalent mode I stress intensity factor, IC_C, invoking a unified kinetic diagram and calculated crack increments, a _D13 and a _D=Δ_c, where Δ_c is the maximum value of the calculated size of plastic zone. The experimental data for crack growth after an overload had good agreement with the calculated data.     

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.     

AN EXPERIMENTAL PARAMETER Jmax IN ELASTIC-PLASTIC FATIGUE CRACK GROWTH

Abstract— Imitating Garwood's 3-parameter technique, an experimental parameter J _max was introduced to predict fatigue crack growth rate (d a /d N ) over a wide range including small scale yielding and large scale yielding. It was found that for a Δ K -increasing fatigue test condition, J _max is a valid parameter. A significant crack growth acceleration, caused by a transition of fracture mechanism, occurs when J _max= J _IC The fracture mechanism involving striation formation when J _max < J _IC becomes ductile tearing when J _max > J _IC Equations to predict the effect of stress-ratio on J _max as well as on d a /d N are given.     

THE SIZE OF PLASTIC ZONES AND FATIGUE CRACK GROWTH BEHAVIOUR OF THREE FORMS OF A Ti–6Al–2.5Mo–1.5Cr ALLOY

The effect of microstructure on the fatigue properties of Ti–6Al–2.5Mo–1.5Cr alloy was investigated. The experimental results for both the fatigue crack initiation and propagation behaviour, as well as the dynamic fracture toughness ( K _Id ) showed clearly that a lamellar microstructure is superior to two other structures. It was found that, as in the case of steels, the initiation and subsequent growth of cracks in the titanium specimens with a sharp notch may also occur on loading levels below the threshold values of the K factor (Δ K _th ) determined for long fatigue cracks. In addition, measurements by interferential-contrast of the plastic zone size on the surface of specimens revealed that the different rate of crack growth at identical values of Δ K in individual structural states can roughly be correlated with the size of the plastic zone. A general relationship between the fatigue crack growth rate and plastic zone size, the modulus of elasticity and the role of crack tip shielding is discussed.     

SLOW FATIGUE CRACK GROWTH AND THRESHOLD BEHAVIOUR IN AIR AND VACUUM OF COMMERCIAL ALUMINIUM ALLOYS

Abstract— Fatigue crack growth and threshold behaviour have been examined in three commercial aluminium alloys in both air and vacuum environments. It was observed that, in air, the threshold stress intensity range Δ K _t, varied linearly with the Δ K _t ratio. In contrast Δ K , in vacuum was found to be independent of R. Over the whole growth rate range examined fatigue crack growth in vacuum was Δ K controlled and failure occurred by a dimple and ductile striation mechanism. This also applied to failure in the intermediate growth rate ranges in air. However, at slow growth rates in air, fatigue crack growth was structure sensitive and crystallographic facets were formed during the crack propagation process.     

FATIGUE CRACK GROWTH FROM A CIRCULAR NOTCH UNDER HIGH LEVELS OF BIAXIAL STRESS

Abstract— A series of experiments have been conducted on cruciform specimens to investigate fatigue crack growth from circular notches under high levels of biaxial stress. Two stress levels (Δσ₁= 380 and 560 MPa) and five stress biaxialities (λ=+1.0, +0.5, 0, −0.5 and −1.0; where λ=σ₂/σ₁ were adopted in the fatigue tests in type 316 stainless steel having a monotonic yield strength of 243 MPa. The results reveal that fatigue crack growth rates are markedly influenced by both the stress amplitude and the stress biaxiality. A modified model has been developed to describe fatigue crack growth under high levels of biaxial stress.     

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.