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.     

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 NEW METHOD FOR THE MEASUREMENT OF MODE II FATIGUE THRESHOLD STRESS INTENSITY FACTOR RANGE ΔKτth

Abstract— In order to evaluate the threshold value Δ K _τth for mode II fatigue crack growth, a new measurement method of mode II fatigue crack growth has been developed. This method uses a conventional closed-loop tension—compression fatigue testing machine without additional loading attachments. Mode II fatigue tests for structural steel and rail steel have been carried out. This method has proved successful and has reproduced mode II fatigue fracture surfaces similar to those found in the spalling of industrial steel-making rolls. The crack length during testing was measured by an AC potential method. The relationships between d a /d N and Δ K _τ and AK _τth for several materials have been obtained.     

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.     

STUDY ON FATIGUE THRESHOLD BEHAVIOUR AND FATIGUE CRACK PROPAGATION IN A CAST Co-Cr-Mo ALLOY USED FOR SURGICAL IMPLANTS

Abstract— —Fatigue crack propagation rates (d a /d N ) and fatigue crack thresholds (Δ K _th) have been studied in a cast Co-Cr-Mo alloy used for surgical implants with various grain sizes. Results for materials with average grain sizes of about 400 and 60μm respectively are presented. Threshold values close to 10–15 MPam have been measured with decreasing values observed on increasing the grain size. Similar effects of grain size are found on the crack propagation behaviour at higher growth rates, where a coarse grain size material show a higher crack growth rate than a fine grain size material at the same Δ K levels. The effects of microstructure on fatigue properties of the cast Co-Cr-Mo alloy are caused not only by grain size variation but are also attributed to the microstructural differences: a coarse-grained material with a directionally grown dendritic structure vs a fine-grained material with an equiaxed grain structure.     

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 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.     

A STUDY ON THE CHANGE OF FATIGUE FRACTURE MODE IN TWO TITANIUM ALLOYS

The appearance of the fatigue fracture surface and crack growth curve have been examined for a Ti–2.5Cu alloy with different microstructures (two equiaxed and two lamellar microstructures), and for TIMETAL 1100 with a lamellar microstructure. With increasing Δ K , a slope change in the crack growth curve correlates with a transition in the fracture surface appearance (induced by a fracture mode transition); this being found in each microstructure. The microstructure size that controls the fatigue fracture is found to be the grain size for equiaxed microstructures and the lamella width for lamellar microstructures. The transitional behaviour can be interpreted in terms of a monotonic plastic zone size model in microstructures having a coarse microstructure size and in terms of a cyclic plastic zone size model for microstructures having a fine microstructure size.     

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.     

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.     

Microcrack nucleation, growth, coalescence and propagation in the fatigue failure of a powder metallurgy steel

Detailed quantitative micrographic data are presented for Stages I and II of a Powder Metallurgy Fe-1.5Cr-0.2Mo-0.7C steel specimen fatigued in bending with R  =−1 at 24 Hz and a stress amplitude of 312 MPa. The fatigue limit was ∼240 MPa, at which stress level no microcracks were detected in static loading. Testing was interrupted at 100 cycles and at further 29 intervals until failure after 49 900 cycles. For each arrest, surface replicas were made in the two regions where maximum stress was applied. Microcracks could nucleate below 100 cycles, when their sizes ranged from <5 to ∼20 μm. Fractographic examination identified the failure-originating site, which was then associated with the crack system observed on the 'last' pre-failure micrograph. Detailed examination of the eventual failure region showed nucleation, at various cycle intervals, of 18 microcracks, their subcritical growths, arrests and coalescences with continuing cycling to form a critical crack 2.25 mm deep. Stepwise microcrack growth was probably rapid – to the next arrest or coalescence. For each (micro)crack size stress intensity factors, K _a s, were estimated and, at the end of Stage II, for the coalesced crack, K _a reached K _1C, independently estimated to be ∼36 MPa m^1/2.     

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.     

CONSTANT AMPLITUDE AND POST-OVERLOAD FATIGUE CRACK GROWTH BEHAVIOR IN PM ALUMINUM ALLOY AA 8009

Abstract— The fatigue crack growth behavior of a recently developed, rapidly solidified, powder metallurgy, dispersion strengthened aluminum alloy, AA 8009, was studied at room temperature in laboratory air. Constant amplitude/constant Δ K and single spike overload conditions were examined. Alloy 8009 exhibited high fatigue crack growth rates and low closure levels in comparison to typical ingot processed aluminum alloys. It was proposed that minimal crack roughness and crack path deflection, along with limited slip reversibility, resulting from the ultra-fine microstructure were responsible for the relatively poor (versus ingot processed aluminum alloys) d a /d N versus Δ K performance of AA 8009.     

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 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.     

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.     

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.     

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.     

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.