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 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.     

PREDICTION OF THE FATIGUE THRESHOLD FOR A CRACKED BODY USING SHAKEDOWN THEORY

Abstract— In this paper, the fatigue threshold Δ K _th of a cracked body is studied. Unlike other approaches given in the literature, the shakedown theory is used for predicting Δ K _th. A crack is considered as a sharp notch, the radius of which, at the threshold stress level, is a material constant. The threshold of crack propagation is explained as being due to shakedown of the cracked body, and a simple but reasonable model is derived. The value of Δ K _th is found to be proportional to the yield stress multiplied by the square root of the effective crack tip radius. Using this model, Δ K _th is calculated for some materials. Comparison of the predicted fatigue thresholds with those obtained by experiments, or by using other approaches, indicates that our model provides satisfying results.     

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.     

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.     

INVERSION OF THE STRAIN-LIFE AND STRAIN-STRESS RELATIONSHIPS FOR USE IN METAL FATIGUE ANALYSIS

Abstract— Two methods are described for inverting the strainrange/life and strainrange/stressrange equations commonly used in fatigue analysis in order to obtain closed-form expressions for life and stressrange in terms of strainrange. In the Collocation approach the form used is N _f= A (Δε—Δε₀)γ or N _f= A (Δε)Ψ(Δε—Δε₀)γ. In the Spline-Function approach the curve is divided into two regions. At strainranges above where the elastic and plastic lines intersect the equation is N _f= N _T R ^1/c exp δ R α; at lower strainranges it is N _f= N _T R ^1/b exp δ R β, where N _T is transition life, R is strainrange normalised to transition strainrange, and b, c , α, β, δ are constants determinable from the constants of the equation to be inverted. Similar expressions are derived for the cyclic stress/strain curve in terms of the same constants. The methods are illustrated by an example, and found to have close conformity to the basic equations to be inverted.     

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.     

EFFECT OF FATIGUE CRACK CLOSURE ON NEAR-THRESHOLD CRACK RESISTANCE OF STRUCTURAL STEELS

Abstract— The present paper is an attempt to clarify conditions for plasticity-induced and oxide-induced crack closure as well as to evaluate the effect of crack closure on near-threshold fatigue crack behaviour.
The autocatalytic character of oxide formation at the crack tip has been elucidated in this study. An increase of plastic constraint at the crack tip is shown to intensify the fretting oxide formation process on the fracture surface and thus to cause an increase of the stress intensity factor range controlling the fatigue crack propagation rate. The proposed concept of stress state influence on crack closure allows us to explain the effect of specimen thickness on Δ K _th.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

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.     

FATIGUE MACROCRACK GROWTH IN TEMPERED HY80, HY130, AND 4140 STEELS:THRESHOLD AND MID-ΔK RANGE

Abstract— –The rate of propagation of macrofatigue cracks down to near threshold was measured in air in three tempered martensitic steels; HY80, HY130 and 4140 (650°C temper). The value of Δ K _th was determined by the load-shedding technique in center notched panel specimens. Of the three steels, 4140 tempered at 650°C had the lowest Δ K _th, 3–5 MN/m^3/2, while HY80 had the highest, 4.2 MN/m^3/2. The 4140 (650°C temper) is intermediate in strength between HY80 and HY130. The results are discussed in terms of a recent theory of one of the authors.
The fatigue crack propagation rates in the mid-Δ Krange in HY80 and HY130 in argon were also studied by measuring, with foil strain gages, the cyclic plastic work to propagate a fatigue crack by a unit area, U.HY 80 has a lower crack propagation rate and correspondingly higher U .This was attributed in part to the higher yield strength of HY130 but the dislocation structure and carbide composition and morphology also play roles. Microstructural changes due to cyclic plastic deformation inside the plastic zone in HY80 and HY130 were observed by TEM of thin foils. SEM studies of the fracture surfaces at Δ K = 20 MN/m^3/2 indicate a more ductile fracture mode for HY80 than for HY130. The fatigue crack propagation rate of HY130 is substantially higher in laboratory air (47% relative humidity) than in dry argon. This is not the case for HY80.     

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.     

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.     

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 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.     

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 ACCELERATED TEST METHOD FOR DETERMINING NEAR-THRESHOLD STRESS INTENSITY VALUES IN HSLA STEELS

Abstract— A new method for accelerating the collection of near-threshold corrosion fatigue crack propagation data, using local hydrogen embrittlement in the crack tip region, has been investigated for ASTM A710 HSLA steel. Fatigue tests were conducted at 10 and 0.2 Hz (stress ratio, R = 0.1) on "constant K " contoured double cantilever beam (CDCB) specimens, to establish near-threshold crack growth rates in a locally hydrogen charged region at the crack tip. Hydrogen charging was then discontinued and crack growth rates were monitored in the uncharged material. Near-threshold fatigue crack growth rates were found to be 100 times faster in the locally hydrogen charged specimens than in the uncharged material. Fatigue thresholds, Δ K _th, were defined in less than one fifth the time required for load shedding tests in air at 0.2 Hz. Although demonstrated for HSLA steels, the technique is applicable to any material which can be embrittled by hydrogen.     

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.     

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.     

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.