A GENERAL CRITERION FOR HIGH CYCLE MULTIAXIAL FATIGUE FAILURE

Abstract— A new simple general criterion of failure for high cycle multiaxial fatigue, τ_a/ t _A.B+σ_{n. max}/2σ_T= 1 presented. The failure criterion is based on a critical plane approach where fatigue strength is a function of the shear stress amplitude and the maximum normal stress on the critical plane of maximum shear stress amplitude. The criterion takes account of whether case A cracks, growing along the surface, or case B cracks, growing into the surface, occur. It requires knowledge of the material properties, tensile strength, σ_T, and reversed shear fatigue strength for case A, t _A, or case B, t _B, cracking, whichever is relevant. t _A is the reversed torsion fatigue strength and t _B is found from a case B cracking test case. The criterion is applicable in the region, 0.5 t ≤ t _a≤ t , and 0 ≤σ_n.max≤σ_T.     

FATIGUE STRENGTH OF 7075-T6 ALUMINIUM ALLOY UNDER COMBINED AXIAL LOADING AND TORSION

The fatigue strength of 7075-T6 aluminium alloy under combined axial loading and torsion was examined. The S-N relations were correlated with the von Mises criterion for the high cycle region ( N _f≥ 10⁴ cycles) and with the Tresca criterion for the low cycle region ( N _f < 10⁴ cycles), where N _f is the cycles to failure. This transition at N _r= 10⁴ cycles was related to the occurrence of macroscopic plastic straining and a change in fracture modes. The results are discussed in comparison with those for a high strength steel (SNCM8) in a previous study. Particular attention is given to differences in cyclic deformation behaviour, fracture modes and fatigue crack growth rates between the two materials.     

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.     

PROBABILISTIC ASPECTS OF CLEAVAGE CRACK INITIATION SITES AND FRACTURE TOUGHNESS

Abstract— Fracture toughness tests were performed in the ductile-brittle transition temperature range using 110 specimens of the three-point bend and CT types. Probabilistic characteristics of fracture toughness and cleavage crack initiation sites were analysed in detail, together with the fibrous crack shape, from which the plane strain region in the specimen was deduced. The criterion for obtaining plane strain at the mid plane of the specimen was established as: B ≤ 0.004{ K _c( J )/σ _y }²+ 0.01. The thickness effect of cleavage fracture toughness for the specimen satisfying this equation is mainly caused by the statistical distribution of the weakest points ahead of the crack front (the Weibull volume effect).     

Gigacycle fatigue of ferrous alloys

The objective of this paper is to determine the very long fatigue life of ferrous alloys up to 1 × 10¹⁰ cycles at an ultrasonic frequency of 20 kHz. A good agreement is found with the results from conventional tests at a frequency of 25 Hz by Renault between 10⁵ and 10⁷ cycles for a spheroidal graphite cast iron. The experimental results show that fatigue failure can occur over 10⁷ cycles, and the fatigue endurance stress S _max continues to decrease with increasing number of cycles to failure between 10⁶ and 10⁹ cycles. The evolution of the temperature of the specimen caused by the absorption of ultrasonic energy is studied. The temperature increases rapidly with increasing stress amplitudes. There is a maximum temperature between 10⁶ and 10⁷ cycles which may be related to the crack nucleation phase. Observations of fracture surfaces were also made by scanning electron microscopy (SEM). Subsurface cracking has been established as the initiation mechanism in ultra-high-cycle fatigue (>10⁷ cycles). A surface–subsurface transition in crack initiation location is described for the four low-alloy high-strength steels and a SG cast iron.     

ANALYSIS OF FREE-EDGE STRESS AND DISPLACEMENT FIELDS IN SCARF JOINTS SUBJECTED TO A UNIFORM CHANGE IN TEMPERATURE

The role of free-edge stresses in controlling the initiation of failure from the interface corner of a scarf joint subjected to a uniform change in temperature is examined. In general, the stress field can be expressed by σ _ij = Hr ^{λ −1} + σ _{ij 0} , where r is the radial distance from the interface corner, λ − 1 is the order of the stress singularity, H is the intensity of the singularity, and σ _{ij 0} is a non-singular constant stress. A combination of the finite element method and a path-independent integral is used to evaluate the magnitude of H for two joint configurations: (i) a scarf joint between two long bi-material strips; and (ii) a scarf joint consisting of a thin elastic layer sandwiched between two substrates. The magnitude of H is linearly dependent on a non-dimensional constant function a; the magnitude of a decreases with increasing level of mismatch in the elastic properties of the bonded materials. A comparison between the values of H evaluated by the path-independent integral method and the commonly used extrapolation method indicate that the extrapolation method could be in error by as much as 25%.     

AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH-THICKNESS AND SURFACE FATIGUE CRACKS

Abstract— The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through-thickness physically-short (50–400 μm) cracks, and naturally-occurring microstructurally-small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–^12–10–⁶m/cycle). Results are compared with those predicted numerically using an elastic-plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through-thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near-threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.     

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.     

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.     

Weibull stress model for cleavage fracture under high-rate loading

This paper examines the effects of loading rate on the Weibull stress model for prediction of cleavage fracture in a low-strength, A515-70 pressure vessel steel. Interest focuses on low-to-moderate loading rates ( K˙ _I < 2500  MPa √m  s⁻¹ ). Shallow cracked SE(B) specimens were tested at four different loading rates for comparison with previous quasi-static tests on shallow notch SE(B)s and standard C(T)s. To utilize these dynamic experimental data, we assume that the Weibull modulus ( m ) previously calibrated using quasi-static data remains invariant over the loading rates of interest. The effects of dynamic loading on the Weibull stress model enter through the rate-sensitive material flow properties, the scale parameter ( σ _u ) and the threshold Weibull stress ( σ _w-min ). Rate-sensitive flow properties are modelled using a viscoplastic constitutive model with uniaxial, tension stress–plastic strain curves specified at varying plastic strain rates. The analyses examine dependencies of σ _w-min and σ _u on K˙ _I . Present results indicate that σ _w-min and σ _u are weak functions of loading rate K˙ _I for this pressure vessel steel. However, the predicted cumulative probability for cleavage exhibits a strong sensitivity to σ _u and, consequently, the dependency of σ _u on K˙ _I is sufficient to preclude use of the static σ _u value for high loading rates.     

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.     

FATIGUE OF A PARTICULATE REINFORCED ALUMINIUM METAL MATRIX COMPOSITE SUBJECTED TO AXIAL, TORSIONAL AND COMBINED AXIAL/TORSIONAL LOADING CONDITIONS

Abstract— The goals in this research were to analytically and experimentally investigate the fatigue behavior of a particulate reinforced metal matrix composite subjected to axial, torsional and combined axial/torsional loadings. A series of fully-reversed uniaxial, torsional and combined axial/torsional fatigue tests were performed on a 6061/Al₂O₃/20p-T6 metal matrix composite material. This research investigated the ability of the Fatemi-Kurath and the Smith-Watson-Topper (SWT) damage parameters to correlate the experimentally obtained fatigue life data and also to represent the fatigue life using uniaxial strain-life constants. The Fatemi-Kurath damage parameter correlated the experimental fatigue data from all loading cases better than the SWT damage parameter. Using uniaxial strain-life constants, both damage parameters predicted fairly reasonable fatigue life calculations for the intermediate fatigue lives (10³ to 10⁴ cycles to failure), while producing non-conservative results for the shorter fatigue lives (< 10³ cycles to failure).     

FATIGUE LIFE PREDICTION OF HEAT-TREATED CARBON STEELS AND LOW ALLOY STEELS BASED ON A SMALL CRACK GROWTH LAW

Abstract— Since heat-treated high strength steels are often used as materials for machines and structures that operate under severe service conditions, it is important to evaluate their fatigue life. Hence the growth law of a small fatigue crack must be known in order to estimate the fatigue life of machines and structures since the life of such members is controlled mainly by the behaviour of a small crack. The growth rate of a small crack can not be predicted usually by linear elastic fracture mechanics, but can be determined uniquely by the term σⁿ_a l , where σ_a is stress amplitude, l is crack length and n is a material constant. In this paper, the small-crack growth law of heat-treated carbon steels and low alloy steels was studied. An effective and convenient method based on a small-crack growth law, d l /d N = C ₃(σ_a/σ_a)ⁿ l is proposed, where σ_u is the ultimate tensile strength, for predicting the small crack propagation life of heat- treated steels with different tensile strength levels, together with a method for determining the fatigue life of plain members.     

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch-crack problem is treated in two different ways: if the non-dimensional crack length l /ρ ( l = crack length; ρ= notch root radius) is smaller than the transition crack length l _T/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ ρ is larger than l _T/ρ, the notch-crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, l _T, and for the geometric factor F = K _I/(1.1215K_tσ√π l ) are developed for various notch problems for the crack length range l ≦ l _T. It is found that the stress (σ_yy) normalized by the peak stress (σ_peak), σ_yy/σ_peak, for the pre-cracked component is very similar to the geometric factor for short cracks.     

EFFECTS OF NEUTRON IRRADIATION ON LOW-CYCLE FATIGUE AND TENSILE PROPERTIES OF AISI TYPE 304 STAINLESS STEEL AT 298 K

Abstract— Room temperature studies have been made of the effect of neutron damage on the mechanisms concerned with the low-cycle fatigue and tensile test behaviour of stainless steel AISI Type 304. Samples were irradiated in the HFR at Petten to a fast fluence of 5·10²⁴ n m⁻² ( E > 0·1 MeV) at 333 K followed by mechanical testing at room temperature. The low temperature irradiation caused irradiation hardening: the 0·2 yield stress increased from 230 MN m⁻² for the unirradiated material to a lower yield point value of 540 MN m⁻². Irradiation had no significant effect on fatigue life. The loop type damage was removed by glide dislocations resulting in cyclic softening. Dislocation substructures were observed after fatigue testing: cell structures were more pronounced after fatigue testing to failure the higher the applied strain ranges.
The formation of fatigue cracks at the surface of the specimens was observed in a series of specimens exposed to an increasing number of fatigue cycles.     

THE EFFECT OF STRAIN RATE ON THE TENSILE AND FRACTURE PROPERTIES OF BS 4360 'A' GRADE SHIP STEEL

Abstract— The results of high rate tensile and compact tension fracture toughness tests conducted on BS 4360 'A' grade ship steel are presented. Tensile results are reported for strain rates within the range 10–^2–10³/s and fracture toughness values at rates of increase of J integral within the range 10^3–10⁶ N/mm/s. The tensile properties of upper yield, lower yield and UTS are shown to be linearly dependent on the logarithm of strain rate whilst fracture toughness is shown to decrease with increasing loading rate prior to approaching a minimum value. The decrease in fracture toughness with increasing test rate is shown to be related to a change in the micro-mechanism of fracture.     

THE INFLUENCE OF LOADING RATE ON HYDROGEN INDUCED CRACKING OF MICRO ALLOYED STEELS

Abstract— Since the degradation effect due to environment on the cracking of materials depends on time, the loading rate has an important influence on the parameters that characterise its behaviour. This work analyses the effect of loading rate on the resistance to hydrogen induced cracking (HIC) of two microailoyed steels, E690 and E500. Monotonic loading tests were performed on precracked CT samples using a slow strain rate machine. Tests were done under constant displacement rate varying from 4.1 × 10–⁷ m/s to 8.2 × 10–¹⁰m/s on the two steels that were cathodically charged with hydrogen at different current densities (1, 5 and 10 mA/cm²) to obtain different hydrogen concentration levels inside the material.
Based on an analytical study, the initiation conditions for cracking as well as the crack propagation rates were determined in each case, and analysed as a function of K ₁. An extensive fractographic SEM study has been performed to help in the analysis of the different zones of behaviour obtained as an effect of loading rate, for each material and environmental condition used.     

THE COMBINED EFFECTS OF STRESS RATIO AND YIELD STRENGTH ON THE LEFM FATIGUE THRESHOLD CONDITION

Abstract— Long-crack (LEFM) fatigue threshold, Δ, K ₀ values are predicted which include the commonly observed effects of stress ratio, R , and yield strength, σ _y . It is assumed that the yield strength effect on threshold is indirectly related to grain size and so is not an independent variable. Two intrinsic thresholds of a material are invoked to explain the observations of higher Δ K ₀ values and a higher R -ratio sensitivity of Δ K ₀ in low strength materials compared to high strength materials. The paper shows that Δ K ₀ is almost independent of both yield strength and stress ratio at high values of the stress ratio. Quantitative relations are developed to estimate curves of (i) Δ K ₀ versus R and (ii) Δ K ₀ versus σ _y . These curves show good agreement with experimental data for steels and aluminium alloys. A method is presented that may be used as an alternative procedure for obtaining quick and conservative estimates of Δ K ₀ for design applications.     

Crack growth in the gigacycle fatigue regime for helicopter gears

Investigations were performed on helicopters' gears that had failed in service, using quantitative fractographic analyses. It was shown that a combination of LCF and HCF creates damage in gears on a flight-by-flight basis which produces beach marks on the fatigue surface of the gears that correlate one-to-one with flight cycles. The crack increment between beach marks occurs under HCF at 7000–8000  r.p.m. The ratio of the crack growth period to durability is smaller in the gigacycle fatigue area (more than 10⁸ cycles) than in the high cycle fatigue area (10⁶–10⁷ cycles) for those gears investigated that have stress raisers. This relationship for damaged gears depends not only on durability but also on the type of stress raiser and its location.     

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.