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.     

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.     

Stability analysis and experimental verification for optimum notch configuration in chevron-notched round bar specimens

In some earlier communications [Ray and Poddar, FFEMS, 27 (2004), Sarkar and Ray, FFEMS, 31 (2008)], a methodology to estimate the minimum normalized stress intensity factor for chevron-notched round bar (CVNRB) specimens has been outlined. The primary aim of this report is to theoretically analyse stable crack propagation in CVNRB specimens in order to estimate conservative fracture toughness value associated with this specimen geometry. The theoretical analyses have been substantiated using fracture toughness tests on CVNRB specimens of steel having initial normalized notch lengths (α₀) between 0.2 and 0.5. The major inferences drawn from this investigation are: (1) the optimum notch geometry in CVNRB specimens corresponds to 0.2 < α₀ < 0.3 for the maximum stable crack extension, and (2) the estimated fracture toughness of the steel using CVNRB specimens indicates minimum K_ICV at α₀= 0.29 in good agreement with the theoretical analyses.     

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.     

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.     

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.     

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.     

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.     

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.     

An investigation into the location of crack initiation sites in alumina, polycarbonate and mild steel

The effects of notch root radius on fracture toughness and crack initiation sites have been investigated in this paper using three different classes of materials. Data on alumina which represent ceramics, mild steel from the metals ffeily and polycarbonate representing plastics were obtained and analysed. The locations of crack initiation sites have been pinpointed by scanning electron microscopy. These identified sites more or less are located within the critical process zone or the theoretical plastic zone. The critical process zone size ( D _c ) or the theoretical plastic zone size ( R _YF ) are independent of the notch root radius unlike the plain-strain fracture toughness of notched specimens [ K _{IC (ρ)].} The authors emphasize why the parameters D _c and R _YF are useful for a quantitative evaluation of the reliability of structural materials.     

Effects of notch geometry on the local cleavage fracture stress σf

An elastic–plastic finite element method (FEM) is used to analyse the stress and strain distributions ahead of notches with various depths and flank angles in four-point bending (4PB) specimens of a C–Mn steel. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ _f is measured. By increasing the notch depth and notch flank angle from 2.25 to 8.25 mm and 10 to 90°, respectively, the distributions of high stress and strain at the moment of fracture show considerable variations. However, the value of σ _f stays relatively constant. The critical fracture event is thus shown to be identical, i.e. the propagation of a ferrite grain-sized crack into the neighbouring matrix. It is concluded that σ _f is mainly determined by the length of the critical microcrack, while the notch geometry and its associated stress volume have little effect on the value of σ _f . The cleavage site ahead of a notch is determined by the stress distributions and the positions of the weakest grains.     

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 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.     

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.     

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.     

EFFECT OF WAVEFORM ON CORROSION FATIGUE CRACK GROWTH

Abstract A study was made on the effects of stress rise time T ₁, maximum stress holding time T ₂, stress decreasing time T ₃ and minimum stress holding time T ₄ of a cycle on fatigue crack growth for a low alloy carbon steel in 3% NaCl solution. Measurements of the effective stress intensity range ratio U and observations of crack tip response were performed to clarify the causes of waveform effects.
The results were summarized as follows; T ₁ had a strong accelerating effect due to corrosive dissolution of the fresh surfaces of the crack which were formed during T ₁. The crack growth rate was enhanced as T ₁ increased and reached a constant value (about 3 times that in air) after T ₁= 10s. The crack growth rate at low Δ K , however, decreased as T ₁ increased more than T ₁= 1 s. T ₂, T ₃ and T ₄ decreased the crack growth rate. The extent of decrease not only depended on the period of T ₂ (or T ₃, T ₄), but also on Δ K and T ₁. A previously derived crack growth law which considered waveform and frequency effects, is also valid to a first approximation for the present results.     

The analysis of thermoelastic isopachic data from crack tip stress fields

A computer program—FACTUS (fracture analysis of crack tips using SPATE)—has been developed for the efficient analysis of thermoelastic data obtained from around a crack tip. The program is based on earlier work for the determination of stress intensity factors (SIFs), and also includes a novel solution procedure for the derivation of the non-singular stress term σ _{0 x} . The program has been used in the analysis of a series of large plate specimens with central or edge slots/cracks. The derived SIFs are compared with independent values. Issues, e.g. crack closure and the extent and effect of the plastic zone, are discussed.     

From a local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints

This paper investigates the possibility of unifying different criteria concerned with the fatigue strength of welded joints. In particular, it compares estimates based on local stress fields due to geometry (evaluated without any crack-like defect) and residual life predictions in the presence of a crack, according to LEFM. Fatigue strength results already reported in the literature for transverse non-load-carrying fillet welds are used as an experimental database. Nominal stress ranges were largely scattered, due to large variations of joint geometrical parameters. The scatter band greatly reduces as soon as a 0.3-mm virtual crack is introduced at the weld toe, and the behaviour of the joints is given in terms of Δ K _I versus total life fatigue. Such calculations, not different from residual life predictions, are easily performed by using the local stress distributions determined near the weld toes in the absence of crack-like defects. More precisely, the analytical expressions for K _I are based on a simple combination of the notch stress intensity factors K ₁^N and K ₂^N for opening and sliding modes. Then, fatigue strength predictions, as accurate as those based on fracture mechanics, are performed by the local stress analysis in a simpler way.     

AN ENGINEERING FRACTURE PARAMETER FOR NON-J-CONTROLLED CRACK GROWTH

Abstract— An engineering fracture parameter (CTOA) is studied under non- J -controlled growth. Based on the asymptotic solution of the crack tip field and the concept of the ₁ integral, an analytical relation linking the crack tip opening angle (CTOA) and the ₁ integral is established. A numerical investigation of the process of crack growth is carried out by the finite element method. The whole field solution, fracture parameters and indeterminate parameters are determined by FE analysis. An experimental investigation on a ductile structural steel has also been conducted and the crack resistance curve (CTOA)_R is obtained. The numerical and experimental results validate the theoretical analysis and show that they are consistent. It can be concluded that CTOA is always constant during steady crack propagation.     

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.