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.     

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.     

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 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.     

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.     

CRACK INITIATION AND SMALL FATIGUE CRACK GROWTH BEHAVIOUR OF SQUEEZE-CAST Al-Si ALUMINIUM ALLOYS

Abstract— Fatigue strength, crack initiation and small crack growth behaviour in two kinds of squeeze-cast aluminium alloys, AC8A-T6 and AC4C-T6 were investigated using smooth specimens subjected to rotatary-bending fatigue at room temperature. Fatigue resistance of these alloys was almost the same as that of the wrought aluminium alloys because of their fine microstructure and of the decrease in defect size due to squeeze-casting. Fatigue crack initiation sites were at the eutectic silicon particles on the surface of specimens or at internal microporosity in the specimens. Crack initiation life, defined as a crack length of 50 μm on the specimen surface, was successfully estimated from an evaluation of initiation sites using fracture mechanics and the statistics of extrema. Small fatigue crack growth in the two kinds of alloys obeys the relation proposed by Nisitani et al. , namely that d(2c)/d N = C (σ_a/σ_B)ⁿ· (2 c ), where C is a constant and σ_B is the ultimate tensile strength. It is pointed out that an improvement in fatigue strength of cast aluminium alloys can be expected by refining the eutectic silicon rather than by an increase in static strength.     

Fatigue strength of crack-healed Si3N4/SiC composite ceramics

Si₃ N₄ /SiC composite ceramics were sintered and subjected to three-point bending on specimens made according to the appropriate JIS standard. A semi-circular surface crack of 110 μm in diameter was made on each specimen. By using three kinds of specimen (smooth, cracked and crack healed), crack-healing behaviour, cyclic and static fatigue strengths were determined systematically at room temperature and 1000 °C. The main conclusions are as follows: (i) Si₃ N₄ /SiC composite ceramics have the ability to heal after cracking; (ii) crack-healed specimens showed similar cyclic and static fatigue strengths as smooth specimens, this being caused by crack healing; (iii) crack-healed zones had a sufficient fatigue strength and most fractures occurred outside the pre-cracked zone in those crack-healed specimens.     

INFLUENCE OF LOW-INTENSITY SHOT PEENING ON THE FATIGUE STRENGTH OF AN Al/Al

Metal matrix composites are increasingly utilized in engineering applications because of their favourable strength/weight ratio. However, their applications are still limited because of their relatively poor fatigue resistance, which could be improved by using some appropriate surface treatment. In this paper, an Al/Al₂ O₃ (20%) composite material is considered. In particular its fatigue strength is examined to verify if, how and when shot peening can be used to improve the performances of MMC components that are cyclically loaded. Fatigue tests allow one to evaluate the influence of shot peening on the fatigue limit of both smooth and notched specimens. Residual stress measurements, fracture surface analyses and metallographic examinations allow one to evaluate the role of residual stresses, hardening and grain distortion on the improvement that can be achieved with this treatment. On the basis of these results, some guidelines are drawn on how to optimize the choice of peening parameters.     

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.     

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 particle size on fatigue behaviour in SiC particulate-reinforced aluminium alloy composites

The effect of particle size on rotary bending fatigue behaviour was studied for powder metallurgy 2024 aluminium alloy composites reinforced with 10 wt% silicon carbide particles (SiC_p ). Average particle sizes of 5, 20 and 60 μm were evaluated. Particle size had a significant influence on fatigue strength, indicating an increased fatigue strength with decreasing particle size. The composite with 5 μm SiC particles showed higher fatigue strength than the unreinforced alloy. The incorporation of 20 μm SiC particles led to an increase in fatigue strength at a high stress level, but the improvement diminished with decreasing stress level, and a slightly decreased fatigue strength was observed at low stress level, as compared with the unreinforced alloy. The composite with 60 μm SiC particles exhibited a considerable decrease in fatigue strength. Fatigue cracks initiated at several different microstructural features, e.g. surface defects, inclusions and particle–matrix interfaces, and crack initiation was considerably affected by particle size. Fatigue strength was found to depend strongly on the resistance to crack initiation, because there was no discernible difference in small crack growth between the unreinforced alloy and the composites, particularly at a low maximum stress intensity factor.     

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.     

Theoretical fatigue–effective notch stresses at spot welds

Notch stress formulae are derived for the application of a notch stress approach to the fatigue assessment of spot welds. A keyhole notch is assumed to describe the edge of the weld spot between the overlapping plates. The stress fields at the keyhole notch under 'singular' and 'non-singular' in-plane loading modes inclusive of the stress concentration factors K _t are derived from the relevant Airy stress functions. The formulae are applied to typical loading cases of spot welds and compared with finite element solutions. Fatigue-effective notch stresses inclusive of fatigue notch factors K _f are calculated by applying the microstructural support hypothesis of Neuber. The notch stresses at the keyhole are also derived for out-of-plane shear loading based on the relevant harmonic stress functions. The multiaxial notch stresses at the weld spot edge are thus completely described.     

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.     

Effect of in-plane constraint on mechanical behaviour of a metallic composite in biaxial stress states

This investigation focuses on the effect of in-plane constraint, which is a measure of the hydrostatic tension at the plane stress condition, on the yielding, fracture and fatigue of thin-walled tubes of an alumina particle-reinforced 6061 aluminium alloy composite. The results are compared with that of the unreinforced alloy. The yield surface radius of the particulate reinforced metal matrix composite (PMMC) is larger than that of the alloy in all loading paths. The fracture strength of the PMMC in terms of equivalent stress value is less sensitive to the change of the in-plane constraint of biaxial loading than that of the unreinforced alloy. The fatigue lives of the composite under the same equivalent strain decrease with the increase of the in-plane constraint factor, but by a lesser amount in comparison to that of the alloy.     

FATIGUE CRACK INITIATION LIFE PREDICTION FOR WELDED JOINTS BY LOW CYCLE FATIGUE APPROACH

Abstract— Analytical procedures based on low cycle fatigue theory are used to estimate the fatigue crack initiation life (N_i) for a cruciform welded joint in mild steel under constant amplitude tensile cyclic loading; the fatigue crack initiating at the weld toe. Effects due to welding such as residual stresses, geometrical variability and changes in material properties are handled. It is shown that for high mean stresses the discrepancies observed between the N _i estimates provided by commonly used analytical procedures exceed an order of magnitude. For the base metal (BM) the discrepancies become negligible if cyclic relaxation of notch mean stress is taken into consideration. The differences betwen the N _i estimates for heat affected zone (HAZ) material (where fatigue cracks at the weld toe usually initiate) and for BM are quantified. The applicability of HAZ material properties, estimated from hardness, to N _i prediction is evaluated.     

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.     

THE INFLUENCE OF COMPRESSIVE LOADS ON FATIGUE CRACK PROPAGATION IN METALS

An experimental study on Al alloy 7475-T7351 was conducted to determine the influence of compressive loads on fatigue crack propagation. The investigation was based on the determination of the crack propagation stress intensity factor, K_PR , under three different basic loading sequences involving compressive loads. The data of the entire experimental program collapse onto a single 'master curve' which describes K_PR as a function of K_max and the unloading ratio UR. Load interaction effects are mainly due to the changes of the residual compressive stress state in front of the crack tip, while crack closure plays a minor part. The results give an improved understanding of fatigue crack propagation.     

Small-crack growth and fatigue life predictions for high-strength aluminium alloys. Part II: crack closure and fatigue analyses

Small-crack effects were investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad aluminium alloys. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue and small-crack tests were conducted on single-edge-notch tension (SENT) specimens and large-crack tests were conducted on middle-crack tension specimens under constant-amplitude and Mini-TWIST spectrum loading. A pronounced small-crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite-element and weight-function methods were used to determine stress intensity factors, and to develop equations for surface and corner cracks at the notch in the SENT specimen. (Part I was on the experimental and fracture mechanics analyses and was published in Fatigue Fract. Engng Mater. Struct. 21 , 1289–1306, 1998.) This part focuses on a crack closure and fatigue analysis of the data presented in Part I. A plasticity-induced crack-closure model was used to correlate large-crack growth rate data to develop the baseline effective stress intensity factor range (Δ K _eff ) against rate relations for each material, ignoring the large-crack threshold. The model was then used with the Δ K _eff rate relation and the stress intensity factors for surface or corner cracks to make fatigue life predictions. The initial defect sizes chosen in the fatigue analyses were similar to those that initiated failure in the specimens. Predicted small-crack growth rates and fatigue lives agreed well with experiments.