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.     

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.     

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.     

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.     

A SHEAR STRESS BASED CRITICAL-PLANE CRITERION OF MULTIAXIAL FATIGUE FAILURE FOR DESIGN AND LIFE PREDICTION

Abstract— The use of a previously presented general criterion of failure for high cycle multiaxial fatigue, τ_a/ t _A,B+σ_n.max/2σ_T= 1, is extended to cases where the shear and normal stress on the critical plane are non-proportional and also to give life predictions in the range of 10⁴ to 10⁶ cycles. The criterion takes account of whether case A cracks, growing along the surface, or case B cracks, growing in from the surface, occur.     

Material fatigue properties for assessing mechanical components weakened by notches and defects

This paper addresses the problem of estimating the material fatigue properties for assessing real mechanical components. Initially, some practical rules are proposed to estimate the fully reversed plain fatigue limit, Δσ₀, using the material tensile stress. These rules are obtained by subdividing materials into five different groups: carbon steels, low-alloy steels, high-alloy steels, aluminium alloys and cast irons. Subsequently, using a large database of fatigue data found in the literature, it is demonstrated that the fully reversed torsional plain fatigue limit can be directly estimated from the fully reversed uniaxial plain fatigue limit by simply using Von Mises' formula. Finally, some empirical equations are proposed to estimate El Haddad's short crack constant, a ₀. These equations are based on the assumption that this material property can be derived from the plain fatigue limit determined at a given load ratio, R . Since the a ₀ values depend on the load ratio, so a ₀ versus Δσ₀ relationships can directly account for the R influence. The aim of this paper is to provide engineers engaged in assessing real structural components with empirical rules to estimate the material fatigue properties. All these pieces of information are needed to apply the most modern methods suitable for assessing components weakened by any kind of geometrical feature and subjected to any kind of fatigue loading.     

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.     

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.     

ON THE TRANSITION FROM NEAR-THRESHOLD TO INTERMEDIATE GROWTH RATES IN FATIGUE

Abstract— Evidence is presented that the cyclic stress intensity threshold for fatigue crack growth in A1 2219-T851 is associated with a critical maximum value of stress intensity, K _c. This relationship is discovered by measuring the local value of stress intensity at the crack tip which is less than the applied stress intensity because of fatigue induced compressive residual stresses in the plastic zone. Crack growth rates and values of the crack tip residual stress are measured as functions of load ratio. For local stress intensities greater than K _c, the growth rate follows a power-law relationship, increasing monotonically with δ K . For local stress intensities below K _c, growth rates are also sensitive to the cyclic stress range, δσ. If the stress range is small, a threshold to growth, typical of long cracks, is seen. When the cracks are short and δσ exceeds a critical value, growth rates are a complex function of both δσ and δ K . This behavior is attributed to the effect of δσ on the propagation of the crack front past obstacles such as grain boundaries.     

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.     

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.     

MECHANISMS AND FATIGUE PERFORMANCE OF TWO STEELS IN CYCLIC TORSION WITH AXIAL STATIC TENSION/COMPRESSION

Abstract— Fatigue tests conducted under fully reversed cyclic torsion, with and without superimposed axial static tension/compression loads, were carried out using hour-glass smooth specimens in laboratory air. A high strength spring steel and a 316L stainless steel, were employed to evaluate the effects of mean stress on fatigue performance. Experimental test results show that a biaxial tensile/compressive mean stress had no influence on the cyclic stress-strain response in both materials. However a biaxial tensile mean stress was found to be detrimental to fatigue life of the high strength spring steel but had no effect on the total fatigue life of 316L stainless steel. A compressive mean stress was found to be beneficial to the life of both steels. The fatigue behaviour of the two materials was investigated by experimental observations and the application of theoretical analyses of short crack growth behaviour. Based upon the analysis of surface acetate replicas it has been found that fatigue crack growth is material/stress-state dependent. A biaxial tensile static stress promoted a change in the direction of the Stage I (mode II) crack from the longitudinal direction to a plane normal to the specimen axis in the high strength steel but not in the stainless steel. Consequently a different growth behaviour of Stage I (mode II) cracks was observed for the two materials. The effect of a biaxial mean stress on fatigue crack growth behaviour of the two materials is analysed and described in some detail.     

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.     

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.     

SIF and threshold for small cracks at small notches under torsion

The basic approach to the problem of torsional fatigue strength of pieces containing defects is based on the stress concentration factor concept. However, experiments have shown that the torsional fatigue limit of specimens containing small holes is controlled by the threshold condition for small cracks emanating from small notches. Therefore, the ratio of torsional to bending fatigue limit ( τ _w / σ _w ) for specimens containing small defects must be studied from the viewpoint of fracture mechanics.
The scope of this paper is to address the calculation of the stress intensity factor for a small crack emanating from a three-dimensional hole under a biaxial state of stress by using the weight function method and to apply it to the fatigue limit prediction. The results obtained are in good agreement with experimental results on specimens with defects.     

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.     

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.     

Mechanical behavior of cast SiCp-reinforced Al-4.5%Cu-1.5%Mg alloy

SiC_p-reinforced Al-4.5%Cu-1.5%Mg composite specimens were processed by vigorous stirring of the carbide in a semi-solid alloy slurry, followed by remelting and casting (stir-casting). The tensile and fatigue properties were evaluated in the as-cast and in the heat-treated conditions. In monotonic tensile testing, reinforcement with SiC_p produced a substantial increase in the work hardening of the material. This increase became more significant with increasing volume fraction of carbide. The yield and ultimate tensile strength, and the elastic modulus of the material, increased with heat-treatment and volume fraction of carbide at the expense of ductility. These properties are inferior to those of other reinforced, more complex aluminum alloys processed by other methods. In stress-controlled fatigue tests under fully reversed (R = −1) bending conditions, the fatigue life of the composite was longer than that of the unreinforced specimen at intermediate and lower stress levels. At higher stress levels the improvement was negligible. In heat-treated reinforced alloy specimens the fatigue strength at 1 × 10⁷ cycles decreased with increasing carbide particle size. With solid solution and precipitation strengthening, as well as carbide dispersion strengthening of the alloy, the crack growth threshold stress intensity factor K_th, increased, as did the crack initiation time and the crack growth rate.     

INFLUENCE OF RETAINED AUSTENITE ON FATIGUE CRACK PROPAGATION IN HP 9-4-20 HIGH STRENGTH ALLOY STEEL

Abstract— Industrial multi-pass TIG weldments of HP 9-4-20 high strength alloy steel have been found to contain significant volume fractions (around 10%) of retained austenite which are not readily transformed after stress relieving and subsequent refrigeration procedures. To determine whether the presence of such retained austenite in tempered martensitic structures could be detrimental to fatigue resistance in HP 9-4-20 steel, fatigue crack propagation behavior was examined over six orders of magnitude in growth rate, in commercially heat-treated material (containing less than 3% austenite) and in intercritically heat-treated and tempered material (containing approx. 14% austenite) in an environment of moist, ambient temperature air. Whereas crack propagation rates were unchanged at growth rates exceeding 10⁻⁶ mm/cycle, structures containing 14% austenite showed somewhat superior resistance to near-threshold crack propagation at growth rates less than 10 ⁻⁶ mm/cycle, the threshold for crack growth (Δ K ₀) being over 20% higher than in commercially heat-treated material. The presence of retained austenite further appeared to inhibit the occurrence of intergranular fracture at near-threshold levels. It was concluded that significant proportions of retained austenite are not detrimental to fatigue crack propagation resistance in HP 9-4-20 steel, and may indeed have some beneficial effect at very low, near-threshold growth rates by increasing resistance to environmentally-assisted cracking.     

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.