Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.     

Restraint of fatigue crack growth by wedge effects of fine particles

This paper presents some experimental results which demonstrate restraint of fatigue crack growth in an Al–Mg alloy by wedge effects of fine particles. Fatigue test specimens were machined from a JIS A5083P‐O Al–Mg alloy plate of 5 mm thickness and an EDM starter notch was introduced to each specimen. Three kinds of fine particles were prepared as the materials to be wedged into the fatigue cracks, i.e. magnetic particles and two kinds of alumina particles having different mean particle sizes of 47.3 μm and 15.2 μm. Particles of each kind were suspended in an oil to form a paste, which was applied on the specimen surface covering the notch zone prior to the fatigue tests. In order to make some fracture mechanics approaches, in situ observations of fatigue cracks were performed for the two cases using a CCD microscope, with a magnification of ×1000. The crack length and the crack opening displacement (COD) at the notch root, δ, were measured. First it was ensured by control tests that the wedge effect of the oil itself was negligible. Then it was found that the large size alumina particles were not effective in restraining crack growth because the paste was difficult to make due to the large particle size and the particles could not enter the cracks properly. However, both of the magnetic particles and the small size alumina particles effectively restrained crack growth, especially the latter which produced 143–350% increase in the lifetime to failure. From the in situ observations, in the case of the small size alumina particles, a pronounced retardation of crack growth was observed immediately after the crack length exceeded 0.4 mm, and this is considered to be due to the range of COD value, δ_max ? δ_min , being strongly affected by the wedge effects of the particles. The crack retardation effect continues almost through the entire lifetime if the alumina paste is re‐applied at specified intervals, while the effect is apparently lost after the crack length exceeds ～2 mm when such re‐painting is not continued. After the fatigue tests, some macro‐ and microfractographic analyses were performed using a CCD microscope, a SEM and an EPMA (electron probe microanalyser), in order to examine the mechanism of fatigue crack restraint by the wedge effects of the fine particles. From those analyses, it was reasoned that the fine particles that entered a fatigue crack are subjected to cyclic pressures between the crack faces and then form a kind of wedge which causes significant levels of crack closure that restrain crack growth.     

Fatigue of casting flaws at a notch root under an SAE service load history

Smooth and notched specimens of a 319 cast aluminium alloy were fatigue tested under a Society of Automotive Engineers service load history in the as-cast and hipped conditions. The hipping process, which includes subjecting the cast material to a high pressure at high temperature and then slowly cooling down to eliminate internal flaws, decreased the flaw size and improved the fatigue life of cast Al 319 smooth specimens. A 0.6-mm-diameter hole was drilled at the notch root of notched specimens to simulate a natural flaw at the notch root. Specimens with two different notch sizes were tested. Circular edge notches reduced the fatigue strength and a 0.6-mm-diameter drilled hole at the notch root resulted in a further reduction.
The fatigue lives of smooth specimens, notched specimens and notched specimens with a flaw at the notch root subjected to the service load history were predicted using the strain-life approach, an effective strain-life approach and a strain-based intensity factor crack growth model. In crack growth modelling of the fatigue life of smooth cast aluminium specimens the flaw was modelled as a circular edge notch having the same diameter as the flaw. However, in the case of a flaw at a notch root the flaw was modelled as a three-dimensional cavity subjected to the notch stress field and the crack length was predicted in the longitudinal and transverse directions of the specimen cross-section. The strain-life approach was unconservative for all specimen geometries studied. The effective strain-life approach gave good predictions for smooth and blunt notched specimens but gave very conservative predictions for the specimens with flaws in the notch roots. The crack growth calculations gave accurate predictions for all the specimen geometries.     

EFFECT OF NOTCH STRESS FIELD AND CRACK CLOSURE ON SHORT FATIGUE CRACK GROWTH

Abstract— The growth rate of a short fatigue crack that is partly or wholly embedded within the notch plastic zone, is affected by the extent and intensity of the elastic-plastic notch stress field and closure effect. The notch stress—strain field and plastic zone were analysed by the Finite Element Method (FEM). The growth rate and the closure curve for a short fatigue crack emanating from the notch root were measured. Based on the experimental and numerical analyses, a modified Linear Elastic Fracture Mechanics (LEFM) parameter is proposed for a short through-thickness crack emanating from a notch root under elastic—plastic loading conditions.     

Notch effect on creep–fatigue life for Sn–3.5Ag solder

This paper studies the creep–fatigue crack initiation and failure lives of Sn–3.5Ag solder notched specimens focused on the multiaxial strain at the notch root. Push–pull creep–fatigue tests were performed using three circumferential notched specimens using four kinds of creep–fatigue strain waveforms. Multiaxial strains at the notched section were calculated by finite element (FE) analysis under four kinds of creep–fatigue loading. Creep–fatigue damage laws were applied for evaluating the crack initiation and failure lives using the multiaxial strains obtained by the FE analysis. von Mises equivalent strain at the notch root estimated the crack initiation lives with a large scatter as well as the failure lives. Instead, the mean value of von Mises equivalent strain over the cross section of the notch root estimated the crack initiation and failure lives with a small scatter.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

FATIGUE STRENGTH OF A ROTOR STEEL SUBJECTED TO TORSIONAL LOADING SIMULATING THAT OCCURRING DUE TO CIRCUIT BREAKER RECLOSING IN AN ELECTRIC POWER PLANT

Abstract— The fatigue strength of notched specimens of a rotor steel was examined under variable torsional loading which simulates turbine-generator oscillations resulting from the high speed reclosing of transmission-line circuit breakers. The local stress-strain response at a notch root was analysed using Neuber's rule and the resulting complex strain sequences applied to smooth specimens. Using the rain flow analysis and the linear summation rule, fatigue lives of the smooth specimens were successfully predicted from constant amplitude fatigue life data in association with the cyclic stress-strain curve obtained by the incremental step method. Experimental crack initiation lives for notched specimens subjected to variable torsional loading were in excellent agreement with the theoretical curves derived from results on smooth specimens. According to the view that fatigue damage is equated to crack length, the propagation life of a mode II crack along the notch root was predicted to be actually coincident with the life to crack initiation at the notch root denned in this study, i.e. the life at the stage of finding a continuous circumferential crack.     

Effect of notch root radius on the initiation and propagation of fatigue cracks

Under the conditions of constant nominal applied stress, increasing notch root radius causes an increase in the number of cycles to initiate a fatigue crack at a notch root. An explanation of the effect is given in terms of the effective stress concentration factor of the notch. Data are presented which indicate that variations in notch root radius may cause changes in the crack growth rate during the initial stages of propagation from a notch.     

Microstructure-dependent fatigue damage process zone and notch sensitivity index

The development of simulation methods for calculating notch root parameters for purposes of estimating the fatigue life of notched components is a critical aspect of designing against fatigue failures. At present, however, treatment of the notch root stress and plastic strain field gradients, coupled with intrinsic length scales of grains or other material attributes, has yet to be developed. Ultimately, this approach will be necessary to form a predictive basis for notch size effects in forming and propagating microstructurally small cracks in real structural materials and components. In this study, computational micromechanics is used to clarify and distinguish process zone for crack formation and microstructurally small crack growth, relative to scale of notch root radius and spatial extent of stress concentration at the notch. A new nonlocal criterion for the fatigue damage process zone based on the distribution of a shear-based fatigue indicator parameter is proposed and used along with a statistical method to obtain a new microstructure-sensitive fatigue notch factor and associated notch sensitivity index, thereby extending notch sensitivity to explicitly incorporate microstructure sensitivity and attendant size effects via probabilistic arguments. The notch sensitivity values obtained for a range of notch root radii using the new statistical approach presented in this study predict the general trends obtained from experimental results available in literature.     

PREDICTION OF FATIGUE LIFETIME OF NOTCHED MEMBERS

Abstract— A simple model for the estimation of the total fatigue life of notched members is presented. The number of cycles to failure is estimated as the summation of the cyclic life spent in: (1) the initiation of a dominant fatigue crack at the notch root; (2) the very early growth of this crack within the notch plastic zone; (3) the subsequent fatigue crack growth in the elastic stress-strain field of the notch; and (4) the elastic stress field of the bulk material. Theoretical and experimental results are compared.     

17-4PH末级长叶片叶根的疲劳强度与缺口效应

采用成组法和升降法开展了室温某17-4PH末级长叶片叶根纵、横方向光滑与缺口试样的疲劳试验,获得了两个方向上材料的S-N曲线,并对典型疲劳断裂试样进行了断口宏微观形貌观察。结果表明:叶片叶根纵、横方向的疲劳强度基本一致,在长寿命区,纵向疲劳强度略高于横向;光滑试样的疲劳断裂主要呈现单裂纹源特征,而缺口试样呈现多裂纹源汇聚的断裂形貌。结合试样缺口根部的弹塑性应变分析,进一步讨论了叶片叶根纵、横方向的疲劳缺口效应。     

Evaluation of fatigue crack initiation life from a notch

Local strain at the notch-root and its effect on fatigue crack initiation was investigated in four metals by the real-time, fine-grid method. Special attention was focused on local notch-root strain behaviour until crack initiation. From the application of strain hysteresis at the notch root, the maximum strain under loading conditions during each cycle was investigated in detail. One of the main results was that the maximum strain value at the first cycle of the fatigue test coincided with that at crack initiation. Maximum strain defined from the cyclic strain changes at the notch root was proposed as one possible parameter for estimating fatigue crack initiation life. Based on the curvilinear relationship between maximum strain and number of cycles to crack initiation, a new life evaluation method for fatigue crack initiation is proposed. This approach differs fundamentally from the usual fracture mechanics method based on the stress intensity factor.     

Short crack initiation and growth at 600 °C in notched specimens of Inconel718

The natural initiation and growth of short cracks in Inconel®718 U-notch specimens has been studied at 600 °C in air. U notches were introduced through broaching, and hardness traces and optical microscopy on cross-sections through the U notch broaching showed that the broaching process had introduced a deformed, work hardened layer. Fatigue tests were conducted under load control using a 1-1-1-1 trapezoidal waveform, on specimens with as-broached and polished U-notches. Multi-site crack initiation occurred in the notch root. Many of the cracks initiated at bulge-like features formed by volume expansion of oxidising (Nb,Ti)C particles. In unstressed samples, oxidation of (Nb,Ti)C particles occurred readily, producing characteristic surface eruptions. Scanning electron microscopy on metallographic sections revealed some sub-surface (Nb,Ti)C oxidation and localised matrix deformation around oxidised particles. A mechanism for crack initiation by carbide expansion during oxidation is discussed. Surface short crack growth rates in the notch root of polished specimens were measured using an acetate replica technique. Observed short-crack growth rates were approximately constant across a wide range of crack lengths. However, there was a transition to rapid, accelerating crack growth once cracks reached several hundred micrometers in length. This rapid propagation in the latter stages of the fatigue life was assisted by crack coalescence. Polishing the U-notch to remove broaching marks resulted in a pronounced increase in fatigue life.     

Evaluation of fibre bridging stress of short fatigue cracks in SCS-6/Ti-15-3 composite

Single‐edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X‐ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging.     

Effect of Pre-loading on Short Fatigue Crack Growth at a Notch

Results indicate that under cyclic tension thegrowth rate of short fatigue crack from notch rootwill be lowered greatly by tensile pre-loading,butonly a little change by compressive pre-loading.The effect of tensile pre-loading will decrease withthe increase of stress ratio.The variation of shortfatigue crack growth rate is related to the residualstress distribution around notch root.     

Fatigue strength of carbon steel specimens having an extremely shallow notch

In order to elucidate how the principal dimensions of a notch as small as grains affect the fatigue strength of carbon steel, rotating bending fatigue tests were carried out on annealed 0.45% C steel specimens having an extremely small artificial notch whose depth is either 5 or 10μm. The fatigue processes at notched parts were observed successively.In these extremely shallow notches, the parameter controlling fatigue limits for fracture σ_w was the notch depth, independently of notch sharpness. On the other hand, the crack initiation limits in the notches σ_W1 were determined by a single K_tσ_W1 — χ relation obtained from the tests on ordinary notches, where K_t is the stress concentration factor and χ is the stress gradient at the notch root.These results were studied on the basis of the characteristics of crack initiation process, the stress intensity variations at the crack tip and the stress distribution near the notch root.     

THE INFLUENCE OF NOTCH PLASTICITY ON SHORT FATIGUE CRACK BEHAVIOUR

Abstract— A study has been made of fatigue crack formation and growth at the root of different notch profiles in a structural steel subjected to fully reversed tension-compression loading. The scale of stage I microstructural crack growth at notches decreased with increasing notch root strain and was comparable to the size of stage I cracks in shallow hourglass profile specimens at the same strain. Stage II crack growth rates were faster within the notch plastic field than in the elastic stress field of the bulk material.     

Laser shock peening on fatigue crack growth behaviour of aluminium alloy

The effect of laser shock peening (LPS) in the fatigue crack growth behaviour of a 2024‐T3 aluminium alloy with various notch geometries was investigated. LPS was performed under a ‘confined ablation mode’ using an Nd: glass laser at a laser power density of 5 GW cm^?2. A black paint coating layer and water layer was used as a sacrificial and plasma confinement layer, respectively. The shock wave propagates into the material, causing the surface layer to deform plastically, and thereby, develop a residual compressive stress at the surface. The residual compressive stress as a function of depth was measured by X‐ray diffraction technique. The fatigue crack initiation life and fatigue crack growth rates of an Al alloy with different preexisting notch configurations were characterized and compared with those of the unpeened material. The results clearly show that LSP is an effective surface treatment technique for suppressing the fatigue crack growth of Al alloys with various preexisting notch configurations.     

Mesoscopic mechanisms in fatigue crack initiation in an aluminium alloy

The mechanistic aspects of process of initiation of a mode‐I fatigue crack in an aluminium alloy (AA 2219‐T87) are studied in detail, both computationally as well as experimentally. Simulations are carried out under plane strain conditions with fatigue process zone modelled as stress‐state–dependent cohesive elements along the expected mode‐I failure path. An irreversible damage parameter that accounts for the progressive microstructural damage due to fatigue is employed to degrade cohesive properties. The simulations predict the location of initiation of the fatigue crack to be subsurface where the triaxiality and the opening tensile stresses are higher in comparison with that at the notch surface. Examination of the fracture surface profile of fracture test specimens near notch tip reveals a few types of regions and existence of a mesoscopic length scale that is the distance of the location of highest roughness from the notch root. A discussion is developed on the physical significance of the experimentally observed length scale.     

NOTCH SIZE EFFECT IN FATIGUE

Abstract— The notch size effect (i.e. the decrease of the notched fatigue limit with increasing notch size for the same stress concentration factor) was quantitatively derived by describing the threshold conditions for the propagation of a short semi-elliptical crack nucleated at the notch root. A close relation between the Kitagawa—Takahashi diagram for the short crack threshold stress and the dependence of the notched fatigue limit on the notch size was shown. The derived relation for the notch size effect was experimentally verified for several specimen/notch geometries in the cases of pressure vessel steel and copper.