A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

THE SHORT CRACK PROBLEM

Abstract— The problem associated with short crack growth, defined as situations in which the intensity of the crack tip field is underestimated by linear elastic fracture mechanics analyses, is briefly reviewed.
Two cases are identified, cracks growing in plastically strained materials, such as occurs in high strain fatigue studies and at notch roots, and small cracks growing in single grains as occurs close to the fatigue limit in plain specimens.
Important mechanical and metallurgical features of short cracks are discussed with particular reference to the upper and lower bound definition of a short crack.     

Fatigue strength of rolled JIS SM50A beams

The fatigue strength of rolled beams with stiffeners welded to the web was examined. The state of residual stress in these beams was varied by different cooling and straightening processes. Parallel series of tests were carried out both on plate specimens with corner-notches, simulating the edge notches in the beam-flange tip, and on fillet welded specimens. These test results were analysed using the fracture mechanics concepts of stable crack growth. A new fracture mechanics model for cracks originating from notches is proposed. This is based on the concept that the cyclic plastic zone size at the root of a notch determines the equivalent size of the notch as a fatigue crack. With this model, the severity of notches as well as their size can be taken into account to describe the initial flaw conditions. With the initial crack size estimated, a theoretical crack-growth equation was derived from the fatigue test data of rolled beams and notched plates. The analysing method together with the derived relationship was applied for the evaluation of the fatigue strength of welded beams and transverse fillet welds. The effect of residual stresses on fatigue behavior of these beams and plate specimens was also estimated by assuming an additional effect of the maximum stress on the theoretical crack-growth equation.     

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.     

AN ELASTIC-PLASTIC MODEL FOR FATIGUE CRACK GROWTH AT NOTCHES

Abstract— The development of an elastic-plastic fracture mechanics model for predicting fatigue crack growth rates in notched specimens is presented in this paper. The model is based on experimental short and long crack growth results from un-notched specimens and the distribution of strain ahead of the notch root. This approach may be applied to the assessment of the lifetime of many high technology engineering components.     

Fatigue life prediction for stainless steel welded plate CCT geometry based on Lawrence''s local-stress approach

In the present study, the effect of welding process and procedure on fatigue crack initiation from notches and fatigue crack propagation in AISI 304L stainless steel welds was experimentally investigated. Full penetration, double-vee butt welds have been fabricated and CCT type specimens were used. Lawrence's local-stress approach (a two-stage model) is used to predict the fatigue life. The notch-root stress method was applied to calculate the fatigue crack initiation life, while the fatigue crack propagation life was estimated using fracture mechanics concepts. The fatigue notch factor is calculated using Lawrence's approach. Constant amplitude fatigue tests with stress ratio, R=0 were carried out using 100 kN servo-hydraulic DARTEC universal testing machine with a frequency of 30 Hz. The predicted lives were compared with the experimental values. A good agreement has been reached. It is found that the weld procedure has a stronger effect on lives to initiation than on propagation lives.     

Plasticity spread in mild steel pre-cracked charpy bars

During dynamic service loading, small fatigue cracks are normally seen to emanate from the root of sharp machined stress concentration region. In a recent authors' paper at ICF4, the fracture strength of a charpy type notched beam has been studied in three different engineering materials, when a small fatigue crack emanates from the notch root. Fracture tests on these medium and high strength materials demonstrate the presence of a large size plastic zone near the crack tip [1–6]. To understand the mechanism of fracture for such complex geometry. it is important to know the size and shape of these plastically yielded regions. The present paper is mainly on the experimental measurement of plasticity spread as well as the stress intensity factor (S.I.F.) for such short cracks. Firstly, the S.I.F. is approximately measured by plain transmission photoelasticity on model castolite specimens. Secondly, plastic zones around crack tip are measured for a wide range of notch root radii and crack-length, by using photo-stress PS-3B coating on mild steel pre-cracked charpy type notched specimens. It is observed that for small scale yielding at the crack tip, the plasticity spread is around 60–65° angle to the line of crack-extension. On the contrary, as the gross applied stress approaches the yield strength of the material, the maximum plasticity spreads around 45° angle. Finally, it is noticed that at high stress level, the plastic zone boundary (for short crack) touches the free machined notch surface. These experimental observations explain the nature and degree of non-linearity in a load—C.O.D. diagram during the fracture test of a short cracked-notched specimen. These data are also useful to predict the crack-extension load for an elastic-plastic material.     

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。     

NOTCHED FATIGUE BEHAVIOUR OF TWO COLD ROLLED STEELS

Abstract— A SAE1010 plain carbon steel and a SAE945X HSLA steel were cold rolled to various thickness reductions. Centre notched specimens were tested under stress control at a stress ratio of—1. The effect of loading direction on the fatigue strength was examined. The notched specimen fatigue strength was only slightly increased by cold rolling, since two opposing factors: the smooth specimen fatigue strength and the notch sensitivity, were increased by cold rolling. The notched specimen fatigue strength in the transverse direction was approximately the same as that in the longitudinal direction. An empirical equation and equations derived from fracture mechanics and Neuber's rule were applied to predict the fatigue notch factor for the sharp and blunt notch geometries examined. A reasonable agreement between the predictions and the experimental results was observed for the sharp notches. For the blunt notches, the predicted fatigue notch factors were conservative.     

Notch root radii effects in the fatigue of polymers

Wöhler-type rotating bending fatigue tests have been performed on PVC cantilever specimens containing various sharp and blunt notches of known geometries. An attempt has been made to analyse the data obtained using linear elastic fracture mechanics concepts. Results from the sharp-notched specimens show a good correlation on a stress intensity factor basis and a fatigue limit is revealed. For blunt notches a stress intensity factor had to be calculated allowing for small flaws at the notch root, and some measure of correlation of the stress intensity factor at the fatigue limit for the various specimens is obtained.     

Fatigue crack growth from sharp notches

Notch-like stress raisers occur widely in engineering components. They are preferred sites for crack initiation when the components are subjected to cyclic loadings. Thus the growth of cracks initiated from notches is very relevant to design against fatigue failures. Schematic models proposed to explain the departure of notch crack growth from linear elastic fracture mechanics predictions are briefly reviewed. Different methods of measuring crack closure are compared. It is found that the commonly employed notch-mouth clip-gauge method is not sensitive enough to detect the closure of short cracks in regions of notch plasticity. Various mechanics parameters have been claimed to be able to bring the notch crack and long crack growth rate data to a single base. In the present work on double-edge notched AISI 316 stainless steel specimens, it is found that none of them is able to correlate satisfactory all the experimental data.     

Fatigue life assessment of nodular cast iron containing casting defects

The fatigue behaviour of a nodular cast iron containing casting defects has been investigated in the high-cycle fatigue regime. In this paper, we propose a fatigue life assessment model for flawed materials based on a fracture mechanics approach which takes into account the position and size of the defect, short crack behaviour and the notch effect introduced by the defect. The fatigue behaviour of smooth samples, and long and short crack behaviour have been experimentally determined in order to identify the relevant mechanical parameters; these being introduced into the model. An experimental study has been made both in air and in vacuum in order to account for the position of the defect, noting that internal defects are supposed to be under vacuum conditions. Experimental results, which are based on a two-crack front-marking technique specially developed for this study, show that the propagation of natural cracks is controlled by the effective stress intensity factor in air as well as in vacuum. The K calculation for a short crack in the stress field of a notch is analysed using numerical elastic–plastic results. Comparison between experimental results and the computation of fatigue life for fatigue lives less than 10⁶ cycles shows that the fatigue behaviour of nodular cast iron is controlled by a propagation process. The model proposed is thus relevant for fatigue lives less than 10⁶ cycles so that the defect can be considered as a crack and the initiation stage neglected. Closer to the fatigue limit, this study shows that the initiation stage should be considered in the assessment of fatigue life of nodular cast iron, because a single macroscopic propagation assessment is not enough to describe the whole fatigue life. The defect cannot be considered as a pre-existent crack in the high-cycle fatigue range (>10⁶ cycles), and the initiation stage that contains microcrack propagation around the defect should be evaluated when assessing the high-cycle fatigue life of nodular cast iron.     

Resistance-curve method for predicting propagation threshold of short fatigue cracks at notches

A new resistance-curve method was proposed for predicting the growth threshold of short fatigue cracks near the notch root. The resistance curve was constructed in terms of the experimentally determined threshold value of the maximum stress intensity factor which was the sum of the threshold effective stress intensity range ΔK_effth and the opening stress intensity factor K_opth The ΔK_effth value was constant, irrespective of crack length or notch geometry. The relation between K_opth and crack length was independent of notch geometry. The predicted effects of the notch-root radius and the notch depth on the propagation threshold of short fatigue cracks were compared with the experimental data obtained using center-notched specimens with various notch-root radii and single-edge notched specimens with various notch depths. Excellent agreement was obtained between predictions and experiments.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

EIFS-based crack growth fatigue life prediction of pitting-corroded test specimens

Corrosive environment causes corrosion pits at material surface and reduces the fatigue strength significantly. Fatigue crack usually initiates at and propagates from these locations. In this paper, a general methodology for fatigue life prediction for corroded specimens is proposed. The proposed methodology combines an asymptotic stress intensity factor solution and a power law corrosion pit growth function for fatigue life prediction of corroded specimens. First, a previously developed asymptotic interpolation method is proposed to calculate the stress intensity factor (SIF) for the crack at notch roots. Next, a growing semi-circular notch is assumed to exist on the specimen’s surface under corrosive environments. The notch growth rate is different under different corrosion conditions and is assumed to be a power function. Fatigue life can be predicted using the crack growth analysis assuming a crack propagating from the notch root. Plasticity correction is included into the proposed methodology for medium-to-low cycle fatigue analysis. The proposed methodology is validated using experimental fatigue life testing data of aluminum alloys and steels. Very good agreement is observed between experimental observations and model predictions.     

Strain-based approach to fatigue crack initiation and propagation in welded steel joints with arbitrary notch shape

In this paper, a novel strain-based approach for the fatigue strength modelling of welded steel joints is introduced. The actual weld notch geometry and the variation in the microstructure characteristics of the material are considered, and thus, the approach enables the fatigue crack growth simulation from the crack initiation to the critical crack length before the final fracture. The predicted fatigue strength is in line with the experimental results. By considering the crack tip plasticity and stress triaxiality, the approach is able to describe the different crack growth periods of the fatigue life: the short crack, long crack, and tearing-related long crack growth periods. For a welded joint with a smooth notch shape, the short crack growth period is observed to be dominant and to have a significant influence on fatigue life.     

Influence of sub-micrometer notches on the fracture of single crystal silicon thin films

The influence of notches on the fracture of single crystal silicon thin films was investigated. The tests were conducted on notched and smooth tensile specimens micromachined on a silicon wafer. The specimen geometry was 100 μm long, 50 μm wide and 5 μm thick. For the notched specimen, a V‐shaped sub‐micrometer notch was introduced on one edge of it by using a focused ion beam (FIB) process. The notch lengths ranged from 0.07 to 1.3 μm. Four types of specimens with different surfaces and tensile orientations were tested. The smooth specimens showed scattered fracture strengths and ‘collapsed’ fractures. For the restrictive‐shaped notches, the critical length was 0.5 μm. The short‐notched (<0.5 μm) specimens also showed ‘collapsed’ fractures, and the stress concentrations on notch tips decreased their fracture strengths. For the long‐notched (>0.5 μm) specimens, the notch was equivalent to a crack in the Griffith model and the crack mainly propagated on {111} cleaved planes.     

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.     

Analytical study of fatigue crack growth in AA7050 notched specimens under spectrum loading

An analytical study of fatigue crack growth in aluminium alloy 7050-T7451 notched specimens under a fighter aircraft wing root bending moment spectrum was conducted. The crack growth data were measured by quantitative fractography for three groups of specimens with different stress concentration geometrical features. Under spectrum loading and for each spectrum peak stress level, a minimum of five specimens were tested. Based on the analysis of the measured spectrum crack growth data using linear elastic fracture mechanics, it was found that the concept of geometry factors formulated in the stress intensity factor could not collapse the crack growth rate data derived from each stress concentration feature, particularly near the small crack growth region. In order to investigate the possible reasons for this, three-dimensional elastic-plastic finite element analysis was used to determine notch plastic zone sizes for each stress concentration geometry. As a consequence, an alternative crack growth driving force by considering both notch elastic-plastic stress field and gross net-section stress field was proposed and used to interpret the fatigue crack growth data under spectrum loading. It was found that the predictions of crack growth under spectrum loading for different stress concentration factors at different peak load levels agree reasonably well with the experimental results.