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.     

PROPAGATION AND NON-PROPAGATION OF SHORT FATIGUE CRACKS AT A SHARP NOTCH

Abstract— Sharply notched specimens of a structural low-carbon steel were fatigued under several ratios of the maximum to minimum loads. The growth behavior of a short fatigue crack near the notch tip was analyzed based on crack closure measurements. A fatigue crack first decelerates with increasing crack length, and then accelerates or becomes non-propagating depending on the applied stress. A similar deceleration is seen when the rate is correlated to the stress intensity range. The effective stress intensity range is a unique parameter in correlating the growth rate of a short crack for all the stress levels examined, and the relation is identical to that obtained for a long crack. By considering the increase in crack closure with crack length, a quantitative method is proposed for predicting the non-propagating crack length and the fatigue limit of notched specimens as a function of the applied stress and the notch geometry.     

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.     

A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non-uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024-T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.     

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.     

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.     

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.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Similarities of stress concentrations in contact at round punches and fatigue at notches: implications to fretting fatigue crack initiation

A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P , the ensuing contact is of width 2 b which includes an initial flat part of width 2 a . The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q , is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q /(√( b − a )√ π b ). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a 'notch analogue' by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.     

Two methods for predicting the multiaxial fatigue limits of sharp notches

In this paper the problem of the multiaxial fatigue limit estimation of sharply notched components has been addressed using two different methods: a critical distance method and a method involving modified Wöhler curves. These two methods had been previously developed by the authors, but required modification for use in conjunction with finite element stress analysis of sharply notched specimens subjected to multiaxial loadings. Initially, it was demonstrated mathematically that these methods are equivalent in terms of multiaxial stresses near the notch tip. Subsequently, by employing some well‐known uniaxial notch fatigue concepts, some assumptions have been made in order to extend the use of these methods to in‐phase multiaxial notch fatigue situations. Experimental data were obtained from tests conducted on V‐notched specimens subjected to in‐phase mixed Mode I and Mode II loadings. Both methods were successful in giving fatigue limit predictions with an error usually less than 15%. This is interesting because the two methods make quite different assumptions about the nature of fatigue crack growth in the vicinity of the notch.     

残余应力对金属疲劳强度的影响

残余应力对光滑试样高周疲劳极限的影响可以用Goodman关系来描述，但必须要得到残余应力作用系数m、合理地提取残余应力的表征值和区分开其它因素的影响。残余应力对缺口疲劳极限的作用大于对光滑试样的作用，是由于残余应力也存在应力集中现象，而且不易衰减。残余应力的应力集中系数不仅与缺口几何因素有关，还与材料特性有关。试验研究还表明，表层残余压应力对于承受轴向载荷且疲劳残纹萌生于表面的零件也十分有益。     

High-cycle fatigue crack paths in specimens having different stress concentration features

This paper summarises an attempt to study the high-cycle fatigue cracking behaviour in specimens of low carbon steel weakened by U-notches. The specimens were tested under uniaxial fatigue loading with a load ratio equal to 0.1, and the considered K_t values, calculated with respect to the gross area, ranged from 3.8 up to about 25. The generated crack paths were quite irregular showing a propagation occurring in alternate trans- and intra-crystalline mode: in many cases, this made difficult to unambiguously measure orientation and length of Stage 1 planes. In spite of these experimental difficulties, the observed material cracking behaviour seemed to suggest that a Stage 1-like process could always be assumed to be representative of the crack initiation phenomenon, and this held true independently of the notch sharpness. In light of the fact that, at a mesoscopic level, crack initiations never occurred on material planes parallel to the notch bisector, we attempted to investigate whether it was possible to use a critical plane approach to estimate high-cycle fatigue damage in notched components under uniaxial fatigue loading. In more detail, the generated results have initially been re-analysed by using the Modified Wöhler Curve Method re-interpreted in terms of the Theory of Critical Distances [Susmel L. A unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings. Fatigue Fract Eng Mater Struct 2004;27:391–411]. The accuracy in predicting the high-cycle fatigue behaviour of the considered multiaxial fatigue method was then compared to the accuracy of two other uniaxial approaches: the classical one by Smith and Miller [Smith RA, Miller KJ. Prediction of fatigue regimes in notched components. Int J Mech Sci 1978;20:201–206] and the one recently proposed by Atzori and co-workers [Atzori B, Lazzarin P, Meneghetti G. A unified treatment of the mode I fatigue limit of components containing notches or defects. Int J Fract 2005;133:61–87] and based on the use of some classic LEFM concepts. In particular, this comparison was performed considering virtual specimens having the same geometries as the ones investigated in the present study, but assuming that they were made of materials having mechanical properties known from the literature. This exercise allowed us to see that the high-cycle fatigue damage in notched specimens under uniaxial fatigue loading can satisfactorily be predicted not only using Mode I-crack based methods, but also using multiaxial fatigue criteria modelling the crack initiation phenomenon.     

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.     

Low‐cycle fatigue/high‐cycle fatigue interactions in notched Ti‐6Al‐4V*

Combined low‐cycle fatigue/high‐cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V‐notched cylindrical Ti–6Al–4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10⁷ cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K_t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10⁶ cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity‐induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.     

Vergleichende Untersuchungen zur Anrisslebensdauervorhersage gekerbter Proben mit dem Örtlichen Konzept und dem Nennspannungskonzept am Beispiel des Stahls Cm15

Comparative Investigations on Service Life Assessment of Notched Specimens Based on the Local Strain and the Nominal Stress Approach to Fatigue for a Steel SAE 1017 It is still unclear whether the strain based approach to fatigue or the stress based approach to fatigue should be preferred for service life assessment of notched components. In order to clarify the similarities and differences between these concepts stress and strain controlled fatigue experiments have been performed with notched specimens. It has been found, that stress and strain controlled fatigue testing results in the same number of cycles until failure. Essential for this correlation is that the cyclic stable strain amplitude at the notch root is taken for the entry into the strain‐life diagram in both cases. Starting from an elastic‐plastic analysis of the material behaviour at the notch root it is shown, how the strain‐life curve can be converted into a stress‐life curve. Based on that result service‐life is calculated from both approaches mentioned above. The calculation gives nearly the same service‐lives for both cases, but overestimates the measured data. It becomes obvious, that a S‐N curve determined under one‐level loading doesn’t provide a proper basis for service life assessment. While strain or stress‐life curves always contain crack initiation phase as well as crack propagation phase, the fatigue process under irregular loads is mainly governed by crack propagation. As a consequence, the damage per cycle is underestimated for loads near the fatigue limit, if Miner’s rule is used.     

Größeneinfluß und Dauerfestigkeitseigenschaften unter Besonderer Berücksichtigung optimierter Oberflächenbehandlung

Size Effect and Fatigue Properties with Respect to Optimized Surface-Treatment. A hyperbolic function describes the geometrical size effect of notched specimens made from heat treated steel. An estimation of fatigue properties of components under one level fatigue tests is possible, if there are comparable materials and surface properties. The fatigue properties of specimens are well described by standardized stress-N graphs. The slope of the stress-N graphs in the range of load cycle depends on the concentration factor and not on the size effect. The fatigue properties of components are largely increased by thermal and mechanical surface strengthening. For the determination of the improvement of fatigue properties it is important to known the initiation of cracking. The improved fatigue properties of inductive surface hardened smooth specimens can be explained by the initiation of cracking below the surface. Mechanically strengthened notched specimens start cracking on the surface. The increase of fatigue properties for these specimens is explained by compressive residual stresses. The fatigue properties of notched specimens can be improved by the optimisation of mechanical strengthening, to higher values than for smooth surface strengthened specimens. This is due to compressive residual stresses. They decrease the tensile stresses which are responsible for crack propagation. If the tensile stress is below fatigue limit for initiation of cracking the crack arrests immediately.     

A unified treatment of the mode I fatigue limit of components containing notches or defects

The paper addresses the estimation of the fatigue limit of components weakened either by U- and V-shaped notches or by defects, all under mode I stress distributions. When the influence of the opening angle is absent, a single formula is able to summarise both the notch sensitivity and the sensitivity to defects. Fatigue limit assessments need two material parameters, namely the plain fatigue limit and the threshold value of the long crack stress intensity factor range. The formula is compared with about 90 fatigue limits taken from the literature. Material properties and specimen geometries are given in detail. Afterwards, in the case of V-notches with large opening angles, the formula is modified, but without involving additional material parameters. A generalised Kitagawa diagram is obtained, that encompasses fatigue behaviour of stress raisers of different size, opening angle and notch tip radius.     

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.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

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.