Influence of inclusion size on S-N curve characteristics of high-strength steels in the giga-cycle fatigue regime

Fatigue fracture of high-strength steels often occurs from small defect on the surface of a material or from non-metallic inclusion in the subsurface zone of a material. Under rotating bending loading, the S-N curve of high-strength steels consists of two curves corresponding to surface defect-induced fracture and internal inclusion-induced fracture. The surface defect-induced fracture occurs at high stress amplitude levels and low cycles. However, the subsurface inclusion-induced fracture occurs at low stress amplitude levels and high-cycle region of more than 10⁶ cycles (giga-cycle fatigue life). There is a definite stress range in the S-N curve obtained from the rotating bending, where the crack initiation site changes from surface to subsurface, giving a stepwise S-N curve or a duplex S-N curve. On the other hand, under cyclic axial loading, the S-N curve of high-strength steels displays a continuous decline and surface defect-induced or internal inclusion-induced fracture occur in the whole range of amplitudes. In this paper, influence factors on S-N curve characteristics of high-strength steels, including size of inclusions and the stress gradient of bending fatigue, were investigated for rotating bending and cyclic axial loading in the giga-cycle fatigue regime. Then, based on the estimated subsurface crack growth rate from the S-N data, effect of inclusion size on the dispersion of fatigue life was explained, and it was clarified that the shape of S-N curve for subsurface inclusion-induced fracture depends on the inclusion size.     

The nature of initiation and propagation S-N curves at and below the fatigue limit

The traditional stress-life method of life prediction relies on an S – N curve of stress versus total life. However, the total life of a sample can be divided into two phases—an initiation phase and a propagation phase that leads to ultimate failure. Although this break-up of total life into two phases has been recognized in theory, there has been no experimental method to generate initiation and propagation S – N curves. In this paper a methodology to generate initiation and propagation S – N curves is presented. Acoustic emission technology is used to detect the transition from the initiation phase to the propagation phase. The phenomenon of fatigue limits is also explored and it is shown that the fatigue limit of the traditional S – N curve corresponds to the fatigue limit of the initiation phase and that initiated cracks continue to propagate at stress levels below the initiation endurance limit. It is also shown that no damage is accrued at stress levels below the fatigue limit. A method to extend the propagation life curve below the initiation endurance limit is also presented. The proposed two-phase S – N curve will greatly extend the life-predicting capability of the stress-life method and can explain some of the contradictions observed in experiments.     

A review on fatigue fracture modes of structural metallic materials in very high cycle regime

In S–N diagrams for high strength steels, experimental data in the usual surface fracture mode appears at higher stress levels with fewer loading cycles, whereas the data in the interior fracture mode tends to appear at lower stress levels with the very long fatigue life. Thus, the duplex S–N property was usually confirmed for those high strength steels in such a very high cycle regime. In the case of interior fracture mode, there can be several different types of the crack initiation with/without nonmetallic inclusion at the crack initiation site, and different crack initiation types can be found even for the surface fracture modes in the conventional fatigue life region. In the present work, the authors have attempted to review the overall feature of these fatigue fracture modes appearing at the usual life regime and the very high cycle regime.     

Observations of crack path changes caused by periodic underloads in AA7050-T7451

In order to predict variable amplitude crack growth it is necessary to understand the different mechanisms present in variable amplitude and constant amplitude fatigue crack growth. AFM and SEM observations have been made of the fatigue crack fracture surface in AA7050-T7451 alloy, produced by some simple load sequences consisting of periodic underloads (R = −1) in between groups of high stress ratio (R = 0.5) loading cycles. These observations have revealed complex fracture surface features that include ridges, depressions and fissures. These features are a result of the slip band formation associated with underloads, which reduces the tendency for a new slip band to occur at the crack tip in the same direction as nearby slip bands. These slip bands change the path of the crack and result in the production of a ridge on the fracture surface. This effect suggests a model of striation formation that also explains the formation of ridges and other associated features, based on the influence of two or more active slip systems combined with the planar slip behaviour of this material.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Technical note High-cycle fatigue crack initiation and propagation behaviour of high-strength sprin steel wires

An attempt has been made to characterize high-cycle fatigue behaviour of high-strength spring steel wire by means of an ultrasonic fatigue test and analytical techniques. Two kinds of induction-tempered ultra-high-strength spring steel wire of 6.5 mm in diameter with a tensile strength of 1800 MPa were used in this investigation.
The fatigue strength of the steel wires between 10⁶ and 10⁹ cycles was determined at a load ratio R = −1. The experimental results show that fatigue rupture can occur beyond 10⁷ cycles. For Cr–V spring wire, the stress–life ( S – N ) curve becomes horizontal at a maximum stress of 800 MPa after 10⁶ cycles, but the S – N curve of the Cr–Si steel continues to drop at a high number of cycles (>10⁶ cycles) and does not exhibit a fatigue limit, which is more correctly described by a fatigue strength at a given number of cycles. By using scanning electron microscopy (SEM), the crack initiation and propagation behaviour have been examined. Experimental and analytical techniques were developed to better understand and predict high-cycle fatigue life in terms of crack initiation and propagation. The results show that the portion of fatigue life attributed to crack initiation is more than 90% in the high-cycle regime for the steels studied in this investigation.     

Fatigue strength of small-notched specimens under variable amplitude loading within the fatigue limit diagram

Although the fatigue limit diagram is defined in principle for constant stress amplitude, it is often considered that fatigue failure would not occur, even in varying loading, if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small‐notched specimens that fatigue failure occurred in some special cases of variable amplitude loading, even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two‐step stress and repeated two‐step stress patterns in which the first step stress was chosen to be equal to the fatigue limit with zero mean stress and a mean stress was superposed on the second step stress. A non‐propagating crack was formed by the first step stress. This crack functioned as a pre‐crack for the second step stress with high mean stress. Consequently, fatigue failure occurred even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of a non‐propagating crack and a mean stress change.     

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.     

BIMODAL CONCEPT OF HIGH-CYCLE FATIGUE LIFE PREDICTION FOR CONSTANT AND VARIABLE AMPLITUDE FATIGUE

A bimodal concept for the prediction of the high-cycle fatigue life of structural details subjected to constant- or variable-amplitude loading is considered in this paper. The total fatigue life was separated into two phases: crack initiation and crack propagation. The portion of life spent in crack initiation was estimated by using S–N data obtained on smooth specimens. A fracture mechanics concept was used to calculate the portion of life spent in crack propagation, and the S–N curve, including the fatigue limit of a structural detail, was determined by using material properties and the geometry of the detail. The bimodal concept was applied to a welded stiffener and the results are compared with experimental data reported in the literature.     

Total Fatigue Life Estimation of Notched Structural Components Using Low‐Cycle Fatigue Properties

Abstract: In this investigation, an efficient fatigue life computation method under variable amplitude loading of structural components has been proposed. Attention in this study is focused on total fatigue life estimation of aircraft structural components. Flat specimens with central hole made of quenched and tempered steel 13H11N2V2MF were tested as representatives of different structural components. Total fatigue life of these specimens, defined as sum of fatigue crack initiation and crack growth life, was experimentally determined. Specimens were tested by blocks of positive variable amplitude loading. Crack initiation life was computed using theory of low‐cycle fatigue (LCF) properties. Cyclic stress–strain curve, Masing’s curve and approximate Sonsino’s curve were used for determining stress–strain response at critical point of considered specimens. Computation of crack initiation life was realised using Palmgren–Miner’s linear rule of damage accumulation, applied on Morrow’s curves of LCF properties. Crack growth life was predicted using strain energy density method. In this method, the same LCF properties were used for crack initiation life and for crack growth life computations also. Computation results are compared with own experimentally obtained results.     

Variable amplitude fatigue of autofrettaged diesel injection parts

Experimental and analytical investigations of constant and variable amplitude fatigue life of not autofrettaged and autofrettaged components have been performed. In variable amplitude loading the new standardised CO mmon‐ RA il‐ L oad sequence CORAL has been used as well as two‐level‐tests with small cycles at high mean stresses interrupted by large cycles for the evaluation of load sequence effects. The results of the two level tests show that small cycles with amplitudes far below the fatigue limit cause fatigue damage. Life calculations have been performed according to the nominal stress approach with S‐N‐curves and improved Miner’s Rule, linear‐elastic fracture mechanics with 3D‐weight functions, elastic‐plastic fracture mechanics applying an extended strip yield‐model, and explicit 3D‐FE‐simulation of fatigue crack growth with predefined crack fronts. All approaches are appropriate for predicting realistic variable amplitude lives. From a practical point of view the explicit 3D‐FE‐simulation of fatigue crack growth is too time‐consuming. However, such simulations show that the approaches based on linear‐elastic fracture mechanics and elastic‐plastic fracture mechanics with extended strip yield‐model capture the essential physics of fatigue crack growth in a realistic way.     

Probabilistic high cycle fatigue behaviour of nodular cast iron containing casting defects

Theoretical and experimental investigations were combined to characterize the influence of surface casting defects (shrinkages) on the high cycle fatigue (HCF) reliability. On fracture surfaces of fatigue samples, the defect is located at the surface. The shape used for the calculation is a spherical void with variable radius. Finite-element simulations were then performed to determine stress distribution around defects for different sizes and different loadings. Correlated expressions of the maximum hydrostatic stress and the amplitude of the shear stress were obtained by using the response surface technique. The loading representative point in the HCF criterion was then transformed into a scattering surface, which has been obtained by a random sampling of the defect sizes. The HCF reliability has been computed by using the Monte Carlo simulation method. Tension and torsion fatigue tests were conducted on nodular cast iron with quantification of defect size on the fracture surface. The S – N curves show a large fatigue life scattering; shrinkages are at the origin of the fatal crack leading to the final failure. The comparison of the computed HCF reliability to the experimental results shows a good agreement. The capability of the proposed model to take into account the influence of the range of the defect sizes and the type of its statistical distribution has been demonstrated. It is shown that the stress distribution at the fatigue limit is log-normal, which can be explained by the log-normal defect distribution in the nodular cast iron tested.     

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.     

Non-propagating crack behaviour at giga-cycle fretting fatigue limit

Fretting fatigue fracture of industrial machines is sometimes experienced after a long period of operation. It has been a question whether the fatigue limit which means infinite life really exists in fretting fatigue or not. Fretting fatigue tests in ultra high cycle region up to 10⁹ cycles were performed. Test results showed that the S‐N curve had a knee point around 2 × 10⁷ cycles and a clear fatigue limit was observed in the giga‐cycle regime for partial slip conditions. An electropotential drop technique was applied to detect the crack growth behaviour under the contact pad. The real‐time measurement of crack depth during the fretting fatigue test at the fatigue limit showed that a crack initiated at an early stage and then ceased to grow after 2 × 10⁷ cycles and the crack became a non‐propagating crack. These results indicated that the fatigue limit exists in fretting fatigue and infinite endurance is achieved by the mechanism of forming a non‐propagating crack.     

Small crack growth rates from simple sequences containing underloads in AA7050-T7451

Fatigue crack growth in materials that display confined slip show crack path changes that are dependant on the loading history. In these materials certain variable amplitude loading patterns can produce strong slip bands ahead of the crack tip. One of these patterns of loadings involving bands of high R cycles followed by one or two underloads also produce distinct features or progression marks on the fracture surface that have been used to delimit small blocks of constant amplitude cycles. The same loading pattern also produces strong slip bands ahead of the fatigue crack both in the plane of the crack and out of plane. These slip bands affect the direction and possibly the rate of propagation of the fatigue crack. Thus these loading patterns make an ideal marker to look at small crack growth rates in the presence of slip bands.This paper reports on the crack growth rates for a series of fatigue cracks grown in AA7050-T7451 coupons, from near initiation to near failure. The aim of this work was to generate constant amplitude crack growth data for use in predictions that is more useful for predicting crack growth lives than that obtained from long crack constant amplitude tests. Three simple sequences which applied small bands of constant amplitude loading were used in the fatigue tests preceded by a loading sequence to produce a progression mark to delimit the bands. The fatigue cracks in the coupon initiated from etch pits on the surface of the coupons. The width of the bands of constant amplitude growth in these sequences were measured under a microscope. The growth in these sequences was found to be faster than for long cracks under constant amplitude loading.     

Inclusion-controlled high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel

Axial loading fatigue tests were carried out to study the influence of inclusion on high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel (AISI 11). The fatigue strength of 1538 MPa with endurance life of 10⁷ cycles were obtained by stair-case method. The fatigue specimens were also subjected to a constant maximum stress of 1650 MPa to investigate the relationship among inclusion origin size (10-30 μm), fish-eye size (70-130 μm) and fatigue life (10⁵-10⁷ cycles). The fatigue life was found to be dependent on the inclusion size and the crack propagating length. A compressive residual stress of 300-450 MPa turned out to be present at the specimen surface, and finally induced the interior failure mode. Further investigation into the correlation between stress intensity factors of inclusion origin and corresponding stages of fatigue crack growth and fatigue life revealed that the high cycle fatigue behavior was controlled by crack propagation. According to the fractographic investigation, two distinct zones were observed in fish-eye, representing Paris-Law and fast fatigue crack growth stage, respectively. Threshold stress intensity for crack propagation of 3.9 MPa√m was obtained from the well correlated line on the ΔK_I-log N_? graph. The fracture toughness can also be estimated by the mean value of stress intensity factor ranges for fish-eye.     

Very high cycle fatigue behaviour of 2000-MPa ultra-high-strength spring steel with bainite–martensite duplex microstructure

The very high cycle fatigue and fatigue crack growth (FCG) behaviours of 2000-MPa ultra-high-strength spring steel with different bainite–martensite duplex microstructures (designated as B-M1 and B-M2) obtained through isothermal quenching and fully martensite (designated as M) for comparison were studied in this paper by using ultrasonic fatigue testing and compact-tension specimens. It was found that for the B-M1 sample with well-controlled thin and uniformly distributed bainite, the fatigue crack threshold Δ K _th is higher and FCG rate da / dN at an early stage is lower than those of the M sample. Therefore, the former has rather longer fatigue life at high stress amplitude, though both have almost identical fatigue strength. However, the fatigue properties of bainite–martensite duplex microstructure are significantly deteriorated with the formation of large bainite. Furthermore, like that of the M sample, the S–N curves of the B-M1 and B-M2 samples also display continuous declining type and fish-eye marks were always observed on the fracture surface in the case of internal fractures, which were mainly induced by inclusion. A granular bright facet (GBF) was observed in the vicinity around the inclusion. For each of the three samples, the stress intensity factor range at the boundary of inclusion (Δ K_inc ) decreases with increasing the number of cycles to failure ( N _f), while the stress intensity factor range at the front of GBF(Δ K _GBF) is almost constant with N _f and equals to its Δ K _th. This indicates that Δ K _GBF might be the threshold value governing the beginning of stable crack propagation.     

A general scenario of fish‐eye crack initiation on the life of high‐strength steels in the very high‐cycle fatigue regime

When high‐strength steels are subjected to very high‐cycle fatigue loading, crack initiation site shifts from surfaces to the interior, and a fish‐eye forms on the fracture surface. Majority of the fatigue life is estimated to be associated with the formation of this internal crack morphology. In the present work, features of such internal cracks in two high‐strength steels are studied. Specifically, three initiation patterns are investigated. A general internal crack initiating scenario is proposed base on an understanding of dislocation slip in the materials. A simplified threshold is calculated from Young's modulus and interatomic spacing, defining the transition from the initiation stage to the crack propagation. The relationship between internal crack initiation and slower descending S‐N curves is discussed.     

Comparison of fatigue life assessment by analytical,experimental and damage accumulation modelling approach for steel SAE 1045

Fatigue life assessment for two‐phase steel SAE 1045 has been carried out by experimental and simulation techniques. Analytical approach, termed as fatigue lifetime calculation, was employed making use of a load increase testing procedure and constant amplitude tests equipped with measurement techniques – plastic strain amplitude, change in temperature and change in electrical potential difference. The predicted fatigue life has been validated by constant amplitude tests and compared with fatigue life estimation by microstructure‐based simulation. Simulation has been carried out over the complete cross section of the specimen. The simulation uses damage accumulation in the gage section of the specimen culminating in the macro‐crack propagation, taking into account the inhomogeneous fatigue resistance of the material element. The results show that at the initial intervals of high cycle fatigue range at relatively higher stress amplitudes, the experimental and simulation results are in agreement; whereas in the (high cycle fatigue) region at relatively low stress amplitudes, the simulation results were found more optimistic and the corresponding fatigue scatter is also increased. Each scatter is attributed to the relatively small number of analysed models of the material structure. Scanning electron microscope was used to determine volume fraction of the microstructure for simulation. Fatigue fracture surface analysis shows that crack initiated from internal defect of material and crack propagation is driven by silicon oxide inclusion.     

Stepwise S-N curve and fish-eye failure in gigacycle fatigue

Fatigue failure is normally initiated at the surface of a material. For some materials, failure can be initiated both at the surface and the interior. This twofold materials behaviour in fatigue is represented by a stepwise shape in the S – N curve. An internal failure mode is especially important for fatigue life in the gigacycle range, as this mode is predominant at low stress ranges.
Materials with a hardened surface fail from the surface only at high stresses, and at low stresses from the inside, forming a fish-eye facet on the fracture surface. Exactly the same behaviour can be observed for materials without a hard surface, even at elevated temperatures. This paper displays some of the results obtained at NRIM and discusses possible interpretations.