S–N curve characteristics and subsurface crack initiation behaviour in ultra-long life fatigue of a high carbon-chromium bearing steel

The S – N curve obtained from cantilever-type rotary bending fatigue tests using hour-glass-shaped specimens of high carbon-chromium bearing steel clearly distinguished the fracture modes into two groups each having a different crack origin. One was governed by crystal slip on the specimen surface, which occurred in the region of short fatigue life and a high stress amplitude level. The other was governed by a non-metallic inclusion at a subsurface level which occurred in the region of long fatigue life and low stress amplitude. The inclusion developed a fish-eye fracture mode that was distributed over a wide range of stress amplitude not only below the fatigue limit defined as the threshold for fracture due to the surface slip mode but also above the fatigue limit. This remarkable shape of the S – N curve was different from the step-wise one reported in previous literature and is characterized as a duplex S – N curve composed of two different S – N curves corresponding to the respective fracture modes. From detailed observations of the fracture surface and the fatigue crack origin, the mechanisms for the internal fracture mode and the characteristics of the S – N curve are discussed.     

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.     

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.     

Accelerated fatigue testing method

A method for accelerated fatigue testing of materials, based on a cumulative damage rule, is developed and examined. The method is based on monotonically increasing the stress amplitude with the number of cycles, until failure. When the initial stress amplitude is above the endurance limit, two tests are needed to determine the S/N curve; another test, with an initial stress amplitude below the endurance limit, is needed to determine the fatigue endurance limit. It is shown how to choose the right loading rate and starting level. This method minimizes the number of tests needed for the determination of the fatigue strength endurance limit, and also shortens these tests by reducing the number of cycles, (as each test ends with specimen failure).     

Beitrag niedriger Lastamplituden zur Ermüdungsschädigung von 0,15 %C Stahl

Contribution of low load cycles to fatigue damage in 0.15 %C steel The S‐N curve of 0.15 %C steel shows an endurance limit. Two‐step variable amplitude loading experiments serve to investigate the influence of numerous cycles below the endurance limit on fatigue damage. If high stress amplitudes of the loading sequences are more than approx. 15 % above the endurance limit, low load cycles contribute significantly to fatigue damage. Investigations of fatigue crack propagation under two‐step variable amplitude loading show accelerated crack growth caused by low load cycles. If high stress amplitudes of the two‐step sequences are less than 15 % above the endurance limit, beneficial influences of numerous low load cycles are found. Under these conditions, the material can sustain far greater numbers of load cycles than predicted by Miner damage accumulation calculation. Fatigue crack growth studies show that under these conditions for the high load numerous low load cycles lead to stop of the crack propagation.     

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.     

A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

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.     

Application of fracture mechanics to estimate fretting fatigue endurance curves

This paper presents approximations to fatigue curves in fretting conditions with spherical contact in the alloy Al 7075. The curves are defined for a specific contact geometry and loads applied in the tests (axial load on the specimen, the normal and tangential contact forces). In order to obtain a curve of this type it is necessary to fix all parameters except for one and analyse its influence on life. The method used to estimate life in fretting fatigue combines initiation with propagation. Different approaches to the growth of short cracks are employed and in some cases a fretting fatigue limit is predicted. Various groups of fretting tests have been analysed, evaluating the suitability of each approximation.     

High-cycle fatigue mechanisms in 1045 steel under non-proportional axial-torsional loading

Detailed microscopic analyses have been made on the high-cycle mechanisms in 1045 steel under various stress-controlled axial-torsional loadings. A special attention has been paid to a critical example of non-proportional loading, i.e., 90° out-of-phase loading with different stress ratios. The replica technique has been used to monitor crack initiation and propagation from the microstructure scale. The orientations of persistent slip bands and Stage I cracks are in good agreement with the critical plane concept. The evolutions of crack length with cycle life as well as the crack aspect ratios depend on the loading condition. However at a given life, the data are consolidated in terms of crack depth versus cycle life. The McDiarmid parameter correlates stress-life data under proportional loadings. However, it underestimates fatigue lives under out-of-phase loading at high stress ratio and it overestimates them in the case where all planes experience the same shear stress amplitude (stress ratio = 0.5). More damaging mechanisms are involved in crack initiation and crack propagation. It is recommended to test the fatigue performance of materials in this last condition that involves the worst damage mechanisms.     

Modelling curved S–N curves

The fatigue limit distribution is estimated using fatigue data and under the assumption that the fatigue limit is random. The stress levels for the broken and unbroken specimens are used. For the broken specimen the number of cycles to failure is also used. By combining the finite life and fatigue limit distribution it is possible to get the probability of not surviving a certain life. This probability is used to estimate a curved S–N curve by using the method of likelihood. The whole S–N curve is estimated at the same time. These curves show the predictive life given a certain stress level. The life and the quantile of the fatigue limit distribution are also predicted by using profile predictive likelihood. In this way the scatter around the S–N curve as well as the uncertainty of the S–N curve are taken into account.     

Effect of inclusion on subsurface crack initiation and gigacycle fatigue strength

The effect of inclusions on crack initiation and propagation in gigacycle fatigue was investigated experimentally and analytically in six high strength low alloy steels. Fatigue testing was performed at very high numbers of cycles through ultrasonic fatigue tests at 20 kHz. Inclusions at subsurface are common sites for fatigue crack nucleation in these alloys when cycles to failure was >10⁷ cycles. A significant change in the slope of the S–N curve was observed accompanying the transition from surface to subsurface crack initiation. A deterministic model has been developed to predict the total fatigue life, i.e. crack initiation life and crack propagation life, from the measured inclusion sizes. The predicted fatigue strength agreed reasonably well with the experimental results. It is a tendency that smaller inclusions are associated with longer fatigue life. The results demonstrated that the portions of life attributed to subsurface crack initiation between 10⁷ and 10⁹ cycles are >99%.     

Influence of reverted austenite on fatigue life of 18 % nickel maraging steel

Maraging steels containing 18 % nickel are based on a low-carbon iron-nickel-cobalt-molybdenum system. These steels demonstrate a remarkable combination of high strength and high toughness. To investigate the effect of overaging and resulting austenite reversion on the fatigue behavior of C250 maraging steel, specimens in the solution annealed state were overaged at 510 °C for various intervals, resulting in volume fractions of reverted austenite ranging from 2.6 % to 11.4 %. The staircase method was used to calculate the fatigue limit. S−N curves were generated by testing a minimum of four stress levels and at least three samples at each stress level. Basquin's equation was used to fit the experimental stress-life data, and the Basquin exponent and fatigue strength coefficient were calculated. The presence of 2.6 % reverted austenite in the microstructure improved the fatigue limit and fatigue ratio, without significantly reducing tensile strength. The results can be interpreted in terms of reverted austenite having a crack blunting effect on the propagating cracks. A small amount of reverted austenite in the range of 2 %–3 % vol has a beneficial effect on the fatigue life.     

Proposal for a more accurate physically based S–N curve for welded steel joints

The present article proposes a more accurate S–N curve in the high cycle fatigue regime for fillet welded joints in steel subjected to constant amplitude loading. The S–N curves are constructed based on a physical model of the fatigue damage evolution. It is a two phase model where the crack initiation is treated by a local weld notch approach. The subsequent growth is based on the concept of the stress intensity factor at the crack front by applying the Paris law. According to the proposed model, the time to crack initiation becomes the dominant part of the fatigue life at low stress range levels. The resulting S–N curves are non-linear for a log–log scale and they do not predict any fatigue limit. The curves change slope gradually and the stress range continue to decrease with increasing number of cycles. The curves fit collected life data far better than the conventional bi-linear curves found in rules and regulations. The curves predict considerably longer fatigue lives at low stresses than the conventional curves do, despite the non-existence of a fatigue limit.     

A model for high cycle fatigue

Failure due to fatigue consists of such macroscopic events as crack initiation and propagation. Microscopic events including microcrack nucleation, microcrack growth and coalescence of some of the microcracks are also important in that such crack interactions can be considered to contribute to the development of a critical defect, i.e. a defect which can self propagate and lead to failure. Since crack initiation is important at high cycles, this paper considers a microcrack and computes its growth to advance a high cycle stress-life (S-N_f) formulation for metals and alloys based on crack initiation. In addition to a material's Burgers' vector and grain size, an indirect effort is also made to include the role of its propensity to cracking through a ratio S(σ_I)/S(σ_f), where S(σ_I) and S(σ_f) simply represent steady state crack spacings at stress amplitudes σ_I and σ_f (endurance limit), respectively. Conceptually, a decrease of this ratio suggests an increased tendency for cracking and vice versa. As shown in the text, the model predicts that the crack initiation period varies increasingly with this ratio, and the value of the steady state crack spacing ratio is in and of itself quite sufficient to model the experimental stress-life data in instances where life is controlled by crack initiation period and not the stage II crack propagation. Because of this limitation, extreme care must thus be taken with regard to its application.     

疲劳试验的数据处理

以45钢为例,介绍了疲劳试验数据处理的步骤:整理样本数据,画散点图,用回归分析建立疲劳方程和曲线,计算相对误差,计算残差标准差,建立可靠度-疲劳应力-寿命方程和曲线。讨论的重点是用配对法求得的应力作为截尾寿命的应力;建立带小数幂的疲劳方程;用相对误差代替显著性检验。     

Fatigue of fillet welded A515 steel

A study has been made of the fatigue behavior of fillet welded ASTM A515 steel. As-welded and stress-relieved skip fillet weld specimens were tested under pulsed tension and altering cyclic load to determine stress-life and crack propagation behavior. Crack initiation and propagation features were determined from sectioned surfaces. All fatigue cracks were semi-elliptic and initiated from weld end toes. The length/depth ratio was approximately constant during propagation. There was no consistent effect of tensile residual stress on fatigue life under pulsed tension but there was a detrimental effect under alternating loads. An equivalent crack model has been proposed to quantify the stress concentration effect at the crack initiation site based on the application of the Paris equation. The test results show that the equivalent crack can give a reasonable prediction of the fatigue life of a welded structure and is a potentially convenient tool in fatigue design.     

MICROCRACK PROPAGATION AND MICROSTRUCTURAL PARAMETERS OF FATIGUE DAMAGE

Abstract— Modern approaches to microstructural analysis of fatigue in metallic materials consider the density and the total length per unit area of propagating surface microcracks as useful indicators of fatigue damage. Such parameters, when observed on a carbon steel studied in a previous paper, have a dispersion similar to that of fatigue life and they are linearly correlated with fatigue endurance.
The aim of this paper is to extend the research on fatigue damage in the already studied carbon steel and to examine the scatter of crack propagation rate together with the evolution of surface cracks during fatigue life. The final aim of this work is to study how these two factors are correlated with fatigue life distribution in order to evaluate the effectiveness of damage detection methods.     

Stress-life fatigue assessment of pipelines with plain dents

This paper presents a new algorithm for assessing the fatigue life of dented pipelines. The proposed methodology was conceived according to the current stress-life fatigue theory and design practice: it employs S–N curves inferred from tensile test material properties and uses well established methodologies to deal with the stress concentration, the mean stress and the multi-axial stress state that characterizes a dented pipe. Finite element analyses are carried out to model the denting process and to determine the stress concentration factors of several pipe-dent geometries. Using dimensional analysis over the numerical results, a non-dimensional number to characterize the pipe-dent geometry is determined and linear interpolation expressions for the stress concentration factors of dented pipelines are developed. Fatigue tests are conducted with the application of cyclic internal pressure on small-scale dented steel pipe models. In view of the fatigue test results, the more appropriate S–N curve and mean stress criteria are selected.     

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.