Crack growth rates and microstructure feature of initiation region for very‐high‐cycle fatigue of a high‐strength steel

The S‐N data up to very‐high‐cycle fatigue (VHCF) regime for a high‐strength steel were obtained by fatigue tests under constant amplitude and variable amplitude (VA) via rotating bending and electromagnetic resonance cycling. Crack initiation for VHCF was from the interior of specimens, and the initiation region was carefully examined by scanning electron microscopy and transmission electron microscopy. Crack growth traces in the initiation region of fine‐granular‐area (FGA) were the first time captured for the specimens under VA cycling by rotating bending. The obtained crack growth rates in FGA were upwards to connect well with those in fish‐eye region available in the literature and were associated well with the calculated equivalent crack growth rates in FGA. The observations of profile samples revealed that FGA is a nanograin layer for the specimens under VA cycling, which is a new evidence to support the previously proposed “numerous cyclic pressing” model.     

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.     

A fatigue driving energy approach to high‐cycle fatigue life estimation under variable amplitude loading

In this paper, a concept of fatigue driving energy is formulated to describe the process of fatigue failure. The parameter is taken as a combination of the fatigue driving stress and strain energy density. By assessing the change of this parameter, a new non‐linear damage model is proposed for residual life estimation within high‐cycle fatigue regime under variable amplitude loading. In order to consider the effects of loading histories on damage accumulation under such condition, the load interaction effects are incorporated into the new model, and a modified version is thus developed. Life predictions by these two models and Miner rule are compared using experimental data from literature. The results show that the proposed model gives lower deviations than the Miner rule, while the modified model shows better prediction performances than the others. Moreover, the proposed model and its modifications are ease of implementation with the use of S–N curve.     

High‐cycle and very‐high‐cycle fatigue behaviour of a titanium alloy with equiaxed microstructure under different mean stresses

The fatigue behaviour of a titanium alloy Ti‐6Al‐4V with equiaxed microstructure (EM) under different values of tensile mean stress or stress ratio (R) was investigated from high‐cycle fatigue (HCF) to very‐high‐cycle fatigue (VHCF) regimes via ultrasonic axial cycling. The effect of mean stress or R on the fatigue strength of HCF and VHCF was addressed by Goodman, Gerber, and Authors' formula. Three types of crack initiation, namely, surface‐with‐RA (rough area), surface‐without‐RA, and interior‐with‐RA, were classified. The maximum value of stress intensity factor (SIF) at RA boundary for R < 0 keeps constant regardless of R in HCF and VHCF regimes. The SIF range at RA boundary for R > 0 also keeps constant regardless of R in VHCF regime, but this value decreases linearly with the increase of R for surface RA cases. The microstructure observation at RA regions gives a new result of nanograin formation only in the cases of negative stress ratios for the titanium alloy with EM, which is explained by the mechanism of numerous cyclic pressing.     

A new continuum damage mechanics–based two‐scale model for high‐cycle fatigue life prediction considering the two‐segment characteristic in S‐N curves

In this study, we propose a new two‐scale fatigue model based on continuum damage mechanics. A representative volume element (RVE) consisting of microinclusions and a matrix is constructed. Further, damage‐coupled constitutive equations are derived. The degradation in the mechanical properties of the RVE is determined by the damaged inclusions and matrix using the Mori‐Tanaka scheme. A numerical calculation of the fatigue lives of notched specimens is executed. This new model predicts high‐cycle fatigue (HCF) life more effectively, considering the two‐segment characteristic of S‐N curves of smooth specimens. This study provides novel insights into the evolution mechanism of HCF damage.     

Numerical simulation of the coupling between thermal dissipation and fish‐eye crack growth in very high cycle fatigue regime

In this paper, we study the temperature field associated with the propagation of a fatigue crack in a very high cycle fatigue regime during ultrasonic fatigue testing. We use a Paris–Hertzberg crack growth law to compute the evolution of the crack and a perfectly elastic–plastic constitutive law to compute the plastic dissipation per cycle at the tip of the crack. A thermomechanical finite element model is proposed to estimate the evolution of the temperature field during the crack propagation. Numerical results obtained agree fairly well with experimental results.     

Nanograin layer formation at crack initiation region for very‐high‐cycle fatigue of a Ti–6Al–4V alloy

The microstructural features and the fatigue propensities of interior crack initiation region for very‐high‐cycle fatigue (VHCF) of a Ti–6Al–4V alloy were investigated in this paper. Fatigue tests under different stress ratios of R = ?1, ?0.5, ?0.1, 0.1 and 0.5 were conducted by ultrasonic axial cycling. The observations by SEM showed that the crack initiation of VHCF presents a fish‐eye (FiE) morphology containing a rough area (RA), and the FiE and RA are regarded as the characteristic regions for crack initiation of VHCF. Further examinations by TEM revealed that a layer of nanograins exists in the RA for the case of R = ?1, while nanograins do not appear in the FiE outside RA for the case of R = ?1, and in the RA for the case of R = 0.5, which is explained by the Numerous Cyclic Pressing model. In addition, the estimations of the fatigue propensities for interior crack initiation stage of VHCF indicated that the fatigue life consumed by RA takes a dominant part of the total fatigue life and the related crack propagation rate is rather slow.     

Very high cycle fatigue properties of high‐strength spring steel 60SiCrV7

The very high cycle fatigue properties of spring steel 60SiCrV7 for automotive suspension system with different hydrogen contents were studied by using ultrasonic fatigue testing and fatigue crack growth testing. The results show that the S–N curves exhibit continuous drop of fatigue lives and no obvious horizontal line exists. Similar fracture surface features were observed for all the specimens that failed mainly from internal inclusions with surrounding granular bright facet (GBF). Fatigue strength decreases remarkably with increasing hydrogen content. The applied stress intensity factor range at the periphery of GBF ΔK_GBF is approximately proportional to 1/3 power of the square of GBF area. The average values of ΔK_GBF for uncharged specimens are close to crack growth threshold ΔK_th, which indicates that ΔK_GBF could be regarded as the threshold value governing the beginning of stable fatigue crack propagation. The increase of hydrogen content tends to reduce ΔK_GBF.     

Influence of processing parameters of selective laser melting on high‐cycle and very‐high‐cycle fatigue behaviour of Ti‐6Al‐4V

Orthogonal experiment design together with the analysis of variance was used to examine the processing parameters (laser power, scan speed, layer thickness and hatch spacing) of selective laser melting (SLM) for superior properties of SLM parts, in which nine groups of specimens of Ti‐6Al‐4V were fabricated. The results clarify that the influence sequence of individual parameter on the porosity is laser power > hatch spacing > layer thickness > scan speed. Ultrasonic fatigue tests (20 kHz) were conducted for the SLMed specimens in high‐cycle fatigue (HCF) and very‐high‐cycle fatigue (VHCF) regimes. The S‐N data show that the fatigue strength is greatly affected by the porosity: the group with the smallest porosity percentage having the highest fatigue strength in HCF and VHCF regimes. Then, the tests on the validation group were performed to verify the optimal combination of SLM processing parameters. Moreover, the observations by scanning electron microscopy revealed that fatigue cracks initiate at lack‐of‐fusion defects in the cases of surface and internal crack initiation.     

Low and high‐cycle fatigue properties of an ultrahigh‐strength TRIP bainitic steel

The scope of this study is to characterize the mechanical properties of a novel Transformation‐Induced Plasticity bainitic steel grade TBC700Y980T. For this purpose, tensile tests are carried out with loading direction 0, 45 and 90° with respect to the L rolling direction. Yield stress is found to be higher than 700 MPa, ultimate tensile strength larger than 1050 MPa and total elongation higher than 15%. Low‐cycle fatigue (LCF) tests are carried out under fully reverse axial strain exploring fatigue lives comprised between 10² and 10⁵ fatigue cycles. The data are used to determine the parameters of the Coffin–Manson as well as the cyclic stress–strain curve. No significant stress‐induced austenite transformation is detected. The high‐cycle fatigue (HCF) behaviour is investigated through load controlled axial tests exploring fatigue tests up to 5 × 10⁶ fatigue cycles at two loading ratios, namely R = ?1 and R = 0. At fatigue lives longer than 2 × 10⁵ cycles, the strain life curve determined from LCF tests tends to greatly underestimate the HCF resistance of the material. Apparently, the HCF behaviour of this material cannot be extrapolated from LCF tests, as different damage, cyclic hardening mechanisms and microstructural conditions are involved. In particular, in the HCF regime, the predominant damage mechanism is nucleation of fatigue cracks in the vicinity of oxide inclusions, whereby mean value and scatter in fatigue limit are directly correlated to the dimension of these inclusions.     

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.     

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.     

Gradient‐enhanced damage modelling of high‐cycle fatigue

Continuum damage mechanics can be used to model the initiation and growth of fatigue cracks. However, finite element analyses using standard fatigue damage formulations exhibit an extreme sensitivity to the spatial discretisation of the problem. The mesh sensitivity is caused by the fact that the underlying continuum model predicts instantaneous, perfectly brittle crack growth as soon as a crack has been initiated. The growth of damage localizes in a vanishing volume during this instantaneous growth. This localization is not so much due to loss of ellipticity of the problem, but is caused by the fact that the damage rate is singular at the crack tip. The damage rate singularity can be removed by the introduction of higher‐order deformation gradients in the constitutive modelling. As a result, crack growth at a finite rate and with a positive amount of energy dissipation is predicted. Finite element analyses converge to this solution and are thus no longer pathologically dependent on the spatial discretization. Copyright © 2000 John Wiley & Sons, Ltd.     

1010‐cycle fatigue properties of 1800 MPa‐class JIS‐SUP7 spring steel

10¹⁰‐cycle fatigue tests were conducted at 100 Hz for three years and at 20 kHz for one week on 1800 MPa‐class JIS‐SUP7 spring steel. Uniaxial tests up to 10⁸ cycles were also conducted at 120 and 600 Hz. The 120 Hz tests had larger control volumes. The fatigue limit at 10¹⁰ cycles was lower than at 10⁸ cycles, and any frequency effect was shown to be negligible. A size effect was found; the tests with larger control volumes showed results of lower fatigue strength.     

A convex hull‐based approach for multiaxial high‐cycle fatigue criteria

Design methods against multiaxial high‐cycle fatigue require the formulation of appropriate criteria that differ in the definition of critical measures introduced to quantify damage, as the amplitude of shear stress. The present paper proposes a novel approach to compute the amplitude of shear stress in multiaxial high‐cycle fatigue. The approach is based on the computation of the convex hull enclosing the stress history under investigation and is validated on proportional and non‐proportional paths in several dimensions and for different materials. High accuracy is achieved when compared with alternative methods from the literature.     

Towards improved ODS steels: A comparative high‐temperature low‐cycle fatigue study

Within the frame of this work, the mechanical behaviour of a bimodal ferritic 12Cr‐ODS steel as well as of a ferritic‐martensitic 9Cr‐ODS steel under alternating load conditions was investigated. In general, strain‐controlled low‐cycle fatigue tests at 550°C and 650°C revealed similar cyclic stress response. At elevated temperatures, the two steels manifest transitional stages, ie, cyclic softening and/or hardening corresponding to the small fraction of the cyclic life, which is followed by a linear cyclic softening stage that occupies the major fraction of the cyclic life until failure. However, it is clearly seen that the presence of the nano‐sized oxide particles is certainly beneficial, as the degree of cyclic softening is significantly reduced compared with non‐ODS steels. Besides, it is found that both applied strain amplitude and testing temperature show a strong influence on the cyclic stress response. It is observed that the degree of linear cyclic softening in both steels increases with increasing strain amplitude and decreasing test temperature. The effect of temperature on inelastic strain and hence lifetime becomes more pronounced with decreasing applied strain amplitude. When analysing the lifetime behaviour of both ODS steels in terms of inelastic strain energy calculations, it is found that comparable inelastic strain energies lead to similar lifetimes at 550°C. At 650°C, however, the higher inelastic strain energies of 12Cr‐ODS steel result in significant lower lifetimes compared with those of the 9Cr‐ODS steel. The strong degradation of the cyclic properties of the 12Cr‐ODS steel is obviously linked to the fact that the initial hardening response appears significantly more pronounced at 650°C than at 550°C. Finally, the obtained results depict that the 9Cr‐ODS steel offers higher number of cycles to failure at 650°C, compared with other novel ODS steels described in literature.     

High‐cycle fatigue and fracture behaviours of Cu‐Be alloy with a wide strength range

The high‐cycle fatigue and fracture behaviours of Cu‐Be alloy with tensile strength ranging from 500 to 1300 MPa acquired by different treatments were studied. Fatigue crack initiation, fracture surface morphologies, S‐N curves and fatigue strength show obvious differences due to the change of microstructure. At relatively low‐strength level, some fatigue cracks originated from defects; while at high‐strength level, all the fatigue cracks initiated from cleavage facets. It was found that the fatigue ratio increases linearly and fatigue strength changes quadratically with increasing tensile strength, only considering one strengthening mechanism. Finally, the fatigue strengths of various Cu‐Be alloys were summarized.     

Interior induced fatigue of surface‐strengthened steel under constant and variable loading: Failure mechanism and damage modeling

Pulsating tension tests with constant amplitude (CA) and variable amplitude (VA) were conducted to investigate the interior failure mechanisms of a carburized Cr steel, and a cumulative damage model with the fine granular area (FGA) formation process was proposed in this study. Such a steel represents the continuously descending S‐N (stress‐number of cycles) curve characteristics associated with inclusion‐FGA‐fisheye induced failure even under variable amplitude. Due to crack growth retardations and accelerations resulted from the interaction effect between stepwise resets of the applied stress, the crack morphology under variable amplitude loading is much rougher. The interior failure mechanism was elucidated in combination with the determination of stress intensity factor values at different crack tips. Based on proposed damage model, the agreement between the predicted and experimental results is fairly good within the factor‐of‐two range.     

Physics‐based multiscale damage criterion for fatigue crack prediction in aluminium alloy

In this paper, a physics‐based multiscale approach is introduced to predict the fatigue life of crystalline metallic materials. An energy‐based and slip‐based damage criterion is developed to model two important stages of fatigue crack initiation: the nucleation and the coalescence of microcracks. At the microscale, a damage index is developed on the basis of plastic strain energy to represent the growing rate of a nucleated microcrack. A statistical volume element model with high computational efficiency is developed at the mesoscale to represent the microstructure of the material. Also, the formation of a major crack is captured by a coalescence criterion at mesoscale. At the macroscale, a finite element analysis of selected test articles including lug joint and cruciform is conducted with the statistical volume element model bridging two scale meshes. A comparison between experimental and simulation results shows that the multiscale damage criterion is capable of capturing crack initiation and predicting fatigue life.