A non-local theory applied to high cycle multiaxial fatigue

ABSTRACT The stress gradient effect on the fatigue limit is an important factor which has to be taken into account for an efficient transfer of fatigue data from laboratory tests to design of industrial components. A short review of some multiaxial high cycle fatigue criteria considering this effect is presented. On the basis of the two local mesoscopic approaches of Papadopoulos, two new non‐local high cycle multiaxial fatigue criteria are developed. These proposals are based on the concept of volume influencing fatigue crack initiation. Their predictions are compared with experimental multiaxial fatigue data on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron). The accuracy of the two local Papadopoulos criteria and of the non‐local proposals are compared and discussed, together with the physical interpretation of the threshold defining the volume influencing fatigue crack initiation.     

Factors influencing the GBF size of high strength steels in the very high cycle fatigue regime

The influences of major factors including applied stress amplitude, inclusion size and hydrogen content on granular-bright-facet (GBF) size of high strength steels in the very high cycle fatigue regime were studied in this article. It was found that the GBF size is determined by the applied stress amplitude and material hardness. If the applied stress amplitude is lower, the GBF size is larger. When a specimen containing bigger inclusions, the applied stress amplitude to form GBF can be reduced which results in the increase of GBF size. Hydrogen has different effects on the GBF size. The related reasons were discussed.     

X80管线钢不同缺陷类型的磁记忆检测试验研究

为探究X80管线钢不同缺陷类型的力磁耦合特性,设计了平板试件与穿孔、边缘切槽3种不同试件,通过金属磁记忆检测方法对X80管线钢试件不同缺陷类型的磁记忆信号特征进行了试验研究.采用材料试验机对试件导入不同程度的塑性损伤与应力集中,通过光学应变测量系统获取试件表面的实时应变情况,同时采用磁记忆检测仪对试件表面诱发磁场的法向分量与切向分量进行卸载离线检测.结果表明:随着塑性损伤程度的增加,无缺陷试件的磁记忆信号法向分量与切向分量从平缓趋向波动,但未出现明显的峰值;含穿孔与切槽试件磁记忆信号法向分量在缺陷处出现过零点与反对称双峰,切向分量出现单峰值,并且渐趋明显.初步探究了X80管线钢塑性损伤与磁记忆信号之间的关联性,为油气管道塑性损伤程度的无损定量评价奠定了基础.     

On effect of hydrogen on very high cycle fatigue behaviours of high strength steels

Abstract

In order to analyse the effect of hydrogen on very high cycle fatigue properties, hydrogen was precharged into two high strength steels. The applied stress intensity factor range at the periphery of inclusions before and after being precharged is approximately proportional to the cubic root of inclusion size. In addition, the applied stress intensity factor range at the periphery of inclusions after being precharged was lower compared with uncharged specimens. The additional stress intensity factor range generated by hydrogen ΔK_H is raised after the hydrogen was precharged. A simple prediction equation of S–N curve was proposed by introducing the hydrogen influence factor. The proposed prediction equation can reasonably describe the S–N curves for precharged specimens.     

Comparison of different statistical models for description of fatigue including very high cycle fatigue

In this paper the fatigue behaviour of welded joints and helical compression springs are analysed using two different statistical models. The data consist of results from low cycle, high cycle and very high cycle fatigue and different number of investigated specimens. In particular, the software program ProFatigue is used for derivation of the probabilistic S–N field from experimental fatigue data. The program, based on a former regression Weibull model, allows the estimation of the parameters involved in the S–N field model, providing an advantageous application of the stress based approaches in the fatigue design of mechanical components. The results obtained are compared with the customary Wöhler-curve, represented as a straight line in a double-logarithmic scale. Application to probabilistic assessment of cumulative damage and further program enhancement can be now envisaged.     

Characterizing the effect of residual stresses on high cycle fatigue (HCF) with induction heating treated stainless steel specimens

A new method for introducing a predetermined amount of residual stresses in stainless steel thick-walled hollow fatigue test specimens was developed by the authors [1] using high frequency induction heating. The advantage of the proposed method over more traditional approaches is to avoid any change in other important fatigue parameters, i.e. surface roughness, geometry, and microstructure, while introducing the residual stresses. The last point only holds if the material under study does not undergo any phase transformation within the range of temperatures and time exposures reached during the heat treatment. In this paper, the effect of residual stresses on high cycle fatigue (HCF) life of annealed AISI 304L stainless steel is investigated by introducing a residual stress field in thick-walled hollow fatigue specimens and by comparing the fatigue life obtained with the reference S–N curve. For the particular case studied, a surprising observation is made. Introducing tensile residual stresses beneath the surface of hollow fatigue specimens using the method proposed by Paquet et al. [1] leads to improved HCF lives. Validity of this result is confirmed by a statistical analysis. Residual stresses were analyzed by the X-ray diffraction (XRD) technique to rationalize this experimental result. The increase in fatigue life is explained by residual stresses evolution within the specimen cross section during the fatigue test, leading to a build up of compressive residual stresses beneath its surface. This is a clear demonstration that assimilating residual stresses resulting from fabrication processes to superimposed static mean stresses can lead to considerable errors in fatigue life predictions.     

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.     

Cyclic torsion very high cycle fatigue of VDSiCr spring steel at different load ratios

Cyclic torsion fatigue tests with superimposed static torsion loads are performed with VDSiCr spring steel with shot-peened surface in the high cycle fatigue (HCF) and very high cycle fatigue (VHCF) regime. Fatigue properties are investigated at load ratios R = 0.1, R = 0.35 and R = 0.5 up to limiting lifetimes of 5 × 10⁹ cycles with a newly developed ultrasonic torsion testing method. Increasing the load ratio reduces the shear stress amplitude that the material can withstand without failure. Fatigue cracks are initiated at the surface in the HCF regime. In the VHCF regime, cracks are preferentially initiated internally in the matrix, below the surface layer with compression residual stresses, and less frequently at the surface. Cyclic and mean shear stresses with 50% survival probability in the VHCF regime are presented in a Haigh diagram. Linear line approximation delivers a mean stress sensitivity of M = 0.33 for load ratios between R = −1 and R = 0.5.     

A cumulative damage model for fatigue life estimation of high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes

A cumulative fatigue damage model is presented to estimate fatigue life for high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes with fish‐eye mode failure, and a simple formula is obtained. The model takes into account the inclusion size, fine granular area (FGA) size, and tensile strength of materials. Then, the ‘equivalent crack growth rate’ of FGA is proposed. The model is used to estimate the fatigue life and equivalent crack growth rate for a bearing steel (GCr15) of present investigation and four high‐strength steels in the literature. The equivalent crack growth rate of FGA is calculated to be of the order of magnitude of 10^?14–10^?11 m/cycle. The estimated results accord well with the present experimental results and prior predictions and experimental results in the literature. Moreover, the effect of inclusion size on fatigue life is discussed. It is indicated that the inclusion size has an important influence on the fatigue life, and the effect is related to the relative size of inclusion for FGA. For the inclusion size close to the FGA size, the former has a substantial effect on the fatigue life. While for the relatively large value of FGA size to inclusion size, it has little effect on the fatigue life.     

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.     

Influence of non-metallic inclusions on fatigue life in the very high cycle fatigue regime

The present paper deals with the influence of non-metallic inclusions on fatigue life in the high cycle fatigue and the very high cycle fatigue regime. For that purpose, several castings of steel 42CrMo4 (AISI 4140, DIN EN 1.7225) were produced by using recently developed novel metal-melt filters. The specimens were tested in hot-isostatically pressed and heat treated condition. After fatigue failure every fracture surface was intensively investigated by scanning electron microscopy in order to define the type, the size, the chemical composition, the morphology and the location of the crack initiating discontinuity. Subsequently, Murakami’s √area model was used for the evaluation of the influence of non-metallic inclusions on the fatigue life. In the present investigation four common types of chemical compositions of crack initiating discontinuities were identified. Furthermore, four different internal failure types and their influence on the fatigue life in cast steel were investigated and described. Thus, the present contribution proposes a basic correlation determined from fatigue lives in case of various internal crack initiation types. The key parameters for fatigue life prediction in case of internal fatigue failure in the very high cycle fatigue regime are (i) the size of the crack initiating discontinuity, (ii) the inclusion depth and (iii) the crack initiating failure type.     

Manifestations of dynamic strain aging under low and high cycle fatigue in a type 316LN stainless steel

Influence of Dynamic strain aging (DSA) under low cycle fatigue (LCF) and high cycle fatigue (HCF) loading was investigated by conducting LCF and HCF tests on specimens over a wide range of temperature from 573 to 973 K. DSA was found to be highly pronounced in the temperature range of 823–873 K. DSA was seen to have contrasting implications under LCF and HCF deformation. The cyclic hardening owing to DSA caused an increase in the cyclic stress response under LCF, leading to decrease in cyclic life. On the other hand, the DSA-induced strengthening suppressed the crack initiation phase under HCF where the applied stress remains fixed, leading to an increase in the cyclic life.     

Fatigue behaviour of SiCp-reinforced aluminium composites in the very high cycle regime using ultrasonic fatigue

The fatigue behaviour of a 2009/SiC/15p‐T4 DRA composite has been examined in the very high cycle fatigue (VHCF) regime where 10⁷≤N_f≤ 10⁹ cycles. Ultrasonic fatigue was used to achieve the very high cycle counts. Careful processing yielded a composite with a very homogeneous particle distribution with minimal clustering. Fatigue crack initiation was observed almost exclusively at AlCuFe inclusions with no crack initiation observed at SiC particle clusters. Fatigue lives at a given stress level exhibited minimal scatter and subsurface crack initiation was observed in all cases. This behaviour is consistent with the presence of a low number density of critical inclusions that are responsible for crack initiation very early in fatigue life.     

Initiation and propagation behaviour of fatigue cracks in hard-shot peened Type 316L steel in high cycle fatigue

Observations of fatigue crack growth behaviour were made during rotating‐bend testing of hard‐shot peened Type 316L steel. From the results of these observations, the crack that developed in the axial direction was observed and the mechanism of the fatigue crack properties was clarified as follows: (1) Small circumferential surface fatigue cracks were detected at 60% of the fatigue lifetime. These cracks propagated very slowly in both the circumferential and radial directions. (2) When a radial crack reached a depth of between 150 and 350 μm, axial fatigue cracks were formed. (3) In the next stage, either the radial or the axial fatigue cracks continued propagating, or an inwards growing radial crack formed from the axial crack. (4) In the final stage, the circumferential surface crack began to grow rapidly and resulted in fracture. (5) The fracture type of hard‐shot peened Type 316L is a particular type of surface fracture.     

Micromechanical study of the loading path effect in high cycle fatigue

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 10⁷ cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.     

TC4钛合金的超高周疲劳行为及其竞争失效模型构建

针对现有模型对TC4竞争失效预测的不准确性,建立了基于最大应力强度因子的竞争失效模型。在室温以及两种应力比下,针对TC4钛合金进行超高周疲劳试验,通过试验与最弱键竞争失效理论相结合的方法进行评估,研究其超高周疲劳性能。通过对试样断口形貌的观察,可将其失效模式分为如下两类:表面失效以及内部失效。对试样表面缺陷以及内部解理刻面尺寸进行测量,并评估其最大应力强度因子值。进一步通过正态分布得到最大应力强度因子的累计分布函数,基于两参数泊松分布建立了与最大应力强度因子有关的竞争失效模型。通过模型计算结果,可以得出在任一最大应力强度因子下试样发生各种失效模式的概率,且经分析对比,本文中TC4两种疲劳失效模式的失效概率评估结果与试验数据吻合较好,为分析TC4钛合金超高周疲劳状态下的疲劳失效模式提出了新的评估方法。     

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.     

Very high cycle fatigue of VDSiCr spring steel under torsional and axial loading

Very high cycle fatigue (VHCF) properties of VDSiCr spring steel are investigated with ultrasonic equipment under fully reversed cyclic torsion loading and under cyclic axial loading at load ratios R = –1, R = 0.1 and R = 0.5. Shot‐peened specimens with surface finish similar to valve springs in combustion engines are tested until limiting lifetimes of 10¹⁰ cycles. Under cyclic torsion loading, specimens either fail below 10⁶ cycles with crack initiation at the surface or they do not fail. Under cyclic axial loading, failures above 10⁹ cycles were found for all load ratios with crack initiation at the surface or at internal inclusions. Ratio of mean endurance limit (50% failure probability at 10¹⁰ cycles) under fully reversed cyclic torsion and cyclic tension‐compression loading is 0.86. Cyclic torsion loading slightly below the endurance limit leads to cyclic softening first followed by cyclic hardening whereas cyclic stability is found for tension‐compression loading. Cyclic torsion reduces surface compression stresses whereas they are hardly affected by cyclic tension‐compression loading. Mean endurance limit at 10¹⁰ cycles for R = 0.1 is 61% of the endurance stress amplitude at load ratio R = –1, and for R = 0.5 it is 44% of the tension‐compression endurance limit. Endurance limits for cyclic torsion and cyclic tension‐compression loading are comparable, if effective stress amplitude is used that considers cyclic normal stresses and residual compression stresses at the surface.     

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.