基于局部应变能密度法的缺口多轴疲劳寿命评估

本文提出了包括实验和数值工作在内的综合分析,阐明了缺口行为对比例多轴疲劳寿命的影响。方法对45钢和45QT钢进行了考虑缺口半径和开口角的多轴疲劳试验,基于平均应变能量密度理论的多轴疲劳分析的分析和计算框架进行了研究,以处理能量梯度。结果显示,大量新的疲劳数据首先通过法向应力和剪应力进行汇总,然后通过凹口尖端周围受控体积中的局部应变能密度重新分析。结论缺口角度对比例载荷下多轴疲劳数据的影响较小,而缺口半径是影响疲劳寿命的主要因素。     

Effect of notch root radius on the initiation and propagation of fatigue cracks

Under the conditions of constant nominal applied stress, increasing notch root radius causes an increase in the number of cycles to initiate a fatigue crack at a notch root. An explanation of the effect is given in terms of the effective stress concentration factor of the notch. Data are presented which indicate that variations in notch root radius may cause changes in the crack growth rate during the initial stages of propagation from a notch.     

Fatigue strength of notched specimens made of 40CrMoV13.9 under multiaxial loading

The work deals with multiaxial fatigue strength of notched round bars made of 40CrMoV13.9 steel and tested under combined tension and torsion loading, both in-phase and out-of-phase. The axis-symmetric V-notches present a constant notch root radius, 1 mm, and a notch opening angle of 90°; the notch root radius is equal to 4 mm in the semi-circular notches where the strength in the high cycle fatigue regime is usually controlled by the theoretical stress concentration factor, being the notch root radius large enough to result in a notch sensitivity index equals to unity. In both geometries the diameter of the net transverse area is 12 mm.The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than 120 new fatigue data are summarised in the present work, corresponding to a one-year of testing programme.All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.     

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.     

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.     

Generalised Neuber concept of fictitious notch rounding

The microsupport effect at sharp notches subjected to high-cycle fatigue can be described according to Neuber by averaging the maximum notch stress in a small material volume (microsupport length ρ^*) at the notch root (radius ρ). The averaged stress may be expressed by the maximum stress of a corresponding notch of an enlarged, fictitious radius, ρ_f = ρ + sρ^*, where s is the microsupport factor. The status of Neuber’s concept within his general theory of notch stresses is reviewed, followed by more recent theoretical and application-relevant developments. The theoretical developments refer to the notch angle dependency of the support factor, to its value for pointed versus rounded notches and to in-plane shear loading with out-of-bisector crack propagation. The application developments refer to the fatigue assessment of welded joints.     

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.     

Fatigue tests of notched specimens made from butt joints at steel

The weld toe as well as the weld root of joints acts as a geometrical notch, which decreases the fatigue strength of welded components. Local approaches used for fatigue assessment account for the local stress concentration when referring to the notch stress as a fatigue parameter. This applies also to the approaches based on the notch stress intensity factor like, for example, the averaged strain energy density, neglecting the actual notch radius and considering a sharp notch as a simplification. A uniform S‐N curve valid for different types of welded joints and failure locations was derived from re‐analyses of fatigue test results as documented in literature. The fatigue tests described in this paper aimed at validating that energy‐based S‐N curve by dedicated tests on artificially notched specimens. At first, four parameters were investigated in order to estimate their influence on the fatigue strength and to select appropriate notch geometries for the final step of the test campaign. The advantages of these tests are that both the exact notch geometry and the local stress range at the notch, including misalignment effects, were identified and considered in experimental data analysis. This paper presents the results of the rather comprehensive testing activities and comparisons with the design‐S‐N curve mentioned, yielding unexpected fatigue behaviour. This can be explained by the short crack propagation life.     

陶瓷的断裂韧性与缺口半径 Ⅰ.断裂韧性测试技术

本文用一种新的简单方法制备了不同半径的尖缺口，用单边切口梁试件测试了不同缺口半径氧化铝陶瓷的断裂韧性.对七种不同测试方法测得的、同一种材料的断裂韧性进行了对比，讨论陶瓷材料断裂韧性的最佳测试方法和测试中对缺口半径的要求.     

A micromechanical theory of fatique crack initiation from notches

The fatigue crack initiation along the slip banks emanating from notches is analyzed theoretically with the use of the dislocation dipole accumulation model proposed previously by the authors. The complex function analysis for an elliptical notch under the anti-plane shear gives a quantitative method for assessment of the reduction of fatigue strength as a function of the notch tip radius, the notch size and the elastic stress concentration factor. Special cases of this theoretical analysis yield several semi-empirical formulae commonly used by engineers for data collection. In the derivation, the limitations for each engineering approach are clarified. The material properties are included in the present micromechanical theory as the slip band length and the dislocation frictional stress.     

双频激振下带V形缺口轴的疲劳寿命研究

针对金属轴类零件在实际复杂工况下易产生应力集中而发生疲劳破坏的问题，利用双频激振系统，研究带V形缺口轴的疲劳寿命随缺口几何参数的变化规律。首先，提出了促进轴疲劳裂纹萌生的激振频率控制曲线，同时采用响应曲面法中的Box-Behnken设计法对V形缺口的夹角、圆角半径和深度进行三因素三水平的实验设计；其次，建立了疲劳寿命多元回归预测模型，并采用方差分析法对模型进行可靠性评价；最后，利用响应曲面和等高线图分析了缺口的夹角、圆角半径和深度对轴疲劳寿命的影响规律，并进行了预测模型的应用。研究结果表明：疲劳寿命预测值与实测值之间的误差在4.2%以内，预测精度较高，预测模型可靠；缺口几何参数对疲劳寿命从大到小的影响次序是缺口深度、缺口圆角半径、缺口夹角，以圆角半径和深度的交互作用对轴疲劳寿命的影响最为显著。研究结果可为金属轴类零件的抗疲劳设计提供重要参考。     

陶瓷的断裂韧性与缺口半径 Ⅰ.断裂韧性测试技术

本文用一种新的简单方法制备了不同半径的尖缺口，用单边切口梁试件测试了不同缺口半么氧化铝陶瓷的断裂韧性，地七咱不同测试方法测得的，同一种材料的断裂韧性进行了对比，讨论陶瓷材料断裂韧性的最佳测试方法和测试中对缺口半径的要求。     

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.     

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.     

Notch-Size Effect in fatigue of steel specimens – verification of some calculation methods

New, more accurate fatigue test results were used for verification of different calculation methods and for establishing a more reliable relationship between the notch factor and the notch radius. Scatter bands for the dependence of the notch sensitivity K_F/K_T on the notch radius were obtained for steel specimens with stress concentration factors K_T ≤ 3.6, with particular consideration of test results for large component similar specimens with large notch radii. The scatter bands of test points were ploted separately for tempered and normalized steels but the rotating-bending and tension-compression test results were considered together. Their upper and lower boundaries were expressed analytically with a two-parameter-formula. This formula takes better into account the notch-size effect than the formulas of Neuber, Peterson or Stieler.     

Prediction of fatigue crack initiation lives at elongated notch roots using short crack concepts

Re-initiation lives of fatigue cracks departing from stop-holes roots, previously introduced at the tip of deep cracks on modified SE(T) specimens, have been satisfactorily predicted using their properly calculated notch sensitivity factor q, considering the notch tip stress gradient influence on the fatigue behavior of mechanically short cracks. This is an indispensable detail, since traditional q estimates are only applicable to semi-circular notches, whereas elongated slits can have q values which also depend on their shape, not only on their tip radius. Based on this experimental evidence, a criterion for acceptance of short cracks is proposed.     

Improving fatigue life for aluminium cruciform joints by weld toe grinding

The increase of fatigue life in aluminium cruciform joints by weld toe grinding was the focus of the current study. The test data are presented by both a nominal stress range approach and by the more refined structural and notch stress range approaches. The influence of the weld toe angle, weld leg length and weld toe radius on the structural and notch stress concentration factor (SCF) was systematically studied by means of finite element analysis. Experimental data based on 18 pieces of as-welded and 13 pieces of weld toe-ground specimens made of 12 mm thick plates showed a significant improvement in fatigue life in aluminium by grinding the weld toe and confirmed the permitted improvement in fatigue life by design codes.     

Notch fracture toughness of high-strength Al alloys

In this study, the notch fracture toughness (NFT) of high-strength Al alloys was examined by a non-standardized procedure. The NFT is defined as the critical notch stress-intensity factor (NSIF) K_ρ,c, which is determined by using several methods of analysis and computing. A set of specimens with different notch root radii made from overaged 7xxx alloy forging was selected. The influence of the notch radius on the fracture toughness of the material was considered. It was found that the notch radius strongly affects the fracture behavior of forged 7xxx alloy in overaged condition. The notch fracture toughness was higher than the fracture toughness of a cracked specimen and increased linearly with notch radius. The critical notch radius was related to the spacing of intermetallic (IM) particles which promote an intergranular or transgranular fracture mechanism according to their size. It appeared that ductile transgranular fracture generated by the formation of dimples around dispersoids and matrix precipitates was predominant which indicates that intense strains are limited to a much smaller zone than the coarse IM particles spacing. This double mechanism is also operate for crack propagation of ductile fatigue. The nature and morphology of IM particles exert significant effects on the rate of fatigue crack growth and fracture toughness properties.     

Assessment of the period to fatigue macrocrack initiation near stress concentrators by means of strain parameters

A new approach to the experimental assessment of the local strain at a stress concentrator has been presented. It is based on a procedure of notch opening displacement measurements at certain points in the vicinity of a notch related to the effective notch radius ρ _eff = ρ + d * , where ρ is the notch radius and d * is a material constant. Different stress concentrators in structural elements were modelled for a wide variation of notch radii ( ρ = 0.1–6.5 mm) and different geometries of specimens. Hence, a basic relationship, which directly relates the local strain range Δ ε* to the period of fatigue macrocrack initiation N _i has been established. Thus, by applying the value of Δ ε* , assessed from a direct measurement at the notch root, it is possible to determine the period N _i to initiate a fatigue macrocrack of length a _i = d * for some structural components of complicated geometry.