Comparative analysis of fatigue life predictions in central notched specimens of Al–Mg–Si alloys

The fatigue behaviour of an Al–Mg–Si alloy was studied using notched specimens. Fatigue tests were conducted at two stress ratios R= 0 and R= 0.4 on thin plates with a central hole. Constant and block variable loading amplitudes were applied to the specimens using a servo‐hydraulic machine. The applicability of the local strain approach method to the prediction of the fatigue life was investigated for this type of discontinuity. Two methods, the equivalent strain energy density approach and a modified stress–strain intensity field approach, were used to predict the fatigue strength. For the second one an elastic–plastic finite element analysis was carried out in order to obtain the local strain and stress distributions near the notch root. Based on Miner's rule an equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. The experimental results were compared with the predicted results obtained by the two methods investigated and better agreement was found with the stress–strain field intensity approach, while the strain energy approach gave more conservative results. Miner's rule gives a good correlation between the variable amplitude and constant amplitude results.     

ELASTIC-PLASTIC BEHAVIOUR AND UNIAXIAL LOW CYCLE FATIGUE LIFE OF NOTCHED SPECIMENS

Experimental and numerical analyses were carried out to examine the elastic-plastic behaviour and low cycle fatigue (LCF) life of EN15R steel notched specimens. Notch root strains were measured and compared with estimates obtained from three methods: Neuber, Glinka and hite element (FE) analyses. All methods provided fairly accurate estimates of cyclic strain up to net section yield, from which point the Neuber and Glinka predictions were greater than measured. The finite element results compared well with measured results. The estimated notch root strains were used to predict the life of the notched specimens based on LCF results from unnotched specimens. Uniaxial Coffom-Manson and multiaxial Lohr-Ellison approaches were used. Improved fatigue life predictions were obtained when the FE predictions of the multiaxial strains were combined with a multiaxial strain parameter. The possible influence of strain gradient is inferred by comparing LCF lives for hollow thin-walled and solid bar specimens.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Multiaxial creep–fatigue life prediction for cruciform specimen

This paper describes the high temperature multiaxial creep–fatigue life prediction for type 304 stainless steel. Finite element analyses were performed for determining the stress–strain state in the gage part of a cruciform specimen subjected to creep–fatigue loading under four strain waves at three principal strain ratios. Creep–fatigue lives of cruciform specimens were discussed in relation to the principal stress amplitude calculated by finite element analysis. Creep–fatigue damage was evaluated by linear damage rule and the suitability of three low cycle fatigue and three creep damage parameters was discussed.     

Fatigue life prediction of friction stir spot welds based on cyclic strain range with hardness distribution and finite element analysis

The main aim of the present study is to investigate the fatigue behavior of single friction stir spot welds (FSSW) using strain-based modified Morrow’s damage equation. The correlation between microhardness, cyclic material constants, and mechanical strength of different zones around the FSSW are assumed to be proportional to the base material hardness. Experimental fatigue tests of friction stir spot welded specimens have been carried out using a constant amplitude load control servo-hydraulic fatigue testing machine. ANSYS finite element code has been used to simulate a single tensile shear friction stir spot welded joint, and non-linear elastic-plastic finite element analysis has been employed to obtain the values of local equivalent stress and strain near the notch roots of the joints. The results based on the numerical predictions have been compared with the experimental fatigue test data. It has been shown that the strain-based approach does a very good job for estimating the fatigue life of friction stir spot welded joints.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

高速列车制动盘SiCp／A356颗粒增强铝基复合材料的热疲劳性能研究

通过SiCp／A356颗粒增强复合材料切口试样在20℃-300℃循环下的热疲劳试验,获得热疲劳裂纹形成寿命与试样切口半径及厚度等几何尺寸的关系。采用热弹塑性有限元法模拟热疲劳试验中试样切口根部的应力．应变响应,进而揭示出残余应力形成机制。结合热疲劳试验的裂纹形成寿命与有限元模拟的应力．应变响应,建立起考虑平均应力影响的...     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

Notch effect on creep–fatigue life for Sn–3.5Ag solder

This paper studies the creep–fatigue crack initiation and failure lives of Sn–3.5Ag solder notched specimens focused on the multiaxial strain at the notch root. Push–pull creep–fatigue tests were performed using three circumferential notched specimens using four kinds of creep–fatigue strain waveforms. Multiaxial strains at the notched section were calculated by finite element (FE) analysis under four kinds of creep–fatigue loading. Creep–fatigue damage laws were applied for evaluating the crack initiation and failure lives using the multiaxial strains obtained by the FE analysis. von Mises equivalent strain at the notch root estimated the crack initiation lives with a large scatter as well as the failure lives. Instead, the mean value of von Mises equivalent strain over the cross section of the notch root estimated the crack initiation and failure lives with a small scatter.     

Notched fatigue behavior including load sequence effects under axial and torsional loadings

Notch effects on axial and torsion fatigue behaviors of low carbon steel were investigated. Fully-reversed tests were conducted on thin-walled tubular specimens with or without a transverse circular hole. A shear failure mechanism was observed for both smooth and notched specimens and under both axial and torsion loadings. The notch effect was more pronounced under axial loading, in spite of higher stress concentration factor in torsion. The commonly used nominal S–N approach with fatigue notch factor in conjunction with von Mises effective stress resulted in overly conservative life predictions of both smooth and notched torsion fatigue lives. Neuber’s rule yielded notch root stress and strain amplitudes close to the FEA results for both axial and torsion loadings. The local strain approach based on effective strain obtained from Neuber’s rule or FEA resulted in poor correlation of the fatigue life data of smooth and notched specimens. The Fatemi–Socie critical plane parameter represented the observed failure mechanism and resulted in very good correlations of smooth and notched specimens fatigue data under both axial and torsion loadings. In block loading tests with equal number of alternating axial and torsion cycles at the same stress level, beneficial effect of axial loading was observed. Possible potential reasons for this unexpected behavior are discussed.     

Fatigue limit prediction of notched components using short crack growth theory and an asymptotic interpolation method

Mechanical components have stress risers, such as notchs, corners, welding toes and holes. These geometries cause stress concentrations in the component and reduce the fatigue strength and life of the structure. Fatigue crack usually initiates at and propagates from these locations. Traditional fatigue analysis of notched specimens is done using an empirical formula and a fitted fatigue notch factor, which is experimentally expensive and lacks physical meaning. A general methodology for fatigue limit prediction of notched specimens is proposed in this paper. First, an asymptotic interpolation method is proposed to estimate the stress intensity factor (SIF) for cracks at the notch root. Both edge notched and center notched components with finite dimension correction are included into the proposed method. The small crack correction is included in the proposed asymptotic solution using El Haddad’s fictitious crack length. Fatigue limit of the notched specimen is estimated using the proposed stress intensity factor solution when the realistic crack length is approaching zero. A wide range of experimental data are collected and used to validate the proposed methodology. The relationship between the proposed methodology and the traditionally used fatigue notch factor approach is discussed.     

Analytical study of fatigue crack growth in AA7050 notched specimens under spectrum loading

An analytical study of fatigue crack growth in aluminium alloy 7050-T7451 notched specimens under a fighter aircraft wing root bending moment spectrum was conducted. The crack growth data were measured by quantitative fractography for three groups of specimens with different stress concentration geometrical features. Under spectrum loading and for each spectrum peak stress level, a minimum of five specimens were tested. Based on the analysis of the measured spectrum crack growth data using linear elastic fracture mechanics, it was found that the concept of geometry factors formulated in the stress intensity factor could not collapse the crack growth rate data derived from each stress concentration feature, particularly near the small crack growth region. In order to investigate the possible reasons for this, three-dimensional elastic-plastic finite element analysis was used to determine notch plastic zone sizes for each stress concentration geometry. As a consequence, an alternative crack growth driving force by considering both notch elastic-plastic stress field and gross net-section stress field was proposed and used to interpret the fatigue crack growth data under spectrum loading. It was found that the predictions of crack growth under spectrum loading for different stress concentration factors at different peak load levels agree reasonably well with the experimental results.     

Fatigue life estimation of notched specimens of modified 9Cr-1Mo steel under uniaxial cyclic loading

Accuracy in the estimation of low cycle fatigue life of modified 9Cr-1Mo steel notched specimen by different analytical methods such as linear rule, Neuber’s rule, strain energy density method and numerical method such as finite element analysis have been studied in this investigation. The fatigue tests on notched specimens having notch radius of 1.25 mm, 2.5 mm and 5.0 mm were carried out at 823 K with net stress amplitudes of 250 MPa, 300 MPa and 350 MPa. The fatigue tests on smooth specimens were carried out with strain amplitudes ranging from ±0.3% to ±0.8% with a strain rate of 3 × 10^?3 s^?1 at 823 K to evaluate the fatigue life of notched specimen through strain-life approach. In order to predict the cyclic stress response of the material, Chaboche non-linear hardening model was employed considering two back stress components. Predicted hysteresis loops for smooth specimen were well in agreement with experimental results. Estimated fatigue lives of notched specimens by analytical methods and finite element analysis were within a factor ±16 and ±2.5 of the experimental lives respectively.     

ANALYSIS AND TESTING OF SURFACE COLD-WORK PROCEDURES APPLIED TO NOTCHED, FLAT ELEMENTS

Abstract— Several surface cold work procedures are developed to induce compressive residual stresses adjacent to a notch in a flat element. It would appear that they should all lead to fatigue life enhancement. For sharp notched specimens excellent fatigue life enhancement is observed. For moderately notched specimens only one of the procedures produces this enhancement. In order to shed light on the shortcomings of two of the procedures, the residual stress field is determined by means of finite element analyses in two and three dimensions. It is observed that the two-dimensional analyses predict a residual stress field which should lead to fatigue life enhancement. It is the three-dimensional analyses which help to explain why two of the cold work procedures fail.     

Fatigue of casting flaws at a notch root under an SAE service load history

Smooth and notched specimens of a 319 cast aluminium alloy were fatigue tested under a Society of Automotive Engineers service load history in the as-cast and hipped conditions. The hipping process, which includes subjecting the cast material to a high pressure at high temperature and then slowly cooling down to eliminate internal flaws, decreased the flaw size and improved the fatigue life of cast Al 319 smooth specimens. A 0.6-mm-diameter hole was drilled at the notch root of notched specimens to simulate a natural flaw at the notch root. Specimens with two different notch sizes were tested. Circular edge notches reduced the fatigue strength and a 0.6-mm-diameter drilled hole at the notch root resulted in a further reduction.
The fatigue lives of smooth specimens, notched specimens and notched specimens with a flaw at the notch root subjected to the service load history were predicted using the strain-life approach, an effective strain-life approach and a strain-based intensity factor crack growth model. In crack growth modelling of the fatigue life of smooth cast aluminium specimens the flaw was modelled as a circular edge notch having the same diameter as the flaw. However, in the case of a flaw at a notch root the flaw was modelled as a three-dimensional cavity subjected to the notch stress field and the crack length was predicted in the longitudinal and transverse directions of the specimen cross-section. The strain-life approach was unconservative for all specimen geometries studied. The effective strain-life approach gave good predictions for smooth and blunt notched specimens but gave very conservative predictions for the specimens with flaws in the notch roots. The crack growth calculations gave accurate predictions for all the specimen geometries.     

FATIGUE STRENGTH OF A ROTOR STEEL SUBJECTED TO TORSIONAL LOADING SIMULATING THAT OCCURRING DUE TO CIRCUIT BREAKER RECLOSING IN AN ELECTRIC POWER PLANT

Abstract— The fatigue strength of notched specimens of a rotor steel was examined under variable torsional loading which simulates turbine-generator oscillations resulting from the high speed reclosing of transmission-line circuit breakers. The local stress-strain response at a notch root was analysed using Neuber's rule and the resulting complex strain sequences applied to smooth specimens. Using the rain flow analysis and the linear summation rule, fatigue lives of the smooth specimens were successfully predicted from constant amplitude fatigue life data in association with the cyclic stress-strain curve obtained by the incremental step method. Experimental crack initiation lives for notched specimens subjected to variable torsional loading were in excellent agreement with the theoretical curves derived from results on smooth specimens. According to the view that fatigue damage is equated to crack length, the propagation life of a mode II crack along the notch root was predicted to be actually coincident with the life to crack initiation at the notch root denned in this study, i.e. the life at the stage of finding a continuous circumferential crack.     

Influence of notch severity on thermomechanical fatigue life of a directionally solidified Ni‐base superalloy

The aim of this work is to understand the influence of notches under thermomechanical fatigue (TMF) in a directionally solidified Ni‐base superalloy. Experiments were performed utilizing linear out‐of‐phase and in‐phase TMF loadings on longitudinally oriented smooth and cylindrically notched specimens. Several notch severities were considered with elastic stress concentrations ranging from 1.3 to 3.0. The local response of the notched specimens was determined using the finite element method with a transversely isotropic viscoplastic constitutive model. Comparing the analysis to experiments, the locations observed for crack nucleation in the notch, which are offset from the notch root in directionally solidified alloys, are consistent with the maximum von Mises stress. Various local and nonlocal methods are evaluated to understand the life trends under out‐of‐phase TMF. The results show that a nonlocal invariant area‐averaging method is the best approach for collapsing the TMF lives of specimens with different notch severities.     

Prediction of fatigue lifetime under multiaxial cyclic loading using finite element analysis

Life prediction for GH4169 superalloy thin tubular and notched specimens were investigated under proportional and nonproportional loading with elastic–plastic finite element analysis (FEA). A strain-controlled tension–torsion loading was carried out by applying the axial and circular displacements on one end of the specimen in the cylindrical coordinate system. Uniaxial cyclic stress–strain data at high temperature were used to describe the multi-linear kinematic hardening of the material. The comparison between FEA and experimental results for thin tubular specimen showed that the built model of FE is reliable. A fatigue damage parameter was proposed to predict the fatigue crack initiation life for notched specimen. The results showed that a good agreement was achieved with experimental data.     

TA17合金薄片材料毫小试样疲劳性能研究

关键工程结构、小尺寸零部件和焊接区的疲劳寿命评估中往往无法采用传统大试样进行疲劳试验,因此本文提出了一种采用毫米级别薄片试样获取材料循环本构关系和低周疲劳寿命的新方法。在Care原位试验机上完成毫米级别薄片漏斗试样的加载工装和低周疲劳试验的基础上,通过变幅对称循环试验和等辐循环试验分别实现了材料循环本构关系和低周疲劳性能的获取。该文提出了一种对不同幂律材料和不同几何尺寸构型均具有良好普适性的材料循环本构关系预测模型,并通过有限元实现了模型准确性的正反向预测验证。将循环本构关系用于有限元计算中,给出了薄片漏斗试样漏斗两侧名义应力、名义应变和漏斗根部真实应力、真实应变的转换方程,进而预测材料的低周疲劳寿命。该文完成了TA17合金等直圆棒试样和1.2 mm厚度薄片漏斗试样的对称变幅循环试验和多级等辐循环试验。由模型预测获得的TA17合金循环本构关系与等直圆棒试样的试验结果比较表明:两种曲线的弹性段和0.009 mm/mm~0.011 mm/mm应变段吻合良好,在弹塑性过渡段（0.004 mm/mm~0.009 mm/mm）模型预测结果最大相对误差小于9%。根据两组应力和应变转换方程获得的漏斗试样材料代表性体积单元疲劳寿命和Manson-Coffin寿命预测模型与等直圆棒试样试验结果均吻合良好。