FATIGUE UNDER OUT-OF-PHASE BENDING AND TORSION

Test data on fatigue under out-of-phase bending and torsion has been reanalysed. For the materials tested failure has been found to be consistent with the plane of maximum range of maximum range of maximum principal stress, as for the in-phase case. The critical shear planes are assumed to be those associated with this principal stress plane. A multiaxial fatigue damage parameter based on the maximum range of shear stress on the critical shear plane allowing for the effect of the range of normal stress occurring on this plane has been used to develop a proposed set of design curves for in-phase bending and torsion which are conservative for the long life out-of-phase case.     

A NEW CRITERION OF FATIGUE STRENGTH OF A ROUND BAR SUBJECTED TO COMBINED STATIC AND REPEATED BENDING AND TORSION

Abstract Criteria of fatigue strength of a round bar subjected to combined static and repeated bending and torsion have already been published by Findley and Sines together with empirical formulas by Gough. However, it is only Sines'criterion, by which the fatigue limit under combined bending and torsion is calculated, when completely reversed and pulsating fatigue limits and mean stresses are known. The authors show that Sines'criterion does not conform strictly with experimental results and they correct Sines'criterion so that fatigue failure occurs when the octahedral shearing stress amplitude attains a material constant value which decreases not only in proportion to the octahedral normal mean stress, but also in proportion to the octahedral normal stress amplitude. Applying the authors'criterion to combined repeated bending and torsion, plus coexistent static bending and torsion, a design formula was derived. The formula was compared with experimental results of Gough.     

THE EFFECTS OF MEAN STRESS AND STRESS CONCENTRATION ON FATIGUE UNDER COMBINED BENDING AND TWISTING

The Gough test data on fatigue under combined bending and twisting with superimposed mean bending and torsion stresses with and without stress raisers has been re-investigated in terms of the stresses acting on the plane of maximum range of shear stress. It has been shown that the allowable amplitude of shear stress on this plane can be predicted from an equation of the form τ_a= [t - c₁ (K_t×σ_a)^1.5?c₂σ²_m]/K_t where σ_a and σ_m are the normal stress amplitude and mean normal stress respectively on the plane of maximum range of shear stress, c₁ and c₂ are defined material constants and K_t is the theoretical stress concentration factor.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

钢纤维混凝土等幅弯曲疲劳加载下的疲劳应变和疲劳模量以及损伤研究

利用已有试验数据,对最大疲劳应变和疲劳残余应变进行拟合,得到疲劳应变演化方程,其相关系数均在0.97以上。考虑到等幅弯曲疲劳加载条件下,疲劳模量与疲劳应变成反比关系,利用对称性,由疲劳应变演化方程得到疲劳模量演化方程,通过拟合试验结果,发现由疲劳模量演化方程表达的拟合曲线与试验曲线吻合很好,其相关系数均在0.99以上。最后,利用疲劳应变与疲劳模量定义损伤变量,得到损伤变量演化曲线,经对比发现,由最大疲劳应变和疲劳残余应变定义的损伤变量演化曲线基本一致,且相差很小;而由疲劳模量定义的损伤变量演化曲线明显大于由疲劳应变定义的损伤变量演化曲线。     

基于阈值超越概率的结构耐久性与损伤容限综合分析方法

飞机结构耐久性分析和损伤容限分析都是以裂纹扩展分析为基础的,该文根据二者之间的内在联系,将耐久性分析与损伤容限分析进行综合考虑。该方法以损伤容限设计手册中规定的非概率初始裂纹尺寸作为阈值裂纹尺寸,根据裂纹尺寸超过阈值的概率以及耐久性分析结果确定概率损伤容限分析时的初始裂纹尺寸分布。裂纹尺寸超过阈值的概率可以通过检测数据给出,评估结果较为可靠。在概率损伤容限分析时,为了避免多重积分的计算,给出了结构安全余量的显式表达式以及一次二阶矩方法的计算公式,提高了可靠度计算效率。该文结合工程实例并与现有方法进行了对比分析,结果表明该方法是合理的、有效的。     

ESTIMATED AND EXPERIMENTAL FATIGUE LIVES OF 30CrNiMo8 STEEL UNDER IN-AND OUT-OF-PHASE COMBINED BENDING AND TORSION WITH VARIABLE AMPLITUDES

Abstract— Calculated fatigue lives, based on three criteria for multiaxial random fatigue, were compared with lives obtained from tests on cylindrical specimens of 30CrNiMo8 steel subjected to in- and out-of-phase bending and torsion at variable amplitudes. In the chosen fatigue criteria the expected position of the fracture plane, determined from a variance method for the equivalent stress, were taken into account. The equivalent stress history was related to the rain flow method and fatigue damage was evaluated from the Palmgren–Miner hypothesis. It has been shown that the expected fatigue fracture planes agree with those determined by experiments. The most realistic estimations of fatigue life were obtained by the criterion of maximum shear and normal stresses on the fracture plane using a modified shear stress.     

应用局部应力-应变法计算联轴器膜片疲劳寿命

由于轴线间的角向不对中,联轴器旋转时膜片中产生交变应力,引起疲劳问题。使用中需要考虑其疲劳寿命。本文对六孔圆环形和束腰形膜片,利用有限元方法和薄板弯曲理论建立膜片应力计算模型。引入改进的局部应力－应变法,建立计算膜片联轴器膜片疲劳裂纹形成寿命的模型和方法。定量分析两种形式膜片的应力、附加载荷和疲劳寿命,最后,得出对膜片组设计有参考价值的结论。结论表明,对于设计合理的膜片,其疲劳寿命能满足机组工作要求。     

FATIGUE LIFE AND PENETRATION BEHAVIOUR OF A SURFACE-CRACKED PLATE UNDER COMBINED TENSION AND BENDING

Abstract— The present study is to investigate the fatigue crack propagation behaviour of surface cracks subjected to combined tension and bending stress. An estimation of fatigue crack growth behaviour employed the Newman-Raju formula before penetration, and a K solution, proposed by the authors, after penetration. Crack length a_L at penetration increases with an increase in bending stress. The calculated fatigue crack shape was in good agreement with the experimental shape. It was also found that the crack growth behaviour and the crack shape after penetration can be satisfactorily evaluated using the K solution proposed by the authors.     

拉弯联合载荷下弹塑性J积分估算方法研究

基于计算J积分的等效原场应力方法,利用等效原场应力σeff只有外加载荷意义而不再具有拉伸或者弯曲等载荷类型方面的属性,提出了利用现有含裂纹结构的纯拉伸以及纯弯曲J积分全塑性解直接计算拉弯联合载荷下的J积分简化估算方法。该方法可以直接利用已经存在的J积分纯拉伸和纯弯曲全塑性解来计算拉弯联合载荷下的J积分,简化了拉弯联合载荷下J积分全塑性解的计算;并且可以应用于任意应力-应变材料,包括Ramborg-Osgood关系的材料和任意单调加载非R-O关系材料。计算过程简便。并通过与有限元计算结果对比对之进行验证,说明其工程实用性,为对含裂纹结构进行弹塑性断裂评定奠定基础。     

基于无网格LocalPetrov-Galerkin法的变厚度薄板的弯曲分析

对于厚度变化比较平缓,而且平分厚度的中面仍然是平面的薄板弯曲分析。首先在板上布置节点,选定支持域半径和适当的权函数,然后利用移动最小二乘法(MLS)得到支持域内节点的形函数,将形函数代入控制微分方程,得到支持域内节点的刚度和作用在节点上的力,将节点刚度和力装配成系统的刚度矩阵和力的列向量,求解方程得到各节点的位移以及内力,并用有限元分析软件(ANSYS)对同一问题进行研究,对两种方法所得结果进行了比较,数值结果表明应用无网格Local Petrov-Galerkin法计算变厚度薄板弯曲具有足够的精度和效率。     

FATIGUE STRENGTH OF 7075-T6 ALUMINIUM ALLOY UNDER COMBINED AXIAL LOADING AND TORSION

The fatigue strength of 7075-T6 aluminium alloy under combined axial loading and torsion was examined. The S-N relations were correlated with the von Mises criterion for the high cycle region ( N _f≥ 10⁴ cycles) and with the Tresca criterion for the low cycle region ( N _f < 10⁴ cycles), where N _f is the cycles to failure. This transition at N _r= 10⁴ cycles was related to the occurrence of macroscopic plastic straining and a change in fracture modes. The results are discussed in comparison with those for a high strength steel (SNCM8) in a previous study. Particular attention is given to differences in cyclic deformation behaviour, fracture modes and fatigue crack growth rates between the two materials.     

A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

压弯剪扭作用下异形柱的抗扭性能研究

为研究复合受力下异形柱的抗扭性能, 进行了一根L形柱、四根T形柱和一根十字形柱在压弯剪扭复合受力下抗扭性能的试验研究, 分析了轴压比、扭剪比、截面形状对异形柱抗扭性能的影响情况. 利用有限元软件建立了复合受力下异形柱抗扭性能的数值分析模型, 建议了相应的模型分析参数. 研究结果表明：在试验参数范围内, 轴压比和扭剪比会提高T形柱的抗扭性能. 轴压比为0.314的T形柱的极限扭矩和极限扭转角比轴压比为0.114的提高了203.8%和41.7%. 扭剪比为1.34的T形柱的极限扭矩和极限扭转角比扭剪比为0.57的提高了62.9%和112.5%. 截面形状对压弯剪扭复合受力下异形柱的开裂扭矩、极限扭矩的影响规律较复杂. 建立的有限元模型能够较准确的模拟压弯剪扭作用下异形柱的开裂扭矩和极限扭矩.     

J-INTEGRAL SOLUTIONS FOR SHALLOW CRACK GEOMETRIES UNDER COMBINED TENSION AND BENDING

This paper presents J-integral solutions for geometries with shallow edge cracks (0.05 ≤a/W≤ 0.1) subjected to combined tension and bending. Tension and bending is applied simultaneously and sequentially. Curves of J versus structural strain are obtained from two-dimensional plane strain finite element analyses using medium to low work hardening power laws to represent material behaviour. Empirical equations are derived from the finite element results to estimate the J-integrals, using previously developed J-estimation schemes for SENT and SENB specimens with only minor modifications. The predictions presented are invariably safe, but due to the complexity of the problems studied and the variability of the loadings considered, the degree of conservatism is found to be high in some cases.     

DUCTILE TEARING SIMULATION BASED ON A LOCAL ENERGETIC CRITERION

It is well known that the tearing resistance curve J–Δa is not a material property and that probably the energy dissipation rate is preferable to the integral J to characterize crack growth. The G parameter represents the energy dissipated in plasticity and fracture and, under certain conditions, this parameter could be used directly as a critical value for a criterion based on an energy release rate calculated near the crack tip to simulate propagation. Indeed, we see that a local energy release rate could be calculated near the crack tip to take account only of that portion of energy which participates in the fracture.
We applied this approach to simulate the crack growth for CT specimens with and without side grooves in a 20  MnMoNi 55 ferritic steel, and compared the results with Rousselier's model.     

曲率模态和小波包变换在结构损伤识别中的应用

小波包变换相比传统的Fourier变换,对非平稳信号分析具有良好的特性.利用小波包变换的特性,根据曲率模态损伤检测原理提出了一种基于小波包组分能量变化率作为损伤指标的分析方法.通过一简支梁结构的数值模拟,表明该方法对于判定损伤存在和确定损伤位置是有效的.     

基于局部主频率的子结构损伤识别研究与试验

针对大型复杂结构的整体监测常常面临测量信息不足等困难,提出只利用局部动态响应进行子结构损伤识别的局部主频率方法.子结构的局部主频率指：如果整体模态中含有以局部子结构位移为主的模态,即等价于在局部激励作用下,整体结构的振动主要体现为子结构的振动,并且主要以这阶局部模态振动为主,那么对应的该阶频率即定义为子结构的局部主频率.局部主频率主要反映子结构的局部特性,对子结构损伤的灵敏度高,所以只利用局部主频率就可以识别子结构.当子结构特征不明显时,提出通过附加质量使子结构具有局部主频率的有效方法.该文进行了大型空间桁架的局部动力测试试验,试验中通过附加质量使杆件子结构具有局部主频率,并能准确地识别出杆件损伤的位置和程度.     

MIXED MODE FATIGUE CRACK THRESHOLDS FROM BENDING AND CYCLIC TORSION OF A PLATE

The effects of plate thickness and crack shape on the threshold condition for crack propagation under cyclic bending or torsion, was studied using a through or a surface pre-crack in a carbon steel plate of various thicknesses. It was concluded that the magnitude of the frictional stress acting on the crack surface at the propagation threshold under cyclic torsion was significantly affected by the plate thickness. An estimation method for the threshold condition for crack propagation under mixed-mode loading for a particular plate thickness was proposed on the basis of the strain energy density criterion.     

基于残余应变的多侧压下混凝土受拉疲劳损伤研究

在侧压分别为0.25fc和0.50fc及其组合条件下,进行了混凝土在多侧压下的受拉等幅与变幅疲劳试验,得到了疲劳累积极限应变和残余极限应变,建立了残余应变与疲劳次数关系方程,并给出了残余应变与循环次数关系曲线。根据残余应变的稳定性,也即不受加载历程的影响,主要与侧应力水平和相对疲劳次数有关,以残余应变与相应应力水平下的残余极限应变之比作为损伤变量,建立了损伤变量与疲劳次数关系的统一方程,并给出了损伤变量与疲劳次数关系曲线。同时,对单轴、单、双侧压下的混凝土受拉疲劳的累积极限应变和残余极限应变与相应应力条件下的静态峰值应变进行了比较,其结果是随着侧应力水平的增加,相应的极限应变增加,再次说明了侧应力水平的影响。静态峰值应变与相应条件下的疲劳累积极限应变接近,残余极限应变与静态峰值应变及疲劳累积极限应变的比值较为稳定,其变化区间在0.22~0.28之间,且两种比值之间相差0.0~0.2。最后,对Miner准则进行了改进,并根据所建立的损伤模型与改进的Miner准则,对变幅疲劳寿命进行了预测,其结果是较为合理的。