随机荷载下疲劳裂纹扩展寿命的统计模型

根据断裂力学和随机过程理论,提出了一个随机荷载作用下疲劳裂纹扩展的统计模型。在基于应变能密度因子变程的确定性疲劳裂纹扩展速率公式中引入材料内在的分散性和外部荷载的随机性,将疲劳裂纹扩展近似为连续型马尔可夫过程。应用随机平均法导出了裂纹扩展过程转移概率满足的向后Fokker-Planck方程,并得出相应的边界条件。采用本征函数法进行求解,以收敛的无穷级数表示出疲劳裂纹扩展寿命的分布函数。作为一个算例,具体计算出疲劳裂纹扩展寿命的分布密度曲线。     

INFLUENCE OF TRANSFORMATION-INDUCED CRACK CLOSURE ON SLOW FATIGUE CRACK GROWTH UNDER VARIABLE AMPLITUDE LOADING

Abstract Fatigue crack growth under constant and random loading conditions was investigated for a metastable austenitic-bainitic steel in comparison with a ferritic chromium steel at very low crack growth rates. Experimentally determined random crack growth was compared with linear Miner calculations on the basis of constant amplitude results. It was found that the measured crack growth rates in transforming material are a factor of 10 lower than the calculated values, whereas the difference is only a factor of 2 for the ferritic steel. The reason for the pronounced crack growth retardation in the metastable alloy is transformation of part of the austenitic phase into martensite in the stress field of the crack tip, accompanied by a volume increase and, consequently, residual compressive stresses. Rare high load cycles in the random sequence increase the closure level, which then leads to pronounced retardation of fatigue crack growth for the numerous successive low amplitude cycles.     

PROPAGATION OF FATIGUE CRACKS UNDER POLYMODAL LOADING

Abstract— The influence of steady mode III on mode I fatigue growth behavior is investigated in four materials–a plain carbon steel, a Ni–Cr–Mo–V rotor steel, and titanium alloys, TA6V and TA5E ELI. It is shown that these loading conditions give rise to two main effects: (i) a strong reduction in propagation rate and (ii) a modification in crack path, the fatigue crack adopting a characteristic "factory-roof' aspect. In 2024 Al alloy, it is shown that the superimposition of steady mode II to cyclic mode I leads to crack bifurcation, the angle θ being a function of K _a/ K _tmax. These observations are discussed in the light of a new criterion which is introduced. This criterion is based on two main assumptions: (i) Fatigue cracking is assumed to occur only under the effect of local mode I opening. (ii) It is postulated that a fatigue crack grows in a direction where the crack propagation rate is maximum. A number of limitations of this approach, associated with crack closure phenomenon, are discussed.     

CRACK PROPAGATION UNDER CYCLIC LOADING

Abstract— The crack propagation of a semi-elliptical surface flaw subjected to cyclic combined axial and bending loadings with constant amplitude is numerically examined according to Paris-Erdogan law. The critical crack, for which a given number of cycles is necessary to cause fatigue failure, can be determined from interaction between the theoretical results obtained and the experimental data of the Wöhler curves. Some examples are presented for different stress ranges Δσ _t and loading eccentricities given by e = M/F , where F and M are the axial force and the bending moment, respectively.     

FATIGUE CRACK GROWTH UNDER ULTRASONIC FATIGUE LOADING

Abstract— In this paper, a stress and modal analysis of an ultrasonic vibration system consisting of a notched specimen and one or two amplifying horns have been performed by using 3D finite element calculations. The stress intensity factors in ultrasonic fatigue crack propagation are evaluated by means of displacement and energy approaches. The particular advantages as well as limitations of the two approaches are briefly discussed. Two types of ultrasonic fatigue loading, with a different stress ratio, are exerted on the specimen. From a comparison of the results a conclusion is formed that the energy approach is more accurate; it also has a wide range of practicality in engineering industries.     

CRACK CLOSURE: A CONCEPT OF FATIGUE CRACK GROWTH UNDER EXAMINATION

Abstract— In recent literature it is asserted that the concept of crack closure in fatigue fracture mechanics is not capable of explaining fatigue crack growth behaviour. The reasons given are that both asperity induced crack closure and plasticity induced crack closure should be either negligible or non-existent. We have re-considered these hypotheses since their correctness would completely change the established picture of fatigue crack growth. In order to get mathematically tractable systems the present studies are confined to long cracks loaded in mode I. The results suggest that in case of asperity induced crack closure the proposed hypothesis is only true in special cases and the demonstration of the non-existence of plasticity induced crack closure is proved to be wrong.     

EQUIVALENT CONSTANT AMPLITUDE CONCEPTS EXAMINED UNDER FATIGUE CRACK PROPAGATION BY BLOCK LOADING

Abstract— Fatigue crack growth behaviour under block loading sequences has been studied on the aluminium alloy 2024 T351, using four different equivalent constant amplitude concepts. The root mean squared method gives acceptable results only for relatively long blocks. The equivalent method based on the Paris law (modified to take into account crack closure) gives good predictions for the observed growth rates as does Elbers' method. Finally, a new method based on energy considerations gives excellent results for the studied test conditions.     

FATIGUE CRACK GROWTH UNDER BIAXIAL LOADING

Fatigue crack growth under biaxial loading for long cracks subjected to low cyclic stress levels was investigated. The biaxial stress ratio λ ranging from -0.5 to + 1.0 was considered. The strain energy density factor range was used as the criterion for predicting the crack growth rates and crack path. The agreement between prediction and experimental results was reasonable for crack growth rates and marginal for crack paths. The investigation highlighted the inherent difficulties for crack path prediction and indicated the increased sensitivity to initial crack angle and biaxial stress ratio when the biaxial stress ratio approaches unity.     

ANALYSIS OF FATIGUE CRACK PROPAGATION UNDER BIAXIAL LOADING USING AN INCLINED STRIP YIELD ZONE MODEL OF CRACK TIP PLASTICITY

The work reported in this paper is based upon an inclined strip yield zone model of crack tip plasticity under biaxial remote loading. Equations are developed to predict fatigue crack growth rate under steady state conditions. A qualitative agreement between model predictions and experimental data is shown.     

加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟

采用不同应力比条件下的16MnR钢紧凑拉伸试样,设计了三种有限元分析模型,即不考虑加载历史效应的静态裂纹扩展模型,同时考虑加载历史和裂纹闭合的动态裂纹扩展模型以及仅考虑加载历史的伪动态裂纹扩展模型,对疲劳裂纹闭合过程、裂纹尖端的应力-应变迟滞环、疲劳损伤和裂纹扩展速率进行了数值模拟与分析,进而着重探讨了加载历史和裂纹闭合影响疲劳裂纹扩展行为的交互作用机制。结果表明：对于同类分析模型,应力比越大越不容易产生裂纹闭合;而在应力比相同的情况下,加载历史引起的残余压应力对裂纹闭合有明显的促进作用。裂纹闭合效应阻碍了平均应力的松弛,减小了裂纹尖端附近的应力-应变场强度、疲劳损伤和裂纹扩展速率,而加载历史引起的残余压应力则加快了平均应力的松弛和抑制了棘轮效应。与实验结果比较发现,只有同时考虑了裂纹闭合效应和加载历史影响的动态裂纹扩展模型,才能对疲劳裂纹扩展行为进行准确、定量的模拟。     

J-INTEGRAL APPROACH TO MODE III FATIGUE CRACK PROPAGATION IN STEEL UNDER TORSIONAL LOADING

Mode III fatigue crack propagation tests were conducted on circumferentially cracked bars of a medium carbon steel under a constant value of the J-integral range. The ΔJ value was evaluated from the loading part of the hysteresis loop of the applied torque and the angle of twist. The fracture surface was macroscopically flat for all cases examined in the present study. The crack propagation rate decreased with crack extension, because of the shear contact of the crack faces. The crack propagation rate, without contact shielding, obtained by extrapolating the relation between the crack propagation rate and the crack length to the pre-crack length, was a power function of ΔJ irrespective of the initial notch depth.     

EVALUATION OF LOW CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

Abstract— A series of low cycle fatigue experiments have been conducted on a 42CrMo steel under tension-torsion loading. Thin-walled tube specimens were used. Low cycle fatigue under various loading paths, including circular and square paths, have been investigated.
The plastic work criterion for low cycle fatigue failure has previously been generally accepted, but it is difficult to calculate stress and strain for complex loading paths, especially for non-proportional loading. This present study suggests a simple method for the calculation of the stable cyclic stress and strain values based on a Modified Endochronic Constitutive Theory (MECT) that redefines an intrinsic time scale. The loading path effect under non-proportional loading is also considered when evaluating fatigue life.
The results show that the plastic work approach using the MECT method in multiaxial fatigue calculations correlates reasonably well the data and is a reflection of loading path dependence.     

FATIGUE CRACK GROWTH AND CLOSURE THROUGH A TENSILE RESIDUAL STRESS FIELD UNDER COMPRESSIVE APPLIED LOADING

Abstract— —Fatigue crack growth and closure through a tensile residual stress field under an applied compressive loading is investigated by carrying out various applied stress ratio tests ranging from R = 0 to R = It is found that even under applied compressive loading, fatigue crack growth rates are well correlated with the effective stress intensity factor range and the behaviour of crack closure through a tensile residual stress field is uniquely controlled by an effective stress ratio which takes account of residual stresses. Consequently, the method of predicting fatigue growth rates, using da/d N vs Δ K data from residual stress-free specimens, can be successfully applied to crack growth through a tensile residual stress field. However, previously used simple assumptions may lead to non-conservative estimates of crack growth rates.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

FATIGUE CRACK GROWTH UNDER MIXED MODE LOADING

Abstract —Mixed mode fatigue crack growth is analysed using Sih's strain energy density approach. A centre crack panel geometry loaded under uniaxial cyclic tension is considered. The crack angle is varied from 30° to 90°. A procedure for the determination of crack propagation life is outlined. The crack trajectory due to cyclic loading is predicted. The crack growth rate, the cyclic life and the cyclic life ratio are discussed, for an aluminium alloy and a steel, as a function of initial crack angle, crack length, stress amplitude, and the strain energy density factor.     

FATIGUE CRACK GROWTH UNDER MODE II LOADING

Abstract— The behavior of fatigue crack growth for low and medium carbon steels, an austenitic stainless steel and an aluminum alloy under pure Mode II loading was investigated experimentally, using cruciform specimens. The results show that under pure Mode II loading, fatigue crack propagation has three possibilities, namely, bifurcation into two branches, propagation along the original Mode II direction, and the mixture of these two situations, depending on the material. The growth rate da/dN vs. ΔK_II relation for Mode II propagation is similar to a Pans type law for Mode I growth. Fractographic observations by optical microscopy and SEM were made also on all specimens tested. When a crack branched, striations parallel to the crack front which were often associated with Mode I fatigue crack growth were observed and long marks parallel to the crack propagation direction were also found for slanted fracture surfaces. When a crack propagated along the original Mode II direction, many frictional marks parallel to the crack propagation direction were observed.     

基于Elber型方程的随机疲劳长裂纹扩展概率模型

拓展有效应力强度因子范围的概念为因子范围与门槛值之差,导出了Elber型方程并建立了他的随机疲劳长裂纹扩展概率模型。同时考虑了数据分散性规律和试样数量两方面对概率的影响。模型分别由存活概率、置信度和联合存活概率—置信度下的裂纹扩展率—应力强度因子范围关系曲线组成。在因子范围服从对数正态分布下,应用线性回归技术和极大似然法建立了模型参数的测定方法。通过对LZ50车轴钢试验数据的分析,考察了模型的效果,揭示出模型对数据的拟合精度良好,能合理地预测中高应力强度因子范围的长裂纹稳定扩展和低应力强度因子范围趋于门槛值的概率规律。