Mixed mode crack tip parameters for different wheel positions relative to a vertical crack at the rail foot

Finite element method is used to analyze a rail with a vertical bottom up crack at its foot, under the axle load and surface traction of a wheel. The possibility of crack formation at the foot of the rail in the neighborhood of a welding connection is discussed. A brief review on the importance of T‐stress in brittle fracture is presented. Seven cases with different locations of the crack relative to rail's sleeper contact region are considered. Numerous positions of the wheel are considered, and in each case, 3 crack parameters K_I, K_II, and T‐stress are calculated. Then, the biaxiality ratio and the mixity parameter for each loading and crack condition are calculated. It is shown that the location of crack and wheel can create mixed mode loading in the cracked rail and that the magnitude of crack tip parameters are strongly dependent on these geometric variables. In particular, the magnitudes of T‐stress and biaxiality ratio are significant in some cases. The effect of friction between the crack faces in the presence of compressive mode I loading on the mode II stress intensity factor is studied. Under mixed mode loading, due to the axle load and surface traction, the most critical condition is the formation of vertical cracks near the sleeper contact region.     

在线钢轨断裂原因分析

U75V热轧钢轨铺设在曲线地段使用超过3a(年),其中一支钢轨发生断裂,部分钢轨出现剥离掉块。当查找断裂原因,对断裂钢轨进行了理化检验。结果表明:轮轨接触应力过大,超过了钢轨接触疲劳强度,由于疲劳裂纹萌生和扩展的速率大于磨耗速率,在钢轨塑性变形层表面萌生并形成了疲劳裂纹,并沿变形流线方向疲劳扩展,在轮轨接触圆角处距表面2 mm处形成了疲劳核伤,在车轮的反复作用下发生了断裂。     

均匀热流下导热裂纹Ⅱ型温度应力强度因子的解析解

研究含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角的情况。当垂直于裂纹面方向有定量热流穿过裂纹时,采用复变函数理论,得出了温度、应力与位移场解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12材料进行了数值计算,研究了裂纹导热情况与热流方向对温度场及温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅱ型温度应力强度因子,不产生Ⅰ型温度应力强度因子。热荷载可等效为一个远场均匀作用的剪应力。Ⅱ型温度应力场取决于热流密度沿垂直裂纹面方向的分量,平行于裂纹方向的热流分量对温度应力场没有影响。     

均匀热流作用下含裂纹板I 型温度应力强度因子的解析解

研究一种新的温度边值问题。含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角。当裂纹面上维持一恒定温差时,采用复变函数理论,得出了温度场、温度应力场与位移场的解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12 材料进行了相应数值计算,分析了热流密度大小与方向对温度分布与温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅰ 型温度应力强度因子,不产生Ⅱ 型温度应力强度因子。温度应力场取决于热流密度沿裂纹方向的分量,垂直于裂纹方向的分量对温度应力场没有影响。     

Variation of mixed modes stress intensity factors of an inclined semi-elliptical surface crack

In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D inclined semi-elliptical surface crack in a semi-infinite body under tension. The stress field induced by displacement discontinuities in a semi-infinite body is used as the fundamental solution. Then, the problem is formulated as a system of integral equations with singularities of the form r ^–3. In the numerical calculation, the unknown body force doublets are approximated by the product of fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately for various geometrical conditions. The effects of inclination angle, elliptical shape, and Poisson's ratio are considered in the analysis. Crack mouth opening displacements are shown in figures to predict the crack depth and inclination angle. When the inclination angle is 60 degree, the mode I stress intensity factor F _I has negative value in the limited region near free surface. Therefore, the actual crack surface seems to contact each other near the surface.     

Stress Corrosion Cracking in Plastic Pipes: Observation and Modeling

Stress corrosion cracking (SCC) in engineering thermoplastics is commonly observed in the form of a microcrack colony within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. A probabilistic modeling of SCC initiation is briefly discussed. A deterministic modeling of slow stress corrosion (SC) crack growth process is developed using Crack Layer (CL) theory. Numerical solution of SC crack growth equations is discussed. Comparison of the kinetics of cracks driven by SC and by stress only is presented. Conventional plot of SC crack growth rate vs. the stress intensity factor is constructed and analyzed. An algorithm for conservative estimation of lifetime of engineering thermoplastic subject to a combination of mechanical stresses and chemically aggressive environment is discussed.     

On propagation of short rolling contact fatigue cracks

Recent accidents involving railway rails have aroused demand for improved and more efficient rail maintenance strategies to reduce the risk of unexpected rail fracture. Numerical tools can aid in generating maintenance strategies: this investigation deals with the numerical modelling and analysis of short crack growth in rails. Factors that influence the fatigue propagation of short surface‐breaking cracks (head checks) in rails are assessed. A proposed numerical procedure incorporates finite element (FE) calculations to predict short crack growth conditions for rolling contact fatigue (RCF) loading. A parameterised FE model for the rolling‐sliding contact of a cylinder on a semi‐infinite half space, with a short surface breaking crack, presented here, is used in linear‐elastic and elastic–plastic FE calculations of short crack propagation, together with fracture mechanics theory. The crack length and orientation, crack face friction, and coefficient of surface friction near the contact load are varied. The FE model is verified for five examples in the literature. Comparison of results from linear‐elastic and elastic–plastic FE calculations, shows that the former cannot describe short RCF crack behaviour properly, in particular 0.1–0.2 mm long (head check) cracks with a shallow angle; elastic–plastic analysis is required instead.     

拉—拉疲劳下15MnMoVN多裂纹扩展研究

为分析单裂纹或多裂纹在裂纹面承受疲劳拉伸载荷作用下尖端应力强度因子变化规律和裂纹形貌变化以及疲劳寿命情况,以含不同初始长深比的半椭圆单裂纹或双裂纹的薄片试样为研究对象,对试样在应力比R=0.1的疲劳拉伸载荷下单裂纹或双裂纹情况进行了仿真分析。建立含裂纹试样的有限元模型,仿真分析了裂纹在扩展过程中尖端应力强度因子的分布情况,并将单裂纹扩展结果与双裂纹相互作用影响下的结果进行了对比研究;进行含裂纹试样的疲劳实验,分析了含单裂纹或双裂纹的试样的断裂面的形成原因,并验证仿真结果正确性。结果表明,裂纹面之间的相互作用会逐渐影响裂纹的扩展方向、扩展速率以及在扩展过程中尖端应力强度因子的变化趋势;而且初始形貌为半椭圆形的双裂纹在相互作用影响下会逐渐过渡到半圆形。     

Stress intensity factors and crack opening displacements for slanted axial through-wall cracks in pressurized pipes

This paper proposes elastic stress intensity factors and crack opening displacements (CODs) for a slanted axial through-wall cracked cylinder under an internal pressure based on detailed three-dimensional (3D) elastic finite element (FE) analyses. The FE model and analysis procedure were validated against existing solutions for both elastic stress intensity factor and COD of an idealized axial through-wall cracked cylinder. To cover a practical range, four different values of the ratio of the mean radius of cylinder to the thickness ( R _m/ t ) were selected. Furthermore, four different values of the normalized crack length and five different values of the ratio of the crack length at the inner surface to the crack length at the outer surface representing the slant angle were selected. Based on the elastic FE results, the stress intensity factors along the crack front and CODs through the thickness at the centre of the crack were provided. These values were also tabulated for three selected points, that is, the inner and outer surfaces and at the mid-thickness. The present results can be used to evaluate the crack growth rate and leak rate of a slanted axial through-wall crack due to stress corrosion cracking and fatigue. Moreover, the present results can be used to perform a detailed leak-before-break analysis considering more realistic crack shape development.     

轮轨摩擦接触下钢轨多裂纹相互作用研究

利用热机耦合有限元法,建立了轮轨摩擦接触时钢轨表面多裂纹的热弹性平面应变有限元模型。数值模型中,考虑轮轨摩擦温升对轮轨材料参数的影响,通过移动载荷和热源来模拟运动车轮对钢轨的作用。分析了轮轨滑动接触时多裂纹相互作用和表面裂纹数量对钢轨疲劳裂纹扩展特性的影响。计算结果表明:与单个裂纹相比,多裂纹有降低钢轨疲劳裂纹扩展的作用;钢轨裂纹尖端应力强度因子K1和应力强度因子范围?K2均随裂纹数的增多而减小;钢轨表面裂纹数为5条时可以反映更多裂纹时的裂纹扩展特性。     

Sickle-shaped surface crack in a notched round bar under cyclic tension and bending

A sickle-shaped surface crack, also called crescent-moon (or crescent) crack, is assumed to exist at the root of a circular-arc circumferential notch in a round bar under tension and bending. For different notch sizes (i.e. different values of the stress concentration factor), the stress intensity factor along the crack front is computed through a three-dimensional finite-element analysis. The effect of the stress concentration factor on the stress intensity factor values is examined for several crack configurations. Finally, the surface crack growth under cyclic loading is analysed through a numerical procedure that employs the stress intensity factor values obtained. Some results of the present study are compared with those by other authors.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

The Interaction between a Piezoelectric Screw Dislocation Dipole and an Elliptic Blunt Crack in Elliptical Inhomogeneity

The interaction problem of a piezoelectric screw dislocation dipole with a confocal elliptic blunt crack in elliptical inhomogeneity subjected to remote anti-plane stress field and in-plane electric field is investigated by using the complex method of elasticity. The exact closed-form solutions of a series of quantities, such as singularity stress field, image force and image torque acting on the center of screw dislocation dipole, stress intensity factor and electric displacement intensity factor of crack tip, energy release rate, and generalized strain energy density are obtained. Then the influence laws of remote load, the dip angle of dislocation dipole, the size of blunt crack, and the material constants on the quantities are analyzed. The numerical results show that the image force, image torque, stress intensity factor, and electric displacement intensity factor make periodic variation as the dip angle of dislocation dipole; the energy release rate of crack tip is negative when subjected to pure electric field, however, it can be positive or negative when subjected to the combined action of mechanical field and electric field; the sharp crack is not easy to expand in some combined action of mechanical field and electric field.     

Numerical assessment of the loading of rolling contact fatigue cracks close to rail surface irregularities

Rolling contact fatigue damage of railway rails in the form of squats, characterised by local depressions and cracks located at the rail surface, has been linked to the occurrence of local rail surface irregularities. This study concerns rolling contact fatigue cracks in the vicinity of fairly smooth surface irregularities, here denoted dimples. The influence of factors such as dimple geometry, cluster effects, and crack size is evaluated. To this end, dynamic vehicle–track simulations featuring realistic wheel and rail profiles are employed to characterise the dynamic impact during a wheel passage. The contact load in the vicinity of the dimples is then mapped onto a 3D finite element model of a rail section containing a crack in the rail head. The crack loading is finally quantified by multimodal stress intensity factors. The analyses establish that also shallow dimples might have a significant impact on the crack loading. This effect is increased for larger or multiple irregularities but decreases as the crack grows.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

无网格法模拟复合型疲劳裂纹的扩展

本文提出了用无网格Galerkin法模拟构件在复合变形作用下疲劳裂纹扩展路径并预估其疲劳寿命的方法。该法能够自然模拟疲劳裂纹的扩展,不需要网格重构,避免了裂纹扩展过程中的精度受损。应用无网格数值结果计算了J积分和应力强度因子IK和IIK;按照最大周向应力理论获得了裂纹扩展偏斜角。基于最小应变能密度因子理论,确定了裂纹扩展量aD,并能获得疲劳载荷的循环周数ND。文末对数值模拟结果和实验拟合结果进行了对照。     

Predicting fatigue crack growth rate in a welded butt joint: The role of effective R ratio in accounting for residual stress effect

A simple and efficient method is presented in this paper for predicting fatigue crack growth rate in welded butt joints. Three well-known empirical crack growth laws are employed using the material constants that were obtained from the base material coupon tests. Based on the superposition rule of the linear elastic fracture mechanics, welding residual stress effect is accounted for by replacing the nominal stress ratio (R) in the empirical laws by the effective stress intensity factor ratio (R_eff). The key part of the analysis process is to calculate the stress intensity factor due to the initial residual stress field and also the stress relaxation and redistribution due to crack growth. The finite element method in conjunction with the modified virtual crack closure technique was used for this analysis. Fatigue crack growth rates were then calculated by the empirical laws and comparisons were made among these predictions as well as against published experimental tests, which were conducted under either constant amplitude load or constant stress intensity factor range. Test samples were M(T) geometry made of aluminium alloy 2024-T351 with a longitudinal weld by the variable polarity plasma arc welding process. Good agreement was achieved.     

7050铝合金Ⅰ-Ⅱ复合型疲劳裂纹研究

为研究7050铝合金在Ⅰ-Ⅱ型复合加载下疲劳裂纹扩展规律,在Amsler HFP5000高频试验机上利用Richard加载装置,完成紧凑拉剪(CTS)试样疲劳裂纹扩展试验,利用有限元对Ⅰ-Ⅱ复合型裂纹进行数值模拟,采用APDL命令流计算不同裂纹长度的应力强度因子,并引入最大周向应力准则计算裂纹扩展角,用有限元计算等效应...     

An accumulation damage model for fatigue fracture of ferroelectric ceramics

The accumulated plastic displacement criterion for crack propagation in traditional materials is extended to develop equations to predict the fatigue crack growth of ferroelectric ceramics subjected to combined electromechanical loads. The crack-line is perpendicular to the poling direction of the medium. An electric saturation zone and a stress saturation zone are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. This assumption makes it possible to obtain the accumulated plastic deformation in closed form. A fatigue crack growth law, which is a fourth-power function of the effective stress intensity factor, similar to the well-known Paris law, is derived. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided.     

Ultrasonic Measurement of the Crack Depth and the Crack Opening Stress Intensity Factor Under a No Load Condition

This paper describes a new methodology for evaluating the crack depth and the crack opening stress intensity factor of small closed cracks using an ultrasonic technique. Surface connected back-wall cracks of depth ranging from 0.4 to 4.0 mm in steel specimens are considered. The crack corner echo amplitude of an ultrasonic shear wave, SW, beam of 50° incidence in material is used. First, the ultrasonic echo response of an open crack is determined as a function of crack depth. Next, based on changing the crack closure stress, an empirical relation between the crack closure stress and the crack-echo response is formulated. The crack depth and the crack closure stress of an unknown closed crack based on these relations are determined by inverse analysis of the ultrasonic response of the crack. From the evaluated crack depth and crack closure stress, the crack opening stress intensity factor is determined. The accuracy and reliability of this new nondestructive evaluation (NDE) method is verified by comparing the evaluated crack depth with the actual one. The latter is measured on the fractured surface obtained after carrying out ultrasonic testing. The ultrasonic method developed is proved to be a powerful tool for quantitative and nondestructive evaluation of the crack depth as well as the crack closure stress.