Fatigue cracking and its influence on dynamic response characteristics of spot welded specimens

X-ray imaging has been used to determine the fatigue crack growth behavior and failure mechanisms of spot welded specimens. Cracks critical to final failure of the tensileshear specimens studied are through-thickness plate cracks, which are usually initiated about 0.2–1.0 mm away from the edge of the nugget. In addition, frequency response functions (FRFs), obtained by impact hammer-accelerometer experiments throughout the fatigue process, show that the natural frequencies of these joints nonlinearly decrease with the growth of fatigue cracks. The three-dimensional finite-element analysis results for FRFs of uncracked and cracked spot welded joints are shown to be in good agreement with the experimental data. It is also shown that the fatigue cracks have different degrees of influence on different natural frequencies because of the location of cracks and vibrating modes. The results by both experiment and finite element analysis indicate that analysis of the variation of natural frequencies and vibrating modes may be used to study the fatigue crack propagating shape and the location of the fatigue crack.     

含裂纹圆柱薄壳的动态特性试验研究

 利用时间平均法分别拍摄了含轴向和环向裂纹圆柱薄壳的激光 全息振型图，讨论了裂纹对圆柱薄壳振型及固有频率的影响，把含裂 纹壳体的振型分为三个区，即：裂纹周围的局部振动区，壳体原振动 区和过渡区. 并着重分析了局部振动的特征，得出了局部振动有着自 己的独有振形和固有频率的结论，从而很好解释了含裂纹圆柱薄壳的 复杂振型图及固有频率的反常变化.     

含多处裂纹梁的振动分析

基于传递矩阵方法,提出了一种计算含有任意处裂纹梁固有频率的新方法。将梁内裂纹模拟为无质量的弯曲弹簧,得到了梁的解析特征方程。通过数值模拟计算,讨论了裂纹数量,以及裂纹位置和裂纹深度对梁的固有频率的影响。通过与文献[4]的计算结果比较,验证了本文方法的有效性。     

梁结构中裂纹参数识别方法研究

以等效弹簧模型来模拟裂纹引起的局部软化效应,将该模型同Bernoulli-Euler梁理论、模态分析方法以及断裂力学原理等结合起来,利用传递矩阵法导出含裂纹梁振动的各种边界条件下的特征方程通解。借助于特征方程,提出两种识别裂纹深度和位置参数的数值方法,最后,通过对含裂纹悬臂梁的分析说明文中方法的有效性。     

带裂纹旋转柔性梁系统的刚柔耦合动力学研究

对具有刚柔耦合效应的带裂纹旋转柔性梁进行建模和动力学特性分析研究。采用晶格弹簧离散模型,利用无质量弹簧模拟梁上裂纹,通过考虑梁变形的二阶耦合项建立了带裂纹旋转柔性梁系统的一次近似耦合动力学控制方程。数值计算结果表明,裂纹的存在会使旋转柔性梁的固有频率降低,并且随着梁转速的增大,这种降低效应呈减弱趋势;值得注意的是,裂纹梁的固有频率与裂纹处的弯矩具有正相关关系。此外,裂纹的存在不仅会使转速变化阶段梁的末端位移响应增大,还会对转速稳定后梁的末端振荡产生显著的影响。     

Limitations of growth regimes for cracks initiated in smooth fatigue specimens

The stages of the growth of small cracks initiating at natural flaws in smooth specimens subjected to fatigue loading are characterized and the dominant propagation mechanisms and corresponding fracture paths are described. Characteristic crack lengths are introduced to assess the transition between the regimes of microstructurally small cracks, physically small cracks and long cracks. A log Δσ-log a-diagram is used to derive estimates of these crack lengths. It is shown that simple formulate can be found which relate these characteristic crack lengths to mechanical and material parameters that can be measured using standard fracture mechanics specimens and fatigue tests.     

Eigenfrequency changes of structures due to cracks,notches or other geometrical changes

A first order perturbation method is presented which predicts the changes in resonance frequencies of a structure resulting from cracks, notches or other geometrical changes. The eigenfrequency changes due to a crack are shown to be dependent on the strain energy of a static solution which is easily obtainable for small cracks and other small cut-outs. The method has been tested for three different cases, and the predicted results correlate very closely to experimental and numerical results.     

Modal analysis of cracked continuous Timoshenko beam made of functionally graded material

Abstract

The article addresses development of the Transfer Matrix Method (TMM) for free vibration of cracked continuous Timoshenko beam made of Functionally Graded Material (FGM). The governing equations of free vibration are established for the beam based on the power law of material grading, actual position of neutral plane and double spring model of crack. There is conducted frequency equation of the beam with intermediate rigid supports using the TMM after the transverse displacements at rigid supports have been disregarded. Therefore, the frequency equation is simplified and becomes more useful to compute natural frequencies of continuous FGM Timoshenko beam with a number of cracks. The obtained numerical results show the essential effect of cracks, material properties and also number of spans on natural frequencies of the beam.     

The damage tolerance of elastic-brittle, two-dimensional isotropic lattices

The fracture toughness of elastic-brittle 2D lattices is determined by the finite element method for three isotropic periodic topologies: the regular hexagonal honeycomb, the Kagome lattice and the regular triangular honeycomb. The dependence of mode I and mode II fracture toughness upon relative density is determined for each lattice, and the fracture envelope is obtained in combined mode I-mode II stress intensity factor space. Analytical estimates are also made for the dependence of mode I and mode II toughness upon relative density. The high nodal connectivity of the triangular grid ensures that it deforms predominantly by stretching of the constituent bars, while the hexagonal honeycomb deforms by bar bending. The Kagome microstructure deforms by bar stretching remote from the crack tip, and by a combination of bar bending and bar stretching within a characteristic elastic deformation zone near the crack tip. This elastic zone reduces the stress concentration at the crack tip in the Kagome lattice and leads to an elevated macroscopic toughness.Predictions are given for the tensile and shear strengths of a centre-cracked panel with microstructure given explicitly by each of the three topologies. The hexagonal and triangular honeycombs are flaw-sensitive, with a strength adequately predicted by linear elastic fracture mechanics (LEFM) for cracks spanning more than a few cells. In contrast, the Kagome microstructure is damage tolerant, and for cracks shorter than a transition length its tensile strength and shear strength are independent of crack length but are somewhat below the unnotched strength. At crack lengths exceeding the transition value, the strength decreases with increasing crack length in accordance with the LEFM estimate. This transition crack length scales with the parameter of bar length divided by relative density of the Kagome grid, and can be an order of magnitude greater than the cell size at low relative densities. Finally, the presence of a boundary layer is noted at the free edge of a crack-free Kagome grid loaded in tension and in shear. Deformation within this boundary layer is by a combination of bar bending and stretching whereas remote from the free edge the Kagome grid deforms by bar stretching (with a negligible contribution from bar bending). The edge boundary layer degrades both the macroscopic stiffness and strength of the Kagome plate. No such boundary layer is evident for the hexagonal and triangular honeycombs.     

Micromechanical model of stage I to stage II crack growth transition for aluminium alloys

Stage I to Stage II crack growth transition is a kinetic process that is particularly studied in this work. Crack growth transition is modelled to occur when small fatigue crack growth is deterred by an effective barrier that reduces the crack growth rate to a minimum. Effective blockage of small crack growth due to barriers is characterised by pile-up of dislocations. Crack tip pile-up sliding displacement is formulated by adopting a continuous configuration of dislocation pile-up. Transition condition is quantitatively determined when a crack tip sliding displacement of Stage I cracks just meets a crack tip opening displacement of Stage II cracks. As a result, a dislocation-based micromechanical model is systematically developed that enables kinetic predictions of crack growth transition and growth rates of small fatigue cracks. Moreover, the concept of microstructurally-affected-zone is further interpreted in terms of local microstructure and load levels, leading to good explanations for scatters of small crack growth. All model-based growth rate predictions show a good coincidence with experimental results.     

双周期裂纹压电材料反平面剪切问题断裂力学分析

研究压电材料双周期裂纹反平面剪切与平面电场作用的问题．运用复变函数方法，获得了该问题严格的闭合解，并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式．数值算例显示了裂纹分布特征对材料断裂行为的重要影响．叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用，相反行间小裂纹却起着放大作用，至于钻石形分布裂纹的影响规律则更为复杂．对于某些特殊情形给予了解答并导出一系列有意义的结果。     

A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature

Viscoplastic crack-tip deformation behaviour in a nickel-based superalloy at elevated temperature has been studied for both stationary and growing cracks in a compact tension (CT) specimen using the finite element method. The material behaviour was described by a unified viscoplastic constitutive model with non-linear kinematic and isotropic hardening rules, and implemented in the finite element software ABAQUS via a user-defined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack-growth plane. Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip. Finite element simulation of crack growth was carried out under a constant ΔK-controlled loading condition, again ratchetting was observed ahead of the crack tip, similar to that for stationary cracks.A crack-growth criterion based on strain accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilized in the prediction of crack-growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results.     

A directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions

A directional crack growth criterion in a compressed elastic perfectly plastic material is considered. The conditions at the crack-tip are evaluated for a straight stationary crack with a small incipient kink. Remote load is a combined hydrostatic pressure and pure shear applied via a boundary layer. Crack surfaces in contact are assumed to develop homogenous Coulomb friction.The crack opening displacement of an extended kink is examined in a finite element analysis to judge the risk of opening mode failure. It has been found that the direction that maximizes the crack opening displacement of an extended kink tip coincides very well with a prediction of the crack growth direction obtained by using a criterion for continued crack growth direction discussed by the authors elsewhere [Int. J. Fract. 108 (2001) 351].Moreover, the by the model predicted incipient crack growth directions are qualitatively comparable with reported crack paths obtained in ductile materials in a limited number of experiments performed under a combined load of in-plane shear and compression.     

Evolving crack patterns in thin films with the extended finite element method

This paper develops the extended finite element method (XFEM) to evolve patterns of multiple cracks, in a brittle thin film bonded to an elastic substrate, with a relatively coarse mesh, and without remeshing during evolution. A shear lag model describes the deformation in three dimensions with approximate field equations in two-dimensions. The film is susceptible to subcritical cracking, obeying a kinetic law that relates the velocity of each crack to its energy release rate. At a given time, the XFEM solves the field equations and calculates the energy release rate of every crack. For a small time step, each crack is extended in the direction of maximal hoop stress, and by a length set by the kinetic law. To confirm the accuracy of the XFEM, we compare our simulation to the exiting solutions for several simple crack patterns, such as a single crack and a set of parallel cracks. We then simulate the evolution of multiple cracks, initially in a small region of the film but of different lengths, showing curved crack propagation and crack tip shielding. Starting with multiple small cracks throughout the film, the XFEM can generate the well-known mud crack pattern.     

不确定边界条件下悬臂梁裂纹参数识别方法研究

基于Bernoulli-Euler梁振动理论,以等效弹簧来模拟裂纹引起的局部软化效应和由非完全固支边界条件引起的转角效应。推导了悬臂梁在不确定边界条件下确定其振动频率的特征方程,直接利用该特征方程,提出一种有效估计裂纹参数的优化方法,通过计算测量频率和理论频率之间的误差目标函数最小化即可识别裂纹参数-裂纹位置和深度。最后,应用两个实例-理想固支边界条件下和非完全固支边界条件下的悬臂梁实验来说明本文方法的有效性。实验结果表明:只需梁结构前三阶频率即可识别裂纹位置和深度。对于理想边界条件下的裂纹参数识别,在测量频率存在小误差情况下,该方法仍能给出比较满意的结果,对于非完全固支边界条件下的裂纹参数识别,利用本文方法能得到比Narkis的方法更精确的裂纹位置识别结果。同时本文方法还能给出比较满意的裂纹深度识别结果。     

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in its dynamic response features, such as natural frequencies and mode shapes. But these linear vibration procedures do not always come up to practical results because of their inherently low sensitivity to defects. Since a crack introduces non-linearities in the system, their use in damage detection merits to be investigated. With this aim the present paper is devoted to analysing the peculiar features of the non-linear response of a cracked beam.The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, and quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics, strictly due to the presence of a crack, can be used in non-linear techniques of crack identification.     

Evolution of Natural Frequencies of Longitudinal Vibrations of a Bar as Its Cross-Section Defect Increases

We study the evolution of characteristics of natural longitudinal vibrations of a circular bar in the case of increasing defect in its cross-section. It is shown that, in the limit case where the defect separates the bar into two independent fragments, the natural frequencies of the initially defect-free bar pass into the natural frequencies of its separate parts. The respective evolution of the natural modes of vibrations is observed. The evolution predicted by the theoretical analysis can be observed experimentally by using the resonance method and constantly increasing the defect till the final separation of the bar into two parts.     

The dynamic behaviour of slender structures with cross-sectional cracks

A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.     

基于内聚力模型的白点萌生机理研究

基于内聚力理论、氢压理论和应力作用下氢富集理论,在以往孔洞锻合研究的基础上,建立了白点萌生扩展的有限元分析模型。研究了初始氢浓度、裂纹长度以及多裂纹耦合作用等多种因素对白点萌生的影响,确定了不同条件下白点萌生的临界氢浓度及其变化趋势。结果表明,氢对白点萌生具有重要的影响,在白点萌生过程中,高浓度的氢聚集在裂纹端部,极大地降低了钢的内聚力强度;对于单裂纹,随着裂纹长度的增加,白点萌生的临界氢浓度逐渐减小并趋于稳定值;当多个密集小裂纹同时存在时,裂纹间的耦合效应会导致小裂纹有贯穿形成大裂纹的趋势,而远端裂纹的耦合效应则相对较小;对于多裂纹,白点萌生临界氢浓度具有随裂纹个数的增加而线性递减的趋势。     

Soil-blade dynamics in reverse-rotational rotary tillage

Soil cutting and the clod crack formation process during reverse-rotational rotary tillage in a heavy clay soil were investigated. Of particular interest was the relationship between clod crack formation and tillage resistance during sequential rotations of the tillage blade. Investigation of the crack formation process is helpful to develop and to design more effective and high performance tillage methods. This paper describes two new discoveries. The first is that the tillage resistance showed a higher cross-correlation between sequential rotations within a certain distance of tilling, while there was little or no cross-correlation between different tillage plots that were separated more than 0.4 m. The forward distance of untilled soil that was disturbed by the tillage blade was estimated to be 36.4 mm. This is the distance of two tillage pitches. The second discovery involved the blade frequencies during tilling. Fluctuation in tillage resistance frequencies of a single blade was nearly equal to the predicted occurrence of crack intervals on the tilled clod's surface. This frequency was 120 Hz. When these frequencies were translated into the distance along the trochoid trajectory of the blade cutting edge, they were the same as the length of the clods tilled by the reverse-rotational rotary tiller. These minute vibrations in the tillage resistance were considered the important indexes for recognizing the tilled soil conditions and the tilled clod failure on the reverse-rotational rotary tiller. The analytical results of this paper will be utilized for the active occurrence of the cracks regarding with natural frequency of the blade and the operation condition of the reverse-rotational rotary tiller.