Numerical and experimental determination of three-dimensional multiple crack growth in fatigue

This work is concerned with the assessment of propagation of multiple fatigue cracks in three-dimensions. Computational modelling of fatigue crack propagation is made together with detection and monitoring of the crack shape development. The boundary element method (BEM) is used for automating the modelling of crack propagation in linear elastic as well as elastic–plastic regimes. Strain at several positions on the specimen surface near the crack mouth is measured to monitor crack initiation, shape development and closure levels. Examples are provided to validate the model by comparing the experimental results with those obtained by numerical predictions.     

Stable growth of a central crack

The elastic fracture behavior of a plate subjected to uniform stress surrounding two equal cracks inclined at an angle is investigated. The orientation of the crack plane with applied stress can be varied. Among the cases are: (1) two cracks inclined symmetrically with respect to the vertical and horizontal applied stress, and (2) one crack is horizontal while the other is inclined to the vertical applied stress. The strain energy density criterion is used for determining the combined crack and load arrangement that correspond to the lowest critical load at global instability. The direction of crack initiation is also determined. Quantitative results pertaining to the fracture characteristics are given in graphical forms.     

Numerical computation and analytical estimation of stress-intensity factors for strips with multiple edge cracks

In this paper, stress-intensity factors for a two-dimensional problem are determined. Strips with multiple symmetrical edge cracks in tension are investigated. A simple analytical estimation is compared to numerical results. The influence of penetration of the crack faces and mixed-mode loading on the numerical results is investigated. A simple method to estimate stress-intensity factors for strips with multiple edge cracks is proposed.     

Stress intensity factor of an elliptical crack as influenced by a spherical inhomogeneity

The interaction between an elliptical crack and a spherical inhomogeneity embedded in a three-dimensional solid subject to uniaxial tension is investigated. Both the inhomogeneity and the solid are isotropic but have different elastic moduli. The Eshelby's equivalent inclusion method is applied together with the principle of superposition. An approximate solution for the stress intensity factor is obtained by an approach that expands the distance between the center of the crack and inhomogeneity in series. The local stress field can be increased or decreased depending on the relative modulus of the spherical inhomogeneity and matrix. If the inhomogeneity modulus is larger than that of the matrix, a reduction in the stress intensity factor prevails. Displayed numerically are results to exhibit the influence of inhomogeneity and its distance to the crack.     

Interactive effect of multiple crack growth on fatigue

Interaction of multiple cracks are found in mud when drying and crazing, thin film varnishes or coatings of aeroengine turbine blades. A two-dimensional multiple crack interaction model is developed to simulate the growth of interacting parallel surface cracks. Density and the initial distribution of the microcracks are accounted for in analyzing the growth of a crack to a pre-determined length. Analytical predictions are discussed with reference to experimental observations of fatigue cracks on coated turbine blades. Introduction of a large density of similar cracks can enhance the fatigue life of structural components.     

Stress-intensity factors in plates with a partially patched central crack

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of patches is related to the reduction they cause in the stress-intensity factor of the crack. Hence, an accurate evaluation of SIF in terms of various parameters is required for reliable patch design.In this paper, the influence of patch parameters on the opening-mode stress-intensity factor for a plate with a central crack is studied by employing transmission photoelasticity. Cracked plates made of photoelastic material are patched on one side as well as both sides by epoxy, phenolic and E glass-epoxy composite materials. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of 50 magnification, converted into a polariscope. Irwin's method with extrapolation is employed to compute the stress-intensity factor from photoelastic data. The reduction in the stress-intensity factor is presented in graphic form as a function of pathch parameters, namely stiffness, width and length.     

A domain-independent integral for computation of stress intensity factors along three-dimensional crack fronts and edges by BEM

The present work deals with an evaluation of stress intensity factors (SIFs) along straight crack fronts and edges in three-dimensional isotropic elastic solids. A new numerical approach is developed for extraction, from a solution obtained by the boundary element method (BEM), of those SIFs, which are relevant for a failure assessment of mechanical components. In particular, the generalized SIFs associated to eigensolutions characterized by unbounded stresses at a neighbourhood of the crack front or a reentrant edge and also that associated to T-stress at the crack front can be extracted. The method introduced is based on a conservation integral, called H-integral, which leads to a new domain-independent integral represented by a scalar product of the SIF times some element shape function defined along the crack front or edge. For sufficiently small element lengths these weighted averages of SIFs give reasonable pointwise estimation of the SIFs. A proof of the domain integral independency, based on the bi-orthogonality of the classical two-dimensional eigensolutions associated to a corner problem, is presented. Numerical solutions of two three-dimensional problems, a crack problem and a reentrant edge problem, are presented, the accuracy and convergence of the new approach for SIF extraction being analysed.     

喷砂冲蚀实验中颗粒轨迹的数值预测

针对冲击磨损实验研究中磨粒群体的运动轨迹难以准确表征的问题,在负压喷射砂粒群冲击Q235钢板的实验中宏观测量了砂粒撞击的速度与位置分布,并使用数值方法模拟了实验砂粒与空气在喷嘴内外的双向耦合过程,以实现负压喷射砂粒群的轨迹预测。计算中提出了非球形粒子在相对马赫数接近1时的曳力模型,以反映空气可压缩引起砂粒表面流动分离的现象,并合理选择Magnus升力模型及壁面反射模型,最终数值预测的砂粒碰撞速度以及撞击位置与实验情况吻合良好。     

Numerical computation of an impinging jet with uniform wall suction

The paper presents numerical predictions of a turbulent axisymmetric jet impinging onto a porous plate, based on a finite volume method of solving the Navier-Stokes equations for an incompressible air jet with the K–ε turbulence model. The velocity and pressure terms of the momentum equations are solved by the SIMPLE (semi-implicit method for pressure-linked equation) method. In this study, non-uniform staggered grids are used. The parameters of interest include the nozzle-to-wall distance and the suction velocity. The results of the present calculations are compared with available data reported in the literature. It is found that suction effects reduce the boundary layer thickness and increase the velocity gradient near the wall.     

CT试样三维疲劳裂纹扩展数值模拟

在循环载荷下疲劳裂纹的裂纹形貌在稳定扩展区近似为半椭圆形状,因此通过Paris方法根据疲劳裂纹表面尖端点应力强度因子的变化幅值(△K)得到扩展速率与真实的裂纹速率会有误差.为了更好的研究疲劳裂纹的性质,本文通过分析紧凑拉伸(CT)试样的疲劳裂纹扩展后的三维形貌,采用Jiang-Sehitoglu循环塑性模型和疲劳准则以...     

Numerical simulation on crack growth of multilayered ceramic/metal composites

The present paper develops a numerical technique named FSMS for simulating the crack growth of multilayered composites. Numerical simulations for the crack growth of multilayered ceramic/metal composites are carried out. The effects of some factors such as thickness ratio, initial crack length, material properties and dimensions of the structure on the crack growth are investigated. Numerical results show good agreement with experiments. FSMS is also a simple numerical method to solve crack problems of complex composite structures.     

Energy approach to crack growth in a fiber-reinforced brittle material modeled by an inclusion

Brittle materials randomly reinforced with a low volume fraction of strong, stiff and ductile fibers are considered, with specific reference to fiber-reinforced cements and concrete. Visible cracks in such materials are accompanied by a surrounding damage zone – together these constitute a very complex “crack system”. Enormous effort has been put into trying to understand the micromechanics of such systems. Almost all of these efforts do not deal with the “crack system” propagation behavior as a whole. The propagation process of such a “crack system” includes propagation of the visible crack and the growth of the damage zone. Propagation may take place by lengthening of the visible crack together with the concomitant lengthening of the surrounding damage zone, or simply by broadening of the damage zone while the visible crack length remains unchanged – or simultaneously by growth of both types. A phenomenological completely theoretical model (for an ideal material) is here proposed which can serve to examine the propagation process by means of energy principles, without recourse to the microscopic details of the process. An application of this theoretical approach is presented for the case of a damage zone evolving with a rectangular shape. This shape is chosen because it is expected that it will illustrate the nature of damage evolution and because the computational procedure necessary to follow the growth is the most straightforward.     

Experimental investigation of the growth of an isolated crack

The results are presented of an experimental investigation of the growth of an isolated crack.     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

Dynamics analysis of slender vehicle influenced by random factors

In this paper, the aeroelastic problems of slender vehicles under the influence of random factors and thrust are studied. An aeroelastic dynamic model of a free-free Euler–Bernoulli beam considering thrust and aerodynamic forces is established based on Hamilton’s principle of nonconservative systems. On this basis, considering the influence of random factors, the elastic modulus and viscous drag are regarded as one-dimensional continuous stationary random fields and discretized. The stochastic finite element method is used to solve the dynamic model, and the results are compared with the Monte Carlo simulation results. Then, the influence of the correlation of the random field on the elastic displacement is further analyzed. The following simulation results are obtained: (1) the stochastic factor analysis model established in this paper can reflect the statistical characteristics of aeroelastic response well; (2) the stronger the correlation of the random field is, the greater the expectation of elastic displacement, but as the correlation increases, the expectation tends to be constant; and (3) it is necessary to choose the discrete length of the random field reasonably, and the discrete length depends on the correlation characteristics of the random field studied.     

混凝土裂缝开展宽度计算的有限单元法

本文采用“最大拉应力单元开裂”准则，改进了非线性分析的迭代流程，使其最大可能地模拟实际结构的开裂情况，进而可以基于分布裂缝模式计算裂缝发生位置，裂缝间距，裂缝开展深度和宽度。算例表明，该法所计算的裂缝分布规律是正确的，计算裂缝宽度与试验实测值及规范公式计算值基本吻合，可以推广应用。     

Analysis of multiple cracks in an infinite plate under arbitrary crack surface tractions

Summary Based on the analytical solution derived for a crack under arbitrary crack surface tractions an alternating method is presented to analyze two-dimensional mixed-mode fracture problems with multiple cracks which are arbitrarily distributed in an infinite plate. During the iterative solution process the reversed residual stresses at the location of fictitious cracks induced by other cracks are repeatedly evaluated and treated as new applied loading until the residual stresses on each crack surface are negligible. The influence of interaction effects among cracks on the determination of stresses and deformations is studied in detail. Several numerical example are solved to demonstrate the validity of the method. Good agreement between the computed stress intensity factors and referenced solutions shows the accuracy and efficiency of the this work.

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Analyse mehrfacher risse in einer unendlichen platte mit beliebigen randspannungen am riß

Übersicht Eine alternierende Methode, die auf dem Ergebnis für einen Riß unter beliebigen Spannungen an der Rißoberfläche basiert, wird hier zur Analyse zweidimensionaler mixed-mode Bruchprobleme mit mehrfachen Rissen präsentiert. Die mehrfachen Risse können in der Platte beliebig verteilt sein. Mit einem Iterationsprozeß wird die umgekehrte Restspannung an der Stelle angenommener Risse, die von anderen Rissen verursacht werden, solange berechnet und als neue Last betrachtet, bis die Restspannung in jeder Rißfläche sehr klein geworden ist. Bei der Bestimmung der Spannung und der Verformung wird der wechselseitige Einfluß zwischen den Rissen eingehend untersucht. Um die Genauigkeit der Methode zu prüfen, werden mehrere Beispiele gegeben. Die Ergebnisse zeigen, daß die gerechnete Spannungsintensitätsfaktoren mit bekannten Lösungen sehr gut übereinstimmen.

     

Modelling of crack growth by fracture damage zone

The strain energy density (SED) criterion is applied for analyzing the full range of mixed mode fracture from tensile to shear loading. A fracture damage zone (FDZ) local to the crack tip is defined and discussed in connection with the influence of crack geometry, loading and local material property. The size of FDZ tends to change continuously from statically to cyclically applied load conditions. It can be estimated from the uniaxial mechanical properties of the material. Both experimental and analytical results are examined for subcritical crack growth under static loading that depends on the type steel structures the fracture behavior of which could be represented by a single curve for the given specimen geometry.