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The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function . The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are give 相似文献
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The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete–concrete jointed
interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive
strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending
in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured
before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques
to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement,
crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis
matches well with those measured experimentally. 相似文献
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《International Journal of Solids and Structures》2003,40(15):3853-3868
A comparative analysis of intrinsic and extrinsic cohesive models has been performed for the case of spontaneous and steady-state dynamic crack propagation. Spontaneous crack propagation was simulated using a spectral form of the elastodynamic boundary integral equation, while steady-state solutions were obtained by numerically integrating the governing Cauchy singular integral equation. Spontaneous crack propagation results showed that intrinsic models are less numerically stable than the extrinsic ones. Under steady-state propagation conditions, some intrinsic cohesive models lead to unrealistic results as the crack opening velocity becomes negative at the cohesive zone tip. By imposing a positive crack opening acceleration at the cohesive zone tip, the envelope of the required minimum initial strength has been calculated. 相似文献
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《International Journal of Solids and Structures》1999,36(16):2463-2479
The interface crack problem of a bimaterial thermopiezoelectric solid was treated byapplying the extended version of Strohs formalism and singular integral equation approach. Theinterface crack considered is subjected to combined thermal, mechanical and electric loads.Under the applied loading, the interface crack is assumed to be partially opened. Formulation ofthe problem results in a set of singular integral equations which are solved numerically. Thestudy shows that the contact zone is extremely small in comparison with the crack length. Basedon the formulation, some physically meaningful quantities of interest such as stress intensityfactors and size of contact zone for a particular material group are analyzed. 相似文献
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A general solution for the stresses and displacements of a cracked sliding interface between anisotropic bimaterials subjected to uniform tensile stress at infinity is given by using the Stroh’s formulation. Horizontal and vertical opening displacements on the interface, stress intensity factors, and energy release rate are expressed in real form, which are valid for any kind of anisotropic materials including the degenerate materials such as isotropic materials. It is observed that stresses exhibit the traditional inverse square root singularities near the crack tips, and the vertical opening displacement and energy release rate are intimately related to a real parameter λ determined by the elastic constants of the anisotropic bimaterials. 相似文献
7.
The problem of an interface crack in a half-plane consisting of two bonded dissimilar piezoelectric quarters is considered under antiplane shear and inplane electric loading. The problem is solved under the electrically permeable assumption for a crack. The integral transform technique is employed to reduce the problem to triple integral equations, which is further converted to a hypersingular integral equation for the crack sliding displacement. By solving the resulting equation analytically, the electroelastic field along the interface and the energy release rate are obtained in explicit form, respectively. Several examples are given to illustrate the influence of the material properties and the crack position on the energy release rate. 相似文献
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基于线性压电理论,本文获得了含有中心反平面裂纹的矩形压电体中的奇异应力和电场。利用Fourier积分变换和Fourier正弦级数将电绝缘型裂纹问题化为对偶积分方程,并进一步归结为易于求解的第二类Fred-holm积分方程。获得了裂纹尖端应力、应变、电位移和电场的解析解,求得了裂纹尖端场的强度因子及能量释放率。分析了压电矩形体的几何尺寸对它们的影响。结果表明,对于电绝缘型裂纹,裂纹尖端附近的各个场变量都具有-1/2阶的奇异性,能量释放率与电荷载的方向及大小有关,并且有可能为负值。 相似文献
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Shiqun Guo 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(8):709-723
This paper is concerned with the elastic wave scattering induced by a penny-shaped interface crack in coated materials. Using
the integral transform, the problem of wave scattering is reduced to a set of singular integral equations in matrix form.
The singular integral equations are solved by the asymptotic analysis and contour integral technique, and the expressions
for the stress and displacement as well as the dynamic stress intensity factors (SIFs) are obtained. Using numerical analysis,
this approach is verified by the finite element method (FEM), and the numerical results agree well with the theoretical results.
For various crack sizes and material combinations, the relations between the SIFs and the incident frequency are analyzed,
and the amplitudes of the crack opening displacements (CODs) are plotted versus incident wavenumber. The investigation provides
a theoretical basis for the dynamic failure analysis and nondestructive evaluation of coated materials. 相似文献
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《International Journal of Solids and Structures》2003,40(21):5819-5837
Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed. 相似文献
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In this paper the anti-plane problem for an interface crack between two dissimilar magneto-electro-elastic plates subjected
to anti-plane mechanical and in-plane magneto-electrical loads is investigated. The interface crack is assumed to be either
magneto-electrically impermeable or permeable, and the position of the interface crack is arbitrary. The finite Fourier transform
method is employed to reduce the mixed boundary-value problem to triple trigonometric series equations. The dislocation density
functions and proper replacement of the variables are introduced to reduce these series equations to a standard Cauchy singular
integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition
is approximated as a system of linear algebra equations which can be easily solved. Field intensity factors and energy release
rates are determined numerically and discussed in detail. Numerical results show the effects of crack configuration and loading
combination parameters on the fracture behaviors of crack tips according to energy release rate criterion. The study of this
problem is expected to have applications to the investigation of dynamic fracture properties of magneto-electro-elastic materials
with cracks. 相似文献
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Qin Qinghua 《Acta Mechanica Sinica》1998,14(4):339-352
A solution is presented for a class of two-dimensional electroelastic branched crack problems. Explicit Green's function for
an interface crack subject to an edge dislocation is developed using the extended Stroh formulation allowing the branched
crack problem to be expressed in terms of coupled singular integral equations. The integral equations are obtained by the
method that models a kink as a continuous distribution of edge dislocations, and the dislocation density function is defined
on the line of the branch crack only. Competition between crack extension along the interface and kinking into the substrate
is investigated using the integral equations and the maximum energy release rate criterion. Numerical results are presented
to show the effect of electric field on the path of crack extension.
The work was supported by the Australian Research Council through a Queen Elizabeth II fellowship and by the Australian Academy
of Science through the J.G. Russell Award. 相似文献
15.
T.C. Wang 《International Journal of Solids and Structures》1998,35(36):5033-5050
In this paper, a unified mechanics model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations within the plastic zone in the form of an inverse pile up are treated as discrete elastic edge dislocations. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear governing equations are obtained which take into account for the interaction between the emitted dislocations and cohesive zone and the nonlinear interaction between sliding displacement and the opening displacement. After discretization, the governing equations are transformed into a set nonlinear algebraic equations which are solved with Newton-Raphson Method. The results of calculation for pure shearing and combined tension and shear loading after dislocation emission are given in detail. Finally, the process of dislocation nucleation and emission on a pair of symmetric slip planes of angle α with respect to the crack plane under pure mode I load is analysed. The equilibrium positions and the number of emitted dislocation are determined. Several possible competition behaviors of dislocation emission vs cleavage are revealed. 相似文献
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This is Part I of the work on a two-dimensional analysis of thermal and electric fields of a thermopiezoelectric solid damaged by cracks. It deals with finding the singular crack tip behavior for the temperature, heat flow, displacements, electric potential, stresses and electric displacements. By application of Fourier transformations and the extended Stroh formalism, the problem is reduced to a pair of dual integral equations for the temperature field with the aid of an auxiliary function. The electroelastic field is governed by another pair of dual integral equations. The inverse square root singularity is found for the heat flow field while the logarithmic singularity prevailed for the electroelastic field regardless of whether the crack lies in a homogeneous piezoelectric solid or at an interface of two dissimilar piezoelectric materials. Results are given for the energy release rate and a finite length crack oriented at an arbitrarily angle with reference to the external disturbances. Part II of this paper considers the modelling of a piezoelectric material containing microcracks. A representative cracked area element is used to obtain the effective conductivity and electroelastic modulus. Numerical results are given for a peizoelectric Bati O3 ceramic with cracks. 相似文献
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A.P. Cisilino M.H. Aliabadi J.L. Otegui 《Theoretical and Applied Fracture Mechanics》1998,29(3):181-194
A three-dimensional Boundary Element Method (BEM) implementation of the energy domain integral for the numerical computation of the crack energy release rate is presented in this paper. The domain expression of the energy release rate is naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using the appropriate boundary integral equations. The pointwise crack energy release rate is evaluated along the three-dimensional crack front over a cylindrical domains that surround a segment of the crack front. The accuracy of the implementation is demonstrated by solving several problems, which include geometries containing straight as well as curved crack fronts. 相似文献
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《European Journal of Mechanics - A/Solids》2000,19(3):547-559
This paper focuses on the theoretical basis for the study of wave scattering from an interface crack in multilayered piezoelectric media. The materials are taken to be anisotropic with arbitrary symmetry. Based on the Fourier transform technique together with the aid of the stiffness matrix approach, the boundary value problem of wave scattering is reduced to solving a system of Cauchy-type singular equations. The intensity factors and crack opening displacements are defined in terms of the solutions of the corresponding integral equations for any incident frequencies and incident angles. Numerical results are presented. The effects of incident frequencies and crack location on both the major and coupling intensity factors are illustrated. The influence of the piezoelectricity is also shown. 相似文献
19.
The main objective of this work is the contribution to the study of the piezoelectric structures which contain preexisting defect (crack). For that, we consider a Griffith crack located at the interface of two piezoelectric materials in a semi-infinite plane structure. The structure is subjected to an anti-plane shearing combined with an in-plane electric displacement. Using integral Fourier transforms, the equations of piezoelectricity are converted analytically to a system of singular integral equations. The singular integral equations are further reduced to a system of algebraic equations and solved numerically by using Chebyshev polynomials. The stress intensity factor and the electric displacement intensity factor are calculated and used for the determination of the energy release rate which will be taken as fracture criterion. At the end, numerical results are presented for various parameters of the problem; they are also presented for an infinite plane structure. 相似文献
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Y.T. Zhou K.Y. Lee 《Theoretical and Applied Fracture Mechanics》2011,56(1):22-33
Consider the thermal fracture problem of a functionally graded coating-substrate structure of finite thickness with a partially insulated interface crack subjected to thermal-mechanical supply. A new model is proposed that the heat conduction through the crack region occurs and the temperature drop across the crack surfaces is the result of the thermal resistance. For the first time, real fundamental solutions are derived for the fracture analysis of functionally graded materials. The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically. The asymptotic expressions with higher order terms for the singular integral kernels are considered to improve the accuracy and efficiency of the numerical integration. Explicit expressions of various failure modes including stress intensity factors, energy release rate and strain energy density, are provided. Numerical results are presented to illustrate the effects of non-homogeneity parameters and the dimensionless thermal resistance on the temperature distribution along the crack surfaces and extended crack line, the thermal stress intensity factors and minimum strain energy density. 相似文献