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1.
Summary A boundary value problem for two semi-infinite anisotropic spaces with mixed boundary conditions at the interface is considered.
Assuming that the displacements are independent of the coordinate x
3, stresses and derivatives of displacement jumps are expressed via a sectionally holomorphic vector function. By means of
these relations the problem for an interface crack with an artificial contact zone in an orthotropic bimaterial is reduced
to a combined Dirichlet-Riemann problem which is solved analytically. As a particular case of this solution, the contact zone
model (in Comninou's sense) is derived. A simple transcendental equation and an asymptotic formula for the determination of
the real contact zone length are obtained. The classical interface crack model with oscillating singularities at the crack
tips is derived from the obtained solution as well. Analytical relations between fracture mechanical parameters of different
models are found, and recommendations concerning their implementation are given. The dependencies of the contact zone lengths
on material properties and external load coefficients are illustrated in graphical form. The practical applicability of the
obtained results is demonstrated by means of a FEM analysis of a finite-sized orthotropic bimaterial with an interface crack.
Received 19 October 1998; accepted for publication 13 November 1998 相似文献
2.
I.IntroductionManypracticalproblemsinengineering,suchascompositematerial,weldedjointorribbedslab,needustostudytheinteractionproblemoflineinclusionandcircularinclusionasshowninFig.1.Sotheproblemwasdiscussedinthispaper.Proceedingfromthestressfieldofplanecon… 相似文献
3.
应用复变函数Cauchy积分的方法,对含有椭圆孔或裂纹的各向异性平面,系统地导出了当其在面内受任意集中载荷作用时的复应力函数解或裂纹应力强度因子解析解,即基本解;并通过基本解的迭加,得到了在椭圆孔周或裂纹表面作用一般外载时的解,其特例证实了上述解的正确性。 相似文献
4.
This paper is concerned with the axisymmetrical elastic fields caused by an ellipsoidal inclusion with a slipping interface which undergoes a uniform eigenstrain. The problem is solved under a revolving ellipsoidal coordinate with the aid of Papkovich-Neuber general dipacement formula. In contrast to the perfectly bonded interface, when the interface between the inclusion and the matrix cannot sustain shear stress, and is free to slip, the solution cannot be expressed in closed form and involves infinite series. Therefore, the results are illustrated by numerical examples. 相似文献
5.
M. Rahman 《Journal of Elasticity》2002,66(3):207-235
The article investigates the elastostatic problem of axial translation of a rigid elliptical disc-inclusion embedded into
an elastic solid. The case of constant translation was previously studied by Kassir and Sih. The present study focuses on
the more general case in which the translation is characterized by an arbitrary-order polynomial in the Cartesian coordinates
of the points of the disc. By means of Fourier transforms, the problem is reduced to a two-dimensional integral equation.
Ferrers–Dyson's and Galin's theorems and some of their refinements by the present author are then employed to derive a closed-form
solution of the integral equation, permitting the displacements and the stresses in the entire solid to be expressed in explicit
analytical form. In particular, the behavior of the stress field in the immediate vicinity of the edge of the disc is analyzed
in great detail and closed-form expressions for the stress intensity factors are deduced for an arbitrary-order polynomial
normal shift. Furthermore, these results are generalized, based on an idea by Tada and Paris, to flat rigid inclusions of
an arbitrary shape having an axis of symmetry.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Interaction between an edge dislocation and a circular inclusion with an inhomogeneously imperfect interface 总被引:2,自引:0,他引:2
This research presents an analytical study of the interaction problem of an edge dislocation with a circular inclusion with a circumferentially inhomogeneously imperfect interface. The interface, which is modeled as a spring (interphase) layer with vanishing thickness, is characterized by that in which there is a displacement jump across the interface in the same direction as the corresponding tractions, and the same degree of imperfection is realized in both the normal and tangential directions. Furthermore, the interface parameter is nonuniform along the interface. In order to arrive at an elementary form solution, we introduce a conformal mapping function. Then the stress field as well as the Peach–Koehler force acting on the edge dislocation can be obtained from the derived complex potentials. Calculations demonstrate that the nonuniform interface parameter has a significant influence on the stress field. 相似文献
7.
A rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane
A. Kaczyński B. Monastyrskyy 《International Journal of Solids and Structures》2013,50(16-17):2631-2640
A solution is presented for the three dimensional static thermoelastic problem of an absolutely rigid inclusion (anticrack) in the case when a uniform heat flow is directed along the inclusion plane. By using the potential method and the Fourier transform technique, the problem is reduced to a system of coupled two-dimensional singular integral equations for the shear stress jumps across the inclusion. As an illustration, a typical application to the circular anticrack is presented. Explicit expressions for the thermal stresses in the inclusion plane are obtained and discussed from the point of view of material failure. 相似文献
8.
General coupled solution of anisotropic piezoelectric materials with an elliptic inclusion 总被引:1,自引:0,他引:1
In this investigation, the Stroh formalism is used to develop a general solution for an infinite, anisotropic piezoelectric
medium with an elliptic inclusion. The coupled elastic and electric fields both inside the inclusion and on the interface
of the inclusion and matrix are given.
The project supported by the National Natural Science Foundation of China 相似文献
9.
10.
The interaction of a plane harmonic longitudinal wave with a thin circular elastic inclusion is considered. The wave front
is assumed to be parallel to the inclusion plane. Since the inclusion is thin, the matrix-inclusion interface conditions (perfect
bonding) are formulated on the mid-plane of the inclusion. The bending displacements of the inclusion are determined from
the bending equation for a thin plate. The problem is solved using discontinuous Lamé solutions for harmonic vibrations. Therefore,
the problem can be reduced to the Fredholm equation of the second kind for a function associated with the discontinuity of
normal stresses on the inclusion. The equation obtained is solved by the method of mechanical quadratures using Gaussian quadrature
formulas. Approximate formulas for the stress intensity factors are derived. Results from a numerical analysis of the dependence
of the SIFs on the dimensionless wave number and the stiffness of the inclusion are presented
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 16–21, May 2008. 相似文献
11.
12.
We derive, by virtue of the unified Stroh formalism, the extremely concise and elegant solutions for two-dimensional and (quasi-static) time-dependent Green's functions in anisotropic magnetoelectroelastic multiferroic bimaterials with a viscous interface subjected to an extended line force and an extended line dislocation located in the upper half-plane. It is found for the first time that, in the multiferroic bimaterial Green's functions, there are 25 static image singularities and 50 moving image singularities in the form of the extended line force and extended line dislocation in the upper or lower half-plane. It is further observed that, as time evolves, the moving image singularities, which originate from the locations of the static image singularities, will move further away from the viscous interface with explicit time-dependent locations. Moreover, explicit expression of the time-dependent image force on the extended line dislocation due to its interaction with the viscous interface is derived, which is also valid for mathematically degenerate materials. Several special cases are discussed in detail for the image force expression to illustrate the influence of the viscous interface on the mobility of the extended line dislocation, and various interesting features are observed. These Green's functions can not only be directly applied to the study of dislocation mobility in the novel multiferroic bimaterials, they can also be utilized as kernel functions in a boundary integral formulation to investigate more complicated boundary value problems where multiferroic materials/composites are involved. 相似文献
13.
本文采用边界配置方法计算了受集中载荷作用时椭圆盘中偏心裂纹两端的应力强度因子,其中包括椭圆两半轴不同比值。不同裂纹长度和不同偏心程度的情况,在其特例椭圆盘中心裂纹情形,本文结果与Isida一致;在圆盘偏心裂纹情形,本文给出比Rooke等人更好的结果。 相似文献
14.
Finite element computation are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption
of small scale yielding. The modified Gurson constitutive equation and the element vanish technique introduced by Tvergaard
et al. are used to model the final formation of an open crack. It is found from the calculation that the critical fracture
toughness for crack growth is much lower in bimaterials than that in homogeneous material. The critical fracture toughness
is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads. The interface crack
grows in the more compliant (lower hardening) material or in the weaker (lower yield strength) material. In Mode-I loading,
the crack grows zigzag along the interface.
Project supported by Fok Ying-Tung Education Foundation and National Natural Science Foundation of China. 相似文献
15.
In this paper, with the aid of superimposing technique and the Pseudo Traction Method (PTM), the interaction problem between
an interface macrocrack and parallel microcracks in the process zone in bimaterial anisotropic solids is reduced to a system
of integral equations. After the integral equations are solved numerically, a conservation law among three kinds ofJ-integrals is obtained which are induced from the interface macrocrack tip, the microcrack and the remote field, respectively.
This conservation law reveals that the microcrack shielding effect in such materials could be considered as the redistribution
of the remoteJ-integral.
The project supported by the National Natural Science Foundation of China, and the Doctorate Foundation of Xi'an Jiaotong
University 相似文献
16.
M. P. Malezhik O. P. Malezhik I. S. Chernyshenko 《International Applied Mechanics》2006,42(5):574-581
The paper outlines a technique of determining the dynamic stress-intensity factors (SIFs) in structurally anisotropic composites
from photoelastic measurement data. A composite is considered a linear elastic, homogeneous, orthotropic body. An equation
is derived that relates the fringe order with the SIFs and the far-field stresses at the tip of a crack, which is parallel
to the orthotropy axis
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 95–103, May 2006. 相似文献
17.
W.-J. Feng R.-J. Hao J.-X. Liu S.-M. Duan 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(10):649-663
Summary In this paper, the scattering of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material is investigated by using the wavefunction expansion method and a singular integral equation technique. The debonding regions are modeled as multiple arc-shaped interface cracks with non-contacting faces. The magneto-electric impermeable boundary conditions are adopted. By expressing the scattered fields as wavefunction expansions with unknown coefficients, the mixed boundary-value problem is firstly reduced to a set of simultaneous dual-series equations. Then, dislocation density functions are introduced as unknowns to transform these dual-series equations to Cauchy singular integral equations of the first type,which can be numerically solved easily. The solution is valid for arbitrary number and size of the arc-shaped interface cracks. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond. The effects of incident direction, crack configuration and various material parameters on the dynamic stress intensity factors are discussed. The solution of this problem is expected to have applications in the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks.The work was supported by the National Natural Science Fund of China (Project No. 19772029) and the Research Fund for Doctors of Hebei Province, China (Project No. B2001213). 相似文献
18.
Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material. 相似文献
19.
The J-integral analysis is presented for the interaction problem between a semi-infinite interface crack and subinterface matrix microcracks in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack subjected to different loads and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is deduced to a system of singular integral equations with the aid of a superimposing technique. The integral equations are then solved numerically and a conservation law among three values of the J-integral is presented, which are induced from the interface crack tip, the microcracks and the remote field, respectively. The conservation law not only provides a necessary condition to confirm the numerical results derived, but also reveals that the microcrack shielding effect in such materials could be considered as a redistribution of the remote J-integral. It is this redistribution that does lead to the phenomenological shielding effect. 相似文献
20.
A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side. 相似文献