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1.
P.S. Yang J.Y. Liou J.C. Sung 《International Journal of Solids and Structures》2007,44(25-26):8556-8578
In this paper, the problem of a crack embedded in a half-plane piezoelectric solid with traction-induction free boundary is analyzed. A system of singular integral equations is formulated for the materials with general anisotropic piezoelectric properties and for the crack with arbitrary orientation. The kernel functions developed are in complex form for general anisotropic piezoelectric materials and are then specialized to the case of transversely isotropic piezoelectric materials which are in real form. The obtained coupled mechanical and electric real kernel functions may be reduced to those kernel functions for purely elastic problems when the electric effects disappear. The system of singular integral equations is solved numerically and the coupling effects of the mechanical and electric phenomena are presented by the generalized stress intensity factors for transversely isotropic piezoelectric materials. 相似文献
2.
K. P. Herrmann V. V. Loboda A. V. Komarov 《Archive of Applied Mechanics (Ingenieur Archiv)》2004,74(1-2):118-129
Summary A plane strain problem for a crack with a frictionless contact zone at the leading crack tip expanding stationary along the
interface of two anisotropic half-spaces with a subsonic speed under the action of various loadings is considered. The cases
of finite and infinite-length interface cracks under the action of a moving concentrated loading at its faces are considered.
A finite-length crack for a uniform mixed-mode loading at infinity is considered as well. The associated combined Dirichlet-Riemann
boundary value problems are formulated and solved exactly for all above-mentioned cases. The expressions for stresses and
the derivatives of the displacement jumps at the interface are presented in a closed analytical form for an arbitrary contact
zone length. Transcendental equations are obtained for the determination of the real contact zone length, and the associated
closed form asymptotic formulas are found for small values of this parameter. It is found that independently of the types
of the crack and loading, an increase of the crack tip speed leads to an increase of the real contact zone length and the
correspondent stress intensity factor. The latter increase significantly for an interface crack tip speed approaching the
Ragleigh wave speed. 相似文献
3.
Bao-Lin Wang Naotake Noda Jie-Cai Han Shan-Yi Du 《European Journal of Mechanics - A/Solids》2001,20(6):377
In this paper, we develop a model to treat penny-shaped crack configuration in a piezoelectric layer of finite thickness. The piezoelectric layer is subjected to axially symmetric mechanical and electrical loads. Hankel transform technique is used to reduce the problem to the solution of a system of integral equations. A numerical solution for the crack tip fields is obtained for different crack radius and crack position. 相似文献
4.
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
5.
H. G. Beom K. M. Jeong Y. H. Kim 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,73(3-4):184-198
Summary A subinterface crack paralleling an interface between two dissimilar piezoelectric solids is considered. When the distance between the interface and the crack is small compared to all other in-plane lengths, the problem can be analyzed as an asymptotic problem for a semi-infinite crack lying at some distance away from the interface. An integral equation for the asymptotic subinterface crack is derived, and a solution of the integral equation for small-generalized Dundurs parameters is obtained. Relations between the intensity factors for the subinterface crack and interface intensity factors of the corresponding interface crack are obtained for a conducting crack as well as for an insulating one.This work was supported by the Brain Korea 21 Project in 2000. 相似文献
6.
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
7.
E. Pan 《Journal of the mechanics and physics of solids》2004,52(3):567-589
This paper presents an exact closed-form solution for the Eshelby problem of polygonal inclusion in anisotropic piezoelectric full- and half-planes. Based on the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric fields are first expressed in terms of line integral on the boundary of the inclusion with the integrand being the Green's function. Using the recently derived exact closed-form line-source Green's function, the line integral is then carried out analytically, with the final expression involving only elementary functions. The exact closed-form solution is applied to a square-shaped quantum wire within semiconductor GaAs full- and half-planes, with results clearly showing the importance of material orientation and piezoelectric coupling. While the elastic and piezoelectric fields within the square-shaped quantum wire could serve as benchmarks to other numerical methods, the exact closed-form solution should be useful to the analysis of nanoscale quantum-wire structures where large strain and electric fields could be induced by the misfit strain. 相似文献
8.
Hou Mishan 《Acta Mechanica Solida Sinica》1999,12(1):83-90
The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed
by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric
field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the
electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release
rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity
and electric displacement inside electrically permeable cracks are all constants. 相似文献
9.
Chen Wei-qiu 《Archive of Applied Mechanics (Ingenieur Archiv)》1999,69(5):309-316
Summary The paper presents an exact and complete solution of the problem of a semi-infinite plane crack in an infinite transversely
isotropic piezoelectric body. The upper and lower crack faces are assumed to be loaded symmetrically by a couple of normal
point forces in opposite directions and a couple of point charges. The solution is derived through a limiting procedure from
the one of a penny-shaped crack. The expressions for the elastoelectric field are given in terms of elementary functions.
Received 10 August 1998; accepted for publication 18 November 1998 相似文献
10.
Slip pulse along an interface between two anisotropic elastic half-spaces in sliding contact with separation 总被引:2,自引:0,他引:2
The Stroh sextic formalism, together with Fourier analysis and the singular integral equation technique, is used to study
the propagation of a possible slip pulse in the presence of local separation at the interface between two contact anisotropic
solids. The existence of such a pulse is discussed in detail. It is found that the pulse may exist if at least one medium
admits Rayleigh wave below the minimum limiting speed of the two media. The pulse-propagating speed is not fixed; it can be
of any value in some regions between the lower Rayleigh wave speed and minimum limiting speed. These speed regions depend
on the existence of the first and second slip-wave solutions without interfacial separation studied by Barnett, Gavazza and
Lothe (Proc. R. Soc. Lond. 1988, A415, 389–419). The pulse has no free amplitude directly but involves the arbitrary size
of the separation zone that depends on the intensity of the motion. The interface normal traction and the particle velocities
involve a square-root singularity at both ends of the separation zones that act as energy source and sink. 相似文献
11.
The Laplace transform, Wiener-Hopf technique and Cagniard-de Hoop method are used to solve the problem of a mode III semi-infinite crack which propagates suddenly at constant velocity in an anisotropic medium. The transient displacement field and the dynamic stress intensity factor at the moving crack tip are obtained.This research is supported by the Seismological United Foundation. 相似文献
12.
An explicit full-field expression of the Green's functions for anisotropic piezoelectric bimaterials with a slipping interface
is derived. When the electro-elastic singularity reduces to a pure dislocation in displacement and electric potential, interaction
energy between the dislocation and the bimaterials is obtained explicitly while the generalized force on the dislocation is
given in a real form which is also valid for degenerate materials. The investigation demonstrates that the boundary conditions
at the slipping interface between two piezoelectric materials will exert a prominent influence on the mobility of the dislocation.
Project supported by the National Natural Science Foundation of China (No. 59635140). 相似文献
13.
The main objective of this paper is to study the singular nature of the crack-tip stress and electric displacement field in
a functionally gradient piezoelectric medium having material coefficients with a discontinuous derivative. The problem is
considered for the simplest possible loading and geometry, namely, the anti-plane shear stress and electric displacement in-plane
of two bonded half spaces in which the crack is parallel to the interface. It is shown that the square-root singularity of
the crack-tip stress field and electric displacement field is unaffected by the discontinuity in the derivative of the material
coefficients. The problem is solved for the case of a finite crack and extensive results are given for the stress intensity
factors, electric displacement intensity factors, and the energy release rate.
Project supported by the National Natural Science Foundation of China (No. 10072041), the National Excellent Young Scholar
Fund, of China (No. 10125209) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education
Institutions of MOE, P. R. C.. 相似文献
14.
We present the Stroh formalism for two-dimensional subsonic steady-state motion of anisotropic quasicrystals. Using this new formalism and a series of identities and properties which follow, we investigate subsonic surface and interfacial waves in anisotropic quasicrystals. Our results suggest that there exist at most three subsonic surface wave speeds. This interesting observation is quite different from the unique surface wave speed known for anisotropic crystals. The degenerate case of decagonal quasicrystalline materials is discussed in detail. 相似文献
15.
We examine the effect of surface energy on an anisotropic elastic material weakened by an elliptical hole. A closed-form, full-field solution is derived using the standard Stroh formalism. In particular, explicit expressions for the hoop stress, normal, in-plane tangential and out-of-plane displacement components along the edge of the hole are obtained. These expressions clearly demonstrate the effect of elastic anisotropy of the bulk material on the corresponding field variables. When the material becomes isotropic, the hoop stress agrees with the well-known result in the literature while both the in-plane tangential and out-of-plane displacements vanish and the normal displacement is constant along the entire boundary of the elliptical hole. 相似文献
16.
An analysis is performed for the problem of a finite Griffith crack moving with constant velocity along the interface of a two-layered strip composed of a piezoelectric ceramic and an elastic layers. The combined out-of-plane mechanical and in-plane electrical loads are applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor(DSIF) is determined, and numerical results show that DSIF depends on the crack length, the ratio of stiffness and thickness, and the magnitude and direction of electrical loads as well as the crack speed. In case that the crack moves along the interface of piezoelectric and elastic half planes, DSIF is independent of the crack speed. 相似文献
17.
In this paper a moving mode-III crack in functionally graded piezoelectric materials (FGPM) is studied. The crack surfaces are assumed to be permeable. The governing equations for FGPM are solved by means of Fourier cosine transform. The mathematical formulation for the permeable crack condition is derived as a set of dual integral equations, which, in turn, are reduced to a Fredholm integral equation of the second kind. The results obtained indicate that the stress intensity factor of moving crack in FGPM depends only on the mechanical loading. The gradient parameter of the FGPM and the moving velocity of the crack do have significant influence on the dynamic stress intensity factor. 相似文献
18.
We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing an eccentric Griffith crack off the centre line bonded to two elastic half planes under anti-plane shear loading using the continuous crack-face condition. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and energy release rate are obtained. 相似文献
19.
S 《International Journal of Solids and Structures》2007,44(25-26):8407-8423
The three matrices L(v), S(v) and H(v), appearing frequently in the investigations of the two-dimensional steady state motions of elastic solids, are expressed explicitly in terms of the elastic stiffness for general anisotropic materials. The special cases of monoclinic materials with a plane of symmetry at x3 = 0, x1 = 0, and x2 = 0 are all deduced. Results for orthotropic materials appearing in the literature may be recovered from the present explicit expressions. 相似文献
20.
Yiantai Hu Yuying Huang Lingzhi Cheng Siping Li Weifang Zhong 《Mechanics Research Communications》1998,25(2):863
The problem of collinear periodic elliptic holes in an anisotropic medium is examined in this paper. By means of Stroh formalism and the conformal mapping method, explicit full domain solutions for the periodic hole problems are presented. The solutions are valid not only for plane problems but also for antiplane problems and the problems whose implane and antiplane deformations are coupled. The stress concentration around the holes is analysed. 相似文献