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1.
This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar
piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces.
The explicit analytic solutions are obtained for a single crack in piezoelectrics or on the interfaces of piezoelectric bimaterials.
A class of boundary problems involving many cracks is also solved. For homogeneous materials it is found that the normal electric
displacementD
2 induced by the crack is constant along the crack faces which depends only on the applied remote stress field. Within the
crack slit, the electric fields induced by the crack are also constant and not affected by the applied electric field. For
the bimaterials with realH, the normal electric displacementD
2 is constant along the crack faces and electric fieldE
2 has the singularity ahead of the crack tip and a jump across the interface.
The project is supported by the National Natural Science Foundation of China(No. 19704100) and the Natural Science Foundation
of Chinese Academy of Sciences(No. KJ951-1-201). 相似文献
2.
Wang Zikun 《Acta Mechanica Sinica》1994,10(1):49-60
Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems
for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components
and electric potential functions are represented by a singular function satisfying some special partial differential equations
of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another
form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions
into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore,
the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed
under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The
results show that the stress and the electric displacement components near the crack tip have (r
−1/2) singularity.
The project supported by the Natural Science Foundation of Shaanxi Province, China 相似文献
3.
Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric
ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with
equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed
form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are
obtained. The function of piezoelectric anisotropic direction,p
a
(θ)=cosθ+p
a
sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the
piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip.
Supported by National Natural Science Foundation of China(No. 10072033) 相似文献
4.
The anti-plane shear field in an infinite slab of elasto-damaged material with a semi-infinite crack
This paper deals with an infinite slab with a semi-infinite crack, which is subjected to the anti-plane sheark
III field at infinity. The slab is made of an elasto-damaged material. Analytical solution is obtained by use of conformal mapping.
The shape of damaged-zone, the dissipative energy, the shear opening displacement on the crack surface and several stress
distribution curves are given. The far field condition is checked, The asymptotic behavior near the crack-tip is given.
The project supported by National Natural Science Foundation of China 相似文献
5.
A permeable interface crack between elastic dielectric material and piezoelectric material is studied based on the extended
Stroh’s formalism. Motivated by strong engineering demands to design new composite materials, the authors perform numerical
analysis of interface crack tip singularities and the crack tip energy release rates for 35 types of dissimilar bimaterials,
respectively, which are constructed by five kinds of elastic dielectric materials: Epoxy, Polymer, Al2O3, SiC, and Si3N4 and seven kinds of practical piezoelectric ceramics: PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-7A, P-7, and PZT-PIC 151, respectively. The elastic dielectric material with much smaller permittivity
than commercial piezoelectric ceramics is treated as a special transversely isotropic piezoelectric material with extremely
small piezoelectricity. The present investigation shows that the structure of the singular field near the permeable interface
crack tip consists of three singularities: and , which is quite different from that in the impermeable interface crack. It can be concluded that different far field loading
cases have significant influence on the near-tip fracture behaviors of the permeable interface crack. Based on the present
theoretical treatment and numerical analysis, the electric field induced crack growth is well explained, which provides a
better understanding of the failure mechanism induced from interface crack growth in elastic dielectric/piezoelectric bimaterials.
The project supported by the National Natural Science Foundation of China (10572110), Doctor Foundation of the Chinese Education
Ministry and Doctorate Foundation of Xi’an Jiaotong University.
The English text was polished by Yunming Chen. 相似文献
6.
Accurate high-order asymptotic analyses were carried out for Mode II plane strain crack in power hardening materials. The
second-order crack tip fields have been obtained. It is found that the amplitude coefficientk
2 of the second term of the asymptotic field is correlated to the first order field as the hardening exponentn<n
* (n
*≈5), but asn≥n
*,k
2 turns to become an independent parameter. Our results also indicated that, the second term of the asymptotic field has little
influence on the near-crack-tip field and can be neglected whenn<n
*. In fact,k
2 directly reflects the effects of triaxiality near the crack tip, the crack geometry and the loading mode, so that besidesJ-integral it can be used as another characteristic parameter in the two-parameter criterion.
The project supported by National Natural Science Foundation of China 相似文献
7.
The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by
using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric
displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When
the two piezoelectric materials are identical, the present result will be reduced to the result for the problem of an anti-plane
moving Griffith crack in homogeneous piezoelectric materials.
Supported by the National Natural Science Foundation and the National Post-doctoral Science Foundation of China. 相似文献
8.
The behavior of a Mode-Ⅰinterface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material. 相似文献
9.
The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the
exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases:
one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single
crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the
crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of
electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric
loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material
properties and applied mechanical-electric loads.
The project supported by the National Natural Science Foundation of China (19772004) 相似文献
10.
In this paper, two kinds of circular crack including external circular crack and penny-shaped crack in a transversely isotropic
piezoelectric space are considered. Firstly, we obtain the solution to the problem of an external circular crack in a transversely
isotropic piezoelectric space subjected to antisymmetric normal point forces and point charges. Based on this, the solution
of one-sided loading of an external circular crack is constructed. Secondly, the real shape of an external circular crack
and the opening displacement of a penny-shaped crack under an arbitrary point force and point charge are further obtained.
At last, the results are presented in a graphical form.
The project supported by the National Natural Science Foundation of China (19872060 and 69982009) and the Postdoctoral Foundation
of China 相似文献
11.
In this paper, the concept of energy density factor S for piezoelectric materials is presented. In addition to the mechanical energy the electrical energy is included as well. The direction of crack initiation is assumed to occur when Smin reaches a critical value Scr that can be used as an intrinsic materials parameter and is independent of the crack geometry and loading. The result agrees with empirical evidence qualitatively and explains rationally the effect of applied electric field on fracture strength: positive electric fields decrease the apparent fracture toughness of piezoelectric materials while negative electric fields increase it. 相似文献
12.
The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely
isotropic piezoelectric solid for the plane problem was dealt with. The principle of superpsition and the Plemelj formulation
were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms
are influenced by the elastic and electric constants.
Contributed by WANG Biao
Foundation items: the Nature Science Foundation of Shandong of China (Q99F15); the Post Doctoral Science Foundation of Heilongjiang Provice
of China
Biography: MA Hao (1967≈), Professor, Doctor 相似文献
13.
In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk
ss/kc varies appreciably with the anisotropic hardening parameterM and the hardening exponentN. 相似文献
14.
A high order of asymptotic solution of the singular fields near the tip of a mode III interface crack for pure power-law hardening
bimaterials is obtained by using the hodograph transformation. It is found that the zero order of the asymptotic solution
corresponds to the assumption of a rigid substrate at the interface, and the first order of it is deduced in order to satisfy
completely two continuity conditions of the stress and displacement across the interface in the asymptotic sense. The singularities
of stress and strain of the zeroth order asymptotic solutions are −1/(n
1+1) and −n/(n
1+1) respectively. (n=n
1,n
2 is the hardening exponent of the bimaterials.) The applicability conditions of the asymptotic solutions are determined for
both zeroth and first orders. It is proved that the Guo-Keer solution[10] is limited in some conditions. The angular functions of the singular fields for this interface crack problem are first expressed
by closed form.
The project supported by National Natural Science Foundation of China 相似文献
15.
X.-F. Li 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,72(10):745-758
Summary The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform
electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral
equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and
the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results
are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results
reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors
depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results
reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied
stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack
in a piezoelectric strip.
Received 14 August 2001; accepted for publication 24 September 2002
The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported
by the National Natural Science Foundation of China under Grant 70272043. 相似文献
16.
Propagation of an anti-plane moving crack in a functionally graded piezoelectric strip 总被引:4,自引:0,他引:4
Summary The propagation of an anti-plane moving crack in a functionally graded piezoelectric strip (FGPS) is studied in this paper. The governing equations for the proposed analysis are solved using Fourier cosine transform. The mixed boundary value problems of the anti-plane moving crack, which is assumed to be either impermeable or permeable, are formulated as dual integral equations. By appropriate transformations, the dual integral equations are reduced to Fredholm integral equations of the second kind. For the impermeable crack, the stress intensity factor (SIF) of the crack in the FGPS depends on both the mechanical and electric loading, whereas, the SIF for the permeable crack depends only on the mechanical loading. The results obtained show that the gradient parameter of the FGPS and the velocity of the crack have significant influence on the dynamic SIF.Support from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7081/00E) is acknowledged. Support from the National Natural Science Foundation of China (Project No. 10072041) is also acknowledged. 相似文献
17.
Up to now, the analysis on anisotropic effects of quasi-isotropic composites to material structures has not been found in literatures. In the present paper the strength model for triaxial woven materials proposed in Part (I)
[1]
is applied to study the problems of an infinitely large plate of triaxial woven material containing either an elliptic hole or a crack. To the elliptic hole problem the remote critical loading as a function of the geometric parameters of woven materials is analysed, and to the crack problem, the cracking orientation is examined. Finally, the elasticity and strength models for a triaxial woven material proposed in Part(I) are verified in terms of micro-mechanical analysis.Project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China 相似文献
18.
Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δkth increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio
for different grain sizes are different at the threshold. The maximum stress intensity factor is kmax and σys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10—8 to 10−7 mm/cycle.A dimensionless relation of the form
for collating fatigue crack starting growth data is proposed in which Δkth represents the stress intensity factor range at the threshold. Based on experimental results, this relation attains the value of 0.6 for a fatigue crack to start growth in the Austenitic stainless steel investigated in this work. Metallurgical examinations were also carried out to show a transgranular shear mode of cyclic cleavage and plastic shear. 相似文献
19.
A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in
the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the
strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given.
The project supported by National Natural Science Foundation of China 相似文献
20.
《International Journal of Solids and Structures》2003,40(8):1943-1958
Arbitrarily oriented crack near interface in piezoelectric bimaterials is considered. After deriving the fundamental solution for an edge dislocation near the interface, the present problem can be expressed as a system of singular integral equations by modeling the crack as continuously distributed edge dislocations. In the paper, the dislocations are described by a density function defined on the crack line. By solving the singular integral equations numerically, the dislocation density function is determined. Then, the stress intensity factors (SIFs) and the electric displacement intensity factor (EDIF) at the crack tips are evaluated. Subsequently, the influences of the interface on crack tip SIFs, EDIF, and the mechanical strain energy release rate (MSERR) are investigated. The J-integral analysis in piezoelectric bimaterals is also performed. It is found that the path-independent of J1-integral and the path-dependent of J2-integral found in no-piezoelectric bimaterials are still valid in piezoelectric bimaterials. 相似文献