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1.
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
2.
S.-M. Kwon H.-S. Choi K.-Y. Lee 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(2-3):160-170
Summary The steady-state of a propagation eccentric crack in a piezoelectric ceramic strip bonded between two elastic materials under
combined anti-plane mechanical shear and in-plane electrical loadings is considered in this paper. The analysis based on the
integral transform approach is conducted on the permeable crack condition. Field intensity factors and energy release rate
are obtained in terms of a Fredholm integral equation of the second kind. It is shown for this geometry that the crack propagation
speed has influence on the dynamic energy release rate. The initial crack branching angle for a PZT-5H piezoceramic structure
is predicted by the maximum energy release rate criterion.
Received 23 January 2001; accepted for publication 18 October 2001 相似文献
3.
Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes 总被引:3,自引:0,他引:3
Summary In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through
a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular
integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution
and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of
the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of
applied electric impact.
Received 4 December 2001; accepted for publication 9 July 2002
This work is supported by the National Natural Science Foundation of China through Grant No. 10132010. 相似文献
4.
Summary The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered
under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to
the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral
equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement
and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are
obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary.
The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems.
Received 10 November 2000; accepted for publication 28 March 2001 相似文献
5.
Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts 总被引:1,自引:0,他引:1
Summary The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical
impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform
and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement
intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane
problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The
dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack
configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric
media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic
mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that
in anti-plane problems.
Received 4 September 2001; accepted for publication 23 July 2002
The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation
of Tsinghua University, and the Education Ministry of China. 相似文献
6.
折线型裂纹对SH波的动力响应 总被引:1,自引:0,他引:1
利用Fourier积分变换方法,得出了无限平面中用裂纹位错密度函数表示的单裂纹散射场.根据无穷积分的性质,把单裂纹的散射场分解为奇异部分和有界部分.利用单裂纹的散射场建立了折线裂纹在SH波作用下的Cauchy型奇异积分方程.根据折线裂纹散射场和所得的积分方程讨论了裂纹在折点处的奇性应力及折点处的奇性应力指数.利用所得的奇性应力定义了折点处的应力强度因子.对所得Cauchy型奇积分方程的数值求解,可得裂纹端点和折点处的动应力强度因子。 相似文献
7.
Electro-mechanical analysis of an interfacial crack between a piezoelectric and two orthotropic layers 总被引:1,自引:0,他引:1
Summary The problem of an interfacially cracked three-layered structure constructed of a piezoelectric and two orthotropic materials
is analyzed using the theory of linear piezoelectricity and fracture mechanics. Anti-plane shear loading is considered, and
the integral transform technique is used to determine the stress intensity factor. Numerical examples show the electro-mechanical
effects of various material combinations and layer thicknesses on the stress intensity factor. Interesting results are obtained
in comparison with earlier solutions for interfacially cracked piezoelectric structures.
Received 29 December 2000; accepted for publication 3 May 2001 相似文献
8.
《European Journal of Mechanics - A/Solids》2001,20(3):457-468
The dynamic field intensity factors and energy release rates in a rectangular piezoelectric ceramic medium containing a center crack are obtained for boundary conditions of a permeable and an impermeable crack under electro-mechanical impact loading. An integral transform method is used to reduce the problem to two pairs of dual integral equations, which are then expressed as Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate are obtained to show the dependences upon the geometry and electric field. 相似文献
9.
Summary The fracture behavior of a penny-shaped crack in a axisymmetrical piezoelectric ceramic cylinder of finite radius under mechanical and electrical loads is analyzed under electric continuous boundary conditions on the crack surface. The potential theory and Hankel transform are used to obtain a system of dual integral equations, which is then expressed as a Fredholm integral equation. Singular mechanical and electrical fields and field intensity factors of mode I are obtained. The numerical values of various field intensity factors for PZT-6B piezoelectric ceramics are graphically shown for a uniform load and a ring-shaped load, respectively. The effects of the radius of the cylinder on the field intensity factors are investigated.
This work was supported by the Korea Research Foundation Grant (KRF-2001-041-E00057). 相似文献
10.
Shuling Hu Shengping Shen Toshihisa Nishioka 《International Journal of Solids and Structures》2007,44(25-26):8457-8492
In this paper, a numerical analysis of impact interfacial fracture for a piezoelectric bimaterial is provided. Starting from the basic equilibrium equation, a dynamic electro-mechanical FEM formulation is briefly presented. Then, the path-independent separated dynamic J integral is extended to piezoelectric bimaterials. Based on the relationship of the path-independent dynamic J integral and the stress and electric displacement intensity factors, the component separation method is used to calculate the stress and electric displacement intensity factors for piezoelectric bimaterials in this finite-element analysis. The response curves of the dynamic J integral, the stress and electric displacement intensity factors are obtained for both homogeneous material (PZT-4 and CdSe) and CdSe/PZT-4 bimaterial. The influences of the piezoelectricity and the electro-mechanical coupling factor on these responses are discussed. The effects of an applied electric field are also discussed. 相似文献
11.
J. J. Golecki J. D. Suzdalnitsky 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(9):640-648
Summary Under external forces acting on the face of a notch, cracks originate at corners, and the system is liable to fail. An analysis
is presented of the stress field in the neighborhood of the notch tips, based on the integral representation of the biharmonic
solution and on numerical methods. Computations were performed for constant loading or constant displacement distributed along
one face of the notch. The coefficients in the principal terms of the asymptotic formulae for the circumferential and shear
stresses depend on the angle and height of the notch face and on the boundary conditions. The maximal values of these coefficients
determine the stress intensity factors for the opening and shear modes. The angles corresponding to the maximal values of
the intensity factors indicate the directions of initiation of opening and sliding cracks.
Received 30 May 2000; accepted for publication 3 April 2001 相似文献
12.
与两相材料界面接触的裂纹对SH波的散射 总被引:1,自引:0,他引:1
利用积分变换方法得出了两相材料中作用简谐集中力时的格林函数.根据所得的格林函数并利用Betti-Rayleigh互易定理得出了与界面接触裂纹的散射波场.裂纹的散射波场可分解为两部分,一部分为奇异的散射场,另一部分为有界的散射场.利用分解后的散射场,可得裂纹在SH波作用下的超奇异积分方程.根据裂纹散射场的奇异部分和Cauchy型奇异积分的性质得出了裂纹和界面接触点处的奇性应力指数和接触点角形域内的奇性应力.利用所得的奇性应力定义了裂纹和界面接触点处的动应力强度因子.对所得超奇异积分方程的数值求解可得裂纹端点和接解点处的应力强度因子。 相似文献
13.
Transient response of a cracked piezoelectric strip under arbitrary electro-mechanical impact 总被引:1,自引:0,他引:1
By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around
a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress
intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric
field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric
load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the
width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response
of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation
of the crack depending on the time elapse since the application of the external electro-mechanical loads.
The project supported by the National Natural Science Foundation of China and the Post-Doctor Science Foundation of China 相似文献
14.
Timothy C. Kennedy Jan D. Achenbach 《International Journal of Solids and Structures》1974,10(5):519-530
The rapid extension of a penny-shaped crack under torsion is investigated. Both dynamic and quasi-static loading is considered. The wave motion is analyzed through a Green's function technique which leads to an integral equation for the stress field around the crack. Asymptotic expansions for the stress intensity and displacement rate intensity functions which are valid for a small time are obtained for the two types of loading. The propagation of the crack is analyzed through the balance of rates of energy criterion. 相似文献
15.
DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL 总被引:2,自引:0,他引:2
IntroductionInrecentyears,greatattentionshavebeenpaidtotheresearchofFunctionallyGradedMaterials(FGM).Fromtheviewpointsofappliedmechanics,FGMarenon_homogeneoussolids.Thenon_homogeneityofFGMhasagreatinfluenceontheirmechanicalbehavior,especiallywhenthecomp… 相似文献
16.
分析了SH波对一维六方准晶中直裂纹的散射问题。利用积分变换技术,结合Copson方法,通过求解对偶积分方程,得到声子场和相位子场应力、位移及裂纹尖端动应力强度因子的解析表达式。通过数值算例讨论了裂纹长度、入射角和入射波频率对标准动应力强度因子的影响,此研究在工程材料应用中有一定的参考价值。 相似文献
17.
Xiaohong Chen 《International Journal of Solids and Structures》2009,46(22-23):4025-4037
The transient response of a Mode-III crack propagating in a magneto-electro-elastic solid subjected to mixed loads is investigated through solving the corresponding boundary-initial-value problem in both the cracked solid region and the interior fluid region with treatment of electro-magnetically permeable and impermeable crack face conditions in a unified way. The closed-form results for the dynamic field intensity factors are used to evaluate the dynamic energy release rate through the crack-tip dynamic contour integral. The permeability of the interior fluid region relative to the cracked solid region significantly affects the magneto-electro-mechanical coupling coefficient in the Bleustein–Gulyaev wave function and, consequently, the horizontal shear surface wave speed, the dynamic field intensity factors and the dynamic energy release rate. It is revealed from dynamic fracture mechanics analysis that the dynamic energy release rate thus obtained has an odd dependence on the dynamic electric displacement intensity factor and the dynamic magnetic induction intensity factor. It is also found that the horizontal shear surface wave speed provides the limiting velocity for the propagation of a Mode-III crack in a magneto-electro-elastic solid when there is only applied traction loading. 相似文献
18.
《European Journal of Mechanics - A/Solids》2005,24(2):253-262
In this paper, the dynamic behavior of two collinear symmetric interface cracks between two dissimilar magneto-electro-elastic material half planes under the harmonic anti-plane shear waves loading is investigated by Schmidt method. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. To solve the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. Numerical solutions of the stress intensity factor, the electric displacement intensity factor and the magnetic flux intensity factor are given. The relations among the electric filed, the magnetic flux field and the stress field are obtained. 相似文献
19.
The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor. 相似文献
20.
《International Journal of Solids and Structures》2003,40(13-14):3571-3588
The transient response of a piezoelectric strip with an eccentric crack normal to the strip boundaries under applied electromechanical impacts is considered. By using the Laplace transform, the mixed initial-boundary-value problem is reduced to triple series equations, then to a singular integral equation of the first kind by introducing an auxiliary function. The Lobatto–Chebyshev collocation technique is adopted to solve numerically the resulting singular integral equation. Dynamic field intensity factors and energy release rate are obtained for both a permeable crack and an impermeable crack. The effects of the crack position and the material properties on the dynamic stress intensity factor are examined and numerical results are presented graphically. 相似文献