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1.
In this paper, a simple but inberent relation between theL-integral and the Bueckner work conjugate integral is proved for crack problems in isotropic, anisotropic, and dissimilar
materials, respectively. It is found that, in the above-mentioned three cases, theL-integral, from the mathematical point of view as well as in principle, arises from Betti's reciprocal theorem. This means
that the Bueckner work conjugate integral is a more general path-independent integral than the others since any other path-independent
integrals could be derived by using the Bueckner integral while choosing a different subsidiary stress-displacement field. 相似文献
2.
研究横观各向同性压电材料中裂纹问题,提出了Bueckner功共轭积分在这类材料中的表达式:并通过引出两类辅助的应力-位移-电位移-电势场,证明功共轭积分和这类材料中的J积分和M积分仍然存在简单的两倍关系由此,各类在脆性材料断裂问题中已广泛应用的权函数方法可顺理成章地推广到压电材料的研究中来.这对独立地确定电位移强度因子和经典的I、II型应力强度因子提供了有力的数学上的工具.进而通过计算机械应变能释放率对压电材料中裂纹的稳定做出判断. 相似文献
3.
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
4.
Complex potentials are derived to describe the anti-plane singular shear stress fields around a kinked crack, the main portion of which is embedded along the interface of two dissimilar anisotropic elastic media. This is accomplished by formulating the problem as singular integral equations with generalized Cauchy kernels. The shear stress singularity at the kink differs from the familiar inverse square root of the local distance; it is found to influence the magnitude of the Mode III crack tip stress intensity factor, K3. Numerical results of K3 are obtained and displayed in graphical forms for different degree of material anisotropy and crack dimensions. 相似文献
5.
Steady-state anisotropic thermoelasticity equations are used to obtain the stress intensity factors for a cracked layer sandwiched between two different anisotropic elastic solids. The anisotropy is assumed to arise from discrete fibers whose orientation could alter with reference to the crack edges. A generalized plane deformation prevails in the dissimilar media domain with a line of discontinuity disturbing a uniform heat flow. The flexibility/stiffness matrix approach is used such that the crack problem reduces to solving two sets of singular integral equations. Numerical values of the crack tip stress-intensity factors are obtained for various crack size, crack location, crack surface insulation, fiber volume fraction and orientation angles. The results are displayed graphically. 相似文献
6.
B.M. Singh J. Rokne R.S. Dhaliwal J. Vrbik 《European Journal of Mechanics - A/Solids》2006,25(6):938-949
In this paper the equation of motion is solved when the shear modulus and density are functions of r and z and the latter part of this paper contains an analysis of the interaction of torsional waves normally with penny-shaped crack located in a thick infinite elastic fibre. The infinite elastic fibre is bonded to an infinite elastic matrix. The matrix and the thick elastic fibre are non-homogeneous and are of dissimilar materials. The solution of the problem is reduced to a Fredholm integral equation of the second kind, which is solved numerically. The numerical solution is used to calculate the stress intensity factor at the rim of the penny-shaped crack. Finally the results of the stress intensity factors are displayed graphically. 相似文献
7.
This paper gives a unified approach to analyze two-dimensional elastic deformations of a composite body consisting of two
dissimilar anisotropic or isotropic materials perfectly bonded along a planar interface. The Eshelby et al. formalism of anisotropic
elasticity is linked with that of Kolosov-Muskhelishvili for isotropic elasticity by means of two complex matrix functions
describing completely the arising elastic fields. These functions, whose elements are holomorphic functions, are defined as
the two-phase potentials of the bimaterial. The present work is concerned with bi-materials whose constituent materials occupy
the whole space and are connected by a planar interface. The elastic fields arising in such a bimaterial are given by universal
relationships in terms of the two-phase potentials. Then, the general results obtained are implemented to study two interesting
bimaterial problems: the problem of a uniformly stressed bimaterial with a perfect interfacial bonding, and the interface
crack problem of a bimaterial with a general loading. For both problems, all combinations of the elastic properties of the
constituent materials are considered. For the first problem, the constraints, which must be imposed between the components
of the applied uniform stress fields, are established, so that they are admissible as elastic fields of the bimaterial. For
the interface crack problem, the solution is obtained for a general loading applied in the body. Detailed results are given
for the case of a remote uniform stress field applied to the bimaterial constituents. 相似文献
8.
Ramkrishna Pramanik Subhas Chandra Pal Mohan Lal Ghosh 《European Journal of Mechanics - A/Solids》1999,18(6):1013
The high-frequency elastodynamic problem involving the excitation of an interface crack of finite width lying between two dissimilar anisotropic elastic half-planes has been analyzed. The crack surface is excited by a pair of time-harmonic antiplane line sources situated at the middle of the cracked surface. The problem has first been reduced to one with the interface crack lying between two dissimilar isotropic elastic half-planes by a transformation of relevant co-ordinates and parameters. The problem has then been formulated as an extended Wiener–Hopf equation (cf. Noble, 1958) and the asymptotic solution for high-frequency has been derived. The expression for the stress intensity factor at the crack tips has been derived and the numerical results for different pairs of materials have been presented graphically. 相似文献
9.
《European Journal of Mechanics - A/Solids》2006,25(1):189-197
Over the past twenty years, the well-known weight function theory based on the Bueckner work conjugate integral has been widely used to calculate crack tip fracture dominant parameter such as the stress intensity factor, the energy release rate (or the J-integral) and the T-stress in various kinds of cracked materials (e.g. isotropic materials, anisotropic materials and piezoelectric materials). Meanwhile, the pseudo-orthogonal property of the eigenfunction expansion form of the crack tip stress complex potential function has been proved to play a very important role in the theory. In this paper, we provide a new approach to establish the pseudo-orthogonal properties for crack problems in anisotropic and/or piezoelectric materials. In the latter case associated with mechanical-electric coupling, the electrical boundary conditions under both impermeable and permeable crack models are considered. The approach developed is much simpler than the classical complex variable separation technique proposed by previous researchers and hence the cumbersome and lengthy manipulations are avoided. Moreover, it is shown that, unlike previous works, the orthogonal properties of the material characteristic matrices A and B induced by the Stroh theory are no longer necessary in establishing the pseudo-orthogonal properties of eigenfunction expansion form in cracked piezoelectric materials. The approach can be easily extended to treat many other different crack problems concerning the Bueckner integral involving several complex arguments. 相似文献
10.
两种各向异性材料界面共线裂纹的反平面问题 总被引:2,自引:1,他引:2
本文研究两种各向异性材料界面共线裂纹的反平面剪切问题。利用复变函数方法,提出了一般问题公式和某些实际重要问题的封闭形式解。考察了裂纹尖端附近的应力分布并给出了应力强度因子公式。从本文解签的特殊情形,可以直接导出两种各向同性材料界面裂纹,均匀各向异性材料共线裂纹以及均匀各向同性材料共线裂纹的相应问题公式,其中包括已有的经典结果。 相似文献
11.
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
12.
《International Journal of Solids and Structures》2006,43(5):913-942
An interface crack or delamination may often branch out of the interface in a laminated composite due to thermal stresses developing around the delamination/crack tip when the media is exposed to heat flow induced by environmental events such as a sudden short-duration fire. In this paper, the thermo-elastic problem of interface crack branching in dissimilar anisotropic bi-media is studied by using the theory of Stroh’s dislocation formalism, extended to thermo-elasticity in matrix notation. Based on the complex variable method and the analytical continuation principle, the thermo-elastic interface crack/delamination problem is examined and a general solution in compact form is derived for dissimilar anisotropic bi-media. A set of Green’s functions is proposed for the dislocations (conventional dislocation and thermal dislocation/heat vortex) in anisotropic bi-media. These functions may be more suitable than those which have appeared in the literature on addressing thermo-elastic interface crack branching in dissimilar anisotropic bi-materials. Using the contour integral method, a closed form solution to the interaction between the dislocations and the interface crack is obtained. Within the scope of linear fracture mechanics, the thermo-elastic problem of interface crack branching is then solved by modelling the branched portion as a continuous distribution of dislocations. The influence of thermal loading and thermal properties on the branching behavior is examined, and criteria for predicting interface crack branching are suggested, based on the extensive numerical results from the study of various cases. 相似文献
13.
The magnetoelastic plane strain problem of an interfacial Griffith crack between two dissimilar soft ferromagnetic elastic materials subjected to a uniform magnetostatic field is considered within the framework of linear magnetoelasticity. By making use of the Fourier integral transform technique, the mixed boundary problem is then reduced to a pair of singular integral equations of the second kind. Solutions of the singular integral equations are obtained numerically by means of a Jacobi polynomial expansion method. Effects of the magnetic field, the combinations of the magnetic properties of materials and the geometric parameters on the magnetoelastic stress intensity factors in the vicinity of crack tip are shown graphically. 相似文献
14.
15.
Summary This paper presents an M-integral analysis for the microcracked anisotropic composite materials. By using an elementary solution derived for a single
finite crack subjected to a concentrated force on crack faces, the problem of strong interacting, arbitrarily oriented and
located microcracks in an anisotropic composite materials is reduced to a system of Fredholm integral equations. The crack-tip
fracture parameters, such as the stress intensity factors, are evaluated from a numerical solution of the system of integral
equations. Its dependence on the coordinate system, calculation, and physical interpretation of the M-integral are discussed in the interaction problem. Finally, a numerical example of the damage evaluation by the M-integral analysis is given.
Received 24 September 1999; accepted for publication 8 February 2000 相似文献
16.
《International Journal of Solids and Structures》2007,44(11-12):4206-4219
This paper attempts to investigate the problem for the interaction between a uniformly subsonic moving screw dislocation and interface cracks in two dissimilar anisotropic materials. Using Riemann–Schwarz’s symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interface containing one and two cracks. The expressions of stress intensity factors at the crack tips and image force acting on moving dislocation are derived explicitly. The results show that the stress intensity factors at the crack tips decrease with increasing velocity of dislocation, and larger dislocation velocity leads to the equilibrium position of dislocation leaving from crack tips. The presented solutions contain previously known results as the special cases. 相似文献
17.
A reciprocal work contour integral method for calculating stress intensity factors is extended to treat the problem of two bonded dissimilar materials containing a crack along the bond. The method is based on Betti's Reciprocal work theorem from which the singular stress intensities at the crack tip may be evaluated in terms of an integral involving tractions and displacements on a contour remote from the crack tip. 相似文献
18.
The asymptotic problem of a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation is investigated. The linear transformation method for the problem of the anisotropic bimaterial with a straight interface is proposed. The stress intensity factor for the kinked interfacial crack in the anisotropic composite is obtained from the solution of the transformed problem of the kinked interfacial crack in the isotropic bimaterial based on the linear transformation method. The effects of the material parameters as well as the kink angle on the stress intensity factor are discussed from numerical results of the stress intensity factor. The finite element analysis is carried out to verify the stress intensity factor obtained by using the linear transformation. The influence of the material orientations on the stress intensity factor is investigated for the kinked crack in the bimaterial consisting of dissimilar inclined orthotropic materials. 相似文献
19.
20.
The behaviors of an interface crack between dissimilar orthotropic elastic halfplanes subjected to uniform tension was reworked by use of the Schmidt method. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, of which the unknown variables are the jumps of the displacements across the crack surfaces. Numerical examples are provided for the stress intensity factors of the cracks. Contrary to the previous solution of the interface crack, it is found that the stress singularity of the present interface crack solution is of the same nature as that for the ordinary crack in homogeneous materials. When the materials from the two half planes are the same, an exact solution can be otained. 相似文献