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1.
Xian-Ci Zhong Xian-Fang Li Kang Yong Lee 《International Journal of Solids and Structures》2009,46(6):1456-1463
The elastostatic problem of a mode-I crack embedded in a bimaterial with an imperfect interface is investigated. The crack is in proximity to and perpendicular to the imperfect interface, which is governed by linear spring-like relations. The Fourier transform is applied to reduce the associated mixed-boundary value problem to a singular integral equation with Cauchy kernel. By numerically solving the resulting equation, stress intensity factors near both crack tips are evaluated. Obtained results reveal that the stress intensity factors in the presence of the imperfect interface vary between that with a perfect interface and that with a completely debonding interface. Moreover, an increase in the interface parameters decreases the stress intensity factors. In particular, when crack approaches to the weakened interface closer, the stress intensity factors become larger for a sliding interface, and become larger or smaller for a Winkler interface, depending on the crack lying in a stiffer or softer material. The influences of the imperfection of the interface on the stress intensity factors for a bimaterial composed of aluminum and steel are presented graphically. 相似文献
2.
The plane problem of an elliptically reinforced circular hole in an anisotropic plate or laminate 总被引:11,自引:0,他引:11
Summary Within the scope of linear elasticity, the in-plane problem of an anisotropic plate or laminate with a circular hole and
an elliptical hole reinforcement is considered. Arbitrary anisotropic elastic stiffnesses are allowed for the base plate and
the reinforcement material, and for the reinforcement there is no restriction for its elliptical shape and size. The analysis
of the problem is performed by the complex potential method with appropriately chosen series representations inside and outside
the reinforcement region. The derived closed-form solution provides all resultant in-plane stresses and deformations within
and around the hole reinforcement with little computational effort and at high accuracy. The determined solution allows a
proper and effective assessment of hole reinforcements for many technical applications.
Received 26 June 2000; accepted for publication 26 September 2000 相似文献
3.
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
4.
A plane problem for a thermally insulated interface crack with a contact zone in an isotropic bimaterial under tension–shear mechanical loading and a temperature flux is considered. The expressions for the stresses and the electrical flux as well as for the derivatives of the displacement and the temperature jumps at the material interfaces via sectionally holomorphic mechanical and thermal potential functions are given. After the solution of the thermal problem the inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved exactly. The stresses at the interface and the stress intensity factors at the singular points are presented in a clear analytical form. Special attention is devoted to the case of a small contact zone when the stress intensity factors can be presented in form similar to the associated presentation for an “open” crack model. A transcendental equation and an asymptotic analytic formula for the determination of the real contact zone length are derived. It is shown that for a certain bimaterial this length as well as the correspondent stress intensity factor are defined by a single parameter which depends on the normal-shear loading and the heat flux. 相似文献
5.
Chongmin Song Francis Tin-Loi Wei Gao 《International Journal of Solids and Structures》2010,47(7-8):978-989
The transient response of finite bimaterial plates with interface cracks is analyzed directly in the time domain by using the scaled boundary finite-element method. A bimaterial plate is divided into a few subdomains. Only the boundaries of the subdomains are discretized with line elements leading to great flexibility in mesh generation. The displacement and stress fields are expressed as a series solution which separates the singular stress term from other high-order terms. The oscillatory stress singularity in the radial direction emanating from the scaling center is represented analytically. The complex dynamic stress intensity factors are evaluated directly from either the stresses or the crack opening displacements of the singular stress term. Numerical examples of cracked anisotropic bimaterial plates are presented to verify the accuracy of the present technique and to provide additions to the very limited number of reference solutions in the literature. 相似文献
6.
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
7.
A three-dimensional photoelastic analysis using the stress freezing and slicing techniques was employed to study the stress distribution and the stress-concentration factors around an elliptical hole in a plate of finite thickness. The plate was subjected to simple out-of-plane bending. A special bending device was designed to produce uniform bending moment at the two opposite free edges of the plate. Six plates with various elliptical holes were studied. The stress variation across the plate thickness at the periphery of the elliptical hole was also investigated. The experimental results were correlated with the existing theoretical solutions. 相似文献
8.
9.
Oleg Onopriienko Volodymyr Loboda Alla Sheveleva Yuri Lapusta 《Comptes Rendus Mecanique》2018,346(6):449-459
The interaction of a conductive crack and an electrode at a piezoelectric bi-material interface is studied. The bimaterial is subjected to an in-plane electrical field parallel to the interface and an anti-plane mechanical loading. The problem is formulated and reduced, via the application of sectionally analytic vector functions, to a combined Dirichlet–Riemann boundary value problem. Simple analytical expressions for the stress, the electric field, and their intensity factors as well as for the crack faces' displacement jump are derived. Our numerical results illustrate the proposed approach and permit to draw some conclusions on the crack–electrode interaction. 相似文献
10.
11.
《International Journal of Solids and Structures》2006,43(21):6649-6664
External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete. Debonding along the FRP–concrete interface can lead to premature failure of the structure. In this study, a bond-slip model is established to study the interface debonding induced by a flexural crack in a FRP-plated concrete beam. The reinforced concrete beam and FRP plate are modeled as two linearly elastic Euler–Bernoulli beams bonded together through a thin layer of FRP–concrete interface. The interface layer is essentially modeled as a large fracture processing zone of which the stress–deformation relationship is described by a nonlinear bond-slip model. Three different bond-slip models (bi-linear, triangular and linear-damaging) are used. By dividing the debonding process into several stages, governing equations of interfacial shear and normal stresses are obtained. Closed-form solutions are then obtained for the interfacial shear and normal stresses and the deflection of the beam in each stage of debonding. In such a way, the proposed model unifies the whole debonding process, including elastic deformation, debonding initiation and growth, into one model. With such a superior feature, the proposed model provides an efficient and effective analytical tool to study FRP–concrete interface debonding. 相似文献
12.
An interface crack with an artificial contact zone at the right-hand side crack tip between two dissimilar finite-sized piezoelectric
materials is considered under remote mixed-mode loading. To find the singular electromechanical field at the crack tip, an
asymptotic solution is derived in connection with the conventional finite element method. For mechanical loads, the stress
intensity factors at the singular points are obtained. 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 derived. The dependencies of the contact zone lengths on external load coefficients are illustrated in graphical
form. For a particular case of a short crack with respect to the dimensions of the bimaterial compound, the numerical results
are compared to the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack. 相似文献
13.
M. Aydin Komur 《Mechanics Research Communications》2011,38(2):117-122
This study investigates the elasto-plastic buckling behaviour of simply supported square and rectangular thin steel plates having elliptic cut-outs by means of finite element method. Plates with simply supported in the out-of-plane direction are applied uniform compression in long-edge direction. A50 steel was used in the analysis and the focus was on the effect of plate aspect ratio, elliptical hole size, elliptical hole angle, elliptical hole location and slenderness ratio on buckling behaviour. It was found in the study that as the plate slenderness ratio increases, the critical buckling stress decreases for all the perforated plates. 相似文献
14.
This paper analyzes the anti-plane problem of dynamic self-similar debonding of interface at very high velocity. The debonding is modeled as an interface crack propagating self-similarly from zero-length. The extending speed is assumed to be transonic or supersonic. We first consider the dynamic debonding under moving concentrated loads. The moving dislocation model of self-similar propagation of an interface crack is used to formulate the problem to a singular integral equation which is solved analytically. The singularity of stresses near the crack tip is discussed and the dynamic stress intensity factors are presented. Finally the solution of dynamic debonding underx
2-type loads is obtained by using the superposition method. 相似文献
15.
E. P. Chen 《Theoretical and Applied Fracture Mechanics》1985,3(3):257-262
In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems. 相似文献
16.
17.
Summary An interface crack with an artificial contact zone at the right-hand side crack tip between two piezoelectric semi-infinite
half-planes is considered under remote mixed-mode loading. Assuming the stresses, strains and displacements are independent
of the coordinate x
2, the expression for the displacement jumps and stresses along the interface are found via a sectionally holomorphic vector
function. For piezoceramics of the symmetry class 6 mm and for electrically permeable crack faces, the problem is reduced
to a combined Dirichlet-Riemann boundary value problem which can be solved analytically. Further, analytical expressions for
the stresses, electrical displacements, derivatives of elastic displacement jumps, stress and electrical intensity factors
are found at the interface. Real contact zone lengths and the well-known oscillating solution are derived from the obtained
solution as well. Analytical relationships between the fracture-mechanical parameters of various models are found, and recommendations
are suggested concerning the application of numerical methods to the problem of an interface crack in the discontinuity area
of a piezoelectric bimaterial.
Received 16 March 1999; accepted for publication 31 May 1999 相似文献
18.
Summary The interface crack problem for a piezoelectric bimaterial based on permeable conditions is studied numerically. To find the singular electromechanical field at the crack tip, an asymptotic solution is derived in connection with the conventional finite element method. For mechanical and electrical loads, the complex stress intensity factor for an interface crack is obtained. The influence of the applied loads on the electromechanical fields near the crack tip is also studied. For a particular case of a short crack with respect to the bimaterial size, the numerical results are compared with the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack.One author (V.G.) gratefully acknowledges the support provided by the Alexander von Humboldt Foundation of Germany.accepted for publication 7 June 2004 相似文献
19.
Stress concentration factor expression for tension strip with eccentric elliptical hole 总被引:1,自引:0,他引:1
Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empirical method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli’s photo-elastic experiment and Isida’s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy. 相似文献
20.
Summary A solution to the thin plate bending problem of partially bonded dissimilar strips with two bond lines is presented. The two strips are symmetrically bonded with respect to the interface which is on theX-axis. The complex stress functions approach together with the rational mapping function technique are used in the analysis. A concentrated bending moment applied at each strip is considered. Distributions of bending and torsional moments, as well as the stress intensity of debonding (SID) at the debonding tips are obtained, and the debonding extension is investigated. 相似文献