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1.
This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters. 相似文献
2.
This paper provides the solution to the problem of dissimilar, homogeneous semi-infinite strips bonded through a functionally graded interlayer and weakened by an embedded or edge interfacial crack. The bonded system is assumed to be under antiplane deformation, subjected to either traction-free or clamped boundary conditions along its bounding planes. Based on the Fourier integral transform, the problem is formulated in terms of a singular integral equation which has a simple Cauchy kernel for the embedded crack and a generalized Cauchy kernel for the edge crack. In the numerical results, the effects of geometric and material parameters of the bonded system on the crack-tip stress intensity factors are presented in order to quantify the interfacial fracture behavior in the presence of the graded interlayer. 相似文献
3.
The problem considered here is the response of a non-homogeneous composite material containing some cracks subjected to dynamic
loading. It is assumed that the composite material is orthotropic and all the material properties depend only on the coordinatey (along the thickness direction). In the analysis, the elastic region is divided into a number of plies of infinite length.
The material properties are taken to be constants for each ply. By utilizing the Laplace transform and Fourier transform technique,
the general solutions for plies are derived. The singular integral equations of the entire elastic region are obtained and
solved by the virtual displacement principle. Attention is focused on the time-dependent full field solutions of stress intensity
factor(SIF) and strain energy release rate. As a numerical illustration, the dynamic stress intensity factor of a substrate/functionally
graded film structure with two cracks under suddenly applied forces on cracks face are presented for various material non-homogeneity
parameters. 相似文献
4.
A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases. 相似文献
5.
W.-J. Feng R.-J. Hao J.-X. Liu S.-M. Duan 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(10):649-663
Summary In this paper, the scattering of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material is investigated by using the wavefunction expansion method and a singular integral equation technique. The debonding regions are modeled as multiple arc-shaped interface cracks with non-contacting faces. The magneto-electric impermeable boundary conditions are adopted. By expressing the scattered fields as wavefunction expansions with unknown coefficients, the mixed boundary-value problem is firstly reduced to a set of simultaneous dual-series equations. Then, dislocation density functions are introduced as unknowns to transform these dual-series equations to Cauchy singular integral equations of the first type,which can be numerically solved easily. The solution is valid for arbitrary number and size of the arc-shaped interface cracks. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond. The effects of incident direction, crack configuration and various material parameters on the dynamic stress intensity factors are discussed. The solution of this problem is expected to have applications in the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks.The work was supported by the National Natural Science Fund of China (Project No. 19772029) and the Research Fund for Doctors of Hebei Province, China (Project No. B2001213). 相似文献
6.
The antiplane stress analysis of two anisotropic finite wedges with arbitrary radii and apex angles that are bonded together along a common edge is investigated. The wedge radial boundaries can be subjected to displacement-displacement boundary condi- tions, and the circular boundary of the wedge is free from any traction. The new finite complex transforms are employed to solve the problem. These finite complex transforms have complex analogies to both kinds of standard finite Mellin transforms. The traction free condition on the crack faces is expressed as a singular integral equation by using the exact analytical method. The explicit terms for the strength of singularity are extracted, showing the dependence of the order of the stress singularity on the wedge angle, material constants, and boundary conditions. A numerical method is used for solving the resul- tant singular integral equations. The displacement boundary condition may be a general term of the Taylor series expansion for the displacement prescribed on the radial edge of the wedge. Thus, the analysis of every kind of displacement boundary conditions can be obtained by the achieved results from the foregoing general displacement boundary condition. The obtained stress intensity factors (SIFs) at the crack tips are plotted and compared with those obtained by the finite element analysis (FEA). 相似文献
7.
ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH 总被引:3,自引:0,他引:3
The special case of a crack under mode III conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor (SIF) results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter. 相似文献
8.
An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated and its validity was verified. Finally, the effects of nonhomogeneous material parameter and crack orientation on the stress intensity factor are studied. 相似文献
9.
Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface 总被引:3,自引:0,他引:3
The mechanical model was established for the anti-plane dynamic fracture problem for two collinear cracks on the two sides of and perpendicular to a weak-discontinuous interface between two materials with smoothly graded elastic properties, as opposed to a sharp interface with discontinuously changing elastic properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. The integral equations were solved by Erdogan's collocation method and the dynamic stress intensity factors in the time domain were obtained through Laplace numerical inversion proposed by Miller and Guy. The influences of geometrical and physical parameters on the dynamic stress intensity factors were illustrated and discussed, based on which some conclusions were drawn: (a) to increase the thickness of the FGM strip on either side of the interface will be beneficial to reducing the DSIF of a crack perpendicular to a bi-FGM interface and embedded at the center of one of the FGM strips; (b) To increase the rigidity of the FGM strip where the crack is located will increase the DSIF. However, when the material in one side of the interface is more rigid, the DSIF of the interface-perpendicular embedded crack in the other side will be reduced; (c) To decrease the weak-discontinuity of a bi-FGM interface will not necessarily reduce the stress intensity factor of a crack perpendicular to it, which is different from the case of interfacial crack; (d) For two collinear cracks with equal half-length, when the distance between the two inner tips is less than about three times of the half-length, the interaction of them is intensified, however, when the distance is greater than this the interaction becomes weak. 相似文献
10.
In this paper the anti-plane problem for an interface crack between two dissimilar magneto-electro-elastic plates subjected
to anti-plane mechanical and in-plane magneto-electrical loads is investigated. The interface crack is assumed to be either
magneto-electrically impermeable or permeable, and the position of the interface crack is arbitrary. The finite Fourier transform
method is employed to reduce the mixed boundary-value problem to triple trigonometric series equations. The dislocation density
functions and proper replacement of the variables are introduced to reduce these series equations to a standard Cauchy singular
integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition
is approximated as a system of linear algebra equations which can be easily solved. Field intensity factors and energy release
rates are determined numerically and discussed in detail. Numerical results show the effects of crack configuration and loading
combination parameters on the fracture behaviors of crack tips according to energy release rate criterion. The study of this
problem is expected to have applications to the investigation of dynamic fracture properties of magneto-electro-elastic materials
with cracks. 相似文献
11.
Mohamed Ben-Romdhane Sami El-Borgi Malek Charfeddine 《International Journal of Solids and Structures》2013
In this paper, we consider the elasto-static problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subject to statically applied normal and tangential surface loading. The crack direction is parallel to the free surface. The coating is graded in the thickness direction and is orthogonal to the crack direction. This coating is modelled as a non-homogeneous medium with an orthotropic stress–strain law. The equivalent crack surface stresses are first obtained and substituted in the plane elasticity equations. Using integral transforms, the governing equations are converted into singular integral equations which are solved numerically to yield the displacement field as well as the crack-tip stress intensity factors. This study presents a complete theoretical formulation for the problem in the static case. A numerical predictive capability for solving the singular integral equations and computing the crack-tip stress intensity factors is proposed. Since the loading is compressive, a previously developed crack-closure algorithm is applied to avoid interpenetration of the crack faces. The main objective of the paper is to investigate the effects of the material orthotropy and non-homogeneity of the graded coating on the crack-tip stress intensity factors, with and without using the crack-closure algorithm, for the purpose of gaining better understanding on the behavior and design of graded coatings. 相似文献
12.
Mohammad R. Torshizian Mohammad H. Kargarnovin Cyrus Nasirai 《Mechanics Research Communications》2011,38(3):164-169
In this paper, a two dimensional functionally graded material (2D-FGM) under an anti-plane load with an internal crack is considered. The crack is oriented in an arbitrary direction. The material properties are assumed to vary exponentially in two planar directions. The problem is analyzed and solved by two different methods namely Fourier integral transforms with singular integral equation technique, and then by the finite element method. The effects of crack orientation, material non-homogeneity, and other parameters on the value of stress intensity factor (SIF) are studied. Finally, the obtained results for Mode III stress intensity factor of different methods are compared. 相似文献
13.
This paper examines the dynamic response of an interface crack between two dissimilar magneto-electro-elastic materials subjected to the mechanical and electric magnetic impacts. The magneto-electric impermeable boundary conditions are adopted. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations in Laplace transform domain, which are solved numerically. Lots of numerical results are given graphically in time domain. The effects of electric impact loading and magnetic impact loading on dynamic energy density factors are discussed. Crack growth and propagation is predicted. The study of this problem is expected to have applications to the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks. 相似文献
14.
Summary The paper presents a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions. The mechanical loadings and thermal conditions applied on the crack faces are axisymmetric, being non-symmetric about the crack plane. In similar lines of [7], equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel operators of the first kind. Expressions for stress, displacement, temperature and heat flux functions are obtained in terms of Abel transforms of the first kind of the jumps of stress, displacement, temperature and heat flux at the crack plane. Two types of thermal conditions, that is, general surface temperatures and general heat flux on faces of the crack are considered. In both the cases, closed form solutions have been obtained for the unknown functions solving Abel type of integral equations. Explicit expressions for stresses, displacements, temperature fields, stress intensity factors have been obtained. Two special cases of thermal conditions in which: (i) crack faces are subjected to constant non-symmetric temperatures over a circular ring area, (ii) crack faces are subjected to constant non-symmetric heat flux over a circular ring area, have been considered. In some special cases, results have been compared with those from the literature. 相似文献
15.
V. M. Tikhomirov 《Journal of Applied Mechanics and Technical Physics》2008,49(5):864-871
Crack propagation under alternating loading is investigated. Relations between the growth rate of a fatigue defect and loading
parameters and the expression for the stress intensity factor are derived for compression of a cracked solid taking into account
the possible contact of the crack faces. A model for the deformation of a small region near the crack tip is proposed which
allows one to formulate the conditions of residual opening of a growing fatigue crack. The experimental data obtained in tests
of steel samples are compared with the results of calculation using the developed procedure.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 190–198, September–October, 2008. 相似文献
16.
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
17.
18.
IntroductionQuasicrystalasanewstructureofsolidmatter[1,2 ]bringsprofoundnewideastothetraditionalcondensedmatterphysicsandencouragesconsiderabletheoreticalandexperimentalstudiesonthephysicalandmechanicalpropertiesofthematerial,includingtheelasticitytheoryofthequasicrystal,manyvaluableresultsweregiven[3~ 5 ].Defectsinthematerialwereobservedsoonafterthediscoveryofthequasicrystal[6 ,7].Cracksareonetypeofdefects,theirexistencegreatlyinfluencesthephysicalandmechanicalpropertiesofthequasicrystalinem… 相似文献
19.
20.
Leonid I. Slepyan 《Journal of the mechanics and physics of solids》2010,58(5):636-655
A nonuniform crack growth problem is considered for a homogeneous isotropic elastic medium subjected to the action of remote oscillatory and static loads. In the case of a plane problem, the former results in Rayleigh waves propagating toward the crack tip. For the antiplane problem the shear waves play a similar role. Under the considered conditions the crack cannot move uniformly, and if the static prestress is not sufficiently high, the crack moves interruptedly. For fracture modes I and II the established, crack speed periodic regimes are examined. For mode III a complete transient solution is derived with the periodic regime as an asymptote. Examples of the crack motion are presented. The crack speed time-period and the time-averaged crack speeds are found. The ratio of the fracture energy to the energy carried by the Rayleigh wave is derived. An issue concerning two equivalent forms of the general solution is discussed. 相似文献