共查询到20条相似文献,搜索用时 736 毫秒
1.
V. S. Kirilyuk 《International Applied Mechanics》2006,42(2):152-161
The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical
loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity
factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under
the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc
problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006. 相似文献
2.
In this paper, a problem of a crack in an orthotropic strip is studied under plane strain conditions. It is assumed that normal displacements and shear stresses do not act on neither of the boundaries of the strip. Cauchy-type singular integral equation for the crack problem is derived by using the theory of plane elasticity and the Fourier transformation technique. A quadrature collocation approach is adopted for the numerical solutions of the singular integral equation. The effect of relative thickness and mechanical properties of strip on Mode I stress intensity factors (SIFs) are examined under different loading conditions. Some sample results are given for SIFs; also, material orthotropy and geometrical effects are discussed in detail. 相似文献
3.
Yongping Wan Yanpeng Yue Zheng Zhong 《International Journal of Solids and Structures》2012,49(21):3008-3021
A mode III crack cutting perpendicularly across the interface between two dissimilar semi-infinite magnetoelectroelastic solid is studied under the combined loads of a line force, a line electric charge and a line magnetic charge at an arbitrary location. The impermeable conditions are implied on the crack faces. The technique developed in literature for the elastic bimaterial with a crack cutting interface is exploited to treat the magnetoelectroelastic bimaterial. The Riemann-Hilbert problem can be formulated and solved based on complex variable method. Analytical solutions can be obtained for the entire plane. The intensity factors around crack tips can be defined for the elastic, electric and magnetic fields. It shows that, no matter where the load position is, the electric displacement intensity factors (EDIFs), as well as the magnetic induction intensity factors (MIIFs), are identical in magnitude but opposite in sign for both crack tips, on condition that a line force is solely applied. Alternatively, if only a line electric charge is considered, then the stress intensity factors (SIFs) and the MIIFs exhibit the behavior. Likewise, if only a line magnetic charge is applied, it turns to the SIFs and the EDIFs instead. In addition, the dependence of the intensity factors is graphically shown with respect to the location of a line force. It is found that the SIF for a crack tip tends to be infinite if the applied force is approaching the tip itself, but the EDIF, with the complete opposite trend, tends to be vanishing. Finally, focusing on the more practical case of piezoelectric/piezomagnetic bimaterial, variation of the SIF along with the moduli as well as the piezo constitutive coefficients is explored. These analyses may provide some guidance for material selection by minimizing the SIF. It is also believed that the results obtained in this paper can serve as the Green’s function for the dissimilar magnetoelectroelastic semi-infinite bimaterial with a crack cutting the interface under general magnetoelectromechanical loads. 相似文献
4.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(3):320-330
The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane
perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress
(SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for
a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find
the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity.
The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface
are found as an example
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008. 相似文献
5.
《International Journal of Solids and Structures》2005,42(9-10):2823-2835
Analytical solutions for an anti-plane Griffith moving crack inside an infinite magnetoelectroelastic medium under the conditions of permeable crack faces are formulated using integral transform method. The far-field anti-plane mechanical shear and in-plane electrical and magnetic loadings are applied to the magnetoelectroelastic material. Expressions for stresses, electric displacements and magnetic inductions in the vicinity of the crack tip are derived. Field intensity factors for magnetoelectroelastic material are obtained. The stresses, electric displacements and magnetic inductions at the crack tip show inverse square root singularities. The moving speed of the crack have influence on the dynamic electric displacement intensity factor (DEDIF) and the dynamic magnetic induction intensity factor (DMIIF), while the dynamic stress intensity factor (DSIF) does not depend on the velocity of the moving crack. When the crack is moving at very lower or very higher speeds, the crack will propagate along its original plane; while in the range of Mc1 < M < Mc2, the propagation of the crack possibly brings about the branch phenomena in magnetoelectroelastic media. 相似文献
6.
Rodney A. Stephenson 《Journal of Elasticity》1982,12(1):65-99
This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C. 相似文献
7.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(2):150-157
The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric
loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for
an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is
an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along
the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations
of the crack
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008. 相似文献
8.
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
9.
The dynamic response of an interfacial crack between two dissimilar magnetoelectroelastic layers is investigated under magnetic, electrical and mechanical impact loadings. Four kinds of ideal crack-face assumptions, i.e., magnetoelectrically impermeable (Case 1), magnetically impermeable and electrically permeable (Case 2), magnetically permeable and electrically impermeable (Case 3) and magnetoelectrically permeable (Case 4), are adopted separately. The dynamic field intensity factors and energy release rates are derived. The effects of loading combinations and crack configurations especially for the former on the dynamic response are examined according to energy release rate criterion. The numerical results show that, among others, a negative magnetic (or electrical) loading is generally prone to inhibit the crack extension rather than a positive one for a magnetically (or electrically) impermeable interfacial crack. Results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures. 相似文献
10.
Fracture of magnetoelectroelastic composite materials using boundary element method (BEM) 总被引:4,自引:0,他引:4
F. García-Snchez R. Rojas-Díaz A. Sez Ch. Zhang 《Theoretical and Applied Fracture Mechanics》2007,47(3):192-204
The behavior of cracked linear magnetoelectroelastic solids is analysed by means of the dual Boundary Element Method (BEM) approach. Media possessing fully coupled piezoelectric, piezomagnetic and magnetoelectric effects are considered. An explicit 2-D Green’s function in terms of the extended Stroh formalism for magnetoelectroelastic full-plane under static loading is implemented. Hypersingular integrals arising in the traction boundary integral equations are computed through a regularization technique. Evaluation of fracture parameters directly from computed nodal values is discussed. The stress intensity factors (SIF), the electric displacement intensity factor (EDIF), the magnetic induction intensity factor (MIIF) as well as the mechanical strain energy release rate (MSERR) are evaluated for different crack configurations in both finite and infinite solids subjected to in-plane combined magnetic–electric–mechanical loading conditions. The accuracy of the boundary element solution is confirmed by comparison with selected analytical solutions in the literature. The new results that can be of interest in the design and maintenance of novel magnetoelectroelastic devices are also discussed. 相似文献
11.
A. N. Guz I. A. Guz A. V. Men’shikov V. A. Men’shikov 《International Applied Mechanics》2011,46(10):1093-1100
The paper studies the distribution of the mode I, II, and III stress-intensity factors (SIFs) for a penny-shaped interface
crack in a bimaterial under normal harmonic loading. The dependence of SIFs on the type of a wave (compression–dilatation
or shear), loading frequency, and the mechanical properties of the bimaterial is analyzed 相似文献
12.
Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep
The stress–strain state near cracks on the boundary of a circular hole in a linear elastic orthotropic composite plate under
tension is analyzed. The distribution of stress intensity factors (SIFs) at the crack tip is found from photoelectric measurements.
The dependence of the SIFs on the ratio of crack length to hole radius and on the mechanical properties of the material is
established 相似文献
13.
Within the framework of finite-strain elastostatics an asymptotic analysis is carried out in order to calculate the singular field near the crack tip in a slab under conditions of plane deformation. A class of Ogden-Ball hyperelastic rubberlike materials and general loading conditions ensuring vanishing tractions on the crack faces near the crack tip are considered. It is shown that the singular deformation field near the crack tip can be specified by applying a rigid body rotation with a subsequent parallel translation to a so-called canonical field. The adjective canonical is adopted here to denote the field with symmetrically opening crack faces, just resembling the displacement field of the symmetric mode in linear elastic fracture mechanics. No analogy with the antisymmetric mode is possible, and the crack equilibrium criterion requires only one stress intensity factor to be determined. 相似文献
14.
The anti-plane problem of multiple cracks originating from a circular hole in a magnetoelectroelastic solid is investigated under remotely uniform anti-plane mechanical loading and in-plane electromagnetic loadings. The boundary value problem is reduced to a Cauchy integral equation by a new mapping function and the complex variable method, which is further solved exactly. The analytic expressions of the complex potentials, the field intensity factors and the energy release rate are derived in closed-form under the assumption that the surfaces of the cracks and hole are both electrically and magnetically impermeable. The effects of crack configurations and combined loadings on the energy release rate are shown graphically. Several useful results which may have potential applications to the design and fracture analysis of magnetoelectroelastic structures are given. 相似文献
15.
《International Journal of Solids and Structures》2004,41(24-25):6613-6629
In this paper, we developed a Stroh-type formalism for anti-plane deformation and then investigated the fracture mechanics for an elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-plane electromagnetic and/or anti-plane mechanical loading, which allowed us to take the electromagnetic field inside the cavity into account. Reducing the cavity into a crack, we had explicit solutions in closed forms for a mode III crack, which included the extreme cases for an impermeable crack and a permeable crack. The results were illustrated with plots, showing that in the absence of mechanical loads, an applied electric or magnetic field, positive or negative, always tended to close the crack. On the other hand, in the presence of a mechanical load, a negative electric or magnetic field retarded crack growth, while a positive field could either enhance or retard crack propagation, depending on the strengths of the applied electric/magnetic fields and the level of the mechanical load as well. In other words, the effect of electric/magnetic fields on the fracture behavior is mechanical load-dependent. 相似文献
16.
Mohammad R. Torshizian Mohammad H. Kargarnovin 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(5):625-637
Mixed-mode fracture mechanics analysis of an embedded arbitrarily oriented crack in a two-dimensional functionally graded material using plane elasticity theory is considered. The material properties are assumed to vary exponentially in two planar directions. Then, employing Fourier integral transforms with singular integral equation technique, the problem is solved. The stress intensity factors (SIFs) at the crack tips are calculated under in-plane mechanical loads. Finally, the effects of crack orientation, material non-homogeneity, and other parameters are discussed on the value of SIF in mode I and mode II fracture. 相似文献
17.
T-stress as an important parameter characterizing the stress field around a cracked tip has attracted much attention. This
paper concerns the T-stress near a cracked tip in a magnetoelectroelastic solid. By applying the Fourier transform, we solve the associated mixed
boundary-value problem. Adopting crack-faces electromagnetic boundary conditions nonlinearly dependent on the crack opening
displacement, coupled dual integral equations are derived. Then, the closed-form solution for the T-stress is obtained. A comparison of the T stresses for a cracked magnetoelectroelastic solid and for a cracked purely elastic material is made. Obtained results reveal
that in addition to applied mechanical loading, the T-stress is dependent on electric and magnetic loadings for a vacuum crack. 相似文献
18.
R. Rojas-Díaz F. García-Sánchez A. Sáez 《International Journal of Solids and Structures》2010,47(1):71-80
This paper presents a numerical model for the analysis of cracked magnetoelectroelastic materials subjected to in-plane mechanical, electric and magnetic dynamic time-harmonic loading. A traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time-harmonic Green’s functions (Rojas-Diaz et al., 2008). The hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities. Relevant fracture parameters, namely stress intensity factors, electric displacement intensity factor and magnetic induction intensity factor are directly evaluated as functions of the computed nodal opening displacements and the electric and magnetic potentials jumps across the crack faces. The method is checked by comparing numerical results against existing solutions for piezoelectric solids. Finally, numerical results for scattering of plane waves in a magnetoelectroelastic material by different crack configurations are presented for the first time. The obtained results are analyzed to evaluate the dependence of the fracture parameters on the coupled magnetoelectromechanical load, the crack geometry and the characteristics of the incident wave motion. 相似文献
19.
考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义. 相似文献
20.
We consider an infinite square-cell lattice of elastic beams with a semi-infinite crack. Symmetric and antisymmetric bending modes of fracture under remote loads are examined. The related long-wave asymptotes corresponding to a continuous anisotropic bending plate are also considered. In the latter model, the symmetric mode is characterized by the square-root type singularity, whereas the antisymmetric mode results in a hyper-singular field. A solution for the continuous plate with a finite crack is also presented. These closed-form continuous solutions describe the fields in the whole plane. The main goal is to establish analytical connections between the ‘macrolevel’ state, defined by the continuous asymptote of the lattice solution, and the maximal bending moment in the crack-front beam, that is, to determine the resistance of the lattice with an initial crack to the crack advance. The solutions are obtained in the same way as for mass-spring lattices. Considering the static problems we use the discrete Fourier transform and the Wiener-Hopf technique. Monotonically distributed bending moments ahead of the crack are determined for the symmetric mode, and a self-equilibrated transverse force distribution is found for the antisymmetric mode. It is shown that in the latter case only the crack-front beam resists to the fracture development, whereas the forces in the other beams facilitate the fracture. In this way, the macrolevel fracture energy is determined in terms of the material strength. The macrolevel energy release is found to be much greater than the critical strain energy of the beam, especially in the hyper-singular mode. In both problems, it is found that among the beams surrounding the crack the crack-front beam is maximally stressed, and hence its strength defines the strength of the structure. 相似文献