A periodic system of electrically permeable cracks at the interface between two piezoelectric materials

We constructed a closed solution for a bimaterial plane consisting of two dissimilar piezoelectric half-planes with a periodic system of electrically permeable cracks at the interface between these materials. The presence of zones of smooth contact of the crack lips near their tips was taken into account. By representing the characteristics of electromechanical fields via piecewise analytic functions, we reduced the problem to a Dirichlet–Riemann periodic problem, which was solved exactly. As a result of numerical analysis of the derived solution, we studied the dependence of the relative length of the contact zones and stress intensity factors on the ratio between the crack length and period for different combinations of piezoelectric materials.     

Problem of thermoelectromagnetoelasticity for a piezoelectric/piezomagnetic bimaterial with interface crack

We consider a plane strain problem for a piezoelectric/piezomagnetic bimaterial space with a crack in the region of the interface of the materials. At infinity, tensile and shear stresses and heat, electric, and magnetic flows are set. Using representations for all mechanical, thermal, and electromagnetic factors in terms of piecewise analytic functions, we formulate problems of linear conjugation that correspond to a model of an open crack and models taking into account the contact zone in the vicinity of a crack tip. Exact analytic solutions of the indicated problems are constructed. Expressions for stresses, the electric and magnetic inductions, jumps of derivatives of displacements, and electric and magnetic potentials on the interface are written. The coefficients of intensities of the indicated factors are presented. We derive a transcendental equation for the determination of the real length of the contact zone. The dependences of this length and the coefficients of intensity on the set external influences are investigated.     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

Interfacial fracture of layered magnetoelectroelastic materials

A problem for an interface crack located in a layered magnetoelectroelastic material strip of semi-infinite length is solved. A closed-form solution is obtained for anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for stresses and electric and magnetic fields, together with their intensity factors and the energy release rate, are obtained. The extreme cases of impermeable and permeable cracks are discussed. Using the basic solution for a single crack, solutions for two collinear interface cracks in an infinitely long layered magnetoelectroelastic medium, an interface crack in an infinitely long layered magnetoelectroelastic medium, and an edge crack at the interface of a semi-infinitely long layered magnetoelectroelastic medium are also obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 145–164, March–April, 2008.     

Periodic set of the interface cracks with contact zones

A closed form solution to the plane problem of the theory of elasticity for an infinite isotropic bimaterial space (plane) with a periodic set of the interface cracks with frictionless contact zones near its tips is obtained. By means of the complex function presentation the problem is reduced to the combined Dirichlet–Riemann boundary value problem for a sectionally–holomorphic function and solved exactly. The equations for the determination of the contact zone length as well as the closed form expressions for the stress intensity factors are carried out. The variation of the mentioned values with respect to the distance between the cracks is illustrated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals

A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals is considered. The Fourier transform technique is used to solve a moving crack problem under the action of antiplane shear and inplane electric field. Full elastic stresses of phonon and phason fields and electric fields are derived for a crack running with constant speed in the periodic plane. Obtained results show that the coupled elastic fields inside piezoelectric quasicrystals depend on the speed of crack propagation, and exhibit the usual square-root singularity at the moving crack tip. Electric field and phason stresses do not have singularity and electric displacement and phonon stresses have the inverse square-root singularity at the crack tip for a permeable crack. The field intensity factors and energy release rates are obtained in closed form. The crack velocity does not affect the field intensity factors, but alters the dynamic energy release rate. Bifurcation angle of a moving crack in a 1D hexagonal piezoelectric quasicrystal is evaluated from the viewpoint of energy balance. Obtained results are helpful to better understanding crack advance in piezoelectric quasicrystals.     

Cracks in piezoelectric and electroconductive bodies

Singularities are studied of the elastic and electric fields near a tip of a crack on the interface of two piezoelectric bodies. An analog of the Griffith formula is obtained for the increment of the potential energy of deformation due to development of a rectilinear crack. The external electrical forces result in the decrease of the energy release rate which explains an experimentally-known possibility of controlling the fracture process by some additional electric fields.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Thermo-mechanical modeling of turbine blades taking into account structural defects

In turbine blades of aero-engines typical defects are cracks due to high mechanical and thermal loads. The extended finite element method (XFEM) is used for simulations of fracture mechanics problems with cracks. Discontinuities in the displacement and temperature field are allowed and the crack opening displacement and crack tip stress field are reproduced accurately. Since crack closure and non-physical penetration of the crack surfaces may occur under certain load conditions, it becomes necessary to enforce the non-penetration condition for crack surfaces. This contact formulation is assumed to be frictionless. The node-to-segment approach proposed in [3] is extended to ten-node tetrahedral elements with quadratic shape functions. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermoelastic contact of half-spaces with equal thermal distortivities in the presence of a heat-permeable intersurface gap

We consider the interaction of elastic half-spaces with equal thermal distortivities in the presence of a heat-permeable medium in an intercontact gap caused by a recess on the surface of one of the bodies. Outside the gap, a perfect thermal and frictionless mechanical contact takes place between the bodies. Using the method of functions of intercontact gaps, the formulated contact problem is reduced to a singular integral equation for a derivative of the height of the gap, which is solved analytically, and to a Prandtl-type singular integro-differential equation for the difference of temperature of the surfaces in the region of the gap, for the solution of which we propose an analytic-numerical approach. Plots illustrate the influence of load and the thermal conductivity of the filler on the temperature difference between the edges of the gap, contact stresses, heat flows, and longitudinal strains between the half-spaces.     

Dynamic Tension of a Plate Containing a Stationary Central Crack

A physically substantiated energy model of the formation of a stress concentration zone in the vicinity of the tip of a stationary crack under dynamic loading is developed by a combined theoretical and experimental approach. The hypothetical feasibility of describing the effects of an arbitrarily shaped load pulse on a stationary crack is demonstrated. Analytical expressions are derived for the dynamic stress intensity factor. A new mechanical interpretation of the stress intensity factor is proposed.     

Out-of-plane displacement measurement near the crack tip during a crack propagation: Validation of a 3D formulation for a specimen in PMMA loaded in mode I.

The fundamental aim of this study is the determination zone of the 3D effects and the transient one at the vicinity of the crack tip during a crack propagation in brittle materials ( PMMA ) using an optical method (Michelson interferometer). With the obtained interferograms, we can extract the phase (thus the relief) by using a new numerical approach based on the principle of images correlation between real fringes and virtual fringes. Different dynamic tests are realized by a plate loaded in mode I under a constant loading. We compare the obtained data with the two-dimensional theory of Westergaard (plane stress hypothesis) [1]. With the divergence is established, we propose a new 3D formulation, based on a formulation employed for static crack, which takes into account 3D and transient effects. For the static cracks, the 3D effects relate to a presence of the state of three-dimensional stresses. However in dynamics, the transient effects appear and are related to the crack propagation velocity. The 3D effects and transient effects lead to results equivalent to experimental ones in terms of displacement but are completely different to results given by the two-dimensional theory near the crack tip. It is possible to quantify the zone when the plane stress hypothesis is not valid according to the crack propagation speed V. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of interface cracks in layered piezoelectric composites by a SGBEM

Piezoelectric materials offer many possibilities in advanced engineering structures due to their inherent coupling effects between mechanical and electrical fields and are widely applied in smart devices and structures like transducers, actuators and sensors [2]. An important application of piezoelectric materials is related to layered or laminated composites because they can be optimized to satisfy the high-performance requirements according to different in-service conditions. Beside cracks inside homogeneous domains, one of the most dominant failure mechanisms in layered or laminated composites is the interface failure. Interface cracks and interface debonding may be induced by the mismatch of the mechanical, electrical and thermal properties of the material constituents during the manufacturing process and the in-service loading conditions. This paper presents a hypersingular symmetric Galerkin boundary element method (SGBEM) for crack analysis in two-dimensional (2D), layered and linear piezoelectric solids. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Contact Problem for a Half-Space and a Rigid Base with an Axially Symmetric Recess

An axially symmetric problem of frictionless contact interaction of an elastic half-space and a rigid base that has a small surface recess is considered. A corresponding problem of elasticity theory is formulated. The problem is solved by the method of double integral equations. The contact pressure, the surface shape of the half-space after compression, and the size of the gap are found in closed form.     

带裂纹十次对称二维准晶平面弹性的无摩擦接触问题

借助经典平面弹性复变函数方法，研究了单个刚性凸基底压头作用下，带任意形状裂纹十次对称二维准晶半平面弹性的无摩擦接触问题.利用十次对称二维准晶位移、应力的复变函数表达式, 带任意形状裂纹的准晶半平面弹性无摩擦接触问题被转换为可解的解析函数复合边值问题，进而简化成一类可解的Riemann边值问题.通过求解Riemann边值问题，得到了应力函数的封闭解, 并给出了裂纹端点处应力强度因子和压头下方准晶体表面任意点处接触应力的显式表达式.从压头下方接触应力的表达式可以看出, 接触应力在压头边缘和裂纹端点处具有奇异性.当忽略相位子场影响时, 该文所得结论与弹性材料对应结果一致.数值算例分别给出了单个平底刚性压头无摩擦压入带单个垂直裂纹和水平裂纹的十次对称二维准晶下半平面的结果.该文所得结论为准晶材料的应用提供了理论参考.     

压电体光滑接触界面有局部分离时的滑移脉冲波传播

应用关于压电材料的Stroh方法以及Fourier分析和奇异积分方程技术,研究了压电体光滑接触界面有局部分离时的滑移脉冲波传播问题,分析了其存在的判据．压电体由单向压应力作用而光滑接触并处于一定强度的电场中．待求问题最终转化为含Cauchy核的奇异积分方程组,并给出其解析解．数值计算结果表明:光滑接触界面上有局部分离的滑移脉冲波普遍存在,且界面法向面力和法向电位移在局部分离区两端有奇异性;对某些特殊的材料组合,外载荷不影响滑移脉冲波的存在性．     

压电材料中两平行对称可导通裂纹断裂性能分析

采用Schmidt研究了压电材料中对称平行的双可导通裂纹的断裂性能,利用富里叶变换使问题的求解转换为求解两对以裂纹面位移之差为未知变量的对偶积分方程,并采用Schmidt方法来对这两对对偶积分程进行数值求解。结果表明应力强度因子和电位移强度因子与裂纹的几何尺寸有关。与不可导通裂纹有关结果相比,可导通裂纹的电位移强度因子远小于相应问题不可导通裂纹的电位移强度因子。     

Subcritical and critical states of a crack with failure zones

The problem on the stress–strain state near a mode I crack in an infinite plate is solved in the frame of a cohesive zone model. The complex variable method of Muskhelishvili is used to obtain the crack opening displacements caused by the cohesive traction, which models the failure zone at the crack tip, as well as by the external load. The finite stress condition and logarithmic singularity of the derivative of the separation with respect to the coordinate at the tip of a physical crack are taken into account.The cohesive traction distribution is sought in a piecewise linear form, nodal values of which are being numerically chosen to satisfy the traction-separation law. According to this law, the cohesive traction is coupled with the corresponding separation and fracture toughness. The tips of the physical crack and cohesive zone (geometric variables) along with the discrete cohesive traction are used as the problem parameters determining the stress-strain state. If the crack length is included in the set, then the critical crack size can be found for the given loading intensity.The obtained determining system of equations is solved numerically. To find the initial point for a standard numerical algorithm, the asymptotic determining system is derived. In this system, the geometric variables can be easily eliminated, which make it possible to linearize the system.In the numerical examples, the one-parameter traction-separation laws are used. Influence of the shape parameters of the law on the critical crack size and the corresponding cohesive length is studied. The possibility of using asymptotic solutions for determining the critical parameters is analysed. It is established that the critical crack length slightly depends on the shape parameter, while the cohesive length shows a strong dependence on the shape of cohesive laws.     

Transient response of dissimilar piezoelectric layers with multiple interacting interface cracks

In this study, we examine the dynamic behavior of two bonded dissimilar piezoelectric layers containing multiple interfacial cracks subjected to electro-mechanical impact loading. The problem was formulated through Fourier transformation into singular integral equations in which the unknown variables are the jumps of displacement and electric potential across the crack surface in the Laplace transform domain. The resulting integral equations together with the corresponding single-valued conditions are solved numerically for the densities of electro-elastic dislocations on a crack surface. The dynamic field intensity factors and dynamic energy release rate (DERR) history are obtained for both permeable and impermeable crack. The stress field is also obtained for the interface crack under impact loads. The results show that the field intensity factors at the crack tips and dynamic energy release rate depend on the interfacial crack geometry, electromechanical coupling and the electric boundary conditions on the crack surface.     

Numerical investigations in structures with imperfect material interfaces and cracks

Natural fiber reinforced bio-polymers are in the focus of many research projects to understand and improve the mechanical behavior subjected to different process parameters during production. To provide safe and reliable light weight constructions, special interest is directed towards the damage and fracture behavior of such composite materials. Here, the material's behavior at the imperfect material interface between fiber and matrix plays an essential role and governs inelastic effects at the interfaces on the one hand, and the behavior of growing cracks on the other. The reduction of the elastic potential is related to both energy consuming processes in the system and in general is going along with a reduction of the crack tip loading and a shift of the crack growth direction. In this paper, the crack tip loading analysis in structures with perfect and imperfect material interfaces is presented and applied to different specimens. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)