Electroelastic interaction between piezoelectric screw dislocation and circularly layered inclusion with imperfect interfaces

The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids is theoretically investigated.Here,the dislocation located at arbitrary points inside either the matrix or the inclusion and the interfaces of the interphase layer are imperfect.By the complex variable method,the explicit solutions to the complex potentials are given,and the electroelastic fields can be derived from them.The image force acting on the dislocation can be obtained by the generalized PeachKoehler formula.The motion of the piezoelectric screw dislocation and its equilibrium positions are discussed for variable parameters.The important results show that,if the inner interface of the interphase layer is imperfect and the magnitude of degree of the interface imperfection reaches the certain value,two equilibrium positions of the piezoelectric screw dislocation in the matrix near the interface are found for the certain material combination which has never been observed in the previous studies(without considering the interface imperfection).     

New phenomena concerning a screw dislocation interacting with two imperfect interfaces

Dislocation mobility and stability in nanocrystals and electronic materials are influenced by the material composition and interface conditions. Its mobility and stability then affect the mechanical behaviors of the composites. In this paper, we first address, in detail, the problem of a screw dislocation located in an annular coating layer which is imperfectly bonded to the inner circular inhomogeneity and to the outer unbounded matrix. Both the inhomogeneity-coating interface and coating-matrix interface are modeled by a linear spring with vanishing thickness to account for the possible damage occurring on the interface. An analytic solution in series form is derived by means of complex variable method, with all the unknown constants being determined explicitly. The solution is then applied to the study of the dislocation mobility and stability due to its interaction with the two imperfect interfaces. The most interesting finding is that when the middle coating layer is more compliant than both the inner inhomogeneity and the outer unbounded matrix and when the interface rigidity parameters for the two imperfect interfaces are greater than certain values, one stable and two unstable equilibrium positions can exist for the dislocation. Furthermore, under certain conditions an equilibrium position, which can be either stable or unstable (i.e., a saddle point), can exist, which has never been observed in previous studies. Results for a screw dislocation interacting with two parallel straight imperfect interfaces are also presented as the limiting case where the radius of the inner inhomogeneity approaches infinity while the thickness of the coating layer is fixed.     

Piezoelectric screw dislocations interacting with a circular inclusion with imperfect interface

The electroelastic coupling interaction between multiple screw dislocations and a circular inclusion with an imperfect interface in a piezoelectric solid is investigated. The appointed screw dislocation may be located either outside or inside the inclusion and is subjected to a line charge and a line force at the core. The analytic solutions of electroelastic fields are obtained by means of the complex-variable method. With the aid of the generalized Peach–Koehler formula, the explicit expressions of image forces exerted on the piezoelectric screw dislocations are derived. The motion and the equilibrium position of the appointed screw dislocation near the circular interface are discussed for variable parameters (interface imperfection, material electroelastic mismatch, and dislocation position), and the influence of the nearby parallel screw dislocations is also considered. It is found that the piezoelectric screw dislocation is always attracted by the electromechanical imperfect interface. When the interface imperfection is strong, the impact of material electroelastic mismatch on the image force and the equilibrium position of the dislocation becomes weak. Additionally, the effect of the nearby dislocations on the mobility of the appointed dislocation is very important.     

Interaction between a screw dislocation and viscoelastic interfaces

The analytical solutions for the interaction between dislocations and interfaces are of great importance to materials scientists as well as to mechanics researchers. The interfaces are treated as perfectly bonded in the most of the existing research works, where the traction and displacement vectors are continuous across the interfaces. However, in reality, there are discontinuities of displacements across the interfaces. In the present paper, the interaction between a screw dislocation and an imperfect interface is considered. The imperfect interface is modeled by linear spring and dashpot, i.e. linearly elastic and viscoelastic behaviors are introduced to model the imperfection of the interface. Particularly, we solved the boundary value problem analytically for Kelvin and Maxwell type of interface. In terms of geometrical configurations, we obtained the solutions for two joint half-spaces and a circular inclusion embedded in an infinite matrix. The analytical results show that the force acting on the dislocation depends on the mismatch of materials and the imperfection of the interface and evolves as time elapses.     

Misfit dislocation dipoles in coated fibrous composites

We investigate the stability of a misfit screw dislocation dipole in a coated fibrous composite. The fiber is stiffer whereas the coating is more compliant than the matrix. A critical coating thickness is identified for given material parameters of the composite. For a compliant coating below the critical thickness, there exist an inner unstable and an outer stable equilibrium position in the matrix for the dislocation dipole. However, for a compliant coating above the critical thickness, the dislocation dipole will be attracted to the coating–matrix interface. If the coating thickness is greater than the inclusion radius, the dislocation dipole cannot lodge in the matrix no matter what values of the material parameters are chosen.     

Interaction between an edge dislocation and a circular inclusion with an inhomogeneously imperfect interface

This research presents an analytical study of the interaction problem of an edge dislocation with a circular inclusion with a circumferentially inhomogeneously imperfect interface. The interface, which is modeled as a spring (interphase) layer with vanishing thickness, is characterized by that in which there is a displacement jump across the interface in the same direction as the corresponding tractions, and the same degree of imperfection is realized in both the normal and tangential directions. Furthermore, the interface parameter is nonuniform along the interface. In order to arrive at an elementary form solution, we introduce a conformal mapping function. Then the stress field as well as the Peach–Koehler force acting on the edge dislocation can be obtained from the derived complex potentials. Calculations demonstrate that the nonuniform interface parameter has a significant influence on the stress field.     

A piezoelectric screw dislocation interacting with an imperfect piezoelectric bimaterial interface

A general method is presented for the analytical solution of a piezoelectric screw dislocation located within one of two joined piezoelectric half-planes. The bonding along the half-plane is considered to be imperfect with the assumption that the imperfect interface is mechanically compliant and dielectrically weakly (or highly) conducting. For a mechanically compliant interface tractions are continuous but displacements are discontinuous across the imperfect interface. In this context, jumps in the displacement components are assumed to be proportional to their respective interface traction components. Similarly, for a dielectrically weakly conducting interface the normal electric displacement is continuous but the electric potential is discontinuous across the interface. The jump in electric potential is proportional to the normal electric displacement. In contrast, for a dielectrically highly conducting interface the electric potential is continuous across the interface whereas the normal electric displacement has a discontinuity across the interface which is proportional to a certain differential expression of the electric potential. Explicit expressions are derived for the complex field potentials. The results show that there are two dimensionless parameters measuring the interface “rigidity” as compared to one for the purely elastic case. When the imperfect interface is compliant and weakly conducting, the two dimensionless parameters can be positive real values or complex conjugates with positive real parts. When the imperfect interface is compliant and highly conducting the two dimensionless parameters can only be positive real values. An expression for the image force acting on the screw dislocation due to its interaction with a compliant and weakly conducting interface is also given. It is found that the image force is only dependent on two dimensionless generalized Dundurs constants as well as two dimensionless parameters measuring the interface “rigidity”.     

Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion

Dislocation mobility and stability in inclusions can affect the mechanical behaviors of the composites. In this paper, the problem of an edge dislocation located within a nanoscale cylindrical inclusion incorporating interface stress is first considered. The explicit expression for the image force acting on the edge dislocation is obtained by means of a complex variable method. The influence of the interface effects and the size of the inclusion on the image force is evaluated. The results indicate that the impact of interface stress on the image force and the equilibrium positions of the edge dislocation inside the inclusion becomes remarkable when the radius of the inclusion is reduced to nanometer scale. The force acting on the edge dislocation produced by the interface stress will increase with the decrease of the radius of the inclusion and depends on the inclusion size which differs from the classical solution. The stability of the dislocation inside a nanoscale inclusion is also analyzed. The condition of the dislocation stability and the critical radius of the inclusion are revised for considering interface stresses.     

含界面效应纳米尺度圆环形涂层中螺型位错分析

研究了纳米尺度圆环形涂层(界面层)中螺型位错与圆形夹杂以及无限大基体材料的干涉效应.涂层与夹杂的界面和涂层与基体的界面均考虑界面应力效应.运用复势方法,获得了三个区域复势函数的解析解答.利用求得的应力场和Peach-Koehler公式,得到了作用在螺型位错上位错力的精确表达式.主要讨论了界面应力对涂层(界面层)中螺型位错运动和平衡稳定的影响规律.结果表明,界面应力对界面附近位错的运动有大的影响,由于界面应力的存在,可以改变涂层内位错与夹杂/基体干涉的引斥规律,并使位错在涂层内部产生三个稳定或非稳定的平衡点.考虑界面效应后,有一个额外的排斥力或吸引力作用在位错上,使原有的位错力增加或减小.     

纳米线涂层中失配位错偶极子分析

研究了纳米线环形晶体薄膜涂层中失配位错偶极子与纳米线的干涉效应,并考虑纳米尺度应力效应及纳米线晶格失配的影响。运用弹性复势方法,分别获得了涂层和纳米线区域复势函数的精确解析解。利用求得的应力场和Peach-Koehler公式,得到了作用在螺型位错偶极子上像力和失配应力的精确表达式。算例结果表明,涂层纳米线界面应力和失配应力对涂层中失配位错偶极子的作用影响很大,由于界面应力和失配应力的存在,可以改变涂层内位错偶极子与纳米线干涉的引斥规律。与宏观尺度下的线型材料相比,纳米线材料由于界面效应的影响,位错偶极子在涂层中平衡位置的数量增加,涂层中更容易产生失配位错偶极子。考虑纳米线晶格失配的影响后,位错偶极子在涂层中平衡位置的数量增加。由此可知,减小纳米线晶格失配的影响,可以控制失配位错偶极子的产生。     

Surface/interface effects on elastic behavior of a screw dislocation in an eccentric core–shell nanowire

The elastic behavior of a screw dislocation which is positioned inside the shell domain of an eccentric core–shell nanowire is addressed with taking into account the surface/interface stress effect. The complex potential function method in combination with the conformal mapping function is applied to solve the governing non-classical equations. The dislocation stress field and the image force acting on the dislocation are studied in detail and compared with those obtained within the classical theory of elasticity. It is shown that near the free outer surface and the inner core–shell interface, the non-classical solution for the stress field considerably differs from the classical one, while this difference practically vanishes in the bulk regions of the nanowire. It is also demonstrated that the surface with positive (negative) shear modulus applies an extra non-classical repelling (attracting) image force to the dislocation, which can change the nature of the equilibrium positions depending on the system parameters. At the same time, the non-classical solution fails when the dislocation approaches very close to the surface/interface with negative shear modulus. The effects of the core–shell eccentricity and nanowire diameter on dislocation behavior are discussed. It is shown that the non-classical surface/interface effect has a short-range character and becomes more pronounced when the nanowire diameter is smaller than 20 nm.     

含非完整界面涂层夹杂中螺型位错的弹性分析

研究了含非完整界面圆形涂层夹杂内部一个螺型位错在夹杂、涂层与无限大基体材料中产生的弹性场.运用复变函数函数方法,获得了三个区域复势函数的解析解答.利用求得的应力场和Peach-Koehler公式,得到了作用在螺型位错上位错力的精确表达式.主要讨论了两个非完整界面对位错力的影响规律.结果表明,涂层界面对夹杂内部螺型位错的吸引力随着界面粘结强度的弱化而变大.界面非完整程度增加削弱材料弹性失配对位错力的影响.在一定条件下,非完整界面可以改变夹杂内位错与涂层/基体系统之间的引斥干涉规律,并使位错在夹杂内部产生一个稳定或非稳定的平衡点.     

Influence of imperfect bonding on the reflection and transmission of QP-wave at the interface of two functionally graded piezoelectric materials

This paper studies the reflection and transmission of two dimensional quasi P wave incident at an imperfect interface between two dissimilar Functionally Graded Piezoelectric Materials (FGPM) half-spaces. The imperfect bonding behavior between the two considered half-spaces is described by the interfacial imperfections. The imperfection is characterized by the normal stiffness and tangential stiffness using the linear spring model. These interface parameters (i.e normal stiffness and tangential stiffness) are dependent on the elastic properties of interphase. Secular equations have been derived analytically for both the half-spaces. Different cases of imperfect interfaces namely perfect interface, slip interface, weak bonding interface and unbounded interface have been assumed and discussed. Influence of material gradients on the reflection and transmission coefficients (RTC’s) have been inflicted graphically for all the four considered interface conditions. Further, a comparative study of the RTC’s with respect to the incident angle has been carried out for the different cases of imperfections. The obtained results may be useful for measuring imperfection at the interface and designing of SAW devices.     

Anti-plane time-harmonic Green's functions for a circular inhomogeneity in piezoelectric medium with a spring- or membrane-type interface

The present work focuses on the two-dimensional anti-plane time-harmonic dynamic Green's functions for a circular inhomogeneity immersed in an infinite matrix with an imperfect interface, where both the inhomogeneity and matrix are assumed to be piezoelectric and transversely isotropic. Two types of imperfect interface, the spring-type interface with electromechanical coupling and the membrane-type interface, are considered. The former type is often used to model the electromechanical damage along the interface while the latter is largely employed to simulate surface/interface effect of nano-sized inhomogeneity. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in an unbounded matrix as well as the circular inhomogeneity are respectively derived. The present solutions can recover the anti-plane Green's functions for some special cases, such as the dynamic or quasi-static Green's functions of piezoelectricity with perfect interface as well as the dynamic or quasi-static Green's functions of pure elasticity with imperfect interface. For detailed discussions, selected analytical results are presented. Dependence of the electromechanical fields on circular frequency as well as interface properties is examined. The size effect related to interfacial imperfection is also discussed.     

Size-dependent interaction of an edge dislocation with an elliptical nano-inhomogeneity incorporating interface effects

The elastic behavior of an edge dislocation, which is positioned outside of a nanoscale elliptical inhomogeneity, is studied within the interface elasticity approach incorporating the elastic moduli and surface tension of the interface. The complex potential function method is used. The dislocation stress field and the image force acting on the dislocation are found and analyzed in detail. The difference between the solutions obtained within the classical-elasticity and interface-elasticity approaches is discussed. It is shown that for the stress field, this difference can be significant in those points of the inhomogeneity-matrix interface, where the radius of curvature is smaller and which are closer to the dislocation. For the image force, this difference can be considerable or dispensable in dependence on the dislocation position, its Burgers vector orientation, and relations between the elastic moduli of the matrix, inhomogeneity and their interface. Under some special conditions, the dislocation can occupy a stable equilibrium position in atomically close vicinity of the interface. The size effect is demonstrated that the normalized image force strongly depends on the inhomogeneity size when it is in the range of several tens of nanometers, in contrast with the classical solution where this force is always constant. The general issue is that the interface elasticity effects become more evident when the characteristic sizes of the problem (inhomogeneity size, interface curvature radius and dislocation-interface spacing) reduce to the nanoscale.     

Analytic Solution for a Line Edge Dislocation in a Bimaterial System Incorporating Interface Elasticity

We examine the plane strain deformations of a bimaterial system consisting of a line edge dislocation interacting with a flat interface between two dissimilar isotropic half-planes in which the additional effects of interface elasticity are incorporated into the model of deformation. The entire system is assumed to be free of any external loading. Despite the fact that it is generally accepted that the separate interface modulus describing interface elasticity is permitted to take negative values, we show that simple closed-form solutions for the dislocation-induced stress field and the image force acting on the dislocation are available only when the interface modulus is assumed to be positive; the corresponding system admits no valid solutions when the interface modulus is negative. We present several numerical examples to illustrate our solutions. Additionally, we show that the influence of interface elasticity on the dislocation-induced interfacial stress field decays with increasing hardness of the adjoining half-plane (free of the dislocation). Moreover, we find that for a given (positive) in-plane interface modulus, the corresponding interface effects on the image force (acting on the dislocation) can reach maximum or minimum values when the Burgers vector of the dislocation is either parallel or perpendicular to the interface.     

A circular inclusion with circumferentially inhomogeneous imperfect interface in harmonic materials

In the following analysis, we present a rigorous solution for the problem of a circular elastic inclusion surrounded by an infinite elastic matrix in finite plane elastostatics. The inclusion and matrix are separated by a circumferentially inhomogeneous imperfect interface characterized by the linear spring-type imperfect interface model where the interface is such that the same degree of imperfection is realized in both the normal and tangential directions. Through the use of analytic continuation, a set of first-order coupled ordinary differential equations with variable coefficients are developed for two analytic potential functions. The unknown coefficients of the potential functions are determined from their analyticity requirements and some additional problem-specific constraints. An example is then presented for a specific class of interface where the inclusion mean stress is contrasted between the homogeneous interface and inhomogeneous interface models. It is shown that, for circumstances where a homogeneously imperfect interface may not be warranted, the inhomogeneous model has a pronounced effect on the mean stress within the inclusion.     

Interaction between edge dislocations and amorphous interphase in carbon nanotubes reinforced metal matrix nanocomposites incorporating interface effect

Dislocations mobility and stability in the carbon nanotubes (CNTs)-reinforced metal matrix nanocomposites (MMNCs) can significantly affect the mechanical properties of the composites. However, current processing techniques often lead to the formation of coated CNT (amorphous interphase exists between the reinforcement and metal matrix), which have large impact upon the image force exerting on dislocations. Even though the importance of the interphase zone formed in metal matrix composites has been demonstrated by many studies for elastic properties, the influence of interphase on the local elastoplastic behavior of CNT-reinforced MMNCs is still an open issue. This paper puts forward a three-phase composite cylinder model with new boundary conditions. In this model, the interaction between edge dislocations and a coated CNT incorporating interface effect is investigated. The explicit expressions for the stress fields and the image force acting on an edge dislocation are proposed. In addition, plastic flow occurring around the coated reinforcement is addressed. The influences of interface condition and the material properties of coated CNT on the glide/climb force are clearly analyzed. The results indicate that the interface effect becomes remarkable when the radius of the coated reinforcement is below 10 nm. In addition, different from the traditional particles, the coated CNT attracts the adjacent edge dislocations, causing pronounced local hardening at the interface between the interphase and the metal matrix under certain conditions. It is concluded that the presence of the interphase can have a profound effect on the local stress field in CNT-reinforced MMNCs. Finally, the condition of the dislocations stability and the equilibrium numbers of dislocations at a given size grain are evaluated for considering the interface effect.     

铁磁梁式板磁弹性初始后屈曲及缺陷敏感性分析

从铁磁板的磁弹性广义变分原理出发，通过对铁磁板内外的磁场和板变形 场的摄动技术以及采用经典Koiter理论，对横向磁场中铁磁悬臂、简支、固支梁式薄 板磁弹性稳定性的初始后屈曲行为及缺陷敏感性进行了定性研究. 解析地给出了悬臂板对初 始缺陷敏感，简支和固支板对初始缺陷不敏感等结果，对悬臂梁式板理论预测的临界磁场值 往往大于实验观测结果的现象从定性上给予了合理解释.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE Ⅲ INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode Ⅲ interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. zThe image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.