A screw dislocation interacting with a coated nano-inhomogeneity incorporating interface stress

Effect of interface stress on the interaction between a screw dislocation and a coated nano-inhomogeneity is investigated in the framework of surface elasticity. By using the complex variable function method, the stress fields in heterogeneous materials and the image force acting on the screw dislocation are derived analytically. The results indicate that, when the radius of the coated inhomogeneity is reduced to nanometers, the influence of interface stress on the motion of the dislocation near the inhomogeneity becomes significant and the image force acting on the screw dislocation depends on the size of the coated inhomogeneity, which differs from the classical solution. And it is showed that the thicker coated layer relative to inclusion decreases or increases the influence of a coated inclusion on the image force of dislocation, not as expected.     

A screw dislocation interacting with an interphase layer between a circular inhomogeneity and the matrix

The interaction of a screw dislocation with an interphase layer between a circular inhomogeneity and the matrix is dealt with. By combining the sectionally holomorphic function, Cauchy integral and Laurent series expansion techniques, the relation among the complex potentials for the three material regions is given, and the functional equation in complex potential for the interphase layer are derived. Explicit series solutions are given for the two cases when the screw dislocation is located in the inhomogeneity or in the matrix. The influence of the interphase layer parameters on interaction energy and dislocation force is evaluated and discussed. The present solutions contain a number of novel and previously known results which can be shown to be special cases.     

Screw dislocations interacting with a partially debonded interface in cylindrically anisotropic composites

Interaction between screw dislocations and a partially debonded interface in cylindrically anisotropic composites subjected to uniform stress at infinity is investigated in this paper. Using Muskhelishvili’s complex variable method, the closed forms of complex potentials are obtained for a screw dislocation and a screw dislocation dipole located inside either matrix or inhomogeneity. Explicit expressions of stress intensity factors at the crack tips, image forces and image torques acting on dislocation or the center of dipole are provided. The results show that the crack and dislocation geometry combination plays an important role in the interaction between screw dislocations and interface crack. Furthermore, it is found that the anisotropy of solids may change the shielding and anti-shielding effects arising from screw dislocations and the equilibrium position of screw dislocations. The presented solutions are valid for anisotropic, orthotropic or isotropic composites and can be reduced to some novel or previously known results.     

Contribution to critical shear stress of nanocomposites produced by interaction of screw dislocation with nanoscale inclusion

The contribution to the critical shear stress of nanocomposites caused by the interaction between screw dislocations and nanoscale circular cylindrical inclusions with interface stresses is derived by means of the Mott and Nabarro's model. The effect of the radius of the nanoscale inclusion and the volume fraction of inclusions as well as the interface stress on the critical shear stress is examined. The most important finding is that, when the negative interface stress is considered, a critical value of the radius of the nanoscale inclusion or the volume fraction of inclusions may exist to gain the best strengthening effects for the second-phase strengthened composites which differs from the classical solution without considering the interface stress under same external conditions.     

复合材料中压电螺型位错与含刚性核夹杂的电弹干涉

为了研究压电复合材料中位于基体的压电螺型位错与含共焦椭圆导电刚性核椭圆夹杂的电弹相互作用, 基于复变函数方法, 获得了基体和夹杂区域的精确级数形式解析解。运用广义Peach-Koehler公式, 导出了作用在位错上像力的解析表达式。在此基础上讨论了椭圆刚性核和材料电弹特性对位错像力以及位错平衡位置的影响规律, 同时讨论了压电夹杂和弹性基体的复合情况。结果表明: 椭圆刚性核对位错有着明显的排斥作用, 可以增强硬夹杂对位错的排斥, 减弱软夹杂对位错的吸引; 对于软夹杂, 在界面附近位错存在一个不稳定的平衡位置; 在基体和夹杂的界面上, 像力迅速增大; 当夹杂的剪切模量远小于基体时, 界面附近不会出现位错的平衡位置。     

A crack in a confocal elliptic piezoelectric inhomogeneity embedded in an infinite piezoelectric medium

An effective method is developed and used to investigate the elastic field and the electric field of a crack in a confocal elliptic piezoelectric inhomogeneity embedded in an infinite piezoelectric medium. The matrix is subjected to the remote antiplane shear and inplane electric field. The analytical solution is obtained using the conformal mapping and the theorem of analytic continuation. Specific solutions which are compared with existing ones are provided. The characteristics of the elastic field and electric field singularities at the crack tip are analyzed and the corresponding crack extension forces are derived.     

A piezoelectric screw dislocation in a three-phase composite cylinder model with an imperfect interface

The electroelastic coupling interaction between a piezoelectric screw dislocation and the embedded circular cross-section inclusions with imperfect interfaces in piezoelectric solids is investigated by using a three-phase composite cylinder model. By means of a complex variable technique, the explicit solutions of electroelastic fields are obtained. With the aid of the Peach-Koehler formula, the explicit expression for the image force exerted on the piezoelectric screw dislocation is derived. The image force on the dislocation and its equilibrium positions near one of the inclusions are discussed for variable parameters (interface imperfection and material electroelastic dissimilarity) and the influence of nearby inclusions is also considered. The results show that when compared with the previous solution (the perfect interface), more equilibrium positions of the screw dislocation in the matrix may be available due to the effect of the interface imperfection when the dislocation is close to the electroelastic stiff inclusion. It is also found that the magnitude of the image force exerted on the piezoelectric screw dislocation produced by multiply inclusions is always smaller than that produced by a single inclusion and the impact of nearby inclusions on the mobility of the screw dislocation is very important.     

A line dislocation interacting with a semi-infinite crack in piezoelectric solid

Closed-form analytical solutions are presented for the physical problem of a semi-infinite crack interacting with a line dislocation under the loading of a line force and a line charge in two-dimensional infinite anisotropic piezoelectric medium. The crack can be a conventional Griffith crack or an anti-crack (a rigid line inhomogeneity). Using the extended Stroh formalism and perturbation technique, the explicit expressions of the field intensity factors and the image force on the dislocation are computed as functions of dislocation location and material constants. The results are discussed and compared with those from special cases existed in the literature. The analytical solutions obtained can be applied to studying interacting cracks and crack branching problems in piezoelectric solids.     

Numerical evaluation of inhomogeneity forces in a coating layer due to thermal loading

Abstract

In order to clarify the mechanical state at the interface between substrate and coating material, numerical analyses are implemented on model materials under thermal loads, and the possibilities of debonding are discussed from the configurational mechanics concept. The intensity of the interfacial singularity can be discussed in relation to the inhomogeneity force which is numerically evaluated in the course of thermal loading via finite element analysis. It is shown that interfacial roughness, a small perturbation at the interface, may have a dominant role in the evolution of inhomogeneity. Effects of initial defects, temperature gradient and additional external load are also evaluated. It is confirmed that the inhomogeneity force is a generalisation of the J-integral, i.e. the energy release rate in fracture mechanics, and this is also applicable to interfacial problems. A possible scenario of layer debonding is discussed in terms of the material inhomogeneity and the deformation characteristics of the thin coating layer under thermal loading.     

The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.     

Stress intensity factors of an inclined elliptical crack near a bimaterial interface

In this paper the stress intensity factors are discussed for an inclined elliptical crack near a bimaterial interface. The solution utilizes the body force method and requires Green’s functions for perfectly bonded semi-infinite bodies. The formulation leads to a system of hypersingular integral equation whose unknowns are three modes of crack opening displacements. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of stress intensity factors along the crack front accurately. Distributions of stress intensity factors are presented in tables and figures with varying the shape of crack, distance from the interface, and elastic modulus ratio. It is found that the inclined crack can be evaluated by the models of vertical and parallel cracks within the error of 24% even for the cracks very close to the interface.     

The Interaction between a Piezoelectric Screw Dislocation Dipole and an Elliptic Blunt Crack in Elliptical Inhomogeneity

The interaction problem of a piezoelectric screw dislocation dipole with a confocal elliptic blunt crack in elliptical inhomogeneity subjected to remote anti-plane stress field and in-plane electric field is investigated by using the complex method of elasticity. The exact closed-form solutions of a series of quantities, such as singularity stress field, image force and image torque acting on the center of screw dislocation dipole, stress intensity factor and electric displacement intensity factor of crack tip, energy release rate, and generalized strain energy density are obtained. Then the influence laws of remote load, the dip angle of dislocation dipole, the size of blunt crack, and the material constants on the quantities are analyzed. The numerical results show that the image force, image torque, stress intensity factor, and electric displacement intensity factor make periodic variation as the dip angle of dislocation dipole; the energy release rate of crack tip is negative when subjected to pure electric field, however, it can be positive or negative when subjected to the combined action of mechanical field and electric field; the sharp crack is not easy to expand in some combined action of mechanical field and electric field.     

Analysis of a row of elliptical inclusions in a plate using singular integral equations

This paper deals with the interaction problem of a row of elliptical inclusions under uniaxial tension. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy--type and logarithmic singularities, where the unknowns are densities of body forces distributed in infinite plates that have the same elastic constants as those of the matrix and inclusion. In order to satisfy the boundary conditions along the elliptical boundaries, eight kinds of fundamental density functions, proposed in a previous paper, are applied. In the analysis, the number, shape, and position of inclusions are varied systematically; after which the magnitude and position of the maximum stress are examined. For any fixed shape and size of inclusions, the maximum stress is shown to be linear with the reciprocal of the number of inclusions. The present method is found to yield rapidly converging numerical results for various geometrical conditions of inclusions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Experimental and finite element analyses on stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending

Experimental backtracking technique and finite element analysis have been employed to evaluate the stress intensities along the front of an elliptical surface crack in a cylindrical rod. The finite element solution covers a wide range of crack shapes loaded under end-free and end-constrained axial tension and pure bending. Convenient closed form stress intensity expressions along the whole crack front for each of the loading cases have been given in terms of the crack aspect ratio, crack depth ratio and place ratio.The closed form solutions have been compared against a number of representative solutions collected from the literature. It has been found that different finite element results for the interior points are generally in good mutual agreement, while solutions derived from other methods may sometimes indicate different trends. At the surface interception point agreement is less good because of a complication in the interpretation of stress intensity there.Experimental backtracking results on the end-constrained axial tension case corroborate well with the closed form solution presented. It suggests that the current closed form solution is adequate in describing the stress intensities along the whole crack front of real surface cracks in cylindrical rods.     

An Analysis of a Quarter-Infinite Solid with a Corner Crack of Arbitrary Shape

In this paper, a versatile body force method for a quarter-infinite solid with a corner crack of arbitrary shape is proposed under two types of pressure: constant and linear. New numerical results are obtained for different corner crack cases. Fatigue crack growth from a corner crack has been analysed successively with the present method. Moreover, the stress intensity factor of a corner crack is proposed in a simple form for an arbitrary shape.     

微观状态SiCp/Al复合材料铣削残余应力模拟分析

为了获得更高精度的高体积分数SiCp/Al复合材料铣削加工表面残余应力数据,采用有限元分析软件ABAQUS建立了基于正交切削的微观平面应变模型。复合材料两相材料属性被分别定义,改善了在宏观状态下整体定义材料属性的精度缺陷,并对其微观状态切削残余应力产生过程进行模拟分析。分析并得出了不同切削参数对工件加工表面残余应力的影响规律以及沿工件层深方向的残余应力分布情况。结果表明切削速度和每齿进给量对SiCp/Al复合材料已加工表面残余应力有着相似的影响规律,但每齿进给量的影响作用较为显著。     

Stress and Failure Analysis of Composite Laminates with an Inclusion under Multiaxial Compression-Tension Loading

The present paper investigates the failure of orthotropic laminates with a filled hole subjected to biaxial compression-tension loading. This is an idealised case that simulates a situation where the impact damaged laminate has been repaired by drilling a hole and then plugging the hole with a perfect-fit core made of a dissimilar material. The exact stress distribution in the laminate has been determined using the complex variable mapping method. These stresses are then employed in a fracture mechanics failure model to predict the failure load of a laminate with a filled hole under in-plane compression-dominated multi-axial loading. Failure strength predictions are compared to open hole results and experimental data.     

3D FEM Analysis of the Buckling Delamination of a Rectangular Viscoelastic Composite Plate with an Embedded Rectangular Crack Under Two-Axial Compression

In Akbarov, Yahnioglu and Karatas (2010) a buckling delamination problem for a rectangular viscoelastic composite plate with a band and edge cracks was investigated under uniaxial compression of the plate. In the present study this investigation is developed for the case where the mentioned rectangular plate contains an embedded rectangular crack and in addition it is assumed that the plate is subjected to two-axial compression.
It is supposed that all end surfaces of the considered plate are simply supported and that these ends are subjected to uniformly distributed normal compressive forces with intensity p₁ and p₃ which act along the O_x1 and O_x3 axes, respectively. Moreover, we assume that the plate contains a rectangular embedded crack, the edge-surfaces of which have initial infinitesimal imperfections before the loading.
The evolution of these initial imperfections with time under two-axial compression of the plate is studied within the framework of the three-dimensional geometrically nonlinear field equations of the theory of viscoelasticity for anisotropic bodies.
For determination of the values of the critical force or of the critical time, as well as those of the buckling delamination mode of the considered plate, the initial imperfection criterion is used.
For the solution to the corresponding boundary-value problems, boundary form perturbation techniques; the Laplace transform; the Schapery method for obtaining the numerical inverse Laplace transform of the sought values; and the 3D FEM are used.
The numerical results of the critical force and critical time, as well as of the buckling delamination modes are presented and discussed.