螺型位错偶极子与圆形夹杂界面裂纹的弹性干涉

该文研究了螺型位错偶极子和圆形夹杂界面裂纹的弹性干涉作用。利用复变函数方法,得到了该问题的复势函数以及应力场的封闭形式解答。求出了裂纹尖端的应力强度因子以及作用在螺型位错偶极子中心的像力和像力偶矩,并分析了位错偶极子对应力强度因子的影响及界面裂纹几何条件和不同材料特征组合对位错偶极子平衡位置的影响规律。研究结果表明:位错偶极子对应力强度因子具有很强的屏蔽或反屏蔽效应;硬夹杂排斥位错偶极子,而裂纹吸引位错偶极子,在一定条件下,位错偶极子在裂纹附近出现一个平衡位置;当裂纹的长度和材料剪切模量比达到临界值时,可以改变偶极子和界面之间的干涉机理。同时,裂纹长度对位错偶极子中心像力偶矩也有很大的影响。     

压电材料中螺型位错偶极子与圆弧形界面裂纹的电弹干涉效应

研究了在无穷远力电荷载作用下广义螺型位错偶极子与圆弧形界面裂纹的电弹干涉作用。运用复变函数方法,导出了该问题的一般解答,并获得了界面上只有一条裂纹时的封闭形式解,求得了基体及夹杂区域复势函数、广义应力场、裂纹尖端的广义应力强度因子以及作用在螺型位错偶极子上的位错力和力偶矩。讨论了裂纹长度、压电材料电弹常数以及位错偶极子的位置对裂纹尖端应力强度因子、偶极子中心的位错力和像力偶矩的影响。     

Mechanical equilibrium of an edge dislocation dipole near a crack tip

In this communication we analyze the mechanical equilibrium of an edge dislocation dipole near a crack tip. Based on the stress formula of a single edge dislocation, we obtain the stress field and strain energy of an edge dipole. The image force and image torque on edge dipole are derived from the strain energy. We investigate the mechanical equilibrium of edge dipole on different conditions. A comparison of mechanical equilibrium of edge dipole with mechanical equilibrium of edge and screw monopoles is made.     

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.     

Electro-elastic stress analysis for a wedge-shaped crack interacting with a screw dislocation in piezoelectric solid

The electro-elastic stress investigation on the interaction problem of a screw dislocation near the tip of a semi-infinite wedge-shaped crack in piezoelectric material has been carried out. Explicit closed-form analytical solutions are obtained for the stress intensity factor (SIF) and the electric displacement intensity factor (EDIF) of the crack, as well as the force on dislocation. The derivation is based on the conformal mapping method and the perturbation technique. The dislocation has Burger's vector normal to the isotropic basal plane, with a line force and a line charge being applied at the core of the dislocation. The influence of the location and the wedge angle of the crack on the image force of the dislocation has been discussed in detail. At the same time the effect of the dislocation on the crack behavior has been also examined under different configurations. Two types of PZT materials are used to numerically illustrate the influences of the wedge angle and the location of the dislocation on the image force and the crack intensities. Results obtained in the current study can be fully reduced to various special cases available in the literatures.     

A thermodynamic approach to the interaction between dislocation and crack and its applications

By using a thermodynamic approach, the image force of the dislocation due to the semiinfinite crack in an infinite medium has been completed. If the influence of all the other force can be neglected, the screw dislocation subjected to the crack will approach the crack surface along the direction of the resultant force. The stress intensity factors at the crack tip due to the dislocation dipole are also included. This can be applied to the phase transformation toughening in zirconia.     

The interaction between a screw dislocation and a nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface

The interaction between a screw dislocation and a circular nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface is investigated. By using Riemann-Schwartz’s symmetry principle integrated with the analysis of singularity of complex functions and the conformal mapping technique, the analytical expressions of the stress field in both the circular nano-inhomogeneity and the infinite matrix, the image force acting on the screw dislocation and the stress intensity factor at the crack tip are obtained. The influence of elastic mismatch of materials, inhomogeneity size, interface stress, wedge crack opening angle and the relative location of dislocation on the image force and on the equilibrium position of the screw dislocation and the shielding effect of the screw dislocation are discussed in detail. The results show that interface stress has a significant impact on the movement of dislocations near the interface, and the effect of interface stress enhances when the inhomogeneity radius decreases. With the decrease in the wedge crack opening angle, the influence of interface stress on the movement of the screw dislocation and on the SIF enhances. With the increment of the relative shear modulus, the influence of interface stress weakens with the screw dislocation locating in the inhomogeneity and strengthens with the screw dislocation locating in the matrix. When the screw dislocation is located in the inhomogeneity, the positive (negative) interface stress increases (decreases) the shielding effect, while this phenomenon is opposite when the screw dislocation locates in the matrix.     

A generalized screw dislocation near a wedge-shaped magnetoelectroelastic bi-material interface

The magnetoelectroelastic solution of a generalized screw dislocation interacting with a wedge-shaped magnetoelectroelastic bi-material interface is derived in this paper. The screw dislocation is assumed to be straight and infinitely long in the z-direction and suffers a finite discontinuity in the displacement, electric potential and magnetic potential across the slip plane. The explicit closed-form analytical solution for the generalized stress field is derived by means of the complex variable and conformal mapping methods. The generalized stress intensity factors of the wedge tip induced by the dislocation and the image force acting on the dislocation are formulated and calculated. The influence of the wedge angle and the different bi-material constant combinations on the image force is discussed. Numerical examples for three particular wedge angles are calculated and compared with other available results.     

Screw dislocation in the two-phase isotropic thin film of an interfacial crack

The screw dislocation in the two-phase isotropic thin film of an interfacial crack has been investigated. The stress field, stress intensity factors at the crack tip and for dislocation emission, crack extension force, strain energy and the image force on the dislocation are obtained and found to be related to the thickness and effective shear modulus. The effect of size on fracture is pronounced when the thickness is smaller than the distance between dislocation and crack tip by a factor of 1000. The effect of the second phase on fracture is pronounced when μ⁽²⁾/μ⁽¹⁾ is in the range from 0.01 to 100. Newton's third law is proved to be valid for any thickness and shear modulus ratio. This result can be reduced to three special cases.     

Screw Dislocation Interacting with an Interfacial Edge Crack between Two Bonded Dissimilar Piezoelectric Wedges

This letter is concerned with an interfacial edge crack in a piezoelectric bimaterial wedge interacting with a screw dislocation under antiplane mechanical and in-plane electric loading. In addition to a discontinuous electric potential across the slip plane, the dislocation is subjected to a line-force and a line-charge at the tip. The out-of-plane displacement and electric potentials are obtained in closed-form based on conformal mapping technique and the solution for the screw dislocation in an infinite piezoelectric bimaterial with a semi-infinite interfacial crack. The intensity factors (IFs) and energy release rate (EER) are obtained explicitly. These solutions can be used as a base for constructing solutions for arbitrary coupled antiplane mechanical and in-plane electrical loadings.     

螺型位错偶极子与界面刚性线的弹性干涉

研究了晶体材料中螺型位错偶极子和界面刚性线夹杂的弹性干涉作用。利用复变函数方法,得到了该问题的复势函数以及应力场的封闭形式解答。求出了作用在螺型位错偶极子中心的像力和力偶矩,并分析了界面刚性线几何条件和不同材料特征组合对位错偶极子平衡位置的影响规律。研究结果表明:当位错偶极子不断靠近刚性线时,刚性线对螺型位错偶极子的运动有很强的排斥作用。当刚性线的长度和材料剪切模量比达到临界值时,可以改变偶极子和界面之间的干涉机理。同时,偶极子偶臂的方向对其自身的平衡也有很大的影响。     

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.     

Micro-crack initiation at tip of a rigid line inhomogeneity in piezoelectric materials

For the square-root singularity shear stress found at the tip of a rigid line inhomogeneity (an anti-crack) in piezoelectric media, one possible way of releasing high strain energy is to initiate a micro-crack at the inhomogeneity tip. In our current study, a dislocation pileup model for micro-crack initiation at the inhomogeneity tip is proposed based on Zener-Stroh crack initiation mechanism. An interesting and important physical result that emerges from the analysis is that the critical stress intensity factor for the anti-crack (the line inhomogeneity) can be related to the fracture toughness of a conventional Griffith crack in the same material. Analytical results further show that under mechanical loading, the critical stress and electric displacement intensity factors of an anti-crack are only related to the corresponding intensity factors of stress and electric displacement of the crack, respectively. While if the anti-crack is under displacement loading (with net dislocation pile-up at the inhomogeneity tip), the critical stress and electric displacement intensity factors of an anti-crack depend on both of the total mechanical dislocations b_T and electricity dislocations b_D.     

磁电弹双材料条中螺位错与界面边裂纹的相互作用

研究半无限长磁电弹双材料条中螺位错与界面边裂纹的相互作用。基于镜像原理和保角变换方法,得到了弹性场、电场和磁场的解析解,给出了应力、电位移、磁感应强度、应力强度因子以及像力的显函表达式。以压电-压磁双材料条形介质为例,分析了应力场、电位移和磁感应强度的分布特性,讨论了几何参数、压电和压磁效应对应力强度因子和像力的影响。     

A Griffith crack shielded by a dislocation pile-up

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.     

A piezoelectric screw dislocation interacting with a nonuniformly coated circular inclusion

This paper investigated the interaction of a piezoelectric screw dislocation with a nonuniformly coated circular inclusion in an unbounded piezoelectric matrix subjected to remote antiplane shear and electric fields. In addition to having a discontinuous displacement and a discontinuous electric potential across the slip plane, the dislocation is subjected to a line force and a line charge at the core. The alternating technique in conjunction with the method of analytical continuation is applied to derive the general solutions in an explicit series form. This approach has a clear advantage in deriving the solution to the heterogeneous problem in terms of the solution for the corresponding homogeneous problem. The presented series solutions have rapid convergence which is guaranteed numerically. The image force acting on the piezoelectric screw dislocation is calculated by using the generalized Peach–Koehler formula. The numerical results show that the varying thickness of the interphase layer will exert a significant influence on the shear stress and electric field within the circular inclusion, and on the direction and magnitude of the image force. This solution can be used as Green’s function for the analysis of the corresponding piezoelectric matrix cracking problem.     

Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids

A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.     

Micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in piezoelectric solids

A dislocation emission mechanism for micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in a piezoelectric solid is proposed in the present paper. For a rigid line inhomogeneity embedded in a piezoelectric matrix, dislocations of one sign are driven away from the tip due to high stress level, while the stationary dislocations of the opposite sign are left behind near the tip of the inhomogeneity. As a result, a micro-Zener–Stroh crack is initiated ahead of the line inhomogeneity. In the current study, a dislocation pileup mechanism for micro-crack initiation at the inhomogeneity tip is proposed. An interesting result is that the critical stress intensity factors for a line inhomogeneity perpendicular to the poling direction can be related to the fracture toughness of a conventional crack in the same material. Analytical solutions show that the critical plane shear stress intensity factor depends on the plane shear mechanical and displacement loadings, and the critical opening stress and electric displacement intensity factors depend on not only the mechanical and displacement loadings, but the electric field and displacement loadings as well.     

Comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane

A comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane was made. Four cases of single crystalline material, sliding grain boundary, perfectly bonded interface, and sliding interface were considered. The stress intensity factors arising from edge and screw dislocations and their image forces for the above four cases were compared. The stress intensity factor at a crack tip along the perfectly bonded interface arising from screw dislocation can be obtained from that in a single crystalline material if the shear modulus in the single crystalline material is replaced by the harmonic mean of both shear moduli in the bimaterial. The stress intensity factor at a crack tip along the sliding interface arising from edge dislocation in the bimaterial can be obtained from that along the sliding grain boundary in the single material if the μ/(1−ν) in the single material is substituted by the harmonic mean of μ/(1− ν) in the bimaterial where μ and ν are the shear modulus and Poisson's ratio, respectively. The solutions of screw dislocation near a crack along the sliding grain boundary and sliding interface are the same as that of screw dislocation and its mirror image. Generally, the effect of edge dislocation for perfectly bonded interface on the crack propagation is more pronounced than that for the sliding interface. The effect of edge dislocation on the crack propagation is mixed mode for the cases of perfectly bonded interface and single crystalline material, but mode I fracture for the cases of sliding interface and sliding grain boundary. All curves of Fx versus distance r from the dislocation at interface to the right-hand crack tip are similar to one another regardless of dislocation source for both sliding interface and perfectly bonded interface. The level of Fx for m=0 is larger than that for m=−1. This revised version was published online in August 2006 with corrections to the Cover Date.     

The strip dielectric breakdown model

This paper reports on the analysis of the strip dielectric breakdown (DB) model for an electrically impermeable crack in a piezoelectric medium based on the general linear constitutive equations. The DB model assumes that the electric field in a strip ahead of the crack tip is equal to the dielectric breakdown strength, which is in analogy with the classical Dugdale model for plastic yielding. Using the Stroh formalism and the dislocation modeling of a crack, we derived the relationship between the DB strip size and applied mechanical and electrical loads, the intensity factors of stresses and electric displacement, and the local energy release rate. Based on the results, we discussed the effect of electric fields on fracture of a transversely isotropic piezoelectric ceramic by applying the local energy release rate as a failure criterion. It is shown that for an impermeable crack perpendicular to the poling direction, a positive electric field will assist an applied mechanical stress to propagate the crack, while a negative electric field will retard crack propagation. However, for an impermeable crack parallel to the poling direction, it is found that the applied electric field does not change the mode I stress intensity factor and the local energy release rate, i.e., the applied electric field has no effect on the crack growth.