Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.

Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave （SH-wave）. An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green＇s function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.

SINGULAR BEHAVIORS OF INTERFACIAL CRACKS IN 2D MAGNETOELECTROELASTIC BIMATERIALS

The singular characteristics of stress, electric displacement and magnetic induction fields near the tip of impermeable interracial cracks in two-dimensional magnetoelectroelastic bimaterials are studied using the generalized Stroh formalism. Two types of singularities are obtained： one is the oscillating singularity 1/2±iε, the other is the non-oscillating singularity 1/2±κ. It is found that the non-zero parameters ε and κ cannot coexist for one transversely isotropic MEE bimaterial, a similar result is obtained for transversely isotropic piezoelectric bimaterials.

Interaction between heat dipole and circular interfacial crack

The heat dipole consists of a heat source and a heat sink. The problem of an interracial crack of a composite containing a circular inclusion under a heat dipole is investigated by using the analytical extension technique, the generalized Liouville theorem, and the Muskhelishvili boundary value theory. Temperature and stress fields are formulated. The effects of the temperature field and the inhomogeneity on the interracial fracture axe analyzed. As a numerical illustration, the thermal stress intensity factors of the interfacial crack are presented for various material combinations and different positions of the heat dipole. The characteristics of the interfacial crack depend on the elasticity, the thermal property of the composite, and the condition of the dipole.

INTERFACIAL CRACK ANALYSIS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC BI-MATERIALS BY BOUNDARY INTEGRAL EQUATION METHOD

The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.

HIGHER-ORDER ANALYSIS OF NEAR-TIP FIELDS AROUND AN INTERFACIAL CRACK BETWEEN TWO DISSIMILAR POWER LAW HARDENING MATERIALS

By means of an asymptotic expansion method of a regular series, an exact higher-order analysis has been carried out for the near-tip fields of an in- terfacial crack between two different elastic-plastic materials. The condition of plane strain is invoked. Two group of solutions have been obtained for the crack surface conditions: (1) traction free and (2) frictionless contact, respectively. It is found that along the interface ahead of crack tip the stress fields are co-order continuous while the displacement fields are cross-order continuous. The zone of dominance of the asymptotic solutions has been estimated.

Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole

The interaction between screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under loads at infinity is studied. The closed-form solution is derived for complex potentials. The stress intensity factor and the critical applied stress for the dislocation emission are also calculated. In the limiting cases, well-known results can be obtained from the present solutions. Moreover, new exact solutions for a screw dislocation interacting with some complicated cracks are derived. The results show that the shielding effect increases with the increase in the length of the other cracks and the minor semi axis, but decreases with the increase of dislocation azimuth. The repulsion acting on the dislocation from the other phase and the other crack extend in the horizontal direction, which makes the dislocation emission at the crack tip take place more easily, but the minor semi axis of the elliptical hole extending in the vertical direction makes it more difficult.

ANALYSIS OF A SCREW DISLOCATION INSIDE A CIRCULAR INCLUSION WITH INTERFACIAL CRACKS IN PIEZOELECTRIC COMPOSITES

The electroelastic interaction of a screw dislocation inside a circular inclusion with inteffacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann-Schwarz＇ s symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach-Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has a significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green＇s functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.

ELECTROELASTIC INTERACTION BETWEEN A PIEZOELECTRIC SCREW DISLOCATION AND A CIRCULAR INHOMOGENEITY WITH INTERFACIAL CRACKS

A piezoelectric screw dislocation in the matrix interacting with a circular inhomogeneity with interfacial cracks under antiplane shear and in-plane electric loading at infinity was dealt with. Using complex variable method, a general solution to the problem was presented. For a typical case, the closed form expressions of complex potentials in the inhomogeneity and the matrix regions and the electroelastic field intensity factors were derived explicitly when the interface contains single crack. The image force acting on the piezoelectric screw dislocation was calculated by using the perturbation technique and the generalized Peach-Koehler formula. As a result, numerical analysis and discussion show that the perturbation influence of the interfacial crack on the interaction effects of the dislocation and the inhomogeneity is significant which indicates the presence of the interfacial crack will change the interaction mechanism when the length of the crack goes up to a critical value. It is also shown that soft inhomogeneity can repel the dislocation due to their intrinsic electromechanical coupling behavior.

PERIODICAL INTERFACIAL CRACKS IN ANISOTROPIC ELASTOPLASTIC MEDIA

By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .

Penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers

A penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectromechanical loads is investigated,where the magnetoelectrically impermeable crack surface condition is adopted. By using Hankel transform technique,the mixed boundary value problem is firstly reduced to a system of singular integral equations,which are further reduced to a system of algebraic equations. The field intensity factors and energy release rate are finally derived. Numerical results elucidate the eects of crack configuration,electric and/or magnetic loads,and material parameters of the magnetoelectroelastic layers on crack propagation and growth. This work should be useful for the design of magnetoelectroelastic composite structures.

ANALYSIS OF CRACK-TIP SINGULARITIES FOR AN INTERFACIAL PERMEABLE CRACK IN METAL/PIEZOELECTRIC BIMATERIALS

By modeling metal as a special piezoelectric material with extremely small piezoelectricity and extremely large permittivity, we have obtained the analytical solutions for an interracial permeable crack in metal/piezoelectric bimaterials by means of the generalized Stroh formalism. The analysis shows that the stress fields near a permeable interracial crack tip are usually with three types of singularities： r^-1/2±iε and r^-1/2. Further numerical calculation on the oscillatory index ε are given for 28 types of metal/piezoelectric bimaterials combined by seven commercial piezoelectric materials： PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-7A, P-7 and PZT-PIC 151 and four metals： copper, silver, lead and aluminum, respectively. The explicit expressions of the crack tip energy release rate （ERR） and the crack tip generalized stress intensity factors （GSIF） are obtained. It is found that both the ERR and GSIF are independent of the electric displacement loading, although they seriously depends on the mechanical loadings.

INVESTIGATION OF THE BEHAVIOR OF A GRIFFITH CRACK AT THE INTERFACE BETWEEN TWO DISSIMILAR ORTHOTROPIC ELASTIC HALF-PLANES FOR THE OPENING CRACK MODE

The behaviors of an interface crack between dissimilar orthotropic elastic half-planes subjected to uniform tension was reworked by use of the Schmidt method.By use of the Fourier transform,the problem can be solved with the help of two pairs of dual integral equations,of which the unknown variables are the jumps of the displacements across the crack surfaces.Numerical examples are provided for the stress intensity factors of the cracks.Contrary to the previous solution of the interface crack,it is found that the stress singularity of the present interface crack solution is of the same nature as that for the ordinary crack in homogeneous materials.When the materials from the two half planes are the same,an exact solution can be otained.

NEAR-TIP FIELDS FOR A CRACK GROWING ALONG AN ELASTIC PERFECTLY PLASTIC INTERFACE

The stress and deformation fields near the tip of an anti-plane crack growing quasi-statically along an interface of elastic perfectly plastic materials are given in this paper. A family of solutions for the growing crack fields is found covering all admissible crack line shear stress ratios.

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTH CRACK ON ELASTIC-ELASTIC POWER LAW CREEPING BIMATERIAL INTERFACE

A mechanical model was established for modeⅡinterfacial crack static growing along an elastic_elastic power law creeping bimaterial interface. For two kinds of boundary conditions on crack faces, traction free and frictional contact, asymptotic solutions of the stress and strain near tip_crack were given. Results derived indicate that the stress and strain have the same singularity, there is not the oscillatory singularity in the field; the creep power_hardening index n and the ratio of Young's module notably influence the crack_tip field in region of elastic power law creeping material and n only influences distribution of stresses and strains in region of elastic material. When n is bigger, the creeping deformation is dominant and stress fields become steady,which does not change with n. Poisson's ratio does not affect the distributing of the crack_tip field.

NONLINEAR BUCKLING BEHAVIOR OF DAMAGED COMPOSITE SANDWICH PLATES CONSIDERING THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL AND MECHANICAL PROPERTIES

On the basis of the first-order shear deformation plate theory andthe zig-zag deformation as- sumption, an incremental finite elementformulation for nonlinear buckling analysis of the composite sandwichplate is deduced and the temperature-dependent thermal and mechanicalproperties of composite is consid- ered. A finite element method forthermal or thermo-mechanical coupling nonlinear buckling analysis ofthe composite sandwich plate with an interfacial crack damage betweenface and core is also developed.

Tuning of non-uniform switch toughening in ferroelectric composites by an electric field

This paper deals with a mode III interfacial crack subject to anti-plane stress and in-plane electric fields. The analysis concentrates on the tuning of fracture toughness from non-uniform ferroelectric-ferroelastic domain switching by an electric field. The electric loading changes the size of the asymmetric switching zone. Employing the weight function method, we obtain the electrically-dependent switch toughening for stationary and quasi-static growing interfacial cracks, respectively. Multi-domain solutions are derived for non-poled and fully-poled ferroelectric composites. Numerical results are presented on the electric field tuning of the critical applied stress intensity factor. The research provides ways to optimize fracture properties of ferroelectric composites by altering the electric field.

Swell induced stress in a hydrogel coating

A hydrogel can be coated on various substrates to enable multiple functions.Potential applications include biomedical devices,anti-fouling surfaces and microfluidics.In practical use,hydrogel coatings are often submerged in fluids.The swell of hydrogel coating deteriorates the interfacial bonding with the substrate.This paper presents a stress analysis of a hydrogel coating on a cylindrical metal substrate.We adopt the thermodynamic theory coupling large deformation and water migration and formulate two boundary value problems for the coating-substrate system with and without an interfacial crack.The inhomogeneous stress fields in the hydrogel coating are obtained.The influences of modulus,thickness of the hydrogel coating on the maximum radial stress at the interface are analyzed.These results may guide the design of hydrogel coating to avoid interfacial failure.