Investigations On The Interaction Between Dislocations And Cracks/Inclusions With Imperfect Interface

The interaction of dislocations, inhomogeneities and cracks is a greatly significant subject in the field of solid mechanics and materials science. It has important theoretical significance and scientific value for studying the mechanical characteristic and other physical nature of the materials. For the interaction of dislocations with inclusions, interfacial property is one of the important factors that control the stress fields as well as the image forces on the dislocations. The previous investigation involving the interaction between dislocations and inhomogeneities, a basic assumption was made that the bonding along the interface of two dissimilar materials is perfect. This is an idealization of the complex practical problem. In fact, this condition effectively ignores the presence of interfacial damage between the inclusion and the matrix, for example, damage arising from imperfect adhesions, microcracks and microvoids. It was realized that the significance of damage or imperfection of the interface, in any mechanical analysis, is paramount in understanding the physical behavior of composite materials. Additionally, the partially defects at the interface can be produced inevitably in the manufacturing and using of composite materials. Interfacial cracks and interfacial hard line inclusions are two typical cases.In the present thesis, the interaction of the dislocation and the inhomogeneity with imperfect interfaces is dealt with. Three problems are considered: the elastic interaction between screw dislocations and embedded multiple circular cross-section inhomogeneities with imperfect interfaces in composites; the elastic interaction between multiple screw dislocations, which are located at arbitrary points inside either the matrix or the inhomogeneity, and a coated inhomogeneity with imperfect interfaces; the electroelastic coupling interaction between multiple screw dislocations and a circular inclusion with imperfect interface in piezoelectric solid. In addition, the problems of the elastic interaction between a screw dislocation dipole and a circular inhomogeneity with interfacial defects (interfacial cracks and interfacial rigid lines) as well as the interaction between a wedge inclination dipole and a surface wedge crack are investigated. Lasting, Green's functions of an interfacial crack between an elliptic inclusion and an unbounded matrix in anisotropic materials are presented for a line force and a line dislocation. The detail achievements obtained in this paper are expressed as follows.A three-phase composite cylinder model is utilized to studying the elastic interaction between screw dislocations and embedded multiple circular cross-section inclusions (fibers) with imperfect interfaces in composites. By means of complex variable techniques, the explicit solutions of stress and displacement fields are obtained. With the aid of the Peach-Koehler formula, the explicit expressions of image forces exerted on screw dislocations are easily derived from the solutions of stresses. The motion of the appointed screw dislocation and its equilibrium positions near one of the inclusions are discussed for variable parameters (interface imperfection, material mismatch and dislocation position) and the influence of the nearby dislocations and inclusions is also considered. The results show that the screw dislocation is always attracted by the imperfect interfaces. The effect of material elastic dissimilarity on the image force and the equilibrium position of the appointed screw dislocation becomes weak when the degree of interface imperfection is strong. It is also seen that the magnitude of the image force exerted on the appointed dislocation produced by multiply inclusions is always smaller than that produced by a single inclusion and the impact of the closer dislocations on the mobility of the appointed dislocation is very significant.The theoretical investigation of the interaction between multiple screw dislocations, which are located at arbitrary points inside either the matrix or the inclusion, and a coated inhomogeneity with imperfect interfaces in composites is considered. By means of complex variable techniques, the explicit solutions of stress and displacement fields are obtained. With the aid of the Peach-Koehler formula, the explicit expressions of image forces exerted on screw dislocations are easily derived from the solutions of stresses. The motion of the appointed screw dislocation and its equilibrium positions are discussed for variable parameters (interface imperfection, material mismatch and dislocation position) and the influence of the nearby dislocations is also considered.The electroelastic coupling interaction between multiple screw dislocations and a circular inclusion with imperfect interface in 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 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 electro-mechanical imperfect interface. When the degree of interface imperfection is high, the impact of material electroelastic mismatch on the image force and the equilibrium position of the dislocation becomes infirm. Additionally, the effect of the nearby dislocations on the mobility of the appointed dislocation is very important.The problem of the elastic interaction between a screw dislocation dipole and a circular inhomogeneity with interfacial defects is studied. By using the complex variable method, the closed form solutions of complex potentials and the stress fields produced by the screw dislocation dipole are obtained when the dipole is located in one media. The stress intensity factor at the tip of the crack/rigid line and the image force and the image torque acting on the screw dislocation dipole center are also calculated. The influence of screw dislocation dipole upon stress intensity factor and the equilibrium position of the screw dislocation dipole is examined for various material property combinations and interfacial crack/rigid line geometries. The results show that the screw dislocation dipole has significant shielding or anti-shielding effect on the stress intensity factor, and the hard inhomogeneity always repels the screw dislocation dipole while the interface crack (rigid line) always attracts (repels) it and the screw dislocation dipole can not exist in the neighbor of crack under some combination of them. If the length of the crack or the ratio of two shear moduli reaches a critical value, the presence of the crack can change the interaction mechanism between the dipole and the interface. In addition, the influence of the crack length on the equilibrium of the dipole is significant.The interaction between a wedge disclination dipole and a surface wedge crack is considered. By means of complex variable techniques, the problem is transformed into Riemann-Hilbert boundary value problem. The explicit solutions of stress and displacement fields are obtained. The stress intensity factor at the tip of the crack and the image force and the image torque acting on the wedge disclination dipole center are also calculated. The equilibrium position of the wedge disclination dipole near the tip of the surface wedge crack is examined. The shielding or anti-shielding effect of the wedge disclination dipole on the stress intensity factor is also considered.The Green's functions of an interfacial crack between an elliptic inclusion and an unbounded matrix in anisotropic materials are presented for a line force and a line dislocation. An effective complex potential method for complex multiplying connected region is developed by combining the Stroh formalism, the sectional holomorphic functions, the techniques of conformal mapping, Cauchy-type integral and Laurent series expansion techniques, in terms of which the explicit series form solutions for Green's functions are derived. Based on the obtained complex potentials, the stress intensity factors at the tips of the interfacial crack are evaluated. Using the perturbation technique, the image forces acting on the line dislocation are also calculated. The present solutions contain previously known results.