Investigation On The Interaction Mechanism Of Dislocations With Micro-structures In Composite Materials

Theory of dislocations possesses a very important position in solid mechanics, solid-state physics and materials science. The interaction of dislocations with microstructures (inhomogeneity, interface and crack) is one of the basic theoretical problems in the micromechanics of composite materials. It has important theoretical significance and scientific value for studying the mechanical characteristic and other physical nature.In the present thesis, the interaction mechanism between dislocations and typical inhomogeneities with partially interfacial defects is investigated systematically in composite materials. And the theoretical investigation of the interaction between dislocations and embedded nano-sized inhomogeneities is also considered. The previous investigation involving the interaction between dislocations and inhomogeneities is restricted to the perfect bonding along the interface. This is a convenient idealization of a more complex situation. In addition, the case of the defects at the whole interface had been considered in some previous papers, such as, sliding interface and imperfect interface. 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. Additionally, the previous study is also restricted to the case that the size of the inhomogeneity is equal to the micron dimension or larger than it. If the cross-section of the inhomogeneity has the dimension in nanometer range, the interaction mechanism of dislocations with inhomogeneities will be changed gravely due to the intensive interface effect and size effect. Considering the above practical cases, the problems of the interaction between dislocations and inclusions with partially interfacial defects is dealt with by the use of the general complex variable method and an efficient method for a complex multiply connected region which is developed by the author and collaborators. A series of closed solutions are obtained and the influence of partially interfacial defects upon the interaction between dislocations and inhomogeneities is evaluated. The interaction of dislocations with nano-sized inhomogeneities in nanocomposites is also studied by using the interface stress model and the new interacting mechanism is derived. The detail achievements obtained in this paper are expressed as follows.The interaction of the dislocation and the inhomogeneity with interfacial defects (interfacial cracks and interfacial rigid lines) is dealt with. Three problems are considered: the elastic interaction between an edge dislocation and a circular inhomogeneity with interfacial defects; the magnetoelectroelastic interaction between a generalized screw dislocation and a circular inhomogeneity with interfacial defects; the elastic/electroelastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial defects. A rigorous solution of the image force on the dislocation is derived explicitly. The influence of the length of the interfacial defects, material mismatch and the shape of the inhomogeneity on the equilibrium positions of the edge dislocation near the inhomogeneity is discussed. It is shown that, if the inhomogeneity is hard, an unstable equilibrium point may be available when the edge dislocation moves to the surface of the crack from infinity; if the inhomogeneity is soft, a stable equilibrium point may be available when the dislocation moves to the surface of the rigid line. When the length of the crack or rigid line goes up to a critical value, the presence of the interfacial crack or rigid line can change the interaction mechanism between an edge dislocation and a circular inhomogeneity. The screw dislocation can be repelled by the soft inhomogeneity due to their intrinsic magnetoelectromechanical coupling behavior. If the magnetoelectroelastic constants of the inhomogeneity are larger than those of the matrix, the impact of the interface crack on the image force is great. If the constants of the inhomogeneity are smaller than those of the matrix, the impact of the interface rigid line on the image force is significant. If the case of the hard inhomogeneity and the interface crack is considered, there is a critical value of the curvature of the elliptic inhomogeneity to alter the direction of the image force on the dislocation near the inhomogeneity. The location of the equilibrium point of the dislocation is variable intensively with the change of the curvature of the elliptic inhomogeneity when the dislocation approaches the inhomogeneity.The interaction between the screw dislocation and the interphase layer or the coating layer with interfacial defects is dealt with. Two problems are considered: the electroelastic interaction of a piezoelectric screw dislocation with an interphase layer between the circular inclusion and the matrix; the interaction between a screw dislocation and a circular coated inhomogeneity with interfacial defects. A rigorous solution of the image force on the dislocation is derived explicitly. The influence of the parameters of the interphase layer (thickness and materials constants) and length of the interfacial defects on the equilibrium positions of the dislocation is discussed. The results show that the impact of the inhomogeneity on the dislocation can be shielded and the equilibrium positions of the dislocation can be changed by the interphase layer. If the electroelastic constants of the inhomogeneity and the matrix are smaller than those of the interphase layer, an unstable equilibrium point of the dislocation may be available in the interphase layer. When the electroelastic constants of the inhomogeneity and the matrix are larger than those of the interphase layer, a stable equilibrium point of the dislocation may be available in the interphase layer. If the case of the hard coating and the interface crack is considered, the repulsive force acting on the dislocation can be weakened and there is a critical value of the length of the interfacial crack to alter the direction of the image force. If the case of the soft coating and the interface rigid line is considered, the attractive force acting on the dislocation can be weakened and there also exists a critical value of the length of the interfacial rigid line to alter the direction of the image force. For the case of the hard coating and the interface crack, the repulsive force on the dislocation increases with increment of the thickness of the coating layer and there is a critical value of the thickness to alter the direction of the image force. For the case of the soft coating and the interface rigid line, the attractive force on the dislocation increases with increment of the thickness of the coating layer and there is a critical value of the thickness to alter the direction of the image force.The problem involving the interaction effects between a wedge disclination dipole and the circular inhomogeneity or interfacial cracks is investigated. The image forces acting on the disclination dipole center and the stress intensity factors at the tips of the interfacial crack and are calculated. The equilibrium position of the disclination dipole is discussed for material property combinations and various crack geometries. The influence of the orientation, the dipole arm and the location of the disclination dipole as well as the material mismatch on the stress intensity factors is also discussed. The results show that an equilibrium point of the dipole may be available near the inhomogeneity under certain material combination. There is a critical value of the ratio of two material elastic constants to alter the direction of the image force acting on the disclination dipole center. The disclination dipole has significant shielding and anti-shielding effect on the stress fields at the tip of the crack and the impact of it increases with the rigidification of the material where the dipole is located. The investigation of the interaction between dislocations (screw and edge dislocations) and nano-sized inhomogeneities is studied. Two problems are considered: the interaction of the dislocation with the nano-sized inhomogeneity by using the interface stress model and the contribution to the critical shear stress caused by the interaction; the stability of straight-line dislocations inside a nano-sized cylindrical inhomogeneity. The exact expressions of the image force, the contribution to the critical shear stress of the material and the critical radius of the inhomogeneity of the dislocation stability in the nano-sized inhomogeneity are derived. The results show that the dislocation can be repelled (attracted) by a soft (hard) nano-sized inhomogeneity with interface stress under same conditions. If interface effects are considered, an optimal value of the contribution to the critical shear stress may be obtained when the radius of nano-sized inhomogeneity reaches a critical value under certain conditions. Additionally, there also exists a critical volume fraction to determine the maximal contribution to the critical shear stress of the material. If the radius of inhomogeneity is fixed, there is a critical value of the relative shear modulus between the inhomogeneity and the matrix to change the dislocation stability in the inhomogeneity. The interface stress can change not only the property of the dislocation stability in the nano-sized inhomogeneity, but also the value of the critical radius of inhomogeneity under certain conditions.The interaction between screw dislocations and a nano-sized coated inhomogeneity with interface stresses and the interaction of screw dislocations with multiple nano-sized inhomogeneities are investigated. The exact expression of the image force is derived. The results show that the influence of the value and the direction of the interface stress on the equilibrium position of the screw dislocation is significant and will enhance with the decrease of the thickness of the coating layer. The composite materials may be toughened by the hard nano-sized coated inhomogeneity and may be strengthened by the soft nano-sized coated inhomogeneity when the interface effects are considered. The magnitude of the image force exerted on the dislocation produced by multiply nano-sized inhomogeneity is smaller than that produced by a single nano-sized inhomogeneity and the influence of the direction of Burgers vector and the location of the closer dislocations on the mobility of the appointed screw dislocation is very significant.