Investigation On The Interaction Mechanism Of Generalized Dislocations With Typical Complicated Micro-structures In Non-homogeneours Materials

The interaction of dislocations with micro-structure is one of the interesting and important problem in the micro-mechanics and other physical area. Theory of dislocation and its application is a live and expanding field.In this dissertation, considering composite materials with dislocations and complicated micro-structure, the long-range ineraction or short-range ineraction mechanism between generalized dislocations (screw dislocation, wedge disclination dipole and extended dislocation) and interfaces, interfacial cracks, inclusions are systematically studied in composite materials, and the essential character of the mechanical property can be illustrated precisely. The research results not only contribute to the enrichment and development of elasto-plastic damage theory, but also have an important meaning in the practical engineering. The main results contain as follows. By use of the general complex variable method and some techniques(conformal mapping, series expansion et al), an efficient method for a complex multiply connected region which is developed by the author and collaborators.Aseries of closed form solutions, series form solutions and approximate solutions are obtained. The influence of the orientation of the dislocation, the morphology of the crack, the amount and location of the cracks, the shape and amount of the inclusions and the material elastic dissimilarity on the stress fields, image force shielding effect and the emission criterion are elucidated. Especially new rules are founded when reserching the short-range ineraction between the screw dislocations and inclusions. The research not only contribute to the theory of dislocation and complex variable method, but also have an important meaning in the practical engineering. The main results contain as follows.The interaction between a screw dislocation near an interfacial blunt/cruciform crack is dealt with. The conformal mapping technique are creationary used to solve the complicated interfacial crack problem, the mapping function which can map the blunt crack on to the linear crack and at the same time do not change the shape of the interface are constructed. The closed form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interfacial blunt/cruciform crack. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect increases with the increase of the shear modulus of the lower half-plane, but decreases with the increase of dislocation azimuth angle and the distance between the dislocation and the crack tip. The preset electro properties enhance the shielding effect. The critical loads at infinity for dislocation emission increases with the increment of the emission angle and the curvature radius of the blunt crack tip and the vertical length of the cruciform crack, and the most probable angle for screw dislocation emission is zero. The preset electric properties made dislocation emission easier. The remote electric displacement can also make dislocation emission occur.The interaction between a screw dislocation and an interfacial blunt/cruciform crack and collinear linear cracks under loads at infinity is dealt with. The general solutions of complex potentials to thess problems are presented by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the distance between the two cracks. Which means the present of the microcrack can reduces the shielding effect acted on the macrocrack. The critical loads at infinity for dislocation emission increase with the distance between the two cracks. Which means the attraction force acting on the dislocation from the linear crack makes dislocation emission easier. Dislocation emission occur at blunt crack tip can be easier than it occur at sharp crack tip under certain conditions.The interaction between a screw dislocation and a blunt crack in elastic elliptical inhomogeneity is dealt with. Utilizing the Muskhelishvili complex variable method, the explicit series form solutions of the complex potentials in the matrix and the inclusion regions are derived. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. As a result, numerical analysis and discussion show that the positive screw dislocation can reduce the stress intensity factor of the crack tip (shielding effect) only when it is located in the certain region. The shielding effect increases with the increase of the shear modulus of the matrix. The critical loads at infinity for dislocation emission increases with the shear modulus of the matrix. Which means the repulsion acting on the dislocation from the matrix made dislocation emission more difficult.The interaction between wedge disclination dipole and extended dislocation and crack/ inclusion is dealt with. Utilizing the Muskhelishvili complex variable method, the closed form solutions, explicit series form solutions or approximate solutions are derived. The results show that the equilibrium position of the disclination dipole is discussed in detail. The results show that for certain combinations of materials constants, the disclination dipole has a stable equilibrium point near the annular inclusion. the stable equilibrium point is very much affected by the thickness of the annular inclusion. The wedge disclination dipole can reduce the model I or model II stress intensity factor of the crack tip (shielding effect) only when it is located in the certain region. The shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effect of the morphology of the blunt crack on the stress intensity factor of the crack and the image force is very significant. The equilibrium separation increases as the extended dislocation tends to the blunt crack. If the stacking fault energy is comparable to the critical energy for dissociation in a perfect medium, complete dislocations can dissociate to form extended dislocations near the blunt crack. The critical stress intensity factor (SIF) for extended dislocation emission increases with the stacking fault energy and the curvature radius of the blunt crack tip. The critical SIF for extended dislocation emission is far lower than the critical SIF for edge dislocation emission.The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity is investigated. By using the Fourier transform method, closed analytical solutions are obtained when the inhomogeneity and the matrix have the same gradient coefficient. The explicit expressions of image forces exerted on screw dislocations are derived. The results show that the classical singularity is eliminated. Especially, for the case of a tiny inhomogeneity, the relation of dislocations and inhomogeneities become quite different. The screw dislocation may be attracted by the stiff inhomogeneity and repelled by the soft inhomogeneity when it tends to the interface. So there is an unstable equilibrium position when a dislocation tends to a tiny stiff inhomogeneity and there is a stable equilibrium position when a dislocation tends to a tiny soft inhomogeneity.The boundary value problem of a screw dislocation located near two cylindrical inclusions in an infinite elastically isotropic solid is rigorously solved. The dislocation elastic stress, strain energy and image force are obtained in the form of infinite series by the technique of infinite ensembles of image dislocations. The stress field and image force have been analyzed numerically in detail by means of contour maps and vector fields, respectively. The results show that, the inclusions significantly influence the dislocation stress fields, especially when dislocation close to the inclusion. The stress gradient is rather high near the inclusion interfaces. The effect of stress concentration is also observed there. The stress fields around an inclusion are hardly affected by an other inclusion if the two inclusions are not near enough. The harder inclusion can degrade the stress componentσ_xA^z of the area nearby and the softer inclusion can promote the stress componentσ_xA^z of the area nearby. The vector fields of the image force demonstrate that harder inclusions repel the dislocation while the softer inclusions attract the dislocation, and the larger inclusion exerts a stronger force on the dislocation than the smaller one. There exists a position of stable equilibrium for the dislocation between the two hard inclusions and the stable equilibrium position is closer to the inclusion of the smaller radius or lower shear modules. The harder half-space can degrade the stress componentσ_yA^z of the area nearby and the softer half-space can promote the stress componentσ_yA^z of the area nearby. At the line connecting the inclusion axis and the half-space it has a position of stable equilibrium, and the stable equilibrium position is closer to the inclusion. It is also seen that the effect of the inclusion on the image force is essential at the distances of the order of 4r2 from the inclusion axis and can be neglected at larger distances from the inclusion.