Elastic, Viscoelastic And Moving Interaction Between Composite Materials With Typical Defects And Screw Dislocations

The interaction of dislocation, inhomogeneity and interfacial defects is a greatly significant subject in the fields of solid mechanics and materials science. The elastic, viscoelastic and moving interaction effects between interfacial cracks or rigid line inclusions and screw dislocations are investigated in this paper. The solutions for screw dislocations interacting with circular interfacial defects in cylindrically anisotropic composites, viscoelastic interaction between a screw dislocation and elastic or piezoelectric inhomogeneity with interfacial defects, a uniformly moving dislocation interacting with interfacial defects in piezoelectric or anisotropic bimaterials are presented.Using Riemann-Schwarz's symmetry principle of complex functions, the above problems are transformed into Riemann-Hilbert boundary problems. By combining the analysis of singularity of complex functions, generalized Liouville's theorem, Cauchy model integral and Laplace transform method, the general solutions of above problems are provided. For special example, the closed form solutions to complex potentials in matrix and inhmogeneity regions are derived explicitly when interface contains a single crack or rigid line, and the appropriate expressions of the stress or electro-elastic field intensity factors at the tip of crack or rigid line are examined. Applying perturbation technique, the image force on dislocation is obtained. The dependence of stress intensity factors at the crack or rigid line tip and image force on materials'properties, the length of interfacial crack or rigid line and the velocity of moving dislocation are calculated, plotted and discussed.As a result, analysis and discussion show that the influence of interfacial crack or rigid line inclusion on the interaction between screw dislocation and inhomogeneity is significant, and when the length of defects reach a critical value, the interface cracks lead to the hard inhomogeneity attracting dislocation and the interfacial rigid lines result in the soft inhomogeneity repelling dislocation. The anisotropic properties of cylindrically composites can change the shielding or anti-shielding effects, which arise from screw dislocations, of the interfacial crack of rigid line tip, and also impact the attraction-repulsion mechanism of dislocation and the rotation of dislocation dipole enormously. Due to the viscoelasticity of materials, when the time increases, the soft inhomogeneity may repulse dislocation, the image force decreases dramatically first and then evolves toward a steady-going value, the influences of piezoelectricity of material and the length of interfacial defects on image force attenuate obviously, the image force acting on dislocation will change direction in the case of interfacial defects keeping some lengths. The velocity of moving dislocation can weaken the stress intensity factors at the tips of interfacial defects, and change the equilibrium position of dislocation.The provided results can not only offer a scientific basis for the design of composite structures but also provide basic solutions to further investigation on the strength and toughness of structures. The present solutions can be used as Green functions to obtain a series of solutions of related problems, and also contain a number of previously known results which can be shown to be special cases.