A Study Of The Crack Nucleation Based On The Stress Release Of The Wedge Disclination Dipole

The study of the problems that the nucleation of a Zener crack from a wedge disclination dipole in alloy materials and composite materials has important theoretical significance and scientific value for studying the fracture toughness and other mechanical behavior of alloy materials and composite materials. It is one of the most active areas in the current research.In this paper, the interaction of a Zener crack forced open by a wedge disclination dipole, an elastic circular inhomogeneity and interface is systematically investigated. The original problems can be decomposed into multiple sub-problems with the continuous distributed dislocation technique. By means of complex variable technique, the solutions of the sub-problems are obtained. The formulated Cauchy-type singular integral equations are then solved numerically. The obtained detail achievements are expressed as follows. The nucleation of a Zener crack from a wedge disclination dipole in the presence of a circular inhomogengity is investigated. The characteristics of the nucleated cracks and the influence of the elastic mismatch between the inhomogeneity and matrix, the disclination strength, the distance between the inhomogeneity and disclination dipole, the dipole arm length and inhomogeneity size on the stress intensity factors are systematically studied.The numerical results show that the elastic mismatch between the inhomogeneity and matrix is the most distinct factor that influences the disclinated crack nucleation. All our results indicate that a'soft'inhomogeneity intends to attract the sharp tip of the nucleated crack while a'hard'inhomogeneity intends to repel it. The other parameters such as the distance between the inhomogeneity and disclination dipole and the inhomogeneity size will weaken or strengthen the influence of the elastic mismatch on the crack nucleation when their value changes. The problem of the nucleation of a subinterfacial Zener crack from a wedge disclination dipole is studied with consideration of a contact zone at the sharp crack tip. The singularity behavior of the dislocation density functions and stress components are analyzed in detail. It is found that the normal stress is bounded at the sharp crack tip but singular at the blunt crack tip where a contact zone exists; while the shear stress has square-root singularities at both the crack tips. The influence of the dislocation Burgers vector, Dundurs'constants, the disclination strength, the dipole arm length and the distance between the crack and the interface on the contact zone and the Mode II stress intensity factor are also given.The nucleation of an interfacial Zener crack from a wedge disclination dipole which lies in the interface is also considered. The influence of the dislocation Burgers vector, Dundurs'constants, the disclination strength and the dipole arm length on the contact zone and the stress intensity factors are studied. the results show that, when the glide dislocation is dominant in the glide dislocation and the climb dislocation, the crack contact zone is large and the absolute value of the stress intensity factors of the crack tip is small. With increasing the climb dislocation, the crack contact zone decreases and the absolute value of the stress intensity factors increase. The other parameters such as the disclination strength also have important influence on the crack contact zone and the stress intensity factors.