Study Of The Mode Ⅲ Interfacial Crack-tip Considering The Strain Gadient Effect

There is an impending need to deal with design and manufacturing issues at the level of micros and submicros, along with science and technology developing. Good foundation can be given by the recent strain gradient theory, which can solve those problems.The background and the significance of the strain gradient are expatiated in this paper. The characteristic and interrelation of four strain gradient theories, such as CS strain gradient theory, SG strain gradient theory, MSG strain gradient theory and a new strain gradient theory are given. The equilibrium equation, the geometric equation, the constitutive equation and the strain energy function are obtained. Applications in fracture mechanics and the status of the four strain gradient theories are also expatiated in this paper.In this paper, the couple stress and rotational gradient vector are introduced, and the couple stress theory are expatiated. the constitutive equations and simple boundary conditions of couple stress theory are obtained.The mode â…¢ interfacial crack between elasticity and rigidity is studied by the couple stress theory and the strain gradient theory. The boundary conditions are obtained in the simple boundary conditions of the couple stress theory. By asymptotically analyzing, the stress, strain and displacement of the mode â…¢ interfacial crack-tip between elasticity and rigidity are obtained. And the high singulary stress has r^-3 singularity near the interfacial crack-tip. The symmetric stress and the anti-symmetric stress, strain and displacement of the mode â…¢ interfacial crack-tip between elasticity and rigidity are similar to local solution on mode â…¢ crack-tip by Reference [103].The foundation for further studying the strain gradient theory and applying the strain gradient theory to the fracture mechanics can be given by the result of this paper.