Dislocation generation and crack growth under monotonic loading

The processes of crackgrowth and dislocation emission induced by the crack tip are investigated. A crystal with cubic lattice of atoms under plane strain conditions is considered. The main principles of the nanofracture mechanics approach employed in this study are outlined. Both ductile and brittle mechanisms of crackgrowth in the crystal are examined in nano- or interatomic scale. Only the fundamental constants of the classical theory of dislocations are used which include the interatomic spacing, elastic constants, the Schmid friction constant, and the true surface energy of crystal lattice. The efficient solution of the elastic problem for an arbitrary number of dislocations near the crack tip is obtained in terms of complex potential functions. The equilibrium of dislocation pairs near the crack tip during monotonic loading is investigated. It is shown that dislocation generation at the crack tip occurs at certain quantum levels of external load. The magnitude of external load corresponding to crackgrowth initiation and emission of the first pair of dislocations is calculated. The mathematical problem for an arbitrary N number of dislocation pairs near the crack tip is reduced to a parametric system of Nnonlinear equations, where the stress intensity factor of external load K I plays the role of parameter and N the role of discrete time. The minimum value of K I at which the solution of this system of equations exists corresponds to the stress intensity factor at which the Nth pair of dislocations is generated. The numerical method is presented to determine the minimum value of K I . The approximate method of self-consistent field is employed to reduce the order of the system of nonlinear equations. The approximate method is used to calculate the fracture curve K I (l c ) relating the value of K I which maintains the crackgrowth to the crack length increment l c . The exact solution is also studied, and numerical results are given for a crack in an aluminum specimen and involve the quantum levels of external load corresponding to the moments of dislocation generation and the values of the superfine stress intensity factor up to 150 dislocations.