The processes of crack growth and dislocation emission as induced by a crack tip were investigated. A crystal with a cubic lattice of atoms, under plane-strain conditions, was considered. Both ductile and brittle crack growth mechanisms in the crystal were examined at the nano- and interatomic scales. Only the fundamental constants of the classical theory of dislocations were used, including the interatomic spacing, elastic constants, Schmid friction constant and true surface energy of the crystal lattice. Efficient solution of the elastic problem for an arbitrary number of dislocations near to the crack tip was possible in terms of complex potential functions. The equilibrium of dislocation pairs near to the crack tip during monotonic loading was studied. It was shown that dislocation generation at the crack tip occurred at certain quantum levels of the external load. The magnitude of the external load which corresponded to crack-growth initiation and emission of the first pair of dislocations was calculated. The mathematical problem of an arbitrary number, n, of dislocation pairs near to the crack tip was reduced to a parametric system of n non-linear equations in which the stress intensity factor of the external load played the role of a parameter and n played the role of discrete time. The minimum value of the stress intensity factor at which the solution of this system of equations existed corresponded to the stress intensity factor at which the nth pair of dislocations was generated. A numerical method was used to determine the minimum value of the stress intensity factor. The approximate self-consistent field method was used to reduce the order of the system of non-linear equations. The approximate method was used to calculate the fracture curve which related the level, of stress intensity which maintained crack growth, to the crack length increment. The exact solution was also studied, and numerical results were obtained for a crack in an Al specimen for quantum levels of the external load which corresponded to the moments of dislocation generation and values of the superfine stress intensity factor for up to 150 dislocations.

Dislocation Generation and Crack Growth under Monotonic Loading. G.P.Cherepanov, A.Richter, V.E.Verijenko, S.Adali, V.Sutyrin: Journal of Applied Physics, 1995, 78[10], 6249-64