The stress distribution at the tip of a crack can be expanded as a power series. The first term, usually called the stress intensity factor, determines the initiation of fracture in a brittle material. In this paper it is shown that the second, third and fourth terms have the following effects: (a) the second term controls the stability of the crack's direction, (b) the third term controls the stability of the crack's propagation, (c) the fourth term determines whether the maximum shear stress on the prolongation of the crack increases or decreases with distance from the crack tip.