Crack Stability Diagram.

The crack stability diagram is a generalization of a graphical description of the Griffith criterion for simple homogeneous cracks. That is, for a straight crack in homogeneous material, the Griffith condition is

and is graphed in space as a simple circle. In continuum elasticity, the crack is stable so long as the loads correspond to stress intensity factors lying on the Griffith circle. In the lattice, a crack will be stable over a region in -space containing the Griffith circle, because of lattice trapping. More important, the stability of the crack will be limited by the ability of the core of the crack to sustain shear stresses, and beyond some critical shear, the lattice will break down with emission of a dislocation. A diagram showing such a stable region of loading is shown in Fig. 1 (Use axes ). As explained in the introduction, when the crack is on an interface, the critical parameter for cleavage or emission is not the bare remote or lab stress intensity factor, but the local quantity for the core, Eqn. (5).

A generalization of the stability diagram valid for the interface, for simple straight cleavage on the initial cleavage plane, or for nonblunting emission on that plane, will now look like the full Fig. 1. Here, the local stress intensity factors are rotated relative to the remote axes by the core phase angle, , where the core phase angles for emission and cleavage are assumed to be the same. It is important to note that, except for a term, the -force for a straight interface crack is an invariant in the crack length, and does not contain the phase shift[].

When the crack branches or kinks off the interface ( is assumed), the more general expressions for the local stress intensity factors must be used, and now a contour plot for the values of constant plotted in the remote or lab system of stress intensity factors, is shown in Fig. 2. In the figure, the simple case of zero lattice mismatch (no interface) is shown contrasted with that where the spring constants of the two lattices differ by a factor of 10 (). Note that even when the interface mismatch disappears, the maximum gradient of is rotated off the axes, and the presence of a remote Mode II enhances the tendancy to branch.

The crack stability diagram is completed when the limiting values of cleavage corresponding to dislocation emission and shear breakdown are provided by means of emission criteria for the particular force law. These criteria and actual points for specific cases are plotted on these diagrams in the next section.

Finally, events on the inclined (kinking) plane will compete with events on the initial interface, and by plotting event loci on the stability diagram, it is possible to determine when, for example, emission of a dislocation on the inclined plane will occur before cleavage on the interface, etc.