Emission Variation with Interface Bonding

The principle results are shown in the following figures. Figure shows the critical emission, , for a fixed value of the unstable stacking fault, in the normalized units of the simulation. This choice represents a relatively weak material above the interface, corresponding to the ductile material above the interface, and brittle material below. There are six series of plots, one for each choice of elastic mismatch, and one for each type of force law. For a given choice of force law type and elastic mismatch, the range parameter in the interfacial connecting bond was varied to get a range of values of . Figure shows plotted against for each case. At the lower limiting value for , cleavage on the interface intervenes, and emission does not occur for any combination of loads. The upper limit is set by the fact that the range parameter becomes so short that the hexagonal lattice is no longer stable under shear load.

The plot shows a fairly narrow band of points with a linear slope. That is, all the various cases are represented by a single linear functionality in , which must be considered remarkable in view of all the variables which condense onto this one. But there is an interesting detail in this plot which goes beyond the linearity in . That is, there is a clear lower plateau in several of the plots. Further, these plateaus are all at roughly the same limiting value of 0.01, which is also roughly the value of the unstable stacking fault used in the simulations ().

The first comment about these results is that our rule to set the core radius, , to the range parameter in the force law appears to be an an excellent way to calculate core phase shift effects.

Second, these results are consistent with the findings of ZCT[] in the homogeneous case, and are also consistent with the prediction of Thomson and Carlsson[] that the emission criterion for low values of reverts to the Rice form. However, the functionality observed in Fig. is not quantitatively that predicted by Thomson and Carlsson[]. Those authors predict a linear law, crossing the axis at a finite intercept, , such that , where A is a number which may depend on the elastic constants. That is, the lower shelf or plateau is not predicted by Thomson and Carlsson[], even though a limiting value of is. But the plateau values of fall in the range of , which is the intercept value from Thomson and Carlsson. Thus, Fig. gives support to the general ideas expressed in the work of ZCT[] and Thomson and Carlsson[], even though their predictions are not borne out, quantitatively.