Crack Length Scaling

With the empirical rule adopted to determine the core phase shift, it is important to check the extent to which the core phase actually corresponds to physical reality. We have commented on the fact that the cores do visually exhibit mode shifts, even though we have not been able to use a measured value of in our interpretations. There is one important physical prediction which the elastic theory makes regarding to the phase shifts which must be valid for the actual simulated cracks, and that is the scaling of the phase shift in the core with the crack length, from (). We have noted that the core phases can be reasonably well measured for large elastic mismatch, and for this case, we have investigated the scaling law.

For this excercise, we use in the Uber force law, and measure the value for in the cleavage plane core. We do this by finding the load which makes the shear in the core zero as measured in the simulation, and then set set in (). For this case, , and the condition we seek is for the sin to be zero, or . That is, the load phase is also the core phase. This computation is performed for several crack lengths, and if the core phase shift angle is a physically valid concept, then should be independent of the crack length.

Figure is a plot of the measured core size for the largest range of crack lengths which are possible in our computer, remembering that very short cracks will not be a fair test of the elastic theory. The simulation was done with the UBER force law, with on the interface, and with the unstable stacking fault in material 2 . Certainly for this case, at least, crack length scaling of the core phase is excellent until short cracks are encountered.