*3.2. Discrete Dislocation Models*

The formulation of the discrete dislocation models for continuous elastic-plastic cracks was discussed earlier (Section 2.2). Here we present some results of our calculations [14]. Since the computations are quite involved, the analysis could only be undertaken for microscopically sized cracks. In Figure 11, the effect of μ, the ratio of friction stress to applied stress on the growing elastic-plastic cracks is shown. With the decrease of μ, the glide component increases with the cleavage component. Figure 11 shows the slope of the log(applied stress) vs. the log(crack length) decreases with the decrease of μ. Nevertheless, the exponential relation remains with the exponent of σ vs. a decrease from 0.5. Figure 12 shows the total energy of the growing crack as a function of crack size for two μ values, 0.6 and 0.8, based on the calculations reported in ref. [14]. The crack grows along the path that has lower energy. The figure shows that glide and cleavage components fluctuate until the crack becomes unstable. The relative proportions of the two components vary depending on the μ value. Experiments undertaken with varying H concentrations support these results.

**Figure 11.** Discrete dislocation analysis of continuous elastic-plastic cracks for various μ values.

**Figure 12.** Changes in the relative glide and cleavage components with the change in μ values for continuous elastic-plastic cracks.
