The paper by James R. Rice analyzes dislocation nucleation from a stressed crack tip using the Peierls concept. The analysis assumes a periodic relationship between shear stress and atomic shear displacement along the most highly stressed slip plane emanating from the crack tip. This allows for small slip displacement near the tip under applied loading, which, with increasing loading, becomes unstable and leads to the formation of a fully formed dislocation that moves away from the crack. An exact solution for the critical loading at the nucleation instability is developed using the J-integral when the crack and slip planes coincide, and an approximate solution is provided when they do not. The paper also discusses the emission of dissociated dislocations, particularly partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to \(\sqrt{\gamma_{us}}\), where \(\gamma_{us}\) is a new solid-state parameter identified as the unstable stacking energy. The results are used to evaluate the brittle vs ductile response in fcc and bcc metals, showing that in many cases, solids predicted to first cleave under pure mode I loading should instead emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis also reveals the feature of the near-tip slip distribution corresponding to the saddle-point energy configuration for cracks loaded below the nucleation threshold, which is of interest for thermal activation.The paper by James R. Rice analyzes dislocation nucleation from a stressed crack tip using the Peierls concept. The analysis assumes a periodic relationship between shear stress and atomic shear displacement along the most highly stressed slip plane emanating from the crack tip. This allows for small slip displacement near the tip under applied loading, which, with increasing loading, becomes unstable and leads to the formation of a fully formed dislocation that moves away from the crack. An exact solution for the critical loading at the nucleation instability is developed using the J-integral when the crack and slip planes coincide, and an approximate solution is provided when they do not. The paper also discusses the emission of dissociated dislocations, particularly partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to \(\sqrt{\gamma_{us}}\), where \(\gamma_{us}\) is a new solid-state parameter identified as the unstable stacking energy. The results are used to evaluate the brittle vs ductile response in fcc and bcc metals, showing that in many cases, solids predicted to first cleave under pure mode I loading should instead emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis also reveals the feature of the near-tip slip distribution corresponding to the saddle-point energy configuration for cracks loaded below the nucleation threshold, which is of interest for thermal activation.