Crack-tip dislocation emission arrangements for equilibrium-II. Comparisons to analytical and computer simulation models

Theoretical analyses of thin film effects on an apparent dislocation free zone (DFZ), grain boundary effects on the number of dislocations required for equilibrium and a tip-emission condition to avoid the Rice paradox are compared to the in situ TEM study of Part I. It is first shown that the apparent DFZ is a thin film artifact and, second, that a grain boundary blocked slip band may require half as many dislocations for equilibrium compared to no blockage. It is further shown that the "DFZ" becomes diminishingly small for even relatively low applied stress intensities. Based on a disappearing "DFZ", an asymptotical solution of Li's grain size analysis leads to the number of dislocations in equilibrium for a given applied stress intensity, friction stress and grain size. With an ad hoc failure criterion, this gives a first order prediction of fracture toughness for a large number of ferritic and ferrite-pearlites steels. Finally, based on local stress distributions obtained from a solution containing tip-emission conditions, it is suggested that a local stress intensity presents a more easily defined brittle fracture criterion. This is applied to observations of dislocation arrangements at large applied stress intensity in Part III.