Modelling of dislocations pile-ups at crack tip. Application to silicon

Abstract

ABSTRACT The mechanical analysis of plastic zones at crack tip has progressed very little since the publication of the founding BCS model, 60 years ago. This two-dimensional model, and those that followed, consider the plastic zone as a pile-up of dislocations of one sign only. They assume that the crack absorbs the part of the dislocation loop of the opposite sign. Here the real three-dimensional problem is addressed and we demonstrate that the crack front behaves as an obstacle. This change of paradigm requires the plastic zone to be modelled as a two-sign dislocation pile-up. The model fits well with experimental observations in bulk silicon. In addition, the presence of dislocations of opposite signs completely modifies the amplitude of crack shielding. The closer the dislocation is to the crack front, the more significant the effect. Therefore, the increase in toughness observed experimentally is linked to the part of the loop attached to the crack front, and not to the expanding part of the loop. This conclusion is in direct contradiction to that provided by previous models.