Microrotation has an important effect at the tip of a crack where the stress gradient is large. The growth of a crack is by geometry a bifurcation of crack plane due to incompatibility of microrotation at the crack tip. By means of S(strain)-R(rotation) decomposition theorem developed recently in mechanics of finite deformation, with the concept of incompatibility of finite microrotation, a geometric criterion of fracture is proposed. The criterion is available to analyse crack growth, microcrack nucleation and crack branching. We suggest also a new fracture parameter-microrotation toughness, which is useful in estimating the ability in resisting rupture due to incompatibility of microrotation in polycrystalline material. A determination of displacement field within 0.2 mm range around a crack tip is made by photo-engraving a fine-grid on a tension specimen. The results show the value of the new criterion.
