Cleavage Fracture of Polycrystalline Aggregates

Abstract

BOTH Cottrell1 and Petch2 consider that the fracture process is divided into two parts: (1) the formation of a crack nucleus by dislocation coalescence; (2) the growth of this crack until it reaches a critical size when cleavage fracture spreads catastrophically. Using the well-established relationship between the lower yield stress and grain size3 they show that fracture should just be able to occur at the yield point when: where σy is the lower yield stress, ky is a grain size parameter related to the stress required to unpin a dislocation, β is a mechanical restraint factor, μ is the shear modulus and γ is the effective surface energy of the fractured faces. The effective surface energy, γ, required to produce cleavage fracture in a correctly orientated grain includes a plastic work term and will be larger than the true surface energy. However, it will be smaller than the specific energy G1c, (called the plane strain fracture toughness by Irwin4) required to propagate the fracture through a large number of randomly orientated grains. Thus the size of the microcracks predicted by the Cottrell model1 (using the effective surface energy γ) is an order of magnitude smaller than those observed by Hahn et al.5. Microcracks can only grow larger than one grain under the yield stress given by equation (1) if there are adjacent grains the orientations of which are favourable. Therefore only a small proportion of the microcracks formed will be able to grow large enough to enable the energy release to be sufficient for fracture propagation through a randomly orientated structure.