ABSTRACT
Abstract The failure stress of a cracked quasi-brittle solid scales with the solid's geometrical dimensions at the two extremes of behaviour. With large solid dimensions, where the material non-linearity is confined to the immediate vicinity of the crack tip, linear elastic fracture mechanics procedures are applicable. The other extreme is where the solid dimensions are small when material non-linearity spreads completely across the uncracked ligament of the solid, and limit load procedures are applicable. The scaling factors associated with these two extremes of material/geometry behaviour are different. By analysing simple models, the paper shows how these two extremes are approached, and demonstrates how scaling is not strictly viable in the transition regime between the two extremes. More importantly, the paper formulates criteria which define, for a wide range of softening behaviours, the critical dimensions below which a limiting stress approach can be used and above which linear elastic fracture mechanics procedures are applicable. Keywords: Dimensions, scaling, fracture, quasi-brittle. 1 Introduction A characteristic of quasi-brittle materials is that in the vicinity of a macroscopic crack tip there is a zone of partially fractured material; examples are concrete, rock, particulate reinforced ceramics, composites with brittle matrices, rubber-toughened polymers and ceramics themselves, where the non-fracturing is provided by the interlocking of crystals. What happens in practice is that, when a pre-cracked solid is loaded, the crack extends leaving a zone of partially fractured material between the
actual and initial crack tips. This behaviour is in marked contrast with that of a metallic type material where there is a zone of plastic deformation at a crack tip.
