A Discrete Cohesive Model for Fractal Cracks

The fractal crack model described here incorporates the essential

features of the fractal view of fracture, the basic concepts of

the LEFM model, the concepts contained within the

Barenblatt-Dugdale cohesive crack model and the quantized

(discrete or finite) fracture mechanics assumptions. The

well-known entities such as the stress intensity factor and the

Barenblatt cohesion modulus, which is a measure of material

toughness, have been re-defined to accommodate the fractal view of

fracture.

For very small cracks or as the degree of fractality increases,

the characteristic length constant, related to the size of the

cohesive zone is shown to substantially increase compared to the

conventional solutions obtained from the cohesive crack model. In

order to understand fracture occurring in real materials, whether

brittle or ductile, it seems necessary to account for the

enhancement of fracture energy, and therefore of material

toughness, due to fractal and discrete nature of crack growth.

These two features of any real material appear to be inherent

defense mechanisms provided by Nature.