Models of self-affine cracks in brittle and ductile materials

Crack faces in solids are modelled as non-standard patterns whose standard parts are self-affine fractals. The morphological and mechanical features of brittle and ductile fracture are discussed. A concept of equivalent traction is employed to obtain the asymptotic stress fields near the crack tip, which in turn used to derive the relations between nanofracture and macrofracture toughness for brittle and ductile materials.