applied fracture mechanics

Foundations of Measurement Fractal Theory for the Fracture Mechanics 59L L o(79)It must be noted that the ductile materials by having a high fractality have a crack profilewhich can be better fitted by the equation (76), while brittle materials by having a lowfractality will be better fitted by the equation (79) corresponding the classical model, i.e., aflat geometry for the fracture surface. Furthermore, the cleavage which occurs on themicrostructure of ductile materials tend to produce a surface, where LL0, which could becalled smooth. However, this cleavage effect is just only local in these materials andtherefore the resulting fracture surface is actually rugged.4.3.2. Local Ruggedness of a fracture surfaceDefining the local roughness of a fracture surface, as:dA A A0dA0 dA .(80)owhere A is the rugged surface and A0is the projected surface. In the case of a rugged crackprofile,one has:using (74) in (81), one has that:dL L L0dL0dL (81)o l o1 (2 H)L o l o1 L o 2H22H2(82)From (81) note that when there is no roughness on surfaces (flat fracture) one has that:LL 0, thusdL1.dL (83)odLThe quantity seems be a good definition of ruggedness unlike the definition wheredLothe ruggedness is given by L/L/ /[56, 57] (where L// L0Mcos, see Figure 23) does notsatisfy the requirement intuitive of the ruggednes whenL0, while maintaining, L0 L0M , as shown Figure 23.L0Mis only inclined with respect to