applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 795.3.1. Relationship between the elastic energy released rate rates for smooth, projected andrugged cracksUsing the chain rule, it is possible to write G0in terms of G ,dLG0 G (46)dLThe energetics equivalence between the rugged surface and its projection establishes thatthe energy per unit length along the rugged path is equal to the energy per unit length alongthe projected path. Notice thatsince dL dL0 1 , therefore,dUdLL000dUL (47)dLG0G. (48)The elastic energy released rates for the projected and rugged paths are, respectivelyand2L0 * 0 0dU m LG0 (49)dL E'0 02rdU Lm* LG .(50)dL E'Combining these expressions and including, for comparison, the elastic energy released ratefor a smooth path, one has for infinitesimal crack lengths,dLlm * dLG0 Gl GdL dL0 0(51)Considering that the smooth crack length is equal to the projected crack length, one hasm* dLG0 Gl G dL0(52)Observe that the difference between the elastic energy released rate for the smooth, ruggedand projected cracks is the ruggedness added on crack during its growth. Using athermodynamic model for the crack propagation, it can be concluded that a rugged crackdissipates more energy than a smooth crack propagating at the same speed.