applied fracture mechanics

76Applied Fracture MechanicsWhere UT is the total energy, Uiis the initial potential elastic energy, F is the work done byexternal forces, ULis the change of elastic energy stored in the body caused by the introductionof the crack length L0and U is the energy released to form the fracture surfaces.One can now add the contributions of U L 0and U 0to reproduce Griffith´s energybalance in a fractal vision. In other words,andU U U U F(31)T i L2 22 2H2 2 2H2d L0H 0l 02L oH 0l 0( Ui 1 1 F ) 0dLl2E l 0L 0 2 l 0L 0(32)This new result is shown in Figure 3, which is analogous to the traditional Griffith energybalance graphs, but distorted due to the roughness of the fracture surface. Observe that for areference total energy value the roughness of the crack surface tends to increase the criticalsize of the fractureL L . This isL compared to a material with a smooth fracture 0Cdue to the roughness being a result of the interaction of the crack with the microstructure ofthe material.lCCFigure 3. Griffith´s energy balance in the view of the fractal geometry of fracture surface roughness.5.2. The modification of Irwin in Griffith´s energy balance theory for smooth,rugged and projected cracksIrwin found from Griffith´s instability equation, given by (29), that this instability shouldtake place by varying the crack length, so