applied fracture mechanics

78Applied Fracture MechanicsOr, by using equations (17) and (26) in (35), one has22 2H2m*rL0H0 l 012H2 0.2 E' l 0L 0 (40)Irwin defined the elastic energy released rate G and the fracture resistance R in equation(34), likeandThese definitions can be extended to the terms in equation (35), soGand00 R0G0dL0dF ( U L)G (41)dLdUR .(42)dLdF ( U L) (43)dU0R0 .(44)dLNotice that the proposal made by Irwin extended the concept of specific energy efftothe concept of R-curve given by equation (42), allowing to consider situations where themicrostructure of the material interacts with the crack tip. In this way, it is assumed thatthe surface energy is dependent on the direction of crack growth.Finally, using equations (41) and (42) in (36), the Griffith-Irwin criterion is obtained,0dL dLG R .(45)dL dL0 05.3. Comparative analysis between smooth, projected and rugged fracturequantitiesBased on the results of the previous section, further analyses of the magnitudes of theFracture Mechanics are performed in order to obtain a mathematical reformulation for anirregular or rugged Fracture Mechanics.