applied fracture mechanics

82Applied Fracture MechanicsanddL (65)U lU R lR dL 0In postulate III it was assumed that the rugged crack path satisfies the same energeticconditions of the plan path, but in the LEFM this roughness is not taken into account,causing discrepancies between theory and experiments. For example, it has not beenpossible to explain by an analytical function in a definitive way the growth of the GRcurve. The proposed introduction of the term dL / dL0allows correcting this problem.6. The elastic-plastic fractal fracture mechanicsThe non-linear elastic plastic energy released rate J0for a crack of plane projected path canbe extended from the Irwin-Orowan approach. They introduced the specific energy ofplastic strain pon the elastic energy released rate G0to describe the fracture phenomenonwith considerable plastic strain at the crack tip. Thus, it is possible to define the elasticplastic energy released rate in an analogous way to the definition of the elastic energyreleased rate,wheredF ( UVo)Jo (66)dLoUVois the volumetric strain energy given by the sum of the elastic and plastic ( Upl)contributions to the strain energy in the material.6.1. Influence of ruggedness in elastic plastic solids with low ductilityConsidering elastic plastic materials with low ductility where the effect of the plastic term issmall compared to the elastic term, one can define a crack growth resistance aswhere ( )JRoKRo2 f( v) ,(67)Ef v is a function that defines the testing condition. For plane stress f v1for plane strain 2f v 1 v and K Ro is the fracture toughness resistance curve., andDue to the ruggedness, the crack grows an amount dL dL0and correcting equation (59),one hasSimilarly,dUdL dLR 2 .(68)dL dLdLo e poo