applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 99H1 H1 l0 l0J02 e(2 H) p(2 H) ,L0 L0 elasticplastic(105)For the particular situation where J0 JICand L0 L0C , it can be derived from equation(97),2 2 l 0JIC e pH L0CH1(106)and from equation (72), l oKIC (2 e p) E(2 H)L oc H1(107)Therefore, using the fact that once the experimental value of J ICis determined and thefitting of J-R curve has already yielded the values 2 e p , l 0and H for the material, thevalueL0Ccan be calculated.Fracture Mechanics science was originally developed for the study of isotropic situationsand homogeneous bodies.At the microscopic level, the elastic material is modeled considering Einstein’s solidharmonic approximation where Hooke's law is employed for the force between the chemicalbonds of the atoms or molecules [48]. Therefore, the elastic theory is used to make linearapproximations and it does not involve micro structural effects of the material.At the mesoscopic level the equation of energy used for the fracture does not take intoaccount effects at the atomic scale involving non-homogeneous situations [47]. Based on thearguments of the last paragraphs, it becomes clear why Herrmman et al. [49] needed toinclude statistical weights, as a crack growth criterion, for the break of chemical bonds infracture simulations, as a form of portraying micro structural aspects of the fracture (defects)when using finite difference and finite element methods in computational models.At the macroscopic level, on the other hand, Griffith’s theory uses a thermodynamic energybalance. It is important to remember that the linear elastic theory of fracture developed byIrwin and Westergaard and the Griffith’s theory are differential theories for the macroscopicscale, which means they are punctual in their local limit. These two approaches involve themicro structural aspects of the fracture, since they take a larger infinitesimal local limit thanthe linear elastic theory at the atomic and mesoscopic scales. This infinitesimal macroscopicscale is big enough to include 10 15 particles as the lower thermodynamic limit, where thephysical quantity Fracture Resistance (J-R Curve) portrays aspects of the interaction of thecrack with the microstructure of the material.