applied fracture mechanics

Foundations of Measurement Fractal Theory for the Fracture Mechanics 51d D0,L L (52)dividing the entire expression (52) above by the minimum Mishnaevsky size one has:LaL a 0 d D,(53)orwhered D0,N N (54)NLa: is the number of crack elements a on the non-projected crackN L a : is the number of cracl elements a on the crack projected0 0and yet:where: : is the scaling factor of the fractal crackd : is the Euclidean dimension of the crack projectionD : is the crack fractal dimension. aL 0 ,(55)Within this context the number of microcracks that form the macroscopic crack is given by: a N L o D.(56)In this context (in Mishnaevsky model), the above expression is volumetric and admits cracksbranching generated in the fracture process with opening and coalescence of microcracks.However, he continue equating the process in a one-dimensional way reaching an expressionfor the crack propagation velocity. A complete discussion of this subject, using a self-affinefractal model to be more realistic and accurate, can be done in another research paper.The answer to the question about what should be the best scale to be used for fractal fracturescaling is then given as follows: being the limit of the crack length Lkin any scale, given byLk L (actual size) as well as lk lmin, the value of the minimum size ruler, l 0it must beequal to the minimum crack size, a ( 4 ), given by Mishnaevsky [70], through its energybalance for the fracture of a single monocrystal of the microstructure of a material. Thephysical reason for this choice is because the Mishnaevsky minimum size is determined by a4It is possible that this minimal ruler size be very low than the scale used in fractal characterization of the fracturesurfaces. However, it must to be the smallest possible size for a microcrack.