applied fracture mechanics

50Applied Fracture Mechanicsand Figure 17b) with thickness e 0 . In this case the area of rugged surface can bewritten as:A Le,(49)Figure 17. Scaling of a rugged profile of a fracture surface or a crack, using the Mishnaevsky minimumsize as a "measuring ruler"; a) in the case of a crack is a non-fractal straight line, where D d 1 ; b) inthe case of tortuous fractal crack, with its projected crack length, where d Dd 1 .and the area of the projected surface asA0 Le 0 ,According to the equation (48) the valid relationship is: (50)d Dk o kL( ) L ,(51)where, L( k)is the measured crack length on the scale k, L0is the projected crack lengthmeasured on the same scale, in a growth direction.4.2.8. The self-similarity relationship of a fractal crackThe fracture is characterized from the final separation of the crystal planes. Thisseparation has a minimum well-defined value, possibly given by theory Mishnaevsky Jr.(1994). If it is considered that below of this minimum value the fracture does not exist,and above it the crack is defined as the crystal planes moving continuously (and theformed crack tip penetrates the material), so that an increasing number of crystal planesare finally separated. One can in principle to use this minimum microscopic size as a kindof ruler (or scale) for the measurement of the crack as a whole( 3 ), i.e. from the start pointfrom which the crack grows until its end characterized by instantaneous process of crackgrowth, for example.The above idea can be expressed mathematically as follows:3During or concurrently with its propagation, in a dynamic scaling process, or not