applied fracture mechanics

Foundations of Measurement Fractal Theory for the Fracture Mechanics 57Figure 21. Counting boxes (or strechts) with rectangular sizes L xH where the boxes that recoverso othe profile have different extensions in the horizontal and vertical directions.Making up the counting boxes (or stretch) with rectangular sizes Lo xHowhere the boxesrecovering the profile have different extensions in the horizontal and vertical directionsrespectively, i.e., Ho lothe equation (72). Is simplified to:2H2 l oL Lo1 .L o (74)which plot is shown in Figure 22.The graph in Figure 22 shows the influence of the roughness dimension on the rugged cracklength, L , in function of the projected length, L0. Note that for H0 1.0 , corresponding toa smooth surface, the relation between the rugged and projected length becomesincreasingly linear. While for H0 0 , which corresponds to a rougher surface, the therelation between the rugged and projected length becomes increasingly non-linear.Figure 22. Graph of the rugged length, L , in function of the projected length, L0, showing theinfluence of the Hurst exponent H , in the fractal model of the fracture surface.Note that for Lo Ho, one has, from the equation (62) and (68) the following relationship: l oLo hoL o H,(75)