PSI - Issue 28

Stepan Major et al. / Procedia Structural Integrity 28 (2020) 561–576 Stepan Major/ Structural Integrity Procedia 00 (2019) 000–000

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amplitude parameters are the skewness, S and the kurtosis, K (see Dong et al. (1994) or Gadelmawla et al. (2002)) were not found suitable for quantification of investigated fracture surfaces, Major (2010). As a representative of spacing parameters, the number of peaks per unit length, m 0 , was also used in mentioned work. During the calculation of m 0 , peaks are counted only when the distance between the current peak and the proceeding one is greater 10% of the vertical range R z . Hybrid parameters that reflect both the vertical heights and the spatial connections of profile points are represented by the linear roughness, R L , see Gadelmawla et al. (2002). This dimensionless quantity is determined as the fraction of the true profile length L over its projected length L P onto the macroscopic crack plane: (4) The striking continuity of “roughness structure” through several orders of magnification, has been observed many times. This list of roughness parameters is far from complete. In addition to the mentioned parameters, there are many others in literature. However, the shortcomings of these parameters (when used in fractography) can be easily explained here. On the Fig. 2 are two profiles marked (a) a (b). In each of them we marked three sections on which we measure the value of R a . The second profile (b) is characterized by a significant height step in the middle of the length. You can see, that in the case of short sections (for couple of profiles marked p 1a and p 1b , and also for second couple p 2a and p 2b ), the measured value R a will be same. This is caused by the fact, that the distances between the individual points in both profiles are the same. On other hand, the distances between points differ substantially in the case of measurement on long sections marked as p 3a and p 3b . It is therefore clear, that both the orientation, and the length of the profile significantly affect the results. Which is a problem, if we want to use these parameters to quantify the fracture process. This, is the reason, why a different approach was chosen in this work. In this work, fracture morphology is described by the means of directions vectors of elementary surfaces, that cover analyzed fracture surface. to the description of the fracture surface in this work. L P R L L 

Fig. 2. Effect of profile length on the roughness calculation. (a) Profile with roughness R a(a) , which was calculated along its entire length, is divided into two equally long parts, each of which is characterized by its own partial roughness R a1 (red) and R a2 (blue). (b) The second profile is composed from two same partial profiles, which are characterized by same partial roughness, but these two parts are mutually shifted, e.g. final roughness R a(b) is different. We will now mention fractal parameters briefly. The idea that the fracture surface can be treated as fractal, is now well accepted. In the case of fracture surfaces generated in metallic materials, the fracture surfaces are self-affine rather than self-similar. On the contrary, fracture surfaces in brittle materials (for example concrete) are self-similar. Due the fact, that the fracture surface is self-affine, fractal dimension D is not appropriate for its description. Systems that exhibit self-affine behavior are described by the means of Hurst exponent H . The Hurst exponent takes values between zero and unity. This fractal parameter is calculated with the use so-called bandwidth method (often known by the acronym as the VBM-method). When calculating its value, the studied profile is divided into k moving windows or