PSI - Issue 28

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

565

5

bands. These bands are characterized by fixed width ε . The root mean roughness Rq (parameter already known to us) is calculated for each band, and then averaged over all possible bands: (5) 1 k

1 k    i

R

R

, q i

q

Finally, the wanted exponent H is obtained from log-log plot according to the power law in form:

H

( ) W   

(6) In previous studies, the relationships between bending-torsion loading and fracture morphology was studied, see Balankin (1997) and Slámečka et. al. (2008). The state of combined loading was characterized by loading ratio L R . This loading ratio takes value between 0 and 1. These two values correspond to the pure-bending loading and pure torsion. The loading ratio L R , is defined as: (7) where σ a and τ a are stress amplitudes under bending and torsion loading respectively. In cited studies the significant influence of torsion loading on growth of roughness was shown for both low-cycle and high-cycle fatigue. On the other hand, it must be said, that the roughness described significantly at the edge of the sample with higher portion of sheer stress amplitudes τ a for the case of high-cycle fatigue. 2. Proposed method of morphology description In order to circumvent some of the shortcomings of the ways of describing the quarry area, a slightly different approach has been proposed. Individual studied areas of the surface (as well as the entire fracture area) can be covered with small flats (triangles or squares) which can be characterized by a vector. These vectors are well known from mathematics. This vector is perpendicular to the respective surface (flats) and its size corresponds to the size of the surface. One of the ways to create a faithful 3D-model of the studied area of stereophotogrammetry SEM. The output of such a reconstruction is a set of points coordinates x , y , z , that correspond points on the fractures surface. While the quality of the reconstruction increases with the number of points on studied surface. The set obtained in this way is processed by means of triangulation, thanks to which the surface is covered with a large number of triangles. Because these triangles are very small, we prefer to calculate the mean values of the directional angles for small squares. This step will be useful as soon as we start statistically processing the results. Suppose, we have an elementary square on the fracture surface. There are g triangles in this square. Normal vector of one particular triangle (in a triangulation network) is characterized by normal vector , T i j n  . The subscript j indicates the order of the triangle in a triangulation network. Variable A i,j represents the area size of an elementary triangle. The size of the area A i,j is important for the calculation of the mean vector of the elementary square, i.e. it is actually a weighting factor: (8) Then we determine the angle α between the mean normal vector �⃗ � � and the sample axis, � � ���� ���� . The angle � � ��� corresponds to the surface perpendicular to the sample axis. In a similar way, we can also determine the angular deviation from the primary direction of crack propagation. This angle is called β . Its meaning is evident from Fig. 3, whereas � � ������ ���� . It should be added that while the evaluation of the meaning of the angle α can be a R a a L      , T i j n A  , i j 1 , i j 1 g j M i g j n  A      