PSI - Issue 28

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

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combination of sliding, climbing, propagation difficult, see Pokluda and Pippan (2005). This complex process represents combination of sliding, climbing, sticking, slipping and also deformation of metal grains. Several older studies are devoted to analysis relationship between the fracture morphology generated under variation of combined bending-torsion loading. In these studies, the fracture surface was described using several types of roughness parameters. These roughness parameters were applied on profiles extracted in both parallel and perpendicular directions with respect to the fatigue crack propagation. This approach is very good in the case pure bending or in the situation where torsional stress components are significantly smaller than components caused by bending loading. We can also say, that this approach is effective in the case, where shear loading modes II a III insignificant in comparison to the mode I or opening mode. This is due to the fact, that in the case of a higher proportion of torsion, it becomes an important choice. This problem can be easily explained in the following Fig. 1.

Fig. 1. Influence of length and orientation on profile choice: (a) long profile – global view; (b) short profile - description of local condition.

The individual profiles are usually selected to start at the crack initialization point. On this figure you can see fatigue crack with stop lines and profiles parallel and perpendicular to the direction of crack propagation. On the left side of figure, you can see long profiles denoted p x1 a p y1 , on the right side you can see four other areas in which we selected significantly shorter profiles. Long perpendicular profiles have disadvantage, because their individual sections are at different distances from the respective stop lines. In the case of a more complex morphology, even profiles oriented in the direction of crack propagation (in the region of crack initialization) cannot fully maintain their orientation (in accordance with the local direction of crack propagation) along their entire length. Certain disadvantages also result from the definition itself of selected roughness criteria used in these studies. In order to evaluate different aspects of roughness several types of parameters were used in cited articles. For example, amplitude parameters (which are often used) dependent only on changes in vertical z-coordinate are represented by the root mean roughness, R q , arithmetic roughness, R a , and the vertical range, R z . These quantities are defined as

1 2 2 

1 n

  

n







R

z z



 

(1)

q

i

m



1

i



1 n n  i

i  

(2)

R

z z



a

m

1

(3) where n is the number of valid data for points on the profile. These data are therefore these values: z m is the mean height value, z max and z min are the highest and the lowest profiles points respectively. Two other commonly used max min z R z z  