1. Introduction
Post-mortem analysis is a fundamental engineering procedure to identify the damage accumulation mechanisms associated with fatigue failure. This analysis may provide important clues to improve a material’s performance, to evaluate both structural and mechanical properties and to mitigate the damage mechanisms [
1,
2,
3].
Much research connected with surface metrology has been focused on extensive investigations in which 3D surface roughness parameters have been presented in light of the relationship between surface properties and operation properties [
4,
5,
6,
7,
8]. Although this analysis provides useful information, post-failure fractographic surface examinations allow the cause of failure in materials to be determined [
9,
10,
11,
12]. Researchers have studied the characteristics of fractured surfaces using observational tools, from macro- to nanoscale [
13,
14,
15,
16,
17]. Unfortunately, even though advanced methods such as optical coherence tomography [
18], scanning acoustic microscopy [
19] or energy response approach based on strain energy density histories during variable loading [
20,
21] are described in the literature, usually simple-fracture qualitative analysis conducted with scanning electron microscopy is employed for the evaluation of surface fractures resulting from impact [
22,
23], tensile strength [
24,
25], fatigue [
5,
19], ultra-high fatigue [
26], adhesion testing [
27] or even wear damage description [
28,
29]. However, few studies have investigated the use of profile and surface roughness as a tool for fatigue fracture characterisation.
Moreover, there are few papers devoted to the quantitative analysis of fracture surfaces in elements undergoing combined bending–torsion loading histories [
30,
31,
32,
33]. Therefore, the present study aimed to investigate bending–torsion fatigue fractures in order to establish the dependence between the loading scenario and the characteristic features of their surfaces. The literature describes the influence of loading conditions on the topography of fracture surfaces via either local terms (i.e., crack propagation and rupture) [
34,
35,
36,
37,
38] or based on analysis of the total fracture area [
39,
40]. In this work, the results of both approaches (local and total fracture zones) for specimens with different geometries were compared for three materials. The local approach was defined as the application of linear measurement, and therefore the Ra parameter. Two sections, Ra propagation and Ra rupture, were measured in the study. The first was measured at a distance of about 1 mm from the crack initiation, while the second was measured close to the splitting of the sample into two parts. The total approach was defined by the Sa parameter. In this case, almost an entire fracture surface was analysed. For different loading scenarios (which encompassed bending, torsion and bending–torsion), 2D and 3D surface texture measurement methods were adopted, and the main results were critically compared.
3. Results and Discussion
The fracture plane analysis revealed that, in S355J2 steel samples, the cracks initiated in the plane of maximum shear stresses and then propagated in the plane of maximum normal stresses (
Figure 6a). In contrast, in notched samples, due to the significant predominance of normal stresses, initiation and propagation of cracks took place in the plane of maximum normal stresses (
Figure 6b).
Figure 7 shows representative surface texture measurement results for both total areas and for local profiles (in terms of propagation and rupture). In
Figure 7, the blue frames represent total fracture areas, the propagation profile is shown in green, and the rupture profile is shown in red. In contrast, in the black frame and without the frame, the whole views of fatigue fractures are presented with the measurement areas and profiles marked. In fact, as anticipated in
Figure 5, comparison of the different evaluated parameters for the three materials showed important differences, like greater roughness—for both areas and profiles—in the rupture zone than in the propagation zone.
Thanks to the 3D parameters (S-), surface shape and direction can be assessed. The fracture surface presented large disorderly peaks. Therefore, in the case of the 2D parameters (R-), the randomness and the fortuitousness of the measurement profile direction and location on the surface are important.
Some generic features of the tested specimens (e.g., the dependence of roughness parameters in individual areas on the bending, torsion or combined loading type) that were initially noticed in the measurement results were analysed in this part of the study. For further analysis, Ra and Sa were selected from R- and S-parameters. These parameters demonstrated the best fit, evident dependence on the loading condition and widespread use, regardless of the measuring technique, which was also presented for other studies of fracture surface topography (e.g., in [
8]).
Figure 8 presents an extract of all analysed results for Ra and Sa, by type of loading. Without qualifying the method and place of measuring the fractured surface, it can be seen that, generally, the highest values occurred for a mixed-mode loading and the lowest for torsion.
Figure 9a–c presents the results of all specimens divided into three analysed ways of identifying the fracture (i.e., total area, propagation profile and rupture profile, respectively). For the results of measurements of the total fracture surface Sa parameter (likewise Ra for the propagation profile), the highest values and the greatest dispersion were obtained for bending–torsion. The 10HNAP specimens were the exception. For this case, the torsion Ra parameter had the highest values (
Table 5). In the case of torsion, for which only measurements of samples (a) and (c) were taken, the latter took the lowest values.
In statistical terms, the dependence of surface parameters on the type of loading was presented using box plots with, among other things, percentiles. On each box (
Figure 10), the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the “+” symbol.
As shown in
Figure 10a, the median Sa for all bending specimens was approximately 100 μm. The minimum value was about 10 μm, and the maximum value was about 550 μm. For bending–torsion and torsion, respectively, these values were median Sa 340 μm and 150 μm, minimum values 110 μm and 100 μm, and maximum values 750 μm and 270 μm. Next, taking into account only the medians for propagation area (
Figure 10b), Ra was about 5 μm for bending, 10 μm for bending–torsion and 28 μm for torsion loadings. For rupture area, the measurements were 7 μm, 14 μm and 21 μm.
Table 6 summarises the medians extremum of measurement results for all specimens broken down into reference area and loading scenario. Clear relationships between the size of surface parameters for individual analysed fracture zones are shown in
Figure 4,
Figure 5,
Figure 6,
Figure 7,
Figure 8,
Figure 9 and
Figure 10.
The value of the Ra parameter depends on the place and direction of orientation of the measuring section, and the values for individual measured zones differ. For example, the influence of the asymmetry factor is ambiguous because, for bending, the Ra values increase with the stress ratio R, and for the combination of bending with torsion, this relationship is reversed. Therefore, the results may be ambiguous. However, the influence of the stress ratio R on the value of the Sa parameter showed an increase of this parameter along with an increase in the cycle asymmetry factor from −1 to 0, which is consistent with previously obtained results [
53]. The magnitude of the load also affected all roughness parameters. The values of the roughness parameters Sa and Ra changed with the load; however, this relationship did not change proportionally. For example, for the aluminium alloy, a double increase in the load for the coefficient R = 0 caused the Sa parameter to increase by 10%, while the Ra propagation parameters decreased by 14% and Ra rupture by 25%. In the case of the tested steels, when analysing the influence of load on roughness, one should also pay attention to the influence of the ratio of shear stresses to normal stresses. When the samples were subjected to loads with a predominance of bending stresses, the parameters Sa and Ra decreased, while if the influence of shear stresses increased, the roughness parameters increased. Similar conclusions - linear functions between topography parameters and fatigue variables were found by authors in [
54]. It is worth noting that the notch, which was the initiator of fatigue cracks and which increased the effect of normal stresses, had a significant influence on the parameter values. Among the examined materials, the smallest differences in the variability of Ra parameters were presented by the aluminium alloy, while in the case of steel, the spans were greater. The Sa parameter, as the surface parameter, is independent of the orientation of the measurement direction, making it a more universal value.