Effect of non-zero mean stress bending-torsion fatigue on fracture surface parameters of 34CrNiMo6 steel notched bars

Abstract Modern methods of testing materials require the use of the latest technologies and combining measurement and calculation methods. It is important to find a quantitative way of describing, among other things, the failures so that it can help to design with high accuracy. This paper studies loading orientations on crack shape and fracture surface changes. The advantage of the entire fracture surface method is simplicity and applicability in studies on other materials, shapes and loadings. A higher values of fracture surface parameters (Sx, Vx) was observed in failure specimens with lower σ/τ (B/T) ratios. It has been observed that largest crack lengths with a small number of cycles occur for loading combinations different then B=T. As well as analyzed surface parameters Sx, Vx, are higher for larger number of cycles to crack initiation (Ni) values.


Introduction
Engineering materials with different geometries and shapes are with their nuances increasingly reflected in fatigue tests (Kowal and Szala, 2020;Ulewicz et al., 2014;Ulewicz et al., 2019;Trško et al., 2020;Wu et al., 2020;Robak, 2020). Loading generation also needs to be developed to get as close as possible to the service conditions, both by standard and a special performance of fatigue machines (Jamali et al., 2019;Rozumek et al., 2018;Saito et al., 2020;Pejkowski et al. 2018). Fatigue and Fracture of metals under bending with torsion loading have been studied by authors of this work (Branco et al., 2018;W. Macek et al., 2020). Similar studies were rarely carried out in the past, but for bending-torsion fatigue studies we would like to mention the publications (Böhm et al., 2015;Carpinteri et al., 2008;Rozumek et al., 2018;Singh et al., 2019;Slámečka et al., 2010;Lachowicz and Owsiński, 2020). Singh et al. (Singh et al., 2019) and Susmel with Petrone (Susmel and Petrone, 2003) also analyzed this type of loading for fatigue crack initiation and propagation behavior. Pawliczek and Prażmowski (Pawliczek and Prażmowski, 2015) have tested S355 steel specimens with mean block bending loadings. Samples after fatigue tests were subjected to metallographic examinations. These papers show how important it is to look at the surface and morphology of material in different scales, e.g. from nano-to macro-scale.
The application of metrological technologies and techniques to understand the fracture mechanisms of studied materials have expanded along with the development of measuring technologies, as noted by among others, Jollivet and Greenhalgh (Jollivet and Greenhalgh, 2015) in composite materials, as well as Goldsmith et al. (Goldsmith et al., 2019) for in-service aircraft crack research, respectively. Vanderesse et al ( Vanderesse et al., 2020) have used three techniques for evaluating the fracture mechanisms, as X-ray computed tomography (XCT), laser scanning confocal microscopy (LSCM), and scanning electron microscopy (SEM). Their studies were conducted for pre-mortem and post-mortem characterizations. Sinha et al. (Sinha et al., 2020) have used X-ray microscopy to examine specimens subjected to tension and found that microstructural flexibility induced different tendencies for void growth and ductile fracture mode. Also optical and laser apparatus for areal surface topography investigation, that allow measure at broad range of scales, are becoming more and more popular. This is recognized and conconcluded by Feng et al (Feng et al., 2019) as well as Senin et al. (Senin et al., 2017) on the example of optical technologies measurements covered, among others, by imaging confocal microscopy (ICM), chromatic confocal microscopy, phase shifting interferometry, coherence scanning interferometry (CSI), point autofocus instruments (PAI), and focus variation microscopy (FVM). Stemp et al. (Stemp et al., 2019) and also Macek et al. (Macek et al., 2020a) used FVM measurement systems for their research on stone tools and fracture surfaces, respectively. Fonte et al. (Fonte et al., 2007) showed results for the fatigue crack surface roughness Ra and Rz according to ISO 4287 (ISO, 1997) with the fatigue crack propagation direction at the center of fracture surface. Although similar roughness results were achieved at the center and at the both sides of the fracture, areal surface Sx parameters according to ISO 25178 (ISO, 2012;Arsalani et al., 2020;Yang et. al., 2019) give complete information because a single line cannot identify pits or valleys and show the relationship between surface function, as confirmed by Stach et al. (Stach et al., 2017). The combination of fatigue testing with the surface metrology by the authors of this work (Macek, 2019a(Macek, , 2019b gave promising results in previous studies. Therefore, it was decided to develop this methodology, based on the entire fracture surface, for testing other materials subjected to bending with torsion.

Material
The fracture analysis and the fatigue tests were done using cylindrical specimens (see Fig. 1) made of low alloy steel grade 34CrNiMo6 (Szala, 2017). The samples were oil quenched and tempered according to the procedure described elsewhere (Branco et al., 2016). The chemical composition and the main mechanical properties are shown in Tables 1 and 2, respectively.

Fatigue test
The fatigue tests were carried out using the fatigue test stand exhibited in Fig. 2. The tests were conducted under constant amplitude loading with three ratios of the bending moment (B) to torsion moment (T), more precisely B/T=2, B/T=1, and B/T=2/3. Three orientations of the bending moment with respect to the notch geometry were considered (see Fig. 1), i.e. =0º, 45º, and 90º. A stress ratio equal to 0 was used.

Fig. 2.
Fatigue test stand with own-made gripping system

Fracture surface measurement
The measurements of surface topography were undertaken through the InfiniteFocus G4, with a FVM technology by Alicona, which was placed on the antivibration table (see Fig. 3).

Fig. 3. FVM Alicona G4 setup
The scanned surfaces, whose textures can be seen in Annex A, have been extracted to the form exhibited in Figure 4. The individual steps for cutting the proper surface are also shown in the first fragment of Figure 6.

Fatigue parameters
In the fatigue tests, the crack length was evaluated at periodic intervals varying between 2000 and 10,000 cycles using a high-resolution digital camera. The number of cycles to crack initiation was defined from the curves relating the surface crack length with the number of cycles for a crack length equal to the characteristic material length, a0 = 129 m.

Surface parameters and their definitions
For the purposes of checking the fracture surface dependency on the fatigue loading history, selected parameters were measured and calculated. Table 3 defines the parameters used in this paper which were selected according to ISO 25178 standard.
Height parameters are a class of surface parameters that quantify the Z-axis perpendicular to the surface. They are included in the ISO 25178 standard. The reference plane for the calculation of these parameters is the mean plane of the measured surface.  Both sides of specimens are fixed to the grips, but both move during the tests. One side rotates, and the other one has rotation and translation movements. The side which was measured and analysed corresponds to the former case. Skewness Ssk means the absence of symmetry distribution, and kurtosis Sku indicates how the results obtained are arranged in relation to the normal distribution.

Results
The methodology of extracting areas and selected results obtained for the fatigue fracture surface by the InfiniteFocus® IF G4 focus variation microscope during the experimental investigations is graphically presented in Fig. 6. All 3D parameters have been calculated on the whole current surface, as marked in Fig. 6. The whole current surface was reduced to eliminate the final break, discontinuities and "non-sampling" areas.

Fig. 6. The whole current reduced surfaces
The effect of B/T ratio on height parameters Sx is shown in Figures 7 and 8. The effect of B/T ration on functional (volume) Vx parameters is displayed in Figure 9. For the sake of clarity, the B/T ratios are accounted for in terms of normal stress to shear stress ratios (/), i.e. / = 2, / = 4, / = 4/3, which correspond to B/T=2, B/T=1, and B/T=2/3, respectively. Generally, positive Ssk indicates the presence of more peaks, while negative Ssk shows the presence of more valleys; a Ssk value close to zero indicates symmetrical distribution of surface irregularities. The normal value distribution has a Sku value equal to 3. The Sku parameter reveals the presence of excessively high peaks or deep valleys on the surface for Sku > 3, and lack of these features for Sku < 3.
The same parts of the sample (grip side) were used for the study of surface topography, which is confirmed by the re-sults. All Ssk values were positive, which indicates the predominance of peaks on the surface. While all Sku values were less than 3 what is related to the absence on the surface of inordinately high peaks or deep valleys.
There is a linear relationship with the σ/τ (B/T) ratio for both the Sx and Vx parameters presented in Figures 7 and 9, respectively. Figure 10 presents crack length 2b relative to number of cycles N for different loading scenarios.    (Sa, Vv) in function of the bending moment angle and the bendingtorsion ratio. It is a box and whisker chart, where the mean marker of the selected series is shown as "x", and "o" represents the data points that lie between the lower whisker and the upper whisker lines. The median is excluded from the calculation if the number of values in the data is odd. The two boxplots, showing the average values of the surface parameters Sa and Vv from the bending-torsion ratio, display the same relationships. That is, the smallest average values of Sa and Vv occur for B/T=2, while the largest occur for B/T=2/3. However, the maximum values were found for two subsequent boxplots presenting the average values of the surface parameters Sa and Vv at a bending moment angle equal to 0 (i.e. θ=0°). Surface parameters changes during the crack process do not influence the characteristics of the surface. This is clear by comparing the results of Sku-Ssk presented in Figure 13, since they are close which means that there was no change in configuration of parameters Sku and Ssk. As mentioned before, all Ssk values were positive, which indicates the predominance of peaks on surfaces. While all Sku values were less than 3 which is connected with the absence of inordinately high peaks or deep valleys on surfaces. Such high compliance results from the measurements of only one (the same) sides of broken specimens.

Conclusions
The presented analysis shows that the method used to measure the fatigue fracture is adequate for investigating fractures for a wide range of cases. The most significant results of this study can be presented as follows: • The highest values of Sx and Vx occur for B/T = 2/3 and affects on smaller values for next both levels B/T=1 and B/T=2, respectively; • High compliance of Ssk and Sku parameters proves the large dependence of these parameters on the grip side and, thus, the way it affects the material; • Surface parameters (Sx, and Vx) are higher for higher values of the number of cycles to crack initiation (Ni); • The smallest values of the number of cycles to crack initiation (Ni) and of the surface parameters (Sx, and Vx) were found for B/T=2; • The largest values of the number of cycles to crack initiation (Ni) and of the surface parameters (Sx, and Vx) occurred for B/T=1; • The two conclusions mentioned above confirm the dependence between the surface roughness and the bendingtorsion ratio.