During the test, radial force (Fn), radial displacement (Dn), tangential force (Ft), and tangential displacement (Dt) were obtained. Thus, the Fn-Dn curves and Ft-Dt curves could be plotted.
Figure 3 shows the Ft-Dt curves for the tangential fretting wear. At normal load of 20 N, all Ft-Dt curves were closed to a parallelogram, which indicated that the test was running in gross slip regime. When the normal loads were 40 N and 60 N, the Ft-Dt curves were closed to the parallelogram. When the normal load was 40 N, the Ft-Dt curve was closed to parallelogram for the first hundred cycles, and then, the Ft-Dt curve changed to be linear and remained until the end of the test. The curve characteristics suggested that the test was running in partial slip regime. In addition, a similar phenomenon was observed at a normal load of 60 N.
The Fn-Dn curves for the radial fretting wear were plotted in can be plotted, in Fig.3. As shown in Fig. 4, all Fn-Dn curves were linear at different loads. Additionally, the radial displacement increases with the increase of radial load.
The Fn-Dn curves and Ft-Dt curves for dual-motion fretting wear are shown in Fig. 5. As seen in Fig. 4(a), the shape of the Ft-Dt curve was closed to Parallelogram during the whole test when the radial load was 15~25 N. At the beginning of the test, the friction force was relatively low, so the curve graph presented a flatter trapezoid. As the number of fretting cycles increased, the friction force gradually rise to a stability value. According to the dual-motion fretting wear theory[22], it can be judged that the trapezoidal shape corresponds to the gross slip regime. At a normal load of 30~50 N and 45~75 N, the Ft-Dt curves were closed to the parallelogram at the beginning of the test. As the fretting cycles increased, the shape of Ft-Dt curves were elliptical and linear, which indicated that the tests were running in partial slip regime.
As shown in Fig. 5(b), it can be seen that the Fn-Dn curves were linear at the beginning of the dual-motion fretting wear. With the increase in the number of cycles, the radial displacement gradually increased and then stabilized, and the curve gradually changed to elliptical, indicating that elastic-plastic deformation occurred[23].
The friction coefficient is influenced by multiple factors and undergoes significant changes during the friction process. Therefore, it can be utilized as a dynamic evolution parameter to effectively characterize the comprehensive wear properties of friction contact surfaces. This parameter reflects the microbump contact state of the transient friction cross-section in the micromotor wear process and provides insights into certain micromotor wear characteristics [24].
Figure 6 shows the evolution of COF (friction of coefficient) with the number of fretting wear cycles. As shown in Fig. 6(a), when the normal load was 20 N, there were three stages in COF, i.e., running stage, ascending stage, and fluctuating stage. On the other hand, the stable stage at 40 N and 60 N replaced the fluctuating stage at 20 N. In general, the COF increased with the decrease of the normal load. The COF of 20 N (about 1.02) was almost two times of 60 N (about 0.55). At the beginning of the test, the COF was relatively low due to the existence of oxidation and pollution film. As the number of cycles increased, the film broke down, resulting in direct contact between metals. Due to the influence of surface adhesion and plastic deformation, the COF rise significantly and reached a peak. The formation of the third body played the roles of lubrication and wear reduction, which lead to the decrease of COF. If the formation and rejection of COF reached a balance, the COF was relatively stable, such as at 40 N and 60 N, or the COF fluctuated, i.e., at 20 N. Similarly, the evolution of COF of the dual-motion fretting wear was almost the same as that of the tangential fretting wear.
The frictional dissipation energy is an important indicator for assessing the micromotional wear behavior, and the integration of the envelope area of the hysteresis curve as shown in Fig 7. has further characterized the damage evolution of the material [25,26]. The specific method of calculating the tangential frictional dissipation energy is through the integral method, and the specific calculation formula is shown in Equation (1)
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)
Figure 8 shows the variation curves of frictional dissipation energy. It can be seen in Fig. 6(a) that the tangential fretting wear dissipation energy curves under different normal loads showed the same trend. With the increase of the fretting cycle, the single-cycle dissipation energy first increased and then decreased. Additionally, the peak value increased with the increase of normal load. The maximum of 60 N (2278.6 µJ) was almost two times that of 20 N (1109.6 µJ), which was agreed with COF. In general, the larger the normal load, the higher the peak of single-cycle dissipation energy. The trend of the dissipation energy curve is in accordance with the operation pattern of the fretting wear regime. The final stable single dissipation energy of the specimen in the GSR is close to the peak value; however, the final stable single dissipation energy of the specimen in the PSR tends to be 0 µJ.
From Figure 8(b), it can be seen that the dissipation energy of the dual-motion fretting wear has the same trend as that of the tangential wear. When the normal load was larger, the number of cycles to peak the single dissipation energy was smaller.
Figure 9 shows the SEM image results of the tangential wear scars. Generally, it can be seen that the area of the wear scar gradually decreased as the normal load increased. As shown in Fig. 9(a), when the normal load was 20 N, the wear scar was covered by wear debris. When the normal loads were 40 N and 60 N, the wear scars could be divided into two regions, i.e., stick zone and wear particles accumulated region. Compacted flake debris can be observed at the edge of the wear scar, while the delamination phenomenon can be observed in the center of the wear scar, indicating the occurrence of plastic deformation. As shown in Fig. 9(c), when the normal load was 60 N, it is difficult to observe residual wear debris in the worn region. There is a slight adhesion area of wear in the center of the wear scar, while the ploughing was observed at the edge of the wear scar. Thus, the main wear mechanisms were abrasive wear and delamination when the normal load was 20 N. While the main wear mechanisms were adhesive wear, abrasive wear, and delamination when the normal loads were 40 N and 60 N.
Figure 10 shows the microscopic morphology of the radial fretting wear. Along the fretting direction, the size of the wear scar increased from 208 µm to 451 µm, when the radial load increased from 20 N to 60 N. The surface of the Zr-4 alloy tube in the test was lightly worn, leaving only a shallow circular wear spot on the surface, and deformation and debris can be observed on it, indicating that the increase of radial load would increase the contact area of the specimen, but the change of the damage degree of the specimen was not obvious. The damage to specimens was slight. The results of SEM were agreed with Fig. 4(Fn-Dn).
Figure 11 shows the SEM images of the dual-motion fretting wear scars. As shown in Fig. 11(a), as the radial alternating load was 15~25 N, the plastic flow in the wear scar region is obvious, and the accumulation of granular wear debris can be observed in the wear edge region. And most abrasive chips can play an anti-wear role in fretting wear[27]. Compared to the GSR of the tangential fretting wear, the central area of the wear scar in the dual-motion fretting wear GSR does not show an accumulation of loose debris. However, the wear mechanism was dominated by compacted debris and surface contact fatigue spalling and delamination. For Fig. 11(b), when the radial load was 30~50 N, the surface of the specimen running in the elastoplastic coordinated PSR can be observed to have significant delamination in the center of the wear scar. In addition, there are a few signs of slightly slippery and plastic flow on the edge of the wear scar. As shown in Figure 11(c), the dual-motion fretting wear was running in the elastic coordinated PSR at 45~75 N. The ploughing phenomenon can be observed in the edge of the wear scar. Moreover, there is a clear area of adhesion in the center of the wear scar. The wear mechanism is basically the same as the PSR of the tangential fretting wear.
Figure 12 shows the three-dimensional morphology and two-dimensional profile results of the Zr-4 alloy tube worn surface for the tangential fretting wear. As shown in Fig. 12, it can be seen that there was a large difference in the wear depth in the different fretting wear regimes. In general, the wear debris accumulated at the edge of the wear scar. The maximum area and wear depth of wear scar was observed at 20 N. The shape of the profiles resembled a "U" shape.
Figure 13 shows the three-dimensional morphology and two-dimensional profile results of the worn surface of the Zr-4 alloy tube for the radial fretting wear. As can be seen in Figure 13, it was difficult to observe wear marks in the three-dimensional morphology for radial loads of 20 and 40 N. When the radial load was 60 N, shallow wear marks existed on the surface. Additionally, the wear depth of 60 N was much larger than that of 20 N and 40 N.
Figure 14 shows the three-dimensional morphology and two-dimensional profile results of the worn surface of the Zr-4 alloy tube for the dual-motion fretting wear. As shown in Fig. 14, the wear morphology in different fretting wear regimes differed greatly. When the radial load was 15~25 N, the fretting wear regime worked in the gross slip regime, and the specimen is most seriously damaged under this condition. When the radial load was 30~50 N, the specimen in the elastic-plastic coordinated PSR has less damage compared to the GSR. When the radial load is 45~75N, the damage to the specimen was slight.
The wear volume (V) of specimens was measured directly by the WLI, and the wear rate was calculated by Eq. (2).
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where Vc is the wear rate(mm3/N×m), V is the wear volume (mm3), Fn represents the applied normal load (N), N is the number of fretting cycles, and D represents the displacement amplitude (m).
The wear volume and wear rate of the worn Zr-4 alloy tubes for the different wear as shown in Figure 15. From Fig. 15(a), it can be seen that the wear volume of tangential fretting wear decreased with the increase of normal load, and there is a maximum value of wear volume at 20 N ( about 8.2×105 µm3), while the minimum value of wear volume was examined at 60 N (about 0.7×105 µm3). When the normal load increased from 20 N to 40 N, the fretting wear regime changed from the GSR to the PSR, and the wear volume and wear rate decreased by about 84% and 92%, respectively. The decrease of wear rate was significantly reduced by the change in slip regime.
From Fig. 15 (b), it can be seen that the wear volume and wear rate of dual-motion fretting wear were larger than that of tangential fretting wear, When the relative motion was dual-motion fretting, the wear volume and wear rate decreased by approximately 75% and 90% respectively when the fretting wear regime was changed.
Due to the difficulty of measuring the wear damage of the radial fretting wear, there were no results of wear volume and wear rate. However, as shown in Fig.13, it could be suggested that the wear volume of tangential and dual-motion fretting wear were much larger than that of radial fretting wear.
Figure 16 shows the EPMA results of the worn Zr-4 alloy tubes. Fig. 16(a) shows that the O and Zr elements are distributed relatively uniformly throughout the wear region, where the relative content percentage of Zr elements is lower than that in the unworn region at 20 N. The similarity results were also observed in dual-motion fretting wear at 15 N-25 N. On the other hand, when the test was running in partial slip regime, whether tangential fretting wear or dual-motion fretting wear, the poor-oxygen region was examined in the inner of wear scars. The results indicated the transfer of Zr-4 alloy, which was agreed with SEM (as shown in Fig. 9 and Fig. 11). At the edge of the wear scar, a high content of oxygen was detected. However, when the specimen fretted in the radial fretting wear at 30~50 N, there was almost no oxygen detected in the wear scar due to the slight damage, as shown in Fig. 16(c). In general, GSR's damage was much more severe than that of PSR. Additionally, the sequence of contribution to damage was radial, tangential, and dual-motion.
The specimens in the contact area are fatigue dislodged under the action of tangential alternating force, and the generated wear debris is reduced in granularity and spread in distribution under the extrusion shear of the upper and lower specimens. Meanwhile, the local high temperature generated by the frictional action makes the friction interface undergo oxidative wear, and the oxide debris of Zr is eventually scattered over the entire wear region. Fig. 16(b) shows that the O elements are more concentrated in the distribution of the edge of the wear marks, while the relative content of O elements in the center of the wear marks is extremely low and the relative content of Zr elements is high, which indicates that slightly slippery and debris oxidation occurred in the edge of the wear marks. In contrast, the center part of the wear marks is difficult to be invaded by oxygen due to the material adhesion effect, and therefore no oxidative wear occurs. [28]