*3.5. Self-Heating*

During cyclic loading, self-heating of the specimens may occur, depending on the stress amplitudes and strain rates imposed during each cycle, which may introduce a high amount of plastic deformation. The temperature measurements showed that the self-heating was homogeneous in the middle of the gage section of the run-out samples. For the broken samples; however, a localized and sharp increase of temperature was observed before the final breakdown. Typical chronograms from these measurements are plotted in Figure 7a, and a temperature variation of almost 50 ◦C can be observed before rupture (see red curve). The maximum homogeneous temperature values as a function of the applied stress were measured for samples tested in TC (see Figure 7b). The maximum surface temperature evolution with the applied stress amplitude followed an almost linear trend for both polished and 60 min of SMAT at RT conditions. In the fatigue limit stress range, the polished samples (~205 MPa) exhibited a maximum measured temperature of approximately 50 ◦C, whereas, for 60 min RT SMAT (~245 MPa), this value was higher than 100 ◦C. Nevertheless, the measured temperature values for the highest stress amplitudes were comparable: 320 ◦C for the initial state loaded at 260 MPa and 280 ◦C for the

treated samples loaded at 275 MPa. After SMAT, in order to obtain the same level of self-heating, 15% higher stress amplitudes were required.

**Figure 6.** Secondary electron SEM pictures of surface initiation sites of (**a**) sample tested in rotating–bending after 20 min of cryogenic SMAT (corresponding to Figure 5c), and (**b**) sample tested in tension–compression after 60 min of SMAT at room temperature (corresponding to Figure 5e).

**Figure 7.** (**a**) Typical self-heating chronograms measured during TC loading, for breaking samples (in red) and run-out samples (in blue). (**b**) Maximum stabilized temperature as a function of σa.

### **4. Discussion**

Consistently with the results from the literature [13,15,23], the use of SMAT was found to be an efficient way to increase the fatigue resistance of the 304L stainless steel. Enhancements of 28% and 17% were observed in rotating–bending and tension–compression, respectively. Nevertheless, self-heating of the specimens during testing was not anticipated. The temperature evolutions with applied load presented in Figure 7b show almost linear trends with similar positive slopes for both polished and SMAT samples. In the case of the polished samples, a good accordance with the fatigue results obtained on 316 LN stainless steel by Tian et al. [33] can be noted, especially around 260 MPa where the number of cycles to failure and self-heating values were very similar. Also, for the low stress amplitudes related to the endurance limit, such as 200 MPa and 207 MPa, the maximum surface temperature measured during the fatigue tests was less than 70 ◦C, representing a self-heating that did not exceed 50 ◦C. After SMAT, the same level of self-heating required a 15% higher applied stress amplitude, confirming the difference of cyclic plastic strain accumulation between the SMAT and the untreated samples for the same applied stress amplitude. Indeed, the surface strain-hardening generated by SMAT pushed the onset of the plasticity at the surface to a higher stress range and delayed the generation of significant self-heating. Regarding the thermal exposure during the tests, the work of Kakuichi et al. [23] showed that the exposure to 300 ◦C during rotating–bending fatigue at high and low stress amplitudes does not relax the surface residual stresses of a 304L sample ultrasonic shot-peened at room temperature. This would mean that the observed self-heating mainly behaves as a mechanical property reducer and that the key factor governing the residual stress relaxation is the introduction of supplementary plastic strains.

Meanwhile, the presence and magnitude of residual stresses also play a role in RB and TC fatigue behavior and, as shown in Figure 4, different residual stresses values were measured before and after fatigue tests at the surface of specimens. Before fatigue, the different residual stress states are directly linked to the different studied conditions, whereas, after fatigue, relaxations depend on several testing parameters such as the type of loading or the applied stress amplitude. For example, it was shown in Figure 4 that the residual stress relaxation in austenite for the ground specimen after rotating–bending fatigue was only approximately −10% compared to −75% for the tension-compression testing condition. For the same level of stress amplitudes, due to the stress gradients during RB tests, plastic strains can mainly be introduced at the surface region of the specimen, whereas the whole volume of the TC sample can accommodate plastic strains during TC tests, resulting in more residual stress relaxation. The initial residual stresses can also favor the onset of plasticity, especially when significant compressive residual stresses are present in a part that is mechanically loaded at R = −1. The stress applied during the compressive stage of a fatigue test is added to the residual stress, reaching the material elastic limit at or below the surface, resulting in the relaxation of the residual stresses. Both elements can justify the specific behavior in the tension–compression testing condition. At this stage, the sequence of these different mechanisms is not known, as only surface residual stress relaxations were evaluated before and after the tests. Further investigations of the residual stress gradient evolution during fatigue loading are needed to better explain the behavior of the processed part during fatigue tests. Such an investigation will contribute to understanding when, how, and in which way the residual stress gradients relax during fatigue testing, finally providing a better idea of the role of the residual stresses in the fatigue behavior of 304L stainless steel treated by SMAT.

Concerning the comparison of untreated RB with untreated fully reversed (R = −1) TC fatigue tests, the gradient in the applied load within the specimens in RB is commonly used to explain a lower fatigue limit (approximately −10%) in TC [34]; however, in this study, a decrease of −18% of the fatigue limit was observed. The volume effect of the tested samples can be considered to explain this difference. Indeed, the samples tested in RB had a gauge of 6 mm in diameter and 25 mm in length, whereas the TC ones had a diameter of 9 mm with a length of 12.5 mm. Pogorestskii et al. [35] showed that, for 40Kh steel loaded in four-point rotating–bending, larger gauge length and diameter had a detrimental effect on the fatigue limit, and they defined two different coefficients: −0.18 MPa/mm for the length

and −4.4 MPa/mm for the radius. If similar behavior can be considered for the 304L stainless steel, an increase of 3 mm in diameter and a decrease of 12.5 mm in length would result in an overall decrease of approximately 5 MPa for the RB fatigue limit. The difference in fatigue limit between RB and TC would consequently be reduced to −15%, which is very similar to the −14.9% or the −11.9% proposed by Palin-Luc et al. [36] on 30NCD16 and XC18 steels, respectively.

For the SMAT conditions, a decrease of approximately −25% of the fatigue limit in TC compared to the RB one was obtained in Table 2 (from 320 to 240 MPa). This difference was significantly larger than for the initial state and could be due to the difference in treatment duration and resulting microstructure and mechanical property gradients. Similarly to the work of Sun et al. [37], one can consider that, after SMAT, the obtained functionally grade material behaves like a composite material composed of a SMAT-affected layer and a bulk core. Considering that the mechanical properties are proportional to the hardness, and by using a simple mixing law, the fatigue limit enhancement by SMAT can be determined as follows:

$$Enhuman\ \left[\%\right] = \left(\frac{f\_{\text{SMAT}} \times HV\_{\text{SMAT}} + f\_{\text{bulk}} \times HV\_{\text{bulk}}}{HV\_{\text{bulk}}} - 1\right) \times 100,\tag{2}$$

where *fSMAT* is the volume fraction of the SMAT-affected layer and *HVSMAT* is its mean hardness, where *fbulk* = (1 − *fSMAT*) and *HVbulk* = 210 (as shown in Figure 2a). The data used for the calculation and the obtained estimations are summarized in Table 3. The differences in diameter and hardened depth led to a higher fraction of SMAT-affected layer in the case of RB\_20 min RT (16%) than the two other conditions (11.3% for RB\_20 min CT and 11.8% for TC\_60 min RT). Nevertheless, the difference of mean hardness in the SMAT layer resulted in similar fatigue limit estimations (~267 MPa) for both RB conditions and a lower value for TC (~220 MPa). The estimated fatigue limits were compared to the experimental ones, and the respective errors were calculated.


**Table 3.** Different SMAT conditions with their respective affected volume fraction, mean hardness, and corresponding measured and estimated fatigue limits.

It is worth remembering that the effect of residual stresses and their variation during fatigue tests were not taken into account here. This approximation underestimates the fatigue limit enhancement by SMAT for all tested conditions. As shown in Table 3, the error of approximation was two-fold higher in RB than in TC. Even by considering the differences in sample geometry and hardening state resulting from the treatment conditions, a difference remains which can only be explained by the loading condition difference. An explanation can be that the most solicited area in RB is the SMAT-affected layer that has enhanced mechanical properties and is under significant compressive residual stress state. These facts suggest that the effect of SMAT would be more significant in RB.

In the case of rotating–bending, the use of cryogenic SMAT provided the same effect in terms of fatigue resistance as the SMAT at room temperature. Thus, despite potential beneficial modifications such as a lower roughness, a higher martensite fraction, and a slightly higher compressive residual stresses, the use of SMAT at cryogenic temperature did not bring the desired additional improvement. It is likely that the beneficial modifications induced by CT SMAT were counter-balanced by other factors linked to the sub-surface or to the surface modifications such as the lower hardness below 200 μm (see Figure 2a) compared to the room temperature treatment. Indeed, as shown in Table 3 for CT SMAT, the high surface hardness (~520 HV) together with the limited affected depth (~350 μm) led to

a very similar estimation of the fatigue limit compared to the RT SMAT that was characterized by a lower surface hardness (~450 HV) and a significantly higher affected depth (~500 μm).
