*3.2. Fatigue Properties*

The Wohler curves associated with the three conditions and both types of cyclic loadings are shown in Figure 3. After 10<sup>6</sup> cycles, if failure did not happen, the tests were considered to be run-out tests and a horizontal arrow is attached to them on the graph. Squares are used for rotating–bending, and circles denote tension–compression. Full symbols illustrate the untreated samples, whereas hollow symbols are used for room temperature SMAT and crossed hollow symbols are used for cryogenic treatments. Except for RB\_20 min CT (due to the lack of data), the Stromeyer expression (1) [31] was chosen to fit the experimental results and the constants obtained are given in Table 2.

$$
\sigma\_4 = \sigma\_D + \left(\frac{c}{N}\right)^{\left(\frac{1}{m}\right)},\tag{1}
$$

where σ*<sup>D</sup>* is a value determined from the experimental data, *c* and *m* are fitting parameters, σ*<sup>a</sup>* is the stress amplitude, and *N* is the number of cycles. Nonlinear least squares curve-fitting following a Levenberg–Marquardt algorithm was used to determine *c* and *m*.

As can be seen in Figure 3, a similar trend was found between RB\_G and TC\_P, and, as reported in Table 2, the fatigue limits of the initial material were 250 MPa in rotating–bending and 205 MPa in tension–compression, representing a −18% difference. The effect of SMAT on the fatigue life of 304L was not the same depending on the considered fatigue life range; it is more pronounced in the high cycle fatigue regime than in the low cycle one. After SMAT, a rather high increase of the fatigue limits was obtained, the improvements being +28% in RB and +17% in TC. Even though the phases distributions, microstructures, hardness gradients, and residual stresses were different in RB\_20 min RT and RB\_20 min CT samples, their fatigue behavior was almost identical. Also, the obtained *m* parameter was significantly higher for the SMAT conditions compared to the initial states due to the smooth form of their S–N curves.

**Figure 3.** S–N curves obtained at 10 Hz for (i) RB\_G (filled black squares), RB\_20 min RT (hollow red squares), and RB\_20 min CT (crossed hollow blue squares) treated specimens, and for (ii) TC\_P (filled gray circles) and TC\_60 min RT (hollow orange circles) samples.


**Table 2.** Estimated fatigue limits and fitted constants c and m of Stromeyer expression (1).
