**4. Discussion**

The tests conducted on the untreated and peened specimens show a clear improvement of the fatigue behavior after laser peening. For all of the applied stress levels, a net increase of the fatigue life was observed. The fatigue life of the baseline samples (i.e., 110 kcycles at 220 MPa) is in line with previous findings by the authors of [26], who reported about 120 kcycles at 230 MPa in four-point bending tests of Al 6082 specimens. The fatigue life of the LPwC-treated samples shows an improvement from 1.73 to 3.34 times the baseline value. These findings can be compared to the results in the literature [15], which include the three-point bending of notched specimens treated with conventional laser peening with an ablative layer. The authors reported a net improvement following LSP, with the fatigue lives enhanced by a factor of 10 compared to the baseline; albeit, it should be

noted that a di fferent material, namely Al 7075, was tested. For a better characterization of the scatter in the S–N curves of Al 6082, additional testing would be recommended, which falls beyond the scope of this work.

The Brinell hardness measurements evidence a surface hardness increase in the order of 50% in the peened region. Trdan et al. [24] already reported a micro-hardness increase for Al 6082-T651 after LPwC. A further study [27] of the microstructural evolution of Al 6082-T651 evidenced an increase of the dislocation density after LPwC, with the production of ultra-fine and nano-grains, and related it to the induced residual stresses. In light of this, the increase of dislocation density can be seen as the prime driver of the enhanced surface hardness, as well as being involved in the plastic deformation, which results in the formation of residual stresses.

The improved fatigue life of the peened samples is ascribed mainly to the compressive residual stresses induced by the process. The numerical results confirm that compressive stresses are present at the notch surface along the treated strip, as shown in Figure 10; in particular, compressive residual stresses σ*xx* are computed at the notch. The three-point bending tests produce a tensile stress σ*xx* at the notch, which tends to propagate a crack, normal to the x-direction. The compressive residual stress σ*xx* contributes to closing the crack by decreasing the e ffective stress intensity factor range at the crack tip. For metallic materials, this is known to generate a reduction of the crack growth rate, thus postponing the specimen's failure. This mechanism could explain the prolonged fatigue life of the treated samples observed in Figure 9.

The computed in-depth residual stress field is shown in Figure 11. Also plotted are the experimental findings by the auhors of [24] obtained by hole drilling (HD) measurements on flat Al 6082 specimens treated with LPwC. As two di fferent pulse densities were used in the literature [25], namely 900 and 2500 pulses/cm2, a direct comparison with the numerical results presented here for a density of 1600 pulses/cm<sup>2</sup> is somewhat biased. To this end, an extrapolation of the measurements to a density equal to 1600 pulses/cm<sup>2</sup> is also shown; this is obtained by linearly interpolating the measurements for the upper and lower pulse density. The maximum compressive residual stresses calculated by FEM are about −210 MPa, which is 16% higher than the value of −180 MPa extrapolated from the measurements at the same depth.

The model predicts a compressive stress gradient close to the surface, which is not observed in the measurements. However, the first measurement by the authors of [25] was taken at a depth of 0.1 mm, and the points at 0.03 mm are the result of the method used for post-processing, as explicitly pointed out by the authors themselves. Remarkably, a similar stress gradient was found by the authors of [28] in a numerical study of a flat Al 2050 specimen. When validating the numerical results against X-ray di ffraction measurements, the authors reported on the di fficulty of measuring the residual stress gradient. In light of this, the steep stress gradient observed in the numerical results should not be regarded as an e ffect strictly related to the curvature at the notch. Interestingly, the depth of the compressive region seems to be basically una ffected by the presence of the notch, with compressive residual stresses extending to about 0.7 mm deep, similarly to the case of the unnotched specimen.

The e ffect of the notch on the residual stress can be estimated as follows. Vasu and Grandhi [16] reported that the e ffect of the surface curvature on the residual stresses induced by peening strongly depends on the radius of curvature (RC). Their results can be normalized, taking the ratio of the RC to the laser spot radius (SR); this shows that, for 2.4 < RC/SR < 5, the increase of the maximum compressive stress compared to a flat surface is between 17% and 8%. Assuming a linear variation between these two extremes, the value of RC/SR = 4 used in the present work would result in an increase of about 14% compared to the flat case. A comparison with the results discussed above (i.e., an increment equal to 16%) shows a good consistency for this estimate.
