*3.1. Single Shot Simulations*

Simulations of a single LP shot were used to develop a better understanding of the shock response of laser-peened thin plates under different peening conditions. All thin-section simulations were run on a 2-mm-thick plate of Al2024-T351 (unclad), with the peened area located sufficiently far from the plate boundaries to avoid the effects of reflected waves. Note that due to symmetry, only one half of the plate was modeled.

### 3.1.1. Effects of Peening Pressure

Figure 4 shows the effects of varying the applied pressure for a single layer of peening with a fairly large (5 × 5 mm2) square spot. The contour plots represent a cross-section of the plate taken through the spot center, with the colors representing the range of the in-plane stress component *S*22 normal to the cross-sectional surface. Line plots of stress as a function of depth through the spot center are also shown. Note that in these plots, in contrast to the plots in Figure 3, the stresses are not averaged over a volume; rather, they are extracted directly from the element integration points.

At low pressures (Figure 4a), less than about twice the HEL, surface tensile stresses are absent in the spot center. However, the magnitude of the maximum compressive stress is fairly low and fairly shallow—only about 80 MPa that tapers out after about 0.5 mm depth—and tensile stress persists through the thickness reaching about 60 MPa at a depth just over three-quarters of the way through the thickness.

At pressures about twice the HEL (Figure 4b), small tensile zones appear in the spot centers similar to the experimental findings in [10]. The magnitude of the stress at the surface is about 100 MPa, and the tension persists in a region around the spot center that measures about 250 μm at the surface and extends about 35 μm subsurface. The maximum compressive stresses in this pressure regime are greater than those realized at lower pressures, reaching about −130 MPa, but are not significantly deeper (about 100 μm). It should be noted that the size of the tensile zones predicted by these simulations are generally smaller than what was reported in [10]. This likely results from the pressure pulse approximation assumption of a spatially uniform distribution along with averaging effects in the experimental values.

Increasing the applied pressure to three times the HEL (Figure 4c) increases the size of the surface tensile zone slightly but also drives the compressive stresses deeper into the component thickness. Near to the spot centerline the compression persists throughout the plate thickness; however, the stress state is not uniform across the spot width, with tensile pockets forming subsurface around the compressed region. At very high applied pressures, about four times the HEL (Figure 4d), through-thickness compression is no longer achievable, with tensile stresses forming at the back surface.

*Metals* **2020**, *10*, 93

It should be noted that the specific results for this series of single-shot simulations depend on not only the maximum applied pressure, but also on the shape and length of the pressure pulse and the thickness of the plate. For thicker or thinner sheets, and for different pulse shapes, the precise points at which the nature of the residual stresses change will vary; however, the basic trends are similar.

**Figure 4.** Finite element analysis (FEA)-computed in-plane residual stress from a single square laser peening (LP) shot (5 × 5 mm2) on a 2-mm-thick Al2024-T351 plate at various pressure levels.

A comparison between the LP response of a thicker plate (10 mm) and the response of a thin section (2 mm) is shown in Figure 5. Both simulations used a maximum applied pressure of 2.5 times the HEL, with the plate thickness as the only difference. As can be seen from the line plot in Figure 5, the near-surface tensile stresses around the spot center in the thin section are completely absent from the thick section. In addition, because the thick section does not experience stress reversals resulting from wave reflections off the back surface, the maximum residual compressive stresses are significantly greater in magnitude than that of a thin section, by a factor of about two.

**Figure 5.** Effect of plate thickness on predicted in-plane residual stress (single square LP shot, 5 × 5 mm2, on a 2-mm-thick Al2024-T351 plate).

### 3.1.2. Effects of Peen Layers

When additional layers of peening are considered on a thin section, as shown in Figure 6, the near-surface tensile stresses are mitigated. For the case shown, with an applied pressure of 2.5 times the HEL, a second layer of peening reduces the size and magnitude of the surface tensile field by more than 50%. Adding a third layer of peening completely suppresses the near-surface tension and a fourth layer drives the surface into compression. The maximum subsurface compressive stress is only minimally affected by additional layers, increasing by less than 50 MPa from one layer to four, but the depth of compression more than doubles. At the same time, however, the additional peen layers result in larger tensile stresses on the back surface.

**Figure 6.** Effect of peen layering on predicted in-plane residual stress in thin sections (single square LP shot, 5 × 5 mm2, on a 2-mm-thick Al2024-T351 plate).
