3.1.3. Observations

It should be noted that in all single-shot simulations, the predicted in-plane residual stresses are equi-biaxial, as would be expected due to symmetry. The *S*22 stresses in the plane normal to the *y*-axis are equivalent to the *S*11 stresses in the plane normal to the *x*-axis.

The results of these single-shot simulations sugges<sup>t</sup> that a favorable state of residual stress in thin sections can be realized by selecting a peening pressure high enough to achieve the desired compression without the detrimental subsurface tensile stresses, along with su fficient peen layers to suppress the near-surface tension. As discussed in the following sections, however, a third parameter, namely, the peen patterning, can also strongly influence the resulting stresses in thin sections, and, as will be discussed, observations for single shots do not necessarily hold in multi-shot scenarios.

### *3.2. Simulation of a Peened Line*

Although the single shot simulations provide insight into the e ffects of applied pressure and layering, they cannot capture the interactions between adjacent and overlapping spots, or the e ffects of shot order and patterning. To investigate these e ffects, the FEA model used for the single shot simulations—a 2 mm thick plate of Al2024-T351—was extended lengthwise to accommodate the simulation of peened line under various peening conditions.

### 3.2.1. E ffects of Adjacent Spots

Figure 7 shows the simulation results for a scenario similar to that considered in [10], namely, a single layer of peen spots applied edge-to-edge along a line with minimal overlap. The applied pressure used in the simulations was 2.5 times the HEL. As is shown, the center of each peen spot in the line exhibits a surface tensile stress normal to the peen line with a magnitude of about 110 MPa and extending about 50 μm subsurface. The corresponding stress for a single peen spot is shown for comparison. Although the magnitude of the surface tensile stress is similar for the single spot and the peen line, the magnitude of the maximum compression resulting from the line configuration is about 20% lower than that of a single spot. The overall depth of compression is smaller in the line configuration as well, by about 0.25 mm.

Although the near-surface tensile stresses are contained only in the central regions near the spot center, significant tension (with a peak value of about 100 MPa) builds up subsurface in the regions between adjacent spots. For many fatigue applications these large subsurface tensile stresses can be undesirable, as they can lead to subsurface crack initiation that is undetectable by visual inspection of the component surface.

Figure 7 also compares the through-thickness profiles for the in-plane stresses taken parallel to (*S*11) and transverse to (*S*22) the peen line; as is shown, the stress states in the two directions are noticeably di fferent, with as much as a 50 MPa variation in some locations. In general, the stresses transverse to the peened line are less compressive (or more tensile) than those in the longitudinal direction. This could pose a concern for certain applications in which the peen line was designed to overlay a surface scratch. Because the stresses are of lower magnitude (or even more tensile) in the critical direction (i.e., the direction that would tend to encourage crack formation and opening), the true potential of the LP treatment would not be realized, and could even exacerbate the situation. It should also be noted that through the spot centers, the stresses transverse to the peen line are generally more tensile than those predicted by single shot simulations.

**Figure 7.** Comparison of stress profiles between a single peen spot and a peen line.

### 3.2.2. Effects of Peen Layers

As was the case for single shots, augmenting the peen line with additional layers can help alleviate the surface tensile stresses at the spot centers. In Figure 8, second and third layers of peen spots are applied along the peen line at a 50% offset between one layer and the next, as shown in the schematic. The line plots illustrate the in-plane stress through the center of a spot on the topmost layer (denoted Location L1). Similar to the case of a single peen spot, the surface tensile zones in the spot centers are reduced as additional layers are applied; however, the effects of adjacent spots are very apparent. A second layer flips the surface stress to compression (from 108 MPa to −243 MPa) while a third layer flips it again (from −243 MPa to 46 MPa). The end result is that although the stress at this location is reduced with additional peen layers, shallow tensile regions—about 20 μm deep and 20 μm in width—persist in the center of each spot that comprises the topmost layer of the plate.

It should be noted that while Figure 8 suggests that limiting the peening to two layers would alleviate the surface tensile stress at Location L1, detrimental stresses form elsewhere. Figure 9 illustrates this by extracting stress plots at location L2 after one and two layers of peening. As is shown, the surface stress at this location decreases more than 50% with the addition of the second layer (from 108 MPa to 48 MPa), but the tension persists.

**Figure 8.** Effect of peen layering on predicted in-plane residual stress in thin sections. Stresses were extracted from the FEA model at Location L1 after one, two, and three layers of peening.

**Figure 9.** Effect of peen layering on predicted in-plane residual stress in thin sections. Stresses were extracted from the FEA model at Location L2 after one and two layers of peening.

### 3.2.3. Effects of Peen Patterning

In Figure 10, we consider the effects of altering the peen patterning while still maintaining a coverage of 300% along the central portion of the peen line. Two additional scenarios were evaluated: Pattern 2, which is similar in application to the scenario considered in Section 3.2.2 (denoted in this section as Pattern 1) but reduces the offset between layers from one-half the spot width to one-third (Figure 10a); and Pattern 3, which uses a running overlap (Figure 10b) pattern. As is shown, both of these patterns achieve exactly three layers of peening along the central portion of the peen line.

**Figure 10.** Schematics for achieving 300% peen coverage: (**a**) Pattern 2; (**b**) Pattern 3. Figure 8 shows Pattern 1.

The corresponding contour and line plots for peen Patterns 2 and 3 are shown in Figure 11. As is illustrated, decreasing the offset from one-half to one-third the spot width does not alleviate the tensile stresses at the surface. As was observed with Pattern 1, small regions of tension persist in the spot centers of the topmost layer for Pattern 2. However, the build-up of subsurface tensile stresses is significantly reduced by reducing the offset.

The running peen pattern (Pattern 3), on the other hand, does result in a complete suppression of surface and near-surface tensile stress (Figure 11b), to a depth of almost 1 mm. For the peening parameters used in the simulations, the surface stress in the spot centers decreases from about 60 MPa to about −135 MPa, while the subsurface tension at mid-section decreases from a maximum of 100 MPa for Pattern 1 to about 0 MPa for Pattern 3. Note that the more compressive surface stresses observed from the running overlap pattern result from the beneficial interactions of subsequent peen spots applied over previously induced fields; for other combinations of peening parameters and specimen geometry other surface conditions may arise.

**Figure 11.** Effects of peen layering on predicted in-plane residual stress: (**a**) Pattern 2; (**b**) Pattern 3. The patterns are shown in Figure 10.
