**1. Introduction**

Over the past three decades, laser peening (LP) has emerged as a viable commercial technology for introducing beneficial residual compression into the near-surface regions of metallic components [1,2]. First introduced by Battelle Laboratories, Columbus, Ohio, in the 1970s [3,4], LP uses a high-power-density, short-duration pulsed laser to create a mechanical impact on the surface of a component. The amplitude of the impact, typically at least double the Hugoniot elastic limit (HEL) of the target material, is grea<sup>t</sup> enough that the resultant shock wave creates a region of localized plastic deformation in the target material. The elastic springback of the surrounding material around this plastic core creates a state of self-equilibrating residual stress in the component. Good reviews of the LP process can be found in [5–7].

Because the depth of compression resulting from an LP treatment is typically on the order of 1 mm or greater, depending on the component material, geometry, and selected peening parameters, LP has the potential to significantly mitigate fatigue-inducing tensile stresses that can result from applied cyclic loading. This is of particular interest as a potential means for enhancing the fatigue response of military aircraft in which mission changes and extended lifing requirements often tax the fatigue resistance of the airframes beyond their original design specifications [8].

One application of recent interest is LP of thin aluminum components, on the order of 2–3 mm or less such as aircraft skin or web structure, to mitigate surface damage or enhance fatigue response. If LP parameters and process variables are designed appropriately, a favorable compressive state throughout much of the component depth can be induced [9]; however, as is discussed in more detail below, under certain circumstances LP can also induce detrimental tensile stresses into the near-surface regions of thin sections, extending into the component to depths as grea<sup>t</sup> as 0.5 mm [10–12].

A number of factors can contribute to the challenge of developing favorable residual stress states in thin structures: First, if the laser power density and subsequent plasma pressure are too high, the resulting distortion in the thin section can reduce the magnitude of the compressive stresses [9,13]. Second, even in the absence of significant distortion, the limited depth of material along the propagation direction of the shock wave constrains the induced plastic field, which in turn can limit the magnitude of the residual stresses. Third, because the plastic wave will typically not completely attenuate through the material depth, reflected waves from the opposite free surface can form, with the e ffect of altering the residual stresses from compressive to tensile [14]. Fourth, the work hardening resulting from LP a ffects a greater percentage of the depth of a thin component than a thicker one, and can therefore impact the development of the residual stress fields and also the fatigue response [15]. Finally, the rolling process typically used to produce thin plates induces a crystallographic texture that can influence the development of residual stresses [16].

In early studies, some of these thin section challenges were addressed by splitting the laser beam to peen both sides of the plate simultaneously [9]. While this technique was designed to help minimize overall distortion, the mid-plane collision of the two compressive shock fronts resulted in detrimental, high-magnitude internal tensile stresses [17]. In addition, for many in situ components, such as an aircraft skin, implementation of two-sided peening is not feasible.

More recently, Dorman et al. [10] investigated the use of LP to treat surface scribe marks on thin Al 2024-T351 sheets. Specimens were peened from one side only, with a single layer of square spots patterned in either a line overlaying the scribe mark or a patch covering it, and using an ablative coating on the peen surface and an acoustic damping material on the back surface. The resulting residual stresses were then measured using incremental hole drilling and synchrotron X-ray di ffraction. In all cases—regardless of the depth of the scribe mark, the use of an ablative layer, or the intensity of the peening—the near-surface residual stress, measured in the center of the peen spots normal to the peen line, was either tensile or only slightly compressive. The tensile stresses persisted to subsurface depths ranging from 80 μm at the lowest laser power density to 320 μm at the highest, with magnitudes reaching as high as 100 MPa. In addition, in all cases in which the peening pattern was a single line, the resultant residual stress fields were strongly non-biaxial, with higher compression parallel to the peen line axis than in the transverse direction.

Cellard et al. [15] noted similar results in their measurements of LP-induced residual stresses in very thin (1 mm) Ti-17 plates. The specimens were peened from one side only using square laser spots of varying size, intensity, duration, and coverage. Using X-ray di ffraction to measure the surface residual stresses, they found that nearly all of the thin specimens had some level of tension at the surface, ranging from 13 to 150 MPa. When the same peening parameters were applied to thick specimens (9 mm), however, nearly all demonstrated compressive residual stress on the surface. They attribute this "thickness e ffect" to the redistribution of stresses required to maintain equilibrium over a cross-section of the specimen, and suggested that two-sided peening could yield more favorable stress fields in thin specimens.

In contrast, several researchers studying the e ffects of LP in aluminum sheet have not observed tensile stresses at the surface. Hong and Chengye [18] and Yang et al. [19] peened 2.5-mm-thick Al2024 and observed compressive surface stresses at the centers of round LP spots using conventional XRD. However, as noted in [16], surface XRD measurements can be distorted by rolling-induced texture and thus a secondary stress measurement technique is recommended to reduce uncertainties. Ivetic et al. [20] studied the e ffects of LP on slightly thicker Al 6082-T6 plates, 3 mm in thickness, and measured near-surface compression using synchrotron X-ray di ffraction. However, the depth at which the measurements were recorded was slightly subsurface, 50–250 μm, so that any tensile stresses that might have formed in shallower regions might not have been detected.

In the present work, three-dimensional non-linear finite element modeling is used to investigate the e ffects of laser peening on residual stresses in thin aluminum plates. We explore the relationship between spot layering and peen patterning, with the objective being to better understand the e ffects of processing technique on the resulting residual stress fields.

### **2. LP Process Modeling**

Owing to its flexibility and relative ease of use, finite element analysis (FEA) has emerged as a powerful tool for predicting the full residual stress state that results from the laser peening of an arbitrary three-dimensional metallic body. First used by Braisted and Brockman [21] to simulate single LP shots on semi-infinite bodies, FEA techniques have evolved significantly over the past decade as computer processing has become faster and multiprocessing environments have become mainstream. Recent FEA studies of note include the work of Ding and Ye [22], who used three-dimensional FEA to create detailed stress maps for LP steel; Ocaña et al. [23], who developed a multi-shot FEA model capable of realistic LP simulation; Singh et al. [24], who coupled FEA with numerical optimization; Brockman et al. [25], who used a highly refined, fully three-dimensional model to study local variations in surface residual stresses arising from shot patterning; and Hasser et al. [26], who developed a first-ever FEA capability for studying LP-induced surface roughness.

In the present work, a series of finite element analyses were performed using the commercial FEA package Abaqus [27]. The objective of the analyses was to explore computationally the e ffects of various peening parameters and processing variables on the resulting residual stress fields in thin structures in order to better understand the experimental findings discussed in the previous section: (1) the formation of surface tensile stresses in spot centers that tend to occur in thin plates but not thicker sections, (2) the observed inequality of the residual stresses that occur parallel to and perpendicular to a peen line, and (3) the e ffects of peen patterning on the resulting stress fields.

The key aspects in using FEA to model an LP shock event are the selection of appropriate input models, namely the material model and the pressure model, and selection of a computational strategy and associated computational parameters that provide for an accurate and e fficient solution. In this section, we discuss the material model used to capture high-strain-rate e ffects, the pressure model used to approximate the laser-induced plasma impact, and the computational model used to develop the stress predictions.
