Aluminum skins on the lower wings of most commercial aircraft are shaped using shot peen forming. This process, which involves bombarding the skins with hard shot, uses nonuniform plastic ﬂow to induce curvatures—in the same way that diﬀerential expansion makes metal bilayers bend when heated. Here, we investigate experimentally how constraining conditions aﬀect the ﬁnal shape of peen formed parts. We report peen forming experiments for 4.9 mm thick rectangular 2024–T3 aluminum sheets of diﬀerent aspect ratios uniformly shot peened on one face with a low intensity saturation treatment. Some specimens were free to deform during peening while others were elas- tically prestressed in a four-point bending jig. For each aspect ratio and prestress condition, residual stresses were measured near the peened surface ∗Corresponding author Email address: frederick.gosselin@polymtl.ca (Fr´ ed´ erick P. Gosselin) URL: http://www.polymtl.ca/lm2 (Fr´ ed´ erick P. Gosselin) Preprint submitted to EngrXiv June 23, 2021 with the hole drilling method. Additional residual stress proﬁles were also ob- tained with the slitting method. The residual stress measurements show that the progressive deformation of unconstrained specimens had the same eﬀect as an externally applied prestress. For the peening conditions investigated, this progressive deformation caused unconstrained strips to exhibit curva- tures 33 % larger than identical strips held ﬂat during peening. Furthermore, we found that the relative importance of material anisotropy and geometric eﬀects did determine the bending direction of unconstrained specimens. Keywords: Initial stress, peen forming, platic strain, residual stress, 2024–T3 aluminum alloy 1. Introduction Shot peen forming stands out among sheet metal forming processes by its ﬂexibility and low operating costs. The process consists in bombarding thin metal parts with hard shot such that the incompatibility of deformations between the plastically deformed surface layers and the underlying material 5 causes the part to bend, as illustrated schematically in Figure 1a. Typical applications include forming large wing-skin panels for commercial aircraft [1, 2], forming doubly curved panels for space launchers [3, 4], and correcting small out-of-tolerance distortions on machined parts [5, 6]. Because peening stretches the material in all directions, uniformly peened 10 parts tend to deform into spherical shapes, as illustrated in Figure 1a. To break this symmetry, process engineers use a technique called stress peen 2 Figure 1. Peen forming of a metal plate. Repeated impacts plastically deform a thin layer of material which, as it stretches, causes the plate to deform. (a) Plates peened with low intensity treatments, thick plates, and plates with high aspect ratios tend to deform into spherical shapes. (b) Prebending a plate during peening results in larger curvatures in the prestress direction and smaller curvatures in the transverse direction. (c) Typical in-plane plastic strain and residual stress proﬁles after uniform peening. The in-plane expansion of the upper layers is resisted by the bulk, which causes compressive residual stresses near the surface. Conversely, the upper layers stretch the bulk, which causes tensile stresses deeper into the material. In the bulk, stresses vary linearly owing to the stretching and bending of the specimen. 3 forming where jigs are used to hold parts into a bent shape during peen- ing. This results in larger curvatures in the bending direction and smaller curvatures in the transverse direction, as illustrated in Figure 1b. The ﬁ- 15 nal curvatures of stress peen formed parts was repeatedly observed to be proportional to the prestress curvature. Table 1 compiles the publicly avail- able results we found on stress peen forming of uniformly peened rectangular plates. While many experimental studies dedicated to shot peening investigated 20 residual stresses, roughness, and changes in microstructure induced by peen- ing treatments, see for example the the literature reviews of [7], comparatively fewer considered peening induced distortions. Among these, most aimed at generating data to establish process parameters for a given application. For example, [8] investigated the inﬂuence of shot size, shot velocity, and the 25 plate’s aspect ratio on the curvature of 610 mm long 2024 and 7050 rectan- gular aluminum sheets that were free to deform during peening; [9] generated a dataset of curvature and residual stress proﬁles for 400 ×50 mm 7050 and 7475 aluminum strips for various prestress conditions; and [10] reported sim- ilar results for 76×19 and 76×76 mm 2024–T3 aluminum strips. Additional 30