Eigenstrain‐based analysis of why uniformly shot peened aluminium plates bend more in the rolling direction

Shot peen forming is a process widely used to shape aircraft components such as wing skins, yet its fundamental working is still crudely understood. It is understood that a light conventional peen forming treatment applied uniformly over an initially flat plate will induce isotropic in‐plane stretching of the surface layer and will thus lead to a panel curving with identical curvatures in all directions. However, [1] made the startling observation that uniformly peen formed aluminium plates of different aspect ratios all bent along their laminating direction irrespective of the peening direction. This experimental result is counterintuitive because the residual stresses due to the lamination process are 1 order to 2 orders of magnitude smaller than those induced by the shot peen forming treatment. In the present study, we apply the eigenstrain theory to estimate the effect of the different sources of anisotropy on uniformly peen formed aluminium plates. Potential sources of anisotropy included the plastic anisotropy of rolled aluminium, nonequibiaxial initial stresses that redistribute when their equilibrium is disturbed by peening, the geometry of the specimens and externally applied prestress. For the alloy and peening conditions considered, we show that plastic anisotropy had no discernible influence on the resulting shape of the peen formed specimens. Initial residual stresses, on the other hand, caused slightly larger bending loads in the rolling direction of the alloy. Although the magnitude of these loads was approximately 30 times smaller than peening‐induced loads, it was sufficient to overcome the geometric preference for rectangular sheets to bend along their long side and cause all unconstrained specimens to bend along the rolling direction instead. Our analysis highlights the importance of the history of the material that is being peened. Residual stresses already present in the part before peening must be considered to ensure good simulation predictions.