Formulation of a Generalized Unit Cell and its Application to Shot Peening Simulation

The simulation of the residual stress field achieved by shot peening cannot be carried out on component-large models. Hence, an efficient unit cell model for the simulation of the shot peening process is developed. The model allows both, the simple inclusion of a pre-stress and the evaluation of the up-arching of the Almen strip. For this purpose, generalized coupling constraints for the periodic boundaries of the unit cell are developed. These allow for displacement and rotation of the coupled boundaries relative to each other. In the coupling constraints, this is accomplished by respective variables, which can either be prescribed to the analysis or read out as a result from the analysis. Hence, the unit cell can expand, shear, bend and twist under driving forces like, e. g., residual stresses or thermal effects. At the same time, deformations of the cell’s periodic boundary pairs are kept congruent by the generalized coupling. The ability to cover expansion is novel regarding known periodic boundary conditions. Also, the application of a generalized unit cell to shot peening is new. Results obtained with the generalized unit cell are displayed, demonstrating its capabilities: A fundamental analysis of the residual stress field from shot peening shows inhomogeneities at a fatigue relevant level to be inevitable. A validation of the model was done by comparison with experimental Almen strip shot peening tests reported in literature. Shot peening under pre-stress is demonstrated and its results in terms of residual stress are evaluated. The application of the generalized unit cell is not limited to shot peening. [Display omitted] •Model: Expansion, shear, bending and twist can be either input to or output of the unit cell with generalized periodicity.•Use: Pre-stressing can be modeled by prescribed e. g. expansion and/or bending.•Use: The deformation, e. g. due to residual stresses or thermally caused, can be read out as a result.•Observation: Scatter in residual stress is non-diminishing, even in integral saturation – this may affect fatigue life.