Development of analytical strength estimator for self-piercing rivet joints through observation of finite element simulations

Analytical strength estimators for self-piercing riveted (SPR) metal sheets under the lap-shear and the cross-tension modes are developed. The modeling is based on the local mechanical responses of rivet and sheet metals during the riveting process and joint strength tests, which are investigated using finite element (FE) simulations as virtual experiments. The FE simulations consist of the riveting process model and lap shear test model, and the plastic strain hardening and damage of sheet metals near the riveted zone are transferred between the two models. The cross-sectional geometry of the riveted zone and the load-displacement curve during the lap-shear test are predicted with three different ductile fracture criteria, Cockcroft–Latham, Rice–Tracey, and Drucker–Prager model, to evaluate the accuracy of the FE modeling. The four-parameter joint strength estimator for the lap-shear and cross-tension are proposed based on the observations of the geometrical features and mechanical responses in the FE simulations. The results of prediction are within reasonable accuracy for various combinations of steel and aluminum alloy sheets, particularly 31 among 34 cases showed prediction errors within 25% for the lap shear-tests, and 14 among 18 cases for the cross-tension tests, and average errors for lap-shear and cross-tension mode were 12.1% and 14.4%, respectively.