Algorithm and analytical verification of roller straightening process model considering stress inheritance behavior

With the increasing demand for high-strength thin-gauge plates, the challenge of straightening these materials remains critical. This study investigates the elastic–plastic deformation behavior of plates and strips under significant deformation conditions during the positive and negative bending processes. It focuses on the influence of the stress inheritance effect on the curvature–bending moment (M–K) relationship and establishes an analytical model for the continuous straightening process based on the curvature integral method while incorporating the stress inheritance effect. The proposed model is validated through experiments and finite element simulations, achieving a residual stress error within 10%, confirming its accuracy. In addition, this study examines the effects of the plasticity rate and the number of rollers in the straightening machine. The findings indicated that as the plasticity rate increases, the plate exhibits a significant stress–strain hysteresis effect during multiple positive and negative bending cycles, causing the M–K relationship to enter the nonlinear range prematurely. This phenomenon significantly affects the central deformation of the plate and the final residual stress distribution. In addition, increasing the number of straightening rollers and elastic–plastic deformation cycles results in more residual stress inflection points across the plate section. This leads to a more uniform residual stress distribution, ultimately enhancing plate quality and advancing intelligent straightening technology.