Specimen size effect on the lüders deformation in mild steel sheet

The Lüders or Lüders-type deformation stands as a prominent phenomenon in metallic materials, characterized by Lüders band induced by local plastic softening. This behavior imposes limitations on the structural applications of materials, particularly during the processing of micro-sized specimens. A comprehensive understanding of the internal mechanism behind Lüders deformation can improve the application prospects of such materials, including their deformation characteristics and the evaluation of major internal influencing factors through modeling. Herein, we conducted tensile tests on mild steel sheets with varying specimen thicknesses and employed the Digital Image Correlation (DIC) method to characterize local strain evolution. Our investigation revealed that specimen size affects not only the strength but also Lüders strain and band strain. Specifically, both Lüders strain and band strain demonstrate a decline with decreasing specimen thickness. We developed a finite element (FE) simulation model that utilizes the concept of surface layer model from size effect research. In this model, surface layers with lower and continuous flow stress are added to samples that exhibit discontinuous up-down-up responses, enabling accurate replication of the specimen size effect in Lüders deformation. The strain and stress distribution at the Lüders front from simulation results were extracted and analyzed by data fitting. Factors influencing the magnitude of Lüders strain were elucidated through a concise formula incorporating a stress concentration factor at the Lüders front and work hardening capacity. Additional factors related to sample size, such as shear strain and defects are also discussed in this study.