Evolution of geometrically necessary dislocations in a thin sheet of pure copper and the influence on the springback in micro-bending

The effects of the sample grain size, bending strain gradient, and free surface of surface grains on the evolution of geometrically necessary dislocations in a thin sheet of pure copper and the influence on the springback in micro-bending were studied. Uniaxial micro-tension, micro-bending, and electron back scatter diffraction (EBSD) were performed. The springback angle has the same trend as the flow stress at the mesoscale. As the grain size increased from 15.6 to 90.7 μm, the average geometrically necessary dislocation (GND) density in the annealed samples ranged between 4.4 × 10¹³ and 2.8 × 10¹³ m⁻², corresponding to annealing temperatures between 500 °C and 800 °C. The EBSD results indicated few geometrically necessary dislocations (GNDs) within the grains and that GNDs are mainly concentrated near the grain boundaries in the annealed samples. The Ashby formula is modified by introducing the dislocation cell size, and the GND density of uniaxial micro-tension samples is more accurately predicted. Additionally, since the strengthening effect of the bending strain gradient is similar to that of the strain on the material, it is introduced into the modified Ashby formula, which effectively predicts the GND density along the thickness direction of the bending deformation area. Finally, the effect of the bending strain gradient on the relative amount of statistical storage dislocation (SSD) and GND is revealed. In addition, the contribution of the bending strain gradient to the springback angle of the thin sheet of pure copper gradually increased as the grain size increased.