Influence of size effect and plastic strain gradient on the springback behaviour of metallic materials in microbending process

In micro-bending process, the size effect induced by the variation of grain size and geometrical size (the thickness) of sheet metals, represented by the ratio of surface grain number to the total grain number of workpiece (η), and strain gradient effect are the key factors affecting the bending behaviour and springback angle. The interaction of the grain-based size effect and the strain gradient effect on springback has not yet been fully understood and investigated in micro-scaled bending of metallic materials. In this research, a combined constitutive model simultaneously considering both the grain size effect and strain gradient was proposed. The theoretical calculation was conducted using the proposed model, and quantitative evaluation was made of the contribution from each kind of size effect on the springback angle. The springback angle due to strain gradient size effect decreases with the increase of sheet thickness and the decrease of the grain size. Pure microbending experiments using copper alloy sheet metal samples with the thickness of 0.1, 0.2, and 0.4 mm were conducted, and the springback angles calculated using the established model were corroborated by the experimental results, providing model validation. The reported results thus provide an in-depth understanding of the grain-geometrical size effect and strain gradient size effect influence on the springback behaviour in micro-bending of metallic materials.