Modeling of surface layer and strain gradient hardening effects on micro-bending of non-oriented silicon steel sheet

Non-oriented silicon steel, as the key magnetic material of motors, has a general tendency toward thinner and coarser-grained. The characteristic of countable grain number in thickness leads to the so- called size effect. In the 4 point micro-bending experiments, it is observed that the deformation behaviors of non-oriented silicon steel sheet are size-dependent on both feature size (grain size, thickness) and strain gradient. The results show that the decrease of grain number in thickness direction would decrease the flow stress of overall material, but also expand the effect of strain gradient hardening. To address this issue, a hybrid model involving surface-layer model with conventional strain gradient plasticity theory is proposed. The relationship between shear stress and dislocation density bridges the plastic strain and plastic strain gradient hardening. The proposed hybrid model is adopted to calculate the analytical solution of normalized bending moment, which agrees well with the experimental data. Moreover, the integrated size effect is further illustrated based on the proposed model. It is conclude that which kind of size effect is dominant would depend on the materials microstructure, geometrical and processing parameters. A three-dimensional (3D) region to determine the necessity of considering strain gradient hardening effect in manufacturing is proposed. This research thus advances the understanding of the size effect from material intrinsic characteristics and processing conditions.