Motivated by the already developed micromechanical approach (Abdul-Latif et al., 2002, “Elasto-Inelastic Self-Consistent Model for Polycrystals,” ASME J. Appl. Mech., 69(3), pp. 309–316.), a new extension is proposed for describing the mechanical strength of ultrafine-grained (ufg) materials whose grain sizes, d, lie in the approximate range of 100 nm < d < 1000 nm as well as for the nanocrystalline (nc) materials characterized by d≤100 nm. In fact, the dislocation kinematics approach is considered for characterizing these materials where grain boundary is taken into account by a thermal diffusion concept. The used model deals with a soft nonincremental inclusion/matrix interaction law. The overall kinematic hardening effect is described naturally by the interaction law. Within the framework of small deformations hypothesis, the elastic part, assumed to be uniform and isotropic, is evaluated at the granular level. The heterogeneous inelastic part of deformation is locally determined. In addition, the intragranular isotropic hardening is modeled based on the interaction between the activated slip systems within the same grain. Affected by the grain size, the mechanical behavior of the ufg as well as the nc materials is fairly well described. This development is validated through several uniaxial stress–strain experimental results of copper and nickel.
The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class