Analytic prediction of structural stress-strain relations of microstructured metal

Nanostructured and ultra-fine grained metals have higher strength but extremely limited ductility compared to coarse grained metals. However, their ductility can be greatly improved by introducing a specific range of grain sizes in the microstructures. In the paper, multiscale unit cell approach (UCA) is developed and applied to predict the averaged stress-strain relations of the multi-scale microstructure metals. The unit cell models are three-phase structured at different scale lengths of 100 nm, 1 μm and 10 μm with different volume fractions and periodic boundary conditions. The contributions of multi-scale microstructures to the macroscopic structural properties of metals are also studied using a analytic approach-two-step mean-field method (TSMF), where three microstructural parameters are introduced and thus mechanical properties such as strength and ductility are presented as a function of these parameters. For verification of these proposed numerical and theoretical algorithms, the structural properties of the pure nickel with three-grain microstructures are studied and the results from FEA and the proposed theory have good agreement.