The Micromechanic Theory of Constitutive Relations of Polycrystalline Solids

This research is to derive the macroscopic multi-axial stress-strain and stress-strain-time relations of metals from those of the component crystals. Since the macroscopic stress-strain relation depends on the grain size, the component crystal properties are also dependent on grain size. Hence the component crystal stress-strain relation is here derived from the uniaxial polycrystal tests. This automatically takes care of the grain size effect. The same approach is used to derive the macroscopic stress-strain-time relation creep of metals. In this derivation, the conditions of mechanics i.e., the condition of equilibrium, and the continuity of displacement are fully satisfied. Hence the discrepancy between the calculated and experimental results is likely due to the error in representation of the component crystal characteristics. Recently Bassani 1990 and Wu et. al., 1990 have compressed a single crystal to activate a primary slip system, unloaded this crystal, then reoriented and compressed to activate a second slip system. He found the critical shear stress of the second system increases rapidly, i.e., high rate of hardening. This characteristic is not shown in a single crystal under a tensile loading. In the previous physical theories, the stress-strain relations of the component crystals were calculated from the polycrystal tensile test data Lin, 1971 and this high hardening rate was not encountered. In the present study, this high hardening rate is considered. It is found that the agreement between the calculated and experimental results is much further improved.