Constitutive description of severely deformed metals based on dimensional analysis

A constitutive equation for description of mechanical behaviour of metals at large strains was proposed to relate the important process variables associated with severe plastic deformation. Dimensional analysis based on the so called pi-theorem was used for this purpose; in which the obtained dimensionless groups were related and rewritten to achieve the constitutive equation. The validity of the proposed relationship was investigated using the flow stress data of an aluminium alloy processed by accumulative roll bonding (ARB), copper processed by equal channel angular pressing (ECAP) and low carbon steel processed by constrained groove pressing (CGP) technique. It was shown that the predictions of the proposed model agree well with the experimental observations over a wide range of strain for different materials. Moreover, this model was able to address both hardening and softening at high strains. These prove the applicability of the pi-theorem as an alternative approach to derive the constitutive relationships of heavily deformed metals with emphasis on the microstructure evolution.