The frequently used metallurgical parameters such as activation volume, internal stress, strain rate sensitivity, and dislocation density are identified in ultrafine-grained (UFG) materials through erudite analytical relations. It is difficult to analyze such parameters optically since the material consists of highly distorted and inhomogeneous microstructure due to the large strain imposed during the constrained groove pressing (CGP) process. Hence, transient tests like stress relaxation tests are advantageous over the optical to use. Apart from the identification of parameters in low-carbon steel materials using uniaxial loading and stress relaxation tests, the relationship between the parameters is nobly investigated in as-received and UFG structure samples produced through the CGP process. In the relationship, the exponential-power law constitutive to describe the accurate stress–strain curves, identification of mobile and forest dislocation density during strain hardening, and exponential variation between grain size and activation volume are proposed. The replenishment or exhaustion of mobile and forest dislocation density significantly affects the metallurgical parameters during uniaxial tensile loading followed by stress relaxation testing. In this experimental and analytical work, the CGP process produces a UFG material that has lower activation volume and higher stress drop, mobile dislocation density, forest dislocations density, strain rate sensitivity, and internal stress.