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Fracture initiation in plastic metals is attributed to the development of voids. Analyzing the nucleation and growth processes of voids facilitates the study of plastic deformation and fracture mechanisms in metal materials. Uniaxial tensile tests were conducted on two high-quality carbon structural steels, and the microfracture surface morphology of the tensile specimens was observed by using a scanning electron microscope (SEM). From the perspective of vacancy condensation, the nucleation mechanism of voids in the absence of inclusions or particles was analyzed. Based on the continuum damage mechanics theory and the Rice–Tracy (R-T) model, a damage parameter considering the void volume fraction was derived, and a plastic potential function, hardening curve, and constitutive model for the plastic deformation process of the plastic metal material were established. Based on the uniaxial tensile test data of the two sheets of high-quality carbon steel, the strain range data in the hardening stage were converted into true stress–plastic strain data, and the established hardening curve was used to fit the true stress–plastic strain data. The results showed good agreement between the established hardening curve and the experimental results, which effectively reflected the deformation process of ductile fractures in plastic metal materials.