General constitutive equation for metal powder compaction and its application to closed die compaction and powder rolling

Based on the constitutive equation for cold isostatic compaction of metal powder, which was previously reported by us, the constitutive equation for general stress states has been proposed as follows, alpha(D)J'(2) + beta (D)J(1)(2) = sigma(eq)(2) where alpha(D) = 3/[1 - exp (- V-ex) + V-ex exp (-V-ex/500)] beta(D) = 2/(9V(ex)) and V-ex = (3/4)(2) (D/D-0)(2/3)[(D - D-0)/(1 - D)](2). J'(2) and J(1) are the second deviatoric stress invariant and the first stress invariant respectively and a, is equivalent stress. This equation was applied to estimate pressure transmission transfer coefficient, the relation between uniaxial pressure and relative density for pure aluminum and 7075 aluminum alloy powder in closed die compaction, and rolling load in cold powder rolling for pure aluminum powder. From the comparison of their calculated results with the experimental ones, it was shown that the proposed constitutive equation is correct.