Abstract:A unified linear expression of plastic work rate per unit volume is deduced from the unified linear yield criterion and the associated flow rule. The expression is suitable for various linear yield loci in the error triangle between Tresca’s and twin shear stress yield loci on the π-plane. It exhibits generalization in which the different value of criterion parameter b corresponds to a specific linear formula of plastic work rate per unit volume. Finally, with the unified linear expression of plastic work rate and upper-bound parallel velocity field the strip forging without bulge is successfully analyzed and an analytical result is also obtained. The comparison with traditional solutions shows that when b=1/(1+ ) the result is the same as the upper bound result by Mises’ yield criterion, and it also is identical to that by slab method with m=1, σ₀=0.

Key words: π-plane; flow rule; unified linear plastic work rate; deduction; application