Goya and Ito[Goya, M. et al.:Trans. Jpn. Soc. Mech. Eng., Ser. A, 54-504(1988), 1617-1622.] proposed an expression of plastic constitutive law in which both the direction and magnitude of the plastic strain increment ε˙ ^p are expressed as functions of the stress increment σ˙ ′ and unit normal n_N of the plastic potential function. The expression is developed through the introduction of two independent transition parameters 𝜇(𝛼) and 𝛽(𝛼) , which denote the magnitude and direction angle of the plastic strain increment, respectively, and are defined as functions of the direction angle 𝛼 of the stress increment. The angle 𝛼 is defined as the direction measured from the unit normal n_N in deviatoric stress space. Then, the authors[Ito, K. et al.:Trans. Jpn. Soc. Mech. Eng., Ser. A, 57-533(1991), 141-146.] investigated specific forms of 𝜇(𝛼) and 𝛽(𝛼) through the application of the linear-comparison solid theory to the local necking problem of a rigid plastic plate subjected to biaxial stretching. The specific forms were proposed as functions of three material parameters 𝐾_C |_{Uniaxial Direction}, 𝐾₀ and 𝛾. In this paper, we report on a method to explicitly estimate the parameter values using a forming limit diagram, which has been widely used in many industries as a useful test to evaluate the formability of thin metallic sheets.

Incremental forming is suitable for the low-volume production of various products, but the reduction in sheet thickness caused by ironing is remarkable. Therefore, diaphragm forming was applied to transform a disk-shaped workpiece into a spherical one, and the reduction in sheet thickness was successfully suppressed. However, diaphragm forming was difficult for strip workpieces because of insufficient restraining force. Therefore, incremental pack forming was performed by sandwiching a 2024-T3C sheet between a Steel Plate Cold Commercial (SPCC) cover sheet and a lower sheet made of pure aluminum or rubber. In the case of pure aluminum, semispherical forming without wrinkles was possible, but in the case of rubber, wrinkles appeared at the edges as the material became softer. Moreover, in the case of pure aluminum, the sheet thickness decreased in the region where the forming angle was large, but in the case of rubber, the sheet thickness did not change.