Odkształcenie graniczne przy rozciąganiu blach o własnościach lepko-sprężystych
Limiting deformation of stretched sheet-metal with viscoelastic properties
In the paper the influence is analyzed of the viscous properties of a material, expressed by the exponent m in the equation
σ = C (ε0 + ε)n εm
describing the plastic properties of the deformed material, upon the process of concentration of the deformations of the sheet metal with a certain initial nonhomogeneity for the following kinds of load: a) homogeneous stretching, b) stretching of strips of sheet metal while maintaining constant width, c) biaxial uniform stretching.
The chosen method consists of observing the process of concentration of the deformations at the weakest place of the sheet metal until the moment it breaks. Numerical solution of the differential equations describing the course of the process allows to determine the limits of deformation of the sheet metal subjected to stretching. The graphs obtained in this way indicate that with the increase of the exponent m the process of concentration of the deformations is delayed, and the limiting deformation increases.
References
H.W. Swift, Plastic instability under plane stress, J. Mech. Phys. Sol., 1, 1 (1952).
P.P. Mellor, Plastic instability in tension, The Engineer, 25 (1960).
G.G. Moore, I. F. Wallace, The effect of anizotropy on instability an sheet metal forming.
M.L. Hilleer, Tensik plastic instability of thin tubes, Int. J. Mech. Sci., 8, 7 (1965).
Z. Marciniak, Stability of plastic shells under tension with kinematic boundary conditions, Arch. Mech. Stos., 4, 17 (1965).
Z. Marciniak, K. Kuczynski, Limit strain in the processes of stretch forming sheet metal, Int. J. Mech. Sci., 9 (1967).
Z. Marciniak, Analysis of necking preceding fracture of sheet metal under tension, La Metallurgia Italiana, 8 (1968).