Abstract
A slip-line field theory that includes rotational continuity, published in an earlier article and shown therein to lead to Hill's equiangular net, is extended to include work-hardening. This object is achieved by applying a rule of work-hardening shown in another earlier article to lead to the load observed in plane-strain extrusion experiments, work hardening having been shown to make a substantial contribution. The three-dimensional slip-line field theory developed in the paper is applied to the problem of a tube drawn through a conical die. It is shown how the force necessary to hold the tube against the die and so to prevent wrinkling may be calculated.
References
R.L. BISH, Three-dimensional slip-line field theory with rotational continuity, Engng. Trans., 44, 2, 207-228, 1996.
E.R. PARKER, Modem concepts of flow and fracture, Edward De Mille Campbell Memorial Lecture (ASM), 50, 52-104, 1957.
R.L. BISH, The flow of a work-hardening solid by inviscid slip between elastic domains, Acta Mech., 83, 1-7, 1990.
R.L. BISH, Plane-stress deformation of a fiat plate by slip between elastic elements, Arch. Mech., 46, 1, 3-12, 1994.
W. PRAGER, Recent developments in plasticity, J. Appl. Phys., 20, 235-241, 1949.
W.T. KOITER, Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface, Quart. Appl. Math., 11, 350-354, 1953.
R.L. BISH, Transverse deflection of a cold-worked metal plate clamped around its edge, Engng. Trans., 43, 4, 627-635, 1995.
P. PERZYNA, The constitutive equations for rate-sensitive plastic materials, Quart. Appl. Math., 20, 321-332, 1963.
J.D. JEVONS, The metallurgy of deep drawing and pressing, Chapman & Hall, 1941.
L.E. SAMUELS, Optical microscopy of carbon steels, ASM, 1980.
R.L. BISH, Etching of plastic zones in mild steel, J. Aust. Inst. of Metals, 21, 167-168, 1976.
R.L. BISH, The plane-strain extrusion of a work-hardening solid, Acta Mech., 85, 125-130, 1990.
E.R. PARKER, Modem concepts of flow and fracture, Edward De Mille Campbell Memorial Lecture (ASM), 50, 52-104, 1957.
R.L. BISH, The flow of a work-hardening solid by inviscid slip between elastic domains, Acta Mech., 83, 1-7, 1990.
R.L. BISH, Plane-stress deformation of a fiat plate by slip between elastic elements, Arch. Mech., 46, 1, 3-12, 1994.
W. PRAGER, Recent developments in plasticity, J. Appl. Phys., 20, 235-241, 1949.
W.T. KOITER, Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface, Quart. Appl. Math., 11, 350-354, 1953.
R.L. BISH, Transverse deflection of a cold-worked metal plate clamped around its edge, Engng. Trans., 43, 4, 627-635, 1995.
P. PERZYNA, The constitutive equations for rate-sensitive plastic materials, Quart. Appl. Math., 20, 321-332, 1963.
J.D. JEVONS, The metallurgy of deep drawing and pressing, Chapman & Hall, 1941.
L.E. SAMUELS, Optical microscopy of carbon steels, ASM, 1980.
R.L. BISH, Etching of plastic zones in mild steel, J. Aust. Inst. of Metals, 21, 167-168, 1976.
R.L. BISH, The plane-strain extrusion of a work-hardening solid, Acta Mech., 85, 125-130, 1990.
