On some simple steady forming process of viscoplastic solids. (English) Zbl 0584.73042
Steady drawing and extrusion processes of conventional viscoplastic materials, through wedge-shaped and conical dies, are analyzed. The basic material model assumes that the Eulerian strain rate is the sum of a plastic part and a viscous part. The investigation is restricted to relatively long and tapered dies with small wall friction. Within these limitations it is permissible to treat the flow patterns as being nearly radial. The problem is thus reduced to a single nonlinear differential equation. A few exact solutions are obtained and a further analysis is given for purely viscous solids. For the latter case we demonstrate the existence of optimum die angles where the required drawing tension attains a minimum.
MSC:
| 74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |
| 74C20 | Large-strain, rate-dependent theories of plasticity |
Keywords:
plane-strain; axially-symmetric conditions; viscoplastic constitutive law; strain-hardening material; steady flow; von-Mises flow rule; Eulerian frame of reference; Steady drawing; extrusion processes; conventional viscoplastic materials; wedge-shaped; conical dies; Eulerian strain rate; sum of a plastic part and a viscous part; long and tapered dies; small wall friction; flow patterns; nearly radial; reduced to a single nonlinear differential equation; exact solutions; purely viscous solids; existence of optimum die angles; drawing tension attains a minimumReferences:
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