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KSME Journal

, 6:6 | Cite as

A finite element program for simulating sheet-metal stretch forming processes

  • Y. T. Keum
  • R. H. Wagoner
Article
  • 335 Downloads

Abstract

A finite-element process modeling program, SHEET-3, was developed using triagnular elements for simulating the sheet-metal stretch forming operation of an arbitrarily-shaped punch and dies. The program employs an implicit, incremental algorithm based on a rigid-viscoplastic constitutive equation with corrections for material unloading. Contact and friction are introduced through a mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of the tool surfaces. The membrane approximation is adopted under the plane-stress assumption. In order to promote convergence, equilibrium and contact iterations are split. For describing an arbitrarily-shaped tool surface, a generalized tool description method is introduced. Simple shape of tools, such as the hemispherical punch and rounded flat-top punch can be analyzed. In addition, any tool described by equally-spaced digital data can be used, based on cubic B-spline or piecewise linear basis functions. The validity, accuracy and stability of the FEM formulation were numerically tested using simple stretch forming examples. Excellent agreement between measured and computed strains was obtained.

Key Words

Sheet-Metal Forming Simulation Rigid-Viscoplastic Hardening Press-Die Design Analysis Membrane Shell Theory Finite Element Method Tool Description 

Nomenclature

Δεi

Principal strain increment

\(\Delta \bar \varepsilon \)

Effective strain increment during †t

Δλi

Principal stretch ratio

Δt

Time increment

Δu

Incremental displacement during Δt

Δut

Tangential incremental displacement

Δut

Trial incremental displacement

δu

Correction displacement increment

\(\bar \varepsilon \)

Effective strain

\(\bar \varepsilon \)

Effective strain rate

Fi

Internal force vector

Fe

External force vector

Fn

Normal component ofF e

Ft

Tangential component ofF e

Γ

Contact force direction

Ke

External stiffness matrix

Ki

Internal stiffness matrix

M

Hill's non-quadratic yield function parameter

m

Strain rate sensitivity index

μ

Coulomb friction coefficient

n

Mesh-based normal unit vector

r

Plastic anisotropy parameter

S

Tool surface function,z=S(x,y)

σi

Principal Cauchy stress

\(\bar \sigma \)

Effective stress

t

Time variable; Length parameter

t

Mesh-based tangential unit vector

t0

Reference time

V0

Volume att=t 0

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1992

Authors and Affiliations

  • Y. T. Keum
    • 1
  • R. H. Wagoner
    • 2
  1. 1.CAD/CAM Lab.Korea Institute of Science and TechnologySeoulKorea
  2. 2.Department of Materials Science and EngineeringThe Ohio State UniversityColumbusU.S.A.

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