Acta Mechanica Solida Sinica

, Volume 24, Issue 2, pp 153–165 | Cite as

Sectional finite element analysis of coupled deformation between elastoplastic sheet metal and visco-elastoplastic body

Article

Abstract

The present paper is devoted to developing a new numerical simulation method for the analysis of viscous pressure forming (VPF), which is a sheet flexible-die forming (FDF) process. The pressure-carrying medium used in VPF is one kind of semisolid, flowable and viscous material and its deformation behavior can be described by the visco-elastoplastic constitutive model. A sectional finite element model for the coupled deformation analysis between the visco-elastoplastic pressure-carrying medium and the elastoplastic sheet metal is proposed. The resolution of the Updated Lagrangian (UL) formulation is based on a static explicit approach. The frictional contact between sheet metal and visco-elastoplastic pressure-carrying medium is treated by the penalty function method. Coupled deformation between sheet metal and visco-elastoplastic pressure-carrying medium with large slip is analyzed to validate the developed algorithm. Finally, the viscous pressure bulging (VPB) process of DC06 sheet metal is simulated. Good agreement between numerical simulation results and experimental measurements shows the validity of the developed algorithm.

Key words

viscous pressure forming(VPF) sheet forming sectional finite element analysis coupled deformation visco-elastoplastic pressure-carrying medium 

Nomenclature

E

Young’s modulus

ν

Poisson’s ratio

H′

the slope of the equivalent stress/plastic strain

ε̅p

equivalent plastic strain

σ̅

equivalent stress

ε0

initial yielding strain

K

material strength coefficient

n

work hardening index

A, B, h, α, β, ω

material parameters of visco-elastoplastic body

t

total time

Δt

time increment

εp

plastic strain component

εve

viscoelastic strain component

εvp

viscoplastic strain component

δij

Kronecker delta tensor

σij

Cauchy stress components

σ′ij

deviatoric stress components

σij

Jaumman rate of Cauchy stress

lkl

velocity gradient in the local coordinate system

Dijklep

elastoplastic constitutive matrix

C

compliance matrix

D

elastic matrix

BL

strain matrix

γ

fluidity parameter

F

general yield criterion

J′2

second deviatoric stress invariant

k

shear yield strength

σs

yield strength

λ

integration parameter

kT

tangential penalty factor

kN

normal penalty factor

μ

friction coefficient

τ

time incremental parameter

εe

elastic strain component

rate of traction

c

equivalent contact force virtual power rate

δc

relative nodal velocity

Nc

shape function of contact segment

ġ

penetration (gap) rate

Kc

stiffness matrix of contact elements

n1e, n2e

total element number of sheet metal and visco-elastoplastic body

nc

total number of contact point pair

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringHarbin Institute of TechnologyHarbinChina

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