Solidification Stress Model in Abaqus

24 Pages·2004·6.99 MB·English

CCC Report, May 10, 2004
SSoolliiddiiffiiccaattiioonn SSttrreessss MMooddeell iinn AAbbaaqquuss
Seid Koric
Engineering Applications Analyst
National Center for Supercomputing Applications -NCSA
PhD Candidate at Mechanical and Industrial Engineering
University of Illinois at Urbana-Champaign
[email protected]
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 1
OObbjjeeccttiivveess
To predict the evolution of temperature, shape, stress and
(cid:122)
strain distribution in the solidifying shell in continuous
casting mold by using world’s leading nonlinear commercial
multipurpose finite element package with an accurate
approach.
Validate the model with available analytical solution and
(cid:122)
benchmarks with in-house code CON2D.
To apply new Abaqus model to our real problems with even
(cid:122)
more complex phenomena.
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 2
WWhhyy AABBAAQQUUSS ??
(cid:122) If its convergence problems can be overcome, ABAQUS offers a wide range
of capabilities.
(cid:122) It is relatively simple to use, other modelers in this field can largely benefit
from this work, including our final customers – the steel industry.
(cid:122) Abaqus has imbedded pre and post processing tools supporting import of
the major CAD formats. All major general purpose pre-processing packages
like Patran and I-DEAS support Abaqus.
(cid:122) Abaqus is using full Newton-Raphson scheme for solution of global
nonlinear equilibrium equations and has a powerful contact algorithm.
(cid:122) Abaqus has a rich library of 2D and 3D elements.
(cid:122) Abaqus has parallel implementation on High Performance Computing
Platforms which can scale wall clock time significantly for large 2D and 3D
problems.
(cid:122) Abaqus can link with external user subroutines (in Fortran and C) linked with
the main code than can be coded to increase the functionality and the
efficiency of the main Abaqus code.
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 3
BBaassiicc PPhheennoommeennaa
(cid:122) Initial solidification occurs at the
meniscus and is responsible for the
surface quality of the final product.
(cid:122) Thermal strains arise due to volume
changes caused by temp changes and
phase transformations.
Inelastic Strains develop due to both
strain-rate independent plasticity and
time dependant creep.
(cid:122) At inner side of the strand shell the
ferrostatic pressure linearly increasing
with the height is present.
(cid:122) The mold taper has the task to
compensate the shell shrinkage yielding
good contact between strand shell and
mold wall.
(cid:122) Many other phenomena are present due
to complex interactions between thermal
and mechanical stresses and micro
structural effects. Some of them are still
not fully understood.
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 4
11DD SSoolliiddiiffiiccaattiioonn SSttrreessss PPrroobblleemm ffoorr PPrrooggrraamm VVaalliiddaattiioonn
(cid:122) Analytical Solution exists (Weiner
& Boley 1963)
(cid:122) 1D FE Domain used for validation
(cid:122) Generalized plane strain both in y
and z direction to give 3D
stress/strain state
(cid:122) Yield stress linearly drops with
temp. from 20Mpa @ 1000C to
0.07Mpa @ Solidus Temp
1494.35C
(cid:122) Tested both internal PLASTIC
Abaqus procedure and a special
high-creep function to emulate
Elastic-Prefect Plastic material
behavior
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 5
GGoovveerrnniinngg EEqquuaattiioonnss
Heat Transfer Equation:
 ∂H(T)  ∂T  ∂  ∂T  ∂  ∂T 
ρ = k(T) + k(T)
      
 ∂T  ∂t  ∂x  ∂x  ∂y  ∂y 
Equilibrium Equations 2D:
∂∆σ ∂∆τ
x + xy = ∆F
∂x ∂y x
∂∆σ ∂∆τ
y + xy = ∆F
∂y ∂x y
∫∆σdA= ∆F
z z
∫ x∆σdA= ∆M
z x
∫ y∆σdA= ∆M
z y
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 6
MMoorree EEqquuaattiioonnss::
Constitutive Equations:
{∆σ} = [D]{∆ε}+[∆D]{ε}
1−ν ν 0 ν 
e e
 
where, ν 1−ν 0 ν
 
E(T)
{σ} = {σ σ σ τ }T [D]=(1+ν)(1−2ν) 0 0 1−2ν 0 
 
x y z xy 2
 
{ε} = {ε ε ε ε }T  ν ν 0 1−ν
x y z xy
Generalized Plane Strain Finite Elements Implementations
∂∆u
∆ε = x
x ∂x [K ]{T } + [C ]{T(cid:5)} = {Q }
∂∆u
∆ε = y
y ∂y [K]{∆u} ={∆F }+{∆F }+{F }+{F }
ε ε fp el
1∂∆u ∂∆u  th pl
∆ε = y + x
 
xy 2 ∂x ∂y Incremental Total Strain
 
∆ε = a+bx+cy
{ }
z {∆ε} ={∆ε}+{∆ε }+ ∆ε
e th pl
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 7
CCoonnssttaannttss UUsseedd iinn AAbbaaqquuss NNuummeerriiccaall
SSoolluuttiioonn ooff BB&&WW AAnnaallyyttiiccaall TTeesstt PPrroobblleemm
Conductivity [W/mK] 33.
Specific Heat [J/kg/K] 661.
Elastic Modulus in Solid [Gpa] 40.
Elastic Modulus in Liq. [Gpa] 14.
Thermal Linear Exp. [1/k] 2.E-4
Density [kg/m3] 7500.
Poisson’s Ratio 0.3
Liquidus Temp [O C] 1494.48
Solidus Temp [O C] 1494.38
Initial Temp [O C] 1495.
Latent Heat [J/kgK] 272000.
Number of Elements 300.
Uniform Element Length [mm] 0.1
Artificial and non-physical thermal BC from B&W (slab surface quenched to 1000C),
replaced by a convective BC with h=220000 [W/m2K]
Simple calculation to get h, from surface energy balance at initial instant of time:
∂T 495
33 = h 495
− k = h(T − T ) and for finite values
0.0001
∞
∂x
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 8
TTeemmppeerraattuurree aanndd SSttrreessss DDiissttrriibbuuttiioonnss ffoorr 11DD
SSoolliiddiiffiiccaattiioonn
AAbbaaqquuss aanndd AAnnaallyyttiiccaall ((WWeeiinneerr--BBoolleeyy))SSoolluuttiioonnss
(cid:122) Model is numerically consistent
(cid:122) The numerical representations
and has acceptable mesh
from MATLAB and Abaqus
produces almost identical results
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 9
AAdddd mmoorree ccoommpplleexxiittyy ((pphhyyssiiccss)) ttoo tthhee AAbbaaqquuss mmooddeell
bbyy mmeeaannss ooff uusseerr ssuubbrroouuttiinneess
5
Applied instantaneous Heat Flux from a real plant
4
measurements:
3
2
5−0.2444t(sec.) t ≤1.0sec.

( )
q MW / m3 = 
4.7556t(sec.)−0.504 t >1.0sec. 1

0
0 10 20 30 40 50 60
200 Time Below Meniscus (sec.)
180
160
a)140
P
G
s(120
u
ul
d100
o
M
c 80
Elastic modulus decreases as temperature increase: sti
Ela 60
40
20
0
0 200 400 600 800 1000 1200 1400 1600
Temperature(oC)
Seid Koric
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • 10