advances in numerical modeling of manufacturing processes

RAJIV SHIVPURI : NUMERICAL MODELING OF MANUFACTURING PROCESSES
d 0
At The Ohio State University, microstructure
evolution models for vanadium modified ferritepearlite
microalloyed steel TMS80R were integrated
with the FEM models for process simulations. To
model austenite evolution in a thermomechanical
control process, it is necessary to develop the models
for grain growth kinetics, static recrystallization
kinetics, metadynamic recrystallization kinetics, and
recrystallized grain size ( d
rex
). These models were
developed by conducting controlled heating and hot
compression tests on a Gleeble 3500
thermomechanical testing machine at DSI Inc. Details
on the testing can be found in Pauskar 12 .
2.2.1 Grain growth model
Grain growth using conventional grain growth law
and regression analysis yielded the following grain
growth model for TMS80R
5 5
32 ⎛ 655826 ⎞
d = d0
+ 1.26×
10 t ⋅exp⎜
⎟ (1)
⎝ RT ⎠
Here, d is the austenite grain size at time t (in
microns), is the initial grain size (microns), T
is the absolute temperature (K), R is the universal
gas constant. To apply this isothermal model under
non-isothermal conditions we used incremental
numerical computation. In this procedure, the timetemperature
cooling (or heating) curve is divided into
several small time segments. In each of these segments,
the temperature is assumed to be held constant. If the
initial grain size in time segment 1 is d
01
, the grain
size at the end of m th segment is given by:
n
m m
⎛ Q ⎞
dt
= d01 + K∑∆ti
exp ⎜
⎟
(2)
i=
1 ⎝ RTi
⎠
Where Q is the activity coefficient and K is a constant.
2.2.2 Recrystallization model
Most of the microstructural changes in bar rolling
are due to the static and metadynamic recrystallizations
phenomena. Double hit compression tests were
conducted for modeling recrystallization kinetics using
strain, strain rate, temperature, grain size and interhit
time as the control variables. Details on the
experiments can be found in Pauskar 12 . The kinetics
for static and metadynamic recrystallizations were
modeled using an Avrami type relation
n
⎛ ⎛ t ⎞ ⎞
X = 1 −exp −0.
693
⎜
⎜ ⎟
⎝ ⎝ t ⎠ ⎟
(3)
05 . ⎠
Where X is the material fraction recrystallized at
time t, t 0.5
is the time for 50% recrystallization and
n is the time exponent which is assumed to be a
constant. The value of n was determined to be 1.46
for static recrystallization and 1.0 for metadynamic
recrystallization. Regression analysis on the
experimental data yielded the following models for
Static recrystallization:
t
= 1.73×
10
−10
−1.78
−0.433
0.5
ε ε
Metadynamic recrystallization:
−6
−
t0.5
= 5.78×
10 ε
1.00
&
d
0.15
0
Z
d
0.60
0
−0.6
app
⎛197000
⎞
exp⎜
⎟
⎝ RT ⎠
(4)
⎛ 230000 ⎞
⋅ exp⎜
⎟
⎝ RT ⎠
(5)
⎛197000
⎞
Where Z app
= ε& ⋅ exp⎜
⎟ is the apparent
⎝ RT ⎠
Zener-Hollomon parameter for the deformation in
the roll gap.
Recrystallized grain size:
Experiments were performed with strain, strain rate,
grain size and temperature as the control variables.
The following equations were developed to model
recrystallized grain size ( d ).
Static Recrystallization:
⎛ ⎞
= ⋅
−0.341
⋅
−0.06
0.58 3586
d rex
36.5 ε & ε ⋅ d
0
exp⎜
− ⎟
⎝ T ⎠
(6)
Metadynamic recrystallization:
⎛ ⎞
= ⋅
−0.72
⋅
−0.113
0.39 3544
d rex
53.41 ε & ε ⋅ d
0
exp⎜
− ⎟
⎝ T ⎠
(7)
rex
347