advances in numerical modeling of manufacturing processes

TRANS. INDIAN INST. MET., VOL. 57, NO. 4, AUGUST 2004
2.2.3 Partial recrystallization in a multi-stage
deformation process
Often during the rolling process, the time in the
interstand is not sufficient for complete
recrystallization to occur. In other words, some
amount of strain is retained in the microstructure
when it enters the next deformation pass. Several
approaches have been proposed to handle partial
recrystallization. One of the approaches is to treat
the microstructure as an aggregate. The retained strain
and the effective grain sizes are determined using the
rule of mixtures:
ε
ret
= ε ⋅( 1− X )
(8)
d
eff
( 1−
X ) ⋅ d0
= X ⋅ d +
(9)
rex
where, X is the fraction recrystallized, ε ret
is the
retained strain, d
eff is the effective grain size, d
0
is the initial as heated grain size and d rex
is the
recrystallized grain size.
The other approach is to treat the recrystallized and
unrecrystallized fractions independently (Karhausen
and Kopp 24 ). However, the number of fractions to
be handled increases exponentially, which calls for
tremendous amount of computer memory and time.
Yanagimoto et al. 25 proposed a variation of
Karhausen’s model. In this approach, the number of
fractions increases linearly, which requires
considerably less memory. However, as with the rule
of mixtures, considerable approximation is involved
and the true behavior of the system is not represented.
Here, three hit compression tests were conducted to
determine the validity of the rule of mixtures. In the
three hit compression tests, the first inter hit time
was kept deliberately short to cause partial
recrystallization. The second hit was followed by a
third hit with an inter-hit time between the two. The
amount of recrystallization in the second inter-hit
time was measured using the same procedure as was
used in the double hit compression tests. It was found
that the rule of mixtures shows a better correlation
with the measurements for TMS80R and was hence
used in the integrated model.
2.3 Microstructure dependent flow stress model
Flow stress of steel at hot rolling temperatures was
found to be strongly dependent on the microstructure,
specifically the austenite grain size in addition to
process parameters such as strain, strain rate and
temperature.
f
( ε , & ε , T,
d )
σ = f
(10)
0
A microstructure dependent flow stress model was
developed and integrated into the FEM module. The
flow stress model is capable of modeling the
metallurgical phenomena such as strain hardening,
dynamic recovery and recrystallization. Figures 3 and
4 demonstrate the capability of the flow stress to
model accurately the work hardening and thermal
softening processes occurring during plastic
deformation of steels under constant strain rate as
well as changing strain rate conditions. Details about
the microstructure dependent flow stress model can
be found in Pauskar et al. 16
2.4 Integrated Model and Validation
The central feature of the integrated system is a three
dimensional finite element program ROLPAS for
simulating multi-pass shape rolling. The nonisothermal
deformation analysis in ROLPAS is based
on rigid-viscoplastic assumption of the material
behavior as described earlier and uses eight-node
isoparametric hexahedral elements. Deformation
within the roll gap is assumed to be kinematically
steady. Such an assumption has been successfully
applied earlier to steady state processes such as
extrusion and rolling.
A microstructure evolution module MICON was
developed and integrated into ROLPAS to enable
modeling of austenite evolution. MICON uses the
thermomechanical history computed by the FEM
model in conjunction with microstructure evolution
models to determine the evolution of austenite during
hot rolling. The evolving austenite was found to
significantly affect the flow stress of the material
while the material flow affects recrystallization
kinetics. This situation calls for an iterative approach
in modeling metal flow and austenite evolution. For
the first pass, an initial preheated grain size is input
to the program. After deformation and heat transfer
computations for each pass, the microstructure
evolution module in conjunction with the heat transfer
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