3 Modeling of Friction Stir Welding Processes
121
Fig. 3.9 Schematic of working principle of cellular automation with four iterations, assuming the
simple rules: (i) every white cell adjacent to a black cell turns gray (ii) all gray cells adjacent to
black cells turn black
microstructure on Nb-microalloyed rolled sheet properties [87] and similar studies.
Specifically, in materials processing, the notable works are from Gandin and Rappaz
[33], Davies [24], Lan et al. [50], Shterenlikht and Howard [76] and Madej et al.
[53].
In recent times, CA/CAFE models are applied to FSW for understanding the
significance of process parameters on the microstructures in the weld zone. It also
helps in designing and optimizing the FSW process and selection of tools to minimize
FSW defects and for reducing experimental time and associated costs. For the first
time, Saluja et al. [69] used ABAQUS to develop a CAFE model to predict the size of
grains during FSW of AA6061-T6 thin sheets. In this attempt, the stirring of materials
that takes place physically in real world during FSW is not simulated. Instead, the
strain, heat flux and strain-rate developed during the process are calculated using
existing analytical equations, which are subsequently provided as inputs to FE and
CA cells via user sub-routine. To predict the final size of the grains, a group of CA
cells with initial grain size that are distributed following Gaussian distribution are
created in three-dimensional fashion. The final grain size (D CA ) during FSW has
been obtained using the transition rule,
D CA = Cε
x
˙
ε
y d
z exp
−Q
RT
,
(3.102)
where ε,˙ ε, T are strain, rate of deformation and temperature during FSW, Q is
continuous recrystallization activation energy, d is the initial grain size, and R is
gas constant. x, y, z are material constants evaluated by error minimization. Later,
the tensile behavior of FSW sheet has been predicted by considering the flow stress
evolution at element level and at CA cell level.
The CAFE model has been utilized to develop an artificial neural network (ANN)
model for predicting the yield strength and grain size during FSW [60]. CAFE model
generated yield strength and grain size as a function of FSW parameters, and the
outputs are trained by neural network. Valvi et al. [85] extended the CA model to
predict the dislocation density (ρ) in the FS zone from grain size (D CA ) by using (i)
ρ =
k
α Eb
2 D
−1
CA , where k is a constant, b is the burgers vector, E denotes the elastic
modulus, and (ii) fourth-order polynomial equation relating it with D CA . To predict
121
Fig. 3.9 Schematic of working principle of cellular automation with four iterations, assuming the
simple rules: (i) every white cell adjacent to a black cell turns gray (ii) all gray cells adjacent to
black cells turn black
microstructure on Nb-microalloyed rolled sheet properties [87] and similar studies.
Specifically, in materials processing, the notable works are from Gandin and Rappaz
[33], Davies [24], Lan et al. [50], Shterenlikht and Howard [76] and Madej et al.
[53].
In recent times, CA/CAFE models are applied to FSW for understanding the
significance of process parameters on the microstructures in the weld zone. It also
helps in designing and optimizing the FSW process and selection of tools to minimize
FSW defects and for reducing experimental time and associated costs. For the first
time, Saluja et al. [69] used ABAQUS to develop a CAFE model to predict the size of
grains during FSW of AA6061-T6 thin sheets. In this attempt, the stirring of materials
that takes place physically in real world during FSW is not simulated. Instead, the
strain, heat flux and strain-rate developed during the process are calculated using
existing analytical equations, which are subsequently provided as inputs to FE and
CA cells via user sub-routine. To predict the final size of the grains, a group of CA
cells with initial grain size that are distributed following Gaussian distribution are
created in three-dimensional fashion. The final grain size (D CA ) during FSW has
been obtained using the transition rule,
D CA = Cε
x
˙
ε
y d
z exp
−Q
RT
,
(3.102)
where ε,˙ ε, T are strain, rate of deformation and temperature during FSW, Q is
continuous recrystallization activation energy, d is the initial grain size, and R is
gas constant. x, y, z are material constants evaluated by error minimization. Later,
the tensile behavior of FSW sheet has been predicted by considering the flow stress
evolution at element level and at CA cell level.
The CAFE model has been utilized to develop an artificial neural network (ANN)
model for predicting the yield strength and grain size during FSW [60]. CAFE model
generated yield strength and grain size as a function of FSW parameters, and the
outputs are trained by neural network. Valvi et al. [85] extended the CA model to
predict the dislocation density (ρ) in the FS zone from grain size (D CA ) by using (i)
ρ =
k
α Eb
2 D
−1
CA , where k is a constant, b is the burgers vector, E denotes the elastic
modulus, and (ii) fourth-order polynomial equation relating it with D CA . To predict