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N. Bhardwaj et al.
the flow stress evolution during tensile deformation of FSW sheets, four different
methods were also designed using the CAFE model. Tool selection with various pin
profiles for single- and double-side FSW of sheets was done by Rajpoot et al. [63]
using the CAFE method. In this method, grain size is used as output and optimized
for different pin profiles to select the appropriate one,however, actually the pin profile
used was a different one. The influence of single-side FSW and double-side FSW on
grain size distribution was also analyzed with predictions from CAFE model.
There have been several other researches to predict the evolution of microstructure
during FSW and other FS variants of various sheet grades. For instance, Shojaeefard
et al. [75] optimized the mechanical properties and grain size of FS welds made of
AA1100 using Taguchi method, and the microstructure model was built using CA
model in DEFORM (a commercial FEM package) environment. They predicted the
dislocation density using modified Laasraoui–Jonas (LJ) model in combination with
CA model to optimize rotational speed, transverse speed and tilt angle during FSW.
LJ model is a dislocation density model used to predict flow stresses and evolution
of dislocation densities during a hot working process. The effect of grain boundary
migration on dislocation density is also considered in the modified LJ model. The
dislocation density given by the modified LJ method is expressed as [2].
dρ i = (h − rρ i )dε − ρ i dV,
(3.103)
where ρ i represents the dislocation density for the ith grain; dV denotes volume swept
by the boundaries; ε is the strain; average strain hardening denoted by a parameter
h and recovery coefficient r. Akbari et al. [1] established a FE model in combination with CA, LJ and Kocks−Mecking (KM) models to predict the microstructure
evolution (such as nucleation and grain growth) during dynamic recrystallization of
FSW of AZ91 in DEFORM environment. Besides evaluating the microstructures,
the model predicted macro-outputs such as strain, temperature as a function of sheet
thickness and rotation and traverse speeds. Asadi et al. [4, 5] made similar attempts.
The microstructure evolution by DRX (dynamic recrystallization) in the friction stir
blind riveting process [70], prediction of microstructure during friction stir extrusion
process [7] and CA model development for FSW of titanium alloy [79] are other
notable contributions.
3.6 An Example
Modeling of FSSW carried out by Bhardwaj et al. [14] is described in this section as
an example. The FSSW of AA6061 sheet using H13 tool was modeled using a fully
coupled temperature-displacement finite element model in DEFORM-3D owing to
its efficient remeshing capabilities. Temperature and displacement were calculated at
the same time for each node. The formulation used was Lagrangian implicit, and to
account for severe plastic deformation and mesh distortion, adaptive remeshing was
N. Bhardwaj et al.
the flow stress evolution during tensile deformation of FSW sheets, four different
methods were also designed using the CAFE model. Tool selection with various pin
profiles for single- and double-side FSW of sheets was done by Rajpoot et al. [63]
using the CAFE method. In this method, grain size is used as output and optimized
for different pin profiles to select the appropriate one,however, actually the pin profile
used was a different one. The influence of single-side FSW and double-side FSW on
grain size distribution was also analyzed with predictions from CAFE model.
There have been several other researches to predict the evolution of microstructure
during FSW and other FS variants of various sheet grades. For instance, Shojaeefard
et al. [75] optimized the mechanical properties and grain size of FS welds made of
AA1100 using Taguchi method, and the microstructure model was built using CA
model in DEFORM (a commercial FEM package) environment. They predicted the
dislocation density using modified Laasraoui–Jonas (LJ) model in combination with
CA model to optimize rotational speed, transverse speed and tilt angle during FSW.
LJ model is a dislocation density model used to predict flow stresses and evolution
of dislocation densities during a hot working process. The effect of grain boundary
migration on dislocation density is also considered in the modified LJ model. The
dislocation density given by the modified LJ method is expressed as [2].
dρ i = (h − rρ i )dε − ρ i dV,
(3.103)
where ρ i represents the dislocation density for the ith grain; dV denotes volume swept
by the boundaries; ε is the strain; average strain hardening denoted by a parameter
h and recovery coefficient r. Akbari et al. [1] established a FE model in combination with CA, LJ and Kocks−Mecking (KM) models to predict the microstructure
evolution (such as nucleation and grain growth) during dynamic recrystallization of
FSW of AZ91 in DEFORM environment. Besides evaluating the microstructures,
the model predicted macro-outputs such as strain, temperature as a function of sheet
thickness and rotation and traverse speeds. Asadi et al. [4, 5] made similar attempts.
The microstructure evolution by DRX (dynamic recrystallization) in the friction stir
blind riveting process [70], prediction of microstructure during friction stir extrusion
process [7] and CA model development for FSW of titanium alloy [79] are other
notable contributions.
3.6 An Example
Modeling of FSSW carried out by Bhardwaj et al. [14] is described in this section as
an example. The FSSW of AA6061 sheet using H13 tool was modeled using a fully
coupled temperature-displacement finite element model in DEFORM-3D owing to
its efficient remeshing capabilities. Temperature and displacement were calculated at
the same time for each node. The formulation used was Lagrangian implicit, and to
account for severe plastic deformation and mesh distortion, adaptive remeshing was