126
N. Bhardwaj et al.
3.8 Conclusion
A comprehensive study of the modeling of FSW using both analytical and numerical
methods has been presented in this work. Lagrangian and Eulerian approaches are
primarily used for modeling. In Lagrangian approach, the study is performed on a
set of points which keep moving during deformation. On the other hand, Eulerian
approach assumes a fixed control volume through which material passes. Combining
the two approaches, ALE and CEL are slowly gaining popularity; however, they are
limited by their requirement of higher computation capabilities. Different yield functions are used for encompassing the material behavior in modeling, of which von
Mises and Tresca yield criteria are most commonly used. It is observed that a very
small number of dedicated studies have been conducted on analytical modeling of
FSW. Most of the analytical models concentrate on the thermal aspect of FSW. Some
available models have related torque and plunge force during welding to heat generated during welding. The work of Schmidt et al. [72] is referred by many researchers
in developing heat flux models during FSW. The temperature distribution in the weld
is arrived at by using the heat flux generated by the FSW tool. A numerical model of
FSW may include thermal, mechanical as well as a metallurgical model. A coupled
thermo-mechanical model is more efficient at predicting results closer to experiments.
A thermal model, an elastic–plastic model with temperature-dependent flow stress
and a metallurgical model together can predict mechanical properties like hardness as
well as residual stresses. CAFE model is capable of predicting microstructure evolution during welding. Although advances in modeling of FSW have been taking place,
the extensive simulation time remains one of its major challenges. Further research
is needed to mitigate this problem, either by developing more accurate analytical
models or by enhancing the computational efficiency of the numerical models.
References
1. Akbari M, Asadi P, Givi MB, Zolghadr P (2016) A cellular automaton model for microstructural simulation of friction stir welded AZ91 magnesium alloy. Modell Simul Mater Sci Eng
24(3):035012
2. Al-Badour F, Merah N, Shuaib A, Bazoune A (2013) Coupled EulerianLagrangian finite
element modeling of friction stir welding processes. J Mater Process Technol 213(8):1433–1439
3. Asadi P, Mahdavinejad RA, Tutunchilar S (2011) Simulation and experimental investigation
of FSP of AZ91 magnesium alloy. Mater Sci Eng: A 528(21):6469–6477
4. Asadi P, Givi MKB, Akbari M (2015) Microstructural simulation of friction stir welding using
a cellular automaton method: a microstructure prediction of AZ91 magnesium alloy. Int J Mech
Mater Eng 10(1):20
5. Asadi P, Givi MKB, Akbari M (2016) Simulation of dynamic recrystallization process during
friction stir welding of AZ91 magnesium alloy. Int J Adv Manuf Technol 83(1–4):301–311
6. Awang M (2007) Simulation of friction stir spot welding (FSSW) process: study of friction
phenomena. West Virginia University
7. Behnagh RA, Samanta A, Pour MAM, Esmailzadeh P, Ding H (2019) Predicting microstructure
evolution for friction stir extrusion using a cellular automaton method. Modell Simul Mater
Sci Eng 27(3):035006
N. Bhardwaj et al.
3.8 Conclusion
A comprehensive study of the modeling of FSW using both analytical and numerical
methods has been presented in this work. Lagrangian and Eulerian approaches are
primarily used for modeling. In Lagrangian approach, the study is performed on a
set of points which keep moving during deformation. On the other hand, Eulerian
approach assumes a fixed control volume through which material passes. Combining
the two approaches, ALE and CEL are slowly gaining popularity; however, they are
limited by their requirement of higher computation capabilities. Different yield functions are used for encompassing the material behavior in modeling, of which von
Mises and Tresca yield criteria are most commonly used. It is observed that a very
small number of dedicated studies have been conducted on analytical modeling of
FSW. Most of the analytical models concentrate on the thermal aspect of FSW. Some
available models have related torque and plunge force during welding to heat generated during welding. The work of Schmidt et al. [72] is referred by many researchers
in developing heat flux models during FSW. The temperature distribution in the weld
is arrived at by using the heat flux generated by the FSW tool. A numerical model of
FSW may include thermal, mechanical as well as a metallurgical model. A coupled
thermo-mechanical model is more efficient at predicting results closer to experiments.
A thermal model, an elastic–plastic model with temperature-dependent flow stress
and a metallurgical model together can predict mechanical properties like hardness as
well as residual stresses. CAFE model is capable of predicting microstructure evolution during welding. Although advances in modeling of FSW have been taking place,
the extensive simulation time remains one of its major challenges. Further research
is needed to mitigate this problem, either by developing more accurate analytical
models or by enhancing the computational efficiency of the numerical models.
References
1. Akbari M, Asadi P, Givi MB, Zolghadr P (2016) A cellular automaton model for microstructural simulation of friction stir welded AZ91 magnesium alloy. Modell Simul Mater Sci Eng
24(3):035012
2. Al-Badour F, Merah N, Shuaib A, Bazoune A (2013) Coupled EulerianLagrangian finite
element modeling of friction stir welding processes. J Mater Process Technol 213(8):1433–1439
3. Asadi P, Mahdavinejad RA, Tutunchilar S (2011) Simulation and experimental investigation
of FSP of AZ91 magnesium alloy. Mater Sci Eng: A 528(21):6469–6477
4. Asadi P, Givi MKB, Akbari M (2015) Microstructural simulation of friction stir welding using
a cellular automaton method: a microstructure prediction of AZ91 magnesium alloy. Int J Mech
Mater Eng 10(1):20
5. Asadi P, Givi MKB, Akbari M (2016) Simulation of dynamic recrystallization process during
friction stir welding of AZ91 magnesium alloy. Int J Adv Manuf Technol 83(1–4):301–311
6. Awang M (2007) Simulation of friction stir spot welding (FSSW) process: study of friction
phenomena. West Virginia University
7. Behnagh RA, Samanta A, Pour MAM, Esmailzadeh P, Ding H (2019) Predicting microstructure
evolution for friction stir extrusion using a cellular automaton method. Modell Simul Mater
Sci Eng 27(3):035006