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Figure
3
shows that the viscosity of the AISI 1018 steel decreases with the shear
strain rate. Arora et al. (
2009
) reported that the strain rate during FSW is not more
than 10 s
−
1
by using numerical simulations.
The Reynolds (Re) and Brinkman (Br) numbers are evaluated, using data given
in Table
2
and taking a value of
n
3
4
. Both numbers are very low, meaning that the
flow field is laminar and that viscosity has great influence in FSW (Chiumenti et al.
2013
, p. 357). The results of the temperature profile for the Newtonian case are in
good agreement for low Br values, i.e.,
=
ˁ
H
n
m
0
U
n
−
2
10
−
9
Re
=
=
1
.
92
×
,
(29)
m
0
U
n
+
1
kH
n
−
1
10
−
5
=
T
0
)
=
.
×
.
Br
6
37
(30)
(
T
1
−
4 Conclusions
An analytical solution for the AISI 1018 steel deformation under friction stir welding
process has been presented. The deformed solid exhibits a non-Newtonian behavior.
We found that this behavior obeys a Power Lawmodel compared to the Perzinamodel.
Both models had similar behavior when
n
2
3
4
. The steel dilatant behavior is
more related to the temperature than to the strain rate. The low values of Re and Br
numbers demonstrated that the laminar flow and the heat transfer mechanisms were
by conduction. Future work will entail refining our model in 2-D for getting a more
accurate solution.
=
3
,
References
Arora A, Zhang Z, De A, DebRoy T (2009) Strains and strain rates during friction stir welding.
Scripta Mater 61:863-866
Bathe KJ (1996) Finite element procedures. Prentice Hall, New York
Chiumenti M, Cervera M, de Saracibar CA, Dialami N (2013) Numerical modeling of friction stir
welding processes. Comput Method Appl Mech Eng 254:353-369
Cho HH et al (2013) Three-dimensional numerical and experimental investigation on friction stir
welding processes of ferritic stainless steel. Acta Mater 61:2649-2661
Deng Z, Lovell MR, Tagavi KA (2001) Influence of material properties and forming velocity on the
interfacial slip characteristics of cross wedge rolling. J Manuf Sci Eng Trans ASME 123:647-653
Heurtier P et al (2006) Mechanical and thermal modeling of friction stir welding. J Mat Proc Tech
171:348-357
Naghdi PM, Murch SA (1963) On the mechanical behavior of viscoelastic/plastic solids. J Appl
Mech 30:321-328
Nandan R et al (2007) Three-dimensional heat and material flow during friction stir welding of mild
steel. Acta Mater 55:883-895
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