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An Analytical Solution for Friction Stir
Welding of an AISI 1018 Steel
V.H. Ferrer L., C.A. Hernández C. and R.O. Vargas Aguilar
Abstract
Friction stir welding process has been usually studied from the solid
mechanics point of view although the use of CFD's techniques has been increas-
ing for the numerical treatment of the problem. In this work, a simple analytical
solution using series expansions for Cauchy momentum and energy equation-set is
obtained. The Power Law model takes into account the shear thinning fluid and the
Arrhenius-type relationship the temperature dependent viscosity. Friction dissipation
as an external heat source is considered.
1 Introduction
Friction Stir Welding (FSW) is a solid state welding process used for joining similar
and dissimilar metal alloys. Thomas et al. (
1991
) patented this process in 1991
and developed it at The Welding Institute (TWI). Several authors have analyzed
momentum and heat transfer problem in FSW. Heurtier et al. (
2006
) developed a
kinematical model to determine material flow and temperature distribution in the stir
zone. Three flow fields were solved analytically using potential flow theory (Nunes
2001
). Other authors (Nandan et al.
2007
; Cho et al.
2013
), considered Perzyna's
model (Perzyna
1966
) to take into account viscoplastic response during material
processing in the stir zone. Heurtier et al. (
2006
) also considered both viscous and
friction dissipation in tool/workpiece interface and heat transfer by conduction only,
for an AA2024-T351 aluminium alloy. Schmidt et al. (
2004
) proposed an analytical
model for heat generation regarding viscous and friction dissipation, they simplified
the problem by considering shear strain only.
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