A Transient Thermal Model for Friction Stir Weld. Part I: The Model
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TRODUCTION
THERMAL modeling, which can give global, intuitional, and detailed thermal information of the workpiece, has long been a standing interest in friction stir welding (FSW), a solid-state joining technique invented in 1991 by The Welding Institute (TWI) of the United Kingdom.[1] This is because the high temperature during the FSW process changes the microstructure and mechanical properties of the welds significantly.[2–7] It is very important to obtain temperature profiles during FSW. Although the FSW thermal cycle can be experimentally measured, it is very difficult to record the thermal history of the stir zone (SZ) because of the intense plastic deformation induced by the rotating pin in this zone. In addition, only limited temperature data can be obtained by experimental measurements. In the past decade, several thermomechanical models based on the finite element method (FEM) and thermoflow models based on computational fluid dynamics were established to estimate the heat flow during the FSW process.[8–23] In addition, pure analytical thermal models[24–32] have been also studied. No matter what kind of models are used for FSW thermal analysis, the heat generation rate is the major difficulty because of the unknown friction coefficient, which is affected by many factors. Blau’s study[33] drew our attention to the factors affecting the friction coefficient. According to his study, the main potential factors affecting the frictional coefficient in FSW are as follows: temperature, contact geometry (i.e., macroscale mating of shapes and surface X.X. ZHANG, PhD Student, and B.L. XIAO and Z.Y. MA, Professors, are with the Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P.R. China. Contact e-mail: [email protected] Manuscript submitted October 18, 2010. Article published online May 21, 2011 3218—VOLUME 42A, OCTOBER 2011
roughness), relative motion (i.e., magnitude of relative surface velocity), applied force (i.e., magnitude of normal force), and contact compliance (i.e., sliding or sticking friction conditions). Since many potential factors could affect the friction coefficient, and the relation between them is still not very clear, it is necessary to identify the key factor(s) for a particular case, i.e., FSW in the present study, for the thermal analysis. To deal with the complexity, various approximations are adopted to study the friction coefficient.[34] By using the Coulomb friction law, Frigaard et al.[25] and Song and Kovacevic[26] took a constant friction coefficient to estimate the heat generation. Considering both sliding and sticking conditions, Schmidt et al.[7,29,30] and Nandan and co-workers[13–15] treated the friction coefficient as a function of the material shear strength and the relative speed between the tool and the workpiece. In Sluzalec’s study,[35] the first FEM study of friction welding, a temperaturedependent friction coefficient based on experimental results, was used to estimate the heat generation. In the present study, we also treat th
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