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2.1 Heat transfer in friction stir welding
2.1.3 Representation of heat source
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the welding process but the peak residual strain is typically 30% higher than measured by synchrotron X-ray diffraction. This may be due to stress measurement principles e.g. the area over which it is measured. Heurtier et al. [40] formulate a three dimensional model based on the fluid-velocity fields where the tool shoulder and the plastic strain of base material near the welding tool were heat sources. This semi-analytical model can be used to obtain the strains, strain rates, and estimations of the temperatures and micro-hardness in the various weld zones. The model also predicts the oxide distribution after welding to indicate the presence of a weakened zone in the weld.
Chapter 2 the contact condition. The refinements of the heat source consist of three stages: (i) shoulder heat source only; (ii) shoulder and probe heat source, the latter as a volume flux in the matrix volume displaced by the probe; and (iii) shoulder heat source and probe heat source distributed at the probe/matrix interface. The volume displaced by the probe is removed, thereby avoiding heat transfer through the probe volume. However, Schmidt et al [85]
applied a refined heat source model at tool/matrix contact interface. The heat flux distribution of heat source is radially dependent to obtain detailed transient thermal results, which cannot be simulated using less detailed heat source models. In particular, the estimation of temperatures close to the tool/matrix interface is of interest, because temperatures in the highly deformed zone are difficult to measure experimentally.
The tool-workpiece interface can be further subdivided into shoulder-workpiece and tool pin-workpiece interface. In most of the models [35, -102] the heat generation from the tool pin is neglected. Chao et al. [35] considered heat generation between work-piece and tool shoulder and formulated the standard boundary value problem which is solved by inverse approach by minimizing the error between experimental measured temperature profiles and numerically calculated frictional heat generation at the tool shoulder-workpiece interface. Chao and Qi [86] assumed a constant heat flux input from a tool shoulder- workpiece interface and used a heat transfer model using trial and error procedure in order to adjust the heat input until all calculated temperatures matches with experimental values.
They also developed a moving heat source model in a ο¬nite element analysis and simulated the transient temperature, residual stress, and distortion of the FSW process considering heat generated from shoulder workpiece interface due to friction and plastic deformation [87].
Gould et al. [88] developed an analytical heat transfer model based on the well-known Rosenthal equation which describes a quasi-stationary temperature field over a semi-infinite plate due to a moving heat source by considering frictional heat on tool shoulder. Several authors have find the estimates of the heat source flux distribution in tool shoulder which depends on radial distance from tool center. In early work some researchers adapted the heat generation equation used by Midling and Grong [89] for friction welding.
ππππππ‘πππ = 2
3ππππ 3 (2.1)
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where Ο is the effective material flow stress, Ο is the rotation speed in rad/s and R is the tool radius. Frigaard et al. [90] used an alternative approach based on the surface pressure and coefficient of friction between the shoulder and material:
ππππππ‘πππ =2
3ππππ 3 (2.2)
where ΞΌ is the coefficient of friction and p is the surface pressure. Chao and Qi [35], Colegrove et al. [91] and Song and Kovacevic [92] used a similar approach and adjusted the heat input till there was a good match with the experimental temperature results. They presented a mathematical model to describe the detailed three-dimensional transient heat transfer process in friction stir welding The heat input from the tool shoulder is modelled as a frictional heat and the heat from the tool pin is modelled as a uniform volumetric heat generated by the plastic deformation near the pin. Both of the above analyses assumed that the heat input from the pin could be ignored. Therefore, Colegrove et al. [91] estimated the threaded pin heat input with the following equation:
ππππ= 2πππβπ¦ππ
β3+2πΒ―π¦πππβπ£ππ
β3(1+π2) +4πΉπππ£ππππ π
π (2.3)
Whereas, Schmidt and Hattel [93] adopted an engineering approach in which an inverse method is used to determine the heat flux quantities under the shoulder as shown in Fig 2.3.
The distribution of flux depends on radial distance and intensity of flux is increased as it goes away from tool center which is explained in Eq. 2.4. The heat flux in the FSW process is primarily generated by the friction and the deformation process. This heat is conducted to both the tool and the workpiece. The amount of the heat conducted into the workpiece dictates a successful FSW process, the quality of the weld, shape of the weld, micro- structure of the weld, as well as the residual stress and the distortion of the workpiece.
ππ βππ’ππ ππ = 3ππ‘ππ‘πππ
2ππ π βππ’ππ ππ3 π (2.4)
Chapter 2
Plate thickness
r
Figure 2.3. Schematic view of tool geometry with applied linear heat source on tool shoulder in 2D thermal model.
It is obvious that most of the models consider the heat input from the tool shoulder only, the heat generated at the tool-pin and workpiece interface is rarely considered. But, as previous studies specify that there are two sources of heat generation in FSW. One is due to friction and the other is due to plastic deformation at the tool-workpiece interface and at the thermo-mechanically-affected zone (TMAZ) as volumetric heat generation [94-95].
Colegrove et al. [96] shows that 20% of the total heat is attributed to the pin through the developed moving heat source model although the addition of heat due to the pin had little effect on the thermal profile. Russell et al. [97] investigated the effect of tool shoulder and pin geometry on heat input during FSW and used the Rosenthal equation for a uniformly moving point heat source to describe the effects of pin geometry on heat generation.
Maalekian et al. [98] conducted thermal analysis of friction welding process using various heat generation models based on different friction mechanisms at the tool shoulder- workpiece interface. The inverse heat conduction approach predicted the heat-generation rate accurately, whereas the constant friction coefficient approach produced the most inaccurate temperature profile. Dong et al. [99] carried out a coupled thermo-mechanical analysis of the FSW process using a simpliο¬ed two-dimensional axisymmetric heat transfer model. Song et al. [100-101] used a moving heat source to model the heat transfer during FSW and the heat generated at the tool shoulder/workpiece interface is considered as sliding contact frictional heat. The heat generation between tool-workpiece interfaces is greatly influenced by frictional heat but the effect of heat generated due to plastic deformation is rarely considered. Moreover, the difference in temperature distribution between advancing and retreating sides due to non-symmetric heat flux distribution is rarely observed in
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literatures. There is lack of considerable information about the simplified shape of moving heat source during numerical study of heat transfer process in FSW.