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2.1 Heat transfer in friction stir welding
2.1.2 Mathematical model
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(PCBN) were developed to create FSW tools for use in steel, stainless steel, titanium alloys, and nickel-base alloys. Weinberger et al. [61] analyses the weldability, microstructure and mechanical properties of friction stir welded steel 15-5PH using tungsten based tools. They produced good quality welds on martensitic precipitation hardened steels using a W25Re alloy tool. Park et al. [62] studied the fundamentals of pcBN tool wear during FSW of five types of ferritic, duplex, and austenitic stainless steels. Their results suggest that with increase in the flow stress causes the severe tool wear during FSW of austenitic stainless steels, which results in greater nitrogen pickup in austenitic stainless steel FS welds.
Whereas, Seighalani et al. [63] examine the effect of tool material, tool geometry, tilt angle, tool rotational speed, welding speed, and axial force on the weld quality of titanium alloys.
Due to the excessive erosion, tool material and geometry play the main roles in FSW of titanium alloys. Properties of the resultant welds have been shown to be outstanding.
Although some issues remain (primarily limited tool life with tungsten base tools), FSW has been demonstrated as a technically and economically feasible process in high-temperature materials [64-65]. Zhang et al. [66] studied FSW of commercially pure titanium using a pcBN tool and observed severe tool wear. The debris from the tool reacted with titanium alloy to form titanium borides; both titanium borides and pcBN debris contributed to the grain refinement as well as increase in surface hardness. This situation suggests that a pcBN tool can be utilized for FSW of titanium and its alloys high quality welding.
Chapter 2 etc.), physical phases of FSW, duration of the welding procedure, duration of certain phases of the welding procedure, etc. Furthermore, these parameters initiate other parameters that affect heat generation process: friction coefficient, contact pressure, shear stress, contact condition, etc. However, presented models simplify FSW assuming e.g. constant friction coefficient, constant contact pressure, pure frictional heat generation, heat generation only due work of the largest part of the welding tool, no heat generation when temperature in the workpiece reaches melting point etc. Such assumptions are affecting the usability and the precision of results derived by developed models.
Mijajlovic et al. [67] developed a mathematical model to estimate the generated heat in the welding zone. An attempt was also made to validate the analytical model of the heat generation in the FSW process. Their mathematical model describes/defines contact pressure, contact condition, friction coefficient, thermal history of the welding plates and points out the dual nature of heat generation process in FSW-adhesion and deformation component in total heat generation. They also concluded that the vertical load is crucial parameter and determine the peak temperature, x-direction force, torque and the power features of the process [68]. Khandkar et al. [37] introduced a torque based heat input model where experimentally estimated torque is a heat source. There model improve heat transfer within the FSW process with frictional and deformational heat input into the process. The power, obtained from experimental investigation, has been distributed to the different interfaces formed between the tool and the weld piece based on the torques generated at different tool surfaces. Song and Kovačević [69] investigated the influence of the preheating period on the temperature fields in FSW. A sliding condition of the welding tool over the base metal was assumed and an effective friction coefficient and experimental plunge force are input into the heat source expression.
The plunging force effect contact condition under the shoulder can be described by sliding friction, using a friction coefficient and interfacial pressure, or sticking friction, based on the interfacial shear strength at an appropriate temperature and strain rate.
Mathematical approximations for the total heat generated by the tool shoulder have been developed using both sliding and sticking friction models. Shercliff and Colegrove [70]
developed a material flow model that investigates the influence of threads on the probe on material flow. An advanced viscous material model is introduced and the influence of
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different contact conditions prescribed as the boundary condition is analyzed. A thorough presentation of analytical estimates of the heat generation in FSW and influence of material flow on heat generation is given, as well. Chao and Qi [27] have introduced a 3-D heat transfer model in FSW with constant heat input. Constant heat flux at the shoulder of the welding tool, constant contact pressure and pure Coulomb’s friction law for estimating shear stress, and heat were the main assumptions of the model. The experimental welding of plates made of aluminum alloy 6061-T6 was performed and the temperature history of welding plates was estimated. Heat input was adjusted (“trial and error” principle) until numerical and experimental temperatures were matched. As such, this model is the first model developed for estimating the amount of heat generated during FSW. Schmidt and Hattel [33]
have defined an analytical model for estimating the amount of heat generated during FSW that recognizes the shoulder and the probe of the welding tool as heat sources and concludes that about 89% of heat is generated at the shoulder. Heat has friction and deformation components and the total heat is a sum of both with influence of the contact state variable.
Schmidt et al. [71] provide an excellent discussion on the calculation of interfacial heat generation rates during FSW. A problem in the calculations of heat generation is that the friction coefficient cannot be determined from fundamental principles or it seems, by straight forward representative experiments of relevance to the conditions of FSW. Two contact models, the classical Coulomb contact model and the modified Coulomb contact model, were used in a fully coupled thermo-mechanical numerical model of the FSW and the suitabilities of the two models to simulate the FSW process were analyzed [72]. There is little difference between the numerical results of the two contact models for the FSW at low rotating speeds. In high rotating speed, the classical Coulomb contact model fails because the shear stress at the interface is not limited, but the modified Coulomb contact model may be used. A semi-analytical thermal model for the FSW was proposed [73]. The formulation of heat flow during the FSW process is based on generic solutions of the differential equation for heat conduction in a solid body, formulated for a point heat source with constant linear velocity. The heat generation was considered as a function of the tool-matrix interface temperature, which is calculated by means of a numerical routine written in MATLAB code. A comparison with the experimental measurements taken from the
Chapter 2 literature showed that the results from the present semi-analytical model are in good agreement with the test data. In previous simulation studies, the contact conditions occurring in the FSW are generally described as stick and/or slip, according to different methodologies but these descriptions have their limitations. A new combination method was presented for characterizing the contact conditions that occur during FSW processes [74]. The thermal and mechanical outcomes from models with prescribed stick and slip conditions were compared to identify the results and drawbacks of assuming different contact conditions. This new method yields more reasonable estimates of heat generation, as validated by the experimental thermal measurements [75].
Kumar et al. [76] proposed an experimental model for estimating the friction coefficient during FSW. The model is based on the experimental estimation of the momentum of friction and axial force, which are necessary for estimating the friction coefficient [41]. Frigaard and Grong [77] presented a process model for heat flow in FSW, where they assumed that heat is generated only by friction on the tops of shoulders and probes. Heat input and friction coefficients were adjusted during the welding process to keep the calculated temperature below the melting point of base metal material. Heat input was a moving heat source with a linear distribution of heat flux at the contact surface.
Schmidt et al. [78] presented a model which accounted the compressibility of material by including the elastic response of the aluminum matrix in form of effective yield stress. It is possible to use an effective yield stress, back calculated from the experimentally determined average power input to the system or estimated from the local shear stress using a temperature and strain rate dependent yield stress [37]. Russell and Shercliff [79] provides the theoretical estimation of the heat generation based on a constant friction stress equal to the shear yield stress at elevated temperature, which is set to 5% of the yield stress at room temperature. The heat input is a pure point or line source. Ulysse [80] developed a 3-D visco-plastic FEA model using the commercial software FIDAP. The heat generation was determined to be a product of the effective stress and the effective strain-rate. Results show that the model consistently over predicted the measured temperatures probably from an inadequate representation of the constitutive behavior of the material used in FSW. Steuwer et al. [81] used the experimentally observed mechanical power as input in the model to investigate the influence of tool loads on residual stresses. They identified the asymmetry of
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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.