Results and Discussion
5.2 Numerical model and material properties
Numerical study of heat generation and heat transfer during FSW is important criteria to apprehend a highly complex process comprising several coupled physical phenomena. However, heat transport process in FSW requires understanding several other physical processes such as material flow around the welding tool, contact pressure inflicted by the welding tool, the friction coefficient, wear, change of thermo-mechanical properties and heat transfer coefficients etc. Numerical analysis includes the effect of all these parameters to evaluate heat transfer during welding whereas the reliability of numerical model is greatly depends on temperature dependent material properties, optimum mesh size and other calibrated model parameters. The present section describes the model geometry;
mesh size selection, time step and load step selection for the development of numerical
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model. Thereafter, the thermal and mechanical properties of aluminum and copper are described which has considered in the present work.
5.2.1 Model geometry
The heat transfer analysis of the FSW and P-FSW process is performed using commercial software ABAQUS. The solution domain of the model is assumed as rectangular plate. The element of workpiece domain is meshed using eight-nodded brick element of type DCC3D8. The temperature is considered as single degree of freedom at each node with fine meshing in the weld zone. The size of the welding plate for the simulation is considered as same as experimental condition. The welded workpiece have dimensions 200 mm length and 200 mm width, while the thickness of the workpiece is 6 mm. In the present work, non-uniform meshes are used and shown in Fig. 5.1. The finer mesh is considered near and along the weld center line to capture high temperature gradient of the simulated results and the mesh size increases for rest of the zone in order to reduce the computational time. However, in case of dissimilar joint the solution domain is partition in three section and each section assigned different material properties. The weld zone is designed as functionally graded material. Other two sections are assigned with thermal properties of copper (advancing side) and aluminum (retreating side). In this case, the model geometry and type of mesh and size is similar to Fig. 5.1 except weld zone material property.
Figure 5.1: Finite element mesh for model geometry.
Results and Discussion
5.2.2 Calibration of numerical model
This solution of finite element based numerical model depends on the selection of the number of elements, number of time steps, number of non-linear iterations per time step and the time required for each non-linear iteration. Therefore, the computational time can be reduced by proper and optimum selection of these parameters. Also the accuracy of numerical model depends on assignment of proper material properties. The computed thermal cycles and weld zone isotherm of finite element heat transfer model are sensitive to the element size and the distribution of elements within the model geometry. The accuracy of the predicted result is directly proportional to element size: finer the mesh sizes higher the precision of the model.
In FSW, the plastic deformation of material is occurred at the tool-workpiece interface and creates a shear layer. It is assumed that total frictional heat generated in the whole FSW process is attributed solely in the shear layer thickness [313]. Therefore, to apply volumetric heat flux on boundary shear layer, the size of mesh should be finer than that of mesh in the weld zone. The typical estimate of boundary shear layer thickness is 0.25 mm [78, 314].
To comply with this small size of boundary layer, it considerably increases the element number and consequently the computational time. Hence application of surface heat flux eliminates the complexity arises from the restriction of mesh size due to boundary shear layer thickness. Mesh sensitivity analysis is conducted to select a proper element size to accurately simulate the FSW process to minimize the computational cost. Figure 5.2 indicates that three different meshes are considered in the weld zone. The peak temperature obtained at a thermocouple point is estimated using these three types of meshes and is compared with the experimental value. Finite element model using coarse mesh was found to overestimate the experimental peak temperature at the thermocouple location by more than 12%. On the other hand, the peak temperatures predicted by using fine and very fine mesh are comparable with their experimental counterparts and a maximum difference around ~ 3 % is observed. No improvement in numerical result has observed from the use of fine mesh to very fine mesh. Therefore, fine mesh is used in all subsequent simulations.
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Figure 5.2: Peak temperature obtained at a thermocouple point (TC1) using different meshes.
Published literatures indicates that the selection of backing plate have a significant influence on the thermal history of the workpiece, as the backing plate with high thermal conductivity would allow more heat loss than the plate with low thermal conductivity [32].
It was found that including a proper thermal boundary condition for the backing plate is critical for accurate simulation results. The objective was to minimize the difference between the experimentally measured temperature and the temperature obtained using a 3D FE model [103]. The workpiece backing plate contact conductance is one the uncertain aspect of the thermal model as it cannot be determined accurately with experiments. The contact conductance value is assumed in the most of the previous thermal models as a fixed uniform value. The heat loss to the backing plate, which is essentially contact conduction, is accounted by using an equivalent convection coefficient at the bottom of the plates.
A convective heat transfer coefficient of 25 W/m2-K is used for the top and sides of the work-pieces which is typical for natural convection heat transfer between aluminum and air [315]. However, the higher convective heat transfer coefficient is used for the bottom surface, which is equivalent to the surface film conductance between the workpiece and the backing plate. In the present work, convective heat transfer coefficient of 300 W/m2-K is assumed at the bottom of the workpiece [316]. For the radiation heat loss, the emissivity (š) of 0.4 is considered whereas StefanāBoltzmann constant is 5.6703 10-8 W/m2K4. In
Results and Discussion dissimilar joint, the different convective heat transfer coefficient is used for both the workpieces (Cu & Al) which is typically for natural convection between work-piece and air.
At bottom surface high heat transfer coefficient (500 W/m2-K) is considered due to presence of highly conductive backing plate in copper side.
The procedure of physical modelling is adopted according to the actual experiment where the numerical solution returns the temperature profile in special domains. FSW process is divided into five time instants: plunge time, initial dwell time, welding time, final dwell, and plunge-out time. However, total simulation time depends on welding speed that also includes the cooling period.
5.2.3 Material properties
There are four different types of materials used in numerical analysis of FSW process such as Aluminum 6061, aluminum 7075, aluminum 1100 and pure copper. Figure 5.3 illustrates the temperature dependent thermal conductivity and specific heat of AA 6061 and AA 7075 [27, 317]. Both the thermal properties vary linearly with temperature for AA 6061. The thermal conductivity of AA 7075 remains constant after 500 K. Presence of second phase particles and their distribution in aluminum alloy, and the change of microstructure over temperature and strain rate in real FSW process is accommodated by variation of thermal properties.
Figures 5.4 shows the temperature dependent thermal properties of AA 1100 and pure copper, respectively that are used for finite element simulation [35, 318]. For AA 1100, the value of the thermal conductivity and specific heat increases almost linearly with respect to temperature. However, the thermal conductivity of pure copper is decreased linearly with temperature. Figure 5.5 shows the temperature dependent yield stress of AA1100 and pure copper. The yield strength of both materials is decreased with increase in temperature but yield strength of copper is much higher than aluminum at room temperature.