Numerical Investigation of Friction Stir Welding

Numerical Investigations of Friction Stir Welding of High Temperature Materials

A. Elbanhawy, E. Chevallier, K. Domin
TWI Ltd, Structural Integrity Technology Group  

Presenter: Dr Amr Elbanhawy, Project Leader at TWI Ltd, Granta Park, Cambridge, CB21 6AL, UK 

NAFEMS world congress, Salzburg, Austria, 9-12 June 2013

Summary

Friction Stir Welding (FSW) is an attractive technology for material joining. Contrary to conventional welding methods, friction welding has the ability to produce welds with higher integrity and minimum induced distortion and residual stress. In this paper, the FSW process is simulated for steel and aluminium flat sheets, where the torque, temperature and deformation zones around friction stir tools are investigated. The present simulations are compared to several experimental trials performed at TWI, where different tool profiles are being tested on different steels. Process parameters, such as tool rotational speed and traversing speed, are tested in order to identify the envelope of the process in terms of weld quality and tool integrity.

A three-dimensional, steady state, CFD model is utilised. FSW is classified as a solid state welding process even though there is significant material movement near the tool. The modelling has therefore represented the material using a viscoplastic non-Newtonian fluid. The metal is assumed to behave as a laminar fluid since the viscous forces are much higher than the inertial forces. A second order discretisation is used for the momentum and energy conservation. The thermal field in the computational domain is derived from viscous heating resulting from the shearing exerted by the rotating tool in the deformation zone.

A linear viscosity model has been developed based on a linear relationship between yield strength and temperature, where the viscosity is a function of the uniaxial stress and uniaxial strain rate. A second viscosity model has been tested, where the viscosity was non-linearly related to the strain rate and the local temperature. The results show that the linear viscosity model exhibits reasonable prediction of the thermal field around the tool. However, the non-linear viscosity model showed difficulty in predicting reasonable metal flow due to its sensitivity to the tool’s profile. The CFD model has shown useful predictions with regard to the quality of the weld for challenging materials in industrial FSW.

1: Introduction

Friction Stir Welding (FSW) is a joining process for metals that was invented in 1991 by Wayne Thomas at TWI. Friction stir welding can produce welds with high integrity and minimum induced distortion and residual stress. The process is widely used for aluminium alloys and now more developments are being made for higher melting temperature materials, like steel and its alloys. FSW is a solid state welding process in which the base metal does not melt. A stirring tool rotates along the joint line between two adjacent pieces of metal, creating heat by friction and viscous heating (Figure 1). Therefore, a softening effect is caused and hence the yield strength of the metal is reduced. Such softening results in mixing at temperatures well below melting temperature.

The FSW tool comprises a shoulder and a pin, and has two main features. The shoulder presses downward on the work piece, and when the shoulder rotates, heating-induced softening starts to take place. The combination of the shoulder and the pin stretches and folds material and creates a solid joint between originally free surfaces that are intersected by the pin. In Figure 2, the movement of material can be clearly seen during the FSW process of dissimilar metals. Due to the higher strength of steel, compared to aluminium, FSW tools have to endure higher temperatures and stresses.

There is an established debate among the interested community about the nature of deformation and joining occurring in the metal during FSW. While many models assume the joining process to be caused by heat-induced softening, other evidence indicates that an element of metal deformation takes place during the process, as suggested by Colligan (1999). Furthermore, researchers in this field do not use a consistent approach to simulating the interaction between the tool and the metal. Some approaches assume that metal will stick to the tool’s surface during the welding process. Other approaches assume that a partial-sticking condition exists whereby part of the tool’s surface will be sliding with respect to the adjacent metal layer. However, the behaviour of material round the FSW tool is becoming clearer to welding engineers as a variation of tools and materials are being utilised for FSW experiments. There is increasing evidence from unpublished results at TWI that the sticking condition is related to the tool profile, traversing speed and rotational speed. It is therefore difficult to make universal assumptions for the material behaviour in the FSW process. 

The numerical modelling of FSW is indeed a challenging process, owing mainly to the material assumptions used, and boundary conditions employed. Several thermal and microstructural models have been used with varying degrees of complexity. The majority of FSW simulations had the objective of looking at the tool requirements with respect to profiles, forces/moments and temperature. In such studies, there was no attention given to the material modelling in terms of composition. The attention was rather to model the thermal and flow behaviour of the material round the FSW tool. Therefore, computational fluid dynamics (CFD) solvers have been utilised by many researchers. Colegrove and Shercliff (2004b) have studied the FSW process by looking at the two-dimensional (2D) flow deformation field with a non-sticking model. In the separate works of Colegrove and Shercliff (2004a) and Nandan et al (2006), a partial sticking condition was assumed. Notably, Nandan et al (2006) have studied a 3D model of the FSW process. This category of CFD models has established the fact that FSW is a three-dimensional problem, where material flow round the tool becomes essential for the accurate simulation process. Such models represent the metal as viscoplastic material, and make few assumptions about the modes of heat generation.

In the present study, FSW of stainless steel (304L) and aluminium alloy (AA6082) plates is simulated for a non-profiled tool, for the objective of assessing the effect of traversing speed, rotational speed and material modelling on the tool. Two different relationships for the material viscosity are tested, where a viscoplastic behaviour is assumed for the welded metal. Reference is made to a number of experimental trials conducted at TWI. The objective of the present study is to assess the use of simple models for the successful prediction of the process envelope, in addition to energy required by the FSW machine, and the temperature which the tool has to endure. 

2: Welding Experiments   

In research carried out at TWI (Cater and Perrett, 2011), and other collaborative research at TWI (Project Hilda: A European Commission’s FP7 funded research entitled “High Integrity Low Distortion Assembly), several FSW experiments were conducted for a range of steel alloys. In this paper, two 6mm thick stainless steel (304L) plates are considered for FSW, while the tool was made of a composite refractory metal. The tool’s material is designated WRe-pcBN, and is composed of 60-70% (volume) of polycrystalline boron-nitride in a tungsten-rhenium binder. Several runs were made with traversing speeds between 100 and 350mm/min, and rotational speeds between 100 and 300rpm.

Use is also made of aluminium experiments made on two 6mm sheets of alloy 6082 in the T6 condition, which appeared in a previous TWI publication (Smith and Saraswat, 2009).

3: Computational Method

Three-dimensional CFD simulations are carried out for the FSW process using the code Ansys-Fluent. The computational domain is constructed as shown in Figure 3, where two 6mm thick plates are welded side by side. The computational mesh is carefully designed as illustrated in Figure 4, where the grid becomes finer near the tool. Each plate is 1m long and 0.5m wide, with the tool traversing along the length. The tool’s pin is assumed to take a hemispherical shape (non-profiled) and rotates about the Z axis in the counter-clockwise direction (Figure 5a). The tool’s shoulder and pin have radii equal to 10 and 5mm respectively. Notably, the tool is tilted in the forward direction of motion, as is used in some welding trials to constrain and enhance the metal flow. The tool is tilted about the Y axis with an angle of 2̊.

The simulation is made for a steady state investigation as if the tool is continuously travelling in the metal. Such assumption is reasonable, since experimental evidence has shown that the forces and temperatures are stabilised/steady between the beginning (plunge in) and end of the FSW process (Cater and Perrett, 2011). Section 6 herein refers to this matter.

The steady state welding process is simulated such that the metal plates are moving while the tool pin is fixed. Laminar flow is assumed since the viscous forces are much higher than the inertial forces. Navier-Stokes equations are solved together with the continuity and energy equations. In the energy equation, the viscous heating term is added as the heat generated by the viscous resistance is the main source of heating. The present study assumes that the welding energy is entirely generated by the viscoplastic action, and that sliding (friction) is not present.

The boundary conditions are shown in Figure 3, where the inlet is prescribed a constant velocity profile, and the outlet is assumed to have a constant static pressure (atmospheric). The sides of the domain, and the top and bottom surfaces, are assumed walls with imposed zero shear stress. This assumption is made so that the walls will not contribute to any resistance on the flowing viscoplastic metal. These walls are assumed to exchange heat with the surroundings by surface radiation and forced convection. For this purpose, arbitrary values for the convective coefficient and surface emissivity have been assumed, 10W/m²K and 0.6 respectively.

Only a small section of the tool is used in the model, and that will have implications on the conducted heat within the tool head. However, this is still a valid approximation, similar to that used by Smith and Saraswat (2009), since reported experimental evidence has demonstrated that heat conduction through the tool accounts only to 10% of the total heat transferred in the FSW process in aluminium welds.

The main flow and energy equations are solved iteratively with second order accuracy. The pressure and velocities are solved together during each iteration by the SIMPLEC algorithm, while the gradients inside the computational domain are calculated by a Green-Gauss node-based approach. The convergence tolerance in this simulation has proven to be critical. Several optimisation studies were conducted and came to conclude that at least 10^-5 residual ratio is required for all solution variables.  

4: Material Models

A linear viscosity model has been developed based on a linear relationship between yield strength and temperature, and between yield stress and strain rate, where the viscosity is a function of the uniaxial stress and uniaxial strain rate. In the present paper, the model used by Smith and Saraswat (2009) is used, where material properties are changed to reflect the steel and aluminium alloys used herein. The viscosity in this case is determined from the uniaxial strength via a three dimensional generalisation of the classical relationship between the shear stress and the strain rate. The viscosity is the uniaxial yield stress divided by three times the strain rate (Colegrove, 2001).

However, the linear assumption is an approximation. The metal’s yield stress has a stronger coupling to temperature and strain rate. A second viscosity model has been tested, where the viscosity was non-linearly related to the strain rate and the local temperature. The derivation of the equation for the viscosity of steel is explained as follows. The dependency of viscosity μ from the applied shear stress  σ_e and the shear strain rate ε is generally :

The flow stress σ_e consists of 2 different parts: the plastic contribution σ_p and the viscous contribution σ_v such that:

The plastic contribution represents the flow resistance from dislocation entanglement. The viscous contribution represents the frictional force along the slip plane that resist the dislocation glide. These contributions are defined as follows (Nandan 2006):

 κ is a state variable which characterises the plastic contribution. Its value represents the upper limit of σ_p . Assuming no strain hardening, the following saturation value is used for κ.

where φ denotes the Fisher factor:

The viscosity can be calculated with the flow stress and the effective strain rate using the relationship described in the work of Nandan (2006):

Hence, the viscosity of steel can be described as a function of temperature and strain rate as follows:

The definitions of the symbols and coefficients used above are provided in the Appendix.

5: Results

5.1 Summary of the runs

Table 1 lists the various simulations made with the linear viscosity assumption. The numbers in the table (1, 2, etc) denote the identity of each weld. 

Table 1 FSW simulations matrix on stainless steel with numbers identifying the weld parameters  

Using the non-linear viscoplasticity assumption aforementioned, only one FSW simulation is attempted with a traverse speed of 125mm/min and a rotational speed of 150 RPM. This weld will be denoted number 12. Conversely, for AA6082, one simulation is attempted with traversing and rotational speeds of 350mm/min and 1738RPM respectively. This will be weld number 13.

5.2 Characteristics

The forces and torques predicted by the series of simulations tabulated in section 5.1 are presented in Table 2. 

The forces are calculated by integrating the local pressure and viscous forces over the surface of the pin and shoulder in contact with the metal. The maximum tool temperature is also listed in Table 2, where the location of this maximum value is predominantly predicted on the downstream side of the pin and shoulder as seen in Figure 6.

Table 2 Predicted forces, torque and maximum tool temperature

Of the simulated welds, only a few have been shown to be successful in terms of predicting weld validity. The predicted field of metal viscosity has been used to identify whether a weld is successful or not. The predicted viscosity approaches a value of zero when the metal approaches its molten state. For example, a failed weld is illustrated in Figure 7 where the equivalents of molten penetrations are created in the longitudinal section of the weld. Notably, the location of the molten penetration indicates that the inspection of the longitudinal section is critical for weld soundness, since the penetration is not visible in the cross-section (Figure 8). The location of this molten penetration has been predominant in all the failed welds in the present study. Furthermore, successful welds in this study did not show molten penetration in either of the cross and longitudinal directions, and exhibited a profile similar to that in Figure 8. Figure 9 illustrates the resulting operating envelope of the simulated friction stir welds. 

Table 3 shows the experimental data resulting from a stainless steel weld, which the present model attempts to simulate. The record of this experimental weld is shown in Figure 10, where the values of interest - those reported in Table 3 - will fall in the middle section of the plot resembling a steady state operation. A macro section of this weld is shown in Figure 11, where the thermo-mechanically affected zone (TMAZ) section is clearly shown, and indicates a successful weld. 

The present simulations, based on linear viscosity formulation, predicted a successful weld with the operating parameters used in Table 3. Moreover, the present successful predictions in Figure 9 do agree with recent unpublished results in TWI. However, the predicted failed welds in Figure 9 can currently be considered unvalidated, since the supporting/refuting experimental evidence is in the process of being analysed. It is noteworthy that the comparison between the weld in Table 3 and Welds 2 and 12 can be misleading since the tool profile is different (Figure 5). That will be discussed further in section 6.

Table 3 Experimental parameters and results of FSW for thin stainless steel (304L) plates from Cater and Perrett (2006).

The impact of utilising the non-linear viscosity model is shown by inspecting the thermal field and the stream lines that indicate the direction of the metal flow round the tool’s pin. Figures 12 and 13 show the temperature contours of Welds 12 and 2 respectively. It is clear that the nonlinear model disperses more angular momentum to the metal resulting in a flow of welded metal towards the advancing side of the pin. This is confirmed by the streamlines plotted in Figure 14 showing a considerable movement of metal downstream from the pin. Interestingly, the flow lines exhibit a small change over the depth from the shoulder downwards. In contrast, the simple viscosity model exhibits less skewness in the thermal profile, and shows considerable flow straining along the depth of the pin as shown in Figure 15. The transition of the tool-metal interface from the shoulder to the pin is visible in Figure 16.

6: Discussion  

6.1 Tool profile

The present simulated tool has a non-profiled hemispherical pin that has a smooth surface. The predictions herein were compared with an experimental study made with a profiled tool shown in Figure 5b. Clearly, there is a difference between the modelled pin and the actual pin, and that has its effects on the claims that can be generated in this article. The validity of comparing two different tool shapes in this article stems from earlier work at TWI that compared temperatures and forces on different pins’ profiles (Beamish and Russell, 2011). Therein, the base case study was made with a plain cone pin, and then three grooved patterns were made on that cone to produce three other tool profiles. The study showed relatively minor differences between the shapes studied in the variables listed in Table 3.

There is a noticeable discrepancy between Weld 2 and the weld in Table 3. For example, the predicted torque was half of the measured value. It became clearer to the authors at the completion of this study that the large difference in the pin’s cross-section, herein, may render the comparison of their results challenging. The forces and the torque in Table 2 comprise two components: viscous and pressure forces at the tool-metal interface (equivalent to flow drag over immersed bodies). The data recorded by the model (not reported in Table 2) indicated that the pressure component has always exceeded its viscous counterpart. That indicates that the tool’s cross-section has a considerable effect on the forces and the torque.

Table 2 provides intuitive conclusions such that the torque is reduced when the rotational speed is increased at a constant feeding speed. It also indicated that the increase in feeding speed, at a constant rotational speed, increases the required machine torque/power.  Furthermore, the maximum tool temperature is directly linked to the torque at constant feeding speed (higher required torque induces higher temperature). But the tool temperature decreases - at constant rotational speeds - as the feed speed increases.

The model over-predicts the tool’s temperature, and that may be a result of an excessive over heating due to pure viscoplastic straining, with no interface sliding assumed as was reported in Nandan (2006). Another possible reason for the high temperature prediction is the higher surface area in the hemispherical pin. Viscous heating will rise as more metal flow is disrupted by the presence of the pin. A larger pin’s cross-section can certainly increase the heat generation if viscous heating is the main heating mechanism. The authors are working to confirm that such change can result in an exaggerated temperature rise. Furthermore, experimental evidence in TWI has indicated that a plain cone tool generates a lower tool temperature than a threaded profile (Beamish and Russell, 2011). Notably, the experimental facility on which the weld in Table 3 was made has a cast iron base that is in intimate contact with the welded steel sheets. The boundary conditions in the present model do not account for such a conductive heat sink. Interestingly, such a heat sink is common in FSW experiments, and its effect is rarely considered in FSW numerical models. As there are no supporting measurements to quantify the heat transfer through such a sink, more investigation is needed before the viscous heating becomes blamed for over-heating.

Figure 6 indicates that the FSW tool will undergo a thermal cycle (cooling and heating) as it rotates in contact with the metal. The location of maximum temperature is clarified by the metal flow shown in Figure 16, where metal is drawn from the retreating side around the tool to the advancing side. If another heat dissipation mechanism is added to the setup, such as a metallic base, one may expect a larger spatial variation in the tool’s surface temperature.

6.2 Applicability to weld soundness assessment

A method of predicting weld soundness (validity) is proposed in this article, based on the viscosity field round the tool/pin (see Figures 7 and 8). This approach is directly linked to the temperature field, which affects the yield stress that subsequently decreases the viscosity. Hence, relatively small values for viscosity indicate that the metal is approaching its molten state. Notably, the material data file was produced so that the viscosity will never be zero. However, due to the large variation of viscosity values across the contour levels, values remote from 10⁶ Pas.s fell under the contour value of zero. So far, given its approximations, the model has shown promising predictions for weld validity as compared with a set of experimental data made by TWI, and the weld recorded in Table 3.

It was noticed that the solutions herein are very sensitive to the convergence limits. All simulations were left to fully converge. Convergence was reached when the viscosity pattern was independent of iterative cycles. As mentioned in section 3 above, numerical residual values had to be in the order of 10^-5 to reach such state. Several tests made by the authors have indicated that the FSW model is sensitive to mesh resolution, and that fine resolution is required for successful FSW simulations.

It has to be noted that the operating envelope suggested by Figure 9 is based on the number of attempted simulations. The inspection of Figure 9 reveals that the FSW process is more sensitive to the traversing speed. One would expect that higher traversing speeds can generate sound welds with increasing rotational speeds. However, that is not what the results indicate. This is an interesting result that needs more investigation.

6.3 Viscoplasticity modelling

It is reported in the literature that the non-linear viscosity relation has been successfully used to predict FSW of steel and aluminium (Nandan et al, 2006; and Colegroveand Shercliff, 2004a). The present model has shown differences between the linear and non-linear viscosity relations. Welds 2 and 12 in Table 2 reveal such variation. The nonlinear relation results in a higher required torque, but contrastingly, much lower traverse and downward forces. Comparing the temperature contours in Figures 12 and 13 reveal that the nonlinear model produces an area of more uniform high temperature field round the tool. The flow streamlines, predicted by the non-linear model in Figure 14 show distinctly different flow behaviour than that given by the linear model.

The non-linear model strongly couples the metal’s yield stress to the strain rate and the temperature. Therefore, it is expected that the non-linear model be sensitive to the flow field round the tool. It was mentioned above why the authors believe that the tool’s profile is an important factor for the determination of forces on the tool. The streamlines in Figure14 indicate that the viscosity is quite large compared to what the linear model predicts. The increase in viscosity will raise the amount of viscous heating. However, with high temperature developing near the tool, it seems that the high temperature is not enough to generate a sufficiently low viscosity that changes the flow motion across the tool’s depth. A possible explanation for this condition is the mutual dependence between the viscosity and the strain rate.

By inspecting Figures 17 and 18, it becomes clearer that there is a significant difference in the strain rate that the tool generates for the same welding parameters (Welds 2 and 12). It is therefore believed that the seemingly disappointing results shown by the nonlinear model are due to the tool profile, and its inability to generate the required shearing action. The authors are not aware that the hemispherical pin profile has been tested/modelled in the open literature. Although the nonlinear model was used for plain cylindrical pins (Nandan et al, 2006), the flow behaviour round a hemisphere and a cylinder is quite different. Furthermore, it is noteworthy that the present model neither included any sliding boundaries on the tool, nor stress-clipping assumptions. It was decided to observe the flow evolution round the present simple tool for research purposes.  

Conversely, the linear model has been able to produce metal motion that agrees with images taken for aluminium FSW by Colligan (1999), as shown in Figure 16. The model gave reasonable predictions of the metal flow round the pin and near the shoulder, and exhibited the scattering of material downstream from the tool (Figure 15) as observed experimentally. However, the authors believe that the nonlinear model should have a better ability to capture the metal flow. Further simulations on threaded pins are therefore required to fully assess the behaviour of the nonlinear and the linear model.

7. Conclusion

Numerical simulations have been undertaken on a plain hemispherical FSW tool to assess the ability of the model to predict the operational parameter space. Two material models, linear and nonlinear, were utilised to represent the non-Newtonian flow of metal round the tool. It was observed that with an approximated tool profile, the linear material model has been able to provide a preliminary method for weld assessment. On the contrary, the more accurate nonlinear material model was not able to provide useful weld assessment information with the simple tool profile.

Discrepancy with experimental observations was highlighted. However, with certain experimental factors considered, the present results are not sufficient to fully assess the presented model. Further work has been identified on tool profiles and boundary conditions.

8. Acknowledgement

The authors wish to thank Mr Stephen Cater for his support and fruitful discussions throughout the preparation of this work. The authors wish to also acknowledge the information shared from the partners in Project HILDA.  

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Appendix

Material properties for the non-linear viscoplastic model of stainless steel (304L)