**3. Simulation of a complex FSW joint**

To date, most of the work on simulating the FSW process has been focused on a simple buttjoint geometry model. Such a model is sufficient for academic research. However, for real engineering applications, the numerical model should be robust enough to be able to simulate complex geometries within a reasonable timeframe. In this section, we describe the FSW simulation model and results for a complex geometry. The case considered is of an aluminum alloy bridge deck that is fabricated by extrusion in multiple sections and joined using FSW. The joint geometry can be seen in **Figure 5**. One of the drawbacks of using extruded sections is that the parts tend to fit together with some undesirable qualities for FSW. In this case, the two workpieces join together with a ~0.5-mm step at the top surface of the joint (as shown in **Figure 5**). The left-most workpiece is slightly thicker than the other, and, as such, poses a challenge for FSW. The tool will have to push down an extra 0.5 mm in order to come into contact with the lower of the two surfaces. This in turn causes the formation of a significant flash on the thicker workpiece. The overall height of the joint is 100 mm, the three vertical members are 3 mm thick, the thicker plate (left side of step in image) is 3.7 mm thick, and the thinner plate is 3.2 mm thick.

elements is 0.6 mm in the pin and shoulder region. Large elements are used outside of this

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The entire joint geometry is modeled with elastic-plastic-thermal SPH elements to allow for an improved prediction of the thermal expansion and the stresses in the joint during the welding process. The vertical member below the weld seam carries 90% of the forge force during the welding process. With our modeling approach, the stresses and the possibility that the member could collapse can be evaluated. The tool interacts with the workpieces through a penalty-based contact algorithm that we have developed for FSW (full details in Fraser et al. [35]). The tool has a shoulder diameter of 15 mm, an average pin diameter of 6 mm, and a pin depth of 3.8 mm. The simulation model is composed of only a small region of interest of the

surface of the workpieces was painted black, an emissivity of 0.95) using a novel adaptive thermal boundary condition algorithm (see Fraser et al. [36]). The material parameters of the

**Parameter** Value Units **Parameter** Value Units **Density,** *ρ* 2700.0 Kg/m3 **Conductivity,** *k* 175.0 W/mK **Initial yield,** *σ<sup>y</sup>***<sup>0</sup>** 240.0 MPa **Heat capacity,** *Cp* 895.0 J/kgK

**Room temperature,** *TR* 20.0 °C **Conductivity,** *k* 55.0 W/mK **Melt temperature,** *Tmelt* 605.0 °C **Heat capacity,** *Cp* 485.0 J/kgK **Softening exponent,** *m* 1.34 - **Density,** *ρ* 7850.0 Kg/m3

**Shear modulus,** *G* 26.3 GPa **Tool thermal**

**Mechanical Workpieces Thermal**

K) is included in the model as well as radiation (the

region since contact with the workpieces is only during flash formation.

**Figure 6.** FSW joint simulation model.

actual bridge deck. Convection (10 W/m2

**Speed of sound,** *c* 4722 m/s

**Table 1.** Thermal-physical properties of the aluminum alloy.

aluminum alloy used in the simulation are shown in **Table 1**.

**Figure 5.** Complex joint.

#### **3.1. Model description**

The complex joint geometry is modeled by a combination of SPH for the workpieces and rigid finite elements for the tool. Since the tool is made of hardened steel, it can safely be approxi‐ mated as a rigid body. The simulation model is shown in **Figure 6**; here, we can see the rigid tool and the two workpieces including the step at the top surface. The mesh size for the finite elements is 0.6 mm in the pin and shoulder region. Large elements are used outside of this region since contact with the workpieces is only during flash formation.

**Figure 6.** FSW joint simulation model.

**3. Simulation of a complex FSW joint**

40 Joining Technologies

thinner plate is 3.2 mm thick.

**Figure 5.** Complex joint.

**3.1. Model description**

To date, most of the work on simulating the FSW process has been focused on a simple buttjoint geometry model. Such a model is sufficient for academic research. However, for real engineering applications, the numerical model should be robust enough to be able to simulate complex geometries within a reasonable timeframe. In this section, we describe the FSW simulation model and results for a complex geometry. The case considered is of an aluminum alloy bridge deck that is fabricated by extrusion in multiple sections and joined using FSW. The joint geometry can be seen in **Figure 5**. One of the drawbacks of using extruded sections is that the parts tend to fit together with some undesirable qualities for FSW. In this case, the two workpieces join together with a ~0.5-mm step at the top surface of the joint (as shown in **Figure 5**). The left-most workpiece is slightly thicker than the other, and, as such, poses a challenge for FSW. The tool will have to push down an extra 0.5 mm in order to come into contact with the lower of the two surfaces. This in turn causes the formation of a significant flash on the thicker workpiece. The overall height of the joint is 100 mm, the three vertical members are 3 mm thick, the thicker plate (left side of step in image) is 3.7 mm thick, and the

The complex joint geometry is modeled by a combination of SPH for the workpieces and rigid finite elements for the tool. Since the tool is made of hardened steel, it can safely be approxi‐ mated as a rigid body. The simulation model is shown in **Figure 6**; here, we can see the rigid tool and the two workpieces including the step at the top surface. The mesh size for the finite

The entire joint geometry is modeled with elastic-plastic-thermal SPH elements to allow for an improved prediction of the thermal expansion and the stresses in the joint during the welding process. The vertical member below the weld seam carries 90% of the forge force during the welding process. With our modeling approach, the stresses and the possibility that the member could collapse can be evaluated. The tool interacts with the workpieces through a penalty-based contact algorithm that we have developed for FSW (full details in Fraser et al. [35]). The tool has a shoulder diameter of 15 mm, an average pin diameter of 6 mm, and a pin depth of 3.8 mm. The simulation model is composed of only a small region of interest of the actual bridge deck. Convection (10 W/m2 K) is included in the model as well as radiation (the surface of the workpieces was painted black, an emissivity of 0.95) using a novel adaptive thermal boundary condition algorithm (see Fraser et al. [36]). The material parameters of the aluminum alloy used in the simulation are shown in **Table 1**.


**Table 1.** Thermal-physical properties of the aluminum alloy.

We have used a uniform grid particle distribution of 0.6 mm to discretize the workpieces. This spacing allows for a sufficient number of particles through the thickness without incurring excessive calculation penalty. The time step size is selected based on the Courant-Friedrichs-Lewy (CFL) criteria, *dt*min = CFL[*h*/(*v*max+*c*)]. For this FSW model, we found that CFL = 0.7 was acceptable, leading to *dt*min = 9.8 × 10-8). The small time step size is one of the major drawbacks of using a solid-mechanics approach. Nevertheless, the time step size is required in order to capture the propagation of elastic stresses within the aluminum.

The temperature distribution results for the three cases are shown in **Figure 7** at different times during the simulation. We can see that the maximum temperature for case 2 is lower than for the other two cases. This is because the tool plunges 0.1 mm less, in turn decreasing the forge force and the heat generated due to Eq. (12). The ultimate result is that the quality of the weld in case 2 is significantly lower than in the other cases. Of the three cases, the best weld quality is obtained from case 3. Since the tool rotates clockwise, the advancing side is on the surface of the thicker workpiece. This helps to move the hot material to the thinner workpiece at the front of the tool. This is a favorable situation compared to having the hot material move around the back of the tool (as in cases 1 and 2). We have every advantage to have the advancing side on the thicker workpiece since the pressure is higher there. This causes the workpieces to heat

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up more uniformly than is possible in either case 1 or 2.

**Figure 7.** Temperature and deformation results for the three cases.

The model is run as two distinct phases: plunge and advance. The dwell phase was not part of the process as a ramp-up procedure to full advance speed was used in the experiment. A well-defined ramp-up is good practice to limit the forces and torque on the tool and can replace the dwell phase. The plunge speed is 25 mm/min and the full advance speed is 1250 mm/min with 2100 rpm. The ramp-up is performed linearly for an initial tool displacement of 40 mm; after this point, the tool speed is constant at 1250 mm/min.

Because of the 0.5-mm step, excessive amounts of flash are produced as the tool advances. The flash has to be removed following the welding phase and requires a significant amount of work for the welding technician. In order to attempt to reduce the quantity of flash produced, we investigate three cases as follows:

Case 1- As performed in experiment—Full depth plunge (4.3 mm) until the tool shoulder contacts the lower workpiece surface with a counterclockwise tool rotation. This simulation case uses the same process parameters as the production run. The model serves as the validation case using temperature, force, torque, and flash height.

Case 2- Variation 1—Partial depth plunge (4.2 mm) with a counterclockwise tool rotation.

Case 3- Variation 2—Full depth plunge (4.3 mm) until the tool shoulder contacts the lower workpiece surface with a clockwise tool rotation.

Case 1 represents the actual process parameters used in the experiment. This case is used to validate the tool force and torque, as well as the temperature distribution and history. Cases 2 and 3 are variations on case 1. In case 2, we attempt to reduce the quantity of flash by plunging less (4.2 as opposed to 4.3 mm). This will have the effect of limiting the volume of material that is sheared off the top surface of the thicker plate. In case 3, the flash formation will be reduced by operating the FSW tool with a clockwise rotation. This results in the advancing side being on the surface of the thicker plate. This will increase the weld temperature and help to move more material to the lower side of the step, ultimately creating a superior weld compared to cases 1 and 2.

#### **3.2. Simulation results**

The three cases were run in SPHriction-3D; in this section, we present the results from the three different cases. The production process parameters correspond to case 1 and are used to validate the model. A video of the results for the three cases is available here: https:// www.youtube.com/watch?v=eLOQILkUx-A.

The temperature distribution results for the three cases are shown in **Figure 7** at different times during the simulation. We can see that the maximum temperature for case 2 is lower than for the other two cases. This is because the tool plunges 0.1 mm less, in turn decreasing the forge force and the heat generated due to Eq. (12). The ultimate result is that the quality of the weld in case 2 is significantly lower than in the other cases. Of the three cases, the best weld quality is obtained from case 3. Since the tool rotates clockwise, the advancing side is on the surface of the thicker workpiece. This helps to move the hot material to the thinner workpiece at the front of the tool. This is a favorable situation compared to having the hot material move around the back of the tool (as in cases 1 and 2). We have every advantage to have the advancing side on the thicker workpiece since the pressure is higher there. This causes the workpieces to heat up more uniformly than is possible in either case 1 or 2.

We have used a uniform grid particle distribution of 0.6 mm to discretize the workpieces. This spacing allows for a sufficient number of particles through the thickness without incurring excessive calculation penalty. The time step size is selected based on the Courant-Friedrichs-Lewy (CFL) criteria, *dt*min = CFL[*h*/(*v*max+*c*)]. For this FSW model, we found that CFL = 0.7 was acceptable, leading to *dt*min = 9.8 × 10-8). The small time step size is one of the major drawbacks of using a solid-mechanics approach. Nevertheless, the time step size is required in order to

The model is run as two distinct phases: plunge and advance. The dwell phase was not part of the process as a ramp-up procedure to full advance speed was used in the experiment. A well-defined ramp-up is good practice to limit the forces and torque on the tool and can replace the dwell phase. The plunge speed is 25 mm/min and the full advance speed is 1250 mm/min with 2100 rpm. The ramp-up is performed linearly for an initial tool displacement of 40 mm;

Because of the 0.5-mm step, excessive amounts of flash are produced as the tool advances. The flash has to be removed following the welding phase and requires a significant amount of work for the welding technician. In order to attempt to reduce the quantity of flash produced, we

Case 1- As performed in experiment—Full depth plunge (4.3 mm) until the tool shoulder contacts the lower workpiece surface with a counterclockwise tool rotation. This simulation case uses the same process parameters as the production run. The model serves as the

Case 2- Variation 1—Partial depth plunge (4.2 mm) with a counterclockwise tool rotation.

Case 3- Variation 2—Full depth plunge (4.3 mm) until the tool shoulder contacts the lower

Case 1 represents the actual process parameters used in the experiment. This case is used to validate the tool force and torque, as well as the temperature distribution and history. Cases 2 and 3 are variations on case 1. In case 2, we attempt to reduce the quantity of flash by plunging less (4.2 as opposed to 4.3 mm). This will have the effect of limiting the volume of material that is sheared off the top surface of the thicker plate. In case 3, the flash formation will be reduced by operating the FSW tool with a clockwise rotation. This results in the advancing side being on the surface of the thicker plate. This will increase the weld temperature and help to move more material to the lower side of the step, ultimately creating a superior weld compared to

The three cases were run in SPHriction-3D; in this section, we present the results from the three different cases. The production process parameters correspond to case 1 and are used to validate the model. A video of the results for the three cases is available here: https://

capture the propagation of elastic stresses within the aluminum.

after this point, the tool speed is constant at 1250 mm/min.

validation case using temperature, force, torque, and flash height.

workpiece surface with a clockwise tool rotation.

www.youtube.com/watch?v=eLOQILkUx-A.

investigate three cases as follows:

42 Joining Technologies

cases 1 and 2.

**3.2. Simulation results**

**Figure 7.** Temperature and deformation results for the three cases.

**Figure 9.** Temperature history results for the three cases.

to a decrease in temperature.

The relative difference between the TCs on the thicker and thinner plates gives a good means of diagnosing the quality of the weld. If there is a large difference in the temperature reading, we can conclude that the pressure is higher on one side of the weld than the other. This leads to an unfavorable temperature distribution and the weld quality suffers. Case 2 is an excellent example of such a situation. Notice the large difference in temperature in TC3 and TC4. Since the plunge depth was insufficient, there is not enough pressure on the thinner plate, leading

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The temperature results at MTC1 are also an excellent indication of the weld quality. Since MTC1 follows the tool as it rotates and advances, large temperature fluctuations are suggestive of inadequate process parameters. We can see that the variation in temperature at MTC1 for case 3 is significantly less than in other two cases. The experimental setup that we used did not allow us to embed thermocouples in the workpiece or in the tool. Using an IRcam is beneficial in cases such as this since holes do not need to be drilled in the aluminum or in the tool. The surfaces to be filled should be painted a light coat of flat black paint that can easily be removed with light buffing following welding. Temperature measurements with an IRcam provide a very powerful diagnosis tool in the laboratory or in the hands of an FSW technician at a commercial company. The images obtained can help the technician or an engineer to understand whether their chosen process parameters are adequate and if not give good hints as to why. For example, if the IRcam shows a significantly higher surface temperature on the advancing side than the retreating side, the tool is likely advancing too fast for the chosen rpm. During the plunge phase, the IRcam can again be used to determine whether the plunge speed is too high (surface temperature too low) or low (surface temperature too high) (**Figure 10**).

**Figure 8.** Temperature measurement points in the simulation model.

We have used four measurement points (TCs) for the temperature histories as shown in **Figure 8**. TC1 and TC2 are placed at the middle of the workpiece (along the weld direction). TC3 and TC4 are placed in line with the tool axis during the plunge phase. The four TCs are at the surface of the workpieces and located 11.5 mm from the interface of the two workpieces. MTC1 is a moving temperature measurement point that is located on the underside of the tool and follows the tool as it rotates and advances. MTC1 is located 6 mm from the tool axis on the underside of the tool shoulder.

The temperature was measured experimentally at two points on the surface of the thicker workpiece (at locations TC1 and TC3) using data obtained from an infrared camera (IRcam). Due to the filming angle available with the IRcam (restricted access to work area), temperatures on the thinner workpiece could not be evaluated. **Figure 9** shows that there is a good agreement between the experimental and simulation results. The simulation model has a tendency to slightly overpredict the temperature. Since we have used the perfectly-plastic-thermalsoftening model presented in Eq. (19), there is an overprediction of the plastic deformation and in turn an increase in the heat generated as shown in Eq. (12). Furthermore, the heat capacity and thermal conductivity of the aluminum alloy at high temperature are not known. These parameters play an important role in the coupled thermal-mechanical model.

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**Figure 9.** Temperature history results for the three cases.

**Figure 8.** Temperature measurement points in the simulation model.

the underside of the tool shoulder.

44 Joining Technologies

We have used four measurement points (TCs) for the temperature histories as shown in **Figure 8**. TC1 and TC2 are placed at the middle of the workpiece (along the weld direction). TC3 and TC4 are placed in line with the tool axis during the plunge phase. The four TCs are at the surface of the workpieces and located 11.5 mm from the interface of the two workpieces. MTC1 is a moving temperature measurement point that is located on the underside of the tool and follows the tool as it rotates and advances. MTC1 is located 6 mm from the tool axis on

The temperature was measured experimentally at two points on the surface of the thicker workpiece (at locations TC1 and TC3) using data obtained from an infrared camera (IRcam). Due to the filming angle available with the IRcam (restricted access to work area), temperatures on the thinner workpiece could not be evaluated. **Figure 9** shows that there is a good agreement between the experimental and simulation results. The simulation model has a tendency to slightly overpredict the temperature. Since we have used the perfectly-plastic-thermalsoftening model presented in Eq. (19), there is an overprediction of the plastic deformation and in turn an increase in the heat generated as shown in Eq. (12). Furthermore, the heat capacity and thermal conductivity of the aluminum alloy at high temperature are not known.

These parameters play an important role in the coupled thermal-mechanical model.

The relative difference between the TCs on the thicker and thinner plates gives a good means of diagnosing the quality of the weld. If there is a large difference in the temperature reading, we can conclude that the pressure is higher on one side of the weld than the other. This leads to an unfavorable temperature distribution and the weld quality suffers. Case 2 is an excellent example of such a situation. Notice the large difference in temperature in TC3 and TC4. Since the plunge depth was insufficient, there is not enough pressure on the thinner plate, leading to a decrease in temperature.

The temperature results at MTC1 are also an excellent indication of the weld quality. Since MTC1 follows the tool as it rotates and advances, large temperature fluctuations are suggestive of inadequate process parameters. We can see that the variation in temperature at MTC1 for case 3 is significantly less than in other two cases. The experimental setup that we used did not allow us to embed thermocouples in the workpiece or in the tool. Using an IRcam is beneficial in cases such as this since holes do not need to be drilled in the aluminum or in the tool. The surfaces to be filled should be painted a light coat of flat black paint that can easily be removed with light buffing following welding. Temperature measurements with an IRcam provide a very powerful diagnosis tool in the laboratory or in the hands of an FSW technician at a commercial company. The images obtained can help the technician or an engineer to understand whether their chosen process parameters are adequate and if not give good hints as to why. For example, if the IRcam shows a significantly higher surface temperature on the advancing side than the retreating side, the tool is likely advancing too fast for the chosen rpm. During the plunge phase, the IRcam can again be used to determine whether the plunge speed is too high (surface temperature too low) or low (surface temperature too high) (**Figure 10**).

**Figure 12.** Plastic strain at the end of advancing phase showing the effective weld zone.

experimental data, though the magnitude is diffident (**Figure 11**).

depth is shallower, leading to less contact pressure (**Figure 12**).

A comparison of the spindle torque and the forge force is shown in **Figure 10**. The inertia of the spindle plays a strong role in the experimentally measured torque. Because the plates being welded are very thin, the maximum process torque does not exceed 25 Nm and the average torque during the advancing phase is ~20 Nm. However, the no-load torque measured was ~10 Nm, accounting for almost half of the typical process torque. In the simulation models, the inertial effects of the spindle are not taken into consideration. The simulation torque is calculated by taking the cross-product of the contact forces and the distance vector between the tool axis and an SPH element. For this reason, the torque trends line up well with the

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A good correlation between the forge force from experiment and simulation was obtained. The inertial effects do not play an important role here, leading to a better prediction than was obtained with the torque. There are other factors that lead to a reduction in the precision of the predicted torque and forge force such as the thermophysical properties of the material, the chosen friction law, differences in how the FSW machine and simulation model control the position, and rpm of the tool, as well as discrepancies between the actual geometry of the

Nevertheless, the simulation model provides an excellent understanding of how a change in process parameters effects the torque and forces. We can see that the tool torque and forge force for case 2 are lower than those for cases 1 and 3. This is an intuitive result as the plunge

A flash height of 4.2 mm was measured experimentally; case 1 predicts a flash height of 4.5 mm, 3.9 mm for case 2, and less than 1 mm for case 3. The flash heights are shown in **Figure 11**; notice that the wavy pattern of the flash is well represented in the simulation model for case 1. The images have been cleaned up to show only the continuous flash line by omitting sporadic "flash flakes" that typically do not require much effort to re‐ move. Clearly, the flash produced in case 3 is significantly less than that in other two cases. The reason is entirely due to the change in tool rotation. Flash lines will most com‐ monly be laid down on the retreating side of the weld. By ensuring that the advancing side is on the thicker side, the material is "ripped" from the thicker side and transported to the retreating side. Because of the height change, the flash is not able to attach to the

workpieces and the tool compared to their idealization in the simulation model.

**Figure 10.** Spindle torque and forge-force comparison.

We can conclude that the weld zone has a more uniform temperature distribution. This leads to favorable welding conditions and results in improved weld quality. Of particular interest is the strong oscillation at MTC1 for case 2. Near the end of the simulation, there is a peak-topeak temperature change of over 300°C. The temperature on the thinner plate is too low to allow the aluminum material to flow and the weld is essentially incomplete. This can be verified by investigating the plastic strain contours in the weld zone as shown in **Figure 12**. We can see that case 3 is the only one of the three in which the mechanically effected zone spans the entire diameter of the tool. In case 1, the welded zone gets narrower as the tool advances. For case 2, the welded zone spans no more than half the tool diameter from the edge of the tool pin on the thinner plate into the thicker plate.

**Figure 11.** Flash height comparison at the end of advancing phase.

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**Figure 12.** Plastic strain at the end of advancing phase showing the effective weld zone.

**Figure 10.** Spindle torque and forge-force comparison.

46 Joining Technologies

of the tool pin on the thinner plate into the thicker plate.

**Figure 11.** Flash height comparison at the end of advancing phase.

We can conclude that the weld zone has a more uniform temperature distribution. This leads to favorable welding conditions and results in improved weld quality. Of particular interest is the strong oscillation at MTC1 for case 2. Near the end of the simulation, there is a peak-topeak temperature change of over 300°C. The temperature on the thinner plate is too low to allow the aluminum material to flow and the weld is essentially incomplete. This can be verified by investigating the plastic strain contours in the weld zone as shown in **Figure 12**. We can see that case 3 is the only one of the three in which the mechanically effected zone spans the entire diameter of the tool. In case 1, the welded zone gets narrower as the tool advances. For case 2, the welded zone spans no more than half the tool diameter from the edge A comparison of the spindle torque and the forge force is shown in **Figure 10**. The inertia of the spindle plays a strong role in the experimentally measured torque. Because the plates being welded are very thin, the maximum process torque does not exceed 25 Nm and the average torque during the advancing phase is ~20 Nm. However, the no-load torque measured was ~10 Nm, accounting for almost half of the typical process torque. In the simulation models, the inertial effects of the spindle are not taken into consideration. The simulation torque is calculated by taking the cross-product of the contact forces and the distance vector between the tool axis and an SPH element. For this reason, the torque trends line up well with the experimental data, though the magnitude is diffident (**Figure 11**).

A good correlation between the forge force from experiment and simulation was obtained. The inertial effects do not play an important role here, leading to a better prediction than was obtained with the torque. There are other factors that lead to a reduction in the precision of the predicted torque and forge force such as the thermophysical properties of the material, the chosen friction law, differences in how the FSW machine and simulation model control the position, and rpm of the tool, as well as discrepancies between the actual geometry of the workpieces and the tool compared to their idealization in the simulation model.

Nevertheless, the simulation model provides an excellent understanding of how a change in process parameters effects the torque and forces. We can see that the tool torque and forge force for case 2 are lower than those for cases 1 and 3. This is an intuitive result as the plunge depth is shallower, leading to less contact pressure (**Figure 12**).

A flash height of 4.2 mm was measured experimentally; case 1 predicts a flash height of 4.5 mm, 3.9 mm for case 2, and less than 1 mm for case 3. The flash heights are shown in **Figure 11**; notice that the wavy pattern of the flash is well represented in the simulation model for case 1. The images have been cleaned up to show only the continuous flash line by omitting sporadic "flash flakes" that typically do not require much effort to re‐ move. Clearly, the flash produced in case 3 is significantly less than that in other two cases. The reason is entirely due to the change in tool rotation. Flash lines will most com‐ monly be laid down on the retreating side of the weld. By ensuring that the advancing side is on the thicker side, the material is "ripped" from the thicker side and transported to the retreating side. Because of the height change, the flash is not able to attach to the

thinner side and creates intermittent "flakes" that can be removed in less time than is possible in the case of a continuous flash line on the thicker side (as in cases 1 and 2).

a highly optimized communication strategy between the GPUs (e.g., using MPI). We are

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**•** Improved contact models with different friction treatments (such as including the shear

**•** Improved thermo-physical material representations that more accurately model the

**•** An implicit mesh-free collocation approach that will permit efficient simulation of long

Since the simulation code is developed using a highly optimized parallel-processing strategy, complex 3D-joint geometries can be simulated within a reasonable period. In this work, the three simulation models were run simultaneously on a personal workstation with three individual GPUs. The cost of such a computer is less than five thousand dollars in today's market. Because of the parallel strategy, a cluster with many GPUs can be used with 100% efficiency (as long as an individual GPU has enough memory for each simulation model). In the sense of optimization, a company with access to a GPU compute cluster (say eight or more GPUs) could run parametric models (e.g., varying the rpm and advance speed) simultane‐ ously. The obtained data sets would provide the required information to construct a response

The authors would like to thank NVIDIA for donating the GeForce GTX Titan Black GPU that was used to perform the simulations. We would also like to thank the Portland Group (PGI) for having generously provided a license for PGI Visual Fortran (PVF) with CUDA Fortran. The project is supported in part by funding from FRQNT, CQRDA, GRIPS, REGAL, RTA, and

currently working on various developments in the code, such as follows:

**•** Wear prediction at the surface of the tool using Archard's model;

behavior of the aluminum alloy during the FSW process;

surface and find the optimal advancing speed and rpm.

CURAL. We declare no conflicts of interest associated with this work.

and Laszlo I. Kiss1

\*Address all correspondence to: Kirk.Fraser@PredictiveEngineering.com

1 Université du Québec à Chicoutimi (UQAC), Saguenay, QC, Canada

2 Predictive Engineering, Saguenay, QC, Canada

limit and/or a stick-slip behavior);

duration phases such as cooling.

**Acknowledgements**

**Author details**

Kirk Fraser1,2\*, Lyne St-Georges1
