**Acknowledgements**

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).

In this work, we have presented our approach toward simulating the entire FSW process using a solid-mechanics approach. By using a mesh-free numerical method such as SPH, the large plastic deformation encountered during FSW can be easily calculated. Mesh-based methods struggle to capture all the physics of the process due to discretization errors as the mesh distorts. The fully coupled elastic-plastic-thermal code is able to predict temperature, stress, and deformation histories. Because of the mesh-free Lagrangian nature of SPH, the model is able to predict defects (free surface changes) in a way that other numerical methods cannot. The prediction of defects is an invaluable feature for an engineer working on the design of the joint geometry to be welded. Optimal process parameters can then be chosen that lead to noweld defects. In this manner, the design engineer can find the fastest rate of advance that can

be used to increase the overall profit margin during a high-volume production run.

One of the major advantages of using a solid-mechanics approach compared to a fluid approach is that the simulation models are able to capture the elastic stresses and strains. **Figure 13** shows the effective stress in the joint at the end of the plunge phase. This is the point when the forge force reaches its maximum value. This is of great interest to a joint designer who is interested to know if the joint will withstand the forge force during the welding process. If the vertical members under the weld seam are too thin, they will likely undergo significant plastification and could collapse. This certainly would be disastrous for the finished product. Other benefits of including the elastic stresses and strain are the ability to more precisely predict defect size and shape, as well as residual stresses and deformation following a

Looking toward the future of numerical simulation of FSW, we can see that as the performance of GPUs continues to improve, larger and more complex simulation models will be possible. We are currently working on a multi-GPU parallelization strategy that will allow tens and even hundreds of millions of SPH elements to be simulated. This approach requires the use of

**4. Conclusions**

48 Joining Technologies

cooldown phase.

**Figure 13.** Stress state at the end of plunge phase.

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