**4. Conclusions**

Cold gas dynamic spray impacts on pure copper substrates of nanoscale ductile materials such as Al, Ni, Cu, and Ag are modelled using a molecular dynamic simulation (MD) system for differing material combinations, particle impact velocities, and microstructures. The post-impact behaviour is objectively studied by monitoring the distribution of the thermomechanical variable such as pressure wave, temperature, stress, dislocation density, and microstructural features such as local atomic structural transformation at the nanoscale. We studied the position and the propagation of the compressive shock wave in activating a jet at the interface of particle/substrate impact region.

The findings of the simulation show that the jetting phenomenon, as the material deforms during impact, is due to the interaction between the velocity of the shock wave at the interface of the particle/substrate interfacial zone and the velocity at the edge of particle/substrate interface. The effect produces a compressive wave of approximately 2.8 GPa for the Ag particle impact at the impact speed of 1000 m/s in the impacted zone. This compressive wave moves via the particle at the rear as well as through the interface of particle/substrate region, in conflict with particle/substrate lateral shear motion. The shock wave reaches the periphery of the particle/substrate edge, in this case, leading to the external materials flow and causing the particle and substrate to form a jet. The pressure wave evolution in Al/Cu impact does not seem to interfere with the interface boundary of the particle/substrate periphery and a jet initiation for Al/Cu impact is not observed. The impact of an Ag particle creates the highest-pressure wave propagating into the substrate and particle from the point of impact till around 15 ps, resulting in deformation of particles and substrate as well as heat generation followed by that of Cu, Ni, and Al impact, respectively.

The deformation behavior for individual impacting particles and subsequent dislocation evolution allowed us to classify the stages of deformation into three, after the impact analysis of particle/substrate impact. Firstly, plastic deformation began by the slide of dislocations and nucleation at the exterior end of the particle that is in close contact with the surface of the substrates at impact. Thereafter, with additional

deformation, the analysis of the dense dislocation segmen<sup>t</sup> when comparing the initial and the final microstructures of the splat show dislocation network formation formed at the exterior bottom of the particles, and the upper region remains essentially undeformed. Finally, as seen in the finite element method and microscopy experiments, the upper part the particle deformed as well, causing the usual flattened splat shape. The dislocation density increases to the value of 2.9 × 10<sup>16</sup> m<sup>−</sup>2, 4.3 × 10<sup>16</sup> m<sup>−</sup>2, 5.8 × 10<sup>16</sup> m<sup>−</sup>2, and 6.5 × 10<sup>16</sup> m<sup>−</sup><sup>2</sup> for Al, Ag, Cu, and Ni particles, respectively. The extreme plastic deformation at the interface of the substrate and material particle contributes to the creation of a jet region around the interface region of particle/substrate. The dislocation growth rate in Ni particles is about 55.4%, 33.8%, and 10.7% higher than in Al, Ag, and Cu particles, respectively.

A contrast of the original and final microstructures of the splat shows the creation, near the interface, of "new" atomic structure, which is certified by a combination of atomic boundary mobility stress-led and recrystallization of particle/substrate mechanisms. The recrystallization potential varies with the impact velocities, the thermal evolution and the stored strain energy as seen in the CGDS splats created during 20 ps, which show the local atomic structure. Some of these new structures are established on the bond line, which facilitates close interaction and strengthens CGDS splat bond. These findings expand our awareness about the processes to reinforce cold gas dynamic sprayed deposits from a modelling perspective. CGDS also qualifies as an additive manufacturing procedure to achieve the optimal strength of the deposit (coating) by the interface nucleation of finer atomic structures and the subsequent atomic boundary strengthening.

**Author Contributions:** S.T.O.: Conceptualization, Methodology, Investigation, Software, Visualization, Writing-Original draft. T.-C.J.: Resources, Reviewing and Editing and Supervision. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to acknowledge the financial support from the University Research Committee of the University of Johannesburg and the National Research Foundation of South Africa.

**Conflicts of Interest:** The authors declare no conflict of interest.
