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Jetting Phenomenon in Cold Spray: A Critical Review on Finite Element Simulations

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Abstract

This paper offers a concise critical review of finite element studies of the jetting phenomenon in cold spray (CS). CS is a deposition technique wherein solid particles impact a substrate at high velocities, inducing severe plastic deformation and material deposition. These high-velocity particle impacts lead to the ejection of material in a jet-like shape at the periphery of the particle/substrate interface, a phenomenon known as "jetting". Jetting has been the subject of numerous studies over recent decades and remains a point of debate. Two main mechanisms, Adiabatic Shear Instability (ASI) and Hydrodynamic Pressure-Release (HPR), have been proposed to explain the jetting phenomenon. These mechanisms are mainly elucidated through finite element method (FEM) simulations, a numerical technique rooted in continuum mechanics. However, it is important to emphasize that FEM is limited by the equations established for analysis, and as such, its predictive capabilities are confined to those principles clearly defined within these equations. The choice of employed equations and approaches significantly influence the outcomes and predictions in FEM. While recognizing FEM's capabilities, this study reviews the ASI and HPR mechanisms within the context of CS. Additionally, this paper reviews FEM's algorithms and the core principles that govern FEM in calculating plastic deformation, which can lead to the formation of jetting.

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  1. Centre for Advanced Coating Technologies, University of Toronto, Toronto, ON, Canada

    S. Rahmati, J. Mostaghimi, T. Coyle & A. Dolatabadi

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Appendix A: Cuboid Model

Appendix A: Cuboid Model

In the ABAQUS/Explicit software (Ref 14), a two-dimensional Lagrangian model employing four-node plane strain elements was employed to simulate the impact of a 50 µm copper cuboid onto a rigid wall (utilizing analytical rigid (Ref 14)). A mesh size of 1 µm was opted for to ensure accurate representation of the extensive deformation induced during high-velocity impacts. It's worth noting that various element sizes were evaluated, and 1 μm was selected for its promising results in this study. A schematic representation of the simulation setup is shown in Fig. 16. The impact velocity was set at 500 m/s, and the initial temperature was maintained at room temperature (300 K). Outputs were saved for each increment to capture the progressive behavior. For contact formulation, surface-to-surface contact was employed. The underside of the cuboid that collided with the substrate was defined as the slave surface (second surface), while the rigid wall surface was selected as the master surface (first surface) (Ref 14). The contact property was configured with a normal behavior (hard contact) using the default settings (Ref 14). Additionally, the material behavior was assumed to be linear elastic in this simulation The material properties utilized for this simulation are outlined in Table 1.

Fig. 16
figure 16

Schematic representation of the simulation setup used in this study

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Table 1 Material properties (Ref 10, 49)
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Rahmati, S., Mostaghimi, J., Coyle, T. et al. Jetting Phenomenon in Cold Spray: A Critical Review on Finite Element Simulations. J Therm Spray Tech (2024). https://doi.org/10.1007/s11666-024-01766-8

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