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Research Papers: Applications

# Simulation of the Cold Spray Particle Deposition Process

[+] Author and Article Information
Jing Xie, Hélène Walter-Le Berre

Université de Lyon,
INSA-Lyon,
LaMCoS UMR CNRS 5259,
Villeurbanne F69621, France

Daniel Nélias

Université de Lyon,
INSA-Lyon,
Bât. Joseph Jacquard. 27,
Av. A. Einstein,
LaMCoS UMR CNRS 5259,
Villeurbanne F69621, France
e-mail: daniel.nelias@insa-lyon.fr

Kazuhiro Ogawa, Yuji Ichikawa

Fracture and Reliability Research Institute,
Tohoku University,
Sendai, Miyagi 980, Japan

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 17, 2012; final manuscript received March 27, 2015; published online May 11, 2015. Assoc. Editor: James R. Barber.

J. Tribol 137(4), 041101 (Oct 01, 2015) (15 pages) Paper No: TRIB-12-1182; doi: 10.1115/1.4030257 History: Received October 17, 2012; Revised March 27, 2015; Online May 11, 2015

## Abstract

Cold spray is a rapidly developing coating technology for depositing materials in the solid state. In this work, the cold spray particle deposition process was simulated by modeling high-velocity impacts of spherical particles onto a flat substrate under various conditions. For the first time, we proposed the coupled Eulerian–Lagrangian (CEL) numerical approach as a means of solving the high-strain rate deformation problem. Using this approach, we observed a compressive stress region at the interface between the particles and the substrate induced by large plastic strains in the materials. Due to the high contact pressure (about 1 GPa) and the short contact time (about 40 ns), the high-strain rate ($106 s-1$) plastic deformation region was only a few micrometers deep and was localized mainly at the bottom of the particle and substrate surface. The ability of the CEL method to model the cold spray deposition process was assessed through a systematic parametric study including impact velocity, initial particle temperature, friction coefficient, and materials combination. The higher the impact velocity, the higher the initial kinetic energy, leading to more substantial plastic deformations and significant temperature increases in the substrate. The initial particle temperature has a greater influence on the equivalent plastic strain than on the temperature increase in the substrate. Friction has a limited effect on the temperature distribution and increase in the substrate, and the equivalent plastic strain increases only slightly as the friction coefficient rises. Four combinations of particle/substrate materials (Cu/Cu, Al/Al, Cu/Al, and Al/Cu) were considered in our study. Obviously, the particle's material had a greater influence on the deposition process and on the deformation than the substrate material. Concerning the particle's material, a higher-density material, such as Cu, has a higher initial kinetic energy, which has the advantage of increasing the contact area and contact time, resulting in better bonding between particles and substrate. Compared to other numerical methods (Lagrangian, arbitrary Lagrangian–Eulerian (ALE), and smooth particle hydrodynamics (SPH)), the CEL approach is globally more accurate and more robust in high-strain rate deformation regimes.

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## Figures

Fig. 1

Schematic representations of (a) the 2D axisymmetric model, (b) the 3D SPH model, and (c) the 3D CEL model

Fig. 2

Contours of (a) the equivalent plastic strain and (b) the temperature for Al/Al impact simulation at 700 m/s using the Lagrangian method, aborted at 19 ns

Fig. 3

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature for Al/Al impact simulation at 700 m/s using the Lagrangian method

Fig. 4

Contours of (a) the equivalent plastic strain and (b) the temperature for Al/Al impact simulation at 700 m/s using the ALE method

Fig. 5

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature for Al/Al impact simulation at 700 m/s using the ALE approach

Fig. 6

Contours of the equivalent plastic strain for Al/Al impact simulation at 700 m/s using the SPH method

Fig. 7

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the stress in the substrate for Al/Al impact simulation at 700 m/s using the SPH approach

Fig. 8

Contours of (a) the volume average of the equivalent plastic strain in the Al particle and (b) the equivalent plastic strain in the Al substrate at 700 m/s using the CEL method

Fig. 9

Contours of (a) the volume average of the temperature in the Al particle and (b) the temperature of the Al substrate at 700 m/s using the CEL method

Fig. 12

Time histories of (a) the stable time increment and (b) the artificial strain energy at 700 m/s using the four approaches

Fig. 11

Time history of (a) the normalized kinetic energies and (b) the normalized displacements of the substrate's center at 700 m/s using the four approaches

Fig. 10

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature for Al/Al impact simulation at 700 mm/s using the CEL approach

Fig. 13

Evolution of the mean stress in a 500 m/s Al/Al impact: (a) 5 ns, (b) 10 ns, (c) 20 ns, (d) 30 ns, (e) 40 ns, and (f) 60 ns

Fig. 14

Evolution of the equivalent plastic strain (PEEQ) in a 500 m/s Al/Al impact: (a) 5 ns, (b) 10 ns, (c) 20 ns, (d) 30 ns, (e) 40 ns, and (f) 60 ns

Fig. 24

Time history of the ratio of the friction energy (ALLFD) to the internal energy (ALLIE) in a Cu/Cu impact with 0.2, 0.3, and 0.5 friction coefficient using the CEL approach

Fig. 25

Distribution of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) at the Cu substrate's surface with 0.2, 0.3, and 0.5 friction coefficient using the CEL approach

Fig. 16

Distribution of (a) the contact pressure (CPRESS) and (b) the frictional shear stress (CSHEAR) in a 500 m/s Al/Al impact

Fig. 15

Strain rate distribution over the contact surface in (a) the Al particle and (b) the Al substrate in a 500 m/s impact

Fig. 21

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) for Cu/Al impact with 473 K, 673 K, and 873 K initial particle temperature using the CEL approach

Fig. 22

Distribution of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) at the surface of the Al substrate with 473 K, 673 K, and 873 K initial particle temperature using the CEL approach

Fig. 19

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) for Al/Al impact simulation at 700 m/s, 780 m/s, and 840 m/s using the CEL approach

Fig. 20

Distribution of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) at the surface of the Al substrate at 700 m/s, 780 m/s, and 840 m/s using the CEL approach

Fig. 23

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) in a Cu/Cu impact with 0.2, 0.3, and 0.5 friction coefficient using the CEL approach

Fig. 17

Distribution of the temperature (TEMP) along the contact surface of (a) the particle and (b) the substrate in a 500 m/s Al/Al impact

Fig. 18

Distribution of (a) the contact force (CFORCE) and (b) the normalized displacement of the Al substrate impacted by the Al particle at 500 m/s

Fig. 26

Time history of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) for Al/Al, Cu/Cu, Al/Cu, and Cu/Al impact at 500 m/s using the CEL approach

Fig. 27

Distribution of (a) the equivalent plastic strain (PEEQ) and (b) the temperature (TEMP) of the substrate's surface for various materials combinations using the CEL approach

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