Silver Coating

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Cold Gas Dynamic Spray Coatings

Cold spray is one among the thermal spray variants in which solid metallic particles can be deposited upon supersonic impact onto the substrate owing to their severe plastic deformation. Variety of metallic and alloy powders have been successfully deposited using cold spraying on different substrates for many functional applications. Silver is one among the materials used in electrical contacts in electrical industry. Naveen et. al.[1] deposited silver using cold spray technique. Assadi et. al. and Schimidt et. al.[2] roughly estimated the critical velocity of silver using empirical equations. However it is important to estimate the critical velocity of silver for proper understand of the cold sprayed silver coatings. In cold spraying, critical velocity is the most important parameter among the all other process parameters like particle temperature, Particle velocity, Stagnation Pressure and gas velocity. Critical velocity is defined as the minimum velocity required to adhere the particle to the substrate. When the cold sprayed particle impacts onto the substrate, thermal softening and hardening due to strain and strain rate dominates. Whenever, thermal softening effects dominates over hardening, bonding occurs. It is very well understood that at critical velocity thermal softening dominates. At critical velocity, adiabatic shear instability is considered as important criterion to obtain bonding between the impacting splats / interacting interfaces. This can be characterized as abnormal plastic strain, temperature rise and collapse in flow stress to near zero at impacting interfaces[3]. Based upon this phenomenon, critical velocities for variety of materials have been estimated by different research groups[3].

In order to simulate the plastic deformation of the powder at different impact conditions, the use of strain rate-dependent and temperature dependent constitutive description is required in finite element codes. The flow stress (σ) is expressed as a function of strain (ε), strain are (έ) and temperature (T). In the literature, many models available to describe material behavior in plastic regime. However, Johnson-cook model (J-C)[4] which is widely accepted includes strain hardening, strain rate hardening and thermal softening effects upon high velocity impact of the particles and employed to describe the strain rate and temperature dependence of the material behavior upon impact and subsequent plastic deformation. In this work, systematically, the Johnson cook plasticity model constants were estimated from the existing literature and were applied into the single particle impact model to obtain the critical velocity of silver and the same has been compared with the estimated values available in the literature.

Finite Element Modeling and Simulation

Fig:1 Four-node axisymmetric linear quadrilateral elements

In order to reduce the computational time, axisymmetric two-dimensional finite element analysis was performed. Substrate/particle interaction problem is modelled as silver particle at high temperature is moving with certain velocity and interacts with the silver substrate. In addition, since a particle is in spherical shape, the deformation can be treated as axi-symmetric leading to a simplification of the analysis. High velocity impact of particle on substrate was simulated by specifying an initial temperature and velocity as a boundary condition to the particle. The temperatures and velocities were chosen from the literature. A fixed value of 0.2 for the friction coefficient between the particle and the substrate contact surface was assumed. Four-node axisymmetric linear quadrilateral elements (CAX4R) with reduced integration was used to mesh the model as shown in Fig. 1. To analyze the deformation behaviour more accurately as well as to reduce the simulation time, finer mesh was used in the contact region. Output of simulations were recorded for the time between initiation of the contact to initiation of elastic recovery in both substrate and particle. Typical output of the simulations include, stress and temperature.

Johnson-Cook Model

Fig:2 Temperature distribution of Silver particle in Cold Spray Process

In the present work, ABAQUS/Explicit, a general purpose nonlinear FE analysis program was used to model the impact of silver particle on silver substrate. The Johnson-Cook model is a linear-elastic, rate dependent plastic material constitutive model and typically used to model particle and substrate interaction at high velocities. Hence, this model was employed to simulate the large strain deformation, strain rate and the thermal softening behaviour in the silver particle and substrate. This model accounts the effect of isotropic hardening, strain rate dependency and thermal softening during the particle and substrate interaction. The Johnson-Cook plasticity model is an empirically derived Mises plasticity model in the analytical form of strain. The general form of this model is

σ=[A+B(ε_p )^n ][1+Cln(ε ̇_p/ε ̇_0 )][1-((T-T_tran)/(T_melt-T_tran ))^m ]

Where σ is the equivalent stress at nonzero strain rate, ε_p is the equivalent plastic strain, ε ̇_p and ε ̇_0 are the equivalent plastic strain rate and reference equivalent plastic strain rate, T is the current temperature, T_tran is the transient ambient temperature, T_melt is the melting temperature, A, B, C and n are strength parameters and T_tran, T_melt and m are thermal parameters.The high strain rate materials data used in the equation may be derived from extreme experiments such as split-hopkinson bar test. The flow stress is expressed as a function of elastic-plastic response and thermal softening character at different temperature and strain rates. Input material (strength & thermal) parameters are calculated/estimated from the literature[5][6][7][8].


In order to validate the JC parameters estimated from the literature, simulations were carried out for various initial temperatures and inlet powder velocities used in the literature. Therefore these simulation results also useful to assess whether the powder velocity used in the experimental work was reached critical velocity or not. Bonding between the particle and substrate happens at critical velocity where adiabatic shear instability occurs. This criteria is responsible for sudden temperature rise and collapse in flow stress to near zero at impacting interfaces. Hence, Stress and temperature at the interface between particle and substrate is plotted with respect to contact time for two extreme cases (10 bar, 523 K and 15 bar and 623 K). Figure 2 shows the temperature profile on the powder particle surface for two different conditions. Also, Fig.3 and Fig.4 shows the temperature and stress profiles, respectively at the particle surface with respect to time. As reported in the literature that sudden rise in temperature and collapse in flow stress can be observed in the case of 15 bar and 623 K (strong bonding) while no such variations observed in the case of 10 bar, 523 K(no or weak bonding).

Fig:3 Time Vs Temperature graph
Fig:4 Time Vs Stress graph


During Cold spray process the silver particles undergo deformation which can be considered as an equivalent amount of cold working on those particles. As a result, there is variation in material properties like thermal conductivity [1], hardness, etc. These cold sprayed particles have high stored energy because of the velocity imparted to them and will also attain a high temperature (far below melting point) on impact with the substrate, there a massive chance for recrystallization to occur. So, there is need to model the evolution of microstructure during the cold spray process to get a clear understanding of the properties. The input parameters like dislocation density, temperature on which recrystallization mainly depends are provided from the results of modelling of the cold sprayed process as mentioned above. There have been a number of approaches taken to modelling recrystallisation kinetics and recrystallised grain size, including the Johnson-Mehl-Avrami-Kolgormorov (JMAK) model, the Cellular Automaton model, ABAQUS sub routine:

• JMAK: The classic JMA K model is a semi-empirical approach that encompasses recrystallised grain nucleation and grain growth mechanisms in a single equation. The JMA K model assumes that recrystallised nuclei form randomly, the rates of nucleation and growth remain constant and the growth of recrystallised nuclei is isotropic.

• Cellular Automaton Model: A relatively new approach to modelling static recrystallisation is the cellular automaton (CA) method[9][10]. The CA model is a probabilistic method that can predict grain structures with kinetics. A trial to link the modelling of Cold Sprayed Silver with Cellular Automaton is under progress.

• ABAQUS Sub-routine: A model of Cold Sprayed Silver coatings which is already developed in ABAQUS provides the necessary inputs for a user defined subroutine to model the evolution of the microstructure during the process. This work is still being continued[11].


  1. 1.0 1.1 Chavan Naveen Manhar, et al.,The influence of process parameters and heat treatment on the properties of cold sprayed silver coatings, Surface and Coatings Technology 205.20 (2011): 4798-4807([1])
  2. Schmidt, Tobias, et al., Development of a generalized parameter window for cold spray deposition, Acta materialia 54.3 (2006): 729-742
  3. 3.0 3.1 G Bae, Y Xiong, S.Kumar, C Lee, General aspects of interface bonding in kinetic sprayed coatings.,Acta materialia 56 (2008) 4858-4868
  4. Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proc 7th Int Symp Ballist 21:541–547
  5. Wu, Jiaqi, and Chin C. Lee. "The growth and tensile deformation behavior of the silver solid solution phase with zinc." Materials Science and Engineering: A 668 (2016): 160-165
  6. Carreker, R. P. "Tensile deformation of silver as a function of temperature, strain rate, and grain size." JOM 9.1 (1957): 112-115
  7. Reddy, A. Venugopal, et al. "Correlation between erosion behaviour and stacking fault energy in copper alloys." Acta Metallurgica 32.9 (1984): 1305-1316
  8. Kun, Qin, Yang Li-Ming, and Hu Shi-Sheng. "Strain rate sensitivities of face-centred-cubic metals using molecular dynamics simulation." Chinese Physics Letters 25.7 (2008): 2581
  9. C.H.J. Davies,,” The cellular automaton simulation of static recrystallization in cold-rolled aa1050”, Scripta Materialia, Vol. 40, No. 10, pp. 1145–1150, 1999
  10. Håkan Hallberg,”Simulation of discontinuous dynamic recrystallization in pure Cu using a probabilistic cellular automaton”, Computational Materials Science 49 (2010) 25–34
  11. Xin Wang,, “Modeling and Simulation of Dynamic Recrystallization Behavior in Alloyed Steel 15V38 during Hot Rolling”, Steel Research International · March 2018
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