Ti-6Al-4V is an alloy of titanium that is characterized by excellent bulk mechanical and chemical properties such as very good strength-to-weight ratio (due to low density), high specific strength, low elastic modulus, superior resistance to both corrosion and erosion in many environments, excellent high temperature resistance, and biocompatibility. Hence, the alloy is a favorite material for many applications in the automobile, aerospace, and aeronautical industries. It would have found more versatile applications in these industries were it not for its poor surface properties such as hardness and wear resistance which are due to the high friction coefficient, low hardenability, and the tendency to gall and smear [1
]. These poor surface properties are traced to the low resistance to plastic shearing, low work hardening, and the low protection offered by its surface oxide [2
]. The aforementioned setback of titanium alloy has necessitated various research works, including coating with powder, to enhance the surface properties and performance without altering the bulk composition/chemistry thereby retaining the excellent bulk properties [3
Silicon carbide (SiC), due to its extreme hardness and high wear resistance [4
], is one of such powders for coating titanium alloy in order to confer higher hardness and wear resistance on it. However, SiC decomposes before melting [5
] making high temperature coating processes unsuitable for its deposition. A promising option to high temperature deposition of SiC that will prevent its thermal decomposition is the cold spray process. Cold spray is a material deposition process in which relatively small particles (ranging from approximately 5 to 100 μm in diameter) in solid state are accelerated to a critical high velocity (typically 300–1400 m/s), and are subsequently plastically deformed to form a coating on the substrate [6
]. In cold spray coating, attachment of powder to the substrate otherwise known as bonding is achieved by the kinetic energy of the powder particles rather than the thermal energy as the case in thermal spray processes [8
]. Therefore, the fabrication of the coating of temperature sensitive and nano-structured material is possible by cold spray because no significant change in the microstructure of feedstock is involved in the process [9
]. Bonding takes place when the velocity of the powder particles exceeds a certain value called the critical velocity (CV). Hence, the CV is defined as the velocity the particle must attain before deposition can take place after impacting the substrate [10
]. The CV is a major parameter in cold spray; it is related to the mechanical and thermal properties of the spray materials and their particle sizes, and it determines which of particle deposition or substrate erosion will occur upon the impact of spray particles [11
Typically, the CV is the velocity at which the transition from erosion of the substrate to deposition of the particle takes place [11
]. Below the critical velocity, plastic deformation is too low to cause bonding, above the critical velocity, hydrodynamic penetration leads to strong erosion. Therefore, the optimum conditions for deposition lie between these two characteristic velocities [13
]. According to Assadi [14
], the value of CV is determined by the temperature, thermo-mechanical properties of the sprayed material [15
] and the characteristics of the substrate [13
]. Li et al.
] measured the critical velocity for three metal alloys at different oxidizing conditions. The results showed that besides materials properties, the critical velocity was significantly influenced by the oxidation condition of the particles. The authors concluded that the material’s properties influence the critical velocity more remarkably at low oxygen content than at high oxygen content. Yokoyama et al.
] carried out the analysis of a metal particle impacting onto a metal substrate by using a dynamic finite element code (ABAQUS), and numerically studied the effects of substrate and particle temperature on the critical velocity. It was found that critical velocity decreases with higher stiffness of the substrate, higher particle temperature, and greater particle size. A decrease in gas temperature and pressure also affects coatings density and structure [20
]. Li et al.
] carried out both experimental and theoretical estimates of the critical velocity of copper (Cu) particles during cold spray coating. The authors concluded that the measured critical velocity was independent of the size and velocity distribution of the particle but depends on its temperature. Hence, in order to predict quality of the coating in cold spray, a good understanding of the particle velocity is vital.
Cold spray coating is carried out in a de Lava nozzle of which two variants are currently commercially available, viz.
: the Low Pressure Cold Spray (LPCS) system and the High Pressure Cold Spray (HPCS) system. Inside the nozzle, the flow of high-velocity gas carrying very fine solid particles leads to a two-phase flow of gas-solid suspension. Such flow is usually extremely complex and difficult to understand due to the complexities arising mainly from particle-mean stream interactions, particle-flow turbulence interactions, inter-particle collisions, particle-wall interactions, and particle-shock wave interactions [22
]. Dmitrienko and Uvarova [23
] reported that mathematical modeling of heat and mass transfer in systems of dispersed particles, nano-particles, and nano-fluids, as in the cold spray nozzle, is one of the actual problems at present.
According to Vutova and Donchev [24
], computational modeling and optimization are important for better process studying and understanding, and for quality improvement. Although few literatures are available on mathematical study and optimization of cold spray process parameters [18
], as far as the authors of this work are aware, Computational Fluid Dynamics (CFD) analysis of input temperature to determine the critical velocity, which is the object of this investigation, has not been reported in the literature. The investigation consists of the following parts: (1) statistical computation of the critical velocity for cold spray coating of titanium alloy with SiC. This was done by using a constitutive equation to solve the continuity, momentum, and energy equations governing the flow of fluid inside the de Lava nozzle used in the LPCS system; (2) Computational fluid dynamics (CFD) analysis of the flow through the nozzle to determine the input temperature that will yield the computed velocity at the exit of the nozzle; and (3) verification of the mathematical model by comparing the properties of coatings deposited using the CFD-optimized parameters and some non-optimized parameters.