Particle–Substrate Transient Thermal Evolution During Cold Spray Deposition Process: A Hybrid Heat Conduction Analysis

Abstract

A hybrid analytical heat conduction model was developed to predict the transient thermal evolution at the particle–substrate interface during the deposition of cold spray process. First, three-dimensional heat conduction model based on classical diffusion approach was developed to predict the transient surface temperature of the substrate. To that end, the traveling wave solution technique was utilized in order to take into account the effect of the movement of the cold spray nozzle. The results of the analytical model were validated with the experimentally measured surface temperature which was obtained by employing a low-pressure cold spray unit to generate the impingement of a compressed air jet on a flat substrate. The analytical model was further utilized to investigate the effect of the non-dimensional characteristic velocity of the traveling heat source on the surface temperature profile of the substrate. It was found that both the maximum surface temperature and the spatial variation of surface temperature profile of the substrate decreased as the non-dimensional characteristic velocity increased. The mathematical model was further extended by developing a one-dimensional hyperbolic (non-Fourier) heat conduction model to predict the temperature rise at the particle–substrate interface during the cold spray deposition process. In order to validate the results of the hybrid model, a three-dimensional finite element model was developed in ABAQUS to simulate the thermal and dynamic behavior of a single particle upon impact. The results of the hybrid analytical model for the temperature at the particle–substrate interface were compared to the results of the numerical model, and good agreement was found. It was concluded that by coupling the classical diffusion theory and hyperbolic heat conduction approach, the proposed hybrid analytical model can be utilized to predict the transient temperature of the particle–substrate interface during the cold spray deposition process a priori before experimentation.