Comparison of Residual Stresses in Cold Spray Coatings: Lagrangian vs. Eulerian Finite Element Methods

Cold spray is a novel thermal spray process in which a gas at high temperature and pressure deposits solid particles onto a substrate material. Current research utilizes a variety of methods of modeling techniques in order to capture the physics and dynamics of a cold spray particle impact, incorporating elements of the Lagrangian and Eulerian modeling methods. This research modeled the cold spray event of single and multi-particle impacts using Lagrangian and Eulerian methods. The material of both the particle and substrate are a standard Aluminum 6061-T6 alloy. The objectives of the models are to: (1) obtain particle and substrate deformations and residual stresses as functions of particle velocity, particle temperature, and substrate temperature; (2) establish the minimum number of successive particle layers such that the substrate residual stresses reach steady state; and (3) identify numerical limitations in the Lagrangian and Eulerian modeling methods using ABAQUS/Explicit. The Lagrangian method predicted a maximum von Mises stress 23.72% lower than that of the Eulerian. The Lagrangian models allowed for discrete node tracking, however, thus allowing for improved surface definitions and transient material point tracking. The Eulerian models also better handled the plastic deformation and resultant temperature generation within the model, and thus were able to handle multiple particle impacts while the Lagrangian could not. The multi-particle models using the Eulerian method reported that seven particles were required for the substrate steady-state stress to remain independent of subsequent particle impacts. Concentric initial position multi-particle models saw a maximum 42.00% reduction in von Mises stress compared to the single-particle models and a maximum 53.18% reduction compared to multi-particle modes with randomized initial particle positions. Multi-particle impacts demonstrated a reduction in stress when compared to the single particle impact due to the increased thermal softening present.