High-Fidelity modeling of cold spray: Improved constitutive material model and nonlocal mesh sensitivity mitigation

Finite element method (FEM) is significantly helpful to simulate cold spray (CS) deposition for optimizing the process parameters or evaluating the deposit's physical and mechanical indexes. The simulations’ accuracy, however, is primarily governed by the choice of constitutive material model, while also exhibiting notable sensitive to the mesh size. To enhance predictions and mitigate this sensitivity, here in, we developed an improved material model able to predict the deformation of the deposited particles with higher accuracy compared to the existing models. The model incorporates strain hardening, strain rate effects, and thermal softening into flow stress, utilizing a straightforward expression that facilitates implementation in FEM via a user-defined VUMAT subroutine and enables efficient experimental calibration. The impact of copper particles, as a representative material for CS, was simulated by the proposed model over a wide velocity range of 590–1058 m/s. The simulation results accurately reproduced the experimental particle deformation, local jetting and flatness, with predicted overlapping and flattening ratios exceeding 85% and 95% respectively, demonstrating a significant improvement over existing models at high impact velocities. Subsequent systematic simulations on mesh sensitivity revealed that the primary factors were the intrinsic kinematic issue from high-velocity impacts and the elliptic problem introduced by thermal softening. To address this sensitivity, a novel hybrid nonlocal strategy was introduced combining standard nonlocal and over-nonlocal methods. Specifically, the standard nonlocal method was utilized to mitigate the shear band localization, while the over-nonlocal method was leveraged to strongly regularize the temperature field. The proposed strategy was applied to CS simulations using various mesh sizes, showing its high efficiency in minimizing the effect of mesh size on both particle deformation and shear band localization.