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  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    Numerical analysis of substrate influence on fracture mechanisms in PVD deposited TiN coatings

    • Bartlomiej Kowal
    • Konrad Perzynski
    • Lukasz Madej
    Mathematical Modeling, Vol. 9 (2025), Issue 1, pg(s) 28-35
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    Coatings of titanium nitride (TiN) are widely used due to their high hardness and wear resistance, making them suitable for protective, decorative, and semiconductor applications. However, their tendency toward brittle cracking and low fracture toughness limits their performance in demanding environments. Understanding and accurately modelling fracture behaviour in TiN is therefore essential to improving reliability in microelectronics, protective coatings, or biomedical devices. This work presents a first approach to modelling fractures in TiN films by explicitly representing their columnar morphology. A procedure for generating statistically representative digital microstructures and incorporating them into finite element simulations is described. The approach uses a hybrid cohesive–XFEM fracture model to capture crack initiation and propagation under complex deformation states, particularly during nanoindentation. The numerical results are validated with results from a scanning electron microscopy (SEM) investigation.

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