Internal stress in titanium nitride coatings: Modelling of complex stress systems

The internal stress in sputter-ion-plated titanium nitride coatings has been measured by the well-known sin2ψ method. In such measurements it is usual to assume that the true stress state approximates to a biaxial state which requires that there is a linear variation in lattice strain with sin2ψ. However, this is not always the case, and it is shown that appreciable errors in the calculated values of the principal stresses σ11 and σ22 result if effects such as ψ splitting and curvature in the εφψvs. sin2ψ plots are ignored. Results are presented which compare the values of stress calculated using the simple biaxial approximation with those obtained from a more detailed analysis. As these physical-vapour-deposited coatings thicken it is shown that the levels of internal stress decrease owing to a combination of grain size and porosity effects. These changes in coating microstructure cause curvature in the εφψvs. sin2ψ stress plots and the stress state can be modelled by assuming that the stress varies exponentially with coating thickness.