Simulation of the stress-strain state of thin composite coatings based on solutions of the plane problem of strain-gradient elasticity for a layer

We obtain and investigate the formulation of the problem of strain gradient plane model of elasticity for the composite layer. We used a synthesis of analytical and numerical methods to solve plane problem of gradient elasticity for an infinite layer to allow the distribution of stresses in the plane of ultrathin coatings. We investigate the problem of the impact of surface compressive normal loading on an infinite layer. To solve the problem we use a Fourier integral transform, and the inverse trnsform is computed using a numerical procedure. It is shown that the proposed model can predict the effects of localization interlaminar stresses in the local interphase zones in the coating and consider the influence of non-classical scale factors – the thickness of the coating layers and gradient model parameters. For simulation it is involved the most simple gradient theory of elasticity – applied model of the interphase layer containing single additional physical parameter determining the "gradient" of the environment and the extent of interfacial zones in the border area of the material. This additional physical constant characterizing the contact of dissimilar materials. For the numerical calculations in this paper we use the hypothetical values of the gradient parameter. To solve the problem of practical importance due to the possibility of reliable modelling and optimization of the structure of ultra microstructure protective composite coatings used in the aerospace industry. Also constructed solution can be used to identify additional physical parameters of the gradient theory of elasticity based on a comparison of simulation results and experimental data on the indentation thin layer structures.