On modeling bodies with delaminating coatings taking into account the fields of prestresses

Abstract

The paper presents a model of steady-state oscillations of an inhomogeneous body with a prestressed exfoliating coating based on a general linearized statement of the problem of the motion of a prestressed-strained elastic body. On its basis, the statement of the problem of oscillations of an inhomogeneous strip consisting of a substrate and a prestressed coating is formulated, between which there is a delamination in a certain region. Steady oscillations are caused by a load applied to the upper boundary of the coating. To calculate the oscillations of the two-dimensional structure under consideration, the Fourier transform in the longitudinal coordinate was used and the original problem was reduced to solving a number of auxiliary boundary value problems with respect to transformants of the desired functions. From the conditions that the stress functions vanish (the cover is modeled as a mathematical section) of the substrate and the coating, the operator relations are constructed in the area of delamination to calculate the opening functions. The kernels of these operator relations are singular and are integrals over an infinite interval. A study was made of the behavior of their integrands at infinity, on the basis of which special approaches were used to calculate the kernels. As a result of solving the obtained hypersingular equations with difference kernels, for which the collocation method is used, the originals of the disclosure functions are constructed. Using a similar approach for inverting the Fourier transformations, we constructed relations to calculate the originals of the displacement functions at the upper boundary of the coverage. Based on the computational experiments, an analysis is made of the influence of the initial geometric and mechanical parameters of the substrate and coating on the values of the disclosure functions in the delamination region and the displacement functions at the upper boundary of the layer. The influence of the prestress level on the amplitude-frequency characteristics (AFC) was also investigated. It was found that the most significant effect on the frequency response is in the vicinity of the frequencies of the thick resonances. Based on the information on the displacement fields, it is possible to construct schemes for identifying delamination characteristics.