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To evaluating the limit state of the adhesion layer in a layered composite

Abdurakhmanov A.A., Bogacheva V.E., Glagolev V.V.

#### Abstract:

The model of deformation of a layered composite in the form of a double-console plate is studied on the basis of the concept of an interaction layer in a linearly elastic formulation. It is assumed that the adhesive layer has a finite thickness and does not bind the cantilevers along their entire length. Layer thickness is considered as a linear parameter. The stress-strain state of a layer is considered on the basis of average thicknesses and boundary stresses related by equilibrium conditions. The use of stresses average in thickness allows us not to consider the shape of the end of the layer and to remain within the framework of the regular distribution of the stress field in the end region of the layer. Using the variational formulation of the problem containing a linear parameter, a finite element solution is constructed based on the quadratic distribution of the displacement field on the element. The numerical solution is compared with its analytical approximation with normal separation. The analytical solution was based on hypotheses of the Tymoshenko type taking into account shear deformations in consoles and in the absence of compression deformations. The energy product is introduced into consideration in the form of the product of the increment of the specific free energy by the layer thickness. The energy product of the adhesive layer was investigated as a function of the linear parameter for loading, such as normal detachment and mixed loading mode. It is shown that with a decrease in the linear parameter, the convergence of the energy product takes place. The effect of simplifying hypotheses on the distribution of the displacement field in consoles on the limiting value of the energy product is shown. The limiting value of the energy product at a critical external load is proposed to be considered as a criterial value. In this case, it is possible to isolate the range of values of the linear parameter at which the value of the external critical load will be practically constant.

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