Investigation of thermal stress local effects on the boundaries of layered structures

Аuthors

Lurie S. A.^*, Solyaev Y. O.^1**, Nguyen D. K.^2***, Medvedskiy A. L.², Rabinsky L. N.^2****

1. Institute of Applied Mechanics of Russian Academy of Science, IPRIM RAS, 7, Leningradskiy Prospekt, Moscow, 125040, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: salurie@mail.ru
**e-mail: yos@iam.ras.ru
***e-mail: ndacquang@yahoo.com
****e-mail: f9_dec@mai.ru

Abstract

A stationary problem of the thermoelasticity based on the strain-gradient theory of laminated composite structures is considered. A formulation of the plane strain problem of strain-gradient thermoelasticity is formulated and an solution’s algorithm for the uniform in-plane heating are proposed. It is shown that use of the strain-gradient thermoelasticity models providing deformations continuity in contact areas allows one to consider some phenomena that are not described by the traditional thermoelasticity and can be due to the effect of stress localization in contact areas. As a result the strain-gradient elasticity theory predicts the local additional tensile stresses in the layer with a lower coefficient of thermal expansion. The obtained solution is an generalization of the traditional thermoelasticity solutions and allows one to take into account the effect of scale parameters on stress-strain state of materials.
Some test problems are considered, a heating of a single and a double layer structures. The temperature field in the layers of the considered structure is computed on the basis of the classical thermal conductivity theory. It is shown that the strain-gradient thermoelasticity allows one to take into account the dependence of stresses and strains in layers of varying thickness with the same temperature gradient so that is impossible using the traditional theory. It is shown that the resulting «reinforcement» effect is obtained, the decreasing of the thickness provides the decreasing of strain and stress intensity in layer, so that the material can be interpreted as a material with higher «effective» elastic modulus and yield strength. If the layer thickness is greater than the scale parameter of the material the classical thermoelastic model is obtained, but for the thinner layers the local stresses increase near to the boundaries so that can provide a significant variation of the stress-strain state, particularly the tension in plane of the layers can increase.
It is shown that for two-layer structures the strain-gradient elasticity predicts the occurrence of additional local tensile stresses in the layer with a lower coefficient of thermal expansion. As compared with the solution of the similar problem obtained numerically on the basis of Ansys and with the classical analytical solutions it is shown that the resulting solution generalises the classical thermoelasticity problem and allows one to take into account the effect of the layer thickness and scale parameters of the materials on the stress- strain state of the layered structure.

Keywords:

strain-gradient elasticity, thermal stresses, layered structures, scale parameters

References

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