Modeling of the limit stress state of a matrix composite with oriented fibers under thermodynamic influences


Аuthors

Bardushkin V. V.1*, Kochetygov A. A.2**, Yakovlev V. B.2***

1. Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: bardushkin@mail.ru
**e-mail: aakcht@gmail.com
***e-mail: yakvb@mail.ru

Abstract

A mathematical model is created that allows predicting the stress state (up to the ultimate) of a matrix composite with oriented fibers, which occurs as a result of internal changes in its components due to uneven heating of the fibers and the matrix. The model is based on the genera- lized singular approximation of random field theory and the concept of the stress concentration operator (fourth-rank tensor), which connects the material average stresses with their local va- lues within a single inhomogeneity element. Based on the developed theoretical model, for a composite with a dielectric matrix (silicon dioxide) and metal fibers (copper, aluminum), nu- merical calculations were carried out to determine its ultimate stress state, which appears when an electric current is passed through an inhomogeneous material and leads to cracking of the di- electric. The influence of the composition of the components, their elastic moduli and thermal linear expansion coefficients, the volume fraction of fibers, as well as the differences in the magnitude of the change (jump) in the temperature in the fibers and the matrix on the reaching the ultimate stress state of the composite is studied. The calculation results showed that all fac- tors taken into account in the model make significant contributions to the stress-strain state of the matrix composite of the structure under consideration, which means that they must be taken into account in multilevel metallization of integrated circuits.

The theoretical approach developed in the article to predicting the limiting states of matrix composites with oriented fibers under thermodynamic effects makes it possible at the stage of designing materials to prevent situations that could lead to failure of electronic products.

Keywords:

modeling, composite, fiber, matrix, thermal coefficient of linear expansion, stress tensor, stress concentration operator, tensile strength.

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