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The size changes control is very important in some applications, for example, in space structures. Zero thermal expansion materials is needed in structures subject to temperature changes such as a backplane support structure for a large space telescope, antenna booms, solar array frames and etc. Unlike classical materials, composite laminates can be designed in such a way as to reduce the coefficients of thermal expansion (CTE) in the desired direction to a specified value. This can be done by the appropriate sequence of laminate layers, the angular orientation of each layer and the microstructure properties control. The structure optimization problem of a composite material to obtain the specified mechanical and thermomechanical properties has repeatedly attracted the attention of researchers [1–9]. To reduce the CTE value of CFRP, the researchers design a new kind of multi-functional curing agent for epoxy resin [10] or add inorganic particles such as carbon nanotubes, aluminum nitride, silicon dioxide, and so on [11–18]. There is increasing interest in combining reinforcement scales of nanoscale reinforcements with traditional micron-sized fibers [19; 20]. The authors of the work [21] evaluated the feasibility of using multi-walled carbon nanotubes (MWCNTs) for the control of coefficients of thermal expansion of composite materials. The use of MWCNTs aligned axially was shown to be effective at controlling αx of polymer composites. The authors theoretically calculated the MWCNT volume fraction at which αx of composites based on different type of material and containing MWCNTs become zero. In particular, the authors determined the MWCNT content necessary for zero coefficients of thermal expansion to be about 10 vol.% in the polymer materials at temperature range of −5 °C to 85 °C. Inorganic compounds with negative thermal expansion (ZrW2O8, ScF3, Mn0.98CoGe, Sm2.75C60) can be used to compensate and control the CTEs of CFRP [22–29]. But for many inorganic NTE compounds, their CTE are small in magnitude or the effective temperature window is narrow [30; 31]. The orientation of fibers in composites may result in anisotropic thermal expansion has a small or even negative CTE value [33; 34]. Although the task of the composite’s macrostructure optimization is complicated by the high sensitivity of the theoretically achieved near-zero coefficients of thermal expansion to the lamina properties variability, which inevitably present in practice due to disorientation of reinforcing fibers, and various degrees of cure, volume fraction, residual moisture and etc. However, to date, the literature has not considered the possibility of obtaining a hybrid composite with zero αx, reinforced with carbon fibers in combination with MWCNTs, with an estimate of the density function of the probability distribution of αx under the conditions of lamina properties variability and its disorientation. This paper first describes the methodology of obtaining a layered composite with near zero αx based on estimate E(αx) and Var(αx) as target parameters. Possibilities of reducing the variance of the target parameter by means of an integrated approach to determining the optimal orientation of layers of hybrid composites with different volume content of MWCNT is considered. A detailed description of the calculation procedure for the target parameters using randomly generated lamina’s orientation angle error and lamina properties variability is presented in the next session. The results section discusses the possibility of reducing the Var(αx) using MWCNTs, analyzing the Pareto-optimum front curves. Further, the experimental estimates of αx of the composite are reported in detail.

About the authors

K. A. Pasechnik

Reshetnev University

I. V. Obvertkin

Reshetnev University

A. Y. Vlasov

Reshetnev University

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