Adjustable and negative thermal expansion from multilayered systems

Abstract

The extent to which systems (materials or structures) change shape when subjected to changes in temperature is a subject of great practical importance and has been studied for many years. It is well known that miscalculations of the temperature effects in the design of objects which are subjected to significant temperature changes can lead to disastrous consequences. This led to various studies aimed at designing, analysing, manufacturing and/or testing of materials having very particular coefficients of thermal expansion [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] (including materials exhibiting negative coefficients of thermal expansion, i.e. materials which contract when heated [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Of particular interest are composites having pre-determined coefficients of thermal expansion which are already being used in some niche applications, although there is still an ongoing need to develop simple and non-expensive methods for achieving the same effect on any scale.Here we propose and discuss a multi-layered system constructible at any length scale from conventional materials having different mechanical and thermal properties which may be combined to form systems which exhibit pre-determined values of thermal expansion which could also be negative. In particular we show that to optimise negative thermal expansion (NTE) characteristics, the systems must be constructed based on what is illustrated in Fig. 1, i.e. by combining thin layers of stiff materials having a high positive coefficient of thermal expansion (CTE) characteristics bonded together through thicker layers of a soft material having low CTE values and, more importantly, having Poisson's ratio as high as possible, in analogy to work presented earlier [15][16][17].To simplify our discussion we discuss first the optimal requirements for one of the most basic systems operating through the mechanism we are proposing which can be tailored to exhibit NTE, i.e. the system in Fig. 1(a). As illustrated in Figs. 1(a) and 2, this system may be described as a sandwich structure made from three layers of two different materials A and B having different thicknesses, thermal and mechanical properties which are perfectly bonded together.Let us assume that this sandwich is in the form of a cuboid of overall dimensions x y z ¥ ¥ at temperature T where the z dimension is given by A B 2 , z z + A z and B z being the thicknesses of layers A and B at temperature T, respectively. Let us also assume that (i) materials A and B are isotropic; (ii) that material A is much stiffer than material B, i.e. E A ӷ E B , where E A and E B are the Young's moduli of materials A and B, respectively, and (iii) that necking effects may be ignored. Given these assumptions, if the system is subjected to a change in temperature ΔT, A construct in the form of a multi-layered system built from conventional materials having different mechanical and thermal properties is proposed. This construct can exhibit predetermined values of ...

Negative thermal expansion from disc, cylindrical, and needle shaped inclusions

“…Systems where l ≈ r , would correspond to stubby shaped inclusions. Note that the simulation were t l = 0 with l = 500 would approximately correspond to the simulations reported by Grima et al . Also, it should be emphasized that although the simulations performed here are in the mm range, the effect is scale independent and can also be exhibited at smaller or larger scales.…”

“…Before concluding this discussion, it is important to note that as stated above, the idea that NTE can be obtained for systems with coin shaped inclusions in the axial direction could in theory be explained through the model published by Grima et al for sandwich composite structures designed to exhibit NTE. However, here some caution should be made since in the preliminary model published by Grima et al , one of the assumptions made was that the soft material does not offer any resistance to the growth of the hard material.…”

“…It was recently proposed by Grima et al that NTE can be achieved at any length scale including the microscale from conventional components having different mechanical and thermal properties which may be combined to form composite systems, which exhibit any desired CTE values, in particular negative ones (NTE). In particular, referring to Fig.…”

“…(a) The cylindrical structure proposed by Grima et al consisting of a needle‐like inclusion of material B embedded in a matrix of material A and (b) a cross‐section showing its dimensions. All dimensions being measured at a reference temperature T .…”

Mixed auxeticity of auxetic sandwich structures

“…Auxetic materials, which are defined as solids that exhibit negative Poisson's ratios 1–8, fall under the broad category of negative materials, which include counter‐intuitive properties such as negative stiffness 9, negative thermal expansion 10–14, negative compression 15–22, negative permeability and permittivity 23, and negative refractive index 24, among others. For structural applications, auxetic materials have been incorporated in sandwich plates have been shown to possess superior qualities 25–38.…”