Tailoring strains through microstructural design
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Tailoring strains through microstructural design L.J. Vandeperre and W.J. Clegg Department of Materials Science and Metallurgy, University of Cambridge Cambridge, CB2 3QZ, United Kingdom ABSTRACT Composite structures are presented that allow a wide design space for strains in response to an applied stimulus to be accessed. The basic principle of operation is described and examples of how it can be used to obtain a range of behaviours are given. Experiments were conducted to assess the basic behaviour of building blocks for such composites and it is shown that the results agree reasonable with simple predictions made by considering bending and stretching of the beams in the structures.
INTRODUCTION When developing structures, which respond with a strain upon application of a stimulus such as temperature or an electric field, the fixed relation between the response of a given material and the magnitude of the stimulus puts severe constraints on the design. This problem is commonly dealt with either by design of the shape of the actuator or sensor, or by selecting a material with the appropriate coefficients in response to the field. However, when actuating or sensing functions need to be incorporated within other structures, shapes must be as simple as possible, and the environment where the structure is to be used can put limits on materials selection. Such limitations can be overcome by incorporating the design into the microstructure of materials and a powerful technique for doing so is topology optimisation [1]. However these optimised microstructures are often very complex making their manufacture costly, if it is indeed possible to manufacture them. A much simpler approach is to take a basic unit, which allows levering of strains, and to use these simple shapes to build up a microstructure. For instance, consider an isosceles triangle, in which two sides are made out of a first material and the third side is made out of another material and where all sides are connected so that the joint allows free rotation (see Figure 1). In such a structure, the difference in response to the field of the two materials causes a rotation of the two beams, made out of the same material, and the change in dimension perpendicular to the third beam is governed entirely by the difference in coefficients of the materials and the initial value of the angle, θ [2]. Measurements of the thermal expansion of such structures, made out of aluminium and Invar, with respective coefficients of thermal expansion (CTE) of 24 × 10-6 K-1 and 1 × 10-6 K-1, have shown that a CTE as low as –360 × 10-6 K-1 can be achieved [2].
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Figure 1. (a) Showing how an applied strain giving rise to an increase in dimension of the horizontal beam relative to the other beams causes a strain along the vertical, (b) showing two examples of how the basic triangle can be combined into a self-repeating pattern with isotropic behaviour, and (c) showing a structure with designed anisotropic thermal expansion. In order to produce similar e
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