Thermoelastic Response Analysis of a Shape Memory Alloy Wire Embedded Active Hybrid Bimorph Composite

Abstract

The class of metallic alloys that show the ability to memorize its shape at a specific temperature and recover large deformations on thermal activation are called Shape Memory Alloys (SMA). SMA wire-based Hybrid Composites (SMAHC) is a continuously emerging research area given their versatile applications within the domain of active shape morphing, structural control, deployable space mechanisms, and other adaptive characteristics. We study the simulated behavior of an Active Bimorph Structure (ABS) composed of embedded SMA wires within a fiber-reinforced composite, modeled and analyzed in ABAQUS. The wires are embedded in two layers of the composite at 0$^\circ$ and 90$^\circ$ to obtain a bidirectional bending from the system. The SMAHC plate is fixed at one end and free at another, by introducing heat into the system we observe the deflection obtained. The SMA wires are assumed as fibers and analyzed based on their volume fraction. Further, different orientation angles of wires and boundary conditions are studied to compare the variation in tip displacement of the SMAHC. Various permutations of fiber-matrix combinations are also explored, based on the variation of fiber stiffness—a function of SMA fiber volume fraction, SMA fiber ply thickness, etc. It was observed that with increasing the ply layup in two-layer SMA fiber-reinforcement, a significant bidirectional bending was obtained. It was also found that twisting can be extracted from the plate by varying the SMA fiber orientation angle. The aim of this paper is to model a Deployable Active Bimorph Box Structure (ABBS) such that when the SMAHC is subjected to a thermal field, it first transforms into a cylinder and then into a curved cylindrical element.

Appendix A

1.1 Reduced Stiffness Matrix and Rule-of-Mixtures

$$\begin{aligned} \begin{aligned} Q_{11}=\frac{E_1}{1-\nu _{12}\nu _{21}} Q_{12}=\frac{\nu _{12}E_2}{1-\nu _{12}\nu _{21}} \\ Q_{22}=\frac{E_2}{1-\nu _{12}\nu _{21}} Q_{66}=G_{12} \end{aligned} \end{aligned}$$

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$$\begin{aligned} \begin{aligned} E_{1}=E_a\nu _a + E_{1m}\nu _m E_2=\frac{E_a E_{2m}}{E_a\nu _m + E_{2m}\nu _a}\\ \nu _{12}=v_a\nu _a + v_{12m}\nu _m G_{12}=\frac{G_a G_{12m}}{G_a\nu _m + G_{12m}\nu _a}\\ \int _{T_o}^T \alpha _1(\tau )d\tau =\frac{E_a\nu _a \int _{T_o}^T \alpha _{1a}(\tau )d\tau + E_{1m}\nu _m \int _{T_o}^T \alpha _{1m}(\tau )d\tau }{E_a\nu _a + E_{1m}\nu _m}\\ sgn(\alpha _{1a})=\left\{ \begin{array}{l l} +1 &{} \quad \text {T}<A_s\quad \\ -1 &{} \quad \text {T}\ge A_s\quad \\ \end{array}\right. \ \\ \int _{T_o}^T\alpha _2(\tau )d\tau =\int _{T_o}^T[\alpha _{2a}(\tau )\nu _a + \alpha _{2m}(\tau )\nu _m]d\tau \end{aligned} \end{aligned}$$

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where the subscripts a and m indicate SMA and composite matrix constituents, respectively, $E, \nu , G, \alpha$ are the Young’s modulus, Poisson’s ratio, shear modulus, and effective coefficient of thermal expansion respectively.