Bending Actuation in Polyurethanes with a Symmetrically Graded Distribution of One-way Shape Memory Alloy Wires by H.A. Bruck, C.L. Moore, III and T.M. Valentine ABSTRACT--Structures are being actuated by embedding shape memory alloy (SMA) wires into compliant materials, such as polyurethane. To achieve bending actuation, these wires are placed in opposing wire configurations, where mul- tiple wires are often employed to enhance the amplitude of the bending actuation response. In this investigation, a pro- cedure has been developed for fabricating polyurethanes with a symmetrically graded distribution of SMA wires. The effects of grading the distribution of one-way SMA wires have been characterized using full-field displacement deformation mea- surements obtained with the digital image correlation (DIC) technique. These measurements have been used in a one- dimensional (1D) model of bending actuation to determine the "equivalent two-way shape memory effect (SME)" of the graded wire distribution. To utilize the 1D actuation model, the constitutive properties of the polyurethane structure pre- dicted by rule-of-mixture formulations were reduced to ac- count for the differences in strain between the SMA wires and the polyurethane matrix. The graded wire distribution was also found to significantly stiffen the polyurethane structure. The level of equivalent two-way SME therefore became limited by the maximum recovery stress of the SMA wires, with a max- imum level that was approximately 75% less than previously measured levels in an opposing wire Configuration. However, the bending actuation behavior was more symmetric, and the actuated bending deflections were similar to those observed when using more compliant materials. It was also predicted that the symmetrically graded wire distribution would exhibit abetter balance between actuation amplitude and uniformity, which combined with the more symmetric actuation behavior makes the graded wire distribution potentially more desirable for achieving higher actuation frequencies with distributed ac- tuation concepts in new applications, such as miniaturized double diaphragm pumping devices. KEY WORDS--Functionally graded materials, smart struc- tures, digital image correlation, bending actuation, rule-of- mixtures, equivalent two-way shape memory effect Introduction The choices and availability of materials for engineers have been increasing rapidly over the past few decades) Currently, structures are engineered by using a large H.A. Bruck (SEM member) (bruck@eng.umd.edu) is an Assistant Professor, C.L. Moore, lll is a Graduate Research Assistant, and T.M. Valentine is an Undergraduate Research Assistant, Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA. Original manuscript submitted." September 5, 2002. Final manuscript received: May 14, 2003. DOI" 10.1177/0014485104039751 number of uniform materials that are selected based on func- tional requirements that vary with location. For example, the edge of a knife must be made from hard and wear-resistant materials to remain sharp for cutting purposes, but else- where strong and tough materials must be used to improve durability. Abrupt transitions in material properties within a structure lead to undesirable concentrations of stress that can compromise structural performance by precipitating failure. Attempts at reducing these stresses have led to the concept of functionally graded materials (FGMs), which are defined as components featuring engineered gradual transitions in microstructure and/or composition, the presence of which is motivated by functional requirements that vary with loca- tion within the component. 2 FGMs have been successfully employed to minimize the peak axial stress that develops in nickel-alumina joints. 3-8 Active structures are another technology that can poten- tially benefit from FGM concepts. These structures are typ- ically fabricated by distributing actuators and sensors to re- spond to a changing external or internal environment. 9 They are of interest in a variety of physical systems where there is a need to actively control vibration, noise, aeroelastic sta- bility, damping, shape, and stress distribution. Active struc- tures are being used in a variety of applications, from space systems to fixed-wing and rotary-wing aircraft, automobiles, civil structures, and machine tools. Composite structures are a specific example where active materials, such as shape mem- ory alloy (SMA) wires, have been used as reinforcement to create an active structure with increased buckling strength. SMA wires can exhibit either a "one-way" shape memory ef- fect (SME), where inelastic deformations are recovered only once through a thermally-induced phase transformation, or a "two-way" SME, where the material can be thermally-cycled between an unreformed and a prescribed deformed state. In this particular application, grading the distribution of two- way SMA wire reinforcement has been theorized to further improve structural performance due to the distribution of re- covery stresses. 1~ The description for this problem can be seen in Fig. 1. Experimental investigations have been previously con- ducted into grading the transformation temperature of SMAs in thin filmsJ 1 In this case, the coupling between mate- rial property and thermomechanical stress distributions that develops when the films are heated enables them to ex- hibit a substantial two-way SME in bending as fabricated for microactuator applications, such as micropumps and 62 9 VoL 44, No. 1, February 2004 9 2004 Society for Experimental Mechanics