Fundamentals of Piezoelectricity

The term “piezoelectricity” translates roughly to “pressure electricity” and refers to an effect observed in many naturally occurring crystals; that is, the generation of electricity under mechanical pressure. The effect was first predicted and then experimentally measured by the brothers Pierre and Jacques Curie in 1880. The research was prompted by investigations into a closely related effect, the pyroelectric effect, which is the generation of electricity as a result of a change in temperature. The effect observed by the Curie brothers is also known as the direct piezoelectric effect. A strict definition of the direct effect is “electric polarization produced by mechanical strain, being directly proportional to the applied strain.” A converse piezoelectric effect also exists and is the appearance of mechanical strain as a result of an applied electric field.

The origin of the piezoelectric effect can be traced to fundamental geometric properties of certain crystals. Based on their geometry, crystals are normally classified into seven categories: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. A structure is called centrosymmetric if it has symmetry with respect to a single point. Based on their symmetry with respect to a point, the crystals are further classified into 32 classes, of which only 20 classes can exhibit piezoelectricity. The unit cell of these crystals possesses a certain degree of asymmetry, leading to a separation of positive and negative charges that results in a permanent polarization.

Applications of smart structures technology to various physical systems are primarily focused on actively controlling vibration, performance, noise, and stability. Applications range from space systems to fixed-wing and rotary-wing aircraft, automotive, civil structures, marine systems, machine tools, and medical devices. Early applications of smart structures technology were focused toward space systems to actively control vibration of large space structures [1] as well as for precision pointing in space (e.g., telescope, and mirrors [2]). The scope and potential of smart structures applications for aeronautical systems have subsequently expanded. Embedded or surface-bonded smart material actuators on an airplane wing or helicopter blade can induce alteration of twist/camber of airfoil (shape change), which in turn can cause variation of lift distribution and may help to control static and dynamic aeroelastic problems. For fixed-wing aircraft, applications cover active control of flutter [3, 4, 5, 6, 7], static divergence [8, 9], panel flutter [10], performance enhancement [11], and interior structure-borne noise [12]. Compared to fixed-wing aircraft, helicopters appear to show the most potential for a major payoff with the application of smart structures technology. Given the broad scope of smart structures applications, developments in the field of rotorcraft are highlighted in a subsequent section. Although most current applications are focused on the minimization of helicopter vibration, there are other potential applications such as interior/exterior noise reduction, aerodynamic performance enhancement that includes stall alleviation, aeromechanical stability augmentation, rotor tracking, handling qualities improvement, rotor head health monitoring, and rotor primary controls implementation (e.g., swashplateless rotors) [13].

The previous chapters discuss the properties and behavior of active materials that existed in a solid state. These materials exhibited changes in properties and physical dimensions when subjected to an electric, magnetic, or thermal field. A special class of fluids exists that change their rheological properties on the application of an electric or a magnetic field. These controllable fluids can generally be grouped under one of two categories: electrorheological (ER) fluids and magnetorheological (MR) fluids. An electric field causes a change in the viscosity of ER fluids, and a magnetic field causes a similar change in MR fluids. The change in viscosity can be used in a variety of applications, such as controllable dampers, clutches, suspension shock absorbers, valves, brakes, prosthetic devices, traversing mechanisms, torque transfer devices, engine mounts, and robotic arms. Other applications such as electropolishing do not rely directly on the change in viscosity but rather on the ability to change properties of the fluid locally.

Most mechanical dampers consist of fixed damping that is designed as a compromise between a range of operating conditions. As a result, these devices do not provide an optimum level of damping for any specific operating environment. Using ER/MR fluid dampers, variable damping levels can be obtained, and the system performance can be optimized over a wide range of operating conditions. In such dampers, the resistance to flow and, consequently, the energy dissipation, can be modulated through the applied electric or magnetic field.

The quest for superior capability in both civil and military products has been a key impetus for the discovery of high performance new materials. In fact, the standard of living has been impacted by the emergence of high performance materials. There is no doubt that the early history of civilization is intertwined with the evolution of new materials. For example, different eras of civilization are branded with their material capabilities, and these periods are referred to as the Stone Age, the Bronze Age, the Iron Age, and the Synthetic Material Age. The Stone Age represents the earliest known period of human civilization that stretches back to one million years BC, when tools and weapons were made out of stone. The Bronze Age (sometimes called the Copper Age) spans 3500–1000 BC. Weapons and implements were made of bronze (an alloy of copper and tin) during this period. The alloy is stronger than either of its constituents. Bronze was used to build weapons such as swords, axes, and arrowheads; implements such as utensils and sculptures; and other industrial products. The Iron Age followed the Bronze Age around 1000 BC and was characterized by the introduction of iron metallurgy. Iron ores were plentiful (cheap) but required high-temperature (2800°F) furnaces as compared to copper, which required lower-temperature (1900°F) furnaces. The Iron Age was the age of the industrial revolution, and many of the initial design tools, mechanics-based analyses, and material characterizations were formulated during this period.

Magnetostrictives and electrostrictives are active materials that exhibit magneto-mechanical and electromechanical coupling, respectively. These materials undergo a change in dimensions in response to an applied magnetic or electric field. A common property of both materials is that the induced strain depends only on the magnitude of the applied field and is independent of its polarity. In other words, it can be said that the induced strain has a quadratic dependence on the applied field. It is this behavior that differentiates electrostriction from the piezoelectric effect, which is also caused by an electric field. This chapter discusses the basic mechanisms behind magnetostriction and electrostriction, and it describes how these materials are used to construct practical actuators and sensors. The behavior of magnetic shape memory alloys (SMAs) is also described.

Magnetostriction

A ferromagnetic material placed in a magnetic field generally undergoes a change in shape [1]. The internal structure of a ferromagnetic material consists of randomly oriented magnetic domains. When a magnetic field is applied, the domains rotate to align themselves along the field, causing a change in the material dimensions. This phenomenon is known as “magnetostriction.” The effect is small in most materials but is measurable (on the order of microstrain) in ferromagnetic materials. Some materials, such as Terfenol-D, exhibit magnetostrictive strains on the order of 2000 microstrain (2000 × 10×6). Such materials can be used as both solid-state actuators and magnetic-field sensors. Magnetostrictive materials are available in the form of rods, thin films, and powder.

In 1990, a pilot project was started at the Alfred Gessow Rotorcraft Center (University of Maryland) to build a smart rotor with embedded piezoelectric strips. Soon, it attracted the attention of Dr. Gary Anderson of the Army Research Office (ARO). He encouraged us to put together outlines for a major initiative in the smart structures area, which subsequently resulted in the award of a multi-year (1992–1997) University Research Initiative (URI). This provided us an opportunity to develop an effective team of interdisciplinary faculty from Aerospace, Mechanical, Electrical, and Material Engineering. As a result, there was an enormous growth of smart structures research activities on our campus. Following the success of this URI, we were awarded another multi-year (1996–2001) Multi University Research Initiative (MURI) in smart structures by ARO. For this major program, we collaborated with Penn State and Cornell University. This further nurtured the ongoing smart structures activities at Maryland. We deeply acknowledge the support and friendship of many faculty colleagues at Maryland: Appa Anjannappa, Bala Balachandran, James Baeder, Amr Baz, Roberto Celi, Ramesh Chandra, Abhijit Dasgupta, Allison Flatau, James Hubbard, P. S. Krishnaprasad, Gordon Leishman, V. T. Nagaraj, Darryll Pines, Don Robbins, Jim Sirkis, Fred Tasker, Norman Wereley, and Manfred Wuttig.

While the research frontier in smart structures was expanding at the Alfred Gessow Rotorcraft Center, we also initiated classroom teaching at the graduate level in the smart structures area.

Certain classes of metallic alloys have a special ability to “memorize” their shape at a low temperature and recover large deformations imparted at a low temperature on thermal activation. These alloys are called shape memory alloys (SMAs). The recovery of strains imparted to the material at a lower temperature, as a result of heating, is called the shape memory effect (SME). The SME was first discovered by Chang and Read in 1951 in the Au-Cd (gold-cadmium) alloy system. However, the effect became more well known after the discovery of nickel-titanium alloys.

Buehler and Wiley [1, 2] discovered a nickel-titanium alloy in 1961 called NiTiNOL (i.e., Nickel Titanium alloy developed at the Naval Ordinance Lab) that exhibited a much greater SME than previous materials. This material was a binary alloy of nickel and titanium in a ratio of 55% to 45%, respectively. A 100% recovery of strain up to a maximum of about 8% pre-strain was achieved in this alloy. Another interesting feature noticed was a more than 200% increase in Young's modulus in the high-temperature phase compared to the low-temperature phase. Subsequently, it was determined that the percentage of nickel and titanium influences the material properties of Nitinol and can be varied to control the transformation temperatures in the material [3]. Also, the addition of a third or fourth element (most commonly copper) to NiTi can be used to selectively control some properties of SMA wires.

The previous chapter discussed the modeling of beam-like structures with induced-strain actuation. Many practical structures can be simplified and analyzed as beams, but such an assumption is not accurate in a large number of other structures, such as fuselage panels in aircraft, low aspect-ratio wings, and large control surfaces. It is possible to treat such structures as plates and perform a simple two-dimensional analysis to estimate their behavior. Some of the theories discussed in the previous chapter can be extended to two-dimensional plate-like structures. This chapter describes the modeling of isotropic and composite plate structures with induced-strain actuation. It will combine both the actuators and substrate into one integrated structure to model its behavior. The discussion focuses on induced-strain actuation by means of piezoceramic sheets, but the general techniques may be equally applicable to other forms of induced-strain actuation.

Plate analysis, including induced-strain actuation, is based on the classical laminated plate theory (CLPT), sometimes referred to as classical laminated theory (CLT). It is an equivalent single layer (ESL) plate theory in which the effects of transverse shear strains are neglected. It is valid for thin plates that have thicknesses of one to two orders of magnitude smaller than their planar dimensions (length and width). In the CLPT formulation, a plane-stress state assumption is used.

Classical Laminated Plate Theory (CLPT) Formulation without Actuation

A composite laminate consists of a number of laminae or plies, each with different elastic properties.