Shape and Failure Control of Composite Laminates using Piezoelectric Actuators

Transcription

1 Excert from the Proceedings of the COMSOL Conference 00 Boston Shae and Failure Control of Comosite Laminates using Piezoelectric Actuators Zeaid Hasan * Texas A&M University, College Station, Texas *Corresonding author: zeadnws@gmail.com Abstract: Smart materials are candidates for efficient shae control of high recision surfaces such as antenna reflectors and otical mirrors and there exist several different tyes of iezoelectric materials such as Lead Zircronate Titanate (PZT), Microfiber Comosites (MFCs), and Active fiber comosites (AFCs) which could be used for this urose. The resent wor focuses on the use of iezoelectric materials for shae control of comosite laminates by using several different tyes of actuators using the commercial finite element software COMSOL. Due to the high stress concentration between the interface of the host structure and the active art; embedded actuators are used as an alternative for the atched design where the active art is incororated into one of the layers of the comosite beam during the manufacturing rocess, thus, eliminating the stress concentration while obtaining similar actuation values. A control algorithm is also roosed based on the classical lamination theory (CLT) for redicting the failure load and mode of a comosite laminate under uniaxial loading, and by using active materials, a counter electric otential could be alied to revent failure from occurring. Keywords: Piezoelectric, Comosite Laminates, Actuators. Introduction Human civilization has been influenced significantly by materials technology and most eriods of technological develoment have been lined to changes in the use of materials (e.g the stone, bronze and iron ages). In new generations the driving force for technological changes has led to a new family of engineered materials and structures exhibiting multifunctional caabilities which are naturally seen in biological systems, leading to a new era of smart materials. The structures with surface mounted or embedded sensors and actuators that have the caability to sense and tae corrective action are referred to as smart structures []. These tyes of system find alications in aircraft wings, helicoter rotors and automobiles. One of the main motivations behind the vast attentions on smart materials and structures in recent years is its ability to incororate active materials into the structure as sensors and actuators so that it could be used to monitor the integrity/health of the structure to enable a structure to change its shae or its material roerties [], or to control vibration [3]. These lead to imroving erformance and service life of the system. In shae control, one intends to secify the satial distribution, or the shae, of an actuating control unit, such that the dislacement field of a structure distorted from its original shae eventually vanishes, or such that the structure follows some desired field of ath. The disturbances that distort the shae of structures may be transient (dynamic), or they may be slowly varying in time (quasi-/static). Shae control reresents a branch of structural engineering that is closely related to control engineering. Many researchers can be recognized for their unique wor in shae control using iezoelectric material, [4-5] have several contributions in shae control using iezoelectric layers, where these layers were develoed and exerimentally imlemented so as to excite a secific structural mode, or to measure a secific modal content of the structural vibrations excited by external disturbances. The changes in shaes of fiberreinforced comosite beams, lates, and shells affected by embedded iezoelectric actuators were investigated analytically by []. The distributed structural control of elastic shell continua using satially distributed modal iezoelectric actuators was roosed, and some generic distributed feedbac algorithms with satial feedbac functions were formulated [6]. Finite difference modeling and shae control of iezoelectric actuator embedded elastic lates was also considered [7], estimating otimal actuation voltages to match the deflection of the late to a desired deflection.

2 The mechanics of smart material systems involves couling between electric, magnetic, thermal, and mechanical effects. In addition to this couling, it may be necessary to account for geometric and material nonlinearities. An examle is the use of an electromechanical transducer that is characterized by five imortant roerties including the resonant frequency, acoustic imedance, mechanical daming coefficient, electromechanical couling coefficient and the electric imedance, If nonlinear electroelastic equations are included in the model, some or all of these roerties can be tuned; for instance, in an electrostrictive material, the electromechanical couling coefficient can be tuned with a bias field []. In order to tune the first fundamental resonant frequency of the transducer, thin rubber layers are introduced in a multi-layer PZT laminate [8]. The thin rubber layers necessitate the use of nonlinear elastic relations, such nonlinearity in electroelastic formulations was considered by [9], also, a two-dimensional theory of electrostriction was considered by [0] and solved a simlified boundary value roblem using comlex otentials.. Piezoelectric Materials The henomenon of iezoelectricity was discovered in 880 by the Jacques and Pierre Curie brothers. They found out that when a mechanical stress was alied on crystals such as tourmaline, tourmaline, toaz, quartz, Rochelle salt and cane sugar, electrical charges aeared with oosite signs on oosite surfaces and there charges were roortional to the stress. Significant imetus has been generated by the discovery of iezoelectricity in olycrystalline ceramic materials lie bariumtitanate (BT) in the 940 s and lead-zirconatetitanate (PZT) in the 950 s; the latter still dominates transducer alications. Semicrystalline iezoelectric olymers on the basis of olyvinylidenefluoride (PVDF) usually in the form of thin films have been available since the late 960 s. Newer develoment tendencies are directed towards the imrovement of PZT ceramics by doing them with additional comonents such as LaO3 or roducing artificial iezoelectric monocrystals. Piezoelectric materials exhibit electromechanical couling, which is useful for the design of devices for sensing and actuation. The couling is exhibited in the fact that iezoelectric materials roduce an electrical dislacement when a mechanical stress is alied which is termed the direct iezoelectric effect and can also roduce mechanical strain under the alication of an electric field which is nown as the converse iezoelectric effect. The linear constitutive relations for the th orthotroic lamina in the rincial material coordinates of a lamina including electrical effects are σ Q Q 0 ε σ = Q Q 0 ε σ 0 0 Q ε e3 E 0 0 e E E 3 where Q ij is the lane stress-reduced stiffness, e ij is the iezoelectric moduli of the th lamina, σ i is the stress vector, ε i is the strain vector and E i is the electric field vector referred to the material coordinate system (x, x, x 3 ), resectively. For layers other than iezoelectric layers, the art containing the iezoelectric moduli e ij should be neglected. The iezoelectric stiffnesses are nown in terms of the dielectric constants and elastic stiffnesses as 0 0 e3 0 0 d3 Q Q e = 0 0 d Q Q Q 66 Since the laminate is made of several orthotroic layers, with their material axes oriented arbitrarily with resect to the laminate coordinates, the constitutive equations of each layer must be transformed to the laminate coordinates x, y, z. The transformed stress-strain relations relate the stresses σ xx, σ yy, σ xy to the strains ε xx, ε yy, γ xy and comonents of the electric dislacement vector E x, E y, E z in the () ()

3 laminate coordinates σ Q Q Q 3 ε xx xx σ yy = Q Q Q 3 ε yy σ xy Q Q Q γ xy (3) 0 0 e3 Ex 0 0 e3 Ey 0 0 e E 36 z Because of the discontinuous variation of stresses from layer to layer, it is more convenient to deal with the integrated effect of these stresses on the laminate. Thus, we see exressions relating forces and moments to laminate deformation. The exressions for the resultant forces and moments related to the dislacement gradients and electric fields are given as follows u w N x A A A 6 v w 0 0 N = A A A + y 6 y y N xy A A A u v w w y y w 0 B B B 6 A w0 B B B 6 A y B B B A 6 w 0 xy u + w 0 0 M x B B B 6 v w 0 0 M = B B B + y 6 y M B B B y y + + y xy u v w w w 0 D D D 6 B w0 D D D B 6 y D D D B 6 w 0 xy The A, B, and D matrices are called the extensional, couling, and bending stiffness matrices, resectively. Assuming that the electric fields vary linearly within th layer; the iezoelectric stiffnesses are defined as [] A Qd E E h d Na = ( ) i + ij 3 j = j=,,6 3 j (4) B Q E h z E h z h Na = [ ( 3 ) ( 3 )] i d ij 3 j 6 = j=,,6 (5) Where Na is the number of actuator layers and the electric field E is defined as E V = E = (6) h Where V is the alied voltage across the th layer and h is the thicness of the layer. Detailed analysis can be found in []. 3. Piezoelectric Fiber Comosites In order to imrove the use of iezoelectric materials in structural alications as sensors and actuators, iezoelectric materials are integrated into comosites which allow for imrovement of their constitutive roerties as well as of failure behavior and consequently for an extension of the alication in use. The challenge of modeling these tyes of materials in structural alications has attracted wide attention in recent years due to their advantages in several alications which we will discuss in the next subsections 3. Active Fiber Comosite (AFC) AFC actuators consist of unidirectional, aligned iezoelectric fibers, a resin matrix system, and interdigital electrodes, as shown in

4 Figure, a. The advantages over monolithic iezoceramic actuators include higher lanar actuation strains, tailorable directional actuation, robustness to damage, conformability to curved surfaces, and otential for large area distributed actuation and sensing systems. Piezoceramic fibers of small (~50 μm) characteristic crosssectional dimension rovide increased secific strength over monolithic materials. Integral assive materials laminated into the comosite, such as glass fibers, can further imrove toughness, increasing robustness without comromising the ability to conform to curved shaes. Active fiber comosites oerate in the longitudinal mode and thus have significantly higher secific wor outut than lanar monolithic iezoceramics. In addition, the directional nature of actuation ermits design of modal actuators and sensors without reliance on the host structure to transmit the actuation through structural couling mechanisms. Large area, multile ly AFC actuators are easy to fabricate, simlifying leads and connections, and minimizing technology insertion costs. a Eoxy Matrix PZT Fibers Eoxy Matrix PZT Fibers b Figure : Active Fiber Comosite (a), Microfiber Comosite (b) 3. Microfiber Comosite (MFC) Microfiber Comosite is similar to the AFC in the sense that both consist of the same three rimary comonents; active iezoceramic fibers aligned in a unidirectional manner, interdigitated electrodes, and an adhesive olymer matrix, however, the MFC has one difference that greatly affects the manufacturing rocess and the erformance of the actuator, it has rectangular fibers embedded in the olymer matrix Figure, b. In addition, MFC results in larger fiber volume contents than the AFC moreover; the maximum fiber volume content of AFC is less than because of the restriction in the fiber geometry. The fiber volume content of MFC could reach u to High fiber volume content enhances the erformance of the comosite and imroves the stiffness and strength of the comosites. The MFC is extremely flexible, durable and has the advantage of higher Electromechanical couling coefficients granted through the interdigitated electrodes. Allowing the MFC to be roduced at a much lower cost than the AFC and therefore are causing the AFC to be overlooed when determining the ideal actuator for a secific alication. Additionally, the rectangular fiber geometry of the MFC guarantees consistent contact between the IDEs and iezoceramic fibers, reducing attenuation on the IDE electric field due to the low dielectric constant of the eoxy matrix. Because of the imroved electrical contact, MFC strain erformance exceeds AFC strain erformance by u to 50%. 4. Shae Control of Comosite Laminates The effect of using several different tyes of actuators on the behavior of general comosite laminates are first studied and comared in order to observe their ower to bend the late enough to counteract any tye of external stimuli such as thermal or mechanical deformations. The actuators considered and their roerties are summarized in Table. The comosite laminate is made of Carbon /Eoxy AS4 (350-6) with symmetric laminates [Actuator/0/60/-60/90]s. The finite elements software COMSOL is used to develo a 3D model in order to redict the resonse of a simly suorted and cantilever comosite beam subjected to electric otential difference along the actuators. The finite element mesh is shown in Figure 5. A schematic of the comosite beams and the dimensions used is shown in Figure. Figure 3 and Figure 4 show the resonse of a simly suorted and cantilever beam under a N load alied to the midsection and the free end of the comosite beam resectively; no voltage was alied to the actuator. The max dislacement obtained was.mm and mm for both cases resectively. The resonse of the simly suorted comosite beam by alying a 00V and 400V electric otential to several different tyes of actuators is shown in Figure 6 and Figure 7 resectively. Similarly, Figure 9 and Figure 0 resent the resonse of the

5 cantilever comosite beam. The deflection of a tyical comosite beam is shown in Figure 8. Table : Actuators and comosite beam roerties Variable (Unit) AS4 MFC AFC PZT- 5H PZT- 4A E (GPa) E (GPa) E 3 (GPa) ν ν ν G (GPa) G 3 (GPa) G 3 (GPa) d 3 (m/v) d 3 (m/v) d 33 (m/v) d 5 (m/v) d 4 (m/v) t(mm) Figure 4: Cantilever comosite beam under N load Figure 5: Finite element mesh Figure : Simly suorted and cantilever beam schematics Figure 3: Simly suorted comosite beam under N load Figure 6: Simly suorted beam under 00V electric otential The iezoelectric fiber comosites are actuated through the thicness by using inter digitated electrodes attached to the to and bottom surfaces. The max dislacement was obtained by using PZT-5H due to its high iezoelectric coefficient comared to the other actuators. It can be concluded that by using either tye of the actuators resented, the deflection caused by the

6 Figure 7: Simly suorted beam under 400V electric otential Figure 8: Comosite beam deflection under 00V electric otential Figure 0: Cantiliver beam under 400V electric otential and the active material which might cause delamination of the active art and eventually failure. This tye of failure is very common in smart structures. An alternative design could be by using embedded actuators such that, during the manufacturing rocess, an actuator can be incororated into the layer by becoming a art of one of the comosite layers. This could lead to enhanced behavior of the overall structure and excluding the stress concentration that existed in the revious atched design while obtaining higher actuation values. A comarison between both embedded and atched designs can be shown in Figure ; it is observed that the embedded design not only excluded the stress concentration, yet, it rovided higher actuation values for the same electric otential. Figure 9: Cantilever beam under 00V electric otential mechanical load alied to the comosite beam can be counter reacted. Also; since all the actuators are suitable in overcoming the deflection of the beam, AFC and MFC have the advantage of having a more flexible behavior in addition to their higher actuation values. It is evident that high stress concentration usually occurs near interfaces of different structures, and in our case, it exists between the host structure Figure : Comarison between atched and embedded actuators on the beam deflection under 00V electric otential 5. Control Design In most of the industrial alications, structures are usually subjected to several changes such as thermal gradients or mechanical distortions that may affect their overall behavior. Comosite structures are usually subjected to

7 non-uniform temerature change which can induce imortant thermal distortions. Active control of such structures becomes an essential art of the designing rocess. In the resent study, we roose a controlling methodology which can be imlemented for active controlling of comosite structures. The controlling methodology is shown in Figure. Based on the results obtained from the first ly failure and ultimate laminate failure of comosite structures [], the control circuit is activated in order to bias the active material with the recommended voltage value to overcome the failure load. Moreover, a control circuit is also imlemented using a rogrammable interfacing chi (PIC) which is rogrammed and simulated using the simulation rogram (PROTEOUS). Figure 3 shows a schematic of the control circuit. Figure : Control methodology Figure 3: Simle control circuit 6. Conclusion. The resent study focused on the use of iezoelectric material for active control of comosite structures. It was observed that the use of iezoelectric fiber comosite in smart structures have the advantage of giving higher actuation values yet more flexible structure which give the ability to atch on curved and bent structures. Due to the high stress concentration between the active material and the host structure which may cause debonding and eventually failure. A roosed design where that active art is incororated into one of the comosite layers, in that way the stress concentration is eliminated and higher deflection is obtained for similar electric otential value. A control methodology was also roosed to control comosite structures in order to comensate for any external distortions; in addition, a ractical control circuit was imlemented using a micro controlling chi (PIC) which showed feasibility in ractical use. 7. References [] Gandhi, M.V., Thomson, B. S., Smart Materials and Structures Sringer, (99) [] Koconis, D. B., Kollár, L. P. and Sringer, G. S., Shae Control of Comosite Plates and Shells with Embedded Actuators Journal of Comosite Materials. 8-5, , (994) [3] Agrawal, B.N., Sacecraft vibration suression using smart structures 4th Int. Congress on Sound and Vibration, , (996) [4] Lee, C.K., Theory of laminated iezoelectric lates for the design of distributed sensors/actuators Part I: governing equations and recirocal relationshis, 44 58, (990) [5] Lee, C. K., Piezoelectric laminates: theory and exeriments for distributed sensors and actuators Intelligent Structural Systems. Dordrecht: Kluwer, 75 67, (99) [6] Tzou HS, Zhong JP, Hollam JJ., Satially distributed orthogonal iezoelectric shell actuators: theory and alications J Sound Vib , (994) [7] Agrawal, S.K., Tong, D., Nagaraja, K., Modeling and shae control of iezoelectric actuator embedded elastic lates J Intelligent Mat Syst Struct 54, (994) [8] Atin, R. Shi, X. Bullough, W., Solution of the constitutive equations for the flow of an electrorheological fluid J. Rheol. 35: 44 46, (99) [9] Touin, R.A., The elastic dielectric Archives of Rational Mechanics and Analysis , (956) [0] Knos, R.J., Two-dimensional electrostriction Quarterly Journal of Mechanics Alied Mathematics 77 88, (963)

8 [] Reddy, J.N., Mechanics of laminated lates: theory and analysis Boca raton, FL: CRC Press, (997) [] Hasan, Z., Darwish, F., Failure and Stress Analysis of Fiber Reinforced Comosite Laminate AIAA Regional Student Conference, (00)