სამეცნიერო სიმპოზიუმი: Eleventh International Symposium on Tools and Methods of Competitive Engineering (TMCE 2016)

Metal - Carbon Bi-layer Strips Fabrication and Properties for their Applications as an Unfolding Design

Teimuraz Chichua*. Ilia Lomidze*, TemurChichua#, Nikoloz Minashvili,# Aleksandre Toidze#.

*Georgian Technical University, Tbilisi,Georgia;

# Tbilisi 199th Komarovi School.

Keywords: Composite plates; Bi-stability; S nap-through; d ouble-well potential; Nonlinear; Bi-layer;

Abstract

Carbon composite materials generally have excellent tensile properties, low densities, high thermal and chemical stabilities. Carbon fiber can use for forming flexible composite sheets with the high strength to weight ratio. For experimental purposes were fabricated carbon fiber/epoxy composite cylindrical sheets with discretely changed curvature of a surface. The composite sheets with two curved steady states - the longitudinal and transversal ones are formed using special high temperature curing procedure of a carbon-epoxy composite, at the assembling in a package are forming bi-stable hinge, characterized with double-well potential. Such packages can find application in a space based unfolding designs. Experimentally were proved possibility of application of such kinematic pair, in which there is no rubbing surfaces when the kinematic pairs’ parts are in relative movement, and accordingly, the friction absence among them. As an example of such design, we made deployable solar panels with an original support framework.

We also investigated bi-layer composites of Brass and unidirectional Carbon woven. The thermal expansion coefficient of these substances differs nearly ten times. Therefore, this composite is suitable as “working body” of a “Heat Engine”. Such engine directly transforms thermal energy into rotary kinetic energy. Bi-layer composite sheets with small weights on their ends are fixed on rotor as blades of turbines and balanced. Due to thermal deformation under sunlight (lighting of the powerful lamp), center of the mass displaces from geometrical center of rotor. Thus, it creates force of torque and makes construction to rotate. On the lower part of the engine the working body is cooled, providing cyclic operation of such engine.


1. Introduction

Carbon composite materials are used in a set of technical applications. Composite materials considered application in innovative solutions, such as structures capable to the adapting properties to act optimum at different the field environment known as adaptive structures. In this context, transforming materials and structures appeared, offering increased performance data and an adaptability for several applications [1, 2, 3]. Promising progress in this direction - development of the curve difficult membranes characterized with repeated statically stable configurations [4]. Bistable configurations wakened because of the asymmetric residual thermal efforts caused during process of treatment [5]. Transition between two statically steady states is reached by a snap-through the gear which isn't linear in its character [6]. The property of multistability led to the carbon composite materials considered for folding space structures. Those structures demanded energy only for change between stable forms [7]. Technology to make membrane samples of desirable stable configurations, projecting the caused thermal efforts it was developed [8]. In addition, conceptual transforming applications taking advantage of these capabilities have been proposed [9, 10]. Most of the studies on morphing composites have focused on plates exhibiting two stable configurations, known as bi-stable composite plates. More specifically, these have focused on the identification of the stiffness characteristics [11, 12] and the static load triggering snap-through for bi-stable composites [13, 14, 15]. The nonlinear response confined to a single stable shape of a bi-stable plate has been experimentally studied [16]. Simple one degree-of-freedom models describing the dynamics of square bi-stable plates have been presented [17, 18]. Good qualitative agreement was achieved and evidence of complex dynamics for oscillations involving snap-through was shown. Experimental tests are performed to study the behaviour of the plate for dynamically induced snap-through. The condition to trigger the snap-through phenomenon is modelled and experimentally validated. The relationship between snap-through force and forcing frequency is obtained in order to identify the minimum dynamic force to trigger the jump phenomenon. Strong nonlinear oscillations showing characteristics of chaotic behaviour are observed for constant changes between stable states, this is for constant cross-well oscillations. The experimental behaviour is modelled by extending the simple model presented in Ref. [19].


2. The Snap-through behavior of the Bi-stable composites.

Bistable joints - type of the joints capable to acceptance of two statically stable forms. The schematic chart of stable configurations of a bistable difficult plate is shown in Fig. 1. Ideally bi-stable square plate will show equal curvatures in each of its steady states, it means that each stable configuration would show equal radiuses of a curvature. The direction of a curvature for each state orthogonal to another as shown in Fig. 1.1

This property is defined as fine orthogonal symmetry between stable configurations of a plate with Kyy>0; and Kxx<0. As a result of this property the dynamic answer for the fluctuations limited to a steady state also orthogonally is symmetric, it means that each state will show identical dynamic behavior only with rotation of local structure of 45 degr concerning another. However any real copy will show shortcomings of final forms as production limited accuracy, breaking fine symmetry. In particular the static curvature of each state would have different values for any real copy. Nevertheless, the answer of stable configurations remains qualitatively symmetric despite production shortcomings. Change between steady states is reached through the jump phenomenon known as a snap-through [4]. The gear of the snap-through is a sudden event where the structure is exposed to big offsets of amplitude [20]. This gear was conceptually studied, using the schematical model on which the ends of a plate are drawn by a spring and the spring is squeezed in two positions during a bend inside or outside.

2

A. Stable cylindrical shape at room temperature (labelled 2 in Fig. 2). The colour map, used for illustration only, represents the surface position along the vertical axis. Parameters: Lx = Ly = 125 mm, ΔT = −180°C,F = 0 N.

B. Stable cylindrical shape at room temperature (labelled 3 in Fig. 2). The colour map, used for illustration only, represents the surface position along the vertical axis. Parameters: Lx = Ly = 125 mm, ΔT = −180°C,F = 0 N.

C. Unstable saddle-like shape at room temperature. This equilibrium configuration is analogous to that labelled 1 in Fig. 2. The colour map, used for illustration only, is proportional to the surface position along the vertical axis. Parameters: Lx = Ly = 125 mm, ΔT = −180°C, F = 0 N. (http://www.sciencedirect.com/science/article/pii/S0020768310002982)

The basic principle of model declares that the dynamic reply of system which can undergo a snap-through, only affected to them when critical offset is reached, having caused the jump phenomenon. Based on it, it is supposed that the fluctuations limited to one steady state are unaffected presence of the second steady state. Only, when critical offset is reached, the catch - via the gear plays a role in dynamics of bi-stable structure. This critical offset direct to define for the commixed mass system. The situation is not so for a continuum, such as bi-stable joints which consider here as each point on a plate is exposed to different to offset when the snap-through is caused. However it is supposed that the form of a deviation of a bi-stable plate can be modelled with forms of the linear mode, such that the relative deviation at any moment of the coercion period between points remains proportional. As a result, as soon as point reaches the critical offset, the snap-through is caused as all points in a plate, has to be, also reached the special threshold because of proportionality of forms of a mode. It provides a simple condition to determine the coercion level demanded to cause a catch - through the phenomenon. However the behavior during a snap-through the phenomenon is much more difficult, and the actual form of unstable balance depends on the frequency of the excitement causing a snap-through. Nevertheless, in the recent newspaper the form of a saddle of unstable static balance as showed, was very close to a flat form. More definitely the most distant the distance is far from a flat tangent of the plane to the center of a bi-stable plate of stable forms one order of size is, the unstable form [21] is more in comparison with that from a saddle. So as a first approximation, it is supposed that critical offset for point on a plate is given by the static deviation demanded to reach this flat unstable plane. In this steady condition of point 2 it is defined as the configuration showing a smaller curvature and a steady state 1 existence of the bigger. The X-direction is chosen to coincide with the curve direction of a steady state 1, thus the curve direction of a steady state 2 coincides with the y-direction, apparently in Fig. 2,B. Ideally, i.e. for bi-stable plates with fine orthogonal symmetry, values for critical offset would be equal. However, as noted above actually difficult to reach. Besides, more general rectangular shape bi-stable plates it is integral it is asymmetric because of different of static curvatures and measurements of length, showing only qualitative symmetry in the answer of each configuration. Thus in general each steady state will show to different critical values of offset.

For fabricating the membranes with property of bistability characterized with the "Snap-through" behavior, we carried out a series of experiments, changing carbon fabrics, epoxy resin impregnations and the curing modes. The best result obtained using carbon 1K Plain ultra light twell prepreg impregnated with low temperature carbon epoxy resin with curin temperature 1200c at the first stage (Curing during 60min), and then increasing curing temperature, up to 1350c, and holding during 75 min. During preliminary curing the membrane was fixed in the cylindrical mold with 450 orientation of fibers relative the cylinder axis. In the finish stage of the curing partially cured membrane was turned on 900 and fixed in this position under bondage. Mechanical parameters of the bi-stable membranes experimentally were investigated. 13

The table displays data of experiment where is shown dependence of force on a membrane bending angle ϕ.

Angle ϕ (grad)

F1(N)

F2(N)

F3(N)

<F>

ΔF

Δ F/F (%)

-15

0.132

0.11

0.1

0.114

0.012

10.5

0

0.052

0.05

0.05

0.056

0.006

11.3

15

0.03

0.05

0.06

0.047

0.011

23

30

-0.038

-0.034

-0,03

-0.034

0.0027

7.8

45

-0.095

-0.09

-0.082

-0.089

0.0047

5.2

60

-0.11

-0.10

-0.09

-0.101

0.0067

6.7

75

-0.14

-0.14

-0.13

-0.137

0.022

16.3

90

-0.18

-0.16

-0.16

-0.167

0.009

5.3

105

-0.22

-0.19

-0.20

-0.203

0.0043

2.1

120

-0.25

-0.24

-0.28

-0.257

0.0016

6.2

135

-0.26

-0.25

-0.27

-0.26

0.007

2.6

150

-0.25

-0.25

-0.27

-0.257

0.009

3.5

165

-0.27

-0.26

-0.27

-0.267

0.0013

1.6

180

0.05

0.02

-0.01

0.02

0.013

6.6

195

0.45

0.42

0.42

0.43

0.013

3.1

According to this experiment, having constructed the graph of dependence of the bending tension vs membrane bending angle and accepting schedule points of intersection with the axe of absciss corresponding to a minimum of potential energy, we receive the graph which has the appearance of a double-well potential shown on the right graph.

77

For a realistic case critical offset for each steady state is connected with a static rejection of point lying on a line perpendicular to the flat direction of each configuration. differences bring in a static curvature of any real bi-stable plate to asymmetric double-well potential schematically shown in Fig. 4. It is possible to notice that the energy, necessary to overtake a maximum (top), depends on which state the system originally fluctuates. Therefore, force demanded to cause a snap-through, depends on an initial condition of a plate as critical offset of one of the states will be smaller, than for another.

Conclusion:

Carbon fiber can use for forming flexiblecomposite sheets with the high strength to weight ratio. For experimentalpurposes were fabricated carbon fiber/epoxy composite cylindrical sheets withdiscretely changed curvature of a surface. The compositesheets withtwo curved steady states - the longitudinal and transversal ones are formed using special hightemperature curing procedure of a carbon-epoxy composite, at the assembling ina package are forming bi-stable hinge, characterized with double-wellpotential. Such packages can find application in a space based unfoldingdesigns. Experimentally were proved possibility of application of suchkinematic pair, in which there is no rubbing surfaces when the kinematic pairs’parts are in relative movement, and accordingly, the friction absence amongthem. As an example of such design, we made deployable solar panels with anoriginal support framework.

References:

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[2] R. Maute, G. W. Reich, Integrated multidisciplinary topology optimiza-tion approach to adaptive wing design, Journal of Aircraft 43 (2006) 253–263.

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ბოლო ცვლილება: პარასკევი, ივლისი 10 2015, 02:28