On the flexural rigidity of a spherical cap sandwich composite structure.

Secara, Eugenia ; Purcarea, Ramona

1. INTRODUCTION

In general, composite laminates are formed by thin layers called laminae. These laminates present a quite low stiffness and flexural rigidity. A solution could be their stiffening using ribs. However, there are constructive situations when these ribs cannot be used. Another solution could be the increase of layers number that composes the structure. But this solution presents the disadvantage of the increase of resin and reinforcement consumption with economic and environmental consequences.

2. LITERATURE--CRITICAL OVERVIEW

In general, a sandwich structure is manufactured of three layers: two cover layers called "skins"--that form the carrying structure, layers composed of stiff and resistant material, and an intermediate layer named "core"--which has the main purpose to sustain the skins and to give stiffness to whole structure (Backman, 2005; Baker et al., 2004; Bank, 2006; Daniel & Ishai, 2005). This stiffness is obtained actually through "thickening" the composite structure with a low density core material. This leads to a substantial increase of flexural rigidity of the structure, on the whole, without a significant increasing in its entire weight (Davies, 2001; Donaldson & Miracle, 2001). Sandwich structures are more and more used in various applications due to their high stiffness at bending. Nowadays, there are a great variety of cores such as rigid foams, hexagonal structures made from thermoplastics, metallic and non-metallic materials, expandable and fireproof materials, balsa wood, etc., (Kollar & Springer, 2003; Noakes, 2008; Vinson & Sierakovski, 2008; Zenkert, 1997).

3. THE STRUCTURE

The spherical cap sandwich structure that can avoid the previously presented disadvantages is composed from the following layers:

* 1 x RT500 glass roving fabric;

* 2 x RT800 glass roving fabric;

* 1 x 450 chopped glass fibres mat;

* A nonwoven polyester mat as core;

* 1 x 450 chopped glass fibres mat;

* A gelcoat layer.

The spherical cap sandwich structure can be seen as twelve curved shells bonded together, structure that presents dissimilar skins. The core presents the most important influence in the overall structure's stiffness and flexural rigidity. The core material is a random oriented non continuous nonwoven polyester mat contains microspheres that prevent excessive resin consumption. The most important features of the whole structure using this kind of core are:

* Stiffness increase;

* Weight saving;

* Resin and reinforcement saving;

* Fast build of the structure's thickness;

* Superior surface finish.

The nonwoven polyester mat is soft, present excellent resin impregnation and high drapeability when it is wet and therefore is suitable for complex shapes. It is most often applied against the "gelcoat" to create a superior surface finish for instance on hull sides. The applying of the nonwoven polyester mat against the "gelcoat" layer is more important when dark "gelcoats" are used, to prevent the appearance of the glass fibers reinforcement. This material has a good compatibility with the polyester, vinyl ester and epoxy resins and is suitable for hand lay-up and spray-up processes.

4. STRUCTURE'S FLEXURAL RIGIDITY

According to the ordinary beam theory, the flexural rigidity, here denoted R, of a beam is the product between Young modulus of elasticity E and the moment of inertia I (that depends on structure's cross-section). The flexural rigidity of an open sandwich beam assumed to have thin skins of equal thickness represents the sum between the flexural rigidities of the skins and core determined about the centroidal axis of the whole cross section (Zenkert, 1997):

R = [E.sub.s] x [b x [t.sub.3]/6] + [E.sub.s] x [b x t x [d.sub.2]/2] + [E.sub.c] x [b x [c.sub.3]/12], (1)

Where [E.sub.s] and [E.sub.c] represent the Young moduli of elasticity for skins and core respectively. If the skins present different materials and unequal thickness, with dissimilar skins and taking into consideration that the local flexural rigidities for the skins cannot be neglected, this means that:

d / t > 5.77, (2)

The sandwich flexural rigidity can be written as:

R = b x [d.sup.2] x [E.sub.s1] x [E.sub.s2] x [t.sub.1] x [t.sub.2]/([E.sub.s1] x [t.sub.1] + [E.sub.s2] x [t.sub.2]) + b/12 x ([E.sub.s1] x [t.sup.3.sub.1] + [E.sub.s2] x [t.sup.3.sub.2]). (3)

Considering the beam as a wide one, the authors propose that the structure's flexural rigidity can be computed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

Where the suffixes 1 and 2 refer to the upper and lower skins respectively, b represent the width of the beam cross section, d is the distance between centerlines of opposite skins, t is the skin thickness, c is the core thickness, [[upsilon].sub.s1] and [[upsilon].sub.s2] represent the upper respective the lower skin Poisson ratio.

5. EXPERIMENTAL APPROACH

The three-point bend test has been used to determine the most important features of this test. Twelve specimens have been cut from a sandwich panel and subjected to bending until break occurs. The tests have been carried out on a LR5K-type testing machine (5 kN maximum load) as well as on a Texture Analyser type TA (1 kN maximum load), produced by Lloyd's Instruments.

6. RESULTS

The input data for the theoretical approach are presented in table 1. Some experimental results obtained on twelve sandwich specimens are presented in fig. 1. The sandwich structure with thin nonwoven polyester mat as core presents an excellent bond between skins and core. This has been noticed during the three-point bend tests.

[FIGURE 1 OMITTED]

7. CONCLUSION AND FURTHER RESEARCH

The sandwich structure's flexural rigidity determined experimentally is twelve times greater than the upper skin's one, 57 times greater than the core's one and more than 237 times greater than the lower skin's flexural rigidity (fig. 2). The 30% difference in structure's flexural rigidity determined theoretically and the experimental approach can be a little bit reduced by a better estimation of the upper and lower skin's Poisson ratios. Further researches will be accomplished in the following domains: measuring stress and strains, a finite element analysis as well as dynamic and damping analysis.

[FIGURE 2 OMITTED]

8. REFERENCES

Backman, B.F. (2005). Composite Structures, Design, Safety and Innovation, Elsevier Science, ISBN: 978-0080445458

Baker, A.A.; Dutton, S. & Kelly, D. (2004). Composite Materials for Aircraft Structures, American Institute of Aeronautics & Ast, 2nd ed., ISBN: 978-1563475405

Bank, L.C. (2006). Composites for Construction: Structural Design with FRP Materials, Wiley, ISBN: 978-0471681267.

Daniel, I.M. & Ishai, O. (2005). Engineering of Composite Materials, 2nd ed., Oxford University Press, ISBN: 978-0195150971

Davies, J.M. (2001). Lightweight Sandwich Construction, Wiley-Blackwell, ISBN: 978-0632040278

Donaldson, R.L. & Miracle, D.B. (2001). ASM Handbook Volume 21: Composites, ASM International, ISBN: 978-0871707031

Kollar, L.P. & Springer, G.S. (2003). Mechanics of Composite Structures, Cambridge university Press, ISBN: 978-0521801652

Noakes, K. (2008). Successful Composite Techniques: A practical introduction to the use of modern composite materials, Crowood, 4th ed., ISBN: 978-1855328860

Vinson, J.R. & Sierakovski, R.L. (2008). The Behavior of Structures Composed of Composite Materials, Springer, ISBN: 978-1402009044

Zenkert, D. (1997). Handbook of Sandwich Construction, Engineering Materials Advisory Services Ltd., ISBN: 978-0947817961

Tab. 1. Input data

 Value

Young modulus of bending, [E.sub.s1] (MPa) 6118.6
Young modulus of bending, [E.sub.s2] (MPa) 7172.6
Upper skin Poisson ratio, [upsilon].sub.s1] (-) 0.25
Lower skin Poisson ratio, [upsilon].sub.s2] (-) 0.35