Evaluation of some fibre-reinforced laminates at temperature and humidity variations.

Secara, Eugenia ; Purcarea, Ramona

1. INTRODUCTION

Both fibres and matrix material, presents extreme different deformations at temperature and humidity variations. These variations cause internal stresses in a laminate structure, both at micro and macro mechanical level. This paper takes only the macro mechanical internal stresses into account, stresses that appear, for example, at cooling from the polymerization temperature to the ambient temperature of a laminate structure. These internal stresses, due to temperature variations, are very dangerous and can lead to the damage of the structure even in the absence of an external mechanical loading.

2. LITERATURE--CRITICAL OVERVIEW

Internal stresses, due to temperature variations are more striking in case of carbon fibre-reinforced composite structures, fibres that present extreme different coefficients of linear thermal expansion along and perpendicular to their direction (Bank, 2006). By exposing a laminate composite structure to humidity, inside of it appears an internal stress state caused by the increase in volume of the matrix, due to its swelling (Backman, 2005; Baker et al., 2004). Glass and carbon fibres do not absorb humidity but aramid fibres are strongly influenced by it (Daniel & Ishai, 2005; Davies, 2001; Donaldson & Miracle, 2001).

Various papers took into account the modelling of fibre-reinforced composite laminates, both pre-impregnated and advanced composite materials, subjected to complex loadings (Kollar & Springer, 2003; Teodorescu-Draghicescu et al., 2006; Vlase et al., 2008).

Various fibres-reinforced composite structures have been modeled using different techniques (Teodorescu-Draghicescu et al., 2008; Scutaru et al., 2009; Noakes, 2008).

3. THEORETICAL APPROACH

A fibre reinforced composite laminate is composed from many laminae, unidirectional reinforced, stacked one of each other on their thickness direction. In this way appears only the normal forces [n.sub.xx], [n.sub.yy] and [n.sub.xy] (loading in plane) that cause only the strains [[epsilon].sub.xx], [[epsilon].sub.yy] and [[gamma].sub.xy] without bending or torsions. The coefficients of linear thermal expansion can be calculated as a function of the properties of composite material components and fibres volume fraction. If the fibres are disposed at an angle [theta] with the x-axis direction, the coefficients of thermal expansion in the x and y directions can be determined using [[alpha].sub.[parallel]] and [alpha][perpendicular to]:

[[alpha].sub.xx] = [[alpha].sub.II][cos.sup.2][theta] + [[alpha].sub.[perpendicular]] [sin.sup.2] [theta], (1)

[[alpha].sub.yy] = [[alpha].sub.II][sin.sup.2][theta] + [[alpha].sub.[perpendicular]] [cos.sup.2] [theta], (2)

[[alpha].sub.xy] = (2 sin [theta] cos [theta]) ([[alpha].sub.II] - [[alpha].sub.[perpendicular]]) (3)

where [[alpha].sub.xx] and [[alpha].sub.yy], are coefficients of linear thermal expansion and [[alpha].sub.xy] is the coefficient of shear thermal expansion.

Similar the coefficients of expansion in x and y directions, due to humidity, if the fibres are disposed at an angle [theta] with the x-axis direction, are.

[[beta].sub.xx] = [[beta].sub.II] [cos.sup.2] [theta] + [beta] [perpendicular] [sin.sup.2] [theta], (4)

[[beta].sub.yy] = [[beta].sub.II] [sin.sup.2] [theta] + [beta] [perpendicular] [cos.sup.2] [theta], (5)

[[beta].sub.xy] = (2 sin [theta] cos [theta])([[beta].sub.II] - [[beta].sub.[perpendicular]]), (6)

where [[beta].sub.xx] and [[beta].sub.yy] are coefficients of linear expansion and [[beta].sub.xy] is the coefficient of shear expansion due to the humidity.

The strains of a fibre-reinforced composite lamina due to a [DELTA]T temperature and [delta]H humidity variation, without a mechanical loading, can be calculated in the following manner.

[[epsilon].sub.xx] t - h = [[alpha].sub.xx] x [DELTA]T + [[beta].sub.xx] x [DELTA]H, (7)

[[epsilon].sub.yy] t - h = [[alpha].sub.yy] x [DELTA]T + [[beta].sub.yy] x [DELTA]H, (8)

[[gamma].sub.xy] t - h = [[alpha].sub.xy] x [DELTA]T + [[beta].sub.xy] x [DELTA]H, (9)

where. [[epsilon].sub.xx t-h] and [[epsilon].sub.yy t-h] are strains of lamina in x respective y-axis direction due to a temperature and humidity variation; [[gamma].sub.xy t-h] is the shear strain of lamina due to a temperature and humidity variation. The index t-h denotes the combined action of a temperature and a humidity variation.

4. RESULTS

We considered two applications, a symmetric glass fibre/epoxy composite laminate with the following plies sequence [[0/45/-45/90].sub.S] and a carbon fibre/epoxy composite laminate with plies sequence [[(0/90).sub.2]] subjected to a combined temperature and humidity variation. Data regarding the laminate [[(0/90).sub.2]]: N = 4; t = 1 mm; [t.sub.1-4] = 0.25 mm; [phi] = 60%, [E.sub.F[parallel]] = 540 GPa; [E.sub.F[perpendicular]] = 27 GPa; [v.sub.F] = 0.3; [G.sub.F] = 10.3 GPa; [E.sub.M] = 3.9 GPa; [v.sub.M] = 0.37; [G.sub.M] = 1.4 GPa; [[alpha].sub.F[parallel]] = - 0,5 x [10.sup.-6] [K.sup.-1]; [[alpha].sub.F[perpendicular]] = 30 x [10.sup.-6][K.sup.-1]; [[alpha].sub.M] = 65 x [10.sup.-6][K.sup.-1]; [[beta].sub.M] = 0.18; [[rho].sub.c]=1700 kg/[m.sup.3]; [[rho].sub.M] = 1200 kg/[m.sup.3], [DELTA]T = - 100 K; [DELTA]H = 1%. Data regarding the laminate [[0/45/-45/90].sub.S]: [E.sub.M]=3 GPa; [v.sub.M]=0.35; [[alpha].sub.M]=65 x [10.sup.-6] [K.sup.-1]; [[rho].sub.M] = 1200 kg/[m.sup.3]; [[beta].sub.M] = 0.18; [theta] = 30[degrees]; [E.sub.F] = 73 GPa; [[alpha].sub.F] = 4.8 x [10.sup.-6] [K.sup.-1]; [[rho].sub.M] = 1950 kg/[m.sup.3]; [v.sub.F] = 0.25.

Plies internal stresses of laminate [[0/45/-45/90].sub.S] as well of laminate [[(0/90).sub.2]] subjected to combined temperature- and humidity variation are presented in figs. 1 and 2.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

5. CONCLUSION AND FURTHER RESEARCH

The coefficients of thermal expansion in the case of a glass fibre unidirectional reinforced lamina present very different values for lower fibres volume fractions while the coefficients of humidity expansion present scattered values at upper fibres volume fractions. The extreme different coefficients of linear thermal expansion in case of carbon fibre reinforced laminate [[(0/90).sub.2]] subjected to a temperature variation, lead to significant internal stresses especially transverse to the fibres direction. The internal stresses due to a humidity variation in both laminate types, are comparable, with a plus in case of glass fibre reinforced laminate [0/45/-45/90]S. Further researches will be accomplished in the following domains. stresses and strains determination of various fibre-reinforced laminates, determination of coefficients of thermal and humidity expansion in the case of different unidirectional reinforced laminae as a function of various fibres volume fractions.

6. 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

Scutaru, M.L.; Katouzian, M.; Vlase, S.; Teodorescu-Draghicescu, H. & Chiru, A. (2009). An Estimation of the Viscoelastic Parameters of laminated Composites. Proceedings of the 4th IASME/WSEAS International Conference on Continuum Mechanics (CM'09), pp. 140-145, ISBN. 978-960-474-056-7, Cambridge, February 2009, WSEAS

Teodorescu-Draghicescu, H.; Vlase, S.; Cotoros, D. & Rosu, D. (2006). Damping analysis of an advanced sandwich composite structure. WSEAS Transactions on Applied and Theoretical Mechanics, Vol. 1, No. 2, pp. 147-152, ISSN. 1991-8747

Teodorescu-Draghicescu, H.; Vlase, S.; Mihalcica, V. & Vasii, M. (2008). Modeling some composite laminates subjected to temperature and humidity variations. Proceedings of the 10th WSEAS International Conference on Automatic Control, Modelling & Simulation (ACMOS'08), pp. 215-220, ISBN 978-960-6766-63-3, Istanbul, May 2008, WSEAS

Vlase, S.; Scutaru, M.L.& Teodorescu-Draghicescu, H. (2008). Some considerations concerning the use of the law of mixture in the identification of the mechanical properties of the composites. Proceedings of the 6th International Conference of DAAAM Baltic Industrial Engineering, Katalinic, B. (Ed.), pp. 577-582, ISBN. 978-9-985-597835, Tallinn, April 2008, DAAAM International, Vienna