16th International Conference on Composite Structures ICCS 16 A. J. M. Ferreira (Editor)  FEUP, Porto, 2011

VISCOELASTIC MODELLING AND ANALYSIS OF SANDWICH BEAMS UNDER SUSTAINED LOADING

Ehab Hamed* * Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering University of New South Wales UNSW 2052, Sydney, Australia e-mail: [email protected]

Key words: Composite materials, Creep, Sandwich Structures, .

Abstract. Sandwich beams made of thin and stiff skins, connected by a thick, soft core are widely used in aerospace and ship-building constructions as well as in many other applications. In many cases, viscoelastic core materials are used to minimize the vibration amplitudes and to mitigate fatigue failures [1]. Nevertheless, the viscoelastic core may significantly affect the behaviour of sandwich beams when they are subjected to sustained loads. In such cases, the viscoelastic core tends to creep, leading to variations in the internal stresses over time, which may significantly affect the structural performance. Honeycomb cores (e.g. aluminium or resin coated paper) are widely used in aerospace applications where weight is critical. However, in many cases including civil engineering applications of sandwich panels, polymer or metallic foam cores are preferred. Despite their heavy weight, they offer excellent thermal insulation and may be easily mass produced [2]. However, polymer foams creep at room temperature, and most metallic foams creep at temperatures above almost 0.3 times the melting temperature [3]. Therefore, there is a need to clarify the creep response of sandwich beams, which may limit their use in some applications. Among the physical aspects that make the creep analysis of viscoelastic sandwich beams a challenging task is the deformability of the core in shear and though its thickness especially in soft cores, which results in concentrations mainly near edges or concentrated loads. These stresses play a critical role in the response of the sandwich structure, and, in many cases, govern its failure mechanism by debonding or delaminations. The viscoelasticity of the core material may modify the distributions and the magnitudes of these stresses over time, as well as those of the deflections and stress resultants. In addition, many of the face sheets that are used in sandwich beams are made of fibre reinforced plastics (FRP), which may also exhibit some level of viscoelastic behaviour provided by the matrix, the fibres (e.g. Aramid), or both. To account for these aspects, a detailed step-by-step time analysis is needed. Only few studies have been devoted to the creep response of sandwich beams [2-4], which are based on simplified equivalent models that do not explain many aspects of the structural behaviour. Here, a theoretical model for the viscoelastic creep analysis of sandwich beams is developed. The viscoelastic model accounts for the variation of stresses in time through an incremental step-by-step analysis following Boltzmann’s principle of superposition [5]. The structural modelling accounts for the deformability of the core layer in First A. Author, Second B. Author and Third C. Coauthor.

shear and through its thickness following the high-order sandwich theory [6]. The sign conventions for the modelling of the sandwich beam as a layered structure appear in Figure 1.

Figure 1: Geometry, loads, sign conventions, and stress resultants Variational principles, equilibrium, and compatibility requirements between the structural components are used to formulate the incremental equilibrium equations. The integral constitutive relations and the expansion of the relaxation functions into a Dirichlet series, which allows the use of a differential-type constitutive relations that are based on the generalized Maxwell model, are given by:

t N dε (t') −t T σ = − = µ + (t) ∫ R(t t') dt' ; R(t) ∑ Eµe E∞ (1) dt' µ =1 to where σ and ε are the stress and strain in each component, R is the relaxation function, Eµ is the modulus of the µth Hookean spring in the Maxwell chain, and Tµ is the relaxation time. Findley’s power law is used for estimating the viscoelastic properties of the different materials (core, fibres, matrix), along with a micromechanical model for the FRP faces.

REFERENCES [1] E. Hamed and O. Rabinovitch, "Modeling and dynamics of sandwich beams with a viscoelastic soft core". AIAA Journal, 47(9), 2194-2211 (2009). [2] J.S. Huang and L.J. Gibson, "Creep of sandwich beams with polymer foam cores". J. Mat. Civ. Eng., 2(2), 171-182 (1990). [3] C. Chen, N.A. Fleck and M.F. Ashby, "Creep response of sandwich beams with a metallic foam core". Adv. Eng. Mat., 4(10), 777-780 (2002). [4] J.M. Davies, Lightweight Sandwich Construction, Blackwell Science, Oxford (2001). [5] J.D. Ferry, Viscoelastic Properties of Polymers, John Wiley & Sons, New York (1980). [6] Y. Frostig, M. Baruch, O. Vilanay and I. Sheinman, "High-order theory for sandwich beam behavior with transversely flexible core". J. Eng. Mech., 118(5), 1026-1043 (1992).

2