Keywords: ageing, buckling, composite materials, beam-columns, finite element, viscoelasticity.

The durability of structures made of composite materials is affected by diverse factors, among which creep deformation, ageing and damage. Ageing is related to elapsed time (in different environmental conditions) while damage is related to stress and strain effects. In this paper, expressions for ageing and the corresponding expressions for creep are given. Then, the effects of these phenomena on the short and long term stability of ageing beam columns are analysed. The formulation is used for analytical solutions and also implemented into a finite element program. Several examples for verification of the formulation are presented.

Two types of ageing are considered: physical ageing and chemical (or environmental) ageing. In the first case (here identified as hardening case), an increase the elastic stiffness, and a decrease the viscoelastic compliance are observed; in the second (the softening case) the opposite behaviour may occur.

The analytical results by Distéfano [1] that studied the asymptotic (i.e. for time t->infinity) behaviour of imperfect columns are particularly important, as they allow the determination of safe loads for arbitrary long times. This results are analysed and generalised in the present work through analytical and numerical calculations.

A homogeneous slightly bent bar of length L, with uniform moment of inertia I, subjected to an axially compressive load P(t) is analysed. Loading is applied at tau₀=0, which means that P(t)=0 for t<0. The analysis is restricted to the linearized (for example small displacements) geometrically nonlinear problem. The stability analysis follows that in [2]. Analytical results are presented for the ageing elastic case; for the viscoelastic ageing case, numerical results obtained with a finite element code [3] are given. For both cases it is concluded that the asymptotic results in [1] are restricted to the case in which the rate of loading is lower than the rate of (hardening) ageing. Additional results are given for the case of softening ageing.

1

J.N. Distéfano, "Creep Buckling of Slender Columns", Journal of the Structural Division, ASCE, 91(3), 1965.

2

G.J. Creus, "Viscoelasticity", Springer Verlag, 1986.

3

B.F. Oliveira, G.J. Creus, "An Analytical-Numerical Framework for the Study of Ageing in Fibre Reinforced Polymer Composites", Composite Structures, 65, 443-457, 2004. doi:10.1016/j.compstruct.2003.12.006

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