Keywords: mechanical reliability, fibre-reinforced composites, probabilistic failure.

Fiber-reinforced composite materials are gradually becoming more popular for mechanical applications and especially for civil engineering structures by providing new design perspectives. Indeed, these materials allow significant progress in weight-strength ratio, durability under fatigue solicitations and corrosion resistance. Such mechanical performance is particularly interesting for composite cables used as bridge stays, in pre-stressed structures or for soil reinforcement [1]. According to the important seismic context, the first applications using fibre carbon cables were done in Japan. Today, new developments have expanded the use of such technologies in many countries.

The counterpart of composite materials is related to the important scatter of their mechanical properties due to the manufacturing process. Besides, in the civil engineering context, such structures can be subjected to high variable loads depending on the environmental conditions (wind, swell) that may be difficult to estimate with precision in the design stage. Accordingly, it is crucial to account for these various uncertainties in order to get a realistic evaluation of the reliability of such structures.

This paper aims at associating a mechanical modelling with a reliability approach in order to optimize the design of a fibre-reinforced composite cable. The objective is to investigate the nature of the composite material used and for each case, the impact of variables design parameters (materials properties, loads) on the cable failure. Reliability analysis applied to mechanical structures can be used at different steps of the structure life:

1. for structural design as it provides the range of use to achieve a given reliability level, which consequently helps in the design optimization,
2. for risk control on existing structures by evaluating the failure probability (equally the security level) and, if necessary, by defining the crucial parameters which mainly influence this phenomenon.

Such an approach is then very useful in the concept phase as well as for the maintenance program. Contrary to deterministic approaches, the uncertainties inevitably associated to the structure definition are taken into account which allows a more complete knowledge of the failure prediction [2].

The objective of reliability calculations is then to quantify the influence of random design variables (materials properties, geometrical characteristics, boundary conditions, loads) on the mechanical behaviour of the structure. The first step of a mechanical reliability assessment is to identify the failure modes of the structure. For composites, various patterns are observed: matrix cracking, fiber cracking or even delaminating at the interfaces [3]. Then, in a second step, the design mechanical variables whose uncertainties play a significant role need to be defined. Different levels can be considered:

1. microscopic scale: matrix and fibre volume ratio, fibre orientation, fibre arrangement, constitutive materials properties,
2. macroscopic scale: composite material properties (if working with homogenised material), geometry, boundary conditions, loads.

A composite cable is composed of several parallel strands (generally seven) set out around a central strand and embedded in a flexible jacket. Stands are made up of a matrix reinforced by unidirectional fibres in the longitudinal direction. As the strand represents the basic element of a cable, it plays a crucial role in the mechanical behaviour of these structures. In this article, we will focus our attention on this elementary structure in order to understand the mechanisms involved at this scale and also to optimize its design. Precisely, we have chosen the context of a bridge stay to apply the reliability analysis.

The failure probability of different kinds of single fibre reinforcement has then been evaluated : carbon-epoxy exhibits the best performance related to axial load (better than steel), the behaviour of Kevlar-epoxy is particularly stable according to lateral pressure, whereas glass-epoxy is definitively weak on all these points. The sensitivity analysis shows that some design parameters take a significant part, namely the ultimate tension stresses and should be as high as possible to improve the cable reliability.

1

U. Meier, "Carbon fibre reinforced polymers", Modern materials in bridge engineering, Structural engineering international, 1, 1-12, 1992. doi:10.2749/101686692780617020

2

C. Boyer, A. Béakou, M. Lemaire, "Design of a composite structure to achieve a specified reliability level", Reliability Engineering and System Safety, 56, 273-283, 1997. doi:10.1016/S0951-8320(96)00095-6

3

J.N. Reddy, "Mechanics of laminated composites plates: theory and analysis", Ed. Boca Raton, CRC Press, 1996.

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