Keywords: viscoelastic, micromechanics, creep function, simplified unit cell method, composites, fibre, matrix.

Micromechanical study is an important factor in establishing the overall behaviour of the constituent materials in a composite structure. Various studies have been carried out regarding the mechanical behaviour of the constituent materials. In continuous fibre-reinforced composite materials, the fibre and the matrix behaviour can be modeled in several different ways, for example the elastic fibre and elastic matrix.

In the present analysis, the fibres are assumed to behave elastically and the matrix has a time-dependent behaviour, i.e. viscoelastic behaviour. To evaluate the mechanical properties of such composites various models have been introduced. To simplify the analysis, the randomly distributed fibres in matrix are assumed to have an organized pattern in the matrix, i.e. a hexagonal or a square array of fibres.

Consequently, the representative volume element (RVE) is assumed to be a hexagon with a single fibre at the centre or a square with a single fibre at the centre. In the present analysis a square array of fibres is assumed. Due to the symmetrical properties of the RVE a quarter of the square is taken into account and symmetrical boundary conditions are defined at the appropriate edges.

In general the micromechanical analysis is carried out by either exact elasticity solution or by approximate numerical methods. Regarding the viscoelastic behaviour of composite materials, elasticity solution methods are used. One of these methods is due to Aboudi [1], which is referred to Aboudi's method of cells. A simplified version of Aboudi's method of cells is used in [2] to study the collapse behaviour of metal matrix composites. This method is calleded the 'simplified unit cell method' (SUCM).

In the present analysis the effective creep properties of rate-dependent unidirectional composites have been determined using the SUCM. The primary advantages of the model, with a square array of fibres, are the simplicity it offers at both the derivation of the governing equations and solution procedure. Fibres are assumed to be elastic up to failure while the matrix is assumed to behave as a four-parameter rehological viscoelastic material. Additionally, a finite element micromechanical analysis with various loading conditions is used to predict the overall composite compliances. The results of the SUCM model are graphically compared with those of the finite element results for different fibre volume fractions and loading conditions and available experimental result.

1

Aboudi, J., "A continuum theory for fibre-reinforced elastic-viso-plastic composites", Int. J. Eng. Sci. 20, 605-620, (1982). doi:10.1016/0020-7225(82)90115-X

2

Aghdam M.M., Smith, D.J., Pavier, M.J., "Finite element micromechanical modeling of yield collapse behaviour of metal matrix composites", Jounal of Mechanics and Physics of Solids, 48, 499-528, (2000). doi:10.1016/S0022-5096(99)00041-1

3

Li, J., Weng J., "Effective creep behavior and complex moduli of fibre and ribbon reinforced polymer matrix composites", Composite Science and Technology, 52, 618-629, (1994). doi:10.1016/0266-3538(94)90044-2

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