Multi-scale models for fibre/matrix size effects in thin ply composite laminates

Heterogeneous materials can show size-dependent behaviour under bending in which stiffness can increase or decrease by decreasing size. In other words, while the elastic modulus calculated by the rule of mixtures can predict the tensile behaviour of these materials well, it can overestimate or underestimate their bending behaviour. Composite materials are inherently heterogeneous due to a mismatch of fibre/matrix geometry and material properties. While idealised models assume uniform fibre spacing, realised fibre spacing may be irregular due to perturbations in material quality and processing characteristics. Such variations add more parameters necessary for modelling heterogeneity in composites. Due to emerging spread-tow thin-ply technology that enables manufacturing of plies as thin as 20µm, greater variability in fibre distributions can be expected. Success in manufacturing various thicknesses of composite plies provides the need to quantify a potential size effect under bending. Indeed, the common assumption of a fibre/matrix cube (unit cell) as a representative volume element (RVE) repeated through-thickness a ply loses its validity for thin-ply composites. As a result, the cross-section of a thin composite ply should be considered as an RVE and analysed for modelling its bending behaviour. To address this problem, Euler-Bernoulli beam theory was used to calculate the bending stiffness of the cross-section with different fibre/matrix models for both uniform and non-uniform fibre spacing. An effective bending modulus is defined as the ratio of bending stiffness of heterogeneous media to the second moment of area of an equivalent homogenised cross-section. In order to quantify the size effect, a modulus variation parameter, R, is defined as the relative difference between the bending and tensile modulus. Results show that there is a maximum value of R ' 10% for a ply with three fibres and it is increasing significantly for the non-uniform fibre spacing case (R = 80%). To verify the accuracy of analytical results, finite-element analysis was used for comparison purposes. As analysing heterogeneous composite plies is computationally expensive, homogenisation through micropolar theory was done by determining a bending characteristic length responsible for the size effect. Furthermore, the significant influence of the detected size effect at the ply level on the overall bending behaviour of laminate was validated.