Heterogeneous materials can show size-dependent behaviour in which the bending modulus depends on sample size. In fibre composite materials the interaction between fibre and matrix can lead to such a size effect.Then the effective modulus calculated by the rule of mixtures can either underestimate or overestimate the bending modulus of the laminate, depending on the fibre/matrix material mismatch, the microstructural morphology (fibre distribution) and the laminate thickness. In this work, the bending behaviour of a laminate comprising unidirectional fibre composite plies is considered using Euler-Bernoulli beam theory and the influence of size on the bending modulus is investigated. The effective bending modulus of each ply is calculated and used to formulate the overall bending modulus of the laminate. The results show that the laminate bending modulus depends on the number of plies, the number of fibres through the thickness of each ply, the fibre spacing and radius, and the mismatch of fibre and matrix material properties in each ply. Our analysis shows that accounting for the ply microstructure (fibre spacing and radius and number of fibres per ply) can lead to a 10% difference in the predicted bending modulus in a three ply laminate, when there are less than four fibres through the thickness in each ply.

异质材料可以表现出与尺寸相关的行为，其中弯曲模量取决于样品尺寸。在纤维复合材料中，纤维和基体之间的相互作用会导致这种尺寸效应。 那么根据混合物规则计算的有效模量可以低估或高估层压板的弯曲模量，这取决于纤维/基体材料的不匹配，微观结构形态（纤维分布）和层压板厚度。在这项工作中，使用欧拉-伯努利梁理论考虑了包含单向纤维复合层的层压板的弯曲行为，并研究了尺寸对弯曲模量的影响。计算每层的有效弯曲模量并用于计算层压板的整体弯曲模量。结果表明，层压板弯曲模量取决于层数、穿过每层厚度的纤维数量、纤维间距和半径，以及每层中纤维和基体材料特性的不匹配。我们的分析表明，考虑到层的微观结构（纤维间距和半径以及每层纤维的数量）会导致三层层压板的预测弯曲模量存在 10% 的差异，当整个厚度中的纤维少于四根时每层。