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Multiscale models for fibre-reinforced polymer composites currently lack experimentally validated microscale damage descriptors as input parameters. This work demonstrates the occurrence of strain localisation phenomena at the fibre/matrix level using nanoscale digital image correlation. Unidirectional carbon-fibre reinforced epoxy and glass-fibre reinforced PMMA composites were loaded in transverse compression in a scanning electron microscope. Radial and shear strain maps were extracted and compared with finite element simulations based on a conventional elastoplastic model. Near the interface, an interphase layer is present in the matrix, presumably due to locally different polymerisation conditions. A skin-core structure was found in carbon fibres, corresponding to an increased transverse modulus towards the interface. [Display omitted] • Measurement and simulation of radial strain fields in fibre-reinforced polymers. • Quantitative width measurement of the skin-core structure in carbon fibres. • Fibre/matrix interphase-like response partly due to thermal residual stresses. [ABSTRACT FROM AUTHOR]