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The characterization of the strength and fracture toughness of three common structural fibres, E-glass, AS4 carbon and Kevlar KM2, is presented in this work. The notched specimens were prepared by means of selective carving of individual fibres by means of the focused ion beam. A straight-fronted edge notch was introduced in a plane perpendicular to the fibre axis, with the relative notch depth being a 0 / D ≈0.1 and the notch radius at the tip approximately 50 nm. The selection of the appropriate beam current during milling operations was performed to avoid to as much as possible any microstructural changes owing to ion impingement. Both notched and un-notched fibres were submitted to uniaxial tensile tests up to failure. The strength of the un-notched fibres was characterized in terms of the Weibull statistics, whereas the residual strength of the notched fibres was used to determine their apparent toughness. To this end, the stress intensity factor of a fronted edge crack was computed by means of the finite-element method for different crack lengths. The experimental results agreed with those reported in the literature for polyacrylonitrile-based carbon fibres obtained by using similar techniques. After mechanical testing, the fracture surface of the fibres was analysed to ascertain the failure mechanisms. It was found that AS4 carbon and E-glass fibres presented the lower toughness with fracture surfaces perpendicular to the fibre axis, emanating from the notch tip. The fractured region of Kevlar KM2 fibres extended along the fibre and showed large permanent deformation, which explains their higher degree of toughness when compared with carbon and glass fibres. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’.

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A novel methodology is presented to introduce Periodic Boundary Conditions (PBC) on periodic Representative Volume Elements (RVE) in Finite Element (FE) solvers based on dynamic explicit time integration. This implementation aims at overcoming the difficulties of the explicit FE method in dealing with standard PBC. The proposed approach is based on the implementation of a user-defined element, named a Periodic Boundary Condition Element (PBCE), that enforces the periodicity between periodic nodes through a spring-mass-dashpot system. The methodology is demonstrated in the multiscale simulation of composite materials. Two showcases are presented: one at the scale of computational micromechanics, and another one at the level of computational mesomechanics. The first case demonstrates that the proposed PBCE allows the homogenization of composite ply properties through the explicit FE method with increased efficiency and similar reliability with respect to the equivalent implicit simulations with traditional PBC. The second case demonstrates that the PBCE coupled with Periodic Laminate Elements (PLE) can effectively be applied to the computational homogenization of elastic and strength properties of entire laminates taking into account highly nonlinear effects. Both cases motivate the application of

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