On longitudinal compressive failure of carbon-fibre- reinforced polymer: from unidirectional to woven, and from virgin to recycled by S. T. Pinho, R. Gutkin, S. Pimenta, N. V. De Carvalho, and P. Robinson Philosophical Transactions A Volume 370(1965): April 28, 2012 ©2012 by The Royal Society

(a) Micrograph of a kink band. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a) Kink band propagating from right to left. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Failure mode of carbon fibres during kinking: shear bands form on the side of higher compressive stress at an angle approximately 45° with the longitudinal fibre direction [8]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Micromechanical FE models for the simulation of kink bands, highlighting the initial shape of every 10th fibre: (a) baseline model with mesh detail; (b) model for kink-band propagation into the initially defect-free fibres [3]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

The sequence of events for fibre kinking from the FE micromechanical models [3]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Fibre deflection during kink-band propagation: comparison between FE micromechanical models and experimental results [3]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Development of the analytical model for kink-band formation under pure longitudinal compression [9]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Results from the analytical model for kink-band formation under pure longitudinal compression [9]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Comparison of failure envelopes for longitudinal compression with in-plane shear, measured by four different research groups, showing high scatter and different trends [4]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Micromechanical FE model with periodic boundary conditions. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a) Bimodal failure envelopes obtained using micromechanical FE models, highlighting the sensitivity to matrix constitutive properties. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a,b) Numerical predictions for bimodal failure envelopes against experimental data [10,11]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a) Equilibrium of a fibre under a longitudinal compressive force and a shear force at each end, as well as a distributed shear force across the length. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Failure envelopes predicted by the analytical model (§2b(iii)) [14] against experimental data [10,11]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a–d) Shear-driven fibre compressive failure as an independent failure mode that eventually leads to kink-band formation. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Complete failure envelope prediction for combined longitudinal compression and in-plane shear [14]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a) Tow failed by kinking; (b) several tows failing individually [15]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Differences in failure location between different reinforcement architectures: 2×2 twill and 5H satin [15]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Cross sections of (a) random-stacked, (b) IP and (c) OP laminates. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Longitudinal compression in a 2×2 twill composite [15]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

At the microscale, compressive damage starts with microcracking/plasticity of the matrix, leading to splitting (1) at the interface of the load-aligned tows and/or within the tows. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

(a) Finite-element model of a 2×2 twill rUC. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Kinematic models used to derive the properties of the elastic foundation [17,18]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Equilibrium of a beam element. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Comparison between the numerical, analytical and experimental results [16–18]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Recycled composite with a multi-scale structure consisting of fibre bundles in a short-fibre- reinforced matrix [22]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Compressive failure of short-fibre rCFRPs with fibre bundles [22]. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society

Mechanical response of a woven rCFRP: the compressive performance at the recycled composite level is shown to be insensitive to fibre strength degradation, occurring in the most aggressive recycling conditions. S. T. Pinho et al. Phil. Trans. R. Soc. A 2012;370: ©2012 by The Royal Society