Fibre-dominated compressive failure in polymer matrix composites
Models describing longitudinal compressive failure of carbon fibre reinforced polymers (CFRP) have been attempted for decades. Despite many developments, no single model has surfaced to provide simultaneously a definitive explanation for the micromechanics of failure and validated predictions for a generic stress state. This chapter explores why, by presenting new experimental data (including scanning electron microscope (SEM) observations of loaded kink bands during propagation, and brittle shear fracture at 45 ° to the fibres) and proposing new micromechanics analytical and numerical models. The paper focuses on unidirectional (UD) composites, but studies of woven and recycled composites are also presented, highlighting similarities and differences with UD.
Compressive failure in the fibre direction has been a topic of research for several decades in carbon fibre reinforced polymers (CFRP). This is due to its significance for structural design and to the complexity of the several failure mechanisms that can occur in longitudinal compression.
This chapter explores several of those mechanisms for different types of material: unidirectional (UD) plies and woven plies for virgin carbon, and short fibres and bundles as well as woven architectures for recycled carbon fibres. For each mechanism identified, experimental, numerical and analytical results are presented to fully understand the mechanisms. Wherever possible, the similarities and relations between the failure mechanisms in different carbon/polymer architectures are highlighted. Section 7.2 focuses on UD composites while Section 7.3 focuses on woven and Section 7.4 on recycled composites.
Longitudinal compressive failure in fibre-reinforced composites made of UD plies can take one of three different forms: (i) kink-band formation, (ii) fibre splitting and (iii) shear-driven fibre compressive failure as shown in Fig. 7.1. Despite being induced by stresses acting in the fibre direction, two of these failure modes, namely fibre splitting and kink-band formation, initiate due to matrix failure, while only shear-driven compressive failure is a result of fibre failure.
Kink-band formation is often recognised as the main failure mode under longitudinal compressive loading and is also found in many other materials such as wood , paper  and rocks . Kink-band formation results from the rotation of initially misaligned fibres, which induces shearing of the matrix. When the shear stress in the matrix is large enough to cause failure in brittle resins or yielding in ductile ones, the fibres lose their support, resulting in further fibre rotation and failure localisation. Typical kink-band parameters such as the width w, the propagation angle β and the fibre rotation θ0 + θ (with θ0 the initial misalignment and θ the additional rotation introduced by the compressive loading) are shown in Fig. 7.1(a).
Obtaining experimental evidence on the failure mechanisms behind kink-band formation is challenging due to the unstable nature of failure and the difficulty in observing specimens at the microscale while keeping them under load. Figure 7.2(a) shows a low magnification SEM image of a loaded kink-band propagating from the notch tip in a single edge notch unidirectional specimen . The close-up views (Fig. 7.2(b) and (c)) reveal how kink-band formation is related to the development of microcracks in the matrix (label ‘m’ in Fig. 7.2(c)) which eventually coalesce in splits (label ‘c’ in Fig. 7.2(c)). Moving along the kink-band from the tip (on the left-hand side of the micrograph in Fig. 7.2(a)) to the notch (on the right-hand side), it can be seen how the propagation angle β increases from a shallow value of 5 ° to its final value of 30 °, and how fibres fail at two locations defining the edges of the kink-band. Fibre failure appears relatively late in the process and results from combined bending and axial compressive loading. Carbon fibres fracture due to the formation of shear bands on the side of highest compressive stress (Fig. 7.3).
7.2 Kink-band formation in notched unidirectional composites. The specimen is kept loaded .
7.3 Fibre fracture during kink-band formation .
Kink-bands can either form (and propagate) in-plane (in the 1–2 plane) or through the thickness. The latter is often encountered in thin plies embedded in laminates, as neighbouring plies hinder the rotation of the fibres in-plane, making it energetically more favourable for the kink-band to propagate through the thickness. Such through the thickness kink-bands are shown in the post-mortem observations made on compact compression cross-ply specimens in Fig. 7.4 . These micrographs also highlight the interactions between failure modes in different plies: a matrix crack in the 90 ° layer (label 1 in Fig. 7.4(a)) induces a loss of lateral support for the 0 ° layer, and bending of the fibres, which then results in fibre fracture (label 2) and kink-band formation.
7.4 Through the thickness kink-band formation in cross-ply compact compression specimens .
Kink-bands, and the stress at which they initiate, are sensitive to multiaxial stress state. The effect of hydrostatic pressure has, for instance, been investigated by Oguni et al.  and Parry and Wronski . They reported an increase in the failure stress with increased pressure, as the pressure provides additional support to the fibres and inhibits their rotation, but also because the stiffness and strength of the resin is enhanced by hydrostatic pressure . These studies also reported the formation of complementary kink-bands due to the confined state of the specimens.
Combining in-plane shear to longitudinal compressive loading has been shown to significantly decrease the compressive stress at failure. Figure 7.5 presents failure envelopes by several research groups [8–11] using torsion compression tubes for combined in-plane shear and longitudinal compression. Significant scatter is typical in these tests and the trends reported for the failure envelopes differ for each group. The general shape of the failure envelope is discussed later in the chapter, but fibre kinking typically corresponds to the region where the compressive strength decreases rapidly with the shear stress. In some portion of the failure envelope, fibre kinking competes with fibre splitting. Jelf and Fleck  reported that kinking occurred in all cases except for pure shear (σ1 = 0; τ12 = SL), with SL the in-plane shear strength of the composite, while in Ref. , kinking is found for compressive stresses −σ1/Xc > 0.6, a transition region where either splitting or kinking takes place is observed between 0.5 < −σ1/Xc < 0.6 and splitting occurs for −σ1/Xc < 0.5.
Fibre splitting is in many respects similar to kink-band formation in that it is related to shear failure of the matrix in between fibres. However, in contrast to fibre kinking, splitting does not localise but runs along the fibre/matrix interface, sometimes across the whole specimen as in Fig. 7.1(b). Experimental evidence related to fibre splitting is rather scarce. From the failure envelopes shown in Fig. 7.5, it is known that splitting occurs when large in-plane shear stresses are combined with compressive loading. The transition from kinking to splitting is, however, not visible on these envelopes, i. e. there is no change of trend, which confirms that the mechanisms behind these two failure modes are similar.
Shear-driven fibre compressive failure (Fig. 7.1(c), was first observed by Ewins et al.  in composites with Courtaulds HM-S and HT-S (high modulus and high tensile strength, S is a surface treatment) carbon fibres and by Crasto and Kim  in AS4/PEEK and epoxy. The denomination of this failure mode, shear-driven fibre compressive failure, is better understood from the micrographs in Fig. 7.6, which have been obtained in notched specimens tested in dedicated testing rigs, allowing for greater control over the loading process during longitudinal compressive failure initiation  as well as to keep the specimens loaded during microscopic investigation. Sheardriven fibre compressive failure initiates at the notch and is characterised by a fracture plane oriented at 45 °, indicating that it is driven mainly by shear stresses acting on that plane. The crack propagates through fibres and matrix in a brittle way and with no sign of deformation of the constituents adjacent to the crack faces. In the close-up view (Fig. 7.1(c)), a significant amount of debris and abrasion is found on the fracture surfaces as the two crack faces slide on each other .
7.6 Shear-driven fibre compressive failure in cross-ply single edge notch specimen. The micrograph is taken while the specimen is kept under load .
In Fig. 7.6(c), the interaction between shear-driven fibre compressive failure and kink-band formation is shown. During the propagation of the shear crack, the crack faces slide over each other, inducing a rotation of the fibres at the shear crack tip. This rotation combined with the longitudinal compression favour kink-band formation. In Fig. 7.6(d), it is worth noting that as the specimen is loaded further, the friction force created on the shear crack faces leads to a rotation of the fibres on the lower part of the crack, and eventually these fibres fail due to bending and axial compressive stresses, along a line parallel to the 45 ° shear crack (labels 1 and 2 in Fig. 7.6(d)). It is hypothesised that this type of failure may be more common than expected, given that the evidence of it occurring is easily masked or lost due to the catastrophic and crushing nature of compressive failure.
The difference between the regions failing by shear-driven fibre compressive failure or kink-band formation is also seen from features left on the crosssection of the broken fibres; see close-up views in Fig. 7.1(a) and (c).
Understanding longitudinal compressive failure is experimentally challenging due to its rapidity and often unstable nature. Micromechanical finite element (FE) analyses are therefore a powerful tool to complement experimental work and gain insights into the sequence of events leading to failure. Many models present a 2D representation of the geometry [14, 15] (3D models have also been used in Ref. ), and depending on the purpose of the analysis, an array of several tens of fibre/matrix layers (Fig. 7.7(a) and (b)) or a unit cell with periodic boundary conditions (Fig. 7.7(c)) are used.
Kink-band initiation and propagation have been studied in Ref.  using a model based on an array of 100–200 fibre/matrix layers. (Fig. 7.7(a) and (b). Several modelling approaches have been adopted: sinusoidal or perfectly straight initial fibre geometry, cohesive or plastic constitutive laws for the resin, and elastic or failing fibre response. The numerically obtained load vs. displacement curves and the stress fields (Fig. 7.8) can be correlated with the sequence of events during kink-band formation. Matrix failure occurs immediately prior to the peak load, while fibre failure only takes place much later (on the side of highest compressive stress), after most of the load-bearing capability has been lost. This sequence of events was obtained for all modelling approaches adopted, including when the propagation of a kink band in initially-straight fibres was achieved (Fig. 7.8(b)). These numerical results are in accordance with experimental evidence, both regarding the sequence of events reported in  and the fibre deflections shown in  (Fig. 7.9).
7.8 Sequence of events for fibre kinking from FE micromechanical models . (a) Load vs. fibre deflection (FE model with sinusoidal elastic fibres and cohesive matrix). (b) Stress fields in defect-free (initially straight) fibres during kink-band propagation.
7.9 Fibre deflection during kink-band propagation: comparison between FE micromechanical models and experimental results . (a) Fibre deflection predicted with the FE model with initially straight fibres. (b) Fibre deflection observed experimentally during kink-band propagation (specimen under load).
Unit cell FE models, as shown in Fig. 7.7(c), share similarities with the previous ones, but are preferred when a large number of simulations are necessary, as for generating failure envelopes. The unit cell represents a matrix layer between two half-fibres onto which periodic boundary conditions have been applied to represent actual conditions in the composite. This type of model has been used in Ref.  to obtain quantitative insights into failure envelopes for combined in-plane shear and longitudinal compression as well as to understand the discrepancies found experimentally and shown in Fig. 7.5. The softening induced by matrix microcracking is represented using an elastic-plastic constitutive law for the matrix layer and the fibres use a continuum damage model where the stress carried by the fibres in compression is reduced following a linear softening law once its strength is reached. The effect of imperfections such as initial fibre misalignment is also considered.
The failure envelopes obtained (Fig. 7.10(a)) have a bi-modal shape, with the nonlinear decreasing portion corresponding to kink-band formation and the portion parallel to the τ12 axis corresponding to shear-driven fibre compressive failure. Figure 7.10(a) shows that fibre kinking occurs in composites with large fibre misalignments or high fibre compressive strengths while shear-driven fibre fracture can occur for materials with less significant fibre misalignments or lower fibre strength (leading in these cases to bimodal failure envelopes).
7.10 (a) Failure envelope generated by FE micromechanical models, (b) width of a kink band during longitudinal compression with inplane shear, as a function of applied shear stress .
For fibre kinking, the micromechanical FE models also give the width of the localised failure zone, i.e. the width of the kink-band (Fig. 7.10(b)). For the material system used in Ref. , the models predict that failure only localises for shear stresses lower than ~75 MPa; for higher shear stresses, failure corresponds thus to fibre/matrix splitting.
When used to generate failure envelopes, the unit-cell model is able to capture experimental trends, as shown in Fig. 7.11, and also to explain the different trends observed experimentally as being linked to the initial misalignment in the composite and the occurrence of shear-driven fibre compressive failure (the latter being minor in Fig. 7.11(a) and significant in Fig. 7.11(b)) .
Many models and formulations to predict the compressive strength associated with kink-band formation found in the literature are based on either microbuckling  or fibre kinking [20–22]. The microbuckling theory is based on a micromechanical approach in which the fibres are supported by an elastic foundation provided by the matrix. The compressive strength corresponds to the buckling load and is lowest when the fibres deform inphase:
with Gm the shear modulus of the resin, vf the fibre volume fraction and G12 the in-plane shear modulus of the composites. For typical high performance composites, G12 is between 4 and 6 GPa which implies that compressive strengths predicted by Equation [7.1] are three to four times in excess of experimentally measured compressive strengths (typically 1200–1500 MPa).
Kinking theory is based on the assumption that there is a region of misaligned fibres in the composite. Under a compressive load, the fibres rotate further and failure is predicted when the failure stress of the matrix is reached. In contrast to microbuckling, failure is caused by matrix failure rather than fibre instability. Argon  developed the first kinking model which, assuming small rotation of the fibres and neglecting their bending contribution, gives a compressive strength:
where τY is the shear strength of the matrix. This model has later been extended to account for the rotation of the fibres by Budiansky :
where γY is the shear yield strain of the matrix.
Several micromechanical models, where fibre and matrix are explicitly introduced, have been proposed to study kink-band formation [23–26]. The model presented in Ref. , for instance, is based on the equilibrium of an imperfect (sinusoidal) fibre bending under longitudinal eccentric compression, supported in shear by an elasto-plastic matrix (Fig. 7.12(a)). Before the onset of matrix yielding, adjacent fibres are assumed to deform in-phase, so elastic shear strains in the matrix layers are related to fibre deflection (Fig. 7.12(b)). The onset of matrix yielding defines the peak load and the transition to a softening domain, during which a central band of perfectly plastic matrix grows as compression proceeds; the kink band is considered to be fully formed when fibre stresses locally reach the fibre compressive strength.
7.12 Development of analytical models for kink-band formation under pure longitudinal compression (after  and ). (a) Equilibrium diagram for a fibre on an elasto-plastic matrix. (b) Definition of matrix shear strains in the elastic domain. (c) Equilibrium diagram for a fibre on a brittle matrix.
The analytical model predicts the load vs. displacement curve and the deflection and stress fields accurately; the main events for kink-band formation are predicted by the model, and a good quantitative correlation with FE results is also achieved (Fig. 7.13). Moreover, the analytical model leads to a closed-form prediction of strength as a function of initial misalignments, and to the computation of the kink-band width at the onset of fibre failure .
7.13 Results from the analytical model for kink-band formation under pure longitudinal compression (after ). (a) Load vs. fibre deflection from the analytical model. and ♢ correspond to the load for the stress fields in (b). (b) Maximum fibre stresses along the fibre: analytical (full lines) vs. FE (dashed lines) results.
Under combined loading, the number of approaches based on the physics of kink-band formation is rather limited. Budiansky and Fleck  developed a model where the kink band is seen as a band with its edges lying at angles θ + θ0 and β (see Fig. 7.1(a). The edges of the kink band are well defined, which means that the bending contribution of the fibres is neglected. The band has orthotropic material properties which are rotated in the misaligned coordinate system of the fibres (angle θ + θ0). The stresses (tractions) and displacements are computed in the coordinate system associated with the kink band and their continuities are verified at the boundary with the outer region. The longitudinal compressive strength is evaluated when yielding of the matrix in the band is reached. For a case of longitudinal compression and in-plane shear, applied stresses (σ1; τ12) are related by :
where τ is the shear stress due to (σ1; τ12) in a coordinate system aligned with the rotated fibres.
Dávila and Camanho  proposed a criterion for fibre kinking based on Argon’s approach and the LaRC matrix failure criterion. The stress applied on a UD composite, containing a region of misaligned fibres, is rotated in that misaligned coordinate system. The resolved stresses are then used to evaluate the LaRC matrix failure criterion to test for failure. This approach was developed further in Ref.  to account for the nonlinear response of the composite in shear as well as to handle 3D loading situations.
Models presented so far rely mainly on a plasticity approach. However, experimental observations presented in Fig. 7.2 show that kink-band initiation results from the formation of matrix microcracks and splits in the interfibre region. A model using finite fracture mechanics has therefore been developed in Ref.  to represent better this fracture process. The model is based on the energy balance for a fibre embedded in matrix (Fig. 7.12(c)) and the hypothesis that the strength associated with fibre kinking is reached when the strain energy released per unit area of crack generated between an undamaged state and a damaged state is equal to the energy required to create the cracks (fracture energy). For a linear response of the resin, the criterion for fibre kinking/splitting reads :
where represents a two-dimensional fibre volume fraction and θ0, SL and Gm have the same definitions as those introduced earlier in the chapter. A nonlinear response of the resin can also be introduced (see Ref.  for details.
The predictions using the criterion in Equation [7.5] are shown in Fig. 7.14 and compare favourably to experimental data available in the literature but also to predictions by numerical and another analytical model presented in Fig. 7.11.
As mentioned in Section 7.2.1, shear-driven fibre compressive failure is a brittle failure mode typically taking place in a fracture plane oriented at 45 ° to the loading direction (Fig. 7.6), with both fibre and matrix failing at this orientation. Therefore, Ewins and Ham  proposed that the compressive strength of the composite should be related to the compressive shear strength of the fibre Sf and the compressive shear strength of the matrix Sm by the expression:
Other criteria, which are not based on the physics of compressive failure, can also been used for predictions in longitudinal compressive dominated load cases; e.g. the maximum stress criterion or polynomial criteria. These criteria are plotted in Fig. 7.5, together with the LaRC05 fibre kinking criterion introduced earlier.
Fibre splitting is most likely to occur first, at low levels of longitudinal stress, if large in-plane shear stresses are combined to compression. Localisation into kink band occurs at lower levels of shear stress and higher compressive stresses or when significant, local, initial fibre misalignment is present in the composite. Finally, for composites with well aligned fibres, shear-driven fibre compressive failure occurs at the highest level of longitudinal stresses.
Improving the performance of fibre-reinforced composites in longitudinal compression would therefore result from delaying fibre splitting and kink-band formation. This can be achieved by improving the toughness of the matrix material to delay microcracking and split formation. In the case of kink-band formation, reducing initial fibre misalignment would also improve performance.
In laminates, delaying kink-band formation can be achieved by careful selection of the orientation of the plies adjacent to those loaded in longitudinal compression. For instance, in cross-ply loaded in compression, 90 ° plies stacked next to a 0 ° layer inhibit in-plane fibre rotation and delay in-plane kink-band formation, making shear-driven fibre compressive failure more likely. However, in cases where the 0 ° layer is relatively thin, matrix cracks in 90 ° plies might introduce through-the-thickness fibre misalignment and through-the-thickness kink-band formation. Such tailoring is difficult to achieve empirically and can only be optimised through detailed FE simulations where a physically based damage model, accounting for all failure modes possibly encountered, is used.
The first ingredient in such a damage model is a set of failure criteria able to predict failure initiation for a generic 3D stress state. In this chapter, several criteria have been highlighted for the different failure modes, and accurately predicting failure initiation is best achieved through criteria based on the physics of the failure processes.
The detailed study of the compressive failure mechanisms in woven composites is hindered by: (i) the typically sudden nature of compressive failure, and (ii) the need to understand the effect of the reinforcement geometry on the failure process. Therefore, it is not surprising that most of the literature highlights the final failure morphology rather than the nature and development of the failure process. From the available literature, it is possible to conclude that kink band formation, as well as intra-ply and inter-ply delamination, are the main compressive failure mechanisms of 2D woven composites [31–33]. Final failure results from the interaction of these mechanisms which in turn are determined by variables such as reinforcement architecture, loading rate, confinement and mechanical properties of the resin. The mechanical properties have a decisive influence on the predominance of the different mechanisms. In general, brittle resins favour delamination while tougher resins tend to induce kink-band formation and overall shear failure [33, 34]. In addition, high loading rate and confinement induce kink-band dominated failure [35, 36].
Although the main compressive failure mechanisms have been identified, failure initiation has not been subject to widespread and detailed study. An exception is the work from Reifsnider and Mirzadeh . Compression tests were stopped before final failure, and the edges of the specimens observed. Kinking of the load-aligned tows was identified as the predominant damage mechanism controlling the failure process. Additionally, testing notched specimens, Reifsnider and Mirzadeh  observed that failure initiated not only at the notch but also at the crimp regions of the tows close to the notch. These findings highlighted the importance of the reinforcement architecture in the failure process. Recently, using a four-point bending test setup and a tailored specimen design, damage initiation and the effect of the weave architecture on the compressive failure mechanisms were explicitly studied . Two different 2D woven carbon-epoxy composites were tested, 2 × 2 twill and 5 H satin. Results show the damage morphology is affected by weave architecture and geometry (Fig. 7.15). The load-aligned tows were seen to behave as structural elements at the reinforcement level (Fig. 7.16). Concerning the failure process, it was observed that the load-aligned tows tended to fail predominantly at the crimp region and kinking was identified as the micromechanism responsible for their failure (Fig. 7.17).
7.15 Location of the failure relative to the centre of the crimp region . In (a) the load-aligned tows fail close to the centre of the crimp region, d ≈ 0, while in (b) they fail at a non-negligible distance d.
7.16 Tows fail individually with significant out-of-plane movement . This behaviour highlights the structural role of the tows at the reinforcement level and suggests that load transfer between the first tow failing and the adjacent tow(s) was the mechanism responsible for the local damage propagation.
7.17 Detail of a tow failed by kinking in a twill specimen .
Since woven plies are not flat, when manufacturing a laminate, coincident valleys and peaks of adjacent layers will nest, resulting in a decrease in resin-rich areas. The relative positioning of adjacent layers with the same orientation, hereafter referred to as stacking, determines the number of coincident valleys and peaks between adjacent layers and, therefore, affects strongly the degree of nesting. In a 2D woven laminate, shifting between adjacent layers is generally not controlled, leading to a random configuration (Fig. 7.18(a)). Upon compression, adjacent layers will naturally interact. Few studies have investigated the effect of stacking (and resultant nesting) on the failure of woven composites (e.g. Refs [39–42]). Breiling and Adams , studying the compressive failure of a 5 H satin carbon-epoxy, concluded that varying the stacking configuration (i.e. the relative position of peaks and valleys of adjacent mats with the same orientation), could lead to a reduction of up to 32% on the ultimate strength. However, a relation between the failure mechanisms and the different stacking configurations was not established. The latter was recently investigated by de Carvalho et al. . Using a reduced compact compression test setup (rCC), damage propagation in compression for two different 2D woven composites and the effect of different stacking configurations was investigated. Regarding damage propagation, the main conclusions where that kink-band formation, matrix cracking and transverse tow cracking are the predominant damage propagation mechanisms in compression. The effect of stacking was studied by producing specimens with carefully aligned adjacent layers in an in-phase (IP) configuration, i.e. all load-aligned tows of adjacent layers are in-phase (Fig. 7.18(b)). The failure morphology was seen to change significantly with the support provided by the adjacent layers. As highlighted previously, tows were observed to behave as structural elements within the reinforcement architecture; under compression, the out-of-plane support provided by the adjacent layers affects the bending of the tows and consequently the failure morphology. This effect was also seen to be a function of the reinforcement architecture.
7.18 Cross-sectional view of an idealised laminate with different stacking configurations. All layers have the same orientation . (a) Random-stacked, (b) in-phase (IP), (c) out-of-phase (OP).
At the microscale, compressive failure of woven composites occurs according to the process previously described for UD: microcracking/plasticity of the matrix between fibres (within the tows or at their surface) leading to kinking/splitting (Fig. 7.19).
7.19 Longitudinal compression of a 2 × 2 twill composite : (a) random, (b) in-phase.
Analytical models to predict failure of 2D woven composites can be broadly divided into meso- and macro-scale models. In macro-scale models, no distinction is made between reinforcement and regions of pure matrix. The composite lamina or laminate is regarded as an orthotropic material, defined by its homogenised properties. In meso-scale models, reinforcement and matrix are distinguished, and their geometry and properties considered independently. Few macro-scale models can be found specifically developed for woven composites (e.g. Refs [43, 44]). The main advantages of macroscale models are their simplicity, and capability to be adapted to different reinforcement geometries and types, provided the mechanical tests that define them are performed. The main disadvantage is that, since the reinforcement is not modelled, the actual damage mechanisms are not captured leading to an arguable lack of physical representativeness. Additionally, any change on the reinforcement geometry requires new mechanical tests.
Meso-scale models represent the geometry of the internal reinforcement. To do so, various approaches have been proposed, with different degrees of complexity [32, 45–49]. In general, they are able to provide insight into the stress and strain fields within the reinforcement. Knowing the strains and stresses within tows and matrix (or their equivalent), failure prediction is normally made using failure criteria applied at the constituent level, i.e to tows and matrix, sometimes coupled with a progressive damage approach to account for the material nonlinear response prior to failure. Tows are regarded as a UD composite, and the matrix as an isotropic material. In this approach the effect of the internal reinforcement on the damage mechanisms and failure is explicitly determined. However, the detailed modelling often leads to a complex formulation and narrower range of application (e.g. only plain weave, only satin). Recently, an analytical model to predict the failure of 2D woven composites under tensile and compressive loading has been proposed . It consists of a beam on elastic foundation (Fig. 7.20(a)). The latter provides normal and torsional support (Fig. 7.20(b)). The properties of the elastic foundation are physically derived and account for the weave effect, the support provided by the adjacent layers, and the properties of matrix and transverse tows. Two cases of support, provided by adjacent layers, are considered: IP and OP (Fig. 7.18(b) and (c). The latter define practical limits of support that any layer can have within a laminate, where adjacent layers are randomly shifted (Fig. 7.18(a)). Compressive failure was assumed to occur when the failure of the tows was detected using LaRC05 . The two cases of support define upper and lower bounds for the compressive strength, enabling not only the strength of the material to be estimated but also its variance to be accessed. The results obtained showed good agreement with experiments Fig. 7.20(c)).
7.20 Analytical model description and comparison between analytical and experimental results obtained for a 2 × 2 twill carbon-epoxy composite . (a) Analytical model of 2 × 2 twill reduced unit cell. (b) Loads applied to an infinitesimal element of the tow. The elastic foundation provides normal and torsional support, p and τ, respectively. (c) Comparison between analytical and experimental results for the compressive failure strength.
The finite element method (FEM) has been extensively used to study the mechanical properties and failure of woven composites. Typically, the finite element model of a representative region is made at the meso-scale, distinguishing between tows and matrix (e.g. Figure 7.21(a)). One of the main advantages of the FEM is the possibility of obtaining an accurate and complete stress–strain field at the constituent level. Moreover, the FEM is also generally applicable; any weave can be modelled. Traditionally, failure is modelled through a nonlinear analysis that couples a damage progression scheme, to capture the nonlinear response of tows and/or matrix prior to failure, and failure criteria applied at the constituent level.
7.21 Finite element model used comparison between numerical and experimental results. (a) Reduced unit cell of a 2 × 2 twill composite : 3D view of the tows without matrix (top), 2D view of the mesh including matrix (bottom). (b) Comparison between the numerical and experimental results obtained .
Few works in the literature show compressive failure predictions . The majority focus on the tensile failure prediction [52–56]. Recently, numerical results for the compressive strength of a 2 × 2 twill carbon-epoxy composite have been presented . The numerical model used consisted of a reduced unit cell of a 2 × 2 twill weave (Fig. 7.21(a)). Tows were modelled as an elastic orthotropic material, with the material orientations following the tow central path. The matrix was assumed to be an elastoplastic isotropic material. Its plastic response was modelled using a linear Drucker–Prager model with hardening. Additionally, the possibility of intra-ply delamination was accounted for through the definition of cohesive contact at the interface between tows and matrix. Finally, failure was assumed to occur after failure within the tows was detected using LaRC05 .
Periodic boundary conditions were used to apply the loading and define two cases of out-of-plane support: IP and OP (Fig. 7.18(b), and (c), respectively). As mentioned previously, the latter define practical limits of support that any layer can have within a laminate, where adjacent layers are randomly shifted (Fig. 7.18(a)). Using a similar approach to that used in Ref. , described previously, the two cases of support define bounds for the compressive strength, enabling the strength of the material and its expected variance to be estimated. Analysing Fig. 7.21(b), it is possible to conclude that the numerical model predicts accurately the compressive failure strength. The constitutive response predicted also shows good agreement; however, the nonlinear response of the material close to failure is slightly under-estimated.
Experimental results show that, under compressive loading, kinking is the predominant failure mechanism responsible for the failure of the load-aligned tows. Additionally, also intra- and inter-ply delamination, transverse tow cracking and matrix cracking can be observed. The load-aligned tows behave as structural elements at the reinforcement level. Therefore, it is natural that the damage morphology is affected by the weave architecture/geometry and stacking.
To capture the features identified experimentally, it is necessary to explicitly model the internal reinforcement. Additionally, in 2D woven composites, variables that strongly affect failure can vary significantly and in a random fashion, e.g. stacking. These variations should also be taken into account when modelling. Therefore, it is desirable that the models used to predict failure provide not only an estimate of the most likely failure value, but also its expected variance. Finite element and analytical modelling can be used successfully to predict failure of 2D woven composites. Besides their capability to predict failure of existing materials, they have a great potential in the development and optimisation of new materials. Rather than being regarded as mutually exclusive, the two approaches (analytical and numerical) should be used in a synergistic fashion to help improve accuracy and generalise their application.
Failure criteria developed for UD composites are often applied to predict the failure of 2D woven composites. Experimental results indicate that, to capture the physics of the compressive failure of 2D woven composites, the weave architecture needs to be considered, both at lamina and laminate level. Therefore, it is important to highlight that use of failure criteria for UD to predict the failure of 2D woven composites should be practised with caution.
Motivated both by environmental pressure and economic opportunities, a new class of composites is currently under development: recycled carbon fibre composites [59, 60]. In these materials, the reinforcement is directly obtained by reclaiming the carbon fibres from CFRP waste, using a thermochemical recycling process to remove the polymeric resin and release the fibres [61–64]. The quality of the recycled fibres is highly sensitive to the type of recycling process employed and its exact tuning, but retentions of mechanical properties over 90% are common for optimised conditions [65, 66]; the amount of residual resin left on the surface of recycled fibres is also generally small, although its effect may become pronounced (see Section 7.4.2) .
Several types of recycled CFRP (rCFRP) have been produced by re-impregnating recycled carbon fibres (rCFs) with new polymeric resins [68–71]. Although their mechanical performance is again largely sensitive to several factors – e.g. quality of the recycled fibres, matrix type, re-manufacturing process – many rCFRPs proved to be compatible with structural applications, as their specific properties surpass those of discontinuous glass-fibre composites and even those of structural aluminium alloys [67, 68, 71]. Consequently, several proof-of-concept rCFRP demonstrators have been produced, mainly applied to non-safety critical structures for the automotive and aircraft industries .
As rCFRPs establish themselves as greener alternative materials for structural applications, more recent studies started focusing on the in-depth analysis of their mechanical response [67, 72, 73]; these studies have revealed very complex and unique microstructures and mechanical responses in the recyclates. Particularly, results from compressive testing of several rCFRPs have highlighted that, on the one hand, these materials are fundamentally different from their virgin precursors, and do require dedicated analyses and studies; on the other hand, rCFRPs can actually provide additional insight on the failure mechanisms previously described for UD and woven virgin composites.
The most common type of rCFRP features a randomly oriented discontinuous architecture (Fig. 7.22) [68, 71, 74]. As in the corresponding type of virgin fibre composites, the reinforcement in these recyclates is unstructured – in contrast to the UD and woven CFRPs analysed in Sections 7.2 and 7.3 – and characterised by statistical distributions of fibre length and orientation; these vary considerably for different recycling and re-manufacturing processes.
7.22 Recycled composite with a multiscale structure consisting of fibre bundles in a short-fibre-reinforced matrix (from Ref. ).
A distinct feature of short-fibre rCFRPs is the presence of fibre bundles (highlighted in Fig. 7.22) [67, 74]; these are structured groups of aligned fibres, held together by residual matrix not completely removed during the recycling process. The size and number of bundles depends on the architecture of the virgin material and specific recycling and re-manufacturing conditions, but they generally confer a multiscale character to the reinforcement in rCFRPs.
The compressive failure of recycled composites with such unstructured and multiscale architecture is complex, as distinct mechanisms tend to appear in the dispersed phases and in the neighbourhood of fibre bundles. Only a few studies are currently available, all focusing on rCFRPs with aerospace-graded fibres recycled by pyrolysis and re-impregnated with epoxy matrices; typical fibre volume contents in these composites are approximately 30% .
In areas with no bundles (Fig. 7.23(a), (b)), a fracture plane starts forming at low angles (<20 °) and then rotates up to ~54 ° through plastic shear deformation of the matrix. In early states, the failure morphology presents considerable similarities to fibre kinking – namely the localised material rotation with a narrow shear band, oriented at an initially small but progressively increasing angle. However, the microstructures of this rCFRP and a UD composite are completely different. The lower level of matrix confinement and the unstructured fibre architecture in the recyclate make it unlikely that the initiation of such shear band is due to initial fibre misalignments and consequent matrix shearing, as generally considered for UD composites. In the rCFRP case, the shear band seems to develop and propagate from the matrix (shear banding is a known compressive failure mode of many unreinforced polymers), forcing the fibres to rotate locally. The higher band inclination at final failure in the recyclates, when compared to longitudinally compressed UD composites (for which the typical orientation is β ≤ 40 °), supports the existence of a locking mechanisms in the latter, due to matrix confinement between fibres within the kink band; this confinement is practically non-existent in the rCFRP’s shear band, which is therefore allowed to rotate more freely up to higher angles.
7.23 Compressive failure of short-fibre rCFRPs with fibre bundles . (a) Shear band at initial stage (β ≈ 20 °). (b) Shear band at final failure (β ≈ 54 °). (c) Bending of an isolated fibre bundle. (d) Kink band in a supported fibre bundle
In areas with fibre bundles aligned with the loading direction, compressive failure resembles that of tows in woven composites, as described in Section 7.3.1. Isolated bundles (Fig. 7.23(c)) fail under bending, producing a similar morphology to that observed for the in-phase woven composite (Fig. 7.19(b)); conversely, longitudinal bundles adjacent to transversely oriented ones fail by fibre kinking (Fig. 7.23(d)), as seen before in randomly stacked woven composites (Fig. 7.19(a)). As in woven composites, the compressive failure mechanisms of longitudinal bundles in recycled composites are highly dependent on the support provided by the adjacent material: strongly supported bundles develop narrow kink bands, while softer surroundings favour less localised bending of bundles.
End-of-shelf-life CFRP prepreg rolls offer the possibility of recycling the fibres while maintaining the weave architecture; re-impregnating this recycled weave with fresh resin therefore produces recycled composites with a structured architecture, mimicking that of the virgin CFRP (vCFRP) precursor. These woven rCFRPs offer clear advantages over the short fibre recyclates presented in Section 7.4.2, as the continuous fibre form and the higher reinforcement contents greatly improve mechanical performance; this has recently triggered the use of woven rCFRP in a prototype for an environmentally friendly racing car .
In addition, woven rCFRPs offer the possibility to study the effect of fibre properties on the mechanical performance of a woven composite: by tuning the recycling conditions, fibre strength can be either fully recovered or severely downgraded, while keeping all other micromechanical parameters unaffected. This motivated the manufacture of recycled composites from the virgin 5H woven satin previously analysed in Section 7.3: samples of out-of-date prepreg were recycled under different pyrolysis conditions, and re-impregnated with the same epoxy resin present in the virgin material; both virgin and recycled materials were fully characterised at the filament and composite levels .
The most aggressive reclamation cycle yielded recycled fibres with only 25% of the tensile strength of the virgin fibres, although the stiffness . remained statistically unchanged (Fig. 7.24(a)). The corresponding recycled composite, when tested under tension, evidenced a direct effect of the fibre mechanical properties on the macro response: the tensile modulus of the rCFRP approached that of the vCFRP, while the tensile strength of the recyclate was near 25% of the virgin precursor (Fig. 7.24(b)). However, under compression, the performance of the recycled composite was statistically equal to that of the vCFRP, fully recovering both stiffness and strength (Fig. 7.24(c)); in addition, the morphology of compressive failure in the rCFRP (Fig. 7.24(d)) was remarkably similar to that of the virgin material (Fig. 7.19(a)): both show kink bands with identical geometry, and cracking of transverse tows.
7.24 Mechanical response of a woven rCFRP (mechanical properties are relative to virgin material): the compressive performance at the recycled-composite level is shown to be insensitive to fibre strength degradation, which occurred in the more aggressive recycling conditions. (a) Recycled carbon fibre properties. (b) Recycled CFRP tensile properties. (c) Recycled CFRP compressive properties. (d) Morphology of compressive failure.
Altogether, these results show that the tensile strength of carbon fibres does not play a role in the compressive failure of woven composites, nor in the formation of kink bands. This provides additional support to fibre-kinking models based on failure of the resin or fibre-matrix interface (as presented in Section 7.2.3).
This section introduced some experimental studies on the compressive failure of several recycled CFRPs with distinct reinforcement architectures. It has been shown that, while the mechanical response of the recyclates is extremely complex and diverse failure modes have been found for the different architectures, these novel materials can actually provide additional insight on failure mechanisms observed in the more common UD or woven virgin composites.
Compressive failure of discontinuous recycled composites (Section 7.4.2) reflects the complexity of their multiscale architecture. Failure occurs by shear banding, although damage morphology depends on the local microstructure. Similarities to failure of UD and woven composites support some of the modelling approaches developed for the latter, namely the importance of resin shearing in fibre kinking and the effect of the adjacent support tows in woven composites.
By testing woven recycled composites under compression (Section 7.4.3) it was found that, as long as the architecture of the virgin material is retained, the compressive strength at the macroscale is independent of the microscale strength of the individual filaments. Kink bands of similar geometries are also found regardless of single fibre strength, which further validates kinking models governed by resin/interfacial properties.
Although recycled CFRPs are still under development, there are strong indications that they will succeed as environmentally friendly and high performance materials . A key aspect to support their reintroduction into (non-critical) structures is the development of specific design tools for the recyclates, for which a deep understanding of their micromechanics is fundamental. Different materials from the ones reviewed here will be developed as processes are further optimised, so the mechanical analysis and modelling of recycled composites will surely become an extremely active field of research in the near future.
This chapter presented experimental and micromechanical FE programmes which were conducted with the aim of developing analytical models for longitudinal compressive failure in composites. Predictions from such models are shown to compare favourably with the numerical and experimental results. The existence and importance of a shear-driven fibre failure mode under longitudinal compression is highlighted, as it is shown to be critical for explaining different trends observed in experimental failure envelopes. Woven composites show some similarities to UD composites in their longitudinal compressive failure modes, but also show some unique features such as the dependence of the failure process on the exact nesting between the different plies. Knowledge and experience gathered during the past decades in analysing longitudinal compressive failure of advanced composites appear to be very valuable for the analysis of novel types of composites, such as recycled composites. The latter can have a wide range of architectures, from short random fibres and bundles, to woven, but the micromechanical features observed under longitudinal compression show similarities to those in virgin composites.
Different parts of this work were funded by EPSRC, DSTL, Airbus and Renault F1 (EP/E0Z3169/1), as well as the Portuguese Foundation for Science and Technology (FCT projects SFRH/BD/36636/2007 and SFRH/B D/44051/2008).
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