Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications

Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications Filipe Ribeiro1, José Sena-Cruz2, Fernando G. Branco3, Eduardo Júlio4, Fernando Castro5 1 PhD Student, CERIS, Instituto Superior Técnico, University of Lisbon, Portugal. E-mail: [email protected] 2 Associate Professor, ISISE, Department of Civil Engineering, University of Minho, Portugal. E-mail: [email protected] *Corresponding Author 3 Assistant Professor, ISISE, Department of Civil Engineering, University of Coimbra, Portugal. E-mail: [email protected].pt 4 Full Professor, CERIS, Instituto Superior Técnico, University of Lisbon, Portugal. E-mail: [email protected] 5 Full Professor, CT2M, Department of Mechanical Engineering, University of Minho, Portugal. E-mail: [email protected] Abstract The performance of a progressive damage model in quantitative hybrid effect prediction of a comprehensive set of different 16 unidirectional interlayer (layer-by-layer) hybrid composites was assessed. Composites, produced by the hand lay-up method, made out of 4 different commercially available dry unidirectional fabric materials, namely high-modulus carbon, standard carbon, E-glass and basalt were tested. Tensile tests on single fibres were performed in order to determine their Weibull strength distribution parameters, which were used as inputs of the progressive damage model. Reasonably good agreement between analytical and experimental hybrid effect results was obtained, which allowed to estimate satisfactorily the reference strengths of the unidirectional low strain composite materials. Next, an existing analytical model for the simulation of stress-strain curve of hybrid composites was adapted to contemplate the hybrid effect, which allowed to predict the following properties of unidirectional hybrid combinations: ‘yield’ stress (or pseudo-yield stress), pseudo-ductile strain, and strength. It was verified as well that predictions of the three properties referred to were in close agreement with test results. Finally, damage mode maps were used in the analysis of these properties and, furthermore, of the hybrid effect and the elastic modulus of hybrid combinations. Keywords Hybrid composites, Hybrid effect, Analytical modelling Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. Introduction The linear elastic behaviour up to the point of sudden brittle failure, without sufficient warning and residual integrity of the traditional unidirectional (UD) Fibre Reinforced Polymers (FRP) composite materials, leads to limitations in the full exploitation of their great inherent mechanical advantages, namely the high tensile strength due to conservative safety design limits 1, 2. For this reason, the unfavourable failure characteristic of these materials restricts the spread of their application. In this way, the possibility to promote a gradual failure to the composites, improving their safety and maintaining their mechanical virtues simultaneously, has a tremendous interest for different industries, in particular for civil engineering, in which ductile materials are required in several applications (e.g. development of reinforcing bars for RC structures, externally bonded strengthening solutions for RC structures, pultruded profiles for new structures, and cables for long-span bridges). In fact, the possibility of avoiding tensile catastrophic failure with composites entirely constituted by brittle materials is one of the major advantages of hybridisation, since the latter can effectively contribute to increase structural safety. This is true for different industries, but it has particular interest for civil engineering. In this industry, it is common to apply composites as reinforcing bars for RC structures or as externally bonded strengthening solutions for reinforcing concrete (RC) structures. As it is known, RC has the potential of resisting significant tensile stresses, unlike plain concrete, since the reinforcing steel bars provide ductility to the concrete RC members that otherwise would exhibit a brittle behaviour. In practical terms, this implies that, if a properly reinforcing concrete element were to fail in tension, then such a failure would, fortunately, be preceded by large displacement caused by the yielding of steel reinforcing bars, thereby giving ample warning of the impending collapse. Thus, it is seem seen with great interest the possibility of applying hybrid composite (pseudo-ductile) on concrete elements (fragile). As it is known, composite materials have superior mechanical strength advantage and they have better potential durability when compared with steel. For this reason, their use may provide more cost-effective solutions in civil engineering applications. Hybridisation, defined as the incorporation of two fibre types with different strain failures, usually designated as Low Strain (LS) and High Strain (HS) fibres, within the same polymeric matrix 3, allows overcoming the lack of ductility. With this innovative solution, it is possible to achieve a mechanical non-linear and non-catastrophic behaviour characterized by presenting a flat-topped stress-strain curve in monotonic tensile tests. This desired behaviour is reached by selecting appropriate relative thickness of the involved materials (i.e. proportion of the LS to HS material layers) and absolute thickness of the LS material layers. It is important to note that achieving non-catastrophic behaviour is possible with some configuration of UD hybrid composites, by selecting appropriate relative thickness of the involved materials (i.e. proportion of the LS to HS material layers) and absolute thickness of the LS material layers. However, if the hybrid configuration is not carefully designed, because of the delamination propagation, the hybrid composite may break suddenly. Additionally, it can also shows a lower strength than the individual constituents. Non-catastrophic behaviour hybrid composites is not repeatable on subsequent unloadings/reloadings. In this context, this behaviour is known as pseudo-ductile 4, 5. Pseudoductile behaviour is characterized by fragmentation of the LS fibres and dispersed delamination of the LS fibres fragments from the undamaged high strain HS fibres. In addition to the potential to introduce pseudo-ductility to the UD composite materials, hybridisation promotes synergies between the involved reinforcing materials, leading, for instance, to the increase (until 50% 5, 6) of the apparent failure strain of LS fibres. This phenomenon has been described as “hybrid effect” and it was reported, for the first time, in 1972, by Hayashi 7. Today, there is some controversy about the best way how to define the baseline tensile failure strain of a UD non-hybrid composite, against which, the strain at failure of the hybrid composite is compared in the determination of the hybrid effect. In standard tensile tests of UD non-hybrid composites, stress concentrations can arise where the load is applied 8, leading to the reduction of the baseline strain. This effect can lead to premature failures and may be responsible for some of the variability observed in tensile results, published worldwide. It should be noted that, according to standards (e.g. EN 527-5), clamping system shall not cause premature facture at the grips. However, the information about the failure mode is not referred to in many works. This leads to difficulties in interpreting the results. A potential specimen type to suppress premature failures Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. is presented in 8. However, the proposed specimen type is not yet widely widespread. Swolfs et al. 5 pointed out changes in three main mechanisms as cause of hybrid effect: (1) residual thermal stresses, (2) fracture propagation effects and (3) dynamic stress concentrations. Relatively to the first change, in a more recent work, Sowlfs et al. 9 state that using representative thermal expansion coefficients and longitudinal Young's moduli of fibres, the influence of residual thermal stresses in hybrid effect is small for carbon/glass hybrid composites. Wisnom et al. 8 supported the previous view, mentioning that a low effect of thermal residual stresses would be expected in UD hybrid composites, where stresses are driven by the difference in fibre expansion coefficients rather than by matrix contraction. Relatively to the second change, it is possible to understand that hybridisation can modify the stress concentrations and stress recovery at a broken fibre due to the presence of neighbouring fibres with different stiffness 10. In fact, it is believed that substantial increase in strain of the LS fibres is caused by the restraint from the adjacent HS fibres, which inhibits the formation of broken clusters of LS material 8. Relatively to the third change, it has been poorly investigated in the past two decades 5, 8. Finally, in addition to the 3 main changes cited before, the size effect has also been shown to influence the hybrid effect 6, 8, 9. This fact is understandable because, for a constant sample size, the number of LS fibres is reduced by the hybridisation, leading to lower probability of finding a flaw and, consequently, to superior strains at the failure of LS fibres in hybrid composites. Nevertheless, the magnitude of the size effect is not quantified 9. Over time, different analytical models to predict the mechanical response of UD hybrid composites have been developed. Zweben 11, in 1977, extended a previous developed shear lag model for UD non-hybrid composites. This model assumes that fibres carry all the axial load and the matrix only the shear load. A strain concentration factor is responsible to increase the stress in the HS fibre next to a single LS broken fibre. It is assumed that a broken LS fibre locally loses its load transfer capacity over a certain length, by the definition of an ineffective length. Later, Fukuda 12, in 1983, improved Zweben’s model, introducing more accurate stress concentration factors and ineffective lengths and turning the model independent to the ratio of failure strains between fibres. One of the most relevant disadvantages of the models of Zweben 11 and Fukuda 12 is that they consider a fixed ratio of LS over HS fibres, which means that it is not possible to check the influence of the variation of LS fibres relative volume fraction (vol%) with these models. This parameter is a crucial factor on mechanical hybrid response 6, 9, 13. In last years, Global Load Sharing (GLS) theory, developed by Curtin 14, 15 and expanded by Hui et al. 16 for UD non-hybrid composites, has been adapted for UD hybrid composites 9, 17, 18. GLS incorporates the mechanics and statistics of fibre fragmentation and assumes that the stress dropped by a broken fibre is redistributed equally to all other fibres in the plane of the break 17. Analytical models based on GLS theory, sometimes referred to as Progressive Damage Models (PDMs) 19, should be able to reproduce the on-axis non-linear behaviour of a UD composites, where the mechanical properties are fibredominated. Although the GLS theory omits many real phenomena, such as fragmentation, local load sharing (stress concentrations), size effects, delamination between composite layers and fibre dispersion, it remains a very useful tool for exploring the effect of constituent properties on the composite performance 17. In fact, if the shear yield strength of the matrix is sufficiently low, then the local stress concentrations cannot be too large and the stress must be redistributed over a large number of fibres 15. Given the analytical nature of the model, there is the advantage of exploring rapidly the hybrid tensile response of different combinations. An extensive revision about GLS theory can be found in 15, 17, 19. Swolfs et al. 9 applied GLS theory in a parametric study of hybrid effect. The developed model allowed the prediction of the hybrid effect of carbon/glass combination. The influence of several factors on the hybrid effect was evaluated, namely the Weibull modulus (see the definition in Weibull fibre strength distribution (input data) section) of carbon fibres and glass fibres, the failure strain ratio, the stiffness ratio and the strength ratio between the involved fibres. It was concluded that hybrid effect is mainly affected by two of the referred to factors: the Weibull modulus of carbon fibres and the stiffness ratio between the fibres. Furthermore, in terms of the strength predictions, it was concluded that the GLS model essentially follows the bilinear rule-of-mixtures (as defined in 5, 20-23). Rajan and Curtin 17 used as well GLS model to study the tensile response of different UD hybrid combinations of continuous or discontinuous fibres. The analytical model predictions were supported by experimental results obtained in 24. They concluded that using discontinuous LS fibres improves hybrid composite performance, because such fibres fragment more gracefully over a wide range of strain. However, quantitative Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. comparisons with experimental results were not presented. Tavares et al. 18 extend a PDM, initially developed by Turon et al. 19 for UD non-hybrid composites, to UD hybrid composites. An analytical parametric study was performed analysing essentially the influence of the vol% of the constituent materials (3 carbon types and 1 alkali resistant glass) on the tensile response of the resulting hybrid combinations. Through two different models (one that takes into account only the statistical strength distribution of fibre and another that, in addition, considers the influence of the shear yield strength of the matrix) it was possible to conclude that the matrix–fibre interface lead to significant differences in the tensile response. However, a proper justification to this phenomenon (or the identification of pattern) was not reported in the paper. Despite great progress achieved in last studies with GLS models in hybrid composite, an experimental quantitative validation of fitness of the hybrid effect prediction hasn’t been carried out yet consistently 17. Research in hybrid FRP composites for civil engineering application dates back to the 1990s. At that time, the investigation has been fundamentally focused in the development of three main systems: (i) reinforcing bars for reinforced concrete (RC) structures; (ii) externally bonded strengthening for RC structures, and (iii) pultruded profiles for new structures. More recently, some work has also appeared on the development of cables for long-span bridges. The main motivation for the development of such systems has been the interest by their mechanical performance, i.e., the search for non-abrupt failures. As it is known, large structural deformations and significant load-carrying capacity prior to ultimate failure are critical in civil engineering structures, in which sudden failures are unacceptable. This is import because, in extreme event, it is expected that structures give forewarning of failure and prevent total collapse. As ultimate load is approached, some sections of the structure may reach their ultimate strength before others. In earthquake-resistant design, energy absorption by plastic deformations is necessary for ductile response of structures under seismic loads where load reversal and energy release occur. Particularly, in retrofitting applications, it is very common to apply composites made in-situ through the hand lay-up method, i.e., forming the composite on the surface of the structural member to be strengthened, using flexible dry fibre fabrics or sheets and liquid adhesives. This has proved to be a cost effective method and, in addition, the composite can adopt versatile shapes and sizes using simple tools. Despite its advantages, the hand lay-up method is dependent on the skill of the worker, and thus quality control plays a major role to ensure that defects and voids are avoided. According to the best practices suggested in the guidelines, e.g. 25, hand lay-up system shall be referred to the area of dry fibres only because, in this case, the final thickness of the composite cannot be deterministically estimated. Since this is a very common manufacturing method of composites in strengthening reinforced concrete structures, analytical models developed to hybrid composites must be validated for civil engineering applications, i.e., considering the specificities of the used the materials, production methods and guidelines. A first main goal of the present work is to demonstrate that GLS models can be used to estimate the hybrid effect of UD hybrid composites produced with commercial materials intended for civil engineering applications. The focus of this work is to analyse composites manufactured by the hand layup method. In this way, the performance of the analytical approach developed recently by Tavares et al. 18 was assessed using the experimental results published by the authors in 6. The statistical strength scatter parameters of the fibres were determined experimentally, through the single fibre tests, to be used as inputs of the model. Secondly, the model of Jalalvand et al. 13 was modified to take into account the hybrid effect predictions obtained with the model of Tavares et al. 18. The evolution of hybrid properties (such as hybrid effect, ‘yield’ stress, pseudo-ductile strain, elastic modulus and strength) was investigated as function of the configuration of UD hybrid composites by means of novel Damage Mode Maps (DMMs) presented in 26. Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. Modelling assumptions Progressive damage model for hybrid composites The PDM of Tavares et al. 18 aims at establishing the degradation of the tensile mechanical properties of the UD hybrid composites resulting from fibre fragmentation that leads to the stiffness-loss simulation of the two constituent reinforcing materials. Traditional brittle fibres used in composites are characterized by their strength scatter due to the presence of flaws introduced during processing and handling. In this way, strength distribution is contemplated in cited PDM, considering the two parameters of Weibull cumulative failure probability distribution, as described in next sections. Weibull fibre strength distribution (input data) Fibres are characterized by breaking as soon as the weakest link is overloaded 27. As most part of physical systems, successive observations of the strength do not produce exactly the same result. In this way, strength of a single fibre cannot be accurate modelled with one single average value. Usually, the strength variable of fibres is described by the Weibull distribution 28: 𝑃(𝜎)=1−𝑒𝑥𝑝(−(𝐿 𝐿0)(𝜎 𝜎0)𝑚) (1) where L is the characteristic gauge length, L0 the reference gauge length, σ the fibre strength, σ0 the Weibull scale parameter and m the Weibull modulus. The Weibull modulus m varies with the scatter around the average value: a large Weibull modulus indicates little scatter in the fibre strength. The reference length L0 is usually introduced just for convenience, because then L/L0 becomes a nondimensional quantity, and the Weibull scale parameter has the dimension of stress. The choice of L and L0 implies modification of σ0 parameter value. The Weibull distribution parameters are usually determined by testing individual fibres, as described in tensile single fibre test section. However, tensile tests of single fibres could be associated to some sources of error, such as specimen alignment with respect to the load direction (that leads to bending stresses in the fibre) and premature fibre failure within the adhesive or at the tabs 29. Furthermore, the extraction of fibres from a bundle may cause the weakest ones to fracture in the process, thus effectively censoring the fibre sample that undergoes the test 29. Today, there is a discussion about the best number of tests and the gauge length of specimen, that may influence the estimation of Weibull parameters 27. Swolfs et al. 30 published a detailed literature review about the experimental and statistical issues related with single fibre testing. The fibre preselection, clamping effects, number of tests, gauge length and fibre cross-sectional variation were addressed. It was concluded that, despite many detailed investigations by different researchers, measuring the Weibull distribution remains particularly difficult. Researchers have not yet agreed on the best testing practices. In the present work, as described in tensile single fibre test section, the test setup follows the guidelines laid down in ASTM D3379-75 31. In this work, the Weibull distribution parameters from single fibre tests, described in tensile single fibre test, were determined by the maximum likelihood method (MLM) 32, which is believed to be more accurate than least squares regression 27, 32. However, these values can be seen as susceptible of being altered, according to the sources of error previously reported. The chi-square goodness-of-fit test was used to check distributional assumptions. Model description The analytical approach proposed by Tavares et al. 18 is an adaptation for UD hybrid composites of the model developed by Turon et al. 19. Essentially, this approach assumes that the fibre fragmentation phenomena of single fibre fragmentation tests (a test in which a single fibre embedded in the matrix is loaded and the number of fibre breaks as a function of the applied load is monitored) has the same nature of the stiffness loss of the UD non-hybrid composite due to fibre breakage. In this way, exactly the same model could be used to predict both behaviours. A synopsis of the model and the underlying assumptions are described as follows. Ideally, the model considers the behaviour of a single brittle fibre embedded along the centre line of a Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. dog-bone-shaped matrix specimen, in which the matrix have a much larger cross-sectional area and larger strain to failure than the fibre material. As the strain is increased, the fibre fails progressively at randomly positioned flaws producing an increasing number of shorter fragments. The apparent stiffness of the system, matrix and fibre, decreases with the number of fibre breaks, due to their loss of ability to carry the load. Assuming that the influence of other damage modes (matrix cracking, delamination between plies, and debonding and subsequent pull-out between fibres and the matrix material) is neglected, the number of breaks at a given stress could be related to the apparent axial stiffness of the composite. Equation (2) gives the relationship between the mean number of breaks in a fibre, <N>, and the length L under a defined σ: ⟨𝑁⟩=𝐿 𝐿0(𝜎 𝜎0)𝑚 (2) When a fibre breaks, the load carried by the fibre drops down to zero at the position of the break, and the load is transferred by shear between the fibre and the matrix. This causes a stress redistribution near fibre break. The model assumes a linear increase of the axial stress from a fibre break, until a total recovery occurs at a certain distance from it. The length of this load recovery region, lex, is defined as: 𝑙𝑒𝑥 =𝑅𝑓 𝜏𝐸𝑓𝜀 2 (3) where Rf is the fibre radius, Ef is the elastic modulus of fibres, τ the matrix–fibre interfacial shear strength and ε the applied strain. The average fibre stress along the fibre, σm, can be computed by integrating the axial stress over all of the fibre fragments along the fibre length, resulting, after some simplifications (please see the details in 19), in the following closed-form analytical solution: where Λ is the number of breaks in a fibre per unit length: 𝛬=⟨𝑁⟩ 𝐿=1 𝐿0(𝜎 𝜎0)𝑚 (5) In case of hybrid composites, the developed model assumes that there are two ‘sub-composites’ in parallel, one for each reinforcing material, subjected to the same applied axial strain. The model defines how a fibre failure affects the stresses in the remaining intact fibres and assemble the mechanical behaviour of the constituents in the composite material. Given the tensile responses for the two pure composites using GLS (equation (4)), the stress-strain response for the hybrid composite can be described simply by considering the contribution of two materials, taking into account the vol% of the constituents. Damage in the matrix is not considered, since the tensile failure of composite materials is mainly a fibre dominated process 18: where 𝑙𝑒𝑥,𝐿, 𝛬𝐿, 𝐸𝐿,𝑓 and 𝑡𝐿 are the length load recovery region, the number of breaks in a fibre per unit length, the elastic modulus and the half thickness of a layer of the LS fibres and 𝑙𝑒𝑥,𝐻, 𝛬𝐻, 𝐸𝐻,𝑓 and 𝑡𝐻 are the length load recovery region, the number of breaks in a fibre per unit length, the elastic modulus and the half thickness of a layer of the HS fibres. Vf is the volume of fibres. In the present work, the PDM was used to estimate the hybrid effect, defined here as apparent failure strain enhancement of the LS fibre in a hybrid composite compared to the failure strain of a LS fibrereinforced non-hybrid composite. The failure strain of the LS fibres was considered as the strain at first local maximum point of the stress-strain diagram, see Figure 1. However, in some cases, especially in combination with low vol% of LS fibres, a clear local maximum point was impossible to achieve, since the analytical stress-strain diagrams presented only a global maximum point due to statistical issues. This fact is illustrated in the example of Figure 1 (a): contrary to the case with 50% of HM carbon fibres, in which it is possible to distinguish clearly two local maxima, in the case of 10% of LS fibres, only a global maximum is observable. The lower the volume of LS fibres, the less distinguishable is the first local maximum. This occurs because the contribution of LS fibres to the tensile response of the composite gradually decreases. Although a local maximum is unnoticeable in the analytical stress strain diagrams, certainly hybrid effect exists in combinations with very low vol% of LS fibres. This happens 𝜎𝑚(𝜀)=(1−𝑒−2𝑙𝑒𝑥𝛬 2𝑙𝑒𝑥𝛬+𝛬𝑙𝑒𝑥𝑒−𝐿𝛬)𝐸𝑓𝜀 (4) 𝜎(𝜀)=((1−𝑒−2𝑙𝑒𝑥,𝐿𝛬𝐿 2𝑙𝑒𝑥,𝐿𝛬𝐿+𝑙𝑒𝑥,𝐿𝛬𝐿𝑒−𝐿𝛬𝐿)𝐸𝐿,𝑓𝑉𝐿+(1−𝑒−2𝑙𝑒𝑥,𝐻𝛬𝐻 2𝑙𝑒𝑥,𝐻𝛬𝐻+𝑙𝑒𝑥,𝐻𝛬𝐻𝑒−𝐿𝛬𝐻)𝐸𝐻,𝑓𝑉𝐻)𝜀 (6) Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. because the most important factor that influences the hybrid effect is the restraint of clusters formation of break LS fibres due to the adjacent HS material. Evolution of hybrid properties (damage mode maps) The effect of the configuration (geometric and material parameters) of hybrid composites on different responses of UD hybrid composites can be clearly interpreted using a novel representation of the damage modes, known as damage mode maps (DMMs), recently developed by Jalalvand et al. 26. The DMMs are a very interesting graphical construction that facilitates interpretation and allows subsequent analysis and better visualization of the evolution of hybrid responses. DMMs have been used 1, 2, 26, 33 to analyse the evolution (through colormaps) of pseudo-ductile strain, defined as the strain between the final failure strain and the strain on the extrapolated initial slope line at the failure stress of the stress-strain diagram, and ‘yield’ stress, defined as the stress at first local maximum point of stress-strain diagram, of hybrid combinations (see Figure 2). In the cited works, the focus was to study the LS layer fragmentation and LS fragmentation and stable delamination damages modes in order to maximize the pseudo-ductile and ‘yield’ stress. In this way, the DMMs can easily be used as a design tool to achieve optimal hybrid composites with desired damage modes 2. DMMs divide all possible configurations of a UD hybrid composite into four possible damage modes: i. Premature HS failure, in which the whole hybrid specimen fails at first LS fracture; ii. Unstable delamination, in which delamination occurs at first LS fracture; iii. LS layer fragmentation, in which the energy released at first LS layer is not enough to drive unstable delamination, allowing that other fractures take place in the LS layer until saturation; iv. LS fragmentation and stable delamination in which the fragmented LS segments are pulled-out stably from the HS layers. In DMMs, the horizontal axis is the ratio between the thickness of the two fibre type layers and the vertical is the absolute thickness of the LS layer. The boundaries between different zones can be determined by equating any two of the three stress levels described in 13: (i) the stress level at which the first crack in the LS material occurs, σ@LF, (ii) the stress level at which delamination development occurs, σ@del, and (iii) stress level at which the high strain material fails, σ@HF, in accordance with the equations (7) to (9), respectively. 𝜎@𝐿𝐹 =𝑆𝐿𝛼𝛽+1 𝛼(𝛽+1) (7) 𝜎@𝑑𝑒𝑙 = 1 1+𝛽√(1+𝛼𝛽 𝛼𝛽 )(2𝐺𝐼𝐼𝐶𝐸𝐻 𝑡𝐻) (8) 𝜎@𝐻𝐹 = 1 (1+𝛽) 𝑆𝐻 𝐾𝑡√𝑉 𝑚𝐻 (9) where SL and SH are the reference strength of the LS and HS materials, α and β are the modulus and thickness ratios of the LS to HS fibre layers, GIIC is the mode II interlaminar fracture toughness of the interface between LS layers and HS layers of the hybrid composite, EH the elastic modulus of the HS fibres, mH is the Weibull strength distribution modulus of the HS fibre, SH is the reference strength of the HS material, Kt is the stress concentration factor in the high strain material and V is the volume of the specimen (free length × width × total fibre layer thickness). Hybrid configurations in which fragmentation in the LS material initiates before delamination should satisfy the σ@LF < σ@del condition, resulting after some simplifications in the following inequality: 𝑡𝐿<2𝐺𝐼𝐼𝐶𝐸𝐻 𝑆𝐿2𝛼(1−𝛾) (𝛼𝛾+1−𝛾) (10) where γ is defined as: 𝛾= 𝑡𝐿 𝑡𝐿+𝑡𝐻=𝛽 1+𝛽 (11) Hybrid configurations in which LS material fragmentation takes place before failure in the HS material should satisfy σ@LF < σ@HF condition, resulting after some simplifications in the following inequality: Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. √𝑡𝐿 𝑚<𝑆𝐻 𝐾𝑡𝑆𝐿(𝛼 𝛼𝛽+1)√𝛽 2𝑊𝐿 𝑚𝐻 (12) where W is the width and L is the free length of specimens. Hybrid configurations in which the HS material delamination stress failure stress, σ@HF > σ@del, delamination propagation is expected before final failure, satisfying the next inequality: 𝑡𝐿(1 2−1 𝑚𝐻)> 𝛽−1 𝑚𝐻𝐾𝑡 𝑆𝐻√2𝑊𝐿 𝑚𝐻√2𝐺𝐼𝐼𝐶𝐸𝐻√1+𝛼𝛽 𝛼 (13) In all last models, SL is assumed as a constant mean value, not taking into account the hybrid effect variation as function of the vol% of LS fibres, which would greatly contribute to ‘yield’ stress and pseudo-ductile strain of hybrid composites. In the present work, an actual strength of the LS material, SL,a, was considered assuming the hybrid effect (computed according the PDM described in model description section). 𝑆𝐿,𝑎 =𝑆𝐿+(𝑆𝐿×𝑓𝐻𝐸(𝑉𝐿×100)) (14) where fHE is the hybrid effect a function of vol% of LS fibres. DMMs were used to analyse the evolution and to identify the trade-offs between different responses in all damages modes, namely hybrid effect, ‘yield’ stress, pseudo-ductile strain, strength and elastic modulus. All the responses, with the exception of the elastic modulus (Ehybrid), were predicted with model of Jalalvand et al. 13, taking into account the equation (14). Ehybrid was predicted according to the rule of mixtures (see equation (15)) that has been proven to accurately estimate this property 6. 𝐸ℎ𝑦𝑏𝑟𝑖𝑑 =𝑉𝐿𝐸𝐿+𝑉𝐻𝐸𝐻+𝑉𝑀𝐸𝑀 (15) where VL, VH, VM, EL, EH, and EM are the volume and elastic modulus of the LS fibre, HS fibre and matrix, respectively. In the present work, the mechanical properties experimentally characterized of UD non-hybrid composites were used as input variables of model (15) (see Table 1). The exact volume of resin was not directly controlled during the manufacturing. Cross-sectional area of the composite was computed considering only the thickness of the dry fabrics, according to the usual practice of the hand lay-up method 25. In this way, EL and EH were considered the elastic modulus of LS and HS one layer composites, respectively. Therefore, the contribution of 𝑉𝑀𝐸𝑀was contemplated in VLEL and VHEH terms, leading to VL + VH = 1 and 𝑉𝑀𝐸𝑀=0. Experimental procedure Materials Commercial dry UD fabrics available for civil engineering applications, with a similar areal mass of 400 g/m2, were used in this work, namely UD HM carbon (S&P C-Sheet 640), ST carbon (S&P C-Sheet 240), E-glass (S&P G-sheet E 90/10) and basalt (Dalla Betta Group U400B-40-50-03). An epoxy-based material (S&P Resin Epoxy 55) was used as matrix for laminating the studied composites. According to the supplier, this epoxy has the following main properties 34: (i) a tensile strength of 35.8 MPa; (ii) a strain at the failure of 2.3%; and, (iii) an elastic modulus of 2.6 GPa. In Table 1 the density, areal mass, and fibre layer thickness (areal mass density divided by the volumetric mass density) of UD fabrics are presented. Tensile single fibre test For each dry fabric, a reasonable number of single fibres (see Table 1) were randomly taken from the dry fabrics and tested. The method used follows the guidelines laid down in ASTM D3379-75 31 for the Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. tensile testing of fibres. The measurements were performed in a Hounsfield H100KS universal testing machine with a load cell with 2.5 N maximum capacity (with an accuracy of ± 0.2% of applied force across load cell force range). In total, 200 fibres were individually mounted in the jig by means of a paper template with a fixed gauge length of 20 mm, see Figure 3. Fibre ends were bonded to the paper template by an ethyl cyanoacrylate-based adhesive. Then the tab ends were gripped in the jaws of the machine. Before the tensile tests were started, the paper template was cut across, so that just the fibre was fixed as a continuous length within the jig. The measurements were performed at a rate of 1.5 mm/min, until breakage occurred. For each fibre, records of applied load against extension were taken, and using an average mean diameter, determined through the analysis of microscopy images of fibres obtained with Scanning Electron Microscopy (SEM) (see Figure 4), the data registered were converted to stress-strain relationship. In Table 1 it is possible to observe that elastic modulus of single fibres is lower than the elastic modulus of cured composites. This is due to the fact that, in case of composites, the tensile properties were evaluated ignoring the contribution of the resin. This means that tensile strength was computed considering only the dry fabric thickness, which conducted to overestimation of the tensile strength and, consequently, large elastic modulus. Hybrid composites Hybrid composite of HM carbon/glass, ST carbon/glass, HM carbon/basalt, ST carbon/basalt and HM carbon/ST carbon up to 5 layers were studied. As resumed at Table 3, 16 series of hybrid composites results were compared with PDM predictions: 12 combinations with 3 reinforcing material layers and 6 combinations with 5 reinforcing material layers. The combinations of 3 symmetrical layers allowed to analyse the following approximate levels of LS fibre vol%: 0%, 33%, 66% and 100%. In addition, combinations with 5 layers allowed to analyse the following approximate levels of LS fibre vol%: 20%, 40% and 60%. Specimens with 5 layers were only tested on 2 hybrid combinations: HM carbon/glass and ST carbon/glass. Since each series was composed of 4 specimens, a total of 64 tests was carried out. It should be noted that the UD fabrics had slightly different thicknesses and, for this reason, the vol% before mentioned were corrected in the next sections, according to the corresponding thickness layer, assuming that vol% = 𝑡𝐿/(𝑡𝐿+𝑡𝐻)×100. The hybrid composite laminates were manufactured by hand lay-up method, according to the best practices suggested in the guidelines 25, following this protocol: (i) dry fabrics were cut into pieces with 250 mm at parallel direction of fibres and 80 mm at perpendicular direction of fibres; (ii) a layer of epoxy was applied over a teflon film and in the first fabric layer with a brush; (iii) the fabric layer was adjusted manually, and then a ribbed rigid roller was used to apply pressure, in order to force excess resin and air out of the composite; (iv) the above mentioned steps were repeated for further layers. The top of the laminate was left rough, in order to simulate real applications. All the samples were then cured at room temperature (20 ± 0.5ºC) for 40 days. Tensile tests The specimens of each series were obtained from the laminates using a diamond tipped wheel cutter. Tensile tests were performed according to ISO 527-5:2009 standard 35. Specimen dimensions were 250/150/15/[2.1-3.5]/[0.5-1.0] mm overall length/free length/width/total thickness/fibre layer thickness, respectively. Aluminium tabs of 50  15 mm2 were used at each end of the specimen to avoid gripping effects. A clip gauge with a gauge length of 100 mm (with a linear error, including hysteresis of 0.25%) was used. Tensile tests were carried out at room temperature on a universal testing machine (UTM) equipped with a 200 kN load cell (with a linear error less than 0.05% of full scale) and hydraulic grips. The specimens were held between grips of the UTM and extended (at a rate of 1 mm/min) up to failure. As stated before, cross-sectional area of the composite was computed considering only the thickness of Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. 23. Shan Y and Liao K. Environmental fatigue behavior and life prediction of unidirectional glass– carbon/epoxy hybrid composites. International Journal of Fatigue. 2002; 24: 847–859. 24. Yu H, Longana ML, Jalalvand M, Wisnom MR and Potter KD. Pseudo-ductility in intermingled carbon/glass hybrid composites with highly aligned discontinuous fibres. Composites: Part A 2015; 73: 35–44. 25. CNR-DT200. Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures. Advisory Committee on Techincal Recommendations for Construction, National Research Council, Rome, Italy. 2013. 26. Jalalvand M, Czél G and Wisnom MR. Parametric study of failure mechanisms and optimal configurations of pseudo-ductile thin-ply UD hybrid composites. Composites: Part A. 2015; 74: 123–131. 27. Swolfs Y, Verpoest I and Gorbatikh L. A review of input data and modelling assumptions in longitudinal strength models for unidirectional fibre-reinforced composites. Composite Structures. 2016; 150: 153–172. 28. Weibull W. A Statistical Distribution Function of Wide Applicability. 1951: 293-297. 29. Andersons J, Joffe R, Hojo M and Ochiai S. Glass fibre strength distribution determined by common experimental methods. Composites Science and Technology 2002; 62: 131–145. 30. Swolfs Y, Verpoest I and Gorbatikh L. Issues in strength models for unidirectional fibre-reinforced composites related to Weibull distributions, fibre packings and boundary effects. Composites Science and Technology 2015; 114: 42–49. 31. ASTM. D 3379 – 75 - Standard Test Method for Tensile Strength and Young’s Modulus for HighModulus Single-Filament Materials. 1989. 32. Ambrožič M and Gorjan L. Reliability of a Weibull analysis using the maximum-likelihood method. Journal of materials science. 2011; 46: 1862-1869. 33. Fotouhi M, Suwarta P, Jalalvand M, Czel G and Wisnom MR. Detection of fibre fracture and ply fragmentation in thin-ply UD carbon/glass hybrid laminates using acoustic emission. Composites: Part A 2016; 86: 66–76. 34. S&P. Technical Data Sheet S&P Resin 55. 2015. 35. ISO. 527-5 Plastics — Determination of tensile properties; Part 5: Test conditions for unidirectional fibre-reinforced plastic composites. EUROPEAN COMMITTEE FOR STANDARDIZATION. 2009. 36. MATLAB Release 2015b, The MathWorks, Inc., Natick, Massachusetts, United States. 37. Montgomery DC and Runger GC. Applied Statistics and Probability for Engineers. John Wiley & Sons, Inc ISBN-13 9781118539712. 2014. 38. Swolfs Y, McMeeking RM, Verpoest I and Gorbatikh L. The effect of fibre dispersion on initial failure strain and cluster development in unidirectional carbon/glass hybrid composites. Composites: Part A 2015; 69: 279–287. List of Tables Table 1 — Properties of the dry fabrics, fibres and cured composite materials determined experimentally. ....... 18 Table 2 — Weibull distribution parameters. ......................................................................................................... 19 Table 3 — Comparison between experimental and analytical results. ................................................................. 20 Table 1 — Properties of the dry fabrics, fibres and cured composite materials determined experimentally. Material ID Properties of the dry fabric, as reporter by the manufacturer Properties of the fibres (tested according to ASTM D3379) Properties of 1 ply composites 6* Density [g/m3] Areal mass [g/m2] Fibre layer thicknes s [mm/lay er] N. of samples Fibre diameter [µm] (CoV [%]) Elastic modulu s [GPa] (CoV [%]) Tensile strength [MPa] (CoV [%]) Strain at the failure [%] (CoV [%]) Elastic modulus [GPa] (CoV [%]) Tensile strength [MPa] (CoV [%]) Strain at the failure [%] (CoV [%]) Basalt (B) 2.67 420 0.157 50 18.14 (3.56) 61.41 (31.14) 1886.7 0 (40.79) 3.10 (27.73) 102.5 (15.46) 2244.2 (20.17) 2.46 (10.61) E-glass (G) 2.60 400 0.154 50 14.98 (16.25) 76.92 (27.97) 2662.0 6 (33.88) 3.72 (20.45) 81.6 (7.39) 1671.2 (8.59) 2.31 (3.78) ST carbon (C) 1.79 400 0.223 36 7.88 (5.15) 213.95 (43.36) 3920.6 7 (39.37) 1.38 (17.37) 231.3 (12.50) 2565.9 (10.18) 1.09 (8.81) HM carbon (CHM) 2.10 400 0.190 26 11.03 (6.66) 558.07 (24.67) 2934.2 4 (19.16) 0.53 (18.99) 624.1 (11.13) 1749.4 (24.39) 0.27 (19.61) Notes: *The tensile properties were computed considering only the thickness of the dry fabrics, according the recommendation suggested in the guidelines [31]. Elastic modulus is defined as the slope of stress-strain curve between the strains 0.0005 and 0.0025. Table 2 — Weibull distribution parameters. Material ID L0 [mm] L [mm] σ0 [MPa] m pvalue B 20 150 4593.8 3 2.6 1 0.549 6 G 20 150 5965.9 0 2.8 0 0.145 5 C 20 150 9353.4 4 2.6 8 0.026 7 CHM 20 150 4559.5 7 5.5 1 0.054 7 (Hypothetical) CHM* 20 150 2874.0 0 2.7 0 -- Note: *m value was assumed equal to the mean of the 3 other types of fibres because the elimination of the weakest fibres underestimates the strength scatter. Table 3 — Comparison between experimental and analytical results. Hybrid effect SL,a [MPa] Tensile streng Pseudo-ductile strain Combin ations Series ID Volu me of LS fibre [%] Experi mental [%] 6 PDM predicti on [%] Err or [% ] Experim ental [MPa] 6 Based on predict ed HE [MPa] Error [%] Experi mental [MPa] 6 Anal ytical [MPa ] Err or [%] Experim ental [%] 6 Analyt ical [%] Err or [% ] C/B 1C/1B/1C 74.0 -8.99 3.21 135 .7a 2289.9 2648.3 - 15.65 2191.4 (7.28) 2264. 6 -3.3 -- -- -- 1B/1C/1B 41.5 17.37 11.97 31. 1 2960.6 2873.0 2.96 1950.2 (7.51) 1938. 2 0.6 -- -- -- CHM/B 1CHM/1B/1 CHM 70.8 -12.95 1.44 111 .2a 1497.8 1774.6 - 18.48 1150.0 (14.10) 1341. 0 - 16. 6 -- -- -- 1B/1CHM/1 B 37.7 30.19 25.36 16. 0 2246.8 2193.0 2.39 1328.0 (10.74) 1125. 3 15. 3 2.04 (8.84) 1.80 11. 8 CHM/C 1CHM/1C/1 CHM 63.0 -1.50 8.69 680 .1a 1684.8 1901.4 - 12.84 1352.5 (5.10) 1458. 8 -7.9 -- -- -- 1C/1CHM/1 C 29.5 44.52 40.58 8.9 2434.0 2459.3 -1.04 1937.5 (6.79) 1431. 0 26. 1 0.44 (9.57) 0.64 - 45. 5 C/G 1C/1G/1C 74.3 -4.44 3.85 186 .6a 2405.0 2664.7 - 10.77 2176.9 (8.55) 2222. 0 -2.1 -- -- -- Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. 1G/3C/1G 68.5 -0.20 5.13 259 7.5a 2521.2 2697.5 -7.00 2216.0 (8.77) 2143. 7 3.3 -- -- -- 1G/1C/1G/1 C/1G 49.1 9.15 11.01 - 20. 4 2752.5 2848.4 -3.49 1776.3 (10.55) 1910. 4 -7.5 -- -- -- 1G/1C/1G 42.0 16.33 14.22 12. 9 2937.5 2930.8 0.23 1856.0 (5.67) 1830. 6 1.3 -- -- -- 2G/1C/2G 26.6 7.33 25.77 - 251 .7 2706.2 3227.1 - 19.25 1244.4 (1.74) 1693. 6 - 36. 1 -- -- -- CHM/ G 1CHM/1G/1 CHM 71.2 -7.07 2.17 130 .7a 1560.3 1787.4 - 14.56 1168.9 (19.49) 1339. 3 - 14. 6 -- -- -- 1G/3CHM/1 G 64.9 -14.09 2.89 120 .6a 1435.4 1800.0 - 25.40 1053.5 (10.14) 1251. 1 - 18. 8 -- -- -- 1G/1CHM/1 G/1CHM/1G 45.1 27.66 6.52 76. 4 2184.4 1863.5 14.69 1105.8 (9.18) 974.7 11. 9 -- -- -- 1G/1CHM/1 G 38.2 9.97 8.69 12. 8 1872.0 1901.4 -1.56 1054.7 (9.11) 879.1 16. 6 1.21 (23.32) 1.73 - 43. 0 2G/1CHM/2 G 23.6 21.94 19.57 10. 8 2059.5 2091.8 -1.56 1164.7 (14.47) 1004. 6 13. 7 1.4 (15.20) 1.66 - 18. 6 Note: aapparently very high relative errors were registered in cases that hybrid effect was negative. List of Figures Figure 1 — PDM predictions: zoomed stress–strain curves of HM carbon/glass combination and identification of hybrid effect (HE). ................................................................................................................................................ 24 Figure 2 — PDM predictions: identification of stress–strain curve with monotonic increase.Error! Bookmark not defined. Figure 3 — Illustration of nonlinear pseudo-ductility behaviour and definitions of ‘yield’ stress and pseudoductile strain (adapted from [1]). ........................................................................................................................... 25 Figure 4 — Tensile fibre test: (a) illustration of the test and (b) geometry of specimen (dimensions in mm). .... 26 Figure 5 — SEM images of the surface and diameter indication of: (a) glass fibres; (b) basalt fibres; (c) ST carbon and (d) HM carbon. ............................................................................................................................................... 27 Figure 6 — Tensile test: (a) illustration of the test and (b) geometry of specimen (dimensions in mm)....... Error! Bookmark not defined. Figure 7 — Cumulative Weibull fibre strength distribution for: (a) glass fibres; (b) basalt fibres; (c) ST carbon; (d) HM carbon. ...................................................................................................................................................... 28 Figure 8 —PDM strength predictions compared with the bilinear rule-of-mixtures as function of Weibull modulus and relative volume of HM carbon fibres. ............................................................................................................. 29 Figure 9 — Experimental mean hybrid effect results compared with analytical predictions. .............................. 30 Figure 10 — Damage mode map and distribution of hybrid effect of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ........... 31 Figure 11 — Predicted damage mode maps with the experimental configurations of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon composites. ................ 32 Figure 12 — Damage mode map and distribution of ‘yield’ stress of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ........... 33 Figure 13 — Damage mode map and distribution of pseudo-ductile strain of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)................................................................................................................................................................... 34 Figure 14 — Damage mode map and distribution of strength of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ............... 35 Figure 15 — Damage mode map and distribution of elastic modulus of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ........... 36 (a) (b) Figure 1 — PDM predictions: (a) identification of stress–strain curve with monotonic increase; (b) zoomed stress–strain curves of HM carbon/glass combination and identification of hybrid effect (HE). Figure 2 — Illustration of nonlinear pseudo-ductile behaviour and definitions of ‘yield’ stress and pseudoductile strain (adapted from 1). (a) (b) (c) (d) (e) Figure 9 — Predicted damage mode maps with the experimental configurations of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon composites. (a) (b) (c) (d) (e) Figure 10 — Damage mode map and distribution of ‘yield’ stress of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) (a) (b) (c) (d) (e) Figure 11 — Damage mode map and distribution of pseudo-ductile strain of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) (a) (b) (c) (d) (e) Figure 12 — Damage mode map and distribution of strength of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Ribeiro, F.; Sena-Cruz, J.; Branco, F.; Júlio, E.; Castro, F. (2020) “Analytical hybrid effect prediction and evolution of the tensile response of unidirectional hybrid FRP composites for civil engineering applications” Journal of Composite Materials, 54(22), 24. (a) (b) (c) (d) (e) Figure 13 — Damage mode map and distribution of elastic modulus of: (a) HM carbon/glass; (b) ST carbon/glass; (c) HM carbon/basalt; (d) ST carbon/basalt and (e) HM carbon/ST carbon hybrid composites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)