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Hybrid effect and pseudo-ductile behaviour of unidirectional interlayer hybrid FRP composites for civil engineering applications

Abstract An experimental study on the tensile stress-strain curves of interlayer (layer-by-layer) unidirectional hybrid FRP composites was conducted aiming at evaluating the corresponding hybrid effect and pseudo-ductility of this innovative solution. Different combinations of the following dry unidirectional fabric materials, also varying the number of layers, were adopted in tests: high-modulus carbon, standard carbon, E-glass, and basalt. The composites were produced layer-by-layer by hand lay-up method, using an epoxy-based resin as matrix. The results have shown a strain increase at failure of both standard carbon and high-modulus carbon fibres with the volume decrease of these materials in hybrid combinations. It was also concluded that combining high-modulus carbon with E-glass, high-modulus carbon with basalt, or high-modulus carbon with standard carbon can lead to very good pseudo-ductile tensile behaviour. Finally, it should be highlighted that an existing analytical model in the literature was satisfactorily adopted to predict the tensile response of these hybrid composites.


INTRODUCTION
Unidirectional (UD) Fibre Reinforced Polymers (FRP) composites are brittle materials, exhibiting a linear elastic behaviour up to failure. Therefore, structures made of these materials, although apparently without any problem, may fail abruptly [1]. This characteristic does not allow to take full advantage of FRP properties, namely the high tensile strength due to conservative design limits [2]. For this reason, to obtain composites with progressive failure behaviour ensuring safe, strain hardening, and meaningful ultimate tension strain are seen as priority goal by different industries [2], including civil engineering.
Hybridisation, i.e., the incorporation of two or more types of fibres within the same polymeric matrix [3], is an established approach to deal with the problem above mentioned, since this strategy promotes synergies between the adopted reinforcing materials, lessening their intrinsic disadvantages [4]. For instance, when submitted to uniaxial tension, Low Strain (LS) fibres fail earlier than High Strain (HS) fibres and this fracture behaviour can be used as a warning sign before the ultimate failure of the hybrid FRP composite [1,4].
Furthermore, it has been observed that hybridisation increases the apparent strain at LS fibres failure [5]. This phenomenon has been described as "hybrid effect" [6]. In the case of carbon/glass hybrid composites, the values for this effect are typically in the range of 10 to 50% [4]. Nowadays, however, there is some controversy about the hybrid effect definition because, in traditional uniaxial tensile testing configuration, stress concentration at the grips may cause premature composite failure, leading to an underestimation of the strain at the failure of the baseline LS material [7]. For this reason, these results should be critically interpreted.
Nevertheless, the most relevant advantage of hybrid composites is their gradual, and thus non-catastrophic, failure mode that has been registered in UD layer-by-layer configurations [2,8], when both the configuration and materials combination are appropriately selected. This is due to the load transfer between LS and HS layers, fragmentation (a damage process where multiple fractures take place) of the formers, followed by the stable delamination of the LS layers from the HS layers, close to the LS layer fractures, ending with the failure of the latter [1]. This behaviour is known as pseudo-ductility [1,4]. It should be stressed that the term 'pseudo-ductility' is used because it is possible to achieve a flat-topped stress-strain curve of monotonic tensile tests up to the failure of some unidirectional hybrid FRP composites.
The topic of hybrid composites has become a highly active research area in the 1970's and 1980's [3,5,[9][10][11][12][13][14][15][16]. Over the time, several literature reviews on this subject were published [3,4,16]. The study of hybrid composites was essentially motivated in the scope of the aerospace and automotive industries [3,4,17]. It has been demonstrated that hybrid composites have greater advantages over traditional composites. The vast majority proven to be a very efficient design tool for hybrid composites [27,28].
Cui and Tao [35] and Cheung and Tsang [36] conducted works on the development of hybrid composite reinforcing bars. In the design of these solutions four different reinforcing materials, namely carbon, aramid, glass, and steel, were simultaneously used. The resulting hybrid bars demonstrated pseudo-ductile behaviour, with a tensile strength of 644 MPa, a modulus of 140 GPa and an ultimate strain of circa 3%. A series of concrete beams reinforced with the proposed solution were tested and it was demonstrated that the beams had the ability to undergo large inelastic deformations. Pseudo-ductility was found to be similar to that of conventional steel-reinforced beams.
Grace et al. [38] develop a UD fabric composed of two types of carbon fibres and one type of glass fibres.
In this case, the pseudo-ductility of the composite was achieved through the combination of the different ultimate strain of each of the adopted types of fibres. In [39], the same authors further developed the initial concept by introducing fibres in the diagonal direction, thus enabling the use of the hybrid fabric for simultaneous flexural and shear strengthening of concrete beams. The last work resulted in one US patent [56].
Wu et al. [17] developed hybrid composites made of high-strength and high-modulus carbon sheets. The resulting solution was applied in the upgrading of pre-cracked RC beams. It was concluded that the hybrid composites allowed achieving the desired flexural stiffness, 'yielding' strength, and pseudo-ductility.
Several of these attempts (in the field of civil engineering) have been developed/applied without a complete understanding about the behaviour of hybrid composites at material level. In most works, the concept of pseudoductility was defined as the successive fractures of different (more than two) reinforcing materials and not as a result of the previously described phenomena of fragmentation and controlled delamination of LS fibres.
Moreover, with some exceptions [17,44,48,57,58], the hybrid effect has been ignored in this set of works and the factors that controlled the damage mode of the hybrid composites have not been clearly explained.
Nowadays, 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 the best practices suggested in the guidelines, e.g. [59], hand lay-up system shall be referred to the area of dry fibres only because, in this case, final thickness of the composite cannot be deterministically estimated [59].
Due to the above reasons, it is important to study the performance of hybrid composites produced through the hand lay-up method for civil engineering applications. In the context of analytical modelling, Jalalvand et al. [8] have proposed a model to predict with proper accuracy the tensile response of hybrid composites made of prepreg systems, cured at controlled conditions of pressure and temperature. In retrofitting and strengthening, resins are usually impregnated by hand into dry fabrics with curing times being governed by the environmental conditions. In fact, this is one of the most widely used processes for manufacturing FRP composites for structural engineering [60]. In this way, the availability of an analytical model to predict the tensile behaviour of hybrid composites, produced by hand lay-up method, is seen as a very important tool for the design of UD hybrid composites in civil engineering context.
The aim of this research is to investigate the tensile stress-strain responses of 16 different UD interlayer (layer-by-layer) hybrid composite combinations, made through the hand lay-up method, of different commercially available raw materials (fibres' packages + resin). Four dry UD fabric materials were used combined with epoxy resin, namely (i) high-modulus carbon, (ii) standard carbon, (iii) E-glass and (iv) basalt, in order to evaluate the hybrid effect and to achieve pseudo-ductility, fully exploiting the benefits of hybridisation. The hybrid effects and interlayer hybrid FRP composites for civil engineering applications." Construction & Building Materials, 171:871-890.
6 the information of the fibres used in other authors' works, published between 1974 and 2016, were collected with the objective of carrying out a statistical analysis. In this way, the data collection of Manders and Bader [13] and Swolfs et al. [4] was updated in this work. The analysis of the obtained experimental results was complemented with analytical modelling based on the approach developed by Jalalvand et al. [8] for hybrid composites.

Objectives
The main objective of the present work is to contribute to the knowledge on the performance of UD hybrid composites produced by the hand lay-up method. The following specific goals are envisaged: i.
To determine the influence of LS fibres relative volume (vol%) on the hybrid effect of different layer-bylayer hybrid composite combinations made through hand lay-up method; ii.
To understand which non-hybrid properties of the constituent materials influence most the hybrid effect, identifying the correlation between intrinsic mechanical properties of fibres and the obtained response (in the present work, according to general practice [4], failure strains of non-hybrid composite, obtained in tensile tests, were used as the baseline tensile failure strain to compute the hybrid effect); iii.
To evaluate the accuracy of the rule of mixtures (ROM) and of the bilinear ROM to predict respectively the elastic modulus and the tensile strength of the hybrid composites; iv.
To characterize the hybrid pseudo-ductile tensile behaviour; v.
To extend the analytical approach developed by Jalalvand et al. [8] to the present experimental program.
In Table 1 the density, areal mass, fibre layer thickness (areal mass density divided by the volumetric mass density) and the basic tensile properties of the mentioned materials are presented. The tensile properties of the fibres were determined according ASTM D3379-75 [65]. For each dry fabric, a large number of single fibres (see the details in Table 1) were randomly taken from the dry fabrics and tested in tension. The tests were carried out in a Hounsfield H100KS universal testing machine with a maximum load cell capacity of 2.5 N (with an accuracy of ± 0.2% of applied force across load cell force range). Fibres were individually assembled in the tensile jig by 7 means of a paper template with a fixed gauge length of 20 mm. Fibre ends were glued to the paper template by an ethyl cyanoacrylate-based adhesive. Then the tab ends were gripped in the jaws of the machine. The paper template was cut across, so that just the fibre was fixed as a continuous length within the jig, before starting the tensile tests.
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 Electronic Microscopy (SEM), the data were converted to stress against strain.
An epoxy-based material (S&P Resin Epoxy 55) was used as matrix for laminating the studied composites, as recommend by the supplier of three dry fabrics (high-modulus carbon, standard carbon and E-glass). Relatively to basalt fabric, the same resin was used since the corresponding supplier does not provide a package of fibres and resin. According to the supplier, this epoxy has the following main properties [66]: (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.
Each reinforcing material was labelled according to the information included in Table 1. In the present work, in case of composite materials, numbers placed after letters are used for indicating number of layers. The order that letters appear indicate the stacking sequence of the reinforcing materials.

Specimen manufacturing and test setup
The hybrid composite laminates were manufactured by hand lay-up method, following the best practices suggested in the guidelines [59]. Prior to the manufacturing, dry fabrics were cut into 250 mm  80 mm pieces. A Teflon film was used to avoid the adhesion of the produced composite laminate to the rigid base. The following protocol was used to obtain the laminates: (i) application of a layer of epoxy over the Teflon film with a brush; (ii) saturation of the fabric layer with epoxy resin; (iii) placement of the fabric over last layer, adjusting it manually; (iv) pressure application by means of a ribbed rigid roller, in order to expel both the epoxy resin excess and air in the composite, and also stretching the latter; and (iv) repetition of steps ii to iv for subsequent layers. The top of the laminate was left rough, simulating real applications. All the samples were then cured at room temperature (20 ± 0.5ºC) for 40 days.
The four specimens of each series were obtained from the laminates produced according to the protocol previously described, using a diamond tipped wheel cutter. Aluminium tabs of 50  15 mm 2 were used at each end of the specimen to try minimise 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, as shown in Figure 1. The specimens were held between grips of the UTM and extended (at a rate of 1 mm/min) up to failure.

Material combinations
In the present work, it was decided to perform single-factor experiments with several levels of LS fibres vol%. Symmetric specimens were adopted to test the hybrid combinations, in order to minimize load eccentricity and differential thermal contraction during the cure of the epoxy resin, ultimately leading to bending-stretching coupling, and thus causing undesirable warping [3]. Furthermore, in a way to try restrict the stress concentrations at the grips, LS layers were whenever possible sandwiched between HS layers, according to Wisnom et al. [7] conclusions.
All possible hybrid composite combinations until 5 layers were studied. In total, 16 series were considered: 10 combinations with 3 reinforcing material layers, and 6 combinations with 5 reinforcing material layers. Since each series was composed of 4 specimens, a total of 64 tests were performed. The combinations of 3 symmetrical layers allowed to analyse the following approximate levels of LS fibres vol%: 0%, 33%, 66% and 100%. In addition, combinations with 5 layers allowed to analyse the following approximate levels of LS fibres vol%: 20%, 40% and 60%. It should be noted that specimens with 5 layers were only tested on 2 hybrid combinations: HM carbon/glass and ST carbon/glass. As previously mentioned, the UD fabrics had slightly different nominal thicknesses and, for this reason, the relative volume of LS fibres (Vol% LS) was computed in the next sections, according to Equation (1): where tL is the half thickness of the LS layers and tH is the half thickness of the HS layers.
In Table 2 the layer ratio and the stacking sequence of the studied hybrid composite combinations are summarized. In addition to hybrid series, 8 series of non-hybrid composites were produced: half with a single layer of reinforcing material and other half with 3 layers of reinforcing material. Each series was composed of 4 specimens, totalling 32 specimens tested.
In the present work, the exact volume of resin was not directly controlled during the application and crosssectional area of the composite was computed considering only the thickness of the dry fabrics, according the recommendation suggested in the guideline [59]. In this way, mechanical proprieties of impregnated composite (elastic modulus and tensile stress) were computed considering the wet lay-up system similar to an equivalent system of only dry fabrics. However, in order to present an idea of geometric properties, all the composites were measured with a digital calliper (see Table 3).

2.5
Analytical models for hybrid composites

Elastic modulus
The longitudinal elastic modulus of the hybrid composites has been shown to follow the linear rule of mixtures (ROM) [4]. According to this model, the elastic modulus of the hybrid composite, Ehybrid, can be predicted as the sum of the contributions of the three constituents, given by equation (2): where VL, VH, VM, EL, EH, and EM are the volumetric fraction and elastic modulus of the LS fibres, HS fibres and matrix, respectively.
Phillips [14] and Kretsis [16] pointed that some deviations in the predictions of elastic modulus of hybrid composites by using ROM can only be explained by an incorrect use of this rule, namely due to an incorrect input of the volume fraction of reinforcing materials.
In the present work, the linear ROM was used to predict the elastic modulus of hybrid composites in order to check the volume and alignment of the reinforcing materials. To achieve this, the mechanical properties experimentally characterized of non-hybrid composites were used as input variables. The exact volume of resin was not directly controlled during the application and 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 [59].
In this way, EL and EH were considered the elastic modulus of LS and HS one layer composites, respectively.
Therefore, the contribution of was contemplated in VLEL and VHEH terms, leading to VL + VH = 1 and = 0.

Tensile strength
The tensile strength of the hybrid composites do not follow to linear ROM, e.g. [4,13,16,68,69] because if the volume fraction of HS fibres is appropriate when LS fibres fail, the load can be transferred to HS fibres until their final failure. Otherwise, the composite would fail prematurely. For this reason, some authors [13,16,70] have proposed a bilinear ROM (see Eq. (3)) to predict the tensile strength of hybrid composites, σhybrid.
where SL and SH are the reference strengths of the LS and HS one layer composites and εL is the strain at the failure of the non-hybrid LS composite.
Based on this model, if VH is lower than the critical value, Vcrit, the hybrid composite would fail prematurely.
On the contrary, if VH is higher than Vcrit, hybrid composites would keep their integrity up to the failure of HS fibres.
In the present work, the bilinear ROM model was used to evaluate the magnitude of predictions' errors. Vcrit was calculated by equating the two branches of equation (3), taking into account that VL + VH = 1, i.e., VL is equal to 1-VH:

Stress-strain curve
In an UD hybrid composite under uniaxial tension loading conditions, the first damage mode is always the failure of the LS fibres; however, the other following damage modes depend on the properties and configuration of reinforcing materials of the composite [27]. The analytical approach proposed by Jalalvand et al. [8] considers that four different damage modes may occur after the LS fibres failure: (i) premature HS failure, (ii) unstable delamination, (iii) LS layer fragmentation and (iv) LS fragmentation and stable delamination. For each hybrid configuration, three stress levels could be computed [8]: (i) the stress 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) the stress when the high strain material fails, σ@HF, in accordance with the equations (5) to (7), respectively.
where α and β are the modulus and thickness ratios of the LS to HS fibres, GIIC is the mode II interlaminar fracture toughness of the interface between LS layers and HS layers of the hybrid composite, mH is the Weibull strength distribution of the modulus of the HS fibres, 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).
Knowing the magnitude of all three possible stresses allows assessing their order of occurrence and, consecutively, the identification of the damage modes, according to Table 4. The details of the analytical approach are fully discussed in [8].
After the determination of the damage modes, it is possible to plot the stress-strain curve using the characteristic points given in Table 5. In the latter, Esat is the saturated modulus of the composite (according to equation (8)), εH is the strain at the failure of the HS fibres and ε@H-PS is the strain in the composite at the postsaturation phase when the high strain material fails (according equation (9)).
Since the model by Jalalvand et al. [8] does not consider the hybrid effect, the strain at the failure of LS materials in hybrid combination was assumed to be equal to the obtained experimental values (according to the method developed by the author), and SL was computed according to Hooke's law. In the present work, the definitions of 'yield' stress and pseudo-ductile strain suggested by Jalalvand et al. [27] were considered: the 'yield' stress is the stress at the point that response deviates from the initial linear elastic line, i.e., equal to σ@LF and the pseudo-ductile strain is defined as the extra strain between the final failure strain and the strain on the extrapolated initial slope line at the failure stress of the stress-strain diagram (see Figure 2).

Tensile properties of non-hybrid composites
In Figure 3, the dispersion of the obtained results and their mean values are plotted. It can be concluded that, in all cases, the change from 1 to 3 layers of reinforcing material promotes a reduction of the magnitude of the elastic modulus, tensile strength, and tensile strain at failure. The mean values of the tensile properties and their coefficient of variation (CoV) are presented in Table 6, for each series. For each reinforcing material, the t statistical test (t-test) was used to assess whether the mean values of two groups of tensile properties are statistically different from each other, with a significant level of 5%. The mean values that were significantly different are underlined in Table 6. The highest decreases were founded in glass and HM carbon composites: tensile strength and strain at the failure decreases 416.4 MPa (24.9%) and 675.5 MPa (38.6%) and 0.31% (13.4%) and 0.09% (33.3%), respectively. These decreases can be explained by two factors: (i) for one hand, it is well known that there is a size effect in tensile properties of reinforcing fibre due to the higher probability of finding a cluster of weaker fibre in a larger volume of material [7]; (ii) for other hand, in tensile tests, stress concentrations can be more predominate where the load is introduced. As expected, in the elastic modulus non-significant variations were registered in all cases.
In Table 6 is even possible to observe, that tensile strength, and consequently the elastic modulus, of cured composites are higher than the obtained values for single fibres. This is due to the fact that, in case of composites, the tensile properties were evaluated considering only the dry fabric thickness which conducted to overestimation of these properties. For other hand, the strain at failure of composites is lower than the one obtained for single fibres. This was expected because in UD composites fibres break as soon as the weakest link is overloaded. Broken fibre sheds load to the nearby fibres, subjecting them to stress concentrations. Stress concentrations increase the failure probability of the nearby fibres that will lead to the development of fibre break clusters and cause final composite failure [71]. Furthermore, in glass and basalt series the mechanical properties of epoxy could be predominant in the composite failure because the strain of the resin at failure is lower than the strain of fibres at failure.
In Table 6 the obtained failures modes of all specimens are also identified. Each failure mode was labelled according to the information included in ASTM D 3039/D 3039M standard [72]. Numbers placed after letters are used for indicating the number of specimens in which the same failure mode was obtained. As referred before, stress concentrations may be responsible for the variability observed in failure modes and lowering both the average strength and strain. Furthermore, layer overlap, in case of specimens with 3 layers, can lead to the occurrence of more emphasized size effects and different failure modes, such as delamination, that would cause more scatter. Therefore, an accurate way of measuring the strain at failure of non-hybrid composites should be further investigated. For this reason, a hypothetic increase on baseline strain of LS material would lead to a decrease on the values of hybrid effects obtained in the present work. Nevertheless, from Table 6 it is possible to observe that, for series 1C and 1CHM, 3 out of the 4 tested specimens have failed at gage length.

Elastic modulus and tensile strength
of reinforcing materials were computed as a function of their density and areal mass. The tensile strength was defined as the maximum value observed in the stress-strain curve. The results of 1 layer non-hybrid composites were used to serve as reference in the comparisons with the analytical predictions. Relatively to ROM, predictions showed a good agreement with the experimental results. The obtained relative errors varying between -14.5% and 9.6%. This magnitude of the error values is acceptable and it is in agreement with the bibliography [16]. For this reason, it is believed that in the present case there was not a significant deviation in fibres alignment. Therefore, it can be stated that ROM is a model that can be used as a quality control tool for hand lay-up hybrid composites, since it allows checking the volume and the alignment of the reinforcing materials used in this type of composites. were overlapped with bilinear ROM curves. In general, it is possible to distinguish between two types of behaviour: (i) in the combinations that included HM carbon fibres, a small tensile strength variation with increasing LS fibres vol% was registered, and (ii) in the combinations that included ST carbon fibres, a clear tensile strength increase with the increase in LS fibres vol% was observed. This is understandable, since HM carbon exhibits a low tensile strength and, therefore, it is not expectable to observe improvements in the tensile strength by increasing the volume of this material. An opposite behaviour is observed when ST carbon is used.
In the case of bilinear ROM predictions, deviations from the experimental results were also found, varying between -15.7% and 16.9%. In this way, the relative errors were higher than those obtained with ROM. These results were expected, since, as previously explained, the bilinear ROM does not consider delamination and hybrid effect phenomena [8,69]. In Figure 5 it is also possible to observe that there were 5 combinations located in the multiple facture zone: 2G/1CHM/2G, 1G/1CHM/1G, 1G/1CHM/1G/1CHM/1G, 1B/1CHM/1B and 1C/1CHM/1C. All these combinations had in common the use of the HM carbon fibres as LS fibres. In these cases, catastrophic failures were avoided. In the remaining cases, a catastrophic failure of the HS fibres occurred at the moment of LS fibres failure. In this way, the bilinear ROM was capable of predicting satisfactorily the occurrence of multiple fractures. This topic is further discussed in Section 3.2.3.

Hybrid effect
The hybrid effect was computed relatively to 1 layer non-hybrid composite results, according to the Equation (10): where is absolute variation of the strain at the failure of LS material obtained in hybrid and non-hybrid composites.
As previously mentioned, volumes of reinforcing materials were adjusted in accordance with their density and areal mass. Figure 6 shows the scatter diagrams of the obtained hybrid effects, their mean results and their 95% Fisher level of confidence intervals.
As expected, it was possible to observe that the reduction of the LS fibres vol% leads to a clear increase of the hybrid effect. In general, the hybrid effect varied between -14.1% and 44.5%. However, the hybrid effect increase was not linear. In all cases, it was possible to observe that above 60% of relative volume of LS fibres the hybrid effect was close to zero or even negative. As presented above, in non-hybrid composites the use of more layers of the same material caused the reduction of all the analysed tensile properties. The hybrid effect was negative in cases where 2 or 3 layers of LS fibres were used. It should be noted that, since failure strains of 1 layer non-hybrid composite were used as the baseline tensile failure strain to compute the hybrid effect, negative hybrid effects are possible. In fact, it was confirmed that negative hybrid effects never arise when comparisons are made with the results obtained with the 3-layer non-hybrid composites.
Several t-tests at a significance level of 5% were performed to compare all pairs of hybrid effect mean values. Relative to HM carbon/glass case, differences between the 3 initial levels of LS fibres vol% hybrid effect mean values were not significant. The same could be concluded for the last 2 levels. The analysis of the carbon/glass series results led to the same conclusion. Since in the remaining combinations of materials only two levels of LS fibres vol% were analysed, the previous conclusion was not refuted for these combinations either.
In order to understand if there were significant variations due to the replacement of glass with basalt material, t-tests were performed to compare the pairs of hybrid effect mean values between the combinations of HM carbon/glass, HM carbon/basalt, ST carbon/glass, and ST carbon/basalt. It can be concluded that the changes referred to did not conduct to significant differences in hybrid effect results, as it is shown in Figure 7. However, with 38.2% of HM carbon fibres relative volume (1G/1CHM/1G), a significant difference was achieved. From the analysis of Table 7 it can be seen that for the 1G/1CHM/1G combination the worst prediction of elastic modulus was achieved by ROM, indicating that the mentioned difference was probably promoted by some misalignment of the fibres.
The hybrid effects and the information of the fibres used in other authors' works, published between 1974 and 2016, were contemplated in the present work (see Table 8). Although the data collection was mainly focused on the interlayer configurations, the information of intralayer configurations presented by Chamis et al. [73] was also included, since it is one of the few works in which the hybrid effect with more than 70% of LS fibres relative volume was studied.
Associations between hybrid effect and material factors (such as SL, SH, EL, EH, εL and εH) were analysed by a Spearman's rank test using SPSS version 23 (IBM, New York). Additionally, the hybrid effect was also analysed as function of SL/SH, EL/EH and εL/εH ratios, SL-SH, EL-EH and εL-εH differences and a non-dimensional stiffness parameter, END, defined by equation (11). The END was first introduced by Swolfs et al. [25], who indicated that the hybrid effect depends on this parameter.

= (11)
Spearman's correlation coefficient, r, is a statistical measure of the "strength" of a monotonic relationship between paired data. In the present work, spearman's rank of data revealed that statistically significant correlations, at a significance level of 5% between the hybrid effect and mentioned variables, were achieved for the cases of SH, Vol% LS fibres and END. There was a weak negative correlation between hybrid effect and SH (r = -0.311).
On the other hand, moderately strong negative correlations exist between hybrid effect and Vol% LS fibres (r = -0.526) and END (r = -0.515).
The moderate relationships previously mentioned are plotted in Figure 8. The dispersion of results and the low Spearman's correlation coefficients obtained do not allow the suggestion of an appropriate model to describe the results. However, no linear trends are clearly observable in the presented diagrams. It is possible to see in Figure 8 that the results obtained in the present work are in agreement with those in the literature.

Failure modes
As mentioned before, multiple fractures were achieved in some hybrid configurations, according to bilinear ROM predictions (see Figure 5). Usually, multiple fractures in hybrid composites are characterized by 2 successive failures: the LS fibres fail firstly followed by the HS fibres. However, in 4 situations in this work, pseudo-ductile tensile responses with multiple fractures were observed with some combinations that included HM carbon, as it is shown in Figure 9. Two outlier results obtained in 1G/1CHM/1G and 1B/1CHM/1B combinations were ignored.
In the case of 2G/1CHM/2G, a mean 'yield' stress of 732.6 MPa and a mean pseudo-ductile strain of 1.4% were registered (see Figure 9 (a)). In 1C/1CHM/1C combination a mean 'yield' stress of 1504.5 MPa and a mean pseudo-ductile strain of 0.4% were observed (see Figure 9 (d)). The replacement of glass by basalt resulted in slightly different behaviours (see Figure 9 (b) and Figure 9 (c)): with basalt, higher pseudo-ductile strain and 'yield' stress were obtained. The combination with basalt led to a mean 'yield' stress of 1120.7 MPa and a mean pseudo-ductile strain of 2.0%, whereas the combination with glass yielded a mean 'yield' stress of 768.2 MPa and a mean pseudo-ductile strain of 1.2%. Furthermore, two different behaviours were observed: one with (see  In the HM carbon/glass combinations the fragmentation of the HM carbon and delamination could be observed visually during the tensile test due to the translucence of the glass. The specimens were initially black due to the HM carbon natural colour but, after fragmentation and delamination, light was reflected from the interface, and the specimens looked white. Figure 10 shows an example of the aspect of specimen in consecutive phases of the tensile test. The fragmentation of HM carbon is evident. Furthermore, it is possible to observe localised delamination around the carbon layer fractures that developed stably during test until saturation. It is noticed that each stress-strain curve peak, as it is identified in Figure 9 (a), corresponds to a crack of the HM carbon and localised delamination.

Prediction of stress-strain curves
In this section, the predicted stress-strain curves of all hybrid configurations studied in the present work, obtained with the model proposed by Jalalvand et al. [8], are compared with the corresponding experimental curves. One layer non-hybrid composite results were used as input variables. Since the model of Jalalvand et al. [8] is not able to predict the hybrid effect, the εL of the different material combinations was assumed to be equal to the experimental values obtained and SL was computed according to Hooke's law, a similar procedure was used in [8].  Table 4, was analytical achieved. The GIIC was assumed to be constant for the same material combinations. Weibull modulus was assumed to be equal to the value used by Jalalvand et al. [8], i.e., mH = 29.3. The value of the stress concentration factor was assumed constant for all of the specimens, Kt = 0.97. This value is slightly lower than the one used by Jalalvand et al. [8] but allowed the best predictions. All input data is shown in Table 9.
As it can be seen in Figure 11 to Figure 15, there is a good agreement between predictions and experiments. Analysing the curves, three groups of behaviours can be identified: (i) pseudo-ductile behaviours (the same that were discussed in Section 3.2.3), (ii) failure with two peaks (Figure 11 (c), Figure 11 (d) and Figure 14 (a)), and (iii) premature and abrupt failure of HS fibres (in the remaining cases). The chosen way to estimate the GIIC parameter (considering only configurations in which fragmentation and dispersed delamination damage mode occurred) allowed to estimate with good accuracy the remaining cases.
It is also possible to observe that, in the combinations with pseudo-ductile behaviours, the model was not capable of capturing the peaks in the 'flat-topped stress strain curve', since it considers that the fragmentation and delamination occurred consecutively and not simultaneously. In the 1C/1CHM/1C series, the predicted stressstrain curves was somehow conservative. This occurred because SL and SH input properties were probably underestimated because these properties were assumed equal to the experimental values obtained with non-hybrid specimens and there is always some variability in the constituents.
In the 1G/1CHM/1G/1CHM/1G and 1G/3CHM/1G series, the model predicted well the catastrophic delamination damage mode, but the prediction of the delamination branch was much higher than the one observed experimentally. This lack of precision is probably related to some overestimation of GIIC in these cases.
In the case of 1B/1C/1B series, the volume proportion of the constituent materials was between premature failure of HS fibres and catastrophic delamination damage mode. For this reason, the model was not capable of predicting the complete tensile response. A 20% increase in ST carbon thickness, keeping the same volume proportion between the reinforcing materials, was enough to get a correct prediction from the model.

CONCLUSIONS
The tensile behaviour of several layer-by-layer hybrid combinations has been investigated using experimental testing and analytical modelling. All the composites were made through the hand lamination of four different commercially available dry UD fabrics: HM carbon (CHM), ST carbon (C), E-glass (G) and basalt (B).
The following main observations and conclusions were drawn.
It was verified that hybrid effect depends not only on the vol% of LS fibres but also on the non-dimensional stiffness parameter (END), and the elastic modulus of the hybrid composite (Ehybrid). According to the Spearman's rank test carried out, moderately strong negative correlations between hybrid effect and Vol% LS fibres (r = -0.526) and END (r = -0.515) were found. The hybrid effect varied between -14.1% and 44.5%. The maximum hybrid effect was obtained combining HM carbon with carbon, in combination 1C/1CHM/1C, and the minimum was obtained combining HM carbon with glass, in combination 1G/3CHM/1G. In all analysed cases, it was possible to observe that above 60% of LS fibres relative volume, the hybrid effects were nearly zero or negative.
It is believed that the latter results are due to the size effect, since in the present work hybrid effects were computed in respect to 1 layer non-hybrid composite results, and in the cases in which the negative hybrid effect were obtained 2 or 3 layers of LS fibres were used. In this way, the magnitude of the hybrid effect potentially depends on the ply thickness of the LS fibres and this subject should be further studied.
Elastic modulus was well-predicted using the rule of mixtures (ROM The analytical approach developed by Jalalvand et al. [8] allowed to predict all the failure modes successfully. In this way, the presented work validated the developed approach for the set of materials and fabrication method used. However, since the hybrid effect can increase substantially the strain at failure of LS fibres, it is recommend to incorporate a way of predicting the hybrid effect into the model in the future.   Table 4 -Summary of different damage modes in function of stress level (adapted from [27]).