Assessment of damping and flexural behaviour of hybrid fibre-particulate composites

Abstract

Hybrid composites are an advanced solution that offers multifunctional capabilities, including exceptional strength-to-weight ratios, vibrational damping and impact absorption. This work describes the damping capacity and flexural behaviour of a hybrid fibrous-particulate system composed of glass/carbon fabrics and three distinct micro-inclusions: silica particles, carbon waste microfibres, and cement. A statistical methodology based on the full factorial design is applied to identify the effects of fibre stacking sequence, including carbon-C₅, glass-G₅, C₂G₃, G₃C₂, GCGCG and CG₃C, microparticle inclusions and matrix/fibre volume fraction (40/60 and 60/40) on damping and bending responses. A non-linear finite element (FE) analysis is conducted to explore the stress distribution based on the stacking sequence and predict the failure mechanisms of the hybrid laminate. The results indicate significant interaction effects, with hybrid architectures showcasing approximately 33% higher performance compared to glass fibre composites. A greater dependence on the fibre layup sequence is found for the damping factor, flexural modulus and strength. Notably, the incorporation of silica microparticles leads to an increase in flexural strength. Furthermore, a greater volume fraction of the matrix phase enhances the rheological efficiency in terms of the fibre-particle interface. Carbon fibre layers placed symmetrically on both beam sides (CG₃C) and bottom layers (G₃C₂) significantly enhance the bending performance of hybrid composites.

Keywords

Hybrid composite damping behaviour bending properties design of experiment microstructural analysis finite element analysis

Introduction

Hybrid fibre-reinforced polymer (HFRP) is a multifunctional material based on the combination of a matrix phase and two or more fibre and/or particle reinforcements.¹ The hybrid fibre composite is considered a multiscale system that possesses different types of performance, making it appropriate for different working conditions. Not only high levels of strength-to-weight ratio can be achieved, but also positive characteristics, such as vibrational damping and impact absorption capacity, being useful in marine, automotive, aeronautic, biomedical and sports applications.²

The design of hybrid composites is an effective approach due to the diversity of existing reinforcing constituents, resulting in different properties and behaviours. In general, studies on hybrid composites are mainly focused on understanding and predicting mechanical performance and the possibilities to effectively design and integrate new types of fibres or particles. Recent research has explored different constituent parameters of hybrid composites, such as stacking sequence,³ fibre type,⁴ phase proportions⁵ and fibre shapes fibre,⁶ making system analysis complex.

The first review paper on hybrid composites was published by Kretsis.¹ Since then, scientists and engineers have continually worked to further improve the design of hybrid composites. Currently, most hybrid composites are made from synthetic fibres, such as aramid, carbon and glass fibres, aramid and carbon fibres and others. However, recently, hybrid composites consisting of fibres and particles have shown notable promise in terms of improved specific strength⁷ and modal damping loss factor.⁸

The increase in flexural properties can be considered one of the most important reasons for the hybridisation of two different fibres. At the macro and micro levels, the hybrid system introduces further variables in bending characteristics. Under three-point bending, the flexural properties can be primarily determined by the compressive properties of the upper layer and the tensile properties of the lower layer.⁹ Therefore, the flexural properties depend not only on the hybrid composition, but also on the layup sequence of each fibre. Zhang et al.¹⁰ analysed hybrid composites with different configurations of symmetrical stacking with eight woven fabric laminas of glass/carbon hybrid composites in tensile, compression and bending responses. A positive hybrid effect was achieved, especially when two plies of carbon were placed on the outer layers. Wu et al.¹¹ investigated the flexural properties of interlayer and intralayer hybrid composites with different compositions and mixing ratios. The mixed carbon/glass ratio provided a significant effect on the flexural properties of the intralayer hybrid composites. However, in general, the interlayer structures showed better flexural properties than the intralayer hybrid configuration at the same mixing ratio.

Particle inclusions have been used in fibre-reinforced polymers to increase matrix phase strength¹² and interlaminar shear strength,¹³ attributed to the interfacial interaction between particles, fibres and matrix.¹⁴ The bonding condition of the phases in the intralaminar and interlaminar regions plays an important role in the mechanical performance of fibre-reinforced polymers. The incorporation of micro-sized particles, especially in the interlaminar region can provide an interlocking effect, enhancing the in-plane shear performance, consequently contributing to increase the bending properties of the laminates.¹⁵ These effects are also depend on other factors, such as, particle size, particle mass fraction, fibre orientation, functionalisation and manufacturing process. The complex relationship between these factors and their interaction with the matrix and fibrous phases is still far from being well understood.

Zheng et al.¹⁶ found that the inclusion of copper and boron nitride particles into a carbon fibre-reinforced polymer composite increases its thermal conductivity. Detomi et al.¹⁷ showed the incorporation of silica and silicon carbide microparticles leads to an increase in the stiffness of glass fibre-reinforced composites. The improvement in mechanical properties has been attributed not only to the interlocking effect in the interlaminar region favoured by the particles, but also to the increase in stiffness of the matrix phase.¹⁸ Increases in thermal stability,¹⁹ tribological performance (wear and friction),²⁰ mechanical shear strength¹⁵ and damping performance²¹ were also achieved by the presence of particles in FRCs.

The damping capacity of hybrid fibre-particle composites may also depend on the size, shape and concentration of the particles.²² In general, smaller particles with irregular shapes are more effective in dissipating energy than regular coarse particles.²³ Treviso et al.²⁴ revealed that the increase in particle concentration leads to better damping performance up to a certain point. Lv et al.²⁵ also concluded that synergistic strengthening of SiC particles and carbon fibres simultaneously enhanced the mechanical properties and damping capacity of aluminium matrix composites. Katsiropoulos et al.²⁶ reported that the inclusion of graphene nanofiller (GNP) in epoxy and CFRPs leads to a significant increase in damping capacity. The damping ratio ζ increases with the presence of nanofiller; however, both systems showed significant variations in damping behaviour as a function of wt.% content.

Hybrid composites are an advanced and versatile system that offers multifunctional capabilities for various applications. By combining different reinforcing constituents, these composites achieve remarkable strength-to-weight ratios and introduce advantageous features such as vibrational damping and impact absorption. This work describes the effects of carbon wastes, silica or cement particle inclusions on the flexural and damping performance of hybrid glass-carbon composites. The focus is on exploring and utilising the ability of microfillers to tune the energy absorption and mechanical properties of hybrid composite materials for structural applications, rather than just aiming to maximize them. To achieve this goal, a comprehensive experimental investigation of the damping response during free oscillation is carried out. Three-point bending tests are performed to demonstrate the effect of fillers on the mechanical characteristics of the hybrid system. To investigate the stress distribution based on the stacking sequence, a non-linear finite element (FE) analysis is conducted using a VUMAT. The VUMAT is a user-defined material subroutine that allows for the implementation of non-linear material behaviour in the FE analysis. A statistical methodology based on full factorial design is also established to provide a better understanding of the potential enhancement mechanism promoted by these particles in damping and bending behaviours.

Materials and methods

Composite material

Fibrous-particulate composites consist of an epoxy polymer matrix, micro-inclusions (recycled carbon microfibre wastes – CMF, Portland cement or silica) and glass and/or carbon fibres. An epoxy system composed of Renlam M resin and HY 956 hardener was supplied by Huntsman (Brazil). The carbon and glass cross-ply fabrics (200 g/m²) were supplied by Texiglass (Brazil). Silica, Portland cement (ASTM Type III, Holcim, Brazil) and CMF aggregates are combined in the matrix phase in an attempt to increase its stiffness and obtain an interlaminar locking effect. Figure 1 shows the microstructural analysis of the particles by scanning electron microscopy (Hitachi T3000). Silica (Figure 1(a)) and cement (Figure 1(b)) particles are classified as tetrahedral (angular) due to the grinding of quartz ore and clinker, respectively. Carbon wastes were obtained from the CFRP cutting process used to manufacture of fins (Carbontek, Spain). CMF particles are classified as cylindrical microfibres (Figure 1(c)). Portland cement particles can possibly be hydrated in the presence of epoxy polymer, and this effect is still discussed in the literature.²⁷ In this context, the present work evaluates the effects of three distinct functional particles: silica (non-reactive), cement (potentially reactive) and CMF (non-reactive with high aspect ratio) on the damping and flexural characteristics of five-layer hybrid composites.

Figure 1.

Scanning electron microscopy of (a) silica, (b) cement and (c) carbon microfibre wastes.²⁸

Figure 2 shows the particle size analysis obtained by laser diffraction using a Martersizer 2000 device. CMF particles are mostly found between 15 and 40 μm, with a small fraction below 1 μm. Cement particles are characterised by three average sizes, with particles less than 1 μm and two ranges from 3 to 50 μm and from 300 to 1000 μm. This type of distribution implies that other materials, comminute separately, were added to the cement mixture. Silica shows particle sizes from 2 to 70 μm.

Figure 2.

Particle size distribution curves of microfillers.

Fabrication

Fibre-particle reinforced laminates are manufactured using the hand lay-up technique at controlled room temperature (24 ± 1°C, RH 52 ± 1%). To get rid of air bubbles and reduce viscosity to facilitate particle dispersion, the epoxy resin is oven-heated at 50°C. Silica, cement and CMF are added to the epoxy resin and hand mixed for 5 min. Subsequently, the hardener is added and mixed for 2 min; then the epoxy system is spread onto glass or carbon fabrics. Five cross-ply fabric laminates composed of two matrix/fibre volume fractions (40/60 and 60/40) and different stacking sequences (G₅, C₅, G₃C₂, C₂G₃, CG₃C and GCGCG, where G and C correspond to glass and carbon fibres) are manufactured. Note that G₃C₂ and C₂G₃ are asymmetric conditions. The volume fraction of the particles (9 wt.%) was defined based on a preliminary investigation²⁹ aiming to obtaining a polymer with greater mechanical performance. The particle weight fraction is calculated based on the amount of matrix phase in the system to maintain an even particle distribution. Apparent density measurements of Portland cement and silica are obtained through gas pycnometer tests (Micromeritics model AccuPyc 1330). The composites are then compacted under a vacuum at a pressure of 0.8 bar and cured for 28 days at controlled room temperature at 22°C ± 1% and RH 50 ± 1%. The resulting samples are shown in Figure 3.

Figure 3.

Damping and flexural laminates samples.²⁸

Damping ratio & bending responses

The damping ratio of the first vibration mode is driven by the hammer impact test (Figure 4). Samples are fixed to one end of a rigid support and the other end is free to vibrate, which eliminates the effects of any external clamps or joints on the resulting damping ratios. The sample is excited by a short impact using a small modal hammer (B&K, Type 8204) and the response is measured using a laser vibrometer (PDV-100 Portable Digital Vibrometer). Based on the excitation and response measurements, a frequency response function is calculated, and the damping ratio is subsequently derived from that frequency response function using the least-square complex frequency (LSCF) estimator. The LSFC method is theoretically described in Petters et al.³⁰ being related to the eigenfrequencies $ω_{r}$ and damping rations $ξ_{r}$ as shown in equation (1). To correctly account for random experimental errors, each sample is tested three times and the results are presented in terms of means and standard deviations.

λ_{i}, λ_{i}^{*} = - ξ_{r} ω_{r} \pm j \sqrt{1 - ξ_{r}^{2}} ω_{r}

(1)

where λ is related to the poles,

ω_{r}

the eigenfrequencies (rad/s) and

ξ_{r}

the damping ratio.

Figure 4.

Experimental setup for damping analysis.

The three-point bending testing is performed on a Shimadzu AG-X Plus machine equipped with a 100 kN load cell. Tests were performed at 1 mm/min following ASTM D790 standard³² at room temperature (∼24°C) and a humidity level of 58%.

Experimental design

Full factorial design (DoE) is a methodology that employs various statistical techniques to plan, execute, and analyse experiments in a structured manner.³¹ The DoE is crucial to determine the most significant factors and interactions that affect the overall properties of composites.^32,33 Factorial design is adopted to quantify and understand the relationship between mechanical/modal responses and the following factors, particle type, matrix/fibre volume fraction and fibre stacking sequence. Thus, the behaviour of the experimental data is attributed to mathematical models, which describe the characteristics of the hybrid system. In general, the DoE describes and explains the variation of information, analysing the actual process that reflects that variation. Therefore, the data output must be evaluated statistically correct using a least square technique. The linear statistical model for the hybrid system can be expressed as:

Y_{ijkl} = μ + τ_{i} + β_{j} + γ_{k} + {(τ β)}_{ij} + {(τ γ)}_{ik} + {(β γ)}_{jk} + {(τ β γ)}_{ijk} + ε_{ijkl}

(2)

where: i = 1, 2 (levels for matrix/fibre volume fraction), j = 1, 2 (levels of particle type), k = 1, 2, 3, 4, 5, 6 (levels of fibre stacking sequence) and l = 1, 2 (number of replicates). Υ_ijkl is the response (out), µ is the global mean of the responses for all statistical treatments, τ_i represents the main effect of the input parameter matrix/fibre volume fraction, β_j represents the main effect of the particle type, γ_k represents the main effect of stacking sequence, (τβ)_ij represents the effect of interaction between τ_i and β_j, (τγ)_ik is the effect of the interaction between τ_i e γ_k, (βγ)_jk is the effect of the interaction between β_j and γ_k, (τβγ)_ijk is the effect of the interaction between τ_i,β_j and γ_k, and ε_ijkl is the mathematical random error.

Two full factorial designs, 2¹4¹5¹ (Table 1) and 2¹4¹6¹ (Table 2) are perform to investigate the effects of stacking sequence, volume fraction and particle type on damping and mechanical responses of hybrid composites, respectively. The following factors are kept constant: particle amount (9 wt.%), resin-hardener mixture time (5 min), fibre grammage (200 g/cm²) and curing time (28 days). The particle weight fraction (9 wt.%) is calculated based on the matrix amount. The apparent density of Portland cement (2.80–2.95 g/cm³) and silica (2.65–2.70 g/cm³) is obtained by gas pycnometer tests using a Micromeritics model AccuPyc 1330. Tables 1 and 2 show matrix design with factors and levels for each response. Six samples are fabricated for each experimental condition and each experimental trial. Minitab 17 software is used to treat the data.

Table 1.

Matrix planning for damping response (2¹4¹5¹).

Factors	Experimental levels
Stacking sequence	Only glass fibres (G₅)
	Only carbon fibres (C₅)
	(G₃C₂) = (C₂G₃) for damping response
	Carbon/glass/glass/glass/carbon (CG₃C)
	Glass/carbon/glass/carbon/glass (GCGCG)
Matrix/fibre volume fraction	40/60
Matrix/fibre volume fraction	60/40
Type of particle	Without particle
	Silica
	Cement
	CMF

Table 2.

Matrix planning for flexural responses.

Factors	Experimental levels
Stacking sequence	Only glass fibres (G₅)
	Only carbon fibres (C₅)
	Glass/glass/glass/carbon/carbon (G₃C₂)
	Carbon/carbon/glass/glass/glass (C₂G₃)
	Carbon/glass/glass/glass/carbon (CG₃C)
	Glass/carbon/glass/carbon/glass (GCGCG)
Matrix/fibre volume fraction	40/60
Matrix/fibre volume fraction	60/40
Type of particle	Without particle
	Silica
	Cement
	CMF

Tables 6 and 7 show the significance and contribution of each factor and interaction on the damping ratio and bending responses, respectively. The contribution parameter represents the relevant ratio, which is the variation ratio calculated by the adjusted square mean (adjust MS) for each factor by the adjusted square mean error (MS error). p-values less than or equal to 0.05 in Tables 6 and 7 indicate significant effects considering a 95% confidence interval. R² indicates how well the variability of the observed response values can be explained by the independent variables (volume fraction, particle type and stacking sequence) and their interactions. Thus, when R² approaches 1 (100%), the prediction of composite properties is more accurate. Anderson Darling´s normality test measures the normal distribution of the statistical model for each response in the hybrid system. In this case, p-values greater than .05 indicate that the residual of the response variables follows a normal distribution, validating ANOVA. In addition, Tukey’s multiple comparison method is used to compare experimental levels as a grouping of treatments, where statistically equivalent means are represented by equal letters. Tukey’s test results are illustrated in the main effect and interaction plots (Figures 6–11).

Finite element modelling

Finite Element (FE) analysis was employed to investigate the stress distribution in hybrid carbon/glass fibre configurations based on their stacking sequence. The analysis was conducted using a commercial software package, Abaqus^TM/Explicit, which incorporates a damage VUMAT subroutine. The simulation focused on three-point bending, as depicted in Figure 5. To accurately capture the behaviour of the hybrid composite, the FE model incorporated various nonlinearities, including damage, failure behaviour, and geometric/contact effects. A quarter of symmetry was considered along the X-axis and Z-axis, allowing for more efficient computation. Symmetry conditions were applied in lateral planes to further simplify the analysis. In order to model the supports, discrete rigid surfaces were used and fixed in place using reference points (RPs). These RPs were connected to the supports using tie constraints and boundary conditions (BCs), ensuring that the supports were accurately represented in the simulation. The lower support RP imposes restrictions on displacements and rotations, with all degrees of freedom (Ux, Uy, Uz, Urx, Ury, Urz) set to zero. On the other hand, the upper support RP allows for displacement in the Z-direction, while restricting displacements and rotations in other directions (Vx, Vy, VRx, VRy, VRz = 0). During the analysis, a flexural displacement rate of 1 mm/min is applied along the Z-axis at the upper support RP. The reaction force in the RP is closely monitored to understand the structural response. To accurately represent the cross-ply laminates, the meshing is done using three-dimensional elements (C3D8R). These elements are eight-node linear brick elements, which provide a reliable representation of the geometry and behaviour of the laminates. In order to ensure accurate results and capture the behaviour under three-point bending loads, the mesh is refined. This refinement is guided by the loading conditions and involves 130 elements in the length direction and 43 elements in the width direction. Additionally, there is one element per layer in the thickness direction to capture the behaviour through the laminate’s thickness. To simulate three-point bending, a dynamic non-linear step with explicit integration is utilized in the analysis. This approach, implemented in Abaqus/Explicit, efficiently solves the dynamic equilibrium equation without the need for iteration. It explicitly advances the kinematic state from the previous increment and updates the stiffness matrix to account for changes in geometry and material properties. Given that the explicit solver is employed, the time interval is set to 0.01 s to correspond to the bending test conditions. The proposed model comprehensively addresses the structural response, including damage delamination, and considers various stacking sequences of glass and carbon plies. To ensure accuracy and reliability, the predictions obtained from this model are compared against experimental conditions. This comparison allows for the assessment of the model’s accuracy in capturing the behaviour of the hybrid composites under three-point bending. In the FE simulations, the elastic properties of glass and carbon plies (Table 3), as well as the damage properties (Table 4), are extracted from reputable sources such as Rahimian Koloor et al.,³⁴ Ribeiro et al.,³⁵ Ribeiro Junior et al.,³⁶ while the values of fracture energies are obtained from the properties provided by Shi et al.³⁷ By utilizing data from these sources, the model can effectively capture the mechanical response of the hybrid composites in the FE simulations.

Figure 5.

Representative FE model for three-point bending analysis.

Table 3.

Ply constants.

Elastic properties
	Glass ply	Carbon ply
E₁₁ (GPa)	105.5	36.9
E₂₂ (GPa)	7.2	10.6
E₃₃ (GPa)	7.2	10.6
G₁₂ (GPa)	3.4	3.3
G₁₃ (GPa)	3.4	3.3
G₂₃ (GPa)	2.52	3.6
υ₁₂	0.34	0.39
υ₁₃	0.34	0.39
υ₂₃	0.378	0.44

Table 4.

Constitutive damage model parameters.

Damage properties		Glass ply	Carbon ply
Longitudinal tensile strength, MPa	X_T	1340	820
Longitudinal compressive strength, MPa	X_C	1192	500
Transverse tensile strength, MPa	Y_T	19.6	80.6
Transverse compressive strength, MPa	Y_c	92.3	322
Longitudinal shear strength, MPa	S_L	51	54.5
Transverse shear strength, MPa	S_T	23	161.2
Longitudinal tensile fracture energy, N/mm	G_XT	48.4	32
Longitudinal compressive fracture energy, N/mm	G_XC	60.3	20
Transverse tensile fracture energy	G_YT	4.5	4.5
Transverse compressive fracture energy, N/mm	G_YC	8.5	4.5

Contact between supports and laminate structure

To enhance the accuracy and efficiency of the model, a general contact interaction is implemented using surface contact pairs. This implementation aims to prevent any overlap or interpenetration between the ply fibres and the flexure support surfaces. By establishing contact pairs, interaction surfaces are defined within the components, carefully considering the geometry, position, and size of these selected surfaces prone to contact. The contact pairs consisted of three surfaces. The first and second surfaces correspond to the discrete rigid upper and lower supports, respectively. The third surface combines all exterior and interior element surfaces within the composite structure. By leveraging the “all-inclusive” contact surface formulation in ABAQUS/Explicit, this integration is facilitated, proving particularly advantageous for this model. This approach allows the algorithm to access the internal surfaces of the mesh within the composite structure. As the elements experience bending due to the upper support, the general contact algorithm effectively tracks the internal surfaces of the adjacent elements. This ensures a thorough and accurate representation of the contact behaviour in the model.

Cohesive behaviour between adjacent plies

The interaction between adjacent plies in the interlaminar region, specifically the matrix-fibre interface, is considered in the model. To accurately represent this interaction, a general contact formulation incorporating a cohesive zone model (CZM) is employed. This formulation allows for the prediction of the behaviour between adjacent plies through cohesive surface behaviour. In the case of ply-ply contacts, a hard contact assumption is made for normal behaviour. This means that there was no separation or sliding allowed between the plies in the normal direction. For the tangential behaviour, a friction coefficient value of 0.32 is assigned to govern the contact between plies. This friction coefficient controlled the resistance to sliding or shearing between the adjacent plies, providing an approximation of the real-world behaviour.

Damage modelling

Intra-laminar damage within the composite material is formulated using a VUMAT subroutine. A stress-based criterion is employed to detect the initiation of damage in different modes, including fibre failure in tension and compression, matrix failure in tension and compression, and in-plane shear failure (Table 5). To model the evolution of damage, the principles of continuum damage mechanics (CDM) laws are followed. These laws are designed to degrade the stresses within the affected regions and help mitigate any potential numerical instability that may arise during the analysis.

Table 5.

Failure criteria for damage onset detection.

Failure mode	Failure criteria
Fibre in tension	$F_{f}^{t} (σ_{1}) = \frac{σ_{11}}{X_{t}} \geq 1.0$
Fibre in compression	$F_{f}^{c} (σ_{1}) = \frac{\| σ_{11} \|}{X_{c}} \geq 1.0$
Matrix in tension	$F_{m}^{t} = {(\frac{σ_{22}}{Y_{t}})}^{2} + {(\frac{τ_{12}}{S_{L}})}^{2} \geq 1.0$
Matrix in compression	$F_{m}^{c} = {(\frac{σ_{22}}{{2 S}_{L}})}^{2} + [{(\frac{Y_{C}}{{2 S}_{L}})}^{2} - 1] \frac{σ_{22}}{Y_{c}} + {(\frac{τ_{12}}{S_{L}})}^{2} \geq 1.0$
In-plane shear	$F_{L} (τ_{12}) = \frac{\| τ_{12} \|}{S_{L}} \geq 1.0$

The parameters X_t, X_c, Y_t, Y_c, S_L represent the tensile strength and compressive strength in the fiber direction, the tensile and compressive strength in the matrix direction, the out-of-plane shear strength, and the in-plane shear strength, respectively. The stresses σ₁₁, σ₂₂, τ₁₂ represent the applied stress in the fiber direction, the matrix direction, and the in-plane shear stresses, respectively.

The interlaminar constitutive model is developed using the ABAQUS/Explicit formulation code, which employs explicit central-difference time integration. Within this model, cohesive interface elements are integrated using a general contact formulation between adjacent plies. This combination of cohesive interface elements and the general contact formulation enables the prediction of failure initiation and the evolution of damage through a traction-separation law. The traction-separation law assumes an initially linear elastic behavior and accounts for separation stresses t_n (normal direction), t_s (13 direction), and t_t (23 direction) associated with mode I delamination. Additionally, the model considers shear stress in the first direction for mode II delamination and shear stress in the second direction for mode III delamination.

Results and discussions

Damping factor

A full factorial design of 2¹4¹5¹ is considered to evaluate the damping factor. Table 6 shows the ANOVA result for the damping factor. The Anderson Darling’s normality test performed for the generated residuals reveals a p-value of .097 (>.05), validating ANOVA. A third-order interaction is significant, where the stacking sequence is the main factor affecting this response (contribution of 24.63%, Table 6), followed by its interaction with the volume fraction factor.

Table 6.

ANOVA results for damping factor.

Main factor and interactions	Full factorial design 2¹4¹5¹ = 40
	Damping factor (%)
	Contribution	p-value ≤.05
Volume fraction	16.67%	.000
Particle type	6.03%	.000
Stacking sequence	24.63%	.000
Fraction*particle type	6.42%	.000
Fraction*stacking	23.88%	.000
Particle type*stacking	10.64%	.000
Fractionparticle typestacking	11.25%	.000
R² (adj)	99.52%
Anderson-darling test (p-value ≥.05)	0.097

Damping factor data vary between 1.29% and 4.85%. In general, more flexible and ductile structures lead to a higher damping factor.³⁸ Figure 6 shows the main effect plots for the mean damping factor. Even with a smaller amount of polymer (40/60), greater damping capacity is obtained (Figure 6(a)). The same factor also provided greater porosity, as reported by Ribeiro Filho et al.,³⁹ which probably affected the stiffness of the composite. Ashorth et al.⁴⁰ reported that the damping factor is largely dependent on the composition and manufacture parameters, that is, higher levels of porosity increase the scattering and dispersion of the damping waves. Furthermore, due to the viscoelastic behaviour, a greater amount of epoxy matrix phase tends to increase the modal response, besides making the composites denser.^39,40

Figure 6.

Main effect plots for the mean damping factor. (a) Volume fraction (b) particle type (c) stacking sequence.

The incorporation of particles leads to reductions in the damping capacity, mainly for silica (31.4%), followed by CMF (22.68%) and cement (10.88%) particles (Figure 6(b)). This can be attributed to the increase in stiffness attributed to the inclusion of particles. A higher damping factor obtained by cement-reinforced composites (Figure 6(b)) indicates a possible chemical interaction between the matrix and the particles. Javanmardy et al.³⁸ found that there is a tangible physical relationship between modal changes and stiffness in a composite system. Likewise, a large percentage variation (74.7%) between glass and carbon fibre composites is shown in Figure 6(c). Hybrid stacking sequences achieve different behaviours between the limits of pristine laminates (glass and carbon). Despite the complexity of the system, note that hybridisation can be a good option to enhance the damping characteristics of carbon fibre-reinforced composites. The highest damping factor is achieved by glass fibre laminates (G₅) manufactured without particles and with a volume fraction of 40/60 (Figure 6(a)–(c)).

Figure 7 presents the interaction effect plot for the mean damping factor. A larger matrix volume fraction (60/40) does not provide significant changes in the damping factor (Figure 7(a)). The laminates without particles achieve a higher damping factor at the 40/60 level (Figure 7(a)). The high geometric aspect ratio of the CMF and the possible hydration of cement grains in the interlaminar region may be responsible for increasing the stress distribution of the composites, contributing to increase their damping capacity. Fibre hybridisation also promotes some increments in the damping factor, especially at the 40/60 level (Figure 7(b)). The particle effect, mainly for CMF and cement, is more pronounced with glass fibre laminates (G₅) than with carbon fibres (C₅), as shown in Figure 7(c).

Figure 7.

Third-order interaction effect plot for the mean damping factor: (a) volume fraction x particle type, (b) volume fraction x stacking sequence and (c) particle type x stacking sequence.

Flexural strength and stiffness

The ANOVA findings in Table 7 reveal that first and third-order interactions significantly affect flexural responses. A p-value greater than .05, obtained by the Anderson-Darling test for the flexural residuals, validates the normal distribution of the data. Considering the contribution parameter, the most relevant effect on flexural modulus and strength is the ‘Stackinq sequence’, with a contribution of 82.65% and 40.78%, respectively (Table 7). This behaviour was expected, since fibres play an important role in the mechanical performance of composites, mainly on the bottom beam side, which is under tensile stress.

Table 7.

ANOVA results for flexural responses.

Main factor and interactions	Full factorial design 2¹4¹6¹ = 48
	Flexural modulus (GPa)		Flexural strength (MPa)
	Contribution	p-value ≤.05	Contribution	p-value ≤.05
Volume fraction (wt.%)	0.03%	0.183	24.91%	0.000
Particle type	2.10%	0.000	1.69%	0.000
Stacking sequence	82.65%	0.000	40.78%	0.000
Fraction*particle type	1.55%	0.000	2.64%	0.000
Fraction*stacking	3.96%	0.000	20.33%	0.000
Particle type*stacking	3.50%	0.000	1.99%	0.000
Fractionparticle typestacking	6.11%	0.000	7.56%	0.000
R² (adj)	99.81%		99.79%
Anderson-darling test	0.313 (p-value ≥.05)		0.378 (p-value ≥.05)

Flexural modulus data range from 6.64 to 29.7 GPa. Figures 8 and 9 show the main effect and third-order interaction effect plots for the flexural modulus of the hybrid composites, respectively. The presence of particles in the hybrid structures leads to a decrease in flexural modulus, except for the inclusion of silica (Figure 8(a)). An increase of 10.11% in flexural modulus is obtained by incorporating silica particles in comparison with the reference condition (Figure 8(a)). This effect is more evident when considering the 40/60 level (Figure 9(a)). The interaction plot (Figure 9(c)) shows that silica particles provide superior stiffness to all stacking sequences compared to CMF and cement, except for carbon composites. This improvement may be related to the increase in shear strength between orthogonal laminae and ceramic particles under bending loadings. The increase in shear strength is caused by the effect of friction in the interlaminar transition zone due to the presence of rigid particles.^17,39 Cao and Cameron⁴⁰ also commented that microparticles placed directly on fabrics increase the interfacial interaction (fibre-matrix), namely as the interlocking effect. In addition, the silica particles provided greater rigidity than the matrix phase, contributing to increase the resistance to interlaminar failure⁴¹ and, consequently, to increase the elastic modulus and strength of the hybrid system. Oliveira et al.⁴² also revealed an increase in stiffness when 10 wt.% silica was added to the epoxy polymer.

Figure 8.

Main effect plot for the mean flexural modulus. (a) Particle type (b) stacking sequence.

Figure 9.

Third-order interaction effect plot for the mean flexural modulus: volume fraction x particle type, (b) volume fraction x stacking sequence and (c) particle type x stacking sequence.

The presence of two layers of carbon fibre (C₂G₃, G₃C₂ and CGGGC) contributes substantially to increase the flexural stiffness of the composites in relation to the glass fibre condition (G₅) (Figure 9(c)). Some studies^3,11,12,39 reveal that the pattern of the fibre layers is one of the most important parameters that affect the bending behaviour. Jesthi et al.⁴³ reported that replacing glass fibre with carbon fibre in the upper layer increases the flexural modulus by 62%. Wu et al.¹¹ stated that, as interlayer hybrid composite structures contain more carbon fibre, the average flexural modulus is higher. Zhang et al.⁴⁴ showed a positive effect on different symmetrical stacking configurations of the glass/carbon hybrid structure, especially when two carbon plies were placed on the outer layer. The modulus of the carbon fibre composite is 187.86% greater than that of the glass fibre composite (Figure 8(b)). The hybrid laminates G₃C₂, C₂G₃ and GCGCG presented a similar flexural modulus, revealed by Group C; however, superior stiffness is achieved by CG₃C composites, being attributed to the symmetrical and balanced beam configuration, including the carbon fibres in the outer layers, like a sandwich panel, as reported by Zhang et al.¹⁰ This effect is most evident when using the volume fraction of 40/60 and the silica particles, as shown in Figure 9(b) and (c), respectively.

Flexural strength data vary from 213.09 to 509.106 MPa. Figures 10 and 11 show the main and interaction effect plots for mean flexural strength, respectively. Higher flexural strength is obtained when considering a greater amount of matrix (60/40) (Figures 10(a), 11(a) and (b)), which is attributed to the greater wettability of the fibres and the reduction of micro voids in the system, as shown in Ribeiro Filho et al.²⁸ According to Ribeiro Filho et al.¹² and Detomi et al.,¹⁷ porosity levels play an important role in crack propagation, reducing the flexural strength of composites.

Figure 10.

Main effect plot for the mean flexural strength. (a) Volume fraction (b) particle type (c) stacking sequence.

Figure 11.

Third order interaction effect plot for the mean flexural strength: (a) volume fraction x particle type, (b) volume fraction x stacking sequence, and (c) particle type and stacking sequence.

Flexural strength increases by 9.43% mainly when silica is added, followed by CMF (4.13%) and cement particles (2.96%), as shown in Figures 10(b) and 11(c). This behaviour can be addressed to the interlocking effect between particles and fibres. These findings confirm the results reported by Ribeiro Junior et al.,³⁶ who obtained greater flexural strength of hybrid composites containing glass fibres and silica particles.

Figure 10(c) shows that the highest flexural strength is achieved by carbon fibre composites, followed by hybrid fibre configurations. The findings revealed by fibre hybridisation imply that the resistance mechanism is based not only on the number of carbon plies, but also on their stacking position and symmetry, which affects the distribution of shear and normal loads generated by bending. Among hybrid fibre composites, the symmetric configuration (GCGCG) achieves higher strength values, as shown in Figures 10(c) and 11(c).

Finite element analysis

Figures 12 and 13 present the force versus displacement curves for various hybrid carbon-glass stacking configurations C₂G₃ (Figure 12(a)), G₃C₂ (Figure 12(b)), CG₃C (Figure 13(a)) and GCGCG (Figure 13(b)). The numerical results show a reasonably good agreement with the experimental data. The curves initially exhibit a quasi-linear behavior in the elastic zone, followed by a decline attributed to interfacial damage and fiber/matrix failure. This decline is more pronounced in the experimental curves, where a progressive reduction in force is observed. In contrast, the numerical model shows a more gradual decrease. In the flexural test, the peak forces for the C₂G₃ (Figure 12(a)), G₃C₂ (Figure 12(b)), CG₃C (Figure 13(a)) and GCGCG (Figure 13(b)) glass-carbon (60/40 matrix-fibre ratio) stacking sequences are 221.6 N, 236.1 N, 283.2 N, and 273.9 N, respectively. These results demonstrate a good correlation between the numerical predictions and experimental data, with a maximum deviation of 9.42% from the test results.

Figure 12.

Experimental and numerical force-displacement curves for (a) C₂G₃ and (b) G₃C₂.

Figure 13.

Experimental and numerical force-displacement curves for (a) CG₃C (b) GCGCG.

While the FE model encountered challenges in accurately predicting variations in delamination, it successfully demonstrates the impact of stacking sequence on flexural stress within the laminates. Figures 14 and 15 visually depict the stress distribution throughout the thickness of the laminate during failure. Notably, the carbon layer experiences lower stresses due to its higher stiffness compared to the glass fibre layer. In the case of the C₂G₃ configuration, the carbon-ply reinforced composites exhibit lower stresses on the top side compared to the G₃C₂ configuration on the bottom side. For the asymmetric designs, such as C₂G₃ and G₃C₂, the highest stress concentrations are observed at the glass-ply region. These stress concentration locations align with the failure positions observed in the experiments. The asymmetric distribution of fibres along the thickness direction, as shown in Figure 16(a) and (b), alters the centre of gravity of the sample cross-section, thereby affecting the stress distribution depicted in Figures 14 and 15 and the moment of inertia of the hybrid system. In symmetrical configurations, as shown in Figure 16(c) and (d), the moment of inertia and mass are balanced under compressive and tensile loads. The presence of two layers of carbon fibre on the lower side of the beam (CCGGG) can overload the three layers of glass on the upper side, potentially leading to premature failure and reduced strength, as illustrated in Figures 14 and 15. Conversely, the G₃C₂ composite exhibits a slight improvement in strength. As mentioned earlier, the symmetrical configuration featuring alternating fibres (GCGCG) achieves superior strength, as shown in Figure 15. Therefore, the negative effects of asymmetric structures outweigh the advantages obtained through fibre hybridization, particularly when carbon fibres are positioned below the neutral line (Figure 16(b)) during bending loads.

Figure 14.

Flexural stress distribution of (a) C₂G₃ and (b) G₃C₂ (c) CG₃C and (d) GCGCG at first failure (stage 1 of the force-displacement curve).

Figure 15.

Flexural stress distribution of (a) C₂G₃ and (b) G₃C₂ (c) CG₃C and (d) GCGCG at progression of damage (stage 2 of the force displacement curve).

Figure 16.

Representative scheme of asymmetric (a-b) and symmetric stacking sequence (c-d).

Failure analysis

Fractures of hybrid composites are analysed using an optical microscope (Figures 17–20), in order to assess damage mechanisms and anomalies that affect flexural performance. A common failure mode under bending loading is delamination due to the presence of shear stress provided by the combined compressive and tensile loads. Generally, delamination occurs transversely, along with the fibre and polymeric matrix, at the bottom of the beam.¹²

Figure 17.

Fractured G5 samples with volumetric fraction of (a) 40/60 and (b) 60/40.

Figure 18.

Fractured G₃C₂ (a) and C₂G₃ (b) samples without particles and matrix/fibre volume fraction of 60/40.

Figure 19.

Fractured GCGCG (a) and CG₃C (b) samples without particles and matrix/fibre volume fraction of 60/40.

Figure 20.

Optical images of G5 laminates with inclusions (a) silica (b) cement (c) CMF at 60/40 volume fraction.

Images of the fractured G5 glass laminate for the two levels of volume fraction are shown in Figure 17. The main damages consist of cracks in the matrix with subsequent fibre tearing on the compressive beam side and fibre pull-out on the tension side. Although a delamination process is common under bending loading, no delamination is evident, and this is a clear indication of good interfacial bonding. The fracture behaviour of laminates is similar for both amounts of matrix phase. Its noteworthy, however, that the lower content of the epoxy matrix leads to a greater presence of voids in the glass configuration (Figure 17(c) and (d)), which can be attributed to the lower flexural strength shown in Figure 10(a). Oliver et al.,⁴⁵ Dong et al.³ and Sudarisman and Davies⁴⁶ also reported that voids substantially affect the bending properties of laminates.

Figure 18 shows the micrograph of the fractured G₃C₂ (a-c) and C₂G₃ (b-d) hybrid laminates. Both configurations resulted in interfacial debonding and, in some cases, fibre buckling and fibre pull-out. However, the delamination of the C₂G₃ pattern is more significant than that of G₃C₂. Such mechanisms are also observed by Sudarisman and Davies⁴⁶ and Chen et al.,⁴⁷ who noted that glass fibre properties are not optimally used in the neutral plane. This implies that the negative effect is preponderant over the benefits achieved by the fibres in the outer layer. Unbalanced stiffness and strength also affect the stress distribution and moment of inertia of the area, contributing to premature failure of the laminate. In this way, the incorporation of glass fibres in the upper layer reduced cracks in the matrix and debonding, with the bridging of the glass fibres and the rupture of the carbon fibres.

Figure 19 shows the micrographic images of the fractures of the symmetric laminates: (a-c) CG₃C and (b-d) GCGCG. The alternate lay-up scheme reveals a positive effect in reducing failure on the upper side of the composite. In general, tensile cracks and matrix failure are found; composites containing two layers of carbon fibre on the outer surfaces present better mechanical performance, revealing glass fibre bridging and rupture of carbon fibres. Bader et al.⁴⁸ and Rassool et al.⁴⁹ also reported these failure modes, including shear fracture and damage, leading to lower bending properties.

Figure 20 shows the micrographic images of G₅ hybrid laminates with (a) silica, (b) cement and (c) CMF particles. The failure modes of hybrid laminates are characterised by a partial rupture of the lower layers. Although the fibre pull-out effect is more evident for laminates without particles (Figure 18), shear failure seems to predominate, as indicated in the literature.¹⁰ Micro voids and matrix cracks are also evident on all surfaces, especially those with cement and CMF inclusions. However, the presence of silica in the FRCs reduced the shear stresses, which, in turn, increased the interlocking effect in the interlaminar region. This failure behaviour appears to be the reason for the high bending properties of the silica particles.

Conclusions

A robust statistical methodology is conducted to comprehensively evaluate the influence of different micro-macro reinforcement configurations on the damping and bending performances of hybrid systems. Based on the experimental assessment, a greater dependence on the fibre layup-sequence was found in terms of damping factor, flexural modulus and strength. The hybridisation of composite plates significantly affects their damping capacity. The use of more compliant fibres, that is, glass fibres, decreases the stiffness of the plate, resulting in greater energy absorption. The highest damping factor is obtained when considering a smaller amount of matrix phase and glass fibres.

Flexural strength and stiffness are mainly enhanced by the interaction between the presence of particles and fibres in the system. The highest flexural behaviour is achieved when silica particles and carbon fibres (C₅) are combined. A greater amount of matrix phase also contributes to a slight increase in flexural strength of hybrid FRCs. The flexural modulus and strength of hybrid glass and carbon fibre composites are dominated by the incorporation of particles. Composites C₅ without particle (40/60) and C₅ with silica (60/40) provided superior flexural modulus and strength, respectively, while CG₃C configuration achieved the most balanced flexural properties.

The experimental and numerical analyses demonstrate a significant correlation between the predicted and observed behaviour of hybrid carbon-glass stacking configurations under flexure testing. Although the finite element (FE) model faced challenges in accurately predicting variations in delamination, it effectively highlighted the influence of stacking sequence on flexural stress within the laminates. Specifically, the results showed that carbon-ply reinforced composites (C₂G₃) on the top side experienced lower stresses compared to the bottom carbon sample (G₃C₂). The presence of stress concentrations at the glass-ply region in asymmetric designs aligned with the experimental failure positions. Additionally, configurations with alternating fibres (GCGCG) exhibited superior strength. However, it was observed that asymmetric structures, particularly those with carbon fibres positioned below the neutral line, experienced negative effects that outweighed the benefits of fibre hybridization, especially during bending loads.

The main failure mechanisms of the hybrid system consist of matrix cracks with subsequent fibre tearing on the compressive beam side, and fibre pull-out on the tension side. Although a delamination process is common under bending loading, no delamination is evident, and this is a clear indication of good interfacial bonding. Damage features are similar for both matrix phase amounts. In general, tensile cracks and matrix failures are found. The fibre lay-up has a positive effect in reducing failure on the upper side of the composite. Composites containing two layers of carbon fibre on the outer surfaces show better mechanical performance. The incorporation of glass fibres in the upper layer reduced cracks in the matrix and debonding, with bridging of the glass fibres and rupture of the carbon fibres. In general, the failure modes of hybrid laminates are complex and may depend on a variety of factors. Understanding these failure modes is important for designing and optimising the performance of composite materials in specific applications.

Footnotes

Acknowledgements

The authors acknowledge Elsevier for giving permission to reuse Figures 1 and 2 from (Copyright Elsevier).

Author contributions

SLMRF: Investigation, Methodology, Validation, Visualisation, Writing - Original draft. CTG: Resources, Conceptualisation, Methodology, Writing - Review. LMD: Methodology, Writing - Review. ALC: Supervision, Data curation, Writing - Review. VO: Investigation, Methodology. MES: Methodology, Software, Funding acquisition, Writing – Review. THP: Supervision, Conceptualisation, Software, Funding acquisition, Writing - Review. Fabrizio Scarpa: Conceptualisation, Writing - Review.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge the Brazilian Research Agencies, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (MSc scholarship), Conselho Nacional de Desenvolvimento Científico e Tecnológico (PQ-305553/2023-2) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (APQ 01012-18) for the financial support provided.

ORCID iDs

Sergio Luiz Moni Ribeiro Filho

Carlos Thomas Garcia

Luís Miguel P Durão

Tulio Hallak Panzera

Data availability statement

Derived data supporting the findings of this study are available from the corresponding author on request.*

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