1 Introduction

In the fields of industries, applications of Fiber Reinforced Polymers (FRP) for both structural and non-structural purposes became widespread in the last decades (Ref 1, 2). The main advantages of these structures lie in the anisotropic and heterogeneous character of the material as well as in their capacities to provide elevated performance components with high mechanical strength and stiffness, coupled with reduced weight. This led to many studies about their mechanical behavior both in quasi-static and dynamic conditions (Ref 1, 3). One of the most important characteristics of FRPs is the material impact resistance which was proved to be a vital criterion when composites are considered for critical load-bearing applications (Ref 4, 5). Often when undetectable to visual inspection, or barely visible on the surface, damages due to foreign object impact can be significant within the material, promoting fatal failures under various operating loads (Ref 6, 7). Even without any visible external damage, the low-velocity impact withstand is a key issue for FRPs, reducing the laminate strength and stiffness, mainly due to multiple delaminations produced (Ref 8, 9). The damage induced by impact loads on composites is more critical than in metals, being complicated by the nonhomogeneous and anisotropic nature of the material. Since it begins in the form of internal delamination, matrix cracking or fiber-to-matrix debonding, it may be hardly observable by visual inspections as well as by destructive and non-destructive techniques. Many studies were devoted to solving the problem in the last years, and several methods were proposed in literature to reduce the low-velocity impact damages (Ref 4, 5). It is clear the interest of the researchers toward the study of the dynamic response and the related damage mechanisms of composite materials, such as FRPs, being to date still open questions. More recently, several methodologies have been exploited to enhance impact damage resistance of FRPs, with the purpose to tailor the impact response and maximize the impact energy absorption. A possible solution was found in hybridizing laminates, taking advantage of the characteristic properties of different fibers in the same matrix (Ref 10, 11). Also, in optics to minimize the costs, glass fibers represent a suitable option, especially when associated with more performing fibers like carbon. Hybrid carbon/glass composite laminates demonstrated a better damage tolerance with respect to their full carbon counterparts (Ref 12) A key factor governing the hybrid composite impact energy absorption capability resulted to be the stacking sequence (Ref 13). That means the hybrid laminates should be properly tailored in the lay-up sequence to reduce the damages under low-velocity impacts. Experimental tests allowed to investigate the material behavior in a wide range of impact energies (Ref 14). The related post-failure analysis, conducted by adopting non-destructive inspections such as ultrasonic testing and thermo-scanning methodologies, estimated the total damage in terms of extension in the plane of the laminate (Ref 5, 15). However, little information can be provided about the nature and localization of the damage into the FRP thickness through non-destructive approaches. The need to deepen the damage mechanisms topology and characterization occurring in FRPs materials under dynamic loads, guided the development of numerical approaches to the problem. (Ref 2, 16). Despite the adoption of numerical approaches to study the LVI response of FRPs is a well-established practice, few investigations have been numerically conducted on the effect of hybridization, as well as on the influence of hybrid lay-up sequence on the laminate damage tolerance and energy absorption capability. Therefore, in this study, the low-velocity impact response of woven carbon and glass hybrid laminates, was studied through both experimental and numerical approaches. Three different stacking sequences were considered and drop impact tests were conducted under rising impact energy levels (5, 10 and 20 J) aiming to analyze the influence of the lay-up stratification on the LVI response of the hybrid laminates. Finite element models (FEM) of the considered laminates were developed and validated based on the low-velocity impact experimental campaign. It allowed to widely investigate the different damage mechanisms, their distribution in the material thickness and their extension on the plane of the laminate. Depending on the stacking sequence and the impact energy, the energy absorption capacity was estimated and related to the dominant damage mechanism. The percentage contribution of both interlaminar and intralaminar damage on the total damage was evaluated. The delaminated region for each ply-to-ply interface and the contribution of each ply to the total intralaminar damage were explored. The developed model was proved to be a helpful instrument to thoroughly investigate the impact damage mechanisms within the composite and to study the effects of the staking sequence, namely the influence of the hybridization, on the laminates’ dynamic behavior in order to optimize the design and the manufacturing of the reinforced hybrid panels.

2 Materials and Methods

In the following sections, the different hybrid stacking sequences are going to be described and their manufacturing technologies deepened. Then the experimental set-up will be presented, and the conducted experiments typology specified. Subsequently, a detailed explanation of the adopted numerical approach will be presented, and the material and model parameters reported and motivated.

2.1 Experimental Methodology

Composite laminates were manufactured through vacuum infusion technique by using vinyl ester resin and carbon and glass woven fabrics with an areal weight of about 300 g/m2. The manufactured composite laminates showed a nominal thickness of t = 3.5 ± 0.25 mm and a fiber volume fraction of Vf ≃ 58%. Three different stacking sequences were considered in the present study. One of them was built by alternating one ply of carbon every two plies of glass for a ([G2C]5G2) final symmetric sequence. It was labeled as GC layup for the sake of brevity. The remaining two layup typologies were produced with the same asymmetric stacking sequence by grouping 10 plies of glass and 5 of carbon, which was tested once on the carbon side (referred as C5G10) and once on the glass side (referred as G10C5). An illustrative sketch of the lay-up sequence configurations is shown in Fig. 1.

Fig. 1
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Hybrid layup sequence configurations: (a) [G2C]5G2 symmetric layup; asymmetric stacking sequences (b) C5G10 and (c) G10C5

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According to the ASTM D7136 international standard (Ref 17), the experimental campaign consisted of impact tests conducted using a drop tower machine. A hemispheric shape impactor of 19.8 mm diameter with a total mass of 3.62 kg was dropped from different heights to obtain the desired energy level of 5, 10 and 20 J. At least three tests were performed for each layup and impact energy combination. The specimens, consisting of rectangular plates with dimensions of 100 × 150 mm, were positioned in the testing area by clamping all the edges. A load cell connected to the falling indenter allowed to measure the impact force and an interferometric displacement sensor provided the displacement measurement. The panel absorbed energy was evaluated by integrating the area under the force vs displacement curves.

2.2 Numerical Methodology

The hybrid laminates’ impact behavior was numerically reproduced by adopting a commercial finite element analysis explicit solver. Since a mesoscale modeling approach was necessary to deepen the damage mechanisms in the dependence on the stacking sequence, a FE model was developed for each configuration. The laminates were modeled ply-by-ply, with each ply obtained as a 3D geometry, meshed adopting 8-node quadrilateral elements, with reduced integration and hourglass control enhanced. Given the symmetry of the tested geometry, the normal impact of the indenter on the panel was modeled as a symmetric quarter model, as shown in Fig. 2.

Fig. 2
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Schematization of the mesoscale numerical impact quarter model with symmetry cutting planes and applied constraints and load

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A single-biased mesh refinement was chosen to guarantee the necessary finer element size in the impact region. In contrast, a coarser mesh was progressively imposed on the rest of the panel. A mesh sensitivity study was conducted to guarantee a quasi-constant total energy with negligible values of artificial strain energy during the simulation, associated with an adequate degree of accuracy for stress and strain. The resulting maximum deviation in total energy lower than 4% and the maximum artificial strain energy about 3% suggested choosing a minimum and maximum element size of 0.5 and 2 mm. The elements’ thickness was fixed as equal to 0.234 mm, according to the single ply thickness. A finer mesh was proved to produce negligible improvement in results accuracy with a significant increase in the computational cost. The laminates were obtained by overlaying the plies according to the stacking sequences. A Cohesive Zone Model (CZM) was adopted to model the interlaminar connection among the adjacent plies. The resulting panels, shown in Fig. 2, were constrained by suppressing the out-of-plane displacements and the in-plane rotations of the symmetry cutting planes. All the degrees of freedom were suppressed on the rest of the panel edges. The indenter was obtained as a rigid body surface. To facilitate the contact algorithm convergency, a discretized rigid body option was chosen, thus the geometry was meshed with 0.5 mm uniform size quadrilateral elements. For the indenter-to-panel interaction, a General Contact algorithm with a friction coefficient of 0.3 was adopted (Ref 18). The single ply mechanical properties were calculated starting from the customers’ material properties data sheets, known the fiber volume fraction, and homogenizing with a woven adapted mixing rule (Ref 1, 16). The analytically computed properties were verified through experimental tensile and three-point bending tests, conducted by the authors and available in literature (Ref 11). The elastic properties of carbon-resin and glass-resin plies are both reported in Table 1.

Table 1 Carbon-resin and glass-resin plies elastic properties
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The Hashin damage criterion (Ref 19) was adopted for the intralaminar damage modeling. The adopted materials’ damage properties are reported in Table 2 and available in literature (Ref 11). The delamination phenomena were considered by imposing a CZM. A bilinear traction–separation law was assumed both for the normal and shear damage modes, here referred as n,s,t. It describes the actual contact stress as proportional to the contact surfaces displacement according to a penalty stiffness coefficient. This coefficient is much stiffer respect to the in-contact materials and automatically computed by the software. This is up to the maximum nominal stress σi* is reached. Then the damage initiates and a progressive reduction in stress over the surfaces displacements occurs. The cohesive properties degradation is proportional to the imposed fracture toughness Gic. The described cohesive law properties are found in Table 3. The damage mixing mode was chosen to be governed by the Benzeggagh and Kenane (B-K) energy fracture criterion (Ref 20). The experimental impact tests were numerically reproduced with the proposed model. First, the impacts on the considered hybrid laminates were simulated at the three energy levels of 5, 10 and 20 J. Next, the resulting contact force, panel deflection and absorbed energy trends were compared to those experimentally measured to validate the model. The interlaminar and intralaminar damages were then highlighted for each hybrid composite and their contribution to the panels’ absorbed energy was shown. Finally, some considerations about the correlation between the panels’ damage typology and distribution, connected to the stacking sequence, were presented.

Table 2 Hashin damage properties of carbon-resin and class-resin plies
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Table 3 CZM penalty stiffness, initiation stresses and fracture toughness properties
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3 Results and Discussion

The experimental outcomes, reported in Fig. 3, show a rising in the maximum values of force and deflection with the increase in the impact energy, regardless of the stacking sequence. That means the higher the impact energy, the higher both the force transmitted to the panels and the deformation. It can be seen for each energy level, the less inflected panels, are those impacted on the glass fiber side (namely GC and G10C5).

Fig. 3
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Maximum impact force (a) and panel deflection (b) for the tested energy levels grouped by stacking sequence

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Interesting considerations about the investigated hybrid laminates impact response can be made by studying the force to deflection curves grouped by the impact energy, as here reported in Fig. 4. Compared under the same impact energy, the rigidity of the laminates GC and G10C5 resulted comparable, while C5G10 showed to be less rigid. This trend was found for all the examined energies. The panel rigidity looks to be dominated by the properties of the bottom side of the laminate, where the stress field is mainly of traction and the strength results governed by the traction properties of the fibers. While in the top region of the panel, where the compression stress is dominant, the strength of the laminate is governed by the resin and fiber buckling mechanisms which are quite independent of the reinforcement type (Ref 3). The GC and G10C5 panels, presenting a higher percentage of carbon on the bottom of the panel, resulted in a more rigid impact response. That is the reason for the trend of the results reported in both Fig. 3 and 4 that show as both the GC and G10C5 panels are less inclined to deform than the C5G10 laminates. A hybrid laminate parameter of interest in this study is represented by the energy absorption capability, which is strictly connected to the panel damage. It is here reported in Fig. 5 in the form of energy absorption rate (i.e., the percentage ratio between the absorbed and the available energy). It represents an index of damage, given that the greater the energy absorbed, the greater the overall damage in the impacted components. As reported in Fig. 5, an impact energy increase produces significant differences in the trend of the energy absorption rates of the considered layups. The C5G10 and G10C5 sequences, always show an increase in the absorption rate. While the GC layup, first shows a quasi-constant absorbed energy, about 26.8 ± 0.5%, between 5 and 10 J, and then a growth of over 35% at 20 J. Moreover, for the relatively high impact loads (10 and 20 J), the C5G10 panels absorbed the highest amount of energy compared to both GC and G10C5 configurations. A different behavior was found when the laminates were impacted at 5 J with the GC panels that would seem to be the most energy absorbing. According to the stacking sequence, the reasons for such a difference in the material’s capability to dissipate the impact energy could lie in the weight of the different damage mechanisms contributing to the damage of each panel. With the purpose to deepen the role of intralaminar and interlaminar damages into the total damage, the proposed numerical model was validated by comparing numerical simulations of all the tested conditions with the experimental results. In Fig. 6, the numerical curves of impact force to time and impact force to panel deflection, are reported and compared to those experimentally obtained. For the sake of brevity, it was chosen to show only one different level of impact energy for each stacking sequence. The capability of the model to reproduce the impact behavior, regardless of the different stacking sequences and the impact energy levels, can be appreciated. The numerical outcomes are in good correlation with the experimental results. The R-squared value, computed among all the simulated impact conditions, always resulted between 0.85 and 0.97. Also, regarding the maximum contact force, maximum panel deflection and the total time of impact, the model was proved to be in good accordance with the experimental evidence. The percentage error, between the experimentally measured and the numerically calculated values of maximum impact force and panel deflection, is here reported in Table 4, for all the studied combinations of impact energy and stacking sequence.

Fig. 4
figure 4

Experimental force to deflection curves for each stacking sequences, grouped by the impact energy level in (a) for 5 J, in (b) for 10 J and in (c) for 20 J

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Fig. 5
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Energy absorption rate of each stacking sequence

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Fig. 6
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Experimental and numerical comparison of impact force to deflection and force to time curves, for C5G10 layup at 5 J (a), GC layup at 10 J (b) and G10C5 layup at 20 J (c)

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Table 4 Percentage error between the experimentally measured and the numerically calculated values of maximum impact force and panel deflection
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Since the proposed model correctly predicts the impact behavior of the considered hybrid stacking sequences in all the impact energy conditions, it has been used to investigate the laminates’ damage distribution. In Fig. 7, the weight of the Hashin damage and delamination on the total damage for each stacking sequence and all the studied impact energies is reported.

Fig. 7
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Distribution of Hashin damage and delamination damage respect to the total damage for each stacking sequence and impact energy levels

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The hybrid laminates GC and G10C5 showed a similar trend in the damage distribution. At the lowest impact energy, the delamination-dominated behavior is promoted by the more resistant carbon plies on the bottom of the panels that remain undamaged. On the contrary, the C5G10 laminate results governed by the Hashin damage because of the presence of fiberglass on the bottom of the panel which is less performing than carbon. This causes the traction failure of the plies on the panel bottom postponing the delamination advent (Ref 21, 22).

The above-mentioned difference in the damage mechanism is observed in Fig. 8, where the numerically computed Hashin damage distribution into the panel thickness is shown both for GC and C5G10 laminates in the correspondence of the maximum impact force time. While the GC stacking sequence presented a damage localized on the top of the laminate, mainly due to the compression matrix cracking and the contact with the impactor, the C5G10 resulted in a damage localized on the panel bottom due to the fiberglass and matrix tensile failure. Different behavior can be observed with the increase in the impact energy when the percentage of Hashin damage increases (i.e., the percentage of delamination damage reduces) for both GC and G10C5 laminates and reduces for C5G10 panels. The reason is that, under the relatively higher impact energies (10 and 20 J), the carbon fibers placed in the bottom areas of the panels fail, so promoting the Hashin damage of both GC and G10C5 laminates, as clearly shown in Fig. 9. The progressive failure of glass fibers in C5G10 panels also promoted the delamination damage which occurs among the carbon–carbon interfaces in the top region of the laminate, as reported in Fig. 10. The presence of the grouped glass plies on the bottom of C5G10 panels promoted wider damage, with respect to the carbon grouped plies on the bottom of the G10C5 panels, where the higher traction strength of carbon limited the damage to the most external surface, without significantly affecting the inner layers.

Fig. 8
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Hashin damage distribution in GC and C5G10 laminate thickness for 5 J impact energy

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Fig. 9
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Hashin damage distribution in GC (a) and G10C5 (b) laminate for 20 J impact energy

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Fig. 10
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Delamination damage on carbon–carbon interfaces of C5G5 laminate under 5 J impact energy

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4 Conclusions

This paper aimed to study the response of hybrid laminates, made of vinyl ester resin reinforced with carbon and glass fibers under low-velocity impact conditions, through an experimental–numerical approach. For this purpose, impact tests were conducted on three different hybrid lay-up and rising impact energy levels. FE models were developed and validated on the low-velocity impact experimental campaign. Based on the results above, the following conclusions can be drawn:

  • The hybrid laminates showed competitive performances in terms of maximum load and absorbed energy. In particular, the G10C5 laminate revealed the best performances showing the highest maximum impact load and the minimum value of the absorbed energy. The discussed good results additionally support the advantage of saving cost, since the low number of costly carbon layers in the laminates.

  • The proposed model, reproducing the impact behavior regardless of the stacking sequences and impact energy levels (R-squared value always between 0.85 and 0.97), allowed the prediction and characterization of both the intralaminar damage and delamination damage.

  • The numerically computed Hashin damage and delamination damage were studied. The lower impact energy resulted to be dominated by delamination in the GC and G10C5 laminates. While the C5G10 laminate showed to be Hashin damage governed, with most of the absorbed energy spent for the intralaminar damage. Such difference in the dissipation mechanisms, characterizing the lower impact energy, seems to fade away at the higher energies where the dissipation is governed by the Hashin damage independently by the stacking sequence. This suggests an activation threshold exists and it is dependent not only on the plies’ strength but also on their arrangement. Once this threshold is reached, the dominant energy absorption mechanism is not more influenced by the stacking sequence.

The absorbed energy distributions into the laminate thickness, due to the Hashin damage were evaluated ply-by-ply. The study has confirmed the prevalence of Hashin damage in C5G10 panels, due to the glass plies on the rear impact side promoting more comprehensive damage. On the other hand, carbon grouped plies on the impact rear side are characterized by a higher traction strength producing damage to the most external surface without significantly affecting the inner layers.