1 Introduction

Additive manufacturing has evolved tremendously since its conceptualization in 1984 (Ref 1), to the point where it is now widely accepted to have revolutionized the production of complex geometries, like structural electronics (Ref 2), batteries (Ref 3), medical implants (Ref 4) and the fabrication of impact-absorbing components (Ref 5). The latter structures have become ubiquitous in recent years, finding applications in the automotive (Ref 6) and the aeronautical sector (Ref 7), conformal body protection (Ref 8), technical/athletic footwear (Ref 9), helmets (Ref 10) and many others. Despite the fact that the impact-mitigating properties of these components are predominantly based on their structural characteristics (i.e., porosity), the employed material drastically modulates their absorbing properties as well.

The majority of commercialized applications of impact-absorbing materials are based on polymer matrixes, as they are easy to produce and are widely accepted to be ideal structures for impact dissipation (Ref 11). Owing to their ductility and exceptional density-to-strength ratio, these polymeric components facilitate the controlled dissipation of energy (Ref 12). However, there is a consensus in the literature that the porosity induced into these components severely restricts their structural integrity compared to their bulk counterparts (Ref 13). This largely confines the application of porous polymers to absorbing components of low intensity impact. Recent studies (Ref 14) have, however, indicated that the use of fiber-reinforced composites could counteract these limitations and therefore provide the required structural rigidity through the addition of carbon- (Ref 15), or glass-fibers (Ref 16). This could facilitate the use of polymeric impact-mitigating structures (Ref 17) in strenuous conditions, capitalizing on arguably their predominant advantage over metallic ones, namely the available fabrication modalities, with additive manufacturing dominating the production of free-form structures (Ref 13). Despite the fact that impact-mitigating structures such as honeycombs (Ref 18), straight and helical struts (Ref 8), gyroid (Ref 19) and even auxetic ones (Ref 20) have been produced and extensively characterized as to their mechanical (Ref 21), physical (Ref 22) and even wear-related properties (Ref 23), there is an evident lack in literature concerning guidelines as to the required impact characteristics (e.g., energy, in terms of impact speed and mass) for porous polymeric structures.

Recent literature indicates the effect of several process variables of popular 3D printing technologies that have a significant effect on the functional properties of the manufactured component, e.g., deposition height and orientation, infill pattern and density, etc. (Ref 24, 25) However, in the absence of a norm on how porous polymers (e.g., produced with additive manufacturing) should be tested, researchers deploy different devices to test impact strength, i.e., Izod impact (Ref 26) vs. drop tests (Ref 12), while also evaluating different impact characteristics which may lead to incoherent results. Deceleration values, for example are systematically neglected during the evaluation of impact-dissipating properties (Ref 26) (Ref 27) although it could be argued that sacrificial cladding providing a constant deceleration plateau is far more protective to than a structure absorbing higher energy while exhibiting excessively large deceleration values.

The lack of consistent literature data is even more prevalent to fiber-reinforced composite polymers. There are just a few existing studies on the impact absorption capacity of polymeric components fabricated with additive manufacturing. These studies (Ref 12) (Ref 28), however, focus on how these properties are affected by production related parameters like infill density, etc. (Ref 12), rather than examining the impact parameters themselves.

The hypothesis of this investigation is that the progressive crushing modes of impact-mitigating structures differs not only based on the material employed, but is also highly dependent on the structure’s design. Toward this end, different infill densities are examined along with an altering density of solid peripheral layers and compared to fracture mechanisms of different materials available in literature.

2 Materials and Methods

2.1 Specimens’ Fabrication

All specimens were produced via a Fused Filament Fabrication (FFF) technique on a MarkForged Mark II (Gen2) printer using Onyx as the deposition material. The matrix of this material was a nylon-6 (PA-6) plastic (polyamide), while T300 carbon fibers (short fibers) were used as the reinforcement, corresponding to a volume fraction of 13.94%. Different sample series were prepared for tensile, impact (and compression) tests. The purpose was to evaluate the effect of infill and solid wall density (solid layers, peripheral to the infill) on the mechanical response of the samples.

2.1.1 Tensile Specimens

All tensile tests were performed with Type I specimens, in accordance with ASTM:D638 (Figure S1, in supplementary material) and used to evaluate the mechanical characteristics of Onyx with different infill densities. Solid samples contained 20 layers of 0.1 mm thickness each, deposited in 45° orientations (of a 90° altering sequence, respectively). Three types of samples were fabricated as to examine the effect of infill density and whether the use of solid perimeters can compensate for a potential loss in density.

  • Sample 2.55, exhibiting a 55% infill density surrounded by 2 solid layers of Onyx.

  • Sample 2.37, exhibiting a 37% infill density surrounded by 2 solid layers of Onyx.

  • Sample 4.37, exhibiting a 37% infill density surrounded by 4 solid layers of Onyx.

Beside these differences, all samples featured a triangular filament deposition pattern with 4 solid layers toward their top and bottom surface. The selection of the specific infill densities was based on the recommended manufacturer of the printer. The 37% infill percentage was used as it corresponds to the default setting of the employed MARKFORGED 3D printer. Since the use of lower densities is not recommended by manufacturer, we opted for a comparison to a higher density commonly employed in literature.

An overview of the tensile specimens is provided in Table S1 (supplementary material).

2.1.2 Cylindrical Samples

Specimens subjected to compression and the impact tests were of a cylindrical shape with a 16 mm diameter and deposited by 300 consecutive layers of a 0.1 mm thickness, and all remaining fabrication parameters were identical to those utilized for the tensile specimens, i.e., 4 solid layers toward their top and bottom surface of the cylinders while employing the aforementioned infill and solid wall densities.

2.2 Testing Conditions

Tensile tests were performed to provide a reference point with existing literature data, whereas compression tests were used to calibrate the impact energy and seek an analog between the compression response of these samples to their shock mitigating capacity.

2.2.1 Tensile Tests

The tensile tests were displacement-driven and performed using wedge grips on a universal testing system (Instron 5989). Specimens were tested in standard ambient conditions (SATP) of temperature and pressure with 50% relative humidity, employing a 9 mm/min strain rate, monitored through an extensometer.

2.2.2 Compression Tests

The same device was utilized for the compression experiments to determine the energy absorption of the cylindrical samples up to a 50% strain. To facilitate this, 2501 series INSTRON platens were used to uniaxially compress the samples at a constant deformation of 9 mm/min, at SATP. The energy required for the compression was calculated as the area beneath the force/displacement curve recorded by the device.

High-Velocity Impacts

Conventionally, the high-speed impact energy of cellular materials is calculated on the basis of static compressive tests, as described in 2.2.2. Mainly applied to metallic specimens, the corresponding standards (Ref 29) define the energy absorbed up to a compressive strain of 50% as sufficient to evaluate their compressive response at higher speeds. A proper threshold for the impact energy is highly prevalent as the crashworthiness of specimens should ideally be tested within the range of progressive structural failure (e.g., not exceeding its catastrophic failure modes). In line with this, the drop weight tests were performed on a fully automated drop tower system (CEAST 9350 by Instron), considering three impact velocities: 1 m/s, 6 m/s and 8.3 m/s, along three different impact masses 5.504 kg, 6.504 kg and 7.504 kg, respectively. Three specimens were tested for each of the above combinations, resulting in a total of 27 tests conducted for each specimen type (2.37, 2.55 and 4.37).

3 Results

3.1 Tensile Tests

Five samples were tested for each specimen type, and the longitudinal displacement was monitored along with the required force (displacement-driven experiments). Rupture of the sample, or a 50% reduction in the recorded load, was considered as the failure criterion of the tensile experiments. The average values for each specimen type are summarized in Fig. 1(a).

Fig. 1
figure 1

(a) Stress–strain curves of the uniaxial tensile experiments and (b) energy required to compress the carbon fiber-reinforced samples to a 50% strain

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Since the samples were not isotropic, an effective (longitudinal) elastic modulus (E) can be calculated in the elastic regime of each specimen, based on the stress/strain ratio of the initial portion of the slope, as shown in Fig. 1(a).

This resulted in the values presented in Table 1.

Table 1 Effective elastic moduli of the carbon fiber-reinforced nylon samples (ONYX)
Full size table

To provide a comparison for the simulated values, analytical predictions (also depicted in Table 1) were based on the two following formulas:

$$ E_{{{\text{porous}}}} = E_{{{\text{bulk}}}} \left( {{1} - f} \right)^{{2}} $$
(1)
$$ E_{{{\text{porous}}}} = E_{{{\text{bulk}}}} \left( {{1} - {2}f} \right) \, \left( {{1} + {4}f^{2} } \right) $$
(2)

where f is the equivalent pore volume fraction.

As expected, the effective elastic modulus of the porous specimens decreases with porosity, while analytical predictions systematically overestimated this effect.

3.2 Compression Tests

The static compressive tests revealed the progressive failure modes of the specimens by triggering stress concentrations that initiated failure, which then propagated through the structure. The energy absorbed up to a compressive strain of 50% is illustrated in Fig. 1(b), for all three specimen types. Notably, the progressive crushing modes differed in between the specimen types despite all of them consisting of the same matrix and brittle fiber reinforcement.

3.3 High-Velocity Impacts

During these tests, the speed of the component impacting upon the specimen decreases from its set value to rest, as the specimen absorbs the kinetic energy. The cushioning capacity of the specimens is characterized by the resulting force, which directly correlates to the produced deceleration.

The peak force recorded during impact depends on the specimen itself (infill pattern & density, solid layers, etc.) as well as the impact energy, which is expressed as a function of the impact mass and its velocity. A comparative 3D diagram reflecting how these parameters associate with one another is presented in Fig. 2. The variation of the peak force documented at low impact velocities was similar for all samples, and seemingly unrelated to the impact module’s mass. Differences increased, however, along the velocity values and were especially pronounced in-between samples 2.37 and 4.37, with the latter exhibiting a max. impact force reduced by 46.6%.

Fig. 2
figure 2

Peak force recorded during the impacts denoting the shock mitigating capacity of the carbon fiber-reinforced samples

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A correlation of max. and mean deceleration, as catalogued during the impacts, is summarized for all samples in Fig. 3. Catastrophic failure was, in all cases, characterized by a disproportional increase of max. deceleration to its mean value, leading to peak loads that initiate failure. As a result, the magnitude of absorbed energy is comparably low, while exposing the structure to high forces. This is evident in Fig. 3, according to which specimen type 4.37 exhibits an excellent deceleration plateau along with the preferable mean to max. deceleration ratio.

Fig. 3
figure 3

Max. and mean deceleration values of the impact component, indicating sock magnitude and plateau, respectively

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In the absence of impact testing protocols for porous polymer samples, the methodologies described in ISO 17340:2020 (Ref 29) were examined, to determine whether these can be extrapolated to non-metallic samples. In these terms, the deceleration provided by the carbon fiber-reinforced samples subjected to the high-velocity impacts was plotted against the applied impact energy (as shown in Fig. 4). In accordance with ISO 17340:2020 (Ref 29), the energy required to compress these samples to a 50% strain should be indicative of the specimens’ cushioning capacity and was thus superimposed on to this figure. This was, however, only the case for samples 2.55 and 4.37, indicating that no direct analog can be drawn from the compressive response of composite specimens to their crashworthiness, when employing testing protocols used for metallic samples.

Fig. 4
figure 4

Correlation of impact energy to the cushioning capacity of the carbon fiber-reinforced samples with respect to the energy required to compress the samples to a 50% strain

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The cushion factor (C) of the specimens was calculated at an impact mass and speed of 5.5 kg and 6 m/s, respectively, and is illustrated in Fig. 5. This represents a plot of the average stress over a cross-section of the sample (normalized by the absorbed energy) against the said average stress. The cushion factor is representative of a porous material’s capacity to absorb energy (via high-velocity impacts) which can be related to its uniaxial stress-strain behavior (Ref 30). Interestingly, all samples exhibited similar trends as to their cushioning factors, with the average stress being inversely correlated with their equivalent volume fraction.

Fig. 5
figure 5

Cushion factor of the carbon fiber-reinforced samples

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4 Discussion

The results of the tensile experiments, as shown in Fig. 1a, are in line with current literature (Ref 31). Interestingly, the peripheral solid layers seemed to have a more pronounced effect on the reduction of elasticity than the increase of infill density (i.e., E4.37 > E2.55), which may be attributed to the samples’ equivalent porosity (i.e., f4.37 > f2.55). The above is not reflected by the theoretical calculations, which are unable to accurately estimate the elastic modulus of the porous specimens due to the addition of brittle external layers to the specimen 4.37.

It should be noted that equation (1), which is commonly used to predict the equivalent modulus of elasticity for low values of porosity (Ref 32), leads to closer predictions of the materials’ elastic response. The Gibson and Ashby formula instead, i.e., equation (2) (used for higher values of porosity (Ref 33)) clearly overestimates the materials’ elastic response. This is most likely due to assuming an idealized structure, which is fundamental to this particular theoretical prediction, but not appropriate in the case of 3D printed specimens.

In the compression tests (Fig. 1b), the specimen type 2.37 (exhibiting a slightly higher elasticity to the other ones) folded more progressively through the formation of local buckles. This is likely due to the low infill in combination with the only two peripheral solid layers, leading to an early plastic yielding of the structure, thus requiring less compressive energy than the other specimens. Type 4.37, owing to its denser extremity (4 peripheral solid layers), failed predominantly due to transverse shearing, characterized by wedge-shaped laminate cross-sections. Specimen types 2.55 exhibited the highest compression energy, which is in line with literature data and can be attributed to the specimen’s higher infill density (Ref 34). The principal failure mode of these specimens was lamina bending induced by the growth of inter- and intra-laminar cracks.

A close examination of Fig. 2 reveals that both an increasing number of peripheral solid layers and infill density lead in most cases to higher peak forces during impact. This should, however, be evaluated with respect to the failure modes of the samples as the majority resulted in catastrophic failure at impact velocities higher than 6 m/s. This is reflected in the consistency in which the specimens are able to absorb energy. Ideally, impact-mitigating structures should lead to a force plateau of a low magnitude, i.e., constant deceleration values, not varying significantly from the max. deceleration. As demonstrated in Fig. 3.

Interestingly, the equivalent pore volume fraction, as provided in Table 1, seemed to affect the applicability of the methodology described in ISO 17340:2020 (Ref 29). The methodology seemed to hold true at low values, e.g., specimens 2.55, but diverged significantly for porosities beyond 26%. This was, however, to be expected, as the scope of this ISO standard is applicable to cellular metals having a porosity of more than 50%. Furthermore, the progressive crushing modes of impact-mitigating structures differ significantly based on their material. While metallic components collapse due to extensive plastic deformation (buckling and/or folding) (Ref 35), composites fail through a sequence of fracture mechanisms involving the growth of inter- and intra-laminar cracks (Ref 36), fiber-matrix de-bonding (Ref 37) and de-lamination (Ref 38).

Despite similar tendencies observed for the samples’ cushion factor (see Fig. 5), it should be noted that the evaluation of this parameter is complicated significantly when testing different impact energies. An increase in impact energy is bound to affect the average stress, while the absorbed energy will not increase beyond a certain point. As a result, higher impact speeds than the one used to plot Fig. 5 will lead to a disproportional increase in the average stress, while lower impact speeds (within the impact energy threshold of the porous material) will result in a significantly higher cushion factor. An increase in infill density leads to higher average stress values, which is again in line with recent literature finding (Ref 25).

5 Conclusions

The tested structures’ design and fabrication parameters have, as expected, a dominant effect on their failure progression in terms of stress concentrations that trigger fracture mechanisms and the sequence with which these occur.

The results presented here indicate that an increased pore volume fraction is expected to dissipate the kinetic energy of a high-velocity impact effectively. In addition, lamina orientation (e.g., solid layers) seems to significantly improve the structural integrity of the structure, which consequently yields at lower forces, providing more consistent deceleration values perpendicular to this reinforcement. However, the use of solid layers is not necessarily a one-stop solution for impact-mitigating structures, as the impact may occur from multiple directions and these structures are not expected to offer omni-directional protection.

Although the interpretation of the results presented here is limited by the lack of a wider range of specimens (more combinations of peripheral layers and infill densities are required), we would suggest that the impact energy employed to test the crashworthiness of fiber-reinforced polymer samples requires a cumulative consideration of equivalent pore volume fraction and compressive strength. Nevertheless, more experiments are needed to provide a guideline for calculating impact energies suitable for evaluating the progressive crushing modes experienced by such structures.