The importance of print orientation in numerical modelling of 3D printed structures under impact loading

Anisotropy is commonly observed in 3D-printed polymer and composite parts, particularly when manufactured by fused filament fabrication (FFF). This anisotropy can lead to difficulty obtaining accurate material properties during mechanical characterisation. This study establishes a connection between the print parameters used in specimen characterisation and their influence on the accuracy of numerical models for 3D-printed cellular structures under impact. Material properties from only one of the characterisation variants studied, with a parallel infill, accurately represented the force response and physical damage of the experimental samples. In contrast, the default characterisation specimen with a ±45° infill underpredicted the peak force and overpredicted the impact duration, potentially leading to underestimating impact severity. This discrepancy could result in greater damage to a person or structure being protected. It is recommended that the parallel infill pattern be used when characterising materials for use in FFF cellular structures under impact loading to ensure more reliable simulations and improved design of impact-resistant structures.


Introduction
Cellular structures are often used for impact protection due to their lightweight and high energy absorbing capabilities [1,2].With the continuous improvement in additive manufacturing (AM) methods, it is now possible to produce cellular structures with complex geometries [3,4].3D printed cellular parts offer significant benefits in high energy impact and blast protection [5][6][7], automotive applications [8,9] as well as for lower energy impacts such as hip pads [10][11][12] and helmets [13,14].Additive manufacturing, particularly FFF, is also widely used in the military for developing complex components [15].
Previous studies have highlighted the anisotropy of 3D-printed parts, specifically when produced by FFF, where the material is extruded in layers [16][17][18][19].This effect is amplified when printing with composite materials, both short fibre [20][21][22][23] and continuous fibre [24][25][26][27], due to the alignment along the extrusion direction [28].The lack of standardised test methods for characterising 3D printed material leads to wildly varying properties obtained for the same material when printed with different parameters [20,29,30].Mishra et al [31] have shown that the impact strength, using the Izod impact test, of 3D-printed material is strongly influenced by infill properties such as density and raster angle.Fisher et al [20] characterised two materials, both manufactured by Markforged: 'Nylon White' an engineering grade PA6 filament and 'Onyx', a PA6 filament reinforced with 14 wt% [32] short carbon fibres approximately 130μm in length [33].Tensile specimens were designed and 3D printed according to ASTM D638-14 standard.Three infill variations (D: default, E: on-edge, P: parallel) of the type IV geometry were considered, as shown in figure 1(a), and the specimens were loaded at three strain rates.The study revealed that both print orientation and strain rate significantly influence the mechanical properties of the material.
Despite these insights, the relationship between print orientation during material characterisation and its effect on accurately modelling the impact response of these structures is not well understood.This work addresses this gap by investigating the print orientation required during material characterisation to accurately model the impact response of 3D-printed cellular structures.Nylon and short carbon fibre-reinforced nylon are explored using experimental and numerical approaches.Johnson-Cook plasticity and damage models are calibrated to test data and employed in numerical simulations to replicate experimental impacts.This research seeks to provide a deeper understanding of the importance of print orientation when modelling the impact response to assist in developing reliable predictive models for their behaviour.

Materials and methods
Two materials 'Nylon White' and 'Onyx', as described in the introduction, were chosen for this study allowing for the effect of short-fibre reinforcement to be explored.Data from previous material characterisation [17] was imported into MCalibration [30] software to calibrate Johnson-Cook plasticity models to be used in the numerical simulation.MCalibration uses an inverse method optimisation procedure to fit constitutive material model parameters to experimental data.This procedure includes a range of algorithms, such as NEWUOA and Levenberg-Marquardt [34].The input parameters for Johnson-Cook plasticity models with strain-rate dependence were generated for each of the print orientations using the formulation shown in equation (1).
where A is the initial yield stress (MPa), B is the plastic hardening parameter (MPa), C is the strain rate factor, 0  is the reference strain rate (1/s), and n the strain hardening parameter.Material failure was initiated using the ductile damage approach within Abaqus with the fracture strain at damage initiation, e, the corresponding strain rate, r (s −1 ), given by MCalibration at each of the three strain rates.Damage evolution was assumed to be linear and displacement controlled with a displacement at failure of 0.02, guided by MCalibration.
To validate the material models, hexagonal structures were printed by FFF using the Markforged Mark Two printer with a layer height of 0.2 mm, consistent with the parameters used for characterisation.The structure consists of a 6 × 4 array of hexagonal unit cells printed out of plane, figure 1(b), with a wall thickness of approximately 0.7 mm and overall dimensions of 120 × 50 × 70 mm.Due to the thin wall sections, the print path follows the wall direction.
The structures were subjected to impact testing using an Instron Dynatup drop tower at velocities of 2 m s −1 and 4 m s −1 .The impactor used was a 5.482 kg hemispherical hardened steel projectile, 'TUP', with a 16 mm diameter.The samples were placed on a rigid steel base with stops on both sides, as depicted in figure 2. This reduced movement and ensured consistency in the impact conditions.Each test was repeated at least five times and the force was measured using a load cell integrated into the drop tower system.
The experimental impacts were replicated in Abaqus 2020 FE platform [35], figure 3, by means of an explicit analysis.The hardened steel impactor was modelled as a discrete rigid part, meshed with R3D4 finite elements, and assigned a pre-defined velocity field of either 2 or 4 m s −1 .The stops and base were also defined as rigid with R3D4 finite elements.The hexagonal structure was modelled using S4R shell elements, with default hourglass control enabled, and assigned the calibrated Johnson-Cook plasticity models obtained from MCalibration software.Hard contacts with a penalty friction of 0.3 were applied to the whole model [36,37].The force and time responses were monitored throughout the simulations through the reference point on the tup and compared with the experimental data.

Results and discussion
The calibrated Johnson-Cook plasticity parameters are given in table 1 along with the elastic modulus, E, and the ductile damage parameter pairs: rate (r, s −1 ) and plastic strain (e) generated by MCalibration.The influence of the different material properties is shown clearly in figures 4-5 where the force-time plots of the experimental impact tests are compared with the numerical predictions.
Figure 4(a) shows the numerical and experimental force-time curves for the Onyx structures impacted at 2 m s −1 .The default material data results in a significant overprediction of the impact duration and underprediction of the peak force.This is due to the reduced stiffness caused by the default specimen's off-axis infill.No failure is observed as the default specimens underwent a high strain to failure during characterisation and this strain level was not reached in the impact tests.A lower, longer pulse such as this is typically correlated with a less severe injury as the energy is dissipated over a longer time [38,39].This model could therefore lead to underpredicting the severity of an impact.The on-edge model captures the pulse duration and initial stiffness well, however, it overpredicts the peak force as it fails to capture the failure of the material at 10ms, also due to the significant elongation to failure for the tested material geometry.This material failure was well captured by the parallel model, which accurately represents the experimental plots and the damage seen experimentally (figure 6).Similar trends were seen in the force-time plots for the nylon structure (figure 4(b)).The default material data produced a longer, lower force-time pulse than the experiments.The on-edge data captured the stiffness and pulse duration accurately but did not capture the full extent of the failure at 10 ms.The parallel model most closely represents the experimental with the experimental stiffness, pulse duration and material failure.However, it overpredicted the peak force by approximately 15%.   Figure 5(a) shows the mechanical response of the Onyx structure impacted at 4 m s −1 .Due to the higher velocity, the impactor hit the solid steel base under the structure at ≈12.5 ms, thus only the data before this point is considered.The default model captures the force response relatively well, however, it did not capture any damage to the structure.The reduced force is instead attributed to the lower stiffness, as previously described.The on-edge sample also did not capture any damage and its high stiffness resulted in a significant overestimation of the force.The parallel sample slightly overestimated the force however captured the physical behaviour well.The damage of the unit cells during perforation is seen on the graph as drops in force, as reflected in the experimental photos (figure 6).The nylon behaved similarly with the closest match produced using the parallel material model (figure 5(b)), where the material failure is again observed as drops in the force.
Given the parallel material model most accurately predicted the force-time response for both materials, the damage predicted by the parallel model was compared to the experimental damage observed.For the Onyx structures impacted at 2 m s −1 there was minor damage, limited to the first unit cell however full perforation was experienced for Onyx impacted at 4 m s −1 .In both cases, the damage was limited to the close vicinity of the impactor.The parallel material model captured the damage predictions well in both cases, as seen in figures 6(a), (b).The depth of damage as well as the localisation in the x direction matches the experimental observations  fairly well.The numerical model predicted more plastic deformation in the y (build) direction than was seen experimentally due to the delamination of layers that occurred which restricted deformation in the y direction.
The damage in the nylon samples, figures 6(c), (d), also closely matched the numerical predictions.For the parts impacted at 2 m s −1 , a small amount of plastic deformation and cracking was observed localised to the impact zone which is closely matched by the numerical prediction.Slightly more damage was predicted in plane (z) though this did not affect the overall deformation of the structure.Significantly more damage was observed in the 4 m s −1 impact and this was reflected in the numerical results.The damage in this case was not localised to the impact zone suggesting that delamination of print layers was less significant compared to the Onyx structure.
Delamination was not considered in the numerical modelling due to the significant added complexity required.Nevertheless, the predicted force-time responses matched the experimental results well, thus indicating little influence of delamination.Neglecting delamination did, however, limit the accuracy of the damage predictions, particularly for the Onyx samples, resulting in an overprediction of the damaged area in the build direction.Delamination effects could be modelled using cohesive zone modelling (CZM) [40] which would further improve the accuracy.Although strain rate dependency has been accounted for, the viscoelastic behaviour of these materials has not been explored.Viscoelastic characteristics influence the dynamic impact response of structures [41].Given that the viscoelastic behaviour of a 3D-printed material is influenced by print direction [42], this should be accounted for in future studies for more accurate impact predictions.

Conclusions
In this study, three Johnson-Cook material models for nylon and short carbon fibre-reinforced nylon were calibrated.These models were based on tensile test data using three different print orientations: default, parallel, and on-edge.Each model was implemented in a finite element model of 3D-printed hexagonal structures under low-velocity impact.Only one print orientation, parallel, successfully replicated both the force-time response and damage characteristics of the physical specimens subjected to experimental impact loading.The accuracy of the damage prediction for the Onyx samples was limited by the lack of delamination modelling and as such it should be considered if accurate numerical damage assessments are required.
This study highlighted the importance of considering the print orientation when characterising a 3D printed material and suggests a suitable print orientation to use when investigating 3D printed cellular structures under impact loads.Strain rate-dependent Johnson-Cook plasticity and damage models are presented for both materials in the three orientations considered.The data presented will assist researchers and industry professionals when using such materials for 3D printing.

Figure 1 .
Figure 1.3D printed parts (a) infill orientation of characterisation specimens: default (D), parallel (P) and on-edge (E); (b) hexagonal structure printed out of plane with 0.7 mm wall thickness.

Figure 2 .
Figure 2. The experimental impact set-up showing (a) hexagonal structure on a rigid base with fixed stops and (b) position in the Instron Dynatup drop tower.

Figure 3 .
Figure 3. Impact set-up showing the hexagonal structure placed on a rigid base with stops to prevent lateral movement.

Figure 4 .
Figure 4. Force-time responses for (a) Onyx and (b) nylon structures subject to 2 m s −1 impact.

Figure 5 .
Figure 5. Force-time responses for (a) Onyx and (b) nylon structures subject to 4 m s −1 impact.

Figure 6 .
Figure 6.Front and side views of the damaged area from the impactor for (a), (b) Onyx and (c), (d) nylon materials under the two different impact velocities (2 m s −1 and 4 m s −1 ).Experimental photos and numerical plots of the damaged areas are shown.

Table 1 .
Material parameters for the Johnson-Cook model obtained from the calibration procedure.