Bi-directional porous beams under low-velocity impact: Made of carbon fiber reinforced PLA,fabrication with 3D printer and testing with impact equipment

Abstract

In this article, two-dimensional functionally graded porous types $\wedge$ and $\vee$ (2D-FGP $\wedge$ and 2D-FGP $\vee$ ) are manufactured using a 3D printer. This is made feasible by technological advancements that have made it possible to make complicated parts that were before unattainable. The Polylactic acid reinforced with carbon fiber (PLA-CF) is fed into a 3D printer to create the beams. The low-velocity impact attributes of the beams, such as histories of contact force, impactor displacement, and absorbed energy, are extracted using drop-weight impact testing equipment. The 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with varied hole diameters are tested in a variety of impactor initial energies till are broken. The significant findings indicate that the 2D-FGP $\wedge$ distribution’s peak contact force is greater than the 2D-FGP $\vee$ distribution and that this trend is reversed for impact time, absorbed energy and peak impactor displacement. In both 2D-FGP $\wedge$ and 2D-FGP $\vee$ scenarios, the beams break at a lower energy as the hole diameter grows. A non-linear polynomial equation that incorporates the inputs of hole diameters, impactor initial energy and hole type distribution is provided to forecast the peak contact force and absorbed energy.

Introduction

3D printing is a process of additive manufacturing in which physical objects are produced through digital design and then fused using thin layers of material. The use of 3D printers allows for the creation of designs that would not have been possible with traditional production. A porous medium or a porous material is a material with pores in materials science. Two important factors that characterize porosity are the volume of void space and the distribution of plasma size. PLA is a thermoplastic monomer manufactured from biomass sources such as maize starch or sugar cane. PLA-CF generates products with a stunning carbon black surface finish and increases the filament’s stiffness. Generally, porous PLA-CF may be impacted by other objects and there is a need to investigate this problem.

A review of the experimental testing of composite materials is carried out in this part. As a way to improve structural performance under dynamic load and reduce cracking and spalling phenomena by increasing stiffness, fiber-reinforced concrete was used in structural applications. ¹ To assess the impact resistance for different composite sandwich beam types, vibration response changes were studied. ² The purpose of the study of Evci and Gülgeç ³ was to investigate the Hertzian failure and impact damage progress in three composite types (Unidirectional E-Glass, woven E-Glass and woven Aramid structures samples), as well as determine a peak force threshold. Under low-velocity impact, Hassan et al. ⁴ addressed the performance of laminated plastics reinforced with glass fibers using experimental tests and finite element simulation. A computational and experimental investigation of the reaction of the hybrid titanium composite laminates to low-velocity impact was given by Reiner et al. ⁵ To obtain the effect of nano-silica on the response of perforation, flexural and tensile behavior of composites and nanocomposites, tensile, three-point bending and impact tests were carried out. ⁶

The impact and post-impact performance of hybrid sandwiches with aluminum alloy cores and face sheets reinforced with carbon fiber were studied by He et al. ⁷ Margabandu and Subramaniam ⁸ investigated the influence of fabric stacking functions on the impact and flexural properties of epoxy composites reinforced by jute/carbon fibers. In both experimental and numerical terms, the performance of woven glass and epoxy composite plates to impact loading was investigated by Gunaryo et al. ⁹ Panciroli and Giannini ¹⁰ carried out the experimental and numerical analysis of low-velocity impacts on the glass/epoxy and flax/epoxy composites. Boukar et al. ¹¹ presented the impact tests on the composites reinforced by biaxial glass fiber. Avazpoor et al. ¹² studied the low-velocity impact on the composites reinforced by glass fiber. The effect of composite fixture type on the low-velocity impact tests was investigated by Ma et al. ¹³

In this section, an overview of the research conducted on the mechanical properties of composites made by 3D printing is discussed. Wang et al. ¹⁴ fabricated the panel made of glass fibre reinforced polymer skins and a core made of a 3D printed composite of glass fibre and polyamide 12. The core extended from the 3D re-entrant auxetic unit cell, which was composed of four umbrella-shaped elements arranged in a specific way. The auxetic behavior was a result of the ‘folding up' or ‘opening' of these elements. The tetrachiral sandwich structure made of PLA was 3D printed by Sadikbasha and Pandurangan ¹⁵ and used under high-velocity impact tests. Akhoundi et al. ¹⁶ conducted a study to determine the printing speed required for accurate printing of PLA/continuous glass fiber composites using a fused filament fabrication 3D printer. The Markforged system was used to 3D print a sequence of continuous glass fiber-reinforced composites, which were then incorporated between layers of aluminum alloy to create hybrid laminate structures. ¹⁷ The laminates underwent testing for tensile strength, interfacial fracture toughness, as well as low-velocity and high-velocity impact resistance. Chihi et al. ¹⁸ carried out the compressive behavior of 3D-printed carbon fiber-reinforced polyethylene terephthalate glycol composites to optimize various infill parameters under high impact pressures (strain rates). The influence of structure volume fraction and unit cell shape on the vibration and mechanical characteristics of 3D-printed lattice structures are investigated by Singh et al. ¹⁹ The polyethylene terephthalate glycol composites reinforced by graphene were 3D printed to investigate the characteristics of tensile, compression, flexural and impact behaviors. ²⁰ Chen et al. ²¹ conducted a study on the effects of localized impact on a 3D-printed polymeric hexachiral frame filled with open-cell soft polyurethane foam.

A study of low-velocity impact on porous materials is included in this part. The low-velocity impact research of FGP circular plates was given by Khatounabadi et al. ²² using graphene platelet reinforcements and first-order shear deformation theory (FSDT). Serajzadeh and Malekzadeh ²³ studied low-velocity impact on the curved sandwich beams with FG carbon nanotube-reinforced composite face sheets and porous core using a layerwise-FE approach based on the 2D elasticity theory. Al-Menahlawi et al. ²⁴ carried out the modeling of the FGP plate reinforced by carbon nanotubes using ABAQUS FE software and high-order shear deformation plate theory (HSDT). Zheng et al. ²⁵ simulated sandwich beams with two face sheets made of aluminum alloy and a porous aluminum core reinforced by graphene platelets that are under low-velocity impact using the ABAQUS FE code. Zheng et al. ²⁶ used the ABAQUS FE program to analyze the low-velocity impact data of sandwich plates with two face sheets made of titanium alloy and a porous aluminum foam core reinforced by FG graphene platelets.

Examining the studies conducted on low-velocity impact on FGP materials suggests that theoretical modeling or numerical simulations were carried out in this case. This article focuses on the experimental fabrication of FGP beams using a 3D printer with different hole diameters. In this article, the input material for fabricating 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams using 3D printers is PLA-CF. The low-velocity impact properties of the utilized materials are initially assessed through drop-weight impact testing equipment. To determine the required impact energy to break the FGP beams, various impactor initial energies are used. Finally, based on experimental tests, new theoretical equations are presented to predict the peak contact force and absorbed energy related to the low-velocity impact on 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams.

Materials and methods

In this research using a 3D printer, 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams made of PLA-CF with a length of 140 mm, a width of 20 mm and a height of 20 mm are fabricated using a 3D printer (Figure 1).

Figure 1.

The 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams fabricated by 3D printer.

First, the beams are designed in SolidWorks software and given to the 3D printer for manufacturing. The FGP beams design in SolidWorks software and sectioned samples made by a 3D printer are shown in Figure 2. It is important that the meaning of 2D in this research is that if one direction is considered from three directions in a rectangular coordinate system, the distributions are FG in two directions. The 2D-FGP $\wedge$ distribution shows the highest number of holes at the bottom level of the beam and the lowest number at the top level, while the opposite is true for the 2D-FGP $\vee$ distribution. The diameter of the holes is considered to be 2 and 3 mm. The holes in Figure 2 are the hollow spheres embedded inside the beam.

Figure 2.

The FGP beams design in SolidWorks software and sectioned samples made by 3D printer, a) 2D-FGP $\wedge$ with 2-mm hole diameter, b) 2D-FGP $\vee$ with 2-mm hole diameter, c) 2D-FGP $\wedge$ with 3-mm hole diameter and d) 2D-FGP $\vee$ with 3-mm hole diameter.

In factories, the TY-7004 type single screw extrusion equipment is used to manufacture the PLA-CF filament, with an extrusion temperature of 180 °C and a screw speed of 200 r/min. In this article, the device available in Kermanshah University of Technology is used to perform simple tensile and three-point bending tests (Figure 3(a)). Fabricating dumbbell-shaped beams using a 3D printer requires the utilization of PLA-CF material and adhering to the recommendations outlined in the ASTM D638 standard for assessing plastic tensile properties. To perform the three-point bending test, beams 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 2-mm hole diameter are also considered. The stress-strain diagram extracted from the tensile test is presented in Figure 3(b) and force-extension diagram based on a three-point bending test of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 2-mm holes diameter is parented in Figure 3(c).

Figure 3.

a) The device used for tensile and three-point bending tests of Kermanshah University of Technology, b) the stress-strain diagram of PLA-CF based on the tensile test and c) the force-extension diagram based on the three-point bending test of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 2-mm hole diameter.

In Table 1, the porosity and density of the fabricated beams, as well as the mechanical properties obtained from the tensile and three-point bending tests, are presented. Considering that the beam with 2D-FGP $\vee$ distribution has a higher percentage of porosity compared to the beam with 2D-FGP $\wedge$ distribution at the loading point, the maximum bending force of 2D-FGP $\wedge$ is 1.05 times that of 2D-FGP $\vee$ . However, because the beam breaks in the bending test at the bottom level of the beam and the 2D-FGP $\wedge$ beam has a higher percentage of porosity at the bottom level than the 2D-FGP $\vee$ beam, the breaking force of 2D-FGP $\vee$ is greater than 2D-FGP $\wedge$ .

Table 1.

The porosity and density of fabricated beams and the mechanical properties of PLA-CF obtained from the tensile and three-point bending tests.

	2D-FGP $\wedge$ with 2-mm hole diameter	2D-FGP $\vee$ with 2-mm hole diameter	2D-FGP $\wedge$ with 3-mm hole diameter and	2D-FGP $\vee$ with 3-mm hole diameter
Porosity (%)	2/96	2/96	9/99	9/99
Density (g/cm3)	1/08	1/08	1.04	1.04
Tensile test of PLA-CF
	Young’s modulus (GPa)	Tensile strength (MPa)	Toughness (J/m3)	Failure strain
	1.65	22.23	0.68	0.04
Three-point bending test of FGP beam with 2-mm hole diameter
	Peak force (N)	Peak extension (mm)	Break force (N)	Break extension (mm)
2D-FGP $\wedge$	1433.20	3.07	1191.40	3.56
2D-FGP $\vee$	1368.50	2.49	1322.40	2.56

The drop-weight impact testing equipment available at the Razi University of Kermanshah is applied for low-velocity impact analysis (Figure 4).

Figure 4.

The drop-weight impact testing equipment of Razi University of Kermanshah.

This equipment contains a spherical impactor tip with a 6.4 mm radius and 2.88 kg mass. This impactor strikes the center of the upper surface of the 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with varying energies. The clamped boundary conditions are used for both sides of the beam in this device so that the effective length of the beam becomes 115 mm. Different impact energies can be produced with different impactor heights. The contact force history ( $F_c\left(t\right)$ ) between the impactor tip and the upper surface of the beam can be obtained from the drop-weight impact testing equipment and the impactor velocity ( $v_i\left(t\right)$ ), impactor displacement ( ${\delta }_i\left(t\right)$ ) and absorbed energy ( $E_i\left(t\right))$ can be calculated using the equations ²⁷ :

$v_i\left(t\right)=v_{i0}+gt-{\int }_0^t\frac{F_c\left(t\right)}{m}dt$

(1)

${\delta }_i\left(t\right)={\delta }_{i0}+v_{i0}\mathrm{t}+\frac{g{t}^2}{2}-{\int }_0^t\left({\int }_0^t\frac{F_c\left(t\right)}{m}dt\right)dt$

(2)

$E_i\left(t\right)=\frac{m\left({v_{i0}}^2-{v_i\left(t\right)}^2\right)}{2}+mg{\delta }_i\left(t\right)$

(3)

Where $v_{i0}$ , $g$ , $t$ , $m$ and ${\delta }_{i0}$ are the impactor initial velocity, the gravity acceleration, the time from the moment of the collision, the impactor mass and the impactor initial displacement, respectively. Assuming that $E_{i0}$ is the impactor initial energy, at $t$ = 0 the values of ${\delta }_{i0}$ and $v_{i0}$ are equal to 0 and $\sqrt{\frac{2E_{i0}}{m}}$ , respectively.

Results and discussions

In this section using drop-weight impact testing equipment, 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams made of PLA-CF are tested in various impactor initial energies and different diameters of beam holes. Impact tests are carried out from the 1.5-J impactor initial energy to the fracture energy. To validate the obtained impact responses, three samples were fabricated by the 3D printer from each beam. To investigate the results of low-velocity impact, histories of contact force, impactor displacement and absorbed energy and contact force-displacement diagram are illustrated and studied in detail. Figure 5 shows the 1.5-J and 3-J impact responses of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 2-mm hole diameter.

Figure 5.

Low-velocity impact on 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 2-mm hole diameter fabricated from PLA-CF material based on the drop-weight impact tests with 1.5-J and 3-J impactor initial energies, diagrams of a) contact force-time, b) impactor displacement-time, c) absorbed energy-time and d) contact force-displacement.

The characteristics of the same graph for energies of 6 J and 9 J are presented in Figure 6. As this Fig. shows, in beams with 2-mm hole diameter, the 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams both are broken at an energy of 9 J.

Figure 6.

Low-velocity impact on 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 2-mm hole diameter fabricated from PLA-CF material based on the drop-weight impact tests with 6-J and 9-J impactor initial energies, diagrams of a) contact force-time, b) impactor displacement-time, c) absorbed energy-time and d) contact force-displacement.

Also, Figure 7 illustrates the impact responses of 1.5-J and 3-J for 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 3-mm hole diameter.

Figure 7.

Low-velocity impact on 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 3-mm hole diameter fabricated from PLA-CF material based on the drop-weight impact tests with 1.5-J and 3-J impactor initial energies, diagrams of a) contact force-time, b) impactor displacement-time, c) absorbed energy-time and d) contact force-displacement.

The corresponding graph for 6-J energy can be found in Figure 8. In this Fig., it can be observed that in the 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 3-mm hole diameter, fracture at an energy level of 6 J is occurred.

Figure 8.

Low-velocity impact on 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams with 3-mm hole diameter fabricated from PLA-CF material based on the drop-weight impact tests with 6-J impactor initial energy, diagrams of a) contact force-time, b) impactor displacement-time, c) absorbed energy-time and d) contact force-displacement.

Photographs of the beam surfaces in failure energies after impact using a BEL photonic microscope (70x magnification) are presented in Figure 9.

Figure 9.

Photographs of the beam surfaces in failure energies after impact using a BEL photonic microscope (70x magnification), a) 2D-FGP $\wedge$ beam with 2-mm hole diameter under 9-J impact energy, b) 2D-FGP $\vee$ beam with 2-mm hole diameter under 9-J impact energy, c) 2D-FGP $\wedge$ beam with 3-mm hole diameter under 6-J impact energy and d) 2D-FGP $\vee$ beam with 3-mm hole diameter under 6-J impact energy.

As Figure 9 shows, at the impact surface, there is an indentation caused by the collision of the impactor. On the bottom surface, linear cracks have occurred. Non-linear cracks have occurred on the side surfaces of the beam, which have decreased in width from the edge of the collision surface to the edge of the bottom surface. It is important to mention that with the increase in the diameter of the beam holes, fracture occurs at a lower energy, which is due to the increase in the volume of the porosity of the beam and the decrease in its strength.

Based on the presented diagrams in a range of different initial energies of the impactor and different hole diameters of the beam, the exact results of the impact responses of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams are presented in Table 2. In both cases of 2D-FGP $\wedge$ and 2D-FGP $\vee$ distributions, increasing the diameter of the holes decreases the peak contact force and increases impact time, absorbed energy and peak impactor displacement.

Table 2.

Impact responses of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams in a range of different initial energies of the impactor and different hole diameters of the beam, made of PLA-CF, fabricated by the 3D printer and based on the drop-weight impact test results.

Diameter of holes (mm)	Impactor initial energy (J)	Peak contact force (N)		Impact time (ms)		Absorbed energy (J)		Peak impactor displacement (mm)
		FGP $\wedge$	FGP $\vee$	FGP $\wedge$	FGP $\vee$	FGP $\wedge$	FGP $\vee$	FGP $\wedge$	FGP $\vee$
2	1.5	1975.31	1666.67	4.38	4.68	0.67	0.84	1.41	1.56
	3	2539.68	2378.43	4.74	4.78	1.37	1.67	2.21	2.27
	6	3305.62	3063.74	4.8	4.84	3.80	4.15	3.21	3.23
	9	3703.70	3765.43	7.74	6.64	6.39	7.11	4.98	4.15
3	1.5	1748.97	1687.24	4.92	5.02	0.76	0.84	1.68	1.70
	3	2176.87	2136.56	5.04	5.18	2.29	2.51	2.45	2.67
	6	2716.05	2469.14	7.82	6.72	5.02	4.64	4.31	4.48

For the impactor initial energy of 3 J and the 2D-FGP $\wedge$ holes distribution, with the diameter change from 2 to 3 mm, the peak contact force and impact time, absorbed energy and peak impactor displacement are changed −14.29%, 6.33%, 67.33% and 10.66%, respectively. When the initial energy of the impactor is 3 J and the 2D-FGP $\vee$ holes distribution is considered, with a change in diameter from 2 to 3 mm, the peak contact force and impact time, absorbed energy and peak impactor displacement are altered by −10.17%, 8.37%, 49.87%, and 17.87%, respectively. In fact, due to the increase in the diameter of the beam holes, the porosity of the beam is correspondingly increased, the strength of the beam is reduced, and the impactor moves more into the beam, but due to the decrease in strength of the beam, the peak contact force is reduced according to the Hertz relation. The variations in impact properties of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams compared to the energy level of 1.5 J are presented in Table 3. This table confirms that as the energy level increases for a given distribution 2D-FGP $\wedge$ or 2D-FGP $\vee$ and hole diameter 2 mm or 3 mm, all impact responses the peak contact force and impact time, absorbed energy, and peak impactor displacement increase. The greatest effect of increasing the energy level on the absorbed energy and the least effect is the duration of contact. To physically justify the responses, it can be emphasized that increasing the initial impactor energy increases the initial impactor velocity and, as a result, increases the impactor displacement and the contact force.

Table 3.

Percentage of impact properties changes (%) of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams compared to the energy of 1.5 J, made of PLA-CF, fabricated by the 3D printer and based on the drop-weight impact test results.

Diameter of holes (mm)	Impactor initial energy (J)	Peak contact force		Impact time		Absorbed energy		Peak impactor displacement
		FGP $\wedge$	FGP $\vee$	FGP $\wedge$	FGP $\vee$	FGP $\wedge$	FGP $\vee$	FGP $\wedge$	FGP $\vee$
2	3	28.57	42.71	8.22	2.14	103.37	98.29	57.19	45.26
	6	67.35	83.82	9.59	3.42	463.97	391.87	128.02	107.01
	9	87.50	125.93	76.71	41.88	847.85	741.38	253.36	165.98
3	3	24.47	26.63	2.44	3.18	200.31	198.92	46.18	57.33
	6	55.29	46.34	58.94	33.87	557.00	452.69	157.34	163.67

The ratio of $\frac{2\mathrm{D}-\text{FGP}\bigwedge }{2\mathrm{D}-\text{FGP}\bigvee }$ for impact properties of the FGP beams made of PLA-CF, fabricated by the 3D printer and based on the drop-weight impact test results are presented in Table 4. A comparison of Figure 2 with this Table confirms that distribution $2\mathrm{D}-\text{FGP}\bigwedge$ has fewer holes compared to $2\mathrm{D}-\text{FGP}\bigvee$ at the impact surface and therefore has a higher strength in this area. For this reason, the peak contact force of $2\mathrm{D}-\text{FGP}\bigwedge$ distribution is greater than that of $2\mathrm{D}-\text{FGP}\bigvee$ distribution, but the impact time, the absorbed energy and the peak impactor displacement distribution $2\mathrm{D}-\text{FGP}\bigwedge$ are less than $2\mathrm{D}-\text{FGP}\bigvee$ . Due to the fluctuations above the graph in the fracture energy of 9 J corresponding to the 2 mm diameter and 6 J corresponding to the 3 mm diameter, the responses in these rows may not follow the listed trend.

Table 4.

The ratio of $\frac{2\mathrm{D}-\text{FG}\mathrm{P}\bigwedge }{2\mathrm{D}-\text{FG}\mathrm{P}\bigvee }$ for impact properties of the FG beams made of PLA-CF, fabricated by the 3D printer and based on the drop-weight impact test results.

Diameter of holes (mm)	Impactor initial energy (J)	Peak contact force	Impact time	Absorbed energy	Peak impactor displacement
2	1.5	1.19	0.94	0.80	0.90
	3	1.07	0.99	0.82	0.98
	6	1.08	0.99	0.91	0.99
	9	0.98	1.17	0.90	1.20
3	1.5	1.04	0.98	0.91	0.99
	3	1.02	0.97	0.91	0.92
	6	1.10	1.16	1.08	0.96

As a result, considering the high cost of using the 3D printer for the fabrication of 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams, innovative equations based on the results of experimental tests are presented in this section to predict the peak contact force ( $PCF$ ) and absorbed energy ( $AE$ ). The equations provided for the distribution of 2D-FGP $\wedge$ are as follows:

$PCF\hspace{0.17em}\left(D,E\right)=1552.2-108.1987D+627.4876E-81.6474\hspace{0.17em}DE-22.3825E^2$

(4)

$AE\left(D,E\right)=2.9701-1.2010D-2.1932E+1.0130DE+0.3755E^2-0.1017E^2-0.0091E^3$

(5)

Where $D$ and $E$ are hole diameter and impactor initial energy, respectively. The equations presented for the distribution of 2D-FGP $\vee$ are outlined below:

$PCF\hspace{0.17em}\left(D,E\right)=575.9805+249.9076D+756.0666E-152.4705DE-17.3556E^2$

(6)

$AE\left(D,E\right)=3.4546-1.5215D-2.3373E+1.2365DE+0.4095E^2-0.1503D{E}^2-0.0046E^3$

(7)

The difference in the impact results of the presented equations compared to the actual experimental values ​​based on the results of the drop-weight impact tests for 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams are presented in Table 5. This table confirms that the peak difference is below 5%.

Table 5.

The error rate (%) of the presented equations compared to the actual experimental values based on the drop-weight impact test results for 2D-FGP $\wedge$ and 2D-FGP $\vee$ beams made of PLA-CF, fabricated by a 3D printer.

Diameter of holes (mm)		2				3
Impactor initial energy (J)		1.5	3	6	9	1.5	3	6
Peak contact force	FGP $\wedge$	0.33	−0.50	0.29	−0.09	0.12	−0.14	0.04
	FGP $\vee$	2.81	−4.437	3.07	−0.94	2.81	−3.33	0.96
Absorbed energy	FGP $\wedge$	−0.04	−0.08	−0.17	−0.31	−0.04	−0.06	−0.15
	FGP $\vee$	0.00	−0.01	−0.05	−0.09	0.00	−0.00	−0.03

Finally, Figure 10 provides a comparison between the graphs based on the presented equations and also the real test data.

Figure 10.

Surface fitting provided equations of the maximum contact force of distributions of a) 2D-FGP $\wedge$ and b) 2D-FGP $\vee$ and absorbed energy of distributions of c) 2D-FGP $\wedge$ and d) 2D-FGP $\vee$ .

Conclusions

In this research, to carry out low-velocity impact tests using drop-weight impact testing equipment, PLA-CF beams with distributions of 2D-FGP $\wedge$ and 2D-FGP $\vee$ were fabricated using the 3D printer. A range of different impactor energies and hole diameters were used to study the fracture energy as well as contact force, absorbed energy and displacement histories. The results showed that in beams with the same hole diameter, the 2D-FGP $\wedge$ and 2D-FGP $\vee$ distribution both failed at the same energy. Increasing the hole diameters reduces the peak contact force and increases impact time, absorbed energy, and peak impactor displacement in both 2D-FGP $\wedge$ and 2D-FGP $\vee$ distribution scenarios. As the diameter increased, the fracture energy of both distributions decreased. For any given distribution (2D-FGP $\wedge$ or 2D-FGP $\vee$ ) and hole diameter (2 mm or 3 mm), the peak contact force and impact time, absorbed energy, and peak impactor displacement all increase as the energy level rises. In different diameters and energies, distribution 2D-FGP $\wedge$ had more peak contact force than distribution 2D-FGP $\vee$ , while distribution 2D-FGP $\vee$ had more impact time, absorbed energy and peak impactor displacement than 2D-FGP $\wedge$ . For each of the 2D-FGP $\wedge$ and 2D-FGP $\vee$ distributions, innovative equations were presented to predict the peak contact force and energy absorbed by considering the hole diameter and impactor initial energy inputs with high accuracy.