Toward Zero-Support Design for Irregular Manifold Manufacturing with Composite Materials Based on Layered Adhesion Equalization

Abstract

This article proposes a toward zero-support design method for irregular manifold manufacturing of composite materials based on layered adhesion equalization (LAE). Especially, external support in holes of irregular 3D manifold manufacturing by additive manufacturing (AM) is difficult to remove, which means toward zero-support design is indispensable to some complex curved surface components. AM largely depends on three main constraints, such as external support, layer thickness, and build time, which are mainly affected by building orientation and infill trajectory. Moreover, considering problems that variable layer thickness will bring material imbalance and residual stress heterogeneity, the layered orthogonal projection areas of the virtual printing prototype on the orthogonal planes, such as the positive plane and side plane in the 3D printing coordinate system, are introduced as LAE constraints to realize equilibrium reinforcement design (ERD) for both LAE and external support. Subsequently, using transient thermal structure coupling via finite element analysis, the transient thermal structure coupling analysis of fiber composite under multiple working conditions is further obtained. In particular, the influence mechanism of continuous fiber forming on the mechanical behavior of the topological configuration is revealed. Taking the irregular three-way manifold by concept design as an example, a specimen was fabricated using polylactic acid (PLA) with carbon fiber on the strength of fused deposition modeling. The infrared thermographs using thermal field measurement were carried out to obtain the temperature distribution during manufacture. The innovatively proposed LAE method is propitious to improve the additive manufacturability and adaptability of lightweight thin-wall structures, especially for fiber-reinforced composites. This is advantageous for utilisation in the domain of aerospace components.

Keywords

toward zero-support design additive manufacturing composite materials layered adhesion equalization residual stress heterogeneity transient thermal structure coupling

Introduction

The three-dimensional (3D) printing (3DP), also called rapid prototyping or additive manufacturing (AM), is entangled with computer-aided design, materials processing, and forming technology, in biomedical engineering, high-end manufacturing, aerospace and other multidisciplinary, including aeronautical thin-walled round tube, long endurance unmanned aerial vehicle (UAV), flapping wings UAV, and its high-aspect-ratio composite wing. The diverse technical requirements result in different processes,^1–5 including commonly fused filament fabrication (FFF), laser beam melting, laser powder bed fusion, binder jetting, patched area printing, etc.

The huge emerging demands of end-use functional artifacts result in technological development. People studied the change of temperature field in the process of melt deposition⁶ and analyzed the influence of temperature change on the thermal properties of materials by exploring the nonlinear changes of thermal conductivity and specific heat. The accurate control of temperature provides the basis for the reconstruction of biological tissue structure with activity.⁷ Kabir et al. have studied the effect of temperature on the emission rate of microparticles in the printing process of fused deposition modeling (FDM), and pointed out that the emission rate of particles will be higher at higher working temperature.⁸ Kuncius et al. improved the FDM production technology of continuous carbon fiber composites.⁹ Spratt et al. analyzed the build quality and compression properties of thin-walled 304L honeycomb structures manufactured by selective laser melting (SLM). Four honeycomb wall thicknesses vary from 0.2 to 0.5 mm.¹⁰

Composite material is an excellent type of wearable and high-temperature resistant material, widely employed in military and special civilian technology areas like high-temperature equipment protection, aircraft brake discs, etc. Mohammadizadeh and Fidan studied the effect of fiber parameters on the tensile properties of manufactured components.¹¹ Kubota et al. conducted tensile tests on samples with different stacking directions and studied the influence of printing path.¹² Kranz et al. presented experimental investigations on the influence of part position and orientation on the dimension accuracy and surface quality of laser additive manufacturing.¹³ Saharudin et al. conducted mechanical tests on the model produced by continuous filament fabrication (CFF) and concluded that it improved the surface quality. Adding carbon fiber as filler to other materials for 3DP also has a good improvement effect.¹⁴

Metal matrix composites (MMCs) have been widely adopted with the intention to assimilate the robust, malleable, and conductive attributes of metallic substances with the rigid, inflexible, and wear-resistant characteristics inherent in ceramics, or often, intermetallic substances, thereby achieving an ideal amalgamation or synergy of these two distinct properties.¹⁵ MMCs are extraordinary engineering materials as they provide customizable characteristics, mutually drawing upon the desirable properties of both reinforcement and matrix constituents, hence enhancing their inherent structural and functional benefits.¹⁶ Powder-based AM techniques, like SLM, exhibit significant versatility, accommodating a broad spectrum of powder-based materials, thus being particularly versatile to process a variety of powder materials for composite manufacturing.¹⁷

M’Saoubi et al. discussed the material cutting process of aerospace alloys and composite materials employed in aero-engines.¹⁸ Launay et al. designed a testing device to measure the material compressive strength of continuous fiber composite materials.¹⁹ Kucewicz et al. experimentally compressed two different topologies of cellular structures fabricated with FDM of acrylonitrile butadiene styrene plus (ABS+) material with similar relative densities for five different deformation velocities: quasi static (1.0, 5.0, and 10.0 mm/s) and dynamic (1520.0 and 2400.0 mm/s).²⁰ Meshkinzar et al. amplified the acoustic field generated by a uniform thickness piezoelectric cylindrical shell by introducing a stepped thickness variation at predetermined axial locations.²¹ Grauers et al. carried out mechanical compression tests of laminates, made of carbon fiber unidirectional fabric with epoxy, and studied the energy-absorbing damage mechanisms.²² Sharma et al. carried out an analysis of the FFF structures subjected to uni-axial compressive and three-point bending load, in order to investigate the effect of strut thickness, shape, loading direction, and functional grading on compressive behavior.²³ Cipollone et al. studied a process for 3DP of an anode scaffold for lithium batteries.²⁴ Körber et al. fabricated 3D-printed polymer positive models for the investment casting of extremely thin-walled single crystals.²⁵

Focusing on the major needs of high-specific stiffness and lightweight structures in the frontier field of aerospace, the existing topology optimization design methods ignore the bottleneck of low fitness and poor manufacturability caused by different material AM processes.

In comparison with previous study²⁶, the optimal build orientation of 3DP for complex curved surface components is determined by taking the support material into account. It is important to note that the optimal build orientation is not immediately apparent for most components fabricated by 3DP. Furthermore, layered orthogonal projection areas are introduced as layered adhesion equalization constraints to ensure manufacturability. In the physical experiment, the carbon fiber that pervades the specimen is clearly observed by the optical 3D surface profilometer.

Based on the previous systematic work^26–29 considering the variation of material and equipment, the mathematical model of toward zero-support design is established. The toward zero-support design achieves equilibrium reinforcement design (ERD) for both layered adhesion equalization (LAE) and external support. Moreover, the physical experiment is implemented to verify the proposed LAE method.

Material Thickness Distribution of an Irregular Thin-Walled Composite

For lightweight design of thin-walled artifact structure $M$ in $R^{3}$ , the specific surface of unit volume $δ$ can be defined as a positive real number.

\begin{matrix} δ = \frac{S_{object}}{V_{object}} δ \in R^{+} \end{matrix}

(1)

The greater the specific surface area, the greater the dispersion. Inspired by bionics, most structures are designed as thin-walled forms to maximize the specific strength, with multifarious ribs. The prototype thickness can be defined as the smallest distance through an object, between opposite surfaces or sides, as distinct from width or height.

\begin{matrix} t = \min (‖ V_{i} - V_{j} ‖) \forall V_{i}, V_{j} \in M i, j \in Z^{+} \end{matrix}

(2)

It should be clarified that wall thickness values are attitude and azimuth independent, whereas the thickness proportional distribution is also size independent. Obviously, wall thickness is a relative concept that depends on scale, which is commonly considered. The distribution of material thickness can be obtained by clustering into certain $m$ classifications.

\begin{matrix} \{\begin{matrix} t_{i} \in [0, \frac{\max (t)}{m}] i = 1 \\ t_{i} \in (\frac{i * \max (t)}{m}, \frac{(i + 1) * \max (t)}{m}] 1 < i \leq m \end{matrix} \end{matrix}

(3)

Figure 1 demonstrates different kinds of external support of the thin-walled workpiece, which is a turbine. The volume of the turbine is 8.2187 × 10⁵ mm³. As demonstrated in Figure 1a, the volume of external support is 3.6790 × 10⁴ mm³, which is 4.48% of the volume of the turbine. As indicated in Figure 1b, the volume of external support is 1.2419 × 10⁵ mm³, which is 15.11% of the volume of the turbine. In Figure 1c, the volume of external support is 2.5467 × 10⁵ mm³, which is 30.99% of the volume of the turbine. In Figure 1d, the volume of external support is 8.0252 × 10⁵ mm³, which is 97.65% of the volume of the turbine.

FIG. 1.

Different kinds of external support of the turbine prototype where (a) is tree type, (b) is columnar type, (c) is reticulation type, and (d) is block type.

Ultrasonic Thickness Measurement of Composite Materials

Figure 2 depicts the wall thickness distribution of a turbine. The redder the color is, the more thin-walled the structure is. From the color distribution, thin-walled structure accounts for the majority. From Figure 2c, within three classifications, the proportions of categories are 55.78%, 5.52%, and 38.70%, respectively, from thin to thick. From Figure 2d, within four classifications, the proportions of categories are 52.63%, 6.06%, 4.43%, and 36.88%, respectively, from thin to thick. From Figure 2e within five classifications, the proportions of categories are 49.80%, 7.39%, 3.08%, 3.9% and 35.73%, respectively, from thin to thick.

FIG. 2.

The wall thickness distribution of a turbine where (a) is the turbine with main/front view, (b) is its section view, in different statistical categories or stratifications of three (c), four (d), and five (e).

Ultrasonic thickness measuring sensors have contactless, nondestructive, and non-radioactive properties and can provide a real-time dynamic measurement for composite material. High temperature thickness measurement, coarse crystal thickness measurement, and some composite thickness measurements are difficult to implement.

The principle of ultrasonic thickness measurement can be described as

\begin{matrix} d = t \times \frac{v_{s}}{2} \end{matrix}

(4a)

\begin{matrix} v_{s} = \sqrt{K / ρ} \end{matrix}

(4b)

\begin{matrix} K = Δ p / (Δ ρ / ρ) \end{matrix}

(4c)

\begin{matrix} K = E / (3 - 6 μ) \end{matrix}

(4d)

where d (m) is the distance. t (s) is the time between transmission and reception of sound waves. v_s (m/s) is the velocity of sound in the medium. K (Pa) is the bulk modulus of the measured medium. Δ represents the variation of corresponding variable.

ρ

(kg/m³) is the density of the medium. p (Pa) is the intensity of pressure on the medium. E (Pa) is the Young’s modulus of the medium.

μ

is the Poisson’s ratio of the medium.

Due to the composite material being different from common metal and uniform nonmetal material, the common high-frequency industrial thickness probe cannot emit a sound pulse. Thus, low frequency, low residual vibration, and high-power thickness probe are required for effective penetration of composite materials. Low residual vibration is an important requirement to shorten the measurement blind area.

Using single and double crystal probes, the most ultrasonic thickness measurement system adopts the pulse-echo method, meaning the thickness of the measured workpiece is calculated by determining the time difference between the two echoes of the bottom surface.

Using a low-frequency and low-after-vibration ultrasonic thickness measuring probe, the transmission and echo signals of 130 mm thick composite materials are measured. According to oscilloscope signals, the duration of after-vibration is not more than 50 µs. The precision of this thickness measurement can reach 0.01 mm.

Fundamentals of Composite Materials for Functional Requirements

In 3D printing coordinate system (PCS), the normalized height $h_{n}$ of the i-th layer can thus be defined as:

\begin{matrix} h_{n} = \frac{z_{i}}{z_{b}} {where h}_{n} \in (0,1] \end{matrix}

(5)

Resistivity and dielectric constant are important indices to evaluate the electrical properties of a material. Electrical resistivity is a physical quantity employed to express the resistance characteristics of various substances. It is not only related to materials but also related to temperature. The calculation formula of ρ_Ω (Ω·m) is as follows.

\begin{matrix} ρ_{Ω} = ρ_{0} \times (1 + α T) \end{matrix}

(6)

where T is the temperature (K), ρ₀ is the resistivity at 0°C, and α is the temperature coefficient of resistivity.

The thermal conductivity refers to the heat transferred through an area of 1 m² within a certain period by a 1 m thick material with a temperature difference of 1 K on both sides of the surface under stable heat transfer conditions. The thermal conductivity k_x (W/(m·K)) can be calculated by the following formula.

\begin{matrix} k_{x} = - \frac{q_{x}^{″}}{(\frac{\partial T}{\partial x})} \end{matrix}

(7)

where x is defined as the heat flow direction, then q_x″ (W/m²) is the heat flux in this direction. ∂T/∂x (K/m) is the temperature gradient in the assigned direction.

Dielectric constant is a physical parameter that characterizes the dielectric property or polarization property of a dielectric material. It is a property of the material itself and a parameter that measures the ability of a material to store charges. Relative permittivity is often employed to characterize the dielectric properties of materials. The relative permittivity ε_r is calculated by measuring the capacitance of the material thin plate, and the calculation formula is as follows.

\begin{matrix} ε_{r} = \frac{C \times d}{ε_{0} \times S} \end{matrix}

(8)

where ε_r is the relative dielectric coefficient of the material, C (F) is the measured capacitance, d (nm) is the thickness of the sample, and S (m²) is the area of the sample. ε₀ is the vacuum dielectric constant, which is 8.854 × 10⁻¹² F/m.

Tensile strength σ_b (MPa) represents the resistance of the material to the maximum uniform plastic deformation and is the maximum stress that the material bears before breaking. Its value can be calculated by the following formula.

\begin{matrix} σ_{b} = \frac{F_{b}}{S_{o}} \end{matrix}

(9)

where F_b (N) is the maximum force applied when the specimen is broken, S_o (mm²) is the original cross-sectional area of the specimen.

The dynamic pore collapse process during AM in viscous liquid can be described in the theory of cavitation. The evolution of pore radius R under the influence of external pressure and surface tension at the pore surface can be expressed in the Rayleigh–Plesset equation³⁰:

\begin{matrix} ρ (R \frac{d^{2} R}{d t^{2}} + 1.5 \times {(\frac{d R}{d t})}^{2}) = P_{g} - P_{l} - \frac{2 γ}{R} - 4 \frac{μ}{R} \frac{d R}{d t} \end{matrix}

(10)

where

ρ

is the density,

P_{g}

is the gas pressure in the pore,

P_{s}

is the liquid pressure at infinity,

γ

is the specific surface energy of the pore, and

μ

is the viscosity of the incompressible liquid around the pore.

Numerical Case of Manufacturability Optimization Design

3D thin-walled structure to be fabricated

The irregular three-way manifold by concept design as displayed in Figure 3 which is a complex curved surface component is employed as a calculation example to verify the foregoing theoretical method. Complex curved surface components usually refer to free-form curved surface components that contain chambers, thin-walled structures, hollow branches, and topological structures. The irregular three-way manifold is delicately designed, with thin-walled ribs. Regarding geometric and topological analysis, it has left and right symmetry. The irregular three-way manifold was designed for the cooling of extruder and filament with merely one fan. The internal channels of air flow are displayed with cut view in Figure 3b.

FIG. 3.

The assembly and sectional view of an irregular three-way manifold by concept design.

The slender, thin-walled functional irregular three-way manifold (Fig. 4) is employed as a calculation example to verify the foregoing theoretical method. The irregular three-way manifold is delicately designed, with thin-walled ribs. Regarding geometric and topological analysis, it has left and right symmetry.

FIG. 4.

Thin-walled irregular three-way manifold with main/front view (a) and its contour lines (b), in different statistical categories or layers of three (c), four (d), and five (e), with $δ$ is 1.8701 via Equation (1).

By default, the length unit is hereinafter inclusive millimeter (mm). The overall dimension ( $x_{b} {, y}_{b}, z_{b}$ ) equals (40.0000, 53.2739, 56.1402) with a ratio of 0.7125:0.9489:1. The center of gravity is located at (30.0000, 37.9162, 32.0463). The total surface area $S_{object}$ = 14505.3251 mm², total volume of enclosed manifold $V_{object}$ = 7756.3691 mm³, specific surface area $δ$ is 1.8701 mm². The minimum bounding sphere lies at (5.0519, −11.8308, 7.2148) with exact spherical radius 36.0306 mm. The mass is 8.1442 g when measured by glass fiber, while 56.7321 g for 316L material.

Using Equation (3), from Figure 4c within three classifications, the proportion of categories are 96.2361%, 2.6639% and 1.1000%, respectively, from thin to thick. From Figure 4d within four classifications, the proportions of categories are 94.0827%, 4.3316%, 0.6185% and 0.9672% orderly, from thin to thick. From Figure 4e within five classifications, the proportions of categories are 88.9012%, 8.5734%, 1.1795%, 0.4535% and 0.8923%, from thin to thick. Concerning the improved thickness, the maximum is 61.8725 mm, mean is 1.0040 mm, median value is 1.0466 mm, standard deviation is 1.3616 mm, variance is 1.8539 mm².

Build orientation of 3DP

Figure 5 indicates build orientation under various constraints which is calculated by the manifold learning method and Powell trust region method instead of trial and error method. In machining coordinate system (MCS), the default field is (56.4396, −30.4833, 11.2981). In Figure 5a-b, the maximum is 28.0186 g at field vector (53.2651, −29.3903, 16.4680), the minimum is 4.8537 g at field vector (57.2634, −27.4090, 16.8108), the mean is 16.3393 g, the variance is 24.8029 g², and the standard deviation is 4.9802 g. There exist 130 3D contour curves with a total of 11683 points. In Figure 5c-d, the default field is (56.4396, −30.4833, 11.2981), the maximum is 6.7984 g at field vector (59.9408, −31.5537, 14.6529), the minimum is 0.9865 g at field vector(55.3287, −33.9022, 15.7373), the mean is 3.3100 g, the variance is 1.9737 g², the standard deviation is 1.4049 g. There exist 88 3D contour curves with a total of 11833 points.

FIG. 5.

Build orientation under various constraints where (a), (b) are before optimization and (c), (d) are after optimization, where the color bar denotes the mass of material.

Different kinds of external supports are illustrated in Figure 6, the surface area of wired wall support is 83.17 cm² as revealed in Figure 6a; the surface area of wired wall support is 113.19 cm² in Figure 6b; the surface area of wired wall support is 85.29 cm² in Figure 6c; the surface area of wired wall support is 156.61 cm² in Figure 6d. There is no external support in the hole of the prototype. Due to stability and structural integrity, a solid type of external support is employed.

FIG. 6.

Different kinds of external support of the irregular three-way manifold where (a) is wired wall type, (b) is punched plate type, (c) is reticulation type, and (d) is solid type.

The manufacturability at each stratification can be visualized per layer by utilizing virtual print technology in Figure 7.

FIG. 7.

Manufacturability at each stratification where (a) is the oblique view and (b) is the lateral view.

The Figure 8 illustrates the percentage of layered surface area and volume. From Figure 8a, in terms of volume of original manifold, maximum is 4.7240% at 42%, standard deviation is 0.0105, variance is 0.0001. In terms of surface area of original manifold, maximum is 4.0397% at 44%, standard deviation is 0.0099, variance is 0.0001. From Figure 8b, in terms of volume of manifold with external support, maximum is 3.3200% at 46%, standard deviation is 0.0096, variance is 0.0001. In terms of surface area of manifold with external support manifold, maximum is 3.0884% at 46%, standard deviation is 0.0082, variance is 0.0001.

FIG. 8.

Percentage of layered area and volume (a) represents original manifold while (b) represents manifold with external support. Volume refers to the percentage of the layered volume relative to the total volume. Area refers to the percentage of the layered area relative to the total surface area.

Layered orthogonal projection areas using digital twins

Based on Euler manifold theory, for any prototype in space, if the original coordinates are continuous, the parallel orthographic projection to any plane is also continuous. Especially, considering problems that variable layer thickness will bring material imbalance and residual stress heterogeneity, the layered orthogonal projection areas of the virtual printing prototype on the orthogonal planes, such as positive plane and side plane in the PCS, are introduced as layered adhesion equalization (LAE) constraints to realize equilibrium reinforcement design (ERD) for both LAE and external support.

Figure 9 depicts the layered orthogonal projection areas of various slicing thicknesses. In Figure 9a, before optimization, using thickness with 40 layers, about the area in vertical plane, maximum value is 57.5797 mm² at 12.8205%, summation is 1875.6806 mm², average value is 48.0944 mm², standard deviation is 12.8594 mm², and meanwhile, variance is 165.3634 mm⁴. About the area in width plane, maximum value is 63.2827 mm² at 43.5897%, summation is 1663.9272 mm², mean is 42.6648, standard deviation is 20.4632 mm², variance is 418.7428 mm⁴. About the sum of prior areas, maximum value is 119.3708 mm² at 43.5897%, summation is 3539.6078 mm², mean is 90.7592 mm², standard deviation is 26.2425 mm², variance is 688.6665 mm⁴.

FIG. 9.

Layered orthogonal projection areas of various slicing thickness where (a), (c) are before optimization and (b), (d) are after optimization. Vertical refers to the layered orthogonal projection area in vertical plane. Width refers to the layered orthogonal projection area in width plane.

In Figure 9b, after optimization, using thickness with 40 layers, about the area in vertical plane, maximum is 54.1803 mm² at 2.5641%, summation is 1743.4440 mm², mean is 44.7037 mm², standard deviation is 9.9288 mm², variance is 98.5815 mm⁴. About the area in width plane, maximum is 75.9019 mm² at 33.3333%, summation is 1666.1659 mm², mean is 42.7222 mm², standard deviation is 24.8400 mm², variance is 617.0274 mm⁴. About the sum of prior areas, maximum is 125.6269 mm² at 33.3333%, summation is 3409.6100 mm², mean is 87.4259 mm², standard deviation is 33.0332 mm², variance is 1091.1917 mm⁴.

In Figure 9c, before optimization, using thickness with 50 layers, about the area in vertical plane, maximum is 45.8287 mm² at 10.2041%, summation is 1875.6806 mm², mean is 38.2792 mm², standard deviation is 10.2171 mm², variance is 104.3882 mm⁴. About the area in width plane, maximum is 50.2854 mm² at 42.8571%, summation is 1663.9272 mm², mean is 33.9577 mm², standard deviation is 16.2589 mm², variance is 264.3514 mm⁴. About the sum of prior areas, maximum is 95.4078 mm² at 42.8571%, summation is 3539.6078 mm², mean is 72.2369 mm², standard deviation is 20.8554 mm², variance is 434.9493 mm⁴.

In Figure 9d, after optimization, using thickness with 50 layers, about the area in vertical plane, maximum is 43.1231 mm² at 2.0408%, summation is 1743.4440 mm², mean is 35.5805 mm², standard deviation is 7.8879 mm², variance is 62.2191 mm⁴. About the area in width plane, maximum is 60.6111 mm² at 32.6531%, summation is 1666.1659 mm², mean is 34.0034 mm², standard deviation is 19.7220 mm², variance is 388.9578 mm⁴. About the sum of prior areas, maximum is 100.2057 mm² at 32.6531%, summation is 3409.6100 mm², mean is 69.5839 mm², standard deviation is 26.2285 mm², variance is 687.9322 mm⁴.

Transient Thermal Structure Coupling Analysis of Composite

The finite element analysis (FEA) is conducted based on transient thermal structure coupling theories, using quasi-linear solution with 8-node three-dimensional thermal solid element. And the structure analysis is implemented via mesh domain decomposition method.

The prototype is simulated with composite PLA as the material. The density of the adopted material is 1.27 g/cm³, the coefficient of thermal expansion is 2.25 × 10⁻⁵ °C^-1, the printing temperature is 220 °C, and the isotropic thermal conductivity is 0.18 W·m⁻¹·°C⁻¹. When implementing simulation, the preheat temperature is set to 55 °C, the room temperature is 25 °C, the scan speed is 600 mm/s, the hatch spacing is 0.13 mm, and the deposition thickness is 0.2 mm.

The simulation conditions of FEA are depicted in Figure 10. Figure 10a illustrates the temperature distribution after manufacturing, with an average temperature of about 99.9831 °C. Figure 10b displays the equivalent elastic strain of the fabricated fan duct with a maximum of 0.0074. Figure 10c demonstrates the total fabricating displacement with the average deformation of 0.0592 mm. Figure 10d–f correspondingly displays the directional displacement along the $x, y, and z$ axes. For the sake of more information, detailed FEA outcomes are listed in Table 1.

FIG. 10.

Finite element analysis of composite materials.

Table 1.

FEA Outcomes with Fiber Composite Materials

FEA outcomes	Values
Material temperature (°C)
Max	220
Min	55.3720
Average	99.9831
Equivalent elastic strain
Max	0.0074
Min	1.0711 × 10⁻⁵
Average	5.1222 × 10⁻⁴
Total material deformation (mm)
Max	0.1151
Min	0
Average	0.0592
Directional deformation along X directions, positive, negative and average (mm)
Max +	0.0699
Max –	0.0699
Average	9.0443 × 10⁻⁶
Directional deformation along Y directions, positive, negative and average (mm)
Max +	0.1113
Max –	0.0639
Average	0.0253
Directional deformation along Z directions, positive, negative and average (mm)
Max +	0.0357
Max –	0.0629
Average	−0.0217

FEA, finite element analysis; Min, minimum; Max, maximum.

Physical Experiment

The FDM equipment is an extrusion-based 3D printer at ambient temperature 25 °C with 55% RH (relative humidity). The layer thickness can be varied among [0.10 mm, 0.35 mm]. The rated power is 350 W, powered by AC (alternating current) 220 V to ensure the high temperature up to 220 °C of composite 3DP.

The adhesion manufacturing process was observed by an infrared thermal imaging camera on the strength of Stefan–Boltzmann law on black-body radiation captured as Figure 11. The measurable temperature range is [−20 °C, 350 °C]. The temperature accuracy is the maximum of ±2% reading and ±2 °C. The field of view is 23° × 17°. The detector type is an uncooled microbolometer with 60 × 120 focal plane array. The scan trajectories could be observed in Figure 11.

FIG. 11.

Infrared imagery of the adhesion manufacturing process where (a)–(c) are full infrared images of scan trajectories while (d) is the infrared image of the extrusion nozzle.

Figure 12 displays the physically fabricated lightweight specimen using the proposed method with composite material. The composite material is polylactic acid (PLA) with carbon fiber. The carbon fiber increases the bending strength and toughness of the specimen. Meanwhile, the carbon fiber improves the heat resistance, abrasive resistance, and corrosion resistance.

FIG. 12.

Physically fabricated lightweight specimens using the proposed LAE method, where (a)–(d) are printed irregular three-way manifolds.

Figure 13 displays the layered adhesion surface topography of the fabricated specimen, where the magnification is 20×. As the surface topography demonstrated, the carbon fiber pervades the specimen.

FIG. 13.

Adhesion surface topography of the fabricated specimen made of fiber composite materials. (a) and (b) are the curved scan trajectories, while (c) and (d) are straight scan trajectories.

Conclusions

(1)

Toward zero-support design for irregular manifold manufacturing of composite materials based on LAE.

The toward zero-support design prototype is built at different layers, by considering build orientation, external support, adaptive thickness, as well as layered orthogonal projection areas. Especially, considering problems that variable layer thickness will bring material imbalance and residual stress heterogeneity, the layered orthogonal projection areas of the virtual printing prototype on the orthogonal planes, such as positive plane and side plane in the PCS, are introduced as LAE constraints. The LAE method can thus improve the overall manufacturability by virtue of toward zero-support design. Overall, the toward zero-support design achieves ERD for both LAE and external support. (2)

Using transient thermal structure coupling to obtain temperature, deformation, and force line response of composite materials.

The temperature and deformation of both noncomposite and composite materials during 3DP are compared to confirm the manufacturability using FEA of transient thermal structure coupling. Transient thermal structure coupling analysis of composite is further obtained. Subsequently, the influence mechanism of continuous fiber forming on the mechanical behavior of topological configuration is revealed, which lays a foundation for the lightweight design of continuous fiber reinforced structures with AM constraints. (3)

A specimen was fabricated using PLA with carbon fiber by FDM.

Taking the irregular three-way manifold which is a complex curved surface component as an example, the infrared thermographs using thermal field measurement are carried out to obtain temperature distribution. Subsequently, the surface topography of the fabricated specimen was observed by a microscope with a magnification of 20×. As the topography demonstrated, the carbon fiber covered the surface and pervaded the specimen to increase the bending strength, toughness, heat resistance, abrasive resistance, and corrosion resistance. The proposed LAE method contributes to improving the additive manufacturability and adaptability of lightweight thin-wall structures, especially for fiber-reinforced composites.

In the future, the proposed method can be utilized in automobile, electromechanical, aerospace, biomedical, and other customized fields, especially heavy load-bearing and special bioelectrical requirements. In particular, the proposed LAE method is propitious to fabricate complex irregular manifolds of aircraft, automobiles, and so on. And it is anticipated that the proposed ERD methodology will facilitate advancements in support-free 3D printing as well as microgravity support balanced reinforcement design for outer space manufacturing.

Authors’ Contributions

M.G. carried out the analytic mathematical programming and theoretical computation in the continuous domain. L.W. conducted the finite element analysis. J.X. finalized the article. S.Z. guided the team’s research as a Principal Investigator. J.T. made constructive suggestions to the work as a Chief Scientist.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

The work is funded by National Key Research and Development Project of China (Grant No. 2022YFB3303303); Key Open Fund of State Key Laboratory of Materials Processing and Die & Mould technology of China (Grant No. P2024-001).

References

Deshwal

, Kumar

, Chhabra

. Exercising hybrid statistical tools GA-RSM, GA-ANN and GA-ANFIS to optimize FDM process parameters for tensile strength improvement. CIRP J Manuf Sci Technol, 2020; 31:189–199; doi: 10.1016/j.cirpj.2020.05.009

A-V

, Khorsand

, Geary

, et al. 3D Printing of scaffolds for tissue regeneration applications. Adv Healthc Mater, 2015; 4(12):1742–1762; doi: 10.1002/adhm.201500168

Najjartabar-Bisheh

, Chang

, Lei

. A layer-by-layer quality monitoring framework for 3D printing. Comput Ind Eng, 2021; 157:107314; doi: 10.1016/j.cie.2021.107314

Poudel

, Zhou

, Sha

. Resource-constrained scheduling for multi-robot cooperative three-dimensional printing. J Mech Des, 2021; 143(7):72002; doi: 10.1115/1.4050380

Saraeian

, Shirazi

. Process mining-based anomaly detection of additive manufacturing process activities using a game theory modeling approach. Comput Ind Eng, 2020; 146:106584; doi: 10.1016/j.cie.2020.106584

Le Duigou

, Chabaud

, Matsuzaki

, et al. Tailoring the mechanical properties of 3D-printed continuous flax/PLA biocomposites by controlling the slicing parameters. Compos Part B Eng, 2020; 203(15):108474; doi: 10.1016/j.compositesb.2020.108474

Compton

, Lewis

. 3D-printing of lightweight cellular composites. Adv Mater, 2014; 26(34):5930–5935; doi: 10.1002/adma.201401804

Kabir

SMF

, Mathur

, Seyam

AFM

. A critical review on 3D printed continuous fiber-reinforced composites: History, mechanism, materials and properties. Compos Struct, 2020; 232:111476; doi: 10.1016/j.compstruct.2019.111476

Kuncius

, Rimašauskas

, Rimašauskienė

. Interlayer adhesion analysis of 3d-printed continuous carbon fibre-reinforced composites. Polymers (Basel), 2021; 13(10):1653; doi: 10.3390/polym13101653

10.

Spratt

, Anandan

, Hussein

, et al. Build accuracy and compression properties of additively manufactured 304L honeycombs. Rpj, 2020; 26(6):1049–1057; doi: 10.1108/RPJ-08-2018-0201

11.

Mohammadizadeh

, Fidan

. Tensile performance of 3D-printed continuous fiber-reinforced nylon composites. JMMP, 2021; 5(3):68; doi: 10.3390/jmmp5030068

12.

Kubota

, Hayakawa

, Todoroki

. Effect of build-up orientations and process parameters on the tensile strength of 3D printed short carbon fiber/PA-6 composites. Adv Compos Mater, 2022; 31(2):119–136; doi: 10.1080/09243046.2021.1930497

13.

Kranz

, Herzog

, Emmelmann

. Design guidelines for laser additive manufacturing of lightweight structures in TiAl6V4. J Laser Appl, 2015; 27(S1):S14001; doi: 10.2351/1.4885235

14.

Saharudin

, Hajnys

, Kozior

, et al. Quality of surface texture and mechanical properties of PLA and PA-based material reinforced with carbon fibers manufactured by FDM and CFF 3D printing technologies. Polymers (Basel), 2021; 13(11):1671; doi: 10.3390/polym13111671

15.

Dadbakhsh

, Mertens

, Hao

, et al. Selective laser melting to manufacture “in situ” metal matrix composites: A review. Adv Eng Mater, 2019; 21(3):1801244; doi: 10.1002/adem.201801244

16.

Fereiduni

, Ghasemi

, Elbestawi

. Selective laser melting of aluminum and titanium matrix composites: Recent progress and potential applications in the aerospace industry. Aerospace, 2020; 7(6):77; doi: 10.3390/aerospace7060077

17.

Spierings

, Leinenbach

, Kenel

, et al. Processing of metal-diamond-composites using selective laser melting. Rapid Prototyp J, 2015; 21(2):130–136; doi: 10.1108/RPJ-11-2014-0156

18.

M’Saoubi

I , Axinte

I , Soo

II , et al. High performance cutting of advanced aerospace alloys and composite materials. CIRP Ann, 2015; 64(2):557–580; doi: 10.1016/j.cirp.2015.05.002

19.

Launay

, Keryvin

, Grandidier

J-C

, et al. Design of a set-up for measuring the residual compressive strength after high load and high cycle compression fatigue on CFRP. Compos Struct, 2022; 286:115294; doi: 10.1016/j.compstruct.2022.115294

20.

Kucewicz

, Baranowski

, Stankiewicz

, et al. Modelling and testing of 3D printed cellular structures under quasi-static and dynamic conditions. Thin Wall Struct, 2019; 145:106385; doi: 10.1016/j.tws.2019.106385

21.

Meshkinzar

, Al-Jumaily

, Harris

. Acoustic amplification utilizing stepped-thickness piezoelectric circular cylindrical shells. J Sound Vib, 2018; 437:110–118; doi: 10.1016/j.jsv.2018.08.033

22.

Grauers

, Olsson

, Gutkin

. Energy absorption and damage mechanisms in progressive crushing of corrugated NCF laminates: Fractographic analysis. Compos Struct, 2014; 110:110–117; doi: 10.1016/j.compstruct.2013.11.001

23.

Sharma

, Hiremath

. Compressive and flexural properties of the novel lightweight tailored bio-inspired structures. Thin Wall Struct, 2022; 174:109169; doi: 10.1016/j.tws.2022.109169

24.

Cipollone

, Yang

, et al. 3D printing of an anode scaffold for lithium batteries guided by mixture design-based sequential learning. J Mater Process Technol, 2021; 295:117159; doi: 10.1016/j.jmatprotec.2021.117159

25.

Körber

, Völkl

, Glatzel

. 3D printed polymer positive models for the investment casting of extremely thin-walled single crystals. J Mater Process Technol, 2021; 293:117095; doi: 10.1016/j.jmatprotec.2021.117095

26.

, Gao

, Zhan

, et al. Towards support-free design for 3D printing of thin-walled composite based on stratified manufacturability reinforcement. CIRP J Manuf Sci Technol, 2022; 38:457–472; doi: 10.1016/j.cirpj.2022.05.017

27.

, Gao

, Feng

, et al. Support diminution design for layered manufacturing of manifold surface based on variable orientation tracking. 3D Print Addit Manuf, 2021; 8(3):149–167; doi: 10.1089/3dp.2020.0203

28.

, Wang

, Sheng

, et al. Energy efficiency optimization for ecological 3D printing based on adaptive multi-layer customization. J Clean Prod, 2020; 245:118826; doi: 10.1016/j.jclepro.2019.118826

29.

, Gao

, Feng

, et al. Dexterity distribution design for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition. Mech Based Des Struc, 2024; 52(3):1764–1784; doi: 10.1080/15397734.2022.2162541

30.

Maximenko

, Olevsky

. Pore filling during selective laser melting - assisted additive manufacturing of composites. Scripta Mater, 2018; 149:75–78; doi: 10.1016/j.scriptamat.2018.02.015