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

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 deposition ⁶ 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 study ²⁶ , 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 $\delta$ can be defined as a positive real number.

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.

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.

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.

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.

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

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. $\rho$ (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. $\mu$ 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:

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.

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.

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.

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.

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 equation ³⁰ :

where $\rho$ is the density, $P_g$ is the gas pressure in the pore, $P_s$ is the liquid pressure at infinity, $\gamma$ is the specific surface energy of the pore, and $\hspace{0.17em}\mu$ is the viscosity of the incompressible liquid around the pore.

Numerical Case of Manufacturability Optimization Design

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 $\mathrm{x},\mathrm{\hspace{0.17em}}\mathrm{y},\mathrm{\hspace{0.17em}}\mathrm{\hspace{0.17em}}\mathrm{and}\mathrm{\hspace{0.17em}}\mathrm{z}$ axes. For the sake of more information, detailed FEA outcomes are listed in Table 1.

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.

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.

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.

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.