Hybrid manufacturing of titanium-based architected structures and implants

Abstract

A method for manufacturing an implant. The method can determine an initial design of the implant. The method can generate a wax model based on the initial design. A method can generate a mold of the wax model. The method can engage the mold in a burnout cycle. The method may introduce a metal into the mold. The method may detach the implant from the mold.

Description

Atty. Dkt. No.: 046434-0920 HYBRID MANUFACTURING OF TITANIUM-BASED ARCHITECTED STRUCTURES AND IMPLANTS CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

[0001] This application claims the benefit of and priority to U.S. Provisional Application No. 63 / 615,569, filed on December 28, 2023, the entire disclosure of which is hereby incorporated by reference herein. TECHNICAL FIELD

[0002] The present disclosure relates generally to hybrid manufacturing of titanium- based architected structures and implants. BACKGROUND

[0003] Metallurgical product techniques are capable of producing a wide range of material properties. In the last decade, metallic cellular materials with periodic properties, also known as metallic lattices, have been the subject of extensive research due to their potential in different engineering disciplines, including but not limited to thermal management, impact and blast mitigation, catalytic reactions, and lightweight structures.

[0004] Several manufacturing techniques have been used to produce metallic lattices of different topologies and cell sizes. Such techniques include, for example, wire-waving, snap fitting, high-temperature forming and diffusion bonding, and additive manufacturing (“AM”) techniques. AM techniques are the most widely investigated literature in the production of metallic lattices. Examples include but are not limited to powder bed fusion techniques, fused deposition modeling (“FDM”), using metal-rich filaments that are subsequently sintered, and binder jetting in which a binder is jetted on metal powder, and the resulting part can be later thermally sintered. AM technologies can also be employed indirectly to produce metallic lattices. For example, metal coating of additively manufactured polymeric substrates followed by subsequent removal of the polymeric substrates either thermally or chemically. Another example involves the infusion of additively manufactured hydrogels produced via vat photopolymerization with metal precursors followed by calcination and reduction to convert the hydrogel lattices into metal replicas. 4932-6762-0872 1Atty. Dkt. No.: 046434-0920

[0005] However, while AM technologies facilitate more design freedom and part complexity, they come with certain drawbacks which relate to the high production cost, relatively low building efficiency, limitations with respect to the used materials, the maximum dimensions that can be manufactured, as well as metallurgical defects which arise from the melting and solidifying processes. Defects of this kind include unmolten powder, oxidation, and hot cracking, while more severe limitations appear for chemically active material alloys. The risks associated with the highly reactive nature of such alloys have resulted in limited relevant research so a rather small number of reactive material-based AM components have been so far engineered with limited use in the fabrication of lattices.

[0006] Casting has been proposed as an inexpensive alternative technique for the manufacturing of periodic metallic lattices. Metal casting is a fabrication technique that can be traced back to around 4000 BC. It is a technique that allows for excellent microstructural and dimensional control over the fabricated parts. However, the main difficulty relates to manufacturing complex molds that often require a skilled toolmaker.

[0007] Recently, AM-assisted investment casting has been proposed as a novel process that takes advantage of the facilitated design freedom offered by AM and the low cost, and versatility of investment casting. AM-assisted investment casting starts with an initial wax model of the part embedded in sand, slurry, or ceramic molds. The mold is subsequently heated to drain or evaporate the wax and form a cavity that takes the shape of the part. This cavity can later be filled with molten metals. After cooling, the metal part is detached from the mold for subsequent post-processing. The development of wax materials suitable for AM and the high geometrical repeatability of additively manufactured parts allowed for the production of highly intricate and highly repeatable wax components for investment casting, eliminating the need for the skilled toolmaker and laborious process of manually producing wax models. As such, AM-assisted investment casting has been classified as a low- complexity method for the production of complex metallic lattices and structural parts. In the manufacturing of AM-assisted casting-based diamond lattices, highly consistent fabricated target relative densities were reported, along with a reproducible stress-strain mechanical performance. What is more, the fabrication of graded sheet-based gyroid lattices that exhibit favorable energy absorption properties has been demonstrated.

[0008] In general, AM-assisted casting addresses the issue of materials limitation in traditional AM techniques. At the material’s level, the mechanical properties of AM metallic 4932-6762-0872 2Atty. Dkt. No.: 046434-0920 parts compared to their AM-assisted cast counterparts for the same alloy are widely investigated. However, it is not clear how the properties translate to lattices. The thin struts and sheet of lattices dictate that process related parameters, such as the cooling rate during solidification affect the microstructure and the effective metamaterial mechanics. SUMMARY

[0009] Described herein are systems and methods for AM-assisted manufacture of biocompatible structures and implants. Some embodiments relate to investment casting as an alternative fabrication process in the manufacturing of metallic lattices. Various alloys are described for use in such systems and methods to result in a manufactured structure or implant, including aluminum and titanium-based alloys.

[0010] It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the subject matter disclosed herein. BRIEF DESCRIPTION OF THE FIGURES

[0011] The foregoing and other features of the present disclosure will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only several implementations in accordance with the disclosure and are therefore not to be considered limiting of its scope, the disclosure will be described with additional specificity and detail through use of the accompanying drawings.

[0012] FIGS. 1A-1C show AM-assisted casting procedure summary: wax specimens (FIG. 1A) are fabricated and placed on a sprue tree, which is in turn immersed in an investment mix within the flask to follow a complete burnout cycle (FIG.1B). The molten material infiltrates the cavities of the investment in a vacuum state to form the final metallic sprue tree (FIG.1B). The AM-assisted cast solid and sheet specimen extracted are presented in (FIG.1C). FIG.1D is a flow diagram showing a method for generating AM-assisted cast lattices. 4932-6762-0872 3Atty. Dkt. No.: 046434-0920

[0013] FIG.2 shows a wax burnout thermal cycle consisting of different heat-up and isothermal stages with a total duration of more than thirteen hours.

[0014] FIGS.3A-3B show AlSi10Mg powder used in the fabrication of the samples. FIG. 3A is a scanning electrode microscope (“SEM”) image showing the shape and size of the powder. FIG.3B shows particle size distribution.

[0015] FIGS.4A-4D show AM-assisted cast and additively manufactured samples: cast sheet-network (FIG.4A), cast solid-network (FIG.4B), PBF sheet-network (FIG.4C), and PBF solid-network (FIG.4D).

[0016] FIGS.5A-5B show light microscope images of PBF (FIG.5A) and AM-assisted casting at a 20 μm zoom scale (FIG. 5B). The melting pool and distinct phases can be discerned in each case.

[0017] FIGS.6A-6F show SEM images of the produced samples: cast sheet-network (FIG.6A), PBF sheet-network (FIG.6B), cast solid-network (FIG.6C), PBF solid-network (FIG.6D), cast solid-network strut showing gas bubbles (FIG.6E), and PBF solid-network strut showing loose powder on the strut surface (FIG.6F).

[0018] FIGS. 7A-7D show CT scan images of the different types of samples and fabrication techniques: PBF sheet-network (FIG.7A), PBF solid-network (FIG.7B), cast sheet-network (FIG.7C), and cast solid-network (FIG.7D).

[0019] FIGS.8A-8F show reconstructed micro-CT images of AM-assisted cast samples showing full scanned lattice (FIGS.8A, 8D), micro-voids (FIGS.8B, 8E), and cut through the reconstructed samples (FIGS. 8C, 8F) for sheet-network (FIGS. 8A-8C) and solid- network (FIGS.8D-8F) samples.

[0020] FIGS.9A-9F show reconstructed micro-CT images of PBF samples showing full scanned lattice (FIGS. 9A, 9D), micro-voids (FIGS. 9B, 9E), and cut through the reconstructed samples (FIGS.9C, 9F) for sheet-network (FIGS.9A-9C) and solid-network (FIGS.9D-9F) samples.

[0021] FIGS.10A-10F show stress-strain response of solid (FIGS.10A, 10C, 10E) and sheet-type (FIGS.10B, 10D, 10F) samples produced through 3D printing without (FIGS. 4932-6762-0872 4Atty. Dkt. No.: 046434-0920 10A-10B) and with an additional heat treatment stage (FIGS. 10C-10D) and investment casting (FIGS.10E-10F).

[0022] FIGS.11A-11D show mean elastic (FIG.11A), peak stress (FIG.11B), plateau stress (FIG.11C), and energy absorption (FIG.11D) for the considered sample classes.

[0023] FIG.12 illustrates a computer system for use with certain implementations.

[0024] FIGS.13A-13D show hybrid manufacturing (HM) and Powder bed fusion (PBF) process (FIG. 13A, 13B) along with the manufactured samples of Gyroid and IWP architected cellular topologies (FIG.13C). Schematic of the fatigue ratcheting and fatigue damage strain development upon compression-compression fatigue loading (FIG.13D).

[0025] FIGS.14A-14H show fatigue performance of PBF-AB Gyroid 30 % and IWP 30 % samples up to 60 K fatigue loading cycles: Experimental stress and strain curves as a function of the loading cycle are provided in FIG.14A and FIG.14B. The rigidity variation over the loading cycle is summarized in FIG.14C and FIG.14D, while the hysteresis loops, cyclic ratcheting, and fatigue damage strains in FIG.14E and FIG.14F and in FIG.14G and FIG.14H, respectively.

[0026] FIGS.15A-15D show average rigidity (FIG.15A), maximum stress (FIG.15B), accumulated fatigue ratcheting strains (FIG.15C), and accumulated fatigue damage (FIG. 15D) for PBF-AB Gyroid 20 %, Gyroid 30 %, and IWP 30 % specimen at 60k and 120k fatigue cycles.

[0027] FIGS. 16A-16D show quasi-static experimental stress–strain curves of hybrid manufactured (cast) and PBF-HT Gyroid 30% (FIG. 16A) and IWP 30% (FIG. 16B) samples. Comparison of Toughness (FIG.16C) and Peak stress (FIG.16D) values.

[0028] FIGS.17A-17H show fatigue performance of hybrid manufactured (Cast) and PBF-HT Gyroid 30 % samples after 500k compression-compression fatigue loading cycles: Experimental stress and strain curves as a function of the fatigue loading cycle are provided in FIG.17A and FIG.17B, and rigidity evolution data in FIG.17C and FIG.17D. The associated hysteresis loops and cyclic ratcheting and fatigue damage strains are provided in FIG.17E and FIG.17F and FIG.17G and FIG.17H, respectively. 4932-6762-0872 5Atty. Dkt. No.: 046434-0920

[0029] FIGS.18A-18H show fatigue performance of hybrid manufactured (Cast) and PBF-HT IWP 30 % samples after 500k compression-compression fatigue loading cycles: Experimental stress and strain curves as a function of the fatigue cycle (FIG.18A, 18B), and rigidity over the fatigue loading cycle (FIG.18C, 18D). The associated hysteresis loops, fatigue ratcheting, and fatigue damage strains are provided in FIG.18E and FIG.18F and FIG.18G and FIG.18H, respectively.

[0030] FIGS. 19A-19D show average rigidity (FIG. 19A), max stress (FIG. 19B), accumulated fatigue ratcheting (FIG.19C) and fatigue damage strains (FIG.19D) for hybrid manufactured (cast) and PBF-HT Gyroid 20 %, Gyroid 30 % and IWP 30 % samples after 120k and 500k fatigue loading cycles.

[0031] FIGS. 20A-20D show least squarefitting of the experimental elastic stiffness degradation data: Gyroid 20% PBF-as built (FIG.20A), Gyroid 20% PBF-HT (FIG.20B), and Gyroid 30% hybrid cast samples. Comparison offitting curves for all hybrid cast, PBF- HT, and PBF-AB specimens (FIG.20D).

[0032] FIGS.21A-21F show quasi-static stress–strain response of cast (FIG.21A, 21C) and PBF-HT (FIG.21B, 21D) Gyroid 20% and 30% samples before and after fatigue loading along with the associated toughness values (FIG.21E, 21F).

[0033] FIGS.22A-22H show fatigue performance of PBF-HT Gyroid 20 % under fatigue loading at a frequency of 5 Hz and out-of-plane fatigue loading at a frequency of 15 Hz: Experimental stress and strain curves as a function of the loading cycle, rigidity, hysteresis data, along with cyclic ratcheting and fatigue damage strains are provided in (FIG.22A, 22C, 22E, 22G) and (FIG.22B, 22D, 22F, 22H), respectively.

[0034] FIGS.23A-23D show average rigidity (FIG.23A), maximum stress (FIG.23B), accumulated fatigue ratcheting strain (FIG.23C), and fatigue damage strain (FIG.23D) for PBF-HT specimens at in-plane 15 Hz and 5 Hz loading and out-of-plane 15 Hz fatigue loading after 120k loading cycles.

[0035] FIGS.24A-24F show failed patterns of as-built Gyroid 20% (FIG.24A) and IWP 30% (FIG.24D) samples after compression-compression fatigue loading. SEM images along with local strut failure insights and fracture surface morphologies are provided in (FIG.24B, 24C) for as-built Gyroid 20% and in (FIG.24E, 24F) for IWP 30% lattices. 4932-6762-0872 6Atty. Dkt. No.: 046434-0920

[0036] FIGS.25A-25G show fatigue life (stress versus cycle number) for as-build PBF samples (FIG.25A), Comparison of the mean accumulated fatigue ratcheting strains after 60k and 120k fatigue loading cycles for Gyroid 20 %, Gyroid 30 %, IWP 30 % samples (FIG. 25B), von-Mises and equivalent plastic strains (PEEQ) for Gyroid 20 %, Gyroid 30 %, IWP 30 % at a macroscopic strain magnitude of 2.5 % (FIG.25C, 25E). Detailed distributions of the von Mises, PEEQ, and shear stress within each topological design are provided in (FIG. 24D, 25F, 25G).

[0037] Reference is made to the accompanying drawings throughout the following detailed description. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative implementations described in the detailed description, drawings, and claims are not meant to be limiting. Other implementations may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented here. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, and designed in a wide variety of different configurations, all of which are explicitly contemplated and made part of this disclosure. DETAILED DESCRIPTION

[0038] Described herein are systems and methods for additive manufacturing (“AM”)- assisted investment casting as an alternative fabrication process to the powder bed fusion (“PBF”) AM technique in the manufacturing of metallic lattices. Embodiments described herein relate generally to systems and methods for hybrid manufacturing of titanium-based architected structures and implants. Specifically, experimental and theoretical investigations analyze the process-microstructure-mechanical property relationship of metallic lattices manufactured through additive manufacturing AM-assisted investment casting and PBF techniques. Additionally, experimental and theoretical investigations analyze the fatigue performance of AlSi10Mg-based architected cellular materials fabricated using hybrid manufacturing and powder bed fusion (PBF) methods. In some embodiments, the systems and methods for hybrid manufacturing of architected structures and implants apply to alloys with high melting temperatures. In some embodiments, the systems and methods for hybrid manufacturing of architected structures and implants are aluminum-based. 4932-6762-0872 7Atty. Dkt. No.: 046434-0920

[0039] Resulting topology, microstructure, and mechanical properties of the sheet- and solid-based lattices are investigated through a particular embodiment utilizing an AlSi10Mg alloy. Fatigue performance of the cellular materials is also investigated through a particular embodiment utilizing an AlSi10Mg alloy. The AlSi10Mg alloy is characterized by its low density, desirable mechanical properties, good cast-ability, heat-treatability, and a narrow solidification range which reduces the hot cracking susceptibility during cooling. Such characteristics make it particularly suitable for manufacturing a wide range of structures from large components to thin parts in a wide range of applications including the aerospace and automotive industries to a variety of engineering parts.

[0040] In a particular embodiment, an analysis of both solid- and sheet-network-based gyroid lattices are manufactured using AlSi10Mg alloy as base material. Micro-tomography and scanning electron microscopy are employed to assess the differences in the as-built structure quality in each design case, identifying method caveats and quantifying differences in the distribution and magnitude of the lattice’s inner porosity. Moreover, their nonlinear compressive mechanical performance is experimentally probed to assess the elastic stiffness, peak, plateau stress, as well as overall energy absorption in each case. Results indicate higher elastic stiffness and peak stress for the PBF-manufactured specimens irrespective of the lattice topology and overall comparable stress and energy absorption properties. However, in contrast to PBF specimens, AM-assisted lattices exhibit a low-stress variability throughout the plateau region, yielding an overall smooth post-elastic stress-strain response, a difference that is particularly prominent for the solid-network type lattice architectures. Methodology.

[0041] Experimental review employed both solid- and sheet-network-based gyroid lattices for the analysis and comparison of the AM-assisted cast and powder bed fusion fabricated specimens. Samples were designed using MSLattice with a 20% relative density, 5 mm unit cell size, and 2×2×3 periodicity in the x, y and z directions, respectively. Each of the manufacturing processes is subsequently elaborated in detail, along with the methods employed for the metallurgical and mechanical assessment of the lattice specimens. AM-assisted casting.

[0042] The method to obtain AM-assisted cast lattices 10 is graphically described in FIGS. 1A-1C and a flow diagram to detailing a method 300 to obtain AM-assisted cast 4932-6762-0872 8Atty. Dkt. No.: 046434-0920 lattices 10 is shown in FIG.1D. It starts at step 302 with the additive manufacturing of wax lattice samples 12 using the vat photopolymerization system Form 2 (Formlabs). To that scope, the castable wax 40 resin is used with a layer thickness of 50 microns and the wax is used with, in some embodiments, a layer resolution as low as 30 μm to allow for the creation of exceptionally intricate features with smooth surface finishing. Samples are then rinsed in Isopropyl alcohol to remove the residual resin. Subsequently, the wax samples 12 are attached to a sprue tree 14 which is placed in a flask 16. An investment mix is prepared using Ransom & Randolph platinum investment and binder and poured into the flask 16 to completely cover the sprue tree. The filled flask 16 is left for two hours in room condition to dry. In the sequel, the flask 16 is placed in an oven 18 to burn out the wax at step 306 and create a cavity 20 in the mold at step 308, following the burnout cycle 30 described in FIG.2. The use of wax 3D- printing (additive manufacturing) methods for the creation of the mold (e.g., negative part) to be subsequently used for the casting step (e.g., investment, centrifugal) is particularly favorable for the creation of porous implant structures with low resolution.

[0043] After the burnout cycle 30 is completed, the flask 16 containing the cavity is placed in a casting system 22. For example, the J2R vacuum-assisted casting system (Rio Grande, Albuquerque, USA) is used. In some embodiments, one of skill in the art will appreciate, there are set process parameters (e.g., melt alloy temperature, exposure time, and rotational force in centrifugal casting) employed at the casting step itself, which have to be associated with the alloy (e.g., titanium) and the porosity of the lattice for a given implant. The set process parameters allow for the proper creation of metamaterial implants and relate to the casting step itself for metamaterial (architected porous topologies) rather than bulk solid parts. For example, AlSi10Mg chunks are used as the target material which is heated up to 1200°C. At step 310, once the system reaches the set temperature and the material is in a molten state, the vacuum pump is turned on to create a vacuum pressure of -1 bar inside the flask 16. Subsequently, the molten metal is allowed to enter the flask 16 through the appropriately designed gate for it to infiltrate the flask 16 at step 312. The flask 16 is kept for 10 min for the metal to cool down and solidify before quenching it in water for the investment to dissolve and the metallic replica 24 of the sprue tree to be obtained. Finally, metal samples 26 are cut from the metal sprue using wire electrical discharge machining at step 314, and metal samples 26 are cleaned by a high-pressure water jet to remove residual investments at step 316. 4932-6762-0872 9Atty. Dkt. No.: 046434-0920

[0044] The burnout cycle 30 involves ramping the temperature from room temperature to 150°C at a rate of 2°C / min followed by dwelling for 180 min. Next, the temperature is ramped again to 300°C at a rate of 2°C / min and dwelled for another 180 min. This is followed by a third ramp in temperature at a rate of 4°C / min to reach 732°C and holding for an additional 180 min at this temperature. Finally, the temperature is reduced at a rate of 5°C / min reaching substantially lower temperature values to be extracted from the furnace and initialize the above-described casting process. Preferably, the burnout cycle 30 leaves zero ash content allowing for a clean burnout. Powder bed fusion.

[0045] Solid and sheet-network gyroid samples with the same geometric specifications are also fabricated using the powder bed fusion system EOS M270 machine equipped with a 200 W laser and a scanning speed of up to 7 m / s. Gas-atomized AlSi10Mg powder, which has a mean diameter of 11 µm ranging from 4 to 34 µm, was utilized to fabricate all samples. The chemical composition of the alloy is listed in Table 1. The layer thickness was set to 30 µm and the scanning direction was rotated by 90⁰ between successive layers. Argon gas was used to maintain the Oxygen level below 0.1%. After fabrication, samples were removed from the building plate using CUT 30P-AgieCharmilles Wire Electric Discharge Machine. An SEM image of the powder along with a bar plot of the particle diameter distribution is provided in FIGS.3A-3B. Al Si Fe Cu Mn Mg Ni Zn Pb Sn Ti Balance 9.0-11.0 ≤0.55 ≤0.05 ≤0.45 0.2-0.45 ≤0.05 ≤0.1 ≤0.05 ≤0.05 ≤0.15 Table 1. Material chemical composition of the Aluminum alloy in wt%.

[0046] As described in FIGS. 3A-3B, the SEM image of the powder particle size distribution 40 indicates a distribution that is dominated by small-size particles well below the scaling size of 50 μm. As shown in FIG.3B, the right-skewed histogram distribution 42 verifies the prevalence of particle diameters below 20 μm, suggesting a refined AlSi10Mg powder quality.

[0047] A set of solid- and sheet-network specimens is subject to an additional heat treatment process. In particular, a heating cycle of 2 hours in the furnace at a constant temperature of 300°C is employed, following a heat post-processing specification. 4932-6762-0872 10Atty. Dkt. No.: 046434-0920 CT scanning, SEM, and mechanical testing.

[0048] The AM-assisted cast and powder bed fusion manufactured specimens are analyzed using micro-CT scanning, SEM, and mechanical testing. The Bruker SkyScan 1272 X-ray machine was used to examine the additively manufactured samples. The acquisition parameters are listed in Table 2. Tube Voltage 100 kV Target Current 100 μa Filter Type 0.11 Cu Exposure Time 2.1 s per projection Image Rotation 0.252° Scan Range 360° Image Pixel Size 9.5 μm3Table 2. X-ray tomography acquisition parameters.

[0049] The scanning slices were reconstructed using the nRecon software (Bruker Pty Ltd.), while the CTAn software (Bruker Pty Ltd.) was used to conduct the quantitative analysis. Thermo Fisher Quanta 3D scanning electron microscope (“SEM”) was used to assess the quality of the fabrication process. Samples were tested under displacement- controlled uniaxial compression using the universal testing machine Instron at a loading rate of 0.001 / s. A 5 kN load cell was employed and a minimum of two repeats for each sample were performed to confirm manufacturing and results reproducibility. Results. Microstructure and topology.

[0050] As shown in FIGS. 4A-4D, insights into the surface quality and fabrication refinement of the AM-assisted cast and powder bed fusion fabricated samples are provided. Images of cast and powder bed fusion manufactured specimens are presented in a comparative form including a cast-sheet network 50, a cast solid-network 52, a PBF sheet-network 54, and PBF solid-network 56. Smooth, shiny surfaces for the cast samples and granule opaque surfaces for the PBF samples are observed.

[0051] As shown in FIGS.5A-5B, light microscopy images of polished samples at a 20 µm zoom scale are presented for PBF samples parallel to the deposition direction 60 and AM- 4932-6762-0872 11Atty. Dkt. No.: 046434-0920 assisted cast samples 62. The melting pool and the distinct cases can be discerned in each sample. The PBF samples exhibit a “fish scale” morphology defined by the Si-rich boundaries of the melt pool. The melt pool has a depth ranging between 60–140 µm and a width of up to 250 µm. While the layer thickness is defined as 30 µm, the depth of the melt pool extends through several layers to insure re-melting and proper bonding of the successive layers. On the other hand, the microstructure of the AM-assisted cast samples exhibits a typical dendritic growth of the α-Al phase and interdendritic eutectic Al-Si phase.

[0052] As shown in FIGS.6A-6F, SEM images give a better surface quality assessment for the produced samples including the cast sheet-network 70, the PBF sheet-network 72, the cast solid-network 74, the PBF solid-network 76. The surfaces of the cast sheet- and solid- network samples are shown in FIG.6A and FIG.6C, respectively. The images display clean smooth surfaces with notable gas porosities 78. The images also show a relatively large (1.7 mm in diameter) spherical inclusion 80 as shown in FIG.6C. This inclusion formed due to the presence of air bubbles in the investment material that covered the wax pattern. When such bubbles get in contact with the surface of the wax, they form spherical inclusions 80. FIG. 6B and FIG. 6D show the surfaces of the sheet- and solid-network samples, respectively. The very rough surfaces are a result of partially fused powder and are a characteristic of lattices produced using PBF techniques.

[0053] CT scan images provide more details about the internal structures of the fabricated samples. FIGS.7A-7D present CT scan slices for the PBF and cast specimens including for the PBF sheet-network 82, the PBF solid-network 84, the cast sheet-network 86, and the cast solid-network 88. Extensive amounts of partially fused powder around the external boundaries of the solid phases can be observed in the PBF samples (FIGS.7A-7B). This is not the case for cast specimens, for which the contours of the solid phases are smooth for both cellular material classes. This is well-aligned with the SEM image observations in FIGS.6A- 6F. Internal micro-voids within the solid phases exist in PBF specimens, however, their sizes and quantity in the CT images are negligible (FIG.7A) and the internal phases seem to be fully solidified. It is worth mentioning here that light microscopy images in FIGS.5A-5B shows micro-voids in the microstructure of the PBF samples, but their sizes are on average around 5µm which is less than the pixel size used in the reconstruction of the CT images (see Table 2). Therefore, they are not captured by the reconstructed CT images. The number and 4932-6762-0872 12Atty. Dkt. No.: 046434-0920 sizes of these micro-voids in the PBF samples were analyzed using the Image J software and the porosity was calculated to be approximately 0.23%.

[0054] On the other hand, cast samples show a very notable and non-negligible density of internal voids as shown in FIGS.7C-7D. Moreover, a visual comparison among the solid and sheet-based CT scan images allows for a direct assessment of the lattice topology effect on the result of the casting process. More specifically, cast sheet lattice specimens contain a high density of spherical inclusions resulting from the trapped gas bubbles during the purring of the investment material around the wax models. Also, investment residuals inside the sheet lattices can be observed. These residuals were not successfully removed during the cleaning of investment materials after casting via the high-pressure water jet due to the complexity and tortuosity of the sheet-networks samples. In the case of the solid-networks samples, the interconnected network of pores allows for better removal of investment materials.

[0055] CT scanning images were reconstructed to obtain three-dimensional models of the fabricated samples. FIGS. 8A-8F display the reconstructed models of the cast samples including a full scanned sheet-network 90, sheet-network micro-voids 92, a cut through the sheet-network samples 94, a full scanned solid-network 96, solid-network micro-voids 98, and a cut through the solid-network samples 100. FIGS.9A-9F display the reconstructed models of the PBF samples including a full scanned sheet-network 102, sheet-network micro- voids 104, a cut through the sheet-network samples 106, a full scanned solid-network 108, solid-network micro-voids 110, and a cut through the solid-network samples 112. CT images in FIG.8B and 8C reveal a spread of porosity throughout the lattice volume that is rather random for the sheet network and follows a through-the-height pattern for solid-based architectures (FIGS.8E-8F). Pore sizes in the sheet lattices are in the order of 0.1 mm while solid-networks lattices exhibit a range of porosities in the 0.1–0.3 mm. The overall pores content in solid and sheet-based designs is 3–5% and 0.9–1.1% respectively obtained from a total of 3 specimen scans in each case.

[0056] The distribution and sizes of micro-voids in PBF lattice specimens (FIGS.9A- 9F) can be well-separated from the ones observed in cast specimens (FIGS.8A-8F). In the PBF case, the major part of micro-voids is substantially lower, being below 0.05 mm. However, the total number of micro-voids is considerably higher, reflecting in most of the cases the micro-porosity in the partially fused regions on the boundaries of the sample and not in its bulk (FIGS.7A-7D). Moreover, increased pores sizes in the order of 0.2 mm and 4932-6762-0872 13Atty. Dkt. No.: 046434-0920 up to 0.5 mm are observed at the sheets or struts facing downward on the loose powder, where the thermal diffusivity difference between the solid and loose powder results in higher density of partially fused powder in these locations.

[0057] Calculating the actual internal porosity in the case of PBF samples depends on the considered boundary as the sample boundary. Including the volume of the loose powder results in porosities in the range of 12–20% while considering the bulk and eliminating the porosity within the loose powder reduces the porosity considerably to 1–2% for both the sheets and solids. In fact, several studies investigated the effect of removing the partially fused powder via chemical etching on the overall relative density of the lattice structure and concluded a substantial decrease in the overall relative density. These studies also showed that partially fused powder increases the apparent relative density but has minimal load- bearing capacity. Removing the partially fused powder results in better mechanical properties per unit mass.

[0058] The actual relative densities were obtained by calculating the volume fraction of samples to void in CT reconstructed samples. PBF samples exhibit average volume fractions of 18.99% for the solid-network lattices, and 16.78% for the sheet-network lattices, while the AM-assisted cast samples exhibit average volume fractions of 18.00% for the solid-network lattices, and 17.03% for the sheet-network lattices. Mechanical performance.

[0059] As shown in FIGS. 10A-10F, the mechanical performance of the fabricated metallic lattices is summarized including the stress-strain response of solid samples produced through 3D printing of solid-type samples 114 and sheet-type samples 116, and the stress- strain response of solid samples produced through 3D printing with investment casting of solid-type samples 122 and sheet-type samples 124. The results cannot be strictly classified as effective metamaterial properties as a moderate number of unit-cell periodicities along the testing direction is employed, but they readily serve as a comparison of the effective performance among the different manufacturing processes. Apart from the cast and PBF samples, the stress-strain response of heat treated (“HT”) solid-network specimens 118 and sheet-network specimens 120 are provided.

[0060] Comparing the performance of cast specimens and PBF specimens, clear differences can be observed, particularly prominent in the solid-network based topologies. In 4932-6762-0872 14Atty. Dkt. No.: 046434-0920 particular, the elastoplastic curves of cast specimens are rather smooth over the entire range of nonlinear strains, with a minor stress variance with respect to their plateau value. Contrariwise, PBF specimens deform following a peaks and valleys pattern, which in the case of solid-type specimens results in an extreme post-elastic stress variance with the stress magnitude at the valley regions to be in the order of a fifth of the mean plateau stress and as low as 5% of the peak stress. The higher performance of PBF specimens compared to cast specimens in terms of elastic stiffness and peak stress observed in the initial loading phase does not extend to the nonlinear plateau region and densification range. The previous observation is well encapsulated in the total energy absorbed by solid-network based gyroid lattices, which is higher for the AM-assisted cast compared to BMF specimens as shown in FIG.10A and FIG.10C. A detailed effective performance comparison is provided in FIGS. 11A-11D including the mean elastic 126, peak stress 128, plateau stress 130, and energy absorption 132 for the considered sample classes.

[0061] A Young’s moduli comparison between cast and PBF specimens indicates an approximately two times higher modulus for the PBF specimens as shown in FIG.11A. An analogous performance scaling factor among cast and BMF lattices is recorded for the peak stress as shown in FIG.11B, with HT samples yielding considerably lower peak stress values, mediating the relevant differences both for solid and sheet network topologies. With respect to the purely non-linear performance metrics, solid network BMF specimens yield lower plateau and energy absorption attributes than cast specimens, an ordering inverted for sheet topologies. The relevant differences are however in the order of 10–20%, suggesting an overall highly comparable response. HT improves the post-elastic performance of BMF specimens in all cases as shown in FIGS.11C-11D. Discussion

[0062] The described AM-assisted casting technique de-associates the additive manufacturing process from the target material. Therefore, it is versatile and applicable to a wide range of metallic materials and alloys. In this work, the method suitability for metallic lattice production with a very high level of geometrical accuracy has been demonstrated.

[0063] This technique is a simple method to produce metallic components without the need for a large capital investment and is, therefore, very cost-effective. A simple cost comparison reveals that the combined cost of the stereolithography, casting system, and 4932-6762-0872 15Atty. Dkt. No.: 046434-0920 burnout furnace is at least one order of magnitude cheaper than the cost of a metal powder bed fusion system and associated auxiliary systems. It is worth noting that the price of the casting system depends on the complexity of the system such as having controlled temperature ramping, centrifuge casting, and the ability to control the vacuum pressure to name a few. Nevertheless, in most cases, it remains well below the cost of a powder bed fusion system. The cost of the latter can vary significantly depending on the technology, build volume, number of lasers, etc. However, the reduced cost of production in comparison to PBF came at the expense of certain mechanical properties, mainly in the elastic region. Notably, comparable, and in some cases, better post-yield properties were achieved by the AM-assisted cast samples making this technique very promising for crashworthiness and impact mitigation in automotive, aviation, aerospace, and defense applications to name a few.

[0064] The surface roughness observed in PBF samples typical for such type of fabrication. This surface roughness is desirable in some applications, as it increases the overall surface area-to-volume ratio. Examples constitute thermal management applications with phase-changing materials and catalytic static mixers, which can be coated using immersion techniques, such as electroplating. However, rough surfaces are not desirable in cases where loadings cycles appear, as in fatigue loading scenarios, where defects work as crack initiation positions that reduce the structural efficiency of cellular materials. Therefore, post-processing, polishing techniques have been proposed to reduce the surface defects and increase the percentage of mechanically efficient material within the cellular materials, leading to a desirable increase in the stiffness-to-density ratio.

[0065] The defects observed in the production of AM-assisted cast lattices are typical of the investment casting process in general. For example, the presence of gas porosity is justified by the entrapment of air or gas in the melt during the very high-speed injection of the molten metal into the cavity. Despite using vacuum-assisted casting, the presence of gas porosity was not entirely eliminated. From a mechanical properties point of view, such defects are believed to be a major reason for obtaining low elastic and peak stress properties in comparison to PBF lattices. Such defects can greatly affect the fatigue behavior of AM- assisted cast lattices as they affect both crack initiation and propagation phases. Hot isostatic pressing (“HIP”) is a useful technique to reduce or eliminate gas porosities which can in turn enhance the fatigue life cycle. 4932-6762-0872 16Atty. Dkt. No.: 046434-0920

[0066] The inclusions and investment casting residuals observed in the sheet-based specimens directly relate to the quality of the slurry and the dimensions and geometry of the cast specimens. In particular, the low density of bubble-type inclusions in the solid-type cast specimens as compared to the sheet lattice suggests that the combination of solid phase thickness and the void phase dimensions within the unit cell are sufficient for the slurry to penetrate the wax voids and remove air bubbles. The same cannot be said for the sheet-based lattices which have more complex tortuosity, larger surface area, and a much smaller thickness although the relative density is the same. These factors make the slurry penetration harder. As such, vacuum-assisted mixing and pouring of the slurry may be a viable option to reduce these inclusions as much as possible. Moreover, these same factors made the removal of investment material after casting a hard task. Sonication of the samples at high frequency after cast may help in removing the residual investment in the sheet-type samples. What is more, the relatively small thickness of the sheet-based lattice results in faster cooling of the molten metal in contact with the mold walls. Consequently, early solidification before the molten metal occupies the full volume of the cavity takes place and results in misrun type defects in the samples. Such defects can be eliminated for this type of lattice by casting while the mold is at temperatures close to the melting temperature of the molten metal.

[0067] The different manufacturing approaches result in different microstructures as shown in FIGS. 5A-5B. The slow cooling in casting produces a dendritic α-Al phase surrounded by Al-Si eutectic phase. The ductility and strength are greatly affected by the Al- Si phase present in the microstructure. AM-assisted cast lattices exhibited relatively low strength but progressive and smooth plateau stress under loading. On the other hand, the melting, solidification, and re-melting cycles in the PBF approach produces a fine Si-rich microstructure and consequently a high density of grain boundaries as well as a high density of precipitates. Such a microstructure hinders the movement of dislocations and hence strengthens the material while promoting brittle fracture. This microstructure explains the post-yield sudden drop in stress and the large fluctuation in stress in the plateau region observed for PBF-produced lattices in FIGS.10A-10F. The stress relief heat treatment results in better diffusion of the Si particles and coarsens the microstructure of PBF samples leading to enhanced ductility at the expense of strength. 4932-6762-0872 17Atty. Dkt. No.: 046434-0920 Conclusion.

[0068] Based on the experimental and theoretical analysis, the effect of the fabrication process on the topology, microstructure, and mechanical properties of AM-assisted cast and PBF lattices provide important insights. Embodiments of the AM components can include either or both strut and sheet-based lattices. The following major conclusions have been derived:

[0069] (1) AM-assisted cast samples exhibit clean smooth surfaces with notable gas porosities, while PBF samples exhibit granule surfaces due to the partially fused metal powder.

[0070] (2) Gas porosities are present in the bulk of the AM-assisted cast lattices while most of the porosity defects in PBF samples appear at the outer boundaries of the samples due to the partially fused powder. The volume and distribution of gas porosity in AM-assisted cast samples depend on the topology of the lattice.

[0071] (3) Residual investment and relatively large spherical inclusions appear in the AM-assisted cast sheet-based samples. This was justified by the level of complexity and surface area of the samples.

[0072] (4) PBF lattices exhibited superior elastic and peak stress properties compared to AM-assisted cast lattices. However, comparable, and in some cases better, post-yield properties were achieved by the AM-assisted cast samples. Titanium-based scaffolds and implants for bio-engineering.

[0073] Further, the results in the study above have demonstrated a cost-effective approach to producing complex metallic lattice materials with comparable mechanical properties to those obtained using the more expensive PBF techniques for the same alloy. These concepts can be further expanded such that one embodiment encompasses titanium-based scaffolds. Some embodiments, relate to hybrid architected, titanium-based scaffolds and implants for bioengineering applications as well as manufacturing methods for the same. Titanium alloys classify among the most used materials for biomedical engineering applications, as of their high specific strength, corrosion resistance and inherent biocompatibility. For several decades they have been employed in the engineering of medical devices and implants, such as dental 4932-6762-0872 18Atty. Dkt. No.: 046434-0920 implants, shoulder, knee and hip joints1. Only in United States, several hundreds of thousands of arthroplastic operations are performed each year with a highly increasing frequency and a cost of several billions of dollars.

[0074] In particular embodiments, methods target the identification of the series of process parameters required for the hybrid casting of such advanced material topologies and include the parameters for the initial 3D-printing of wax equivalent specimens (required wax material, printing speed, layer thicknesses), the parameters for the creation of molds (slurry mixture composition) that can accurately preserve the target topological designs upon thermal processing and the parameters required during casting (investment and centrifugal-type, vacuum conditions, inert gas pressure, centrifuge rotation speeds, temperature settings, cooling rates). In some embodiments, base alloys include the CP-Ti, Ti-6Al-4V (ELI), Ti- 6Al-4V, Ti-6Al-7Nb, Ti-22Al-25Nb, high-entropy TiZrNbTa, as well as modified hydrogenation Ti variants of the previous alloys.

[0075] Additive manufacturing techniques are generally known for use in the production of titanium-based scaffolds and implants. Titanium materials can provide an attractive AM material option in large part because of their capability to engineer complex architected structural patterns, with an inner porosity and shape control, parameters necessary for the fostering of cell proliferation and osseointegration phenomena, as well as for the tailoring of the effective stiffness properties to prevent mechanical incompatibilities, such as stress shielding phenomena. While a wide range of titanium alloys are known, in particular biocompatible alloys, two of the most widely used titanium alloys in the engineering of biomedical implants are the Ti-6Al-4V and Ti-24Nb-4Zr-8Sn typically processed through selective laser melting (“SLM”) and electron beam melting (“EBM”) powder-based techniques. However, the layerwise, laser and powder-based processing results in implant structures and scaffolds with inadequate wear and corrosion resistance, as well as questionable long-term service performance. Despite such techniques ability to produce a product or device, the results do not meet the necessary performance requirements. Moreover, their clinical use requires extensive surface modifications and post-processing for a fundamental enhancement of their as-build properties.

[0076] Up to now, no additive manufacturing method has been presented that favors the creation of internally porous and highly complex geometric patterns and yields not a layered, but a rather continuous, isotropic internal microstructure. In some embodiments, a titanium- 4932-6762-0872 19Atty. Dkt. No.: 046434-0920 based material can be used consistent with the above-described methods utilizing aluminum materials. Such a titanium-based process exploits the capabilities and geometric precision of advanced additive manufacturing, low force stereolithography methods and combines them with casting-based techniques for the engineering of architected porous aluminum-based advanced materials.

[0077] Titanium-based structures and implants using titanium alloys allow for the extension of the embodiment described above to alloys with high melting temperatures up to 2100°C under inert conditions. Embodiments utilizing a hybrid, AM-assisted manufacturing method results in a continuous and not layered-type microstructure, as evidenced from the relevant microscopy type results for aluminum-based architected materials. As such, it behaves as a continuum with a considerable plastification potential that is believed to provide enhanced long-term and fatigue performance, thus improved resistance to wear phenomena. Moreover, it yields inner surfaces without remaining loose powder parts requiring post- processing steps, such as polishing techniques to reduce the surface defects and increase the percentage of mechanically efficient material, increasing the overall production cost.

[0078] Based on the above, some embodiments utilize process parameters (vacuum, centrifugal casting conditions, temperature settings, flow rates) that result in geometrically exact, high wear resistance and strength advanced implant architectures for both strut and sheet-based porous scaffolds and implant topologies for titanium-based alloys. It is believed that such embodiments will be based in the pareto space reported for Ti-6Al-4V base alloys.

[0079] In another embodiment, an analysis of cellular materials with triply periodic minimal surface (TPMS) topologies, including Gyroid and IWP architectures are manufactured and subject to load-controlled, compression-compression, cyclic loading. Quantitative fatigue performance comparisons of hybrid manufactured (cast) with PBF as- built (PBF-AB) and heat-treated (PBF-HT) samples are performed. Cast samples exhibit the highest fatigue rigidity, and resistance to permanent deformation and fatigue damage, followed by PBF-HT samples, with PBF-AB samples yielding the shortest fatigue life. Gyroid 30 % samples consistently outperform Gyroid 20 % and IWP 30 % designs. The dependence of the fatigue performance of PBF-HT samples on the loading frequency and directionality are investigated, with lower loading frequencies and out-of-building plane loads resulting in a significant accumulation of fatigue ratcheting and fatigue damage strains, respectively. The post-fatigue analysis of the quasi-static stress–strain behavior confirms that 4932-6762-0872 20Atty. Dkt. No.: 046434-0920 cast samples maintain high structural integrity, and a low degradation of mechanical properties over a large number of loading cycles. The analysis provides benchmark results on the process-structure-property relationship of advanced AlSi10Mg materials as a function of their manufacturing method and cyclic loading performance. Methodology.

[0080] Experimental review employed two different advanced material topologies based on triply periodic minimal surfaces (TPMS) are considered, namely the Gyroid and Schoen’s IWP (I-graph and wrapped package-graph) lattices. The lattices were designed utilizing in- house developed scripts, with relative densities of 20 % and 30 %, a unit cell size of 5 mm with 5 ×5 ×5 periodicity in the x , y, and z directions, and a total sample size of 25 mm as shown in FIGS. 13A-13D. Additive manufacturing-assisted investment casting 140, also known as hybrid casting, and powder bed fusion 3D printing were used to fabricate the specimens as shown in FIG.13C. The quality of the fabricated samples is subsequently analyzed in detail, along with the assessment of the fatigue and post-fatigue mechanical performance assessment. AM-assisted / Hybrid casting.

[0081] Experimental review employed two different advanced material topologies based on triply periodic minimal surfaces (TPMS) are considered, namely the Gyroid and Schoen’s IWP (I-graph and wrapped package-graph) lattices. The lattices were designed utilizing in- house developed scripts, with relative densities of 20 % and 30 %, a unit cell size of 5 mm with 5 ×5 ×5 periodicity in the x , y, and z directions, and a total sample size of 25 mm as shown in FIGS. 13A-13D. Additive manufacturing-assisted investment casting 140, also known as hybrid casting, and powder bed fusion 3D printing 142 were used to fabricate the specimens as shown in FIG.13C. The quality of the fabricated samples 144 is subsequently analyzed in detail, along with the assessment of the fatigue and post-fatigue mechanical performance assessment 146.

[0082] The additive manufacturing-assisted investment casting process, also known as hybrid manufacturing is used to fabricate the lattices, is graphically described in FIG.13A. The process begins with the photopolymerization-based 3D printing of the metamaterial samples using castable wax resin. The Form 2 resin printer (Formlabs) and the castable Wax 40 V1 were used to fabricate the wax patterns, with a layer thickness of 25 μm for improved 4932-6762-0872 21Atty. Dkt. No.: 046434-0920 surface finishing. Following this step, the samples were linked to a sprue tree, which was then placed in a 4-inch diameter flask. The flask was then filled with Ransom & Randolph platinum investment binder mixer slurry prepared at a 60:40 powder-to-water ratio under vacuum to thoroughly cover the sprue tree. To remove entrapped air bubbles from the filled flask, the assembly was held under vacuum, degassed three to five times in succession, and then allowed to dry at room temperature for two to three hours.

[0083] The mold fabrication step was followed by a thermal burnout cycle to remove the wax and create an architected cavity. The burnout cycle consisted of staged heating at 2°C / min to 150°C, 2°C / min to 350°C, and 4°C / min to 700°C, each heating step followed by a 180-min isothermal hold and a final cooling branch at 5°C / min to 300°C. Upon completion of the burn-out cycle, the flask containing the cavity is placed in the J2R vacuum-assisted casting machine (Neutec®, Albuquerque, NM, USA). Casting is performed with AlSi10Mg material at a temperature of 1200°C and a vacuum pressure of -1 bar inside the flask. The flask is left at room temperature for 40–60 min to allow for the metal to cool and solidify before quenching in water to dissolve the investment and obtain the metallic sprue tree.

[0084] The lattice samples are cut from the metal sprue using a wire electrical discharge machine and then thoroughly cleaned with a high- pressure water jet to remove any remaining investment material. It should be noted that the increased cast metal temperature is used to support the filling of the complex architected flask topology. The arising alloy exhibits a typical growth of the α-Al phase and interdendritic eutectic Al-Si phase. The process results in architected materials with mechanical stiffness, strength, and post-elastic performance directly comparable with the one obtained from PBF methods, as subsequently detailed. PBF-AB and HT architected cellular materials.

[0085] As shown in FIG.13B, architected cellular material specimens were fabricated by powder bed fusion process using an EOS M270 machine equipped with a 200 W laser, operating at a scan speed of up to 7 m / s. A layer thickness of 30 μm and a scan direction rotation of 90° between successive layers was used. Gas- atomized AlSi10Mg powder was used in an inert argon gas environment to maintain oxygen levels below 0.1 %. Upon completion of the PBF process, samples were cut from the building plate using a wire electrical discharge machine. One set of specimens was held in the as-built condition, while another set was heat-treated (HT) in accordance with the HT2 standards. The heat treatment 4932-6762-0872 22Atty. Dkt. No.: 046434-0920 process involved heating and holding the samples at 450°C for two hours, followed by water quenching and aging at 180°C for 12 h. The HT2 process has been shown to substantially increase the ductility of AlSi10Mg alloys, yielding a fundamentally different performance compared to as-built PBF parts. Microstructural characterization.

[0086] Sample quality was evaluated using scanning electron microscopy (SEM) and micro-CT scanning to characterize surface cracking and internal porosity. The Bruker SkyScan 1272 X-ray was used to examine the additively manufactured samples. The scanning slices were reconstructed using the nRecon software (Bruker Pty Ltd.), while quantitative analysis was performed using the CTAn software (Bruker Pty Ltd.). A Thermo-Fisher Quanta 3D scanning electron microscope (SEM) was used to examine the specimen surfaces for cracks after fatigue testing. SEM and CT analysis revealed a high-quality surface finish and high dimensional accuracy for the hybrid fabricated specimens. The average total porosity was less than 4 % for all hybrid manufactured samples, with IWP 30 % specimens having the highest porosity, followed by Gyroid 30 %and Gyroid 20 % samples. The pore distribution was uneven, with varying pore sizes within the structure. PBF samples yielded an overall porosity of less than 1 %, with a poorer surface quality associated with higher surface roughness. Fatigue performance assessment.

[0087] As shown in FIG.13D, fatigue ratcheting and fatigue damage strain development upon compression-compression fatigue loading was performed. Force-controlled compression-compression fatigue tests were performed using a servo-electric fatigue testing machine (Step Lab EA 050) equipped with 25 kN load cells under ambient conditions. The as-manufactured and post-processed cellular structures were subjected to cyclic compression loading at a constant sinusoidal loading frequency of 15 Hz. A subset of the specimens was also tested at a lower cycling frequency of 5 Hz, with a sampling frequency of 4000 Hz in all cases. The fatigue loading stress amplitude was set to 50 % of the mean yield strength (strain offset 0.2 %) for both cast and PBF specimens, applying a stress ratio R of 10. A summary of the tests performed is provided in Table 3. The criterion to stop the tests was either a stiffness reduction of more than 50 % with visible specimen failure or reaching the maximum number of loading cycles. The strain values have been evaluated from the load cell recorded force– 4932-6762-0872 23Atty. Dkt. No.: 046434-0920 displacement data, which is recorded every 100th cycle at a data acquisition frequency of 2000 Hz. In addition, before and after the fatigue testing, the constitutive response of each design was evaluated under displacement-controlled compression using a universal testing 100 kN load cell MTS machine at a loading rate of 0.0167 mm / sec.Table 3. Summary of specimens and fatigue testing.

[0088] In advanced metallic materials under fatigue loads, the primary phenomenon observed is the gradual strain accumulation that leads to the permanent deformation of the loaded specimens. These strain accumulations are generally classified as fatigue ratcheting and fatigue damage strains. Fatigue ratcheting refers to the gradual displacement of the hysteresis loops along the strain axis. It indicates a cumulative effect in which the material undergoes progressive deformation with each cycle, resulting in a gradual increase in strain without immediate failure. This phenomenon is characteristic of cyclic loading conditions and is often associated with the plastic deformation of materials subjected to repeated stress cycles.

[0089] Fatigue damage, on the other hand, is the gradual deterioration of material properties due to cyclic loading. Unlike fatigue ratcheting, which primarily involves plastic deformation, fatigue damage strains involve various mechanisms such as crack initiation, propagation, and eventual failure of the material. These strains represent irreversible changes that occur within the material structure over time under cyclic loading conditions, ultimately leading to fatigue failure. Quantifying both fatigue ratcheting and fatigue damage strains is critical to predicting the fatigue life and durability of materials subjected to cyclic loading. Fatigue ratcheting (FR) and fatigue damage (FD) strains for the kth fatigue cycle can be calculated as follows:(1) 4932-6762-0872 24Atty. Dkt. No.: 046434-0920 ^^^^ = (^^ிோ)^௧ = (^^^^^)^ − (^^^^^)^ = (∆^^^^^)^^(2)

[0090] The accumulation of fatigue ratcheting (AFR) and fatigue damage (AFD) strains can be calculated from the stress–strain data over the total number of fatigue cycles as given below as graphically described in FIG.13D. ^^^^^^ = ^^^ி^ = (^^^^௫ − ^^^^^)ே − (^^^^௫ − ^^^^^)^(3) ^^^^^^ = ^^^ிோ = (^^^^^)ே − (^^^^^)^(4)

[0091] Strain accumulation typically has three distinct stages. In the initial stage (Stage I), which involves a relatively small number of cycles (N <1000), rapid strain accumulation occurs. This rapid strain accumulation indicates that significant deformation has occurred in the material in a short period of time, indicating a high susceptibility to fatigue at the onset of the cyclic loading. Following Stage I, the behavior transitions to Stage II, where strain accumulation becomes relatively constant and bilization of the deformation process, indicating a period of endurance where the material exhibits resilience to further strain accumulation despite prolonged cyclic loading. However, the stability observed in Stage II is interrupted by Stage III, characterized by a sudden and significant increase in strain accumulation after an abrupt point jump in strain. This stage represents a critical point in the fatigue process, where the material undergoes accelerated degradation, leading to rapid strain accumulation and potential failure. The characterization of these distinct stages is critical for evaluating the fatigue behavior and durability of metallic architected materials under cyclic compression-compression loading conditions.

[0092] Experimental results were complemented by finite element analyses to gain insights into the static inner stress and plastification fields developed for each metamaterial topology. Specifically, 5x5x5 unit cell models based on C3D4 volume elements and using an aluminum material (AlSi10Mg) were developed in the commercial software Abaqus. An elastoplastic implicit static analysis was conducted, incorporating a standard plastic hardening model based on Johnson-Cook plasticity. The material parameters for AlSi10Mg used in the Johnson-Cook plasticity model are provided in Table 4. 4932-6762-0872 25Atty. Dkt. No.: 046434-0920 Parameter E (GPA)ѵ р(Kg / m3)A(MPa) B(MPa)έ(s-1)G m n Value 55 0.3 2800 210 230 0.001 0.015 0.859 0.5 Table 4. Mechanical parameters of the AlSi10Mg for the Johnson-Cook FE model.

[0093] For the compressive response, a displacement was applied on the top surface while the bottom surface was fully constrained. Numerical simulations were performed for maximum target compressive strain magnitudes of 2.5 %, encompassing the initial elastic and peak stress responses observed experimentally for different IPC designs. The analysis required approximately 1 million C3D4 elements per metamaterial topology. Computation times on a 64-core AMD Threadripper Pro 5995WX processor were on the order of several hours for each elastoplastic analysis. Results. Fatigue performance of PBF-AB designs.

[0094] As-built PBF specimens were fatigue-tested with sinusoidal cyclic loading at a frequency of 15 Hz. Quasi-static analysis of the samples yielded Young’s moduli values for Gyroid (20 %), Gyroid (30 %), and IWP (30 %) specimens of 354.195 MPa, 729.46 MPa, and 649.57 MPa, respectively. The mean yield stress values (0.2 % strain offset) were calculated to be 14.48 MPa, 28.86 MPa, and 24.21 MPa, respectively, with corresponding toughness values of 1.195 MJ / m3, 2.92 MJ / m3, and 1.595 MJ / m3. The stress amplitude for fatigue testing was set to approximately 50 % of the mean yield strength to 7.2 MPa, 14.4 MPa, and 12.0 MPa for Gyroid 20 %, Gyroid 30 %, and IWP 30 % samples, respectively.

[0095] As shown in FIGS.14A-14H, fatigue performance of PBF-АВ Gyroid 30 % and IWP 30 % lattices are provided. An experimental stress–strain curves of PBF-АВ Gyroid 30 % lattice 148 and the experimental stress–strain curves of IWP 30 % lattice 150 are shown in FIG.14A and FIG.14B respectively under cyclic loading show that both lattice structures reach peak stresses of 14.41 MPa and 12 MPa at strain levels of 2.47 % and 2.35 %, respectively.

[0096] A rigidity variation over the loading cycle of PBF-АВ Gyroid 30% 152 and a rigidity variation over the loading cycle of IWP 30% 154 is shown in FIG.14C and FIG. 14D. The rigidity of PBF-АВ Gyroid 30 % lattice shows a gradual decrease over the fatigue 4932-6762-0872 26Atty. Dkt. No.: 046434-0920 cycles as shown in FIG.14C and FIG.14D, with average stiffnesses of 53.45 MPa / mm (Gyroid 30 %) and 50.90 MPa / mm (IWP 30 %), respectively.

[0097] A hysteresis loop of PBF-АВ Gyroid 30% 156 and a hysteresis loop of IWP 30% 158 is shown in FIG.14C and FIG.14D. The hysteresis loops indicate the energy dissipation behavior during cyclic loading, with the slope of each hysteresis loop representing the change in Young’s modulus. This is depicted for every 10,000 load cycles as shown in FIG.14E and FIG. 14F. The hysteresis loops indicate that the IWP topology dissipates a significantly greater amount of energy than the Gyroid samples of the same relative density, recording higher fatigue damage and fatigue ratcheting values. The cyclic ratcheting and fatigue damage strain plots as shown in FIG.14E and FIG.14F indicate that the Gyroid 30 % lattice has an average fatigue ratcheting value of 4.06e-04 mm / mm and a maximum fatigue damage value of 3.36e-04 mm / mm. In contrast, the IWP 30 % lattice has significantly higher average FR and FD values of 7.45e-04 mm / mm and 6.01e-04 mm / mm, respectively.

[0098] The preceding fatigue ratcheting and damage results demonstrate the distinctive fatigue behaviors of the two lattice types for the same relative density under testing conditions. The average rigidity for Gyroid 20 % is 32.58 MPa / mm. It decreases rapidly during fatigue loading, reflecting a higher fatigue-induced stiffness loss compared to Gyroid 30 % and IWP 30 % designs. The wide hysteresis loops demonstrate the substantial energy loss and the irreversible deformations induced by the cycling loading pattern. A fatigue damage strain plot of PBF-АВ Gyroid 30% 160 and a fatigue damage strain plot of IWP 30% 162 is shown in FIG.14G and FIG.14H. Furthermore, the high average fatigue ratcheting strain of 7.56e-04 mm / mm recorded is nearly double the value obtained for Gyroid 30 % as shown in FIG. 14G, indicating that the material has undergone significant permanent deformation. Further insights into the fatigue performance are provided in the bar plot comparisons as shown in FIGS.15A-15D. FIGS.15A-15D illustrate average rigidity 164, maximum stress 166, accumulated fatigue ratcheting strains 168, and accumulated fatigue damage 170 for PBF-AB Gyroid 20 %, Gyroid 30 %, and IWP 30 % specimen at 60k and 120k fatigue cycles. There-upon, the effect of two different cyclic loading counts, namely of 60k and 120k cycles, on the rigidity, stress, FR and FD values of Gyroid and IWP cellular structures is evaluated.

[0099] It is noteworthy that the average rigidity as shown in FIG.15A decreases upon increasing cycle numbers (60k→120k), indicating that the structural stiffness is progressively 4932-6762-0872 27Atty. Dkt. No.: 046434-0920 degraded in all three lattice types. Gyroid 30 % lattice designs demonstrate a higher rigidity compared to Gyroid 20 % and IWP 30 % architectures, revealing a superior structural integrity. Moreover, Gyroid 30 % and IWP 30 % lattices exhibit a markedly higher stress endurance than Gyroid 20 % designs as shown in FIG.15B.

[0100] The accumulated fatigue ratcheting and fatigue damage strains as shown in FIG. 15C and FIG.15D provide a detailed view of the cyclic deformation behavior. The data indicate that IWP 30 % samples exhibit the highest FR values, with significant plastic deformation accumulation, contrary to Gyroid 30 % (lowest FR). The relative difference in the FR values of Gyroid 20 % and Gyroid 30 % provides insights into the influence of the metamaterial relative density on the magnitude of permanent de-formations developed. In terms of fatigue damage, IWP 30 % exhibits the highest accumulated FD, indicating a higher susceptibility to dam-age accumulation over time. The results demonstrate a clear correlation between the lattice topology, relative density, and fatigue performance. Gyroid 30 % metamaterials yielded the highest rigidity and resistance to permanent deformation, sustaining the lowest fatigue damage among the topologies investigated. Static and fatigue performance of hybrid manufactured and PBF-HT designs. Static response before fatigue loading.

[0101] Quasi-static experimental stress–strain curves for hybrid-cast and PBF-HT samples are graphically summarized in FIGS.16A-16D. Quasi-static experimental stress– strain curves of hybrid manufactured (cast) and PBF-HT Gyroid 30% 172 and IWP 30% 174 samples. Comparison of Toughness 176 and Peak stress 178 values. The stress–strain curves indicate that hybrid cast samples yield higher plateau stresses than PBF-HT samples for both topological designs (Gyroid 30 % and IWP 30 % lattices). In particular, the plateau stress of Gyroid 30 % hybrid cast samples amounts to approximately 21 MPa, in contrast to ~ 14.5 MPa for the PBF-HT samples. Similarly, plateau stresses of IWP 30 % hybrid cast samples amount to ~ 14 MPa, contrary to 12.5 MPa for IWP PBF-HT samples. Thesefindings indicate that the hybrid-cast samples furnish an overall superior constitutive response and energy absorption performance under static loading conditions.

[0102] In terms of toughness, hybrid-manufactured (cast) samples consistently outperform PBF-HT samples. The highest toughness value, approximately 7.5 MJ⋅ m-3, is observed for Gyroid 30 % cast samples, which is ~ 15 % higher than the value obtained for 4932-6762-0872 28Atty. Dkt. No.: 046434-0920 PBF-HT samples (~6.5 MJ⋅ m-3). The toughness values of Gyroid 20 % cast samples are directly comparable with those recorded for their PBF-HT counterparts. Moreover, a higher toughness of IWP 30 % cast compared to IWP 30 % PBF-HT samples is recorded, with the former to yield a value of ~ 5.8 MJ⋅ m-3and the latter a value of ~ 4.8 MJ⋅ m-3. Overall, the post-fatigue loading, static response results suggest that hybrid cast samples have either comparable or enhanced mechanical performance compared to PBF-HT samples in terms of plateau, peak stresses, and toughness. Fatigue performance of Gyroid and IWP cellular designs.

[0103] The fatigue performance of hybrid-cast, and PBF-HT Gyroid 30 % structures are subsequently analyzed in comparative terms. First cast stress–strain curves 180, first PBF- HT stress–strain curves 182, cast rigidity evolution data 184, PBF-HT rigidity evolution data 186, first cast hysteresis loops 188, first PBF-HT hysteresis loops 190, first cast fatigue damage strains and ratcheting 192, and first PBF-HT fatigue damage strains and ratcheting 194 are provided in FIGS.17A-17H.

[0104] The stress–strain curves under cyclic loading indicate that the three metamaterial types exhibit distinct fatigue performances. The cast Gyroid 30 % samples are subject to a maximum stress of 8.01 MPa at approximately 1.69 % strain, while the PBF-HT Gyroid 30 % samples arrive at a maximum stress of 6.41 MPa at ~1.25% strain as shown in FIG.17A and FIG.17B. The overall strain increases more prominently in the PBF-HT samples over the cycles, indicating a higher rate of deformation and reduced fatigue resistance compared to hybrid cast samples as shown in FIG.17A and FIG.17B. The recorded rigidity variations over the fatigue cycles highlight further differences in mechanical stability. The cast Gyroid 30 % samples demonstrate an average rigidity of 55.25 MPa / mm, exhibiting structural integrity and consistent mechanical performance up to 500 K loading cycles as shown in FIG. 17C. In contrast, the PBF-HT Gyroid 30 % samples yield an average rigidity of 40.73 MPa / mm, with a discernible decline over the cycles, indicating a gradual reduction in stiffness and mechanical stability as shown in FIG. 17D. However, the overall performance is markedly enhanced in comparison to the PBF-AB samples, where a considerable rigidity decline over the fatigue loading cycles was recorded as shown in FIG.14C.

[0105] The hysteresis loops are used to characterize the energy loss during cyclic loading, while the change in slope of each hysteresis curve is employed to quantify the modified 4932-6762-0872 29Atty. Dkt. No.: 046434-0920 stiffness parameters as shown in FIG.17E and FIG.17F. The hysteresis loops of cast Gyroid 30 % samples are tightly clustered with a nearly constant slope, suggesting a constant Young’s modulus. However, PBF-HT Gyroid 30 % samples exhibit more spread- out loops, indicative of elevated energy dissipation. These observations are consistent with the elevated strain levels and the stiffness reduction as shown in FIG.17D. It is notable that PBF-AB samples yield even wider hysteresis loops and a more pronounced nonlinear shifting along the strain axis as shown in FIGS.14A-14H, compared to the PBF-HT samples as shown in FIGS.17A-17H.

[0106] Fatigue ratcheting (FR) and fatigue damage (FD) analysis provides further insights into the deformation behavior under cyclic loading as shown in FIG.17G and FIG. 17H. Hybrid cast Gyroid 30 % samples exhibit minimal permanent deformations and damage accumulation, with an average fatigue ratcheting of 3.79e-04 mm / mm and a maximum fatigue damage of 2.01e-04 mm / mm. In contrast, PBF-HT Gyroid 30 % samples exhibit higher permanent deformations and damage accumulation, with an average fatigue ratcheting of 4.33e-04 mm / mm and a maximum fatigue damage of 2.38e-04 mm / mm as shown in FIG. 17G and FIG.17H. The stress–strain analysis indicates that both manufacturing methods achieve similar maximum stress levels. However, the rigidity analysis over cycles reveals that cast Gyroid 20 % maintains higher rigidity compared to PBF-HT, where the average rigidity decreases significantly over fatigue loading. The stress–strain hysteresis loops reveal that cast samples undergo rather negligible changes in the modulus of elasticity over the cycles. Second cast stress–strain curves 196, second PBF-HT stress–strain curves 198, cast rigidity parameters 202, PBF-HT rigidity parameters 204, second cast hysteresis loops 206, second PBF-HT hysteresis loops 208, second cast fatigue damage strains and ratcheting 212, and second PBF-HT fatigue damage strains and ratcheting 214. For PBF-HT samples, a wide range of the hysteresis loops was observed, with lattices are provided in FIG.18A and FIG. 18B. The stress–strain curves under cyclic loading reveal significant differences as shown in FIG.18A and FIG.18B. Hybrid cast IWP 30 % samples exhibited a maximum stress of ~ 6.41 MPa with a strain of ~ 1.6 %, whereas the PBF-HT samples had a maximum stress of 5.21 MPa at ~ 1.56 % strain. The values suggest that PBF-HT samples exhibited a higher rate of strain increase per stress amplitude. The variation in rigidity over the fatigue loading cycles further highlights the differences in mechanical stability as shown in FIG.18C and FIG. 18D. Hybrid cast IWP 30 % samples provided an average rigidity of 48.19 MPa / mm contrary to an average value of 50.51 MPa / mm for PBF-HT IWP 30 % samples. Furthermore, a 4932-6762-0872 30Atty. Dkt. No.: 046434-0920 discernible rigidity decline over the loading cycles was recorded for PBF-HT IWP samples, indicating a gradual reduction in stiffness and mechanical stability.

[0107] The hysteresis loops of PBF-HT samples reveal considerable energy losses, with the change in the modulus of elasticity over the loading cycles accompanied by permanent strain accumulations as shown in FIG.18F. In contrast, the hysteresis loops of hybrid cast samples are tightly clustered as shown in FIG.18E. Concerning fatigue ratcheting and fatigue damage, as shown in FIG.18G, hybrid cast samples had an average fatigue ratcheting strain of 2.82e-04 mm / mm and a maximum fatigue damage strain of 1.57e-04 mm / mm. As shown in FIG. 18H, PBF- HT samples exhibited higher levels of permanent deformation and damage accumulation, with an average FR value of 7.12e-04 mm / mm and a maximum fatigue damage strain of 1.79e-04 mm / mm, values that are 2.50 times and ~ 15 % higher than those computed for hybrid cast samples, respectively.

[0108] As shown in FIGS.19A-19D, a summarized analysis of the fatigue performance of hybrid-cast and PBF-HT samples is presented in the form of bar plots including average rigidity 216, max stress 218, accumulated fatigue ratcheting 222 and fatigue damage strains 224 for hybrid manufactured (cast) and PBF-HT Gyroid 20 %, Gyroid 30 % and IWP 30 % samples after 120k and 500k fatigue loading cycles. Data on the average rigidity, maximum stress, accumulated fatigue ratcheting, and accumulated fatigue damage strains for both Gyroid and IWP lattices at 120k and 500k fatigue loading cycles are provided.

[0109] The average rigidity results as shown in FIG. 19A indicate that hybrid cast samples consistently exhibit higher average rigidity across all cellular de-signs compared to PBF-HT samples, with a consistent stiffening at higher cycle numbers (120k→500k as shown in FIG.19A). Specifically, Gyroid 30 % hybrid cast samples furnish the highest rigidity of approximately 68 MPa / mm, followed by IWP 30 % hybrid cast samples with ~ 61 MPa / mm and Gyroid 20 % samples with ~ 42.6 MPa / mm. The corresponding values for PBF-HT samples are ~ 52 MPa / mm, ~48 MPa / mm, and ~ 29 MPa / mm. With regard to maximum stress as shown in FIG.19B, hybrid cast Gyroid 30 %and IWP 30 % samples yield values in the order of ~ 8.1 and 6 MPa, which are significantly higher than the values of PBF-HT samples, amounting to ~ 6.4 MPa and ~ 5.2 MPa for the same topological de-signs. The maximum stress values of the Gyroid 20 % hybrid cast samples are comparable to those for their PBF-HT counterparts, both at both 120k and 500k loading cycles as shown in FIG.19B. 4932-6762-0872 31Atty. Dkt. No.: 046434-0920

[0110] The accumulated fatigue ratcheting strains as shown in FIG.19C demonstrate notable differences in the fatigue performance of hybrid-cast and PBF- HT samples. In particular, at 120k cycles, hybrid cast samples yield AFR values of 3.41e-04 mm / mm, 0.6e- 04 mm / mm, and 1.11e-04 mm / mm for Gyroid 20 %, 30 %, and IWP 30 % samples as shown in FIG.19C. The corresponding AFR values for PBF-HT samples are approximately three times higher in all cases. At 500k loading cycles, AFR values are substantially increased for all topologies, for both manufacturing methods. For hybrid cast samples, the highest increase is recorded for the IWP 30 % samples, which have AFR values directly comparable with those reported for Gyroid 20 % samples (0.5e-03 mm / mm). The corresponding PBF-HT AFR values are considerably higher, with Gyroid 30 % samples yielding an AFR value that is nearly three times higher, while low-density Gyroid 20 % samples an approximately four times higher mean AFR value.

[0111] The accumulated fatigue damage as shown in FIG.19D yields lower AFD values for the hybrid manufactured Gyroid 20 % and IWP 30 % samples, both for 120k and 500k cycles. The accumulated fatigue damage of cast Gyroid 20 % lattices is higher than that of IWP lattices at 120k cycles, while Gyroid 30 % specimen experience lower accumulated fatigue damage in the same loading range space as shown in FIG.19D. For the lower relative density Gyroid 20 % designs, the AFD values of PBF-HT samples are a multiple of those reported for hybrid-cast samples, both at 120 K and 500 K cycles. It is noteworthy that the increase in the number of loading cycles (from 120 K to 500 K cycles) leads to a higher cumulative AFD percent increase for the higher density designs both for hybrid-cast and PBF- HT samples.

[0112] The cast Gyroid 20 % samples exhibited a rise in their mean FD values from 0.469e-4 mm / mm at 120k cycles to 2.695e-4 mm / mm at 500k cycles. In contrast, the PBF- HT Gyroid 20 % samples exhibited much higher FD values, reaching approximately 4.28e-4 mm / mm. The cast Gyroid 30 % and IWP 30 % samples exhibited FD values of ~ 0.297e-4 mm / mm and ~ 0.288e-4 mm / mm at 120k cycles, respectively, which increased to 2.01e-4 mm / mm and 2.295e-4 mm / mm at 500k cycles. The PBF-HT Gyroid 30 % and IWP 30 % samples exhibited FD values of approximately 0.310e-4 mm / mm and 0.641e-4 mm / mm at 120k cycles, respectively, which then increased to 2.84e-4 mm / mm and 3.18e-4 mm / mm at 500k cycles. It is noteworthy that PBF-HT samples yield consistently the highest fatigue 4932-6762-0872 32Atty. Dkt. No.: 046434-0920 damage, along with the most prominent FD increase for all topological designs, suggesting an inferior fatigue resistance. Comparative strain accumulation analysis and fatigue-induced stiffness degradation.

[0113] As shown in Table 5, a comparative analysis of mean accumulated fatigue ratcheting strains for hybrid-manufactured (cast), PBF-HT, and PBF-AB topologies (Gyroid 20 %, Gyroid 30 %, and IWP 30 %) at 120k and 500k cycles is provided. The PBF-AB specimens reveal the highest ratcheting strains, indicating the most significant accumulation of deformation under cyclic loading, particularly for the IWP 30 % configuration at 120k cycles (1.30 × 10-3). Hybrid cast specimens report the lowest ratcheting strains (0.053 × 10-3) at 120k cycles for Gyroid 30 % de-signs, indicating superior resistance to fatigue-induced deformation. The PBF-HT specimens show intermediate performance, with reduced ratcheting strains compared to PBF-АВ designs, but not as low as those reported for hybrid cast samples. As such, heat treatment improves fatigue resistance. However, hybrid cast specimens appear to be the most robust structures in terms of fatigue ratcheting deformations under prolonged cyclic loading. Table 5. Comparison of the mean accumulated fatigue ratcheting strains for hybrid manufactured (cast), PBF-HT and PBF-as built.

[0114] As shown in FIGS.20A-20D, a summary of the elastic modulus E (stiffness) evolution as a function of the loading cycle is provided. The results of FIGS. 20A-20D provide a summary of the elastic modulus (stiffness) decay as a function of the loading cycle N, for all manufacturing methods and cellular configurations considered including least squarefitting of the experimental elastic stiffness degradation data: Gyroid 20% PBF-as built 226, Gyroid 20% PBF-HT 228, Gyroid 30% hybrid cast samples 232, and comparison of fitting curves for all hybrid cast, PBF-HT, and PBF-AB specimens 234. As shown in FIG. 20A, Gyroid 20 % PBF-AB lattices are presented, undergoing a rapid modulus decline, along 4932-6762-0872 33Atty. Dkt. No.: 046434-0920 with the corresponding least-square exponentialfitting of the elastic modulus (E = f(N)). As shown in FIG. 20B, the corresponding results for Gyroid 20 % PBF-HT samples are provided, revealing a substantially lower decay rate, while as shown in FIG.20C, Gyroid 30 % cast samples are provided. A detailed comparison of all design cases is provided in FIG. 20D in a normalized form.

[0115] PBF-АВ specimens yield fast decaying curves, the steepest decline noted for IWP 30 % samples as shown in FIG. 20D. Accordingly, significant stiffness reductions are reported for PBF-HT and hybrid-cast IWP 30 % samples, with the former undergoing a higher stiffness decline over the investigated cycles. It is noteworthy that the form of the fatigue decay curves is considerably modified after heat treatment, retaining high stiffness modulus values over a large number of cycles. Moreover, hybrid cast samples record the lowest percentage drop in the moduli values for all topologies, below 4 % of their initial stiffness, in accordance with their overall lower fatigue ratcheting and damage metrics. Post-Fatigue loading quasi-static performance.

[0116] The quasi-static stress–strain behavior after fatigue cycling provides additional insights into the performance and durability of hybrid-cast and PBF-HT samples. As shown in FIGS.21A-21F, the differences in compressive stress–strain performance before fatigue loading and after 60k and 120k loading cycles are highlighted.

[0117] Quasi-static stress-strain response of cast 20% samples 236, quasi-static stress- strain response of PBF-HT 20% samples 238, quasi-static stress-strain response of cast 30% samples 242, and quasi-static stress-strain response of PBF-HT 30% samples 244 are shown in FIGS.21A-21D. Hybrid cast Gyroid samples exhibited higher initial peak and average plateau stresses than the corresponding PBF-HT samples. However, significantfluctuations in stress are observed in the post-elastic plastification region, with mixed fatigue loading effects. In the case of the Gyroid 20 % samples, there is a stiffening effect at 60k and 120k cycles, while for Gyroid 30 % samples, a softening effect is recorded as shown in FIG.21A and FIG.21C. Toughness of the cast samples 246 are shown in FIG.21E, and toughness of the PBF-HT samples 248 are shown in FIG.21F. The energy absorption capacity is modified on average by 7 % and 16 %, respectively as shown in FIG.21E. An analogous mixed plastification behavior is recorded for the PBF-HT samples, with minorly lower and higher plateau stresses for Gyroid 20 % and Gyroid 30 % samples. The overall sensitivity of the 4932-6762-0872 34Atty. Dkt. No.: 046434-0920 energy absorption capacity is here lower, with a maximum of 8 % in the Gyroid 20 % case as shown in FIG.21F, recorded for 500k loading cycles. Frequency and loading directionality effects.

[0118] The fatigue performance of the PBF-HT specimens was also evaluated in the out- of-building plane loading direction at 15 Hz, as well as at a lower, in-plane frequency loadings of 5 Hz. The fatigue performance of Gyroid 20 % samples is summarized in FIGS.22A-22H. The analysis is per-formed for HT rather hybrid-cast samples, out of the reported anisotropy of specimen produced employing PBF methods.

[0119] GY20% in-plane (5Hz) cycling loading stress–strain curves 252 and GY20% out- of-plane (5Hz) cycling loading stress–strain curves 254 as shown in FIG.22A and FIG.22B demonstrate notable differences between the in-plane 5 Hz and the out- of-plane 15 Hz results. In particular, the in-plane 5 Hz cyclic loading results in a maximum stress value of 4.01 MPa for a strain magnitude of approximately 2.11 %, in contrast to the out-of-plane 15 Hz loading cases, where the same maximum stress value is attained at a higher strain magnitude of 2.53 %. Consequently, the rate of strain increase is approximately 20 % higher in the out-of-plane loading case, indicating a higher rate-of-deformation compared to the in- plane loading conditions at both 5 Hz and 15 Hz.

[0120] The observed variation in GY20% in-plane (5Hz) rigidity 256 and GY20% out- of-plane (5Hz) 258 rigidity serves to highlight further differences in the mechanical stability of the cellular structures under different testing conditions as shown in FIG.22C and FIG. 22D. In more specific terms, in-plane fatigue loading at 5 Hz yields an average rigidity of 30.68 MPa / mm, with a more pronounced decline over the cycles, compared to the out-of- plane loading at 15 Hz. In this case, a slightly lower average rigidity of 29.77 MPa / mm is recorded, with a more gradual stiffness decline over the loading cycles. The stiffness degradation is approximately three times lower than the one recorded at 5 Hz, indicating that lower frequency loading adversely affects the fatigue performance of the cellular structure.

[0121] As shown in FIG.22E and FIG.22F, GY20% in-plane (5Hz) hysteresis curves 262 and GY20% out-of-plane (5Hz) hysteresis curves 264 suggest that both in-plane low- frequency fatigue loading at 5 Hz and out-of-plane fatigue loading at 15 Hz result in more spread-out loops than the in- plane fatigue loading results at 15 Hz as shown in FIGS.17A- 17H and FIGS.19A-19D, exhibiting pronounced nonlinear shifts along the strain axis. The 4932-6762-0872 35Atty. Dkt. No.: 046434-0920 hysteresis curves exhibit a high degree of dispersion along the strain axis, which is reflected in the GY20% in-plane (5Hz) fatigue ratcheting results 266 and the GY20% out-of-plane (5Hz) fatigue ratcheting results 268 as shown in FIG.22G and FIG.22H. In- plane fatigue loading at 5 Hz yielded an average fatigue ratcheting value of 2.52e-03 mm / mm and a maximum fatigue damage of 3.80e-05 mm / mm. Conversely, out-of-plane fatigue loading at 15 Hz yields an average fatigue ratcheting value of 1.22e-03 mm / mm and a maximum fatigue damage of 2.54e-04 mm / mm. As such, the FR values for out-of-plane 15 Hz loading are approximately half the ones reported for in- plane 5 Hz loading, but the corresponding FD values are more than 6 times higher.

[0122] The previously reported FR values are notably higher than those obtained for in- plane loading conditions at 15 Hz as shown in FIGS.19A-19D. In particular, the mean FR value in the out-of-plane loading conditions is 30 % higher than the in-plane values as shown in FIGS.19A-19D, with the low-frequency, 5 Hz FR results being ~ 175 % higher. Notably, the mean FD values are directly comparable for in-plane and out-of-plane loading at 15 Hz. A comparative summary of the fatigue loading results for in-plane and out- of-plane 15 Hz and in-plane 5 Hz loading conditions is provided in FIGS. 23A-23D. The data for all topological designs and loading conditions are provided, including average rigidity 270, maximum stress 272, accumulated fatigue ratcheting 274, and accumulated fatigue damage 276.

[0123] The highest average rigidity is observed for Gyroid 30 % samples, followed by IWP 30 % and Gyroid 20 % samples, across all testing conditions. The maximum applied stresses as shown in FIG.23B exhibit a similar pattern, indicating that nearly identical rigidity and maximum stress values are observed for a given topological design. However, the distribution of accumulated FR values differs substantially from the average rigidity and applied maximum stress distribution. The highest AFR values are recorded for the lowest relative density Gyroid 20 % structures in all loading cases as shown in FIG.23C. Under in- plane loading, the AFR values of Gyroid 20 % designs are approximately 2.5 times higher than those obtained for Gyroid 30 % samples (~0.3e-03). Accordingly, IWP 30 % samples exhibit approximately 50 % higher AFR values than Gyroid 30 % samples. Out-of-plane fatigue loading results in a 45 % increase in the AFR values of Gyroid 20 % designs, with the AFR values of Gyroid 30 % and IWP 30 % samples more than doubling (~0.85e-03 and ~ 0.9e-03 as shown in FIG.22E and FIG.22F). In-plane fatigue loading of 5 Hz approximately 4932-6762-0872 36Atty. Dkt. No.: 046434-0920 triples the AFR values of both the Gyroid 20 % and 30 % cellular structures, and increases the AFR values of the IWP 30 % samples, though to a lesser extent than out-of-plane loading.

[0124] The accumulated fatigue damage values demonstrate a significant dependence on the combination of the topological pattern and loading frequency as shown in FIG.23D. The highest AFD values are observed for Gyroid 20 % topologies for in-plane loading at 15 Hz. However, when the loading frequency is reduced to 5 Hz (in-plane, as shown in FIG.23D), the AFD values of Gyroid 20 % samples are comparatively smaller, being nearly four times lower than the ones recorded for 15 Hz. It is noteworthy that for a given topology, low- frequency loading (5 Hz) yields lower AFD values than out-of-plane loading, for all topologies investigated. In particular, while the AFD values of Gyroid 30 % and IWP 30 % at 5 Hz are approximately 4.7 and 4 times higher than the ones recorded for in-plane loading at 15 Hz, the corresponding out-of-plane factors are ~ 5 and ~ 10. Discussion

[0125] Ratcheting is regarded as a significant contributing factor to the fatigue failure of porous materials subjected to cyclic loading. The inner components of the metamaterial exhibit localized plastification, resulting in a gradual accumulation of damage. During this process, an in-crease in the fatigue damage strain and the initiation and gradual propagation of cracks in the struts occur. As shown in FIG.24A-24F, failed meta-material samples along with insights into the inner crack patterns and fracture surface morphologies developed by the fatigue loading in the Gyroid and IWP metamaterial topologies, as a result of fatigue loading are depicted. As shown in FIG.24A, the Gyroid 20 % lattice exhibits a predominant pure shear failure mode, as evidenced by the brittle shear fracture surfaces in the SEM images as shown in FIG. 24B. These images reveal sharp fracture edges and relatively smooth surfaces, micro-cracks, and cleavage planes (magnification images as shown in FIG.24C), indicating pure shear failure mechanisms. The same shear failure mode type is recorded for Gyroid 30 % samples (as shown in FIGS.25A-FIGS.25G). In contrast, the IWP 30 % lattice as shown in FIG.24D demonstrates a combination of shear and bending failure modes. As shown in FIG.24E, the SEM images show rougher fracture surfaces with evidence of plastic bending deformation. As shown in FIG.24F, the higher magnification images reveal features such as dimpled rupture surfaces and voids, indicating bending failure mechanisms and crack propagation through the material during fatigue bending under compressive cyclic loads. These observations suggest that AB-Gyroid lattices are more prone to pure shear failure under 4932-6762-0872 37Atty. Dkt. No.: 046434-0920 cyclic loading, while IWP lattices are more susceptible to combined bending and shear mixed failure modes. Combined experimental and numerical results are provided in FIGS.25A- 25G. As shown in FIG.25A, the number of cycles to failure for Gyroid and IWP PBF-AB samples as a function of their maximum stress is illustrated. Further-more, the FR values for each topological design at 60k and 120k cycles are provided in FIG.25B, followed by FEM simulation results as shown in in FIG.25C-25G. In particular, the maximum von Mises stresses and PEEQ strains (2.5 % macroscopic strains with the elastoplastic modeling parameters detailed in

[0015] ), along with the von Mises, and shear inner stress distributions are presented in FIG.25E and FIG.25G. The elastplasticfinite element modeling results are provided for the assessment of influential stress and strain components, thereby revealing the proclivity of a certain topological design to plastification. It should be however emphasized, that the applied fatigue loading lies within the elastic macroscopic loading response limits.

[0126] The distribution of FR values is found to be well-correlated with the number of cycles to failure recorded as shown in FIG.25A. In particular, IWP 30 % samples exhibit the highest FR values at 60k and 120k cycles (1.35x10-3 mm / mm at 120k cycles) and the lowest number of cycles to failure (~6.5x104 cycles). Comparative, yet lower FR values are recorded for Gyroid 20 % structures at 60k and 120k cycles, with failure occurring at approximately ~ 8x104 cycles. Consequently, the highest ratcheting strain values relate to the lowest number of total cycles to failure, with the Gyroid PBF-AB 30 % samples having the largest number of cycles to failure among the topologies investigated.

[0127] It is noteworthy that the failure sequence does not align with the distribution of von Mises stresses as shown in FIG.25C or equivalent plastic strains as shown in FIG.25D. In particular, the maximum equivalent plastic strains for IWP 30 % topologies are four times lower than those recorded for Gyroid 20 % topologies as shown in FIG.25D. Gyroid 20 % cellular structures accumulate principal equivalent plastic strains in the order of ~ 0.09, suggesting a markedly higher degree of plastic deformation and damage compared to the Gyroid 30 % (~0.02) and IWP 30 % (~0.01) samples. Moreover, IWP 30 % topologies undergo comparable, yet lower von Mises (VM) stresses, compared to Gyroid 20 % topologies as shown in FIG.25C. The von Mises stress distribution of all topologies reveals extensive high-stress regions throughout the cellular structures as shown in FIG. 25E. Nevertheless, the failure order as shown in FIG.25A does not correlate with the susceptibility 4932-6762-0872 38Atty. Dkt. No.: 046434-0920 of a given pattern to the accumulation of plastic inner strains, as IWP 30 % cellular designs are thefirst to fail.

[0128] In contrast to thefindings of von Mises and equivalent plastic strains, shear stresses appear to be highly informative regarding the susceptibility of a given topological design to cyclic compression loading failure. In particular, Gyroid 20 % samples exhibit high shear stresses at inner strut junctions, higher than those observed in Gyroid 30 % samples as shown in FIG.25G. These shear stresses have a positive sign in the largest part of the inner material body. As shown in FIG.25G, IWP 30 % samples exhibit comparable magnitude shear stresses with Gyroid 20 % samples, though with tightly concentrated positive and negative shear stress distributions at the ends of the inner elements. Such shear stress concentrations and sign alterations are not present in gyroid samples, a factor that appears to differentiate the internal stress state of the topologies and has been re-ported as critical for the fatigue performance, directly associating with the recorded failure patterns as shown in FIG. 24A and FIG.24D. Conclusion.

[0129] Based on the experimental and theoretical analysis, the fatigue performance of TPMS-based, Gyroid, and IWP, architected cellular materials, engineered with different manufacturing processes, namely hybrid casting and PBF has been investigated, quantifying primal fatigue performance metrics. It has been found that:

[0130] 1) PBF-AB specimens exhibit significantly elevated fatigue ratcheting and damage strain accumulations compared to PBF-HT and hybrid- cast samples, leading to short lifespans for all topological designs.

[0131] 2) Gyroid designs outperformed IWP specimens, with overall lower or directly comparable fatigue ratcheting and damage metrics upon higher stiffness and maximum stress resistance.

[0132] 3) Cast specimens accumulate substantially lower fatigue ratcheting strains and lower or analogous fatigue damage compared to PBF-HT specimens for all metamaterial topologies. 4932-6762-0872 39Atty. Dkt. No.: 046434-0920

[0133] 4) In-plane lower frequency loadings (5 Hz) and out-of-plane loading result in the accumulation of substantially higher ratcheting strains compared to in-plane loading (15 Hz) for all topological designs, the effect being more prominent for lower relative density specimens.

[0134] Further, the results of the aforementioned process-structure–property analysis in the study above are intended to serve as benchmarks for the fatigue performance of AlSi10Mg-based cellular material designs. These concepts can be further expanded such that particular embodiments encompass the examination of the fatigue response of advanced materials engineered with different manufacturing processes, base alloys, and loading frequencies.

[0135] In some embodiments, a titanium-based material can be used consistent with the above-described methods utilizing aluminum materials. As described above, additive manufacturing techniques are generally known for use in the production of titanium-based scaffolds and implants.

[0136] In some embodiments, base alloys include the CP-Ti, Ti-6Al-4V (ELI), Ti-6Al- 4V, Ti-6Al-7Nb, Ti-22Al-25Nb, high-entropy TiZrNbTa, as well as modified hydrogenation Ti variants of the previous alloys.

[0137] Titanium-based structures and implants using titanium alloys allow for the extension of the embodiment described above to alloys with high melting temperatures up to 2100°C under inert conditions. Definitions.

[0138] As used herein, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, the term “a member” is intended to mean a single member or a combination of members, “a material” is intended to mean one or more materials, or a combination thereof.

[0139] As used herein, the terms “about” and “approximately” generally mean plus or minus 10% of the stated value. For example, about 0.5 would include 0.45 and 0.55, about 10 would include 9 to 11, about 1000 would include 900 to 1100. 4932-6762-0872 40Atty. Dkt. No.: 046434-0920

[0140] It should be noted that the term “exemplary” as used herein to describe various embodiments is intended to indicate that such embodiments are possible examples, representations, and / or illustrations of possible embodiments (and such term is not intended to connote that such embodiments are necessarily extraordinary or superlative examples).

[0141] As used herein, the terms “coupled,” “connected,” and the like mean the joining of two additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another.

[0142] As shown in FIG.12, e.g., a computer-accessible medium 220 (e.g., as described herein, storage members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any device such as a hard disk, floppy disk, memory stick, CD-ROM, RAM, ROM, etc., or a collection thereof) can be provided (e.g., in communication with the processing arrangement 210). The computer-accessible medium 220 may be a non-transitory computer-accessible medium. The computer-accessible medium 220 can contain executable instructions 230 thereon. In addition or alternatively, a storage arrangement 240 can be provided separately from the computer-accessible medium 220, which can provide the instructions to the processing arrangement 210 so as to configure the processing arrangement to execute certain exemplary procedures, processes and methods, as described herein, for example. The instructions may include a plurality of sets of instructions.

[0143] System 200 may also include a display or output device, an input device such as a keyboard, mouse, touch screen or other input device, and may be connected to additional systems via a logical network. Many of the embodiments described herein may be practiced in a networked environment using logical connections to one or more remote computers having processors. Logical connections may include a local area network (“LAN”) and a wide area network (“WAN”) that are presented here by way of example and not limitation. Such networking environments are commonplace in office-wide or enterprise-wide computer networks, intranets and the Internet and may use a wide variety of different communication protocols. Those skilled in the art can appreciate that such network computing environments can typically encompass many types of computer system configurations, including personal computers, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, 4932-6762-0872 41Atty. Dkt. No.: 046434-0920 and the like. Embodiments may also be practiced in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination of hardwired or wireless links) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0144] Various embodiments are described in the general context of method steps, which may be implemented in one embodiment by a program product including computer- executable instructions, such as program code, executed by computers in networked environments. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps.

[0145] Software and web implementations could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various database searching steps, correlation steps, comparison steps and decision steps. It should also be noted that the words “component” and “module,” as used herein and in the claims, are intended to encompass implementations using one or more lines of software code, and / or hardware implementations, and / or equipment for receiving manual inputs.

[0146] It is important to note that the construction and arrangement of the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described herein. Other substitutions, modifications, changes and omissions may also be made in the design, operating conditions and arrangement of the various exemplary embodiments.

[0147] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be 4932-6762-0872 42Atty. Dkt. No.: 046434-0920 claimed, but rather as descriptions of features specific to particular implementations of particular inventions. Certain features described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 4932-6762-0872 43

Claims

Atty. Dkt. No.: 046434-0920 WHAT IS CLAIMED IS:

1. A method for manufacturing an implant, the method comprising: generating, through additive manufacturing (AM), a wax model based on an initial implant model; generating a mold of the wax model; engaging the mold in a burnout cycle, removing wax and forming one or more cavities having a shape of the wax model; casting a metal into the one or more cavities of the mold; and detaching the implant from the mold.

2. The method of claim 1, wherein the implant is formed of a biocompatible material.

3. The method of claim 1, wherein the metal is selected from titanium alloys comprising CP-Ti titanium alloy, Ti-22Al-25Nb titanium alloy, high-entropy TiZrNbTa titanium alloy, and Ti-6Al-4V titanium alloy.

4. The method of claim 3, wherein the metal comprises a modified hydrogenation titanium variant of the titanium alloys.

5. The method of claim 1, wherein the metal is selected from aluminum alloys.

6. The method of claim 1, wherein the wax model is configured for a creation of porous implants with low resolution .

7. The method of claim 1, wherein the casting includes process parameters associated with a metal alloy.

8. The method of claim 1, further comprising post-processing.

9. The method of claim 1, further comprising analyzing a quality of the implant based on performance testing.

10. An implant for bioengineering applications, the implant comprising: an additive manufacturing (AM)-assisted cast lattice, made from a metal alloy, comprising: a continuous microstructure; smooth surfaces; 4932-6762-0872 44Atty. Dkt. No.: 046434-0920 internal gas porosities; and spherical inclusions.

11. The implant of claim 10, wherein the implant is formed of a biocompatible material.

12. The implant of claim 10, wherein the metal alloy comprises any alloy with a high melting temperature.

13. The implant of claim 10, wherein the metal alloy is selected from titanium alloys comprising CP-Ti titanium alloy, Ti-22Al-25Nb titanium alloy, high-entropy TiZrNbTa titanium alloy, and Ti-6Al-4V titanium alloy.

14. The implant of claim 13, wherein the metal alloy comprises a modified hydrogenation titanium variant of the titanium alloys.

15. The implant of claim 10, wherein the metal alloy is selected from aluminum alloys.

16. The implant of claim 10, wherein the implant is compatible with a computer system.

17. A method for manufacturing an implant, the method comprising: generating a mold of a wax model; engaging the mold in a burnout cycle; introducing a metal into the mold; detaching the implant from the mold; post-processing; and analyzing a quality of the implant based on performance testing.

18. The method of claim 17, wherein the metal is selected from titanium alloys.

19. The method of claim 17, wherein the metal is selected from aluminum alloys. 4932-6762-0872 45

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