Octet-truss Lattice Structures Research Articles

Influence of fillets onto mechanical properties of octet-truss lattice structures

Influence of fillets onto mechanical properties of octet-truss lattice structures

Numerical investigation of the effective mechanical properties of Octet Truss lattice structures with different strut geometry

Lattice structures have an important role in lightweight structure applications as they can supply their mechanical performance with less material. Porous structures designed with inspiration from nature, has been used in many industries such as aerospace, automotive, defense industry and biomedical field. In order to continue these advances, studies on various design configurations of porous structure geometries are carried out. This study aimed to increase the usage potential of Octet Truss lattice structures in various sectors. A numerical model is created for 3 variable parameters: strut geometry, porosity, and material type. The effective elastic modulus values are determined based on the principles of Hooke's law for each model. Based on the obtained effective elastic modulus values, it has been concluded that differences in strut geometries, porosities, and material types contribute to 1.27%, 68.85%, and 29.86% of the observed effects, respectively. In order to establish a correlation between these factors, the data is transmitted to the MATLAB software, where equations are generated using the curve fitting approach. A total of nine equations have been generated and the R-square for these equations above 0.99. According to the two desired constant values, the effective elastic modulus can be calculated using these equations without any restrictions.

Mechanical performance of heterogeneous lattice structure

Heterogeneous lattice structure was constructed with rhombic dodecahedron and octet-truss lattice structures. The rhombic dodecahedron lattice was bending-dominated, while octet-truss lattice was stretching-dominated. The rhombic dodecahedron lattice fabricated by selective laser melting (SLM) was compressed by a universal testing machine, which was also investigated by finite element model. Afterwards, the validated numerical model was used to study the designed heterogeneous lattice. Calculations indicates that heterogeneous lattice structures outperform the rhombic dodecahedron lattice structure. The introduction of octet-truss unit cell enhances the mechanical behavior of the heterogeneous lattice structure in terms of Young’s modulus and stress magnitude, which depends on the pattern of octet-truss cells.

Modeling and characterizing the dynamic response of Octet-Truss lattice structures using elastic parameters determined from Resonant Ultrasound Spectroscopy

Modeling and characterization of additively manufactured materials and structures is a critical stage in the design process. This presentation will present an approach using Resonant Ultrasound Spectroscopy to determine the elastic tensor of an additively manufactured Octet Truss lattice structure. The lattice structures are fabricated from an alloy of Titanium using a laser powder bed fusion process. Material characterization begins by applying resonance techniques on simple regular parallelepiped shapes. Solid and lattice samples are measured to obtain estimates for the elastic properties of the bulk material and the effective elastic properties of the lattice structure. The measured elastic properties are then incorporated into structural models representing continuum approximations of several test parts. Comparisons between the continuum models and the experimental measurements indicate agreement over a wide frequency range within a long wavelength approximation defined for the lattice. The measurements also suggest that there is additional physics and geometrical effects accounted for in the RUS continuum approximations of the lattice that are not completely captured by the full finite model utilizing only base material properties.

Modeling and characterizing the elastodynamic response of octet-truss lattice structures using resonance techniques

Characterization of additively manufactured materials and structures is an ongoing effort for the advanced manufacturing community. This article will investigate an approach using resonant spectral ultrasound (RUS) to measure the effective elastic constants of an Octet Truss lattice and apply the results to continuum bases models representing the lattice regions in different structures. The study is focused on simple lattices structures fabricated from Ti5553 using a laser powder bed fusion process (LBPF). Solid and lattice samples are measured to determine RUS estimates for the elastic properties of the bulk material and the effective elastic properties of the lattice structure. The estimated elastic properties are then incorporated into 3d finite element models using a continuum approximation of the physical AM parts. Comparisons show good agreement between the experimentally measured eigen frequencies of the Ti5553 LBPF parts and the eigen frequencies calculated using the continuum approximations based on the effective RUS elastic properties. The current results suggest there is additional physics and geometrical effects that are accounted for in the RUS continuum approximation of the lattice that are not captured in the full 3d finite element model of the parts utilizing only the base material properties.

The Energy Absorption Behavior of 3D-Printed Polymeric Octet-Truss Lattice Structures of Varying Strut Length and Radius.

We investigate the compressive energy absorption performance of polymeric octet-truss lattice structures that are 3D printed using high-resolution stereolithography. These structures are potential candidates for personal protective equipment, structural, and automotive applications. Two polymeric resins (high-strength/low-ductility and moderate-strength/high-ductility) were used in this work, and a comprehensive uniaxial tensile characterization was conducted to establish an optimal UV curing time. The external octet-truss structure geometry (3″ × 3″ × 3″) was maintained, and four different lattice cell densities (strut length, L) and three different strut radii (R) were printed, UV cured, and compression tested. The compressive stress-strain and energy absorption (EA) behavior were quantified, and the EA at 0.5 strain for the least dense and smallest R structure was 0.02 MJ/m3, while the highest density structure with the largest R was 1.80 MJ/m3 for Resin 2. The structural failure modes varied drastically based on resin type, and it was shown that EA and deformation behavior were related to L, R, and the structures' relative density (ρ¯). For the ductile resin, an empirical model was developed to predict the EA vs. compressive strain curves based on L and R. This model can be used to design an octet-truss lattice structure based on the EA requirements of an application.

Shock compression behavior of stainless steel 316L octet-truss lattice structures

Lattice structures offer desirable mechanical properties for applications of energy absorption and impact mitigation but limited research has been carried out on their shock compression behavior. In this work, the shock compression behavior of stainless steel 316L (SS316L) octet-truss lattice structures was investigated through experimental techniques and numerical simulations. Plate impact experiments with high-speed imaging were conducted at impact velocities of 270–390 m/s on lattice specimens with 5 × 5 × 10 unit cell geometries additively manufactured (AM) using direct metal laser sintering. High-speed imaging together with digital image correlation was used to extract full-field measurements and define a two-wave structure consisting of an elastic wave and planar compaction (shock) wave which propagated along the impact direction. A linear shock velocity versus particle velocity relation was found to approximate the measurements with a unit slope and a linear fit constant equal to the crushing speed. The shock velocity versus particle velocity relation, full-field measurements, and elastic limit together with the Eulerian form of the Rankine–Hugoniot jump conditions were used to find relations for the stress and internal energy behind the shock. Stress behind the shock increased with relative density and particle velocity, and specific internal energy converged to a single curve similar to that of bulk AM SS316L. Explicit finite element analysis using the Johnson–Cook constitutive model demonstrated similar shock behavior observed in experiments and a linear shock velocity versus particle velocity relation and corresponding Hugoniot calculations were found to be in agreement with experimental results. Numerical simulations confirmed negligible effects of exterior versus interior measurements and further validated the application of one-dimensional shock theory.

Application of Elastic Parameters Estimated from Resonant Ultrasound Spectroscopy to Modeling and Characterizing the Dynamic Response of Octet-Truss Lattice Structures

Application of Elastic Parameters Estimated from Resonant Ultrasound Spectroscopy to Modeling and Characterizing the Dynamic Response of Octet-Truss Lattice Structures

Compressive fatigue characteristics of octet-truss lattices in different orientations

Octet-truss lattice materials have excellent potential for use as lightweight structures due to their high strength and stiffness, but low relative density. Octet-truss lattice specimens fabricated by stereolithography technique with a photopolymer resin were studied in this research. The unit cell orientation effects on the compressive fatigue behaviors of octet-truss lattices were studied using experimental analysis and computer simulation. A detailed comparison was made between the failure modes of static and fatigue failures, and the deformation mechanisms of lattices in different orientations under compressive cyclic load were determined. Both the static mechanical properties and fatigue properties of octet-truss lattices are highly dependent on the lattice orientation. When normalized with respect to their orientation-dependent Young’s moduli, the fatigue endurance of lattices in different orientations conforms very well (R 2 = 0.88) to a single S-N curve described by a power law. Finally, the differences in fatigue performance between lattices in different orientations were explained and a simple compression–compression fatigue mechanism was determined. Highlights Compressive fatigue behaviors of octet-truss lattice structures in three different unit cell orientations were investigated and compared in this research. Orientation-Z structure has the best resistance to fatigue failure in comparison to other orientations. The absolute S–N curves of lattices in different orientations were normalized by their Young’s moduli into a curve that can be expressed by one single power law. The mechanism of compressive fatigue failure of octet-truss lattice structures in different orientations was determined. Comparing with fatigue crack initiation and propagation in struts, cyclic ratchetting made dominant contribution to the compressive fatigue failure. The differences between the fatigue resistances of lattices in three orientations were explained by comparing the mechanical response in the finite element model.

Bending behavior of octet-truss lattice structures: Modelling options, numerical characterization and experimental validation

Selective Laser Melting (SLM) technology has undergone significant development in the past years providing unique flexibility for the fabrication of complex metamaterials such as octet-truss lattices. However, the microstructure can exhibit significant variations due to the high complexity of the manufacturing process. Consequently, the mechanical behavior, in particular, linear elastic response, of these lattices is strongly dependent on the process-induced defects, raising the importance on the incorporation of as-manufactured geometries into the computational structural analysis. This, in turn, challenges the traditional mesh-conforming methods making the computational costs prohibitively large. In the present work, an immersed image-to-analysis framework is applied to efficiently evaluate the bending behavior of AM lattices. To this end, we employ the Finite Cell Method (FCM) to perform a three-dimensional numerical analysis of the three-point bending test of a lattice structure and compare the as-designed to as-manufactured effective properties. Furthermore, we undertake a comprehensive study on the applicability of dimensionally reduced beam models to the prediction of the bending behavior of lattice beams and validate classical and strain gradient beam theories applied in combination with the FCM. The numerical findings suggest that the octet-truss lattices exhibit size effects, thus, requiring a flexible framework to incorporate high-order continuum theories.

Image-based numerical characterization and experimental validation of tensile behavior of octet-truss lattice structures

Abstract The production of lightweight metal lattice structures has received much attention due to the recent developments in additive manufacturing (AM). The design flexibility comes, however, with the complexity of the underlying physics. In fact, metal additive manufacturing introduces process-induced geometrical defects that mainly result in deviations of the effective geometry from the nominal one. This change in the final printed shape is the primary cause of the gap between the as-designed and as-manufactured mechanical behavior of AM products. Thus, the possibility to incorporate the precise manufactured geometries into the computational analysis is crucial for the quality and performance assessment of the final parts. Computed tomography (CT) is an accurate method for the acquisition of the manufactured shape. However, it is often not feasible to integrate the CT-based geometrical information into the traditional computational analysis due to the complexity of the meshing procedure for such high-resolution geometrical models and the prohibitive numerical costs. In this work, an embedded numerical framework is applied to efficiently simulate and compare the mechanical behavior of as-designed to as-manufactured octet-truss lattice structures. The parts are produced using laser powder bed fusion (LPBF). Employing an immersed boundary method, namely the Finite Cell Method (FCM), we perform direct numerical simulations (DNS) and first-order numerical homogenization analysis of a tensile test for a 3D printed octet-truss structure. Numerical results based on CT scan (as-manufactured geometry) show an excellent agreement with experimental measurements, whereas both DNS and first-order numerical homogenization performed directly on the 3D virtual model (as-designed geometry) of the structure show a significant deviation from experimental data.

The effect of wash treatment on the mechanical properties and energy absorption potential of a 3D printed polymethyl methacrylate (PMMA)

Stereolithographic 3D-printing of a Polymethyl Methacrylate (PMMA) resin was used to manufacture miniature dog-bone specimens that were subject to a variety of wash treatments consisting of Isopropyl Alcohol (IP), Hydrogen Peroxide (HP) and a Detergent (D) solution. The washed dog-bone specimens were then tested in uniaxial tension and the mechanical properties were quantified to assess the potential use of the resultant materials for the design of energy absorbing lattice structures. Compared to an As-Printed material, a detergent wash treatment resulted in almost no loss in peak stress, but a 61 % increase in toughness due to enhanced elongation. Moderate decreases in peak stress and high elongation were observed for HP washes. A 5 % (concentration) HP wash with detergent (HP5 + D) resulted in a 90 % greater toughness than the As-Printed material. Isopropyl washed specimens showed low toughness due to low peak stresses. A finite element study was conducted to simulate compression tests of an octet-truss lattice structure for which the tensile test properties were used as model inputs. The simulations revealed some relationships between the predicted energy absorption-tensile properties and showed that the HP5 + D (moderate peak force) and As-Printed + D (high peak force) washed conditions have potential application as energy absorbing octet-truss lattice structures.

Crack path-engineered 2D octet-truss lattice with bio-inspired crack deflection

Abstract Engineered lattice materials with pre-designed crack paths can provide critical component protection and tunable fracture energy. However, most existing crack path design methods require a change in the local topology of the material, which induces inconsistency in the material density and additional topological design complexity. In this study, the authors propose an optical programing method via digital light processing (DLP) to engineer the crack path in lattice materials without altering the material’s topological design. In this method, the effect of curing light intensity on the mechanical properties of the material is studied to develop an effective crack path engineering method, followed by the generation of a bio-inspired crack path deflection on an octet-truss lattice structure. Based on a derived theoretical model of material properties, a crack path engineering method is proposed by applying a grayscale on the desired crack path locations in DLP printing layer images. To mimic the weak crack deflection interfaces of natural materials, vertical crack deflection zones are designed with different relative positions on the octet-truss lattice structures. Consequently, a 15%–152% increase in quantitively controllable fracture energy is observed.

Finite element analysis of gradient lattice structure patterns for bone implant design

PurposeThe objective of this paper is to identify suitable lattice structure patterns for the design of porous bone implants manufactured using additive manufacturing.Design/methodology/approachThe study serves to compare and analyse the mechanical behaviours between cubic and octet-truss gradient lattice structures. The method used was uniaxial compression simulations using finite element analysis to identify the translational displacements.FindingsFrom the simulation results, in comparison to the cubic lattice structure, the octet-truss lattice structure showed a significant difference in mechanical behaviour. In the same design space, the translational displacement for both lattice structures increased as the relative density decreased. Apart from the relative density, the microarchitecture of the lattice structure also influenced the mechanical behaviour of the gradient lattice structure.Research limitations/implicationsGradient lattice structures are suitable for bone implant applications because of the variation of pore sizes that mimic the natural bone structures. The complex geometry that gradient lattice structures possess can be manufactured using additive manufacturing technology.Originality/valueThe results demonstrated that the cubic gradient lattice structure has the best mechanical behaviour for bone implants with appropriate relative density and pore size.

Mechanical behaviors of SLM additive manufactured octet-truss and truncated-octahedron lattice structures with uniform and taper beams

In this paper, three-dimensional lattice structures composed of octet-truss and truncated-octahedron unit cells with regular and tapered beams are proposed, and their mechanical properties are investigated through experiments and simulation comparisons. Firstly, analytical closed form expressions of the relative density functions are derived for different lattice structures. Secondly, in-situ compression samples are fabricated via Selective Laser Melting (SLM) 3D printing technique, monotonic compression experiments are performed for studying the effects of tapered beams on the mechanical properties of lattice structures with ordinary uniform beams, and SEM characterizations of fracture surface morphology are performed for understanding the underlying failure mechanisms. Afterwards, asymptotic homogenization (AH) method is used for evaluating the anisotropy properties of these lattice structures, closed form expression of the mechanical behaviors of unit cells is derived and solved with ABAQUS® using surface traction method. Asymptotic homogenization analysis shows that node enforcement can significantly enhance the modulus and reduce the anisotropy of the lattice.

Experimental investigation of heat transfer and fluid flow in octet-truss lattice geometry

This paper undertakes an experimental measurement of effective thermal conductivity, permeability, inertial coefficient, friction factor and wall convective heat transfer from octet truss lattice (OTL) structures as air-cooled compressive load-bearing light-weight heat sinks. Three aluminium alloy (AlSi10Mg) OTL structures of porosities 70.6%, 86.9% and 91.3% were fabricated using an additive manufacturing technique. Experimentally measured effective thermal conductivity, permeability, inertial coefficient, friction factor and wall Nusselt number for OTL structures are reported. Owing to high solid-to-fluid thermal conductivity ratio (∼4250), heat flows through the metal ligament and air independently and establishes steady-state, i.e. peripheral conduction coupling between solid metal and air is negligible. This is conferred from various theoretical and semi-empirical models from the literature. Friction factor and wall Nusselt number are characterised using a single length scale as against different length-scales often used in the literature. Flows through OTL structures seem to follow Forchheimer's flow law with negligible viscous contribution even at low pressure gradients. Further, the results are compared with previous analytical and experimental results for stochastic open-cellular foams. Owing to periodic nature of OTL structures, friction factor is lower than stochastic foams as mechanical dispersion effects are negligible. In conclusion, OTL structures are an excellent candidate for multifunctional applications where heat sinks are expected to bear compressive loads as well as dissipate heat while being lightweight.

Characterisation of Reinforced Body Centered Cubic, Octahedral-Type and Octet Truss Lattice Structures

Developments in additive manufacturing have encouraged a dramatic increase in the production and integration of the space-filling unit cells known as lattice structures. As designers begin to leverage the useful benefits provided by lattice structures, and these structures are used more frequently in industrial designs of parts, there is a need to characterise the properties that different lattice structures possess to aid the design process. The functional requirements of a specimen will often change during the design stage and this means that a designer will always wish to select the most applicable lattice structure for the optimal result. To date, there is no repository of lattice structure design properties from which a designer can choose a structure that best suits the design requirements. This article aims to propose a methodology for testing the capabilities of lattice structures and building a database of unit cell type design properties through compression and 3-point bending tests. The samples were created with PA2200 manufactured through the selective laser sintering process on an EOS P396. The lattice structure specimens were parameterised in terms of overall specimen unit cell size and strut diameter. Through regression analysis, particular benefits of lattice structures were noted: Reinforced Body Centered Cubic (RBCC) performed best in bending, Octet Truss performed best in compression and Octahedral performed worst in both tests but resisted much greater deformation. Additionally, though increases in strut diameter or number of unit cells per sample increased both Young’s Modulus and Ultimate Compressive Strength, it was strut diameter increases that had a factor of 10 greater of an effect. To complete a repository, it is desirable to increase the number of stages per design parameter and test over a greater range of values - to fully model the shape of the output curve.Scientific Topics: Design Methodology, Design of Lattice Structures, Designing for Additive Manufacturing, Designing for Multifunctional Optimisation of Lattice Structures

Mechanical behaviour of additively-manufactured polymeric octet-truss lattice structures under quasi-static and dynamic compressive loading

Two different polymer resins were used to create three different octet-truss lattice structures of different densities. The mechanical behaviour of these structures has been examined under both quasi-static and dynamic compressive loading. The structures were printed using stereolithography (SLA) additive manufacturing. The basic building octet unit has a fixed strut length of L=10mm, with the designed strut radius varying from R=0.7mm to 1.3mm to provide structures of different densities. It has been found that the mechanical behaviour of the printed octet structures depends on both the relative density and the intrinsic material properties. Higher density structures show larger effective yield and compressive strengths, while the basic printing material fundamentally determines its macroscopic properties: one material provides a brittle mechanical response under compression while the other provides a tough response. The former lattice structures behaved in a brittle manner at all relative densities, fracturing at small strains. For the latter resin lattice structures, on the other hand, under quasi-static compression, the stress-strain curves changed from a slightly stress oscillating mode at low relative density (i.e. ρ¯=0.13) to a stable stress plateau mode at high relative density (i.e. ρ¯=0.41). The Specific Energy Absorption (SEA) of both lattice structures had a monotonically increasing relationship with relative density, the SEA of the brittle resin specimen is higher than that of the tough resin specimen, while the tough resin specimen exhibits its excellent energy absorption under a wide displacement range. For the dynamic compressive tests, the tougher resin structures displayed strain-rate effects, while the more brittle ones did not. The numerically predicted response of both lattice structures agreed closely with the experimental results.

A method to determine the depowdered height in lattices manufactured by electron beam melting

After completing a part in electron beam melting (EBM), a depowdering operation is required to separate the sintered but unmelted powder from the manufactured part. Depowdering lattice structures can be difficult or even impossible due to their intrinsic shape. The aim of this paper is to propose a criterion to ensure that a lattice structure manufactured by EBM can be depowdered. The objective is to use this criterion during the design phase of lattice structures to make them manufacturable and depowderable. Experiments are conducted on depowdering octet-truss lattice structures with variable bars thickness and mesh sizes. Different criteria are introduced, among them the criterion “hydraulic diameter” of a lattice structure, inspired by the Darcy–Weisbach hydraulic law used to calculate the pressure drop in a pipe. This criterion can be determined using only geometrical characteristics of lattices available in the CAD model of the part. Results show that the levels of depowdering for lattice structures are proportional to this hydraulic diameter. As a validation, a bike stem has been manufactured following the criterion and has demonstrated its efficiency.

CAD TOOLS AND FILE FORMAT PERFORMANCE EVALUATION IN DESIGNING LATTICE STRUCTURES FOR ADDITIVE MANUFACTURING

Additive manufacturing has opened the door to the creation of lightweight lattice structures. However, present Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) software are unsuitable for these types of structures. The objective of this research is to examine the performances of current CAD and CAE software to design lattice structures and to demonstrate their limitations and propose requirements for future developments. A performance evaluation of a case study for lattice structure designs was conducted. The criteria used for the evaluation were CAD human-machine-interface, RAM consumption, data exchange between CAD, CAE and CAM tools and finite element analysis (FEA) duration and file sizes. The CAD tool was incapable of executing a repetition function for octet-truss lattice structures of 150 x 150 x 150 mm dimensions or larger and the software stopped working. For 70 × 70 × 70 mm octet-truss lattice structure, the FEA computation file size reached 36.6 GB. The CAD file size of a 200 x 200 x 200 mm octet-truss lattice structure reached nearly 290 MB. In conclusion, this study exposes the performance inadequacy of current CAD and CAE tools and CAD file formats to design lattice structures for additive manufacturing parts.