Benchmark Geometries Research Articles

AscentAM: A Software Tool for the Thermo-Mechanical Process Simulation of Form Deviations and Residual Stresses in Powder Bed Fusion of Metals Using a Laser Beam

Due to the tool-less fabrication of parts and the high degree of geometric design freedom, additive manufacturing is experiencing increasing relevance for various industrial applications. In particular, the powder bed fusion of metals using a laser beam (PBF-LB/M) process allows for the metal-based manufacturing of complex parts with high mechanical properties. However, residual stresses form during PBF-LB/M due to high thermal gradients and a non-uniform cooling. These lead to a distortion of the parts, which reduces the dimensional accuracy and increases the amount of post-processing necessary to meet the defined requirements. To predict the resulting residual stress state and distortion prior to the actual PBF-LB/M process, this paper presents the finite-element-based simulation tool AscentAM with its core module and several sub-modules. The tool is based on open-source programs and utilizes a sequentially coupled thermo-mechanical simulation, in which the significant influences of the manufacturing process are considered by their physical relations. The simulation entirely emulates the PBF-LB/M process chain including the heat treatment. In addition, algorithms for the part pre-deformation and the export of a machine-specific file format were implemented. The simulation results were verified, and an experimental validation was performed for two benchmark geometries with regard to their distortion. The application of the optimization sub-module significantly minimized the form deviation from the nominal geometry. A high level of accuracy was observed for the prediction of the distortion at different manufacturing states. The process simulation provides an important contribution to the first-time-right manufacturing of parts fabricated by the PBF-LB/M process.

A Multiple Scale Approach to Nonlinear Vibrations and Stability of Doubly Curved Shells/Panels Under External and Parametric Excitations

This study focuses on nonlinear vibrations and stability of doubly curved shells/panels. The thin-walled shell structure is assumed to be acted upon by external loads as well as parametric excitation. Using the first-order shear deformation Fülgge theory assumptions, governing equations of motion are derived for a general doubly curved geometry. Nonlinear components which are compatible with the Von-Karman kinematic assumptions are retained in the formulation and the rest of nonlinear components are neglected due to the fact that strains are assumed to be small and rotations to be moderate. The formulation can be readily reduced to any geometry including cylindrical shells and spherical panels, as benchmark examples in this study. Employing the Galerkin discretization approach and applying a modification to the Volmir assumption, a reduced order form of the original system is determined, which is shown to be a great representative of the original system with much more computational advantages. Using the method of multiple scales, the reduced order nonlinear governing equations are solved to discover the primary resonance, forced vibration characteristics and stability margins of thin-walled shells/panels under the action of parametric excitation. Several interesting findings on nonlinear behavior of cylindrical shells and spherical panels (as benchmark geometries) are presented while giving a demonstration of the accuracy and computational advantages of the proposed model.

Elasto-visco-plastic flows in benchmark geometries: I. 4 to 1 planar contraction

We present predictions for the flow of elastoviscoplastic (EVP) fluids in the 4 to 1 planar contraction geometry. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method with the OpenFOAM software. Both the constitutive model and the solution method require using transient simulations. In this benchmark geometry, whereas viscoelastic fluids may exhibit two vortices, referred to as lip and corner vortices, we find that EVP materials are unyielded in the concave corners. They are also unyielded along the mid-plane of both channels, but not around the contraction area where all stress components are larger. The unyielded areas using this EVP model are qualitatively similar to those using the standard viscoplastic models, when the Bingham or the Weissenberg numbers are lower than critical values, and then, a steady state is reached. When these two dimensionless numbers increase while they remain below the respective critical values, which are interdependent, (a) the unyielded regions expand and shift in the flow direction, and (b) the maximum velocity increases at the entrance of the contraction. Increasing material elasticity collaborates with increasing the yield stress, which expands the unyielded areas, because it deforms the material more prior to yielding compared to stiffer materials. Above the critical Weissenberg number, transient variations appear for longer times in all variables, including the yield surface, instead of a monotonic approach to the steady state. They may lead to oscillations which are damped or of constant amplitude or approach a flow with rather smooth path lines but complex stress field without a plane of symmetry, under creeping conditions. These patterns arise near the entrance of the narrow channel, where the curvature of the path lines is highest and its coupling with the increased elasticity triggers a purely elastic instability. Similarly, a critical value of the yield stress exists above which such phenomena are predicted.

Additive manufacturing of thermoplastic elastomer structures using dual material core-shell filaments

Filament-based flexible material extrusion additive manufacturing is highly desirable yet faces critical challenges such as limited print resolution and repeatability. To enhance printability of a thermoplastic elastomer (TPE), a series of core-shell filaments comprising a TPE shell (Shore hardness 75 A) and a rigid ABS core are fabricated, with the ABS volume fraction varying from 11% to 78%. The presence of an ABS core imparts rigidity to the filament to inhibit buckling and allow for successful high-fidelity 3D printing. Rheological characterizations of TPE and ABS using capillary and parallel-plate viscometry point to the optimized extrusion parameters suitable for filament coextrusion, printability, and wettability between the print interfaces. Complex benchmark geometries are printed to verify the print resolution. Printed specimens with less than 20% ABS preserve the shore hardness of 75 A, providing flexibility and a soft touch to the printed structures. Izod impact, 3-point bending, and tensile tests reveal tunable mechanical properties of parts printed in z-direction with ABS+TPE filaments. Lower ABS content exhibits higher flexibility and impact resistance, while higher ABS imparts higher stiffness and tensile strength. Notably, the parts printed with 30–40% ABS exhibit higher toughness and impact strength than specimens composed of ABS or TPE alone. Lastly, a coil spring printed with a ABS+TPE filament exhibits reversible extension up to 120 mm, at least twice the reversible extension of an ABS-printed coil spring.

Benchmark ab initio characterization of the multi-channel Cl + CH3X [X = F, Cl, Br, I] reactive potential energy surfaces.

We determine benchmark geometries and relative energies for the stationary points of the Cl + CH3X [X = F, Cl, Br, I] reactions. We consider four possible reaction pathways: hydrogen abstraction, hydrogen substitution, halogen abstraction, and halogen substitution, where the substitution processes can proceed via either Walden inversion or front-side attack. We perform geometry optimizations and obtain harmonic vibrational frequencies at the explicitly-correlated UCCSD(T)-F12b/aug-cc-pVTZ level of theory, followed by UCCSD(T)-F12b/aug-cc-pVQZ single-point computations to make finite-basis-set error negligible. To reach chemical (<1 kcal mol-1), or even subchemical (<0.5 kcal mol-1) accuracy, we include core-correlation, scalar relativistic, post-(T), spin-orbit-splitting and zero-point-energy contributions, as well, in the relative energies of all the stationary points. Our benchmark 0 K reaction enthalpies are compared to available experimental results and show good agreement. The stationary-point structures and energetics are interpreted in terms of Hammond's postulate and used to make predictions related to the dynamical behavior of these reactive systems.

Quasi-classical trajectory study of the OH- + CH3I reaction: theory meets experiment.

Regarding OH- + CH3I, several studies have focused on the dynamics of the reaction. Here, high-level quasi-classical trajectory simulations are carried out at four different collision energies on our recently developed potential energy surface. In all, more than half a million trajectories are performed, and for the first time, the detailed quasi-classical trajectory results are compared with the reanalysed crossed-beam ion imaging experiments. Concerning the previously reported direct dynamics study of OH- + CH3I, a better agreement can be obtained between the revised experiment and our novel theoretical results. Furthermore, in the present work, the benchmark geometries, frequencies and relative energies of the stationary points are also determined for the OH- + CH3I proton-abstraction channel along with the earlier characterized SN2 channel.

Phosphorus-centered ion-molecule reactions: benchmark ab initio characterization of the potential energy surfaces of the X- + PH2Y [X, Y = F, Cl, Br, I] systems.

In the present work we determine the benchmark relative energies and geometries of all the relevant stationary points of the X- + PH2Y [X, Y = F, Cl, Br, I] identity and non-identity reactions using state-of-the-art electronic-structure methods. These phosphorus-centered ion-molecule reactions follow two main reaction routes: bimolecular nucleophilic substitution (SN2), leading to Y- + PH2X, and proton transfer, resulting in HX + PHY- products. The SN2 route can proceed through Walden-inversion, front-side-attack retention, and double-/multiple-inversion pathways. In addition, we also identify the following product channels: H--formation, PH2-- and PH2-formation, 1PH- and 3PH-formation, H2-formation and HY + PHX- formation. The benchmark classical relative energies are obtained by taking into account the core-correlation, scalar relativistic, and post-(T) corrections, which turn out to be necessary to reach subchemical (<1 kcal mol-1) accuracy of the results. Classical relative energies are augmented with zero-point-energy contributions to gain the benchmark adiabatic energies.

Effect of rigid body motion in phase-field models of solid-state sintering

In the last two decades, many phase-field models for solid-state sintering have been published. Two groups of models have emerged, with and without the contribution of rigid body motion. This paper first describes the previously published phase-field model with an advection term driven by rigid body motion. The model is then used to investigate the differences between models with and without rigid body motion in new benchmark geometries exhibiting markedly different behavior. Sensitivity studies concerning the parameters of the rigid-body motion model are conducted and their effects on equilibrium and kinetic properties explored. In particular, it is shown by simulations that a shrinkage rate independent of system size requires the inclusion of an advection term. Finally, the reason behind this behavior is explored and implications for diffusion-only models are drawn.

A step-by-step investigation of sodium chloride clusters: accurate references, assessment of low-cost methods, and convergence from molecule to salt

In the present study, we use high-level coupled-cluster-based methods to obtain benchmark geometries and lattice energy for small sodium chloride clusters up to (NaCl)15. Reliable geometries can be obtained with the CCSD(T)-F12b method in conjunction with a small double-ζ basis set, while accurate energies can be obtained with relatively economical methods (e.g. DLPNO-CCSD(T1)-F12) by adjusting for systematic bias against higher-level methods (e.g. W2). For the calculation of larger clusters, we find PBE0-D3BJ and GFN1-XTB to be suitable for geometry optimisation, while B97M-V and GFN1-XTB provide an adequate means for energy calculations once they are calibrated against high-level references. For much larger systems, a Born–Landé-type model can be used to obtain fairly good lattice energies. The results show the progression from a single NaCl molecule to bulk salt, with full convergence expected for cluster sizes in the range of 5–10 nm. The protocol for obtaining highly accurate lattice energies and calculating large clusters may be used to examine the energetics of ionic clusters more generally.

Solution of radiative-convective heat transfer in irregular geometries using hybrid lattice Boltzmann-finite volume and immersed boundary method

Immersed boundary method (IBM) is introduced for solving the radiative transfer equation (RTE) to simulate the radiation heat transfer with natural convection in irregular geometries. IBM is organized based on the direct forcing method and sharp interface scheme. The Lattice Boltzmann method (LBM) with double multiple-relaxation-time (MRT)-D2Q9 is adopted in computing the momentum and energy equations, and the finite volume method (FVM) is applied in the numerical solution of RTE with a pseudo-time-stepping approach. The FVM-LBM code is tested in benchmark geometries in two cases. The ability and performance of IBM are examined in an irregular geometry for Rayleigh number, Planck number, and optical thickness on thermal and flow fields. Static and Hopf bifurcation as an attractive effect of radiation heat transfer is noted. The significant benefit of IBM is using a unique mesh in simulating these problems.

Evaluation of the polyhedral mesh style for predicting aerosol deposition in representative models of the conducting airways

A critical factor affecting the accuracy of Computational Fluid Dynamic (CFD) simulations and the time required to conduct them is construction of the computational mesh. This study aimed to evaluate the relatively new polyhedral mesh style for simulating aerosol deposition in the upper conducting airways compared with established meshing techniques and experimental data. Hexahedral and polyhedral mesh solutions were compared in two benchmark geometries: 1) a 90°-bend with flow characteristics similar to the extrathoracic airways of an adolescent child, and 2) a double bifurcation representing bifurcations B3–B5 in an adult. Both 4-block and 5-block hexahedral meshes were used in the 90°-bend to capture the potential of fully-structured hexahedral meshes. In the 90°-bend, polyhedral elements matched polydisperse in vitro deposition data with 20% relative error (RE; averaged across the particle sizes considered), which is an improvement on the accuracy of the 4-block hexahedral mesh (35% RE) and is similar to the accuracy of the 5-block hexahedral mesh (19% RE). In the double bifurcation, deposition fraction relative differences evaluated between polyhedral and hexahedral meshes ranged from 0.3% to 28.6% for the different particle sizes assessed, which is an order of magnitude improvement compared with previous studies that considered hexahedral vs. hybrid tetrahedral-prism meshes for the same flow field. Solution convergence time with polyhedral elements was found to be 50%–140% higher than with hexahedral meshes of comparable size. While application dependent, the increase in simulation time observed with polyhedral meshes will likely be outweighed by the ease and convenience of polyhedral mesh construction. It was concluded that the polyhedral mesh style, with sufficient resolution especially near the walls, is an excellent alternative to the highly regarded hexahedral mesh style for predicting upper airway aerosol transport and deposition, providing a powerful new tool for the assessment of respiratory aerosol dosimetry.

Alternative approaches of evaluating Diffraction Transfer Matrix and Radiation Characteristics using the hybrid source-dipole formulation

The interaction theory presented by Kagemoto and Yue (1986) significantly reduces the computational burden in the wave interaction problem of multiple surface-piercing bodies, particularly arrays of wave energy converters in recent years. Two essential operators of the theory are the so-called Diffraction Transfer Matrix and Radiation Characteristics. Many subsequent researchers (Goo and Yoshida, 1990; Flavià et al., 2018) have implemented the theory using the source distribution method in evaluating the two linear operators of a single unique geometry. However, nowadays, a great majority of boundary element method codes have been written by virtue of the hybrid source-dipole distribution method on account of its high accuracy. In this regard, the present work aims to introduce a full set of mathematical formulations, as well as a complete derivation process of evaluating the two operators based on the hybrid source-dipole distribution method. The proposed formulations are then applied to two benchmark geometries, as given by McNatt et al. (2015) and Flavià et al. (2018). Good agreement is found between the present results and those from the literature. Moreover, two alternative approaches to solve the diffraction problem have been compared to assess both their accuracy and efficiency. It is found that the two methods present similar levels of accuracy but very different computational burden.

Experimental investigation of additively manufactured continuous fiber reinforced composite parts with optimized topology and fiber paths

Additive manufacturing (AM) of fiber-reinforced polymer composites enables various complex geometries in an out-of-autoclave process, eliminates the need for molds and tooling, and eliminates material waste. Accompanying these improvements is the ability to tailor the placement of fibers (intricate fiber steering) within a part to improve its performance for a given state of loading. AM is inherently well-suited for integration with optimization schemes, as the designer can send a geometrically complex model directly to the 3D printer for fabrication. This study investigates the printability and performance of three benchmark geometries and loading scenarios optimized for stiffness. These designs are achieved via topology (part geometry) and fiber placement optimization of AM continuous carbon fiber reinforced polymer composites. Some of the manufacturing constraints were implemented in the optimizer. Post-processing was, however, necessary to apply other AM constraints before parts could be successfully printed. The optimized designs were manufactured, on a printer built in-house, and tested in special load fixtures while parts’ displacements were recorded using digital image correlation (DIC). The stiffnesses found through experiments agreed with the finite element analysis (FEA). The optimized AM parts displayed up to 100% improvement in specific (per weight) stiffness, translating to a maximum of 50% weight reduction over conventional composite parts with unidirectional laminas. This study demonstrates that bridging topology and fiber path optimization with AM of continuous fiber-reinforced composites enables significant weight reduction that would otherwise be impossible.

Reynolds and Weissenberg numbers in viscoelastic flows

One of the greatest challenges in performing numerical simulations of viscoelastic flow is how to choose the model parameters in order to be able to achieve quantitative agreement with experimental measurements in benchmark geometries. In the present work, we revisit the original concepts of Reynolds (Re) and Weissenberg (Wi) numbers in order to provide means to adequately choose those parameters. In particular, we highlight the importance of the Oldroyd-B model as a reference for viscoelastic behavior and propose a new methodology for the comparison between general viscoelastic models and the Oldroyd-B model. We identify inconsistencies in the usual approach consensually adopted in the literature. The historical reason for that seems to have its root on the fact that Reynolds and Weissenberg numbers are recognized as expressions and not as concepts. This paradigm allows the choice of parameters of a model as characteristic quantities. We propose here to choose the Oldroyd-B model parameters for the comparison with more complex viscoelastic models so that Re and Wi concepts are maintained. To illustrate this matter, we simulate a flow which is known for capturing an important viscoelastic effect, the transient extrudate swell problem. We tested three viscoelastic models with intermediate levels of complexity, namely PTT, Giesekus, and FENE-P. The traditional and the proposed approaches are compared and the role of the extra parameter, that endows these models with a nonlinear character with respect to the stress, is reinterpreted. It is demonstrated that the nonlinearity introduced by this extra parameter is overestimated in the usual formulation.

Benchmark multi-layer simulations for residual stresses and deformation in small additively manufactured metal parts

Scan pattern dependent (multi-track) residual stress buildup over multiple layers in the powder bed fusion process is governed by coupled thermo-mechanics. The high computational cost associated with these simulations has resulted in the general adoption of approximate computational methods. The numerical or thermo-mechanical accuracy of assumptions made in these computational methods is not fully characterized. If benchmark multi-track simulations for small size multi-layer parts are available, including temperatures, strain fields and deformation results, it will be possible to scientifically develop new approximation schemes or modify existing ones to improve their accuracy. Present work develops a suggestive benchmark using full multi-track thermomechanical simulations, with comparison to various approximate methods. The target configurations are simple prismatic geometries with 30 layers and up to 120 mm 3 volume, illustrating the influence of domain size on the approximate results. Anticipating the future challenges of measuring stresses and deformation in these small benchmark geometries, an experimental setup based on sheet metal forming principals is demonstrated numerically. The proposed setup will provide a methodology to experimentally validate these benchmarks.

Experimental investigation, using 3D digital image correlation, into the effect of component geometry on the wrinkling behaviour and the wrinkling mechanisms of a biaxial NCF during preforming

This study investigates the effect of component geometry on the wrinkling mechanisms of non-crimp fabrics (NCFs) during preforming. Using 3D digital image correlation, the wrinkling behaviour of a biaxial NCF formed over four benchmark geometries is characterised and related to the NCF’s surface strains. It is shown that the effect of geometry on the severity of wrinkling is highly significant and that there are two possible wrinkling mechanisms (via shear lockup or via compression) for large wrinkles to occur, which are consistent across geometries. Importantly, an increase in local shear resistance (due to the stitches in this case) is shown to cause severe wrinkles in textile reinforcements at low shear angles due to lateral fabric compression. Additionally, tow wrinkling in NCFs is shown to correlate with local tow compression. Thus, it is not always valid to assume that fabrics are only likely to wrinkle during forming due to excessive shearing.

Cross Validation of Aerodynamic Shape Optimization Methodologies for Aircraft Wing-Body Optimization

This paper presents the cross validation of two aerodynamic shape optimization methodologies in order to validate, characterize, and compare the two methodologies. Both methodologies use gradient-based optimization based on the Reynolds-averaged Navier–Stokes equations driven by the discrete adjoint method. The first methodology uses a B-spline surface representation of the geometry coupled with free-form deformation and axial curve-based geometric control, as well an efficient linear elasticity-based mesh deformation method. The second methodology uses class-shape transforms for airfoil geometry control and either in-CAD or out-of-CAD surface modeling. Two benchmark geometries are used for comparison: a wing-body configuration representative of a large transport aircraft, and a wing-body configuration with aft-mounted nacelles typical of a small business jet. Both single-point and multipoint optimizations are performed. Cross validation is conducted such that flow evaluations are performed on the geometries produced by the two methodologies using a single flow solver and consistent meshes. It is found that both methodologies provide similar geometries and performance improvements. The primary differences that exist are a result of the distinct geometry parameterization and control methods that, in some cases, allow for more localized geometric control. The degree of agreement is indicative of the maturity that has been achieved by modern state-of-the-art aerodynamic shape optimization methodologies.

Dimensional Accuracy and Mechanical Properties of Chopped Carbon Reinforced Polymers Produced by Material Extrusion Additive Manufacturing.

Fused Filament Fabrication (FFF), classified under material extrusion additive manufacturing technologies, is a widely used method for fabricating thermoplastic parts with high geometrical complexity. To improve the mechanical properties of pure thermoplastic materials, the polymeric matrix may be reinforced by different materials such as carbon fibers. FFF is an advantageous process for producing polymer matrix composites because of its low cost of investment, high speed and simplicity as well as the possibility to use multiple nozzles with different materials. In this study, the aim was to investigate the dimensional accuracy and mechanical properties of chopped carbon-fiber-reinforced tough nylon produced by the FFF process. The dimensional accuracy and manufacturability limits of the process are evaluated using benchmark geometries as well as process-inherent effects like stair-stepping effect. The hardness and tensile properties of produced specimens in comparison to tough nylon without any reinforcement, as well as continuous carbon-reinforced specimens, were presented by taking different build directions and various infill ratios. The fracture surfaces of tensile specimens were observed using a Scanning Electron Microscope (SEM). The test results showed that there was a severe level of anisotropy in the mechanical properties, especially the modulus of elasticity, due to the insufficient fusion between deposited layers in the build direction. Moreover, continuous carbon-reinforced specimens exhibited very high levels of tensile strength and modulus of elasticity whereas the highest elongation was achieved by tough nylon without reinforcement. The failure mechanisms were found to be inter-layer porosity between successive tracks, as well as fiber pull out.

Prescriptive Data-Analytical Modeling of Laser Powder Bed Fusion Processes for Accuracy Improvement

Laser powder bed fusion (LPBF) has the ability to produce three-dimensional lightweight metal parts with complex shapes. Extensive investigations have been conducted to tackle build accuracy problems caused by shape complexity. For metal parts with stringent requirements, surface roughness, laser beam positioning error, and part location effects can all affect the shape accuracy of LPBF built products. This study develops a data-driven predictive approach as a promising solution for geometric accuracy improvement in LPBF processes. To address the shape complexity issue, a prescriptive modeling approach is adopted to minimize geometrical deviations of built products through compensating computer aided design models, as opposed to changing process parameters. It allows us to predict and control a wide range of shapes starting from a limited set of measurements on basic benchmark geometries. An error decomposition and compensation scheme is developed to decouple the influence from different error components and to reduce the shape deviations caused by part geometrical deviation, laser beam positioning error, and other location effects simultaneously via an integrated modeling and compensation framework. Experimentation and data collection are conducted to investigate error sources and to validate the developed modeling and accuracy control methods.

An assessment of the optimal air-side thermal-hydraulic performance of wavy-fin compact heat exchangers

An optimal assessment of heat transfer and friction power performance is investigated to address a robust method for facilitating performance evaluation of different wavy-fin arrangements. Two benchmark geometries are presented to compare the performance of all the reported wavy-fin arrangements with and without considering heat exchanger compactness. New 21 wavy-fin geometries are numerically studied to represent the unreported arrangements in the literature. The performance results of 105 geometries showed that the reference standard geometries of Kays and London could be used as benchmarks to evaluate the airside arrangements, with and without considering the compactness effect, respectively. Heat transfers versus friction power plots are found to be a useful approach for performance evaluation purpose. The surface GK2 is found to have the optimal thermal-hydraulic performance when comparing the heat exchanger compactness, whereas GI1 and GK1 might represent the geometries having optimal performances when neglecting the compactness importance.