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Critical impact of experimentally-driven strut level anisotropic material models in advanced stress analysis of additively manufactured lattice structures
The rapid acceleration in materials discovery may overshadow the importance of thoroughly understanding the mechanical performance of newly developed materials in demanding environments. The recent interest in combining parametric studies with machine learning techniques to explore how changes in specific processing parameters or model inputs affect the overall behavior of a material system can only be truly beneficial if the governing constitutive relations describing material behavior are accurately established. In this study, we demonstrate the critical impact of accurately representing strut-level anisotropic material behavior in advanced stress analysis of additively manufactured lattice structures (AMLS). We introduce a systematic experimental and modeling approach for developing strut-level anisotropic elastoplastic material models that account for the influence of microstructural features such as porosity, texture, and surface roughness on the development of local anisotropic mechanical properties, which vary with strut orientation relative to the build direction (BD). As a result the presented material model captures and relates the statistics of spatially varying struts’ microstructural features to the local stress distribution. Our findings suggest that incorporating strut-level anisotropic material behavior into unit cell analysis significantly influences the load distribution and evolution of local stresses within the structure. Therefore, accounting for this anisotropy is critical for developing an understanding of unit cell behavior and performance, including subsequent topology/component design optimization based on this analysis.
Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials
Properties of soft materials are influenced by their anisotropic structuring under nonequilibrium fields. Although anisotropic structure-property relationships have been extensively explored theoretically, comparison to experiments requires determination of the microstructural orientation probability distribution function (OPDF) of microstructural elements. Small angle scattering (SAS) measurements encode information about the OPDF, but tools to navigate this connection are incomplete. Here, we develop and validate an explicit framework to link arbitrary OPDFs to SAS measurements. Specifically, we propose, validate, and apply a method, maximum a posteriori scattering inference (MAPSI), whereby the OPDF may be obtained from SAS measurements using a Bayesian estimation method. Using this method, we obtain estimates of the full 3D OPDF for two model semidilute fd-virus (rodlike) dispersions at concentrations that are approximately equal to and twice the overlap concentration. From the OPDF, we calculate its second and fourth moments and compare these to predictions for a dilute suspension of rigid rods and to a recent theory for semidilute suspensions. Finally, we use both the theoretical and measured moments to calculate the stress, both for dilute and semidilute suspensions. These predictions are not only compared to each other, but also to measured values of the shear stress, and point to new insights into the behavior of suspensions of highly elongated particles in the transition between dilute and semidilute behavior. We also use this new framework to provide perspective on the connection between scalar parameterizations of scattering and the OPDF that have frequently been used in the past. Here, the new tools developed in this work provide an unprecedented path toward experimental validation of dynamical theories of rodlike colloids and polymers, and for measurement of nonequilibrium structures and stresses of other complex fluids and soft materials with SAS.
Overview of a Versatile Loading System for Anisotropic Material Property Characterization
Additive manufacturing, cold rolling, and other thermomechanical treatments on metals, especially HCP, can cause texture and oriented grain structures resulting in anisotropic mechanical properties. This can lead to macroscopic response that significantly deviates from isotropic assumptions which motivates studying mechanical properties in multiple directions. In addition, multiaxial loading and complex stress states overlapping the above mentioned material anisotropy can lead to unexpected outcomes. Idaho National Laboratory developed an advanced mechanical testing system to study a range of uniaxial to multiaxial stress states while measuring the anisotropic response bringing insight into the overlap between material properties and stress states. High-temperature capability and stress- or strain-controlled loading is available to enable a variety of experiment types and conditions to measure elastic, plastic, and viscoplastic properties. This poster presents the design and capabilities of this system with preliminary results highlighting the benefits of multiaxial loading and anisotropic analysis in an integrated system.
De Novo Design of Spiro-Type Hole-Transporting Material: Anisotropic Regulation Toward Efficient and Stable Perovskite Solar Cells
2,2',7,7'-Tetrakis(N,N-di-p-methoxyphenyl)-amine-9,9'-spirobifluorene (Spiro-OMeTAD) represents the state-of-the-art hole-transporting material (HTM) in n-i-p perovskite solar cells (PSCs). However, its susceptibility to stability issues has been a long-standing concern. In this study, we embark on a comprehensive exploration of the untapped potential within the family of spiro-type HTMs using an innovative anisotropic regulation strategy. Diverging from conventional approaches that can only modify spirobifluorene with single functional group, this approach allows us to independently tailor the two orthogonal components of the spiro-skeleton at the molecular level. The newly designed HTM, SF-MPA-MCz, features enhanced thermal stability, precise energy level alignment, superior film morphology, and optimized interfacial properties when compared to Spiro-OMeTAD, which contribute to a remarkable power conversion efficiency (PCE) of 24.53% for PSCs employing SF-MPA-MCz with substantially improved thermal stability and operational stability. Note that the optimal concentration for SF-MPA-MCz solution is only 30 mg/ml, significantly lower than Spiro-OMeTAD (>70 mg/ml), which could remarkably reduce the cost especially for large-area processing in future commercialization. This work presents a promising avenue for the versatile design of multifunctional HTMs, offering a blueprint for achieving efficient and stable PSCs.
Resonant ultrasound spectroscopy for anisotropic materials with misaligned geometric and material axes.
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High Speed Hybrid Reluctance Motor Utilizing Anisotropic Materials
With high cost and volatility driving continued efforts to decrease reliance on the critical heavy rare earth materials used in traction drive applications, General Motors developed three variants of heavy rare earth-free (HRE-free) electric motors. The variants focused on taking advantage of advanced magnet technologies and new rotor topologies to improve mechanical strength and achieve power targets. The three variants were a HRE-free permanent magnet reluctance motor, a synchronous reluctance motor utilizing small HRE-free permanent magnets, and an induction motor with inserted copper bars and cast aluminum end-rings. Motors were designed with the intent of primary or secondary traction applications, depending on the topology. Variant 1 achieved performance comparable to HRE-containing permanent magnet motors through optimized topology and validation of HRE-free magnets, focusing on achieving energy products and demagnetization resistance comparable to those of HRE-containing magnets. Demagnetization testing demonstrated the motor robustness to currents and temperatures exceeding expected vehicle conditions, a key challenge to the use of HRE-free magnets. The Variant 1 motor also showed the best capability of meeting the US Drive technology 2020 targets, due to the high power-density of the permanent magnet motor and the potential cost reductions enabled by the removal of heavy rare earth materials. Variant 2 exhibited high efficiency in high speed regions due to the low high-speed losses, an important consideration for secondary traction applications, and significantly thrifted on magnet mass to reduce cost. Variant 3 contained copper bars within the induction rotor to reduce losses compared to cast aluminum, while using cast aluminum end-rings to reduce the cost and mass of the rotor. Optimization of the Cu-Al interface were focused on, as the interface is prone to forming brittle intermetallic compounds during the casting process. Prototypes of each motor variant were built and tested for performance, mechanical strength, and demagnetization resistance (Variants 1 and 2 only), with torque and power resulting close to the predicted values.
Anisotropic inelastic materials milestone 2021
The focus on new fuel and cladding models are drivers for several new capabilities at the MOOSE and BISON levels. Since these materials are anisotropic, they require an extension of our inelastic mechanics capabilities, which currently heavily rely on radial return mapping and the assumption of isotropic stiffness. We plan to add additional code paths to support fully anisotropic materials, without degrading the performance for modeling isotropic materials.
FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials
This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.
Measurement of the angular dependence of the spontaneous Raman scattering in anisotropic crystalline materials using spherical samples: Potassium dihydrogen phosphate as a case example
A specialized experimental configuration was created to allow for more-accurate characterization of the spontaneous Raman scattering properties in anisotropic materials. This need stems from the challenges, arising from the complexity of light propagation, in obtaining accurate measurements of the angular dependence of the Raman scattering cross section in birefringent materials. The nonlinear optical material KH 2 PO 4 (KDP) is used as a model medium. Our report is motivated by the need to improve our understanding and management of transverse stimulated Raman scattering in KDP crystals and its deuterated analog, DKDP, typically used for frequency conversion and polarization control in large-aperture laser systems. Key to this experimental platform is the use of high-quality spherical samples that enable one to measure the Raman scattering cross section in a wide range of geometries using only a single sample. The effect of polarization rotation of both the pump light and the collected Raman signal must be carefully considered in data analysis and can give rise to artifacts, which can, in part, be mitigated by reducing the input and collection cone angles.
SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials
This work examines the frame-invariance (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as informed, directed graphs, where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed, directed graph yield significantly more accurate rotation prediction than the other tested approaches.
Planar hyperbolic polaritons in 2D van der Waals materials
Anisotropic planar polaritons - hybrid electromagnetic modes mediated by phonons, plasmons, or excitons - in biaxial two-dimensional (2D) van der Waals crystals have attracted significant attention due to their fundamental physics and potential nanophotonic applications. In this Perspective, we review the properties of planar hyperbolic polaritons and the variety of methods that can be used to experimentally tune them. We argue that such natural, planar hyperbolic media should be fairly common in biaxial and uniaxial 2D and 1D van der Waals crystals, and identify the untapped opportunities they could enable for functional (i.e. ferromagnetic, ferroelectric, and piezoelectric) polaritons. Lastly, we provide our perspectives on the technological applications of such planar hyperbolic polaritons.
Thermal measurement apparatus and methods for anisotropic thermal materials
A system for characterizing thermal properties of thermally anisotropic heterogeneous samples includes a heating element, a first temperature sensing device, a second temperature sensing device, and a computing system. The heating element is positioned at a first location within a sample and heats the sample. The first temperature sensing device outputs data indicative of temperatures of the first location to the computing device. The second temperature sensing device outputs data indicative of temperatures of the second location to the computing device. The computing device computes a thermal conductivity of the sample based upon the temperatures of the first location. The computing device further outputs an indication of a portion of the sample to which the thermal conductivity pertains based upon the second temperatures.
Thermal measurement apparatus and methods for anisotropic thermal materials
A system for characterizing thermal properties of thermally anisotropic heterogeneous samples includes a heating element, a first temperature sensing device, a second temperature sensing device, and a computing system. The heating element is positioned at a first location within a sample and heats the sample. The first temperature sensing device outputs data indicative of temperatures of the first location to the computing device. The second temperature sensing device outputs data indicative of temperatures of the second location to the computing device. The computing device computes a thermal conductivity of the sample based upon the temperatures of the first location. The computing device further outputs an indication of a portion of the sample to which the thermal conductivity pertains based upon the second temperatures.
Effect of secondary gas-phase reactions (SGR) in pyrolysis of carbon feedstocks for anisotropic carbon materials production – 1: Controlling SGR to modify intermediate coal tar species to improve pitch anisotropy
To meet the increasing demand for graphitizable carbon products, such as needle coke and carbon fiber, more carbon feedstocks capable of forming anisotropy should be utilized. Non-coking coals are widely available but are not typically suitable for producing anisotropic carbons due to lacking proper coal chemistry. This work used secondary gas-phase reactions (SGR) during coal pyrolysis to improve the coal tar chemistry of a non-coking coal for anisotropic carbon production. SGR pyrolysis temperatures and residence times were varied (T = 800–900°C and τ = 0–2.5 s), and analysis of the intermediate coal tar products showed that as these SGR pyrolysis conditions increased, the oxygen and aliphatic concentrations decreased, whereas aromatic contents and molecular weights increased. Without any SGR, microscopy of the thermally-treated coal tar pitch product revealed that the coal tar pitch was isotropic; however, upon using increased SGR pyrolysis conditions, the resulting coal tar pitch samples substantially increased in the percentage and quality of anisotropy formation. Further, the products' analyses show clear trends of modified chemical properties in the intermediate coal tar and improved anisotropy results. Thus, the results presented in this work show that by controlling the SGR during pyrolysis of a non-coking coal, this approach can modify the coal tar chemistry towards a precursor more suitable for quality anisotropic carbon material production.
Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials
Low-symmetry 2D materials—such as ReS 2 and ReSe 2 monolayers, black phosphorus monolayers, group-IV monochalcogenide monolayers, borophene, among others—have more complex atomistic structures than the honeycomb lattices of graphene, hexagonal boron nitride, and transition metal dichalcogenides. The reduced symmetries of these emerging materials give rise to inhomogeneous electron, optical, valley, and spin responses, as well as entirely new properties such as ferroelasticity, ferroelectricity, magnetism, spin-wave phenomena, large nonlinear optical properties, photogalvanic effects, and superconductivity. Novel electronic topological properties, nonlinear elastic properties, and structural phase transformations can also take place due to low symmetry. Lastly, the “Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials” Special Topic was assembled to highlight recent experimental and theoretical research on these emerging materials.
Thermal performance of phase change materials with anisotropic carbon fiber inserts
In thermal energy storage systems, phase change materials (PCMs) are widely used for thermal energy management. Most PCMs have low thermal conductivities, which limits the heat transfer rate within PCM and thus makes the phase-changing process very slow. However, thermal conductivities of PCMs can be altered by inserting targeted additives. We hypothesize that the size and shape of these additive inserts play a key role in thermal management efficiency. To this end, the impacts of carbon fiber (CF) inserts on the phase change behavior and consequent heat transfer efficiencies of inorganic and organic PCMs were investigated using experiments and simulations. Long, anisotropic CFs with high thermal conductivities formed continuous fast heat flux tunnels inside PCMs to enhance the heat transfer. Such CFs could extend the phase change fronts from the limited container-shaped interface to the larger surface of numerous CF inserts inside the PCM. These special CF inserts work with a new heat transfer mechanism, different from conventional small additives or long isotropic CF inserts. The thermal energy release rate increased by 2.5 times with 1 wt.% anisotropic CF inserts in inorganic PCM. However, CF inserts in liquid organic PCM hindered the natural convection and compromised the improved heat conduction. In conclusion, the lab-scale multiphysics simulations support these experimental observations and indicate that CF inserts have potential to enhance heat transfer in inorganic PCMs, but they are less effective in organic PCMs.
Investigation of crossed-twin structure formation in magnesium and magnesium alloys
In this work, the effect of alloying addition on the propensity for twin-twin interactions to transform into crossed-twin structures in magnesium alloys is investigated. A full-field elasto-viscoplastic fast Fourier transform (EVP-FFT) framework combined with a discrete twin model and dislocation density-based hardening law for slip strengths is used to calculate the micromechanical fields in the crystalline matrix around the interacting twins. AZ31 and MgLi alloys are selected along with pure Mg to study the influence of plastic anisotropy in connection with alloying elements. These alloys were selected since their plastic anisotropy measure, which is defined as the ratio between the critical resolved shear stress for pyramidal $\langle$c +a$\rangle$ and basal $\langle$a$\rangle$ slip modes, spanned a wide range. To quantify the role of twin thicknesses, we probe a range of impinging twin thicknesses while fixing the recipient twin thickness. The analysis reveals that: (i) the local driving stress for crossed twin structure formation generated from the interaction of the two twins is lower in a low plastically anisotropic material, like a MgLi alloy, than a high plastically anisotropic material like pure Mg and (ii) the critical impinging twin thickness needed to form the crossed twin structure in pure Mg, AZ31 and MgLi alloys is ~0.5, ~0.75 and ~1.5 times the recipient twin thickness. We propose a relationship between the tendency for crossed twin structure formation and the experimentally observed higher ductility in MgLi alloys compared to pure Mg. Finally, one key implication of the findings is that crossed- twin structure formation can be hindered and the ductility of magnesium alloy thereby improved by properly choosing alloying elements that lower the slip strength for pyramidal $\langle$c + a$\rangle$ slip.