Local Orientation Distribution Research Articles

Investigating the impact of pore structure and surface chemistry on CO2 adsorption in graphitic slit-pores using GCMC simulation

Carbon capture, storage, and utilization from post-combustion processes using adsorption phenomena has emerged as a promising solution to the greenhouse gas emission crisis. The capacity of solid porous adsorbents dictates the performance of such carbon capture processes. Developments of porous adsorbents with favourable structural and chemical characteristics of the pore have been a major research area. Computational tools, notably the Grand Canonical Monte Carlo (GCMC) simulation, are widely employed to characterize the adsorption process in crystalline adsorbents like metal-organic frameworks and zeolites. Activated carbons are becoming promising alternatives to conventionally-used zeolite adsorbents for CO2 adsorption, because of their abundant microporosity and cost performance. However, the amorphous nature of the activated carbon materials poses a challenge in accurately modelling their pore characteristics and their adsorption process. Therefore, this study systematically explores the effect of pore size distribution and type of functional groups on the adsorption of CO2 on activated carbons using a simplified slit-pore graphite structure representing the activated carbon adsorbent. Four different pore sizes (7 Å, 8.9 Å, 18.5 Å, and 27.9 Å) and three oxygen-containing functional groups (Carbonyl, Hydroxyl, and Carboxyl) were selected to model the graphite structures. Results from the GCMC simulation reveal a significant rise in the CO2 adsorption capacity (from 4 mmol/g to 21 mmol/g) as the pore size was increased from 7 Å to 27.9 Å. Likewise, the functional groups enhance the low-pressure adsorption process by reducing the onset pressure of the pore filling by a factor of 100, especially in ultra-micropores. Likewise, we demonstrate the increase in the isosteric heat of adsorption due to the reduction in the pore size and the presence of functional groups. Additionally, the study illustrates the adsorbed phase behaviour of CO2 concerning the pore characteristics, a facet often overlooked in the existing literature. The adsorbed phase local density and molecular orientation distribution are analysed to understand the variation in the adsorption uptake and isosteric heat of adsorption properties. The study further identifies the adsorbed phase monolayer to multilayer transition and the ‘T′-shaped orientation of the adsorbed CO2 molecules as the key contributors to the high isosteric heat of adsorption in 8.9 Å pore size. It is envisaged that this study will navigate the precision adsorbent development for an efficient carbon capture process.

Autocollimators: plane angle measurand ambiguities and the impact of surface form

Abstract A phase shifting interferometer and a deformable mirror were used to study the impact of surface form on autocollimators, which detect the orientation of a plane reflecting surface. As real surfaces are not strictly planar, autocollimators must reduce a distribution of local surface orientations to a single reported angle, implicitly defining a measurand. Plausible choices of the summary statistic used to collapse an angle distribution to a single number can disagree by \SI{4}{\arcsecond} for a surface with a \SI{35}{mm} diameter and \SI{130}{nm} standard deviation from the best-fit plane. Combining a general framework for specifying autocollimator measurand definitions with Monte-Carlo simulation of random test surfaces yields estimates of the plausible differences between autocollimator measurands as a function of surface deformation amplitude, and shows the existence of three separate classes of measurands according to their sensitivity to subsets of the Zernike polynomials. Uncertainties due to surface form and measurand ambiguity can be eliminated by explicitly specifying a plane angle measurand for imperfect surfaces, such as a least-squares plane fit realized using an interferometer.

Micromechanical modelling of short fibre composites considering fibre length distributions

Mechanical response of short fibre composites is varying locally with respect to the microstructural constitution of the material, which in turn is a consequence of flow conditions during manufacturing. This local constitution is described by local fibre volume content, local fibre orientation distribution and local fibre length distribution. For short fibre reinforced plastics, both distributions are affected by flow conditions during an injection moulding process. Current material models for predicting the homogenised material response account for the local volume fraction and local fibre orientation distribution. Fibre length distribution, however, is usually approximated with a single average fibre length. To investigate the effects of fibre length distribution on the elasto-plastic response of short fibre composites, a micromechanical Orientation Averaging model has been extended. Two methods are presented in this work. In the first method, an additional averaging scheme over the fibre length distribution is included. In the second method, a novel representative fibre length is presented based on a stiffness-weighted average. The predictionsobtained from these methods are then compared and evaluated against experimental results of uniaxial tensile tests taken from literature. Good agreements are found using both methods. However, for the investigated behaviour, using a representative fibre length is still beneficial due to the superior computational performance.

Data‐based prediction of the viscoelastic behavior of short fiber reinforced composites

AbstractThe viscoelastic behavior of short fiber reinforced polymers (SFRPs) partly depends on different microstructural parameters such as the local fiber orientation distribution. To account for this by simulation on component level, two‐scale methods couple simulations on the micro‐ and macroscale, which involve considerable computational costs. To circumvent this problem, the generation of a viscoelastic surrogate model is presented here. For that purpose, an adaptive sampling technique is investigated and data are obtained by creep simulations of representative volume elements (RVEs) using a fast Fourier transform (FFT) based homogenization method. Numerical tests confirm the high accuracy of the surrogate model. The possibility of using that model for efficient material optimization is shown.

Imaging 3D molecular orientation by orthogonal-pair polarization IR microscopy.

Anisotropic molecular alignment occurs ubiquitously and often heterogeneously in three dimensions (3D). However, conventional imaging approaches based on polarization can map only molecular orientation projected onto the 2D polarization plane. Here, an algorithm converts conventional polarization-controlled infrared (IR) hyperspectral data into images of the 3D angles of molecular orientations. The polarization-analysis algorithm processes a pair of orthogonal IR transition-dipole modes concurrently; in contrast, conventional approaches consider individual IR modes separately. The orthogonal-pair polarization IR (OPPIR) method, introduced theoretically but never demonstrated experimentally, was used to map the 3D orientation angles and the order parameter of the local orientational distribution of polymer chains in a poly(ε-caprolactone) film. The OPPIR results show that polymer chains in the semicrystalline film are aligned azimuthally perpendicular to the radial direction of a spherulite and axially tilted from the film normal direction. This newly available information on the local alignments in continuously distributed molecules helps to understand the molecular-level structure of highly anisotropic and spatially heterogeneous materials.

Multiscale numerical simulation of the forming process of biaxial braids during thermoplastic braid-trusion: Predicting 3D and internal geometry and fiber orientation distribution

Thermoplastic braid-trusion is a composite manufacturing process that combines braiding and pultrusion of hybrid yarns containing reinforcement and polymer fibers. During pultrusion, the melting of the polymer fibers leads to complex morphological changes at the macro, meso and micro scales. We introduce here a multiscale numerical simulation methodology to model this process. In this methodology, braided yarns are modeled as bundles of virtual discrete fibers using chains of truss elements. A thermoplastic composite braided rod was pultruded according to the simulated braid-trusion. During braid-trusion, it was observed that the braid architecture was significantly modified, which was reliably predicted by the model through macroscopic measurements of 7.6% pitch elongation, 44.0% diameter reduction, and 45.0% nominal angle reorientation. The model also predicts yarns’ cross-section area having high local fiber volume fraction of about 60% due to yarn compaction during pultrusion. These predictions of mesoscopic morphology and internal geometry are quantitatively validated using X-ray micro-computed tomography (CT) scans of the braid-truded rod. Three local fiber orientation distributions of the in-plane, out-of-plane, and with respect to the longitudinal braid axis are extracted using micro-scale analysis of virtual fibers. We found that a significant amount of fibers are oriented around specific radii ranging from 30–70% and 60–100% of the outer radius before and after pultrusion, respectively. By contrast, the local fiber orientation is uniformly distributed along the pitch length. The microscale model also shows considerable discrepancies between local and nominal braid angles.

ODFNet: Using orientation distribution functions to characterize 3D point clouds

Learning new representations of 3D point clouds is an active research area in 3D vision, as the order-invariant point cloud structure still presents challenges for the design of neural network architectures. Recent work explored learning global, local, or multi-scale features for point clouds. However, none of the earlier methods focused on capturing contextual shape information by analyzing local orientation distributions of points. In this paper, we use point orientation distributions around a point in order to obtain an expressive local neighborhood representation for point clouds. We achieve this by dividing the spherical neighborhood of a given point into predefined cone volumes, and statistics inside each volume are used as point features. In this way, a local patch can be represented not only by the selected point’s nearest neighbors, but also by considering a point density distribution defined along multiple orientations around the point. We are then able to construct an orientation distribution function (ODF) neural network that makes use of an ODFBlock which relies on MLP (multi-layer perceptron) layers. The new ODFNet model achieves state-of-the-art accuracy for object classification on ModelNet40 and ScanObjectNN datasets, and segmentation on ShapeNet and S3DIS datasets.

Asymptotic fiber orientation states of the quadratically closed Folgar–Tucker equation and a subsequent closure improvement

Anisotropic fiber-reinforced composites are used in lightweight construction, which is of great industrial relevance. During mold filling of fiber suspensions, the microstructural evolution of the local fiber arrangement and orientation distribution is determined by the local velocity gradient. Based on the Folgar–Tucker equation, which describes the evolution of the second-order fiber orientation tensor in terms of the velocity gradient, the present study addresses selected states of deformation rates that can locally occur in complex flow fields. For such homogeneous flows, exact solutions for the asymptotic fiber orientation states are derived and discussed based on the quadratic closure. In contrast to the existing literature, the derived exact solutions take into account the fiber-fiber interaction. The analysis of the asymptotic solutions relying upon the common quadratic closure shows disadvantages with respect to the predicted material symmetry, namely, the anisotropy is overestimated for strong fiber-fiber interaction. This motivates us to suggest a novel normalized fully symmetric quadratic closure. Two versions of this new closure are derived regarding the prediction of anisotropic properties and the fiber orientation evolution. The fiber orientation states determined with the new closure approach show an improved prediction of anisotropy in both effective viscous and elastic composite behaviors. In addition, the symmetrized quadratic closure has a simple structure that reduces the effort in numerical implementation compared to more elaborated closure schemes.

Enhancing the estimation of fiber orientation distributions using convolutional neural networks

Local fiber orientation distributions (FODs) can be computed from diffusion magnetic resonance imaging (dMRI). The accuracy and ability of FODs to resolve complex fiber configurations benefits from acquisition protocols that sample a high number of gradient directions, a high maximum b-value, and multiple b-values. However, acquisition time and scanners that follow these standards are limited in clinical settings, often resulting in dMRI acquired at a single shell (single b-value). In this work, we learn improved FODs from clinically acquired dMRI. We evaluate patch-based 3D convolutional neural networks (CNNs) on their ability to regress multi-shell FODs from single-shell FODs, using constrained spherical deconvolution (CSD). We evaluate U-Net and High-Resolution Network (HighResNet) 3D CNN architectures on data from the Human Connectome Project and an in-house dataset. We evaluate how well each CNN can resolve FODs 1) when training and testing on datasets with the same dMRI acquisition protocol; 2) when testing on a dataset with a different dMRI acquisition protocol than used to train the CNN; and 3) when testing on a dataset with a fewer number of gradient directions than used to train the CNN. This work is a step towards more accurate FOD estimation in time- and resource-limited clinical environments.

Importance of deformation-induced local orientation distributions for nucleation of recrystallisation

Nucleation in an aluminium tricrystal cold rolled along its columnar direction, to 40% thickness reduction, is studied. This experimental configuration was used to obtain the same deformation microstructure through the sample length, which made it possible to cut it into several slices of similar microstructures and use these slices differently. Some slices served to analyse the deformation microstructure and others to analyse the annealing microstructure. Nucleation developed only in one of the three crystals and not at grain boundaries. The relationship between the crystallographic orientations and the local density of nuclei and different attributes of the parent, deformation microstructure was then analysed. As generally presumed, the nuclei were observed to inherit orientations from the parent matrix. Much more surprisingly, the stored energy alone, which is often considered as the driving force for recrystallisation nucleation, was found not to provide a reliable criterion for recrystallisation nucleation in the investigated sample. Instead, the density of nuclei was the highest where the substructure is composed of sharp bands, which correspond to regions of highly anisotropic orientation distributions. A new energy criterion for recrystallisation nucleation is proposed, which is called “primary stored energy” and depends on the stored energy and the anisotropy of the orientation distribution.

Statistical variation of characteristics of random packed beds of Raschig rings: The influence of the sample size

Many studies on random packed beds have been dedicated to local porosity (void fraction) or orientation distribution of particles. However, despite the random nature of the considered packings, very little attention has been devoted to examination whether the number of particles used in experiments/simulations is sufficiently large to get reproducible results. The reproducibility of the key packing parameters depends on the size of the population of particles (sample size) and ordering effects induced by the confining walls. This work investigates quantitatively the influence of the sample size on the statistical variation of the packed bed characteristics. Packed beds of Raschig rings were generated with a sequential algorithm and three column diameters were considered. It has been found that in the case of the orientation distribution the results depend strongly on the sample size, especially for slender columns, while the porosity profiles are well-reproducible characteristics even for relatively small packings of rings. Some complementary results for full cylinders are also included.

Notch insensitivity in fatigue failure of chopped carbon fiber chip-reinforced composites using experimental and computational analysis

This study focuses on the notch effect on the fatigue failure of chopped carbon fiber chip-reinforced sheet molding compound (SMC) composites by using both experimental and numerical methods. The S-N diagrams of notched specimens are first obtained experimentally, which exhibit large scatter and are shown to depend on the spatial distribution of local fiber orientations. After considering the effect of this spatial distribution by adopting a new fatigue damage parameter to normalize the results, we achieve a much better correlation in the normalized S-N diagram for all the notched specimens with different hole diameters. Next, compared with the fatigue results of smooth specimens without notches, we find that SMC composites under tension-tension fatigue loading exhibit notch-insensitivity, which renders this type of composites a better candidate in joints or similar applications. Meanwhile, the fatigue failure mechanisms of notched SMC composites are explored through a microstructure characterization procedure. On this basis, a computational micromechanics model considering the notch effect and an improved multi-scale progressive damage fatigue law, calibrated by coupon-level fatigue tests of smooth SMC composites under different loading conditions, are employed to predict the fatigue behavior of notched SMC composites. We show that detailed failure processes and fatigue life of notched SMC composites can be efficiently and adequately predicted by this computational framework.

Integrated crystal plasticity and phase field model for prediction of recrystallization texture and anisotropic mechanical properties of cold-rolled ultra-low carbon steels

A multi-scale approach integrating a polycrystal plasticity finite element (CPFEM) and a multi-phase field model (PFM) is developed in this study and employed to the prediction of anisotropic mechanical properties of annealed ultra-low carbon steel. The CPFEM simulates inhomogeneous local deformation and orientation distribution of ultra-low carbon steel, while the PFM predicts microstructure evolution originating from nucleation and growth. The present study highlights a systematic modeling process including reduction of the stored energy by the recovery process, nucleation of grains with preferred orientation based on generalized strain energy release maximization theory (GSERM), and grain growth with consideration of the stored energy difference and misorientation between neighboring grains, which are provided from local effects in the CPFEM. The two computational approaches are numerically mapped by the Wigner-Seitz cell method to efficiently transfer state variables between the domains of finite element and finite difference schemes for CPFEM and PFM, respectively. The proposed multiscale model is quantitatively validated through experimentally measured microstructural characteristics of annealed ultra-low carbon steel after the rolling deformation, i.e., its recrystallization texture in the aspect of pole figures and ODF, grain size, and distributions. Finally, the predicted microstructural information after the thermo-mechanical process is used as input for virtual mechanical tests simulating orientation-dependent tensile properties. The comparison of predicted orientation-dependent yield stresses and Lankford coefficients as measures for anisotropic mechanical properties with those of experiments confirm the validity and accuracy of the proposed CPFEM-PFM approach as an efficient tool for understanding the relationship between the thermo-mechanical process, microstructure, and mechanical properties in the material design stage.

Spin Probe Determination of Molecular Orientation Distribution and Rotational Mobility in Liquid Crystals: Model-Free Approach.

A model-free approach for simulation of EPR spectra of nitroxide spin probes in liquid-crystalline materials was suggested and used to obtain parameters of molecular orientation and rotational mobility. The developed method is based on experimental recording and numerical simulation of the angular dependence of EPR spectra, which is shown to be much more informative in comparison with a single EPR spectrum. Quantitative spectral simulations considering both local orientational ordering and distribution of local directors in the sample were used for discrimination of models of rotational mobility and orientational alignment. The method was applied for detailed quantitative characterization of axial, orthorhombic, and low-symmetry non-orthorhombic molecular orientation distributions. It is shown that the ordinarily used model of rotational diffusion in a mean-field potential is suitable for the description of molecular mobility and orientational ordering only for relatively low sample temperatures and low-mobility probe molecules with large sizes. In cases of high molecular mobility, the more realistic jump mechanism of molecular moves can be approximately described as quasi-librations. For ordered liquid crystals it was found that mostly the order parameters up to rank 12-14 are essential and easily determined. When well-aligned materials are described, the order parameters up to 18th rank or even higher become meaningful. Both molecular and sample biaxiality is analyzed and quantitatively characterized. The local molecular ordering and sample orientational alignment are quantitatively characterized separately.

Effect of fiber orientation distribution on constant fatigue life diagram of chopped carbon fiber chip-reinforced Sheet Molding Compound (SMC) composite

The material behavior of chopped carbon fiber chip-reinforced Sheet Molding Compound (SMC) composite is investigated under both quasi-static and cyclic fatigue loading conditions in the present study. Quasi-static tensile and compressive strength data is collected, followed by a series of fatigue tests under three different cyclic loading conditions, i.e., Tension-Tension (T-T), Compression-Compression (C-C), and Tension-Compression (T-C). The experimental results show a considerable amount of variation for each loading condition, which is found to be induced by the spatial distribution of fiber orientation within the tested specimens. An analytical approach is developed to correlate the fatigue performance of the SMC material with the local modulus, which is determined by the fiber orientation distribution. Additionally, the similar failure modes are observed under different loading conditions. Based on these findings, a new form of Constant Fatigue Life (CFL) diagram is established in which the impact of fiber orientation tensor to the fatigue behavior of SMC is considered. This developed CFL diagram is examined by comparing the measured fatigue performance with prediction where local fiber orientation distribution is quantified from microscopic images.

Analysis of local crystallographic orientation in an annealed Ti60 billet

A heterogeneous microstructure in terms of local orientation distribution is often found in near-α titanium alloys. The presence of large regions with similar crystallographic orientation, called ‘macrozones’, could drastically decrease the fatigue performance of titanium alloys. The present work reports on the crystallographic orientation of a near-α titanium alloy, Ti60, billet after annealing in an α+β phase field. The texture was found to be weak, and no obvious macrozone was found in our measured zone where the variant selection is suppressed. Meanwhile, in-depth electron backscattered diffraction (EBSD) analysis was applied to evaluate the final microstructure, and the mechanisms by which they formed were analyzed.

Fatigue simulation of a short fiber re-inforced oil-filter under high temperature and pressure load

Short-fiber reinforced parts show a distinct anisotropic behavior, caused by the alignment of the fibers during the injection molding process. The injection molding simulation provides the local probability distribution of the fibers (orientation tensor). By applying multi-scale material models it is possible to estimate the local anisotropic stiffness. This leads to considerable more accurate results in a subsequent FEA as with isotropic approaches. This is true even if higher temperatures lead to local plasticity. Tools that enable this integrative simulation approach have been established in the last years. To account for the anisotropic fatigue behavior an interpolation of fatigue strength at a discrete fiber orientation distribution is often used by estimating the anisotropic stiffnesses in direction of the orientation tensor principal directions. This is in most cases not appropriate. In the paper an approach is described that uses a so-called Master SN curve concept which estimates SN curves for varying local fiber orientation distributions. For the application case of high temperatures and local plasticity several enhancements were implemented and tested. The methodology is verified at the example of an oil-filter system under pressure at elevated temperature.

Effect of heat treatment on the crystallographic orientation evolution in a near-α titanium alloy Ti60

The crystallographic orientation of equiaxed primary α (αp) phase is one of the main factors that determine the final texture/microtexture and mechanical properties for near-α titanium alloys. By annealing a forged Ti60 alloy pancake at 1030 and 1040 °C in the α+β two-phase field, two homogeneous bimodal microstructures were obtained, the intensity of secondary α in the {0001} pole figure increasing with the annealing temperature. In this study, the influence of annealing temperature on the crystallographic orientation evolution in the pancake was studied using an electron backscattered diffraction analysis method. In particular, a misorientation angle θ associated with (βΔJβBOR) that could quantitatively evaluate the deviation of the orientation relationship (OR) between αp and the surrounding β grains from Burgers OR was used to understand the role of the αp phase, which is considered as an anisotropic precipitate, in the texture evolution during annealing in the two-phase field. It was found that the αp grains with small θ are more readily preserved during the annealing, while their pinning effect is relatively small, resulting in faster growth of the neighboring β grains. A possible effect of heterogeneous local orientation distribution on the microstructure during the annealing process is also discussed.

Computational estimation of scene structure through texture gradient cues

Analyzing the depth structure implied in two-dimensional images is one of the most active research areas in computer vision. Here, we propose a method of utilizing texture within an image to derive its depth structure. Though most approaches for deriving depth from a single still image utilize luminance edges and shading to estimate scene structure, relatively little work has been done to utilize the abundant texture information in images. Our new approach begins by analyzing the two cues of local spatial frequency and orientation distributions of the textures within an image, which are used to compute the local slant information across the image. The slant and frequency information are merged to create a unified depth map, providing an important channel for image structure information that can be combined with other available cues. The capabilities of the algorithm are illustrated for a variety of images of planar and curved surfaces under perspective projection, in most of which the depth structure is effortlessly perceived by human observers. Since these operations are readily implementable in neural hardware in early visual cortex, they therefore represent a model of the human perception of the depth structure of images from texture gradient cues.

A statistical treatment of the loss of stiffness during cyclic loading for short fiber reinforced injection molded composites

Injection molded short fiber reinforced composites (SFRC) have different local fiber orientation distribution (FOD) at every point. SN curves of short fiber reinforced composites are known to depend on the fiber orientation distribution. Such materials also suffer from continuous loss of stiffness during cyclic loading. It is not known whether the loss of stiffness is different for SFRC with different FOD. A statistical analysis of the loss of stiffness curves is presented in this paper. Tension-tension fatigue experiments are performed and loss of stiffness is collected for every data point in the SN curve. A systematic method for comparing the loss of stiffness is developed. It is concluded that the difference in loss of stiffness curves for coupons of SFRC with different FOD is not statistically significant.