Orientation Distribution Function Research Articles

AtomTex: texture characterization software for atomic configurations

Abstract A software named AtomTex has been developed for characterizing texture/orientation of atomic configurations. The software currently can generate orientation distribution functions, Miller indices, pole figures, inverse pole figures and angle-axis pairs between grains. Utilizing AtomTex, one can explicitly trace orientation evolution of a given atom, resembling an in-situ probe with atomic scale resolution, which is expected to significantly deepen understanding how microstructure evolves upon various thermomechanical treatments.

Microstructure evolution and local mechanical properties of friction stir additively manufactured (FSAM) AA5083/AA6061/AA7075 gradient composite.

The current study is focused on the successful fabrication and characterization of microstructure and properties gradient composite made of 3 mm thick sheets of AA5083-O, AA6061-T6, and AA7075-T6 alloys using friction stir additive manufacturing (FSAM) technique. Two combinations of four layered FSAM builds (6756 and 7567) were fabricated successfully without any major defects at the optimized process parameters of 850 rpm (tool rotational speed) and 55 mm/min (tool transverse speed). The material mixing, interfacial bonding features, microstructure evolution, and mechanical performance within the stir zones (SZ) were thoroughly examined using advanced characterization techniques. Electron backscatter diffraction (EBSD) analysis confirmed a gradient microstructure along the build depth in both FSAM builds, with average grain sizes decreasing from 52 μm (AA5083), 46 μm (AA6061), and 40 μm (AA7075) in base metals to ∼ 4 to 7 μm within the SZ. The remarkable grain refinement within the SZ was mainly attributed to the dominant presence of the continuous dynamic recrystallization (CDRX) mechanism. Texture analysis corresponding to pole figures (PFs) and orientation distribution function (ODF) plots reveals the crystallographic texture evolution along the build depth. The prevalent existence of B/ and C textures throughout all regions of the FSAM builds affirms the presence of ample shear strain during the FSAM procedure. Through thickness miniature tensile and microhardness tests depict the gradient in mechanical performance for both the FSAM builds along the build depth. Microhardness gradients in the range from 80 HV0.1 to 145 HV0.1 were observed along the build depth. The axial sample in the build direction shows appreciable strength (265 MPa and 224 MPa) and uniform elongation (28% and 24 %) for 6756 and 7567 FSAM build, respectively. Furthermore, remarkable strain hardening behaviour corresponding to hardening capacity (Hc) and hardening exponent (n) was noticed for both the axial build samples compared to AA6061-T6 and AA7075-T6 base metals. These findings underscore the potential of FSAM in fabricating functionally gradient composite materials tailored to specific functional requirements.

Analytical modelling of the orientation dependency of 3D printed SHCC at increasing levels of scale

3D printable strain hardening cementitious composites (3DP-SHCC) stand out for their high ductility and increase in tensile strength after initial cracking. Due to the printing process, which includes the pumping and extruding of the material, the fibres are not uniformly orientated in the material but have an orientation dependency due to the specific printing process applied. Three different cases for the fibre orientation distribution functions are presented with increasing levels of relation to the printing process. These three cases have been used in a micro-mechanical model to verify with experimental stress-crack opening results (single crack). Furthermore, a spring model is used to give insight into the potential to develop pseudo strain hardening behaviour (multiple cracking) in various printing directions. The method is also used to model the experimentally obtained spread in uni-axial tensile dogbone test results. From these experimental dogbone tests, average stress-strain relations are determined in two directions. Finally, a multi-layer method is used on the component level to validate the use of these average stress-strain relations for modelling the bending behaviour of printed elements in multiple directions.

Accurate distances measures and machine learning of the texture-property relation for crystallographic textures represented by one-point statistics

Abstract The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g., important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images . Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control.

Crystallographic Texture Evolution in 3D Printed Polyethylene Reactor Blends.

In this work, crystallographic texture evolution in 3D printed trimodal polyethylene (PE) blends and high-density PE (HDPE) benchmark material were investigated to quantify the resulting material anisotropy, and the results were compared to materials made from conventional injection molded (IM) samples. Trimodal PE reactor blends consisting of HDPE, ultrahigh molecular weight PE (UHMWPE), and HDPE_wax have been used for 3D printing and injection molding. Changes in the preferred orientation and distribution of crystallites, i.e., texture evolution, were quantified utilizing the wide angle X-ray diffraction through pole figures and orientation distribution functions (ODFs) for 3D printed and IM samples. Since the change in weight-average molecular weight (Mw) of the blend was expected to significantly affect the resulting crystallinity and orientation, the overall Mw of the trimodal PE blend was varied while keeping the UHMWPE component weight fraction to 10% in the blend. The resulting texture was analyzed by varying the overall Mw of the trimodal blend and the process parameters in 3D printing and compared to the texture of conventional IM samples. The printing speed and orientation (defined with respect to the axis along the length of the samples) were used as the variable process parameters for 3D printing. The degree of anisotropy increases with an increase in the nonuniform distribution of intensities in pole figures and ODFs. All the highest intensity major texture components in IM and 3D printed samples (0° printing orientation) of reactor blends are observed to have crystals oriented in [001] or [001̅]. Overall, for the same throughput, 3D printed samples in the 0° orientation showed greater texture evolution and higher anisotropy compared to IM samples. Most notably, an increase in 3D printing speed increased the crystalline distribution closer to the 0° direction, increasing the anisotropy, while deviation from this printing orientation reduced crystalline distribution closer to the 0° direction, thus increasing isotropy. This demonstrates that tailoring material properties in specific directions can be achieved more effectively with 3D printing than with the injection molding process. Change in the overall Mw of the trimodal PE blend changed the preferential orientation distribution of the crystal planes to some degree. However, the degree of anisotropy remained the same in almost all cases, indicating that the effect of molecular weight distribution is not as significant as the printing speed and printing orientation in tailoring the resulting properties. The 3D printing process parameters (speed and orientation) were shown to have more influence on the texture than the material parameters associated with the blend.

Effect of microalloying with rare-earth lanthanum on dynamic recrystallization behavior and mechanical properties of Ti sheets

This study examines the influence of microalloying with rare earth lanthanum (La) on the dynamic recrystallization behavior and mechanical properties of Titanium (Ti) sheets. A distinctive wedge-shaped specimen was employed for experimental efficiency, enabling continuous gradient strains to be applied to the Ti-La alloy during hot-rolling, facilitating the assessment of changing microstructural, textural, and hardness features as strain increased from low to high levels. The hot-rolled plates were performed using analytical methods such as optical microscopy (OM), X-ray diffraction (XRD), transmission electron microscopy (TEM), and hardness testing. The results show that the hardening process can be divided into four stages under continuous gradient strain (0 ∼ 0.5, 0.5 ∼ 0.7, 0.7 ∼ 1.2 and 1.2 ∼ 1.6). During these stages, grain refinement and dislocation strengthening emerge as critical contributors to changes in hardness. Furthermore, it was determined that dynamic recrystallisation (DRX) of Ti-La alloys during hot rolling occurs at the fourth stage. Analysis of the orientation distribution function (ODF) reveals that the dominant textures during this process include {1̅21̅0}, {011̅0}, and {0001} textures. When compared with commercially pure titanium (CP-Ti), the Ti-La alloy shows significantly delayed DRX under identical conditions. The DRX grain growth appears suppressed, attributable to the presence of La-rich particles on the grain boundaries. Moreover, the texture associated with rolling deformation seems subdued, providing a desirable base for future cold rolling and heat treatment.

Microstructure generation and full-field multi-scale analyses for short fiber reinforced thermoplastics: Application to PA66GF composites

Short Fiber Reinfored Thermoplastics (SFRTs) like PA66GF composites are highly heterogeneous materials with a rather complex microstructure such that the characterization and the prediction of their mechanical behavior remain quite challenging. So far, most of the research efforts have employed phenomenologigal and mean-field multi-scale models to deal with SFRTs. The present contribution rather focuses on a full-field multi-scale approach that incorporates advanced techniques in terms of microstructural representation and material modeling, allowing a deep insight of the dominating deformation mechanisms occurring in PA66GF composites. The proposed approach is based on an automatic periodic mesh generation algorithm for matrix-inclusion Representative Volume Elements (RVE) with randomly positioned fibers that follow a given Orientation Distribution Function (ODF). At the microscopic scale, while the fibers are assumed to be elastic, the behavior of the thermoplastic matrix is described by a phenomenological multi-mechanism constitutive model accounting for viscoelasticity, viscoplasticity and ductile damage. It results an advanced multi-scale model that enables to visualize the local deformation and degradation mechanisms occurring at the microscopic scale while simultaneously analyzing their influence on the macroscopic response of the composite upon monotonic, persistent and cyclic loading. The potential of the proposed approach is further evaluated by comparing the predicted responses against experimental data.

A new compact symmetric shear diamond anvil cell for in situ high-pressure-torsion studies.

In situ studies under severe plastic deformation at high pressures, employing shear diamond anvil cells, have recently gained much interest in the high-pressure community owing to their potential applications in material processing methods, mechanochemistry, and geophysics. These studies, combined with multi-scale computational simulations, provide important insights into the transient hierarchical microstructural evolution, structural phase transitions, and orientation relationship between parent and daughter phases and help establish the kinetics of strain-induced phase transitions under severe plastic deformation. The existing SDACs are mostly used in axial x-ray diffraction geometry due to geometrical constraints providing less reliable information about stress states and texture. Their asymmetric design also poses serious limitations to high-pressure shear studies on single crystals. To overcome these limitations, a new compact symmetric shear diamond anvil cell has been designed and developed for in situ high-pressure torsion studies on materials. The symmetric angular opening and short working distance in this new design help obtain a more reliable crystallographic orientation distribution function and lattice strain states up to a large Q range. Here, we present the advantages of the symmetric design with a few demonstrative studies.

Deep learning microstructure estimation of developing brains from diffusion MRI: A newborn and fetal study

Diffusion-weighted magnetic resonance imaging (dMRI) is widely used to assess the brain white matter. Fiber orientation distribution functions (FODs) are a common way of representing the orientation and density of white matter fibers. However, with standard FOD computation methods, accurate estimation requires a large number of measurements that usually cannot be acquired for newborns and fetuses. We propose to overcome this limitation by using a deep learning method to map as few as six diffusion-weighted measurements to the target FOD. To train the model, we use the FODs computed using multi-shell high angular resolution measurements as target. Extensive quantitative evaluations show that the new deep learning method, using significantly fewer measurements, achieves comparable or superior results than standard methods such as Constrained Spherical Deconvolution and two state-of-the-art deep learning methods. For voxels with one and two fibers, respectively, our method shows an agreement rate in terms of the number of fibers of 77.5% and 22.2%, which is 3% and 5.4% higher than other deep learning methods, and an angular error of 10° and 20°, which is 6° and 5° lower than other deep learning methods. To determine baselines for assessing the performance of our method, we compute agreement metrics using densely sampled newborn data. Moreover, we demonstrate the generalizability of the new deep learning method across scanners, acquisition protocols, and anatomy on two clinical external datasets of newborns and fetuses. We validate fetal FODs, successfully estimated for the first time with deep learning, using post-mortem histological data. Our results show the advantage of deep learning in computing the fiber orientation density for the developing brain from in-vivo dMRI measurements that are often very limited due to constrained acquisition times. Our findings also highlight the intrinsic limitations of dMRI for probing the developing brain microstructure.

Crystallographic texture evolution during friction stir processing of AA7075 alloy

This study investigates the effects of heat input on the crystallographic texture evolution during friction stir processing of AA7075 alloys. Three different heat input levels were applied to develop friction stir-modified regions. Electron backscattered diffraction (EBSD) was utilized to measure the micro-texture in the as-received base metal and friction stir processed (FSPed) stir zones. In particular, inverse pole figure (IPF) maps, pole figures, and orientation distribution functions were employed to compare the micro-textures of different processed regions. The results indicate that as the heat input decreases, the average microhardness of the nugget zone declines, accompanied by an increase in the size of recrystallized grains. The base metal AA7075 exhibits a predominantly rotated cube texture ({001} <110>). After friction stir processing, the stir zone transitions to a rotated cube texture with decreased intensities and the presence of copper texture ({112} <111>). Notably, as the heat input increases, the rotated cube texture transforms into a copper texture.

Applications of the Clifford torus to material textures

This paper introduces a new 2D representation of the orientation distribution function for an arbitrary material texture. The approach is based on the isometric square torus mapping of the Clifford torus, which allows for points on the unit quaternion hypersphere (each corresponding to a 3D orientation) to be represented in a periodic 2D square map. The combination of three such orthogonal mappings into a single RGB (red–green–blue) image provides a compact periodic representation of any set of orientations. Square torus representations of five different orientation sampling methods are compared and analyzed in terms of the Riesz s energies that quantify the uniformity of the samplings. The effect of crystallographic symmetry on the square torus map is analyzed in terms of the Rodrigues fundamental zones for the rotational symmetry groups. The paper concludes with example representations of important texture components in cubic and hexagonal materials. The new RGB representation provides a convenient and compact way of generating training data for the automated analysis of material textures by means of neural networks.

Effect of Annealing on the Microstructure, Texture, and Properties of Cold-Rolled Ti50Ni47Fe3 Shape Memory Alloy Sheets

A systematic study was conducted on the impact of annealing treatments on the microstructure and properties of cold-rolled Ti50Ni47Fe3 alloys using optical microscopy, scanning electron microscopy, electron backscattered diffraction, and an electronic universal testing machine. It was found that, during low-temperature annealing (400 °C and 500 °C), the annealing time had no significant effect on the microstructure or properties of the Ti50Ni47Fe3 alloy. Only elongation (δ) increased with the increase in the annealing time, and the grain orientation of the Ti50Ni47Fe3 alloy was &lt;111&gt;//RD (rolling direction). When annealing at medium–high temperature (600 °C), as the annealing time increased, recrystallization and grain growth processes occurred, resulting in a continuous decrease in strength and an increase in δ. Meanwhile, it was found that the grain orientation of the cold-rolled Ti50Ni47Fe3 alloy changed from &lt;111&gt;//RD during the recovery and recrystallization processes to &lt;101&gt;//RD after the grain growth process. The orientation distribution function cross-section φ2 = 45° results indicate that the texture was mainly distributed along the γ orientation line (φ1 = 0~90°, Φ = 54.7°, φ2 = 45°). When annealed at 400 °C and 500 °C, the texture of the Ti50Ni47Fe3 alloys was (111)[uvw]. When the annealing treatment was 600 °C for 120 min, a (110)[uvw] texture occurred. Additionally, ductile fracture occurred in all specimens, and the crack origin was located on one side of the fracture surface, with obvious “Y”-shaped propagation. This article studied annealing treatments of cold-rolled Ti50Ni47Fe3 alloys, providing corresponding theoretical guidance for subsequent production applications.

EBSD characterization of graphene nano sheet reinforced Sn–Ag solder alloy composites

This research explores the effects of incorporating Graphene Nano Sheets (GNS) on the microstructural characteristics and mechanical behavior of Sn–Ag solder alloys. The research was driven by the need for environmentally friendly, lead-free solder alloys with enhanced mechanical and thermal properties. The methodology involved incorporating graphene into the Sn–Ag alloy through stir casting, followed by a series of surface preparation techniques. The composite samples were then examined using EBSD to analyze crystallographic orientations and SEM/EDS for surface morphology and elemental composition. XRD provided insights into phase transformations and structural changes. Key findings reveal that the addition of GNS significantly refines the grain structure of the Sn–Ag alloy, leading to a bimodal grain size distribution. This refinement is attributed to the role of GNS as a nucleation site during solidification. Moreover, the study demonstrates a pronounced alteration in the texture of the material, with an increase in low-angle grain boundaries post-GNS addition. This texture change is indicative of enhanced mechanical properties. The results also show a shift in the orientation distribution function (ODF), suggesting a stronger crystallographic orientation due to GNS. These findings suggest that GNS incorporation could lead to improved mechanical and thermal properties in Sn–Ag solder, making them suitable for high-performance electronic applications. The study concludes that GNS not only serves as an effective reinforcement in Sn–Ag solder alloys but also significantly alters their microstructural and textural characteristics, contributing to the alloy's potential application in environmentally conscious electronic manufacturing.

Voxel-Wise Fusion of 3T and 7T Diffusion MRI Data to Extract more Accurate Fiber Orientations.

While 7T diffusion magnetic resonance imaging (dMRI) has high spatial resolution, its diffusion imaging quality is usually affected by signal loss due to B1 inhomogeneity, T2 decay, susceptibility, and chemical shift. In contrast, 3T dMRI has relative higher diffusion angular resolution, but lower spatial resolution. Combination of 3T and 7T dMRI, thus, may provide more detailed and accurate information about the voxel-wise fiber orientations to better understand the structural brain connectivity. However, this topic has not yet been thoroughly explored until now. In this study, we explored the feasibility of fusing 3T and 7T dMRI data to extract voxel-wise quantitative parameters at higher spatial resolution. After 3T and 7T dMRI data was preprocessed, respectively, 3T dMRI volumes were coregistered into 7T dMRI space. Then, 7T dMRI data was harmonized to the coregistered 3T dMRI B0 (b = 0) images. Last, harmonized 7T dMRI data was fused with 3T dMRI data according to four fusion rules proposed in this study. We employed high-quality 3T and 7T dMRI datasets (N = 24) from the Human Connectome Project to test our algorithms. The diffusion tensors (DTs) and orientation distribution functions (ODFs) estimated from the 3T-7T fused dMRI volumes were statistically analyzed. More voxels containing multiple fiber populations were found from the fused dMRI data than from 7T dMRI data set. Moreover, extra fiber directions were extracted in temporal brain regions from the fused dMRI data at Otsu's thresholds of quantitative anisotropy, but could not be extracted from 7T dMRI dataset. This study provides novel algorithms to fuse intra-subject 3T and 7T dMRI data for extracting more detailed information of voxel-wise quantitative parameters, and a new perspective to build more accurate structural brain networks.

Unraveling the effects of nano-grained microstructure on mechanical behavior, corrosion, and in vitro biocompatibility of 316L austenitic stainless steel

Nanograins are often beneficial in achieving better cytocompatibility for metallic implants. In this work, we have achieved grains from the micro to nano range in 316L austenitic stainless steel by a combination of cryo-rolling (50%, 70%, and 90% thickness reduction) followed by annealing (750–1000 °C for 2–20 min). The combined effect of grain refinement along with texture on its mechanical, corrosion, and in vitro cellular behavior was thoroughly investigated. Microstructural observations revealed nanograins formation (grain size = 144 nm) only for the 90CRA sample, whereas grain refinement in the micron range was observed for 0-70CRA samples. Electron backscatter diffraction (EBSD) studies showed fully austenitic structures for all the annealed samples while low Kernel Average Misorientation (KAM) values indicated strain-free microstructures. Orientation distribution function (ODF) maps showed the presence of strong γ-fiber (<111>||ND) and weak α-fiber (<110>||ND) in the 90CRA sample. The grain refinement led to an increase in the yield strength and ultimate tensile strength from 470.6 ± 16.21 MPa and 858.35 ± 31.82 MPa (0CRA) to 1662.06 ± 58.44 MPa and 2112.3 ± 51.62 MPa (90CRA), respectively. The potentiodynamic polarization study revealed that the corrosion rate of the 90CRA sample was about eight times less than that of the 0CRA sample. This was further corroborated by Mott-Schottky analysis, which showed a lowering of both acceptor and donor densities with the reduction in grain size. The evolution of a strong <111> texture during cryo-rolling contributed towards enhanced corrosion resistance of nano-grained 316L. Furthermore, grain refinement improved wettability, which in turn led to better cell proliferation and differentiation. At all culture days, MC3T3-E1 cell proliferation and differentiation were considerably higher for nano-grained 316L micron-sized counterparts. Thus, grain refinement to the nano range is an effective technique for the property enhancement of biomedical implants.

Characterization of defects in additively manufactured materials from mechanical properties

Minimization of defects in additively manufactured components is essential for material development and the determination of fabrication process windows. Here, a purely mechanical means of quantifying porosity in a material is developed based on the Mori–Tanaka mean field theory. The micromechanics based defect quantification approach developed here links the elastic properties of a material with the specific defect structures that must exist within it to obtain those properties. Laser powder bed fusion is used to fabricate aluminum 6061 with three different processing conditions to produce nominally identical samples with unique defect microstructures. Test samples are imaged with microcomputed X-ray tomography (μCT) and the images are classified with a machine learning method to identify the volume fraction of pores, solidification cracks, and the orientation distribution function of the solidification cracks. Tensile tests are then conducted in the z-axis and within the xy-plane to measure the respective elastic moduli and the Poisson’s ratio. These three commonly measured material properties are the only inputs to the new micromechanics based approach used to infer the same defect descriptors that were extracted from μCT. Excellent agreement is found between defect descriptors obtained with both methods, and quantities derived from the mechanical properties are found to carry substantially lower uncertainty. Full error propagation maps for the micromechanics based technique are calculated. Notably, defect descriptors from the micromechanics based approach are calculated from strain and load measurements, which are measured on much larger length scales than the defect size. This enables simple quantification of defects for materials containing small defects that are challenging to image.

Nonlinear optimization for compact representation of orientation distributions based on generalized spherical harmonics

An orientation distribution is a necessary input in any crystal plasticity simulation. The computational time involved in crystal plasticity simulations scales linearly with the number of crystal orientations in the input distributions. Reducing the number of crystal orientations in representing the input orientation distributions quantitatively is a critical and necessary requirement for performing computationally efficient crystal plasticity simulations of deformation processes. A procedure for the compaction of orientation distribution functions (ODFs) relying on a spectral representation using series of generalized spherical harmonics (GSH) basis functions was recently developed. Linear fitting of the spectral representation of an ODF containing a compact set of weighted orientations towards a full-size ODF containing many crystal orientations was in the core of the procedure. This paper advances the compaction procedure by replacing the linear with a nonlinear optimization in Matlab for which a suitably defined error, gradient, and Hessian matrix are derived to allow for more efficient, accurate, and greater compactions. The utility of the new procedure is to allow for not only fitting the weights of a compacted set of orientations but to allow for optimizing weighted orientations or a combination of optimizing weights and orientations. The new compaction procedure has been successfully applied to compactions of large ODFs of cubic, hexagonal, and orthorhombic polycrystalline metals. In doing so, the evolution of texture, twinning, and stress-strain are predicted at large plastic strains with compact ODFs to agree with the corresponding full size ODFs using crystal plasticity models. In closing, guidance for effective texture compaction trading off the accuracy and computational gains are provided.

High-resolution simulating of grain substructure in cold rolling and its effects on primary recrystallization in annealing of ferritic stainless steel

In this study, an integrated crystal plasticity and cellular automaton (CA) model has been developed and employed to investigate the processes of cold rolling and annealing in ferritic stainless steel. Crystal plasticity simulates the deformation microstructure, deformation texture and corresponding dislocation density distribution in the cold rolled ferritic stainless steel. Meanwhile, CA predicts the microstructural evolution originating from nucleation and growth. The resolution of the crystal plasticity model has been improved using a newly developed remeshing technique, which allows for the capture of the grain substructure in the deformation microstructure. The developed model has been validated by experimental measurements with electron backscatter diffraction (EBSD) in terms of comparing the orientation distribution functions (ODFs), misorientation, local substructures, and grain size. The good agreement between simulations and experiments indicates that the developed crystal plasticity with CA model is reliable and efficient for predicting the microstructure and texture evolutions during cold rolling and subsequent annealing.

Microstructure-Sensitive Deformation Modeling and Materials Design with Physics-Informed Neural Networks

Microstructure-sensitive materials design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function. A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called the physics-informed neural network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of the Ti-7Al alloy by solving an inverse design problem to match the PINN-predicted final texture prediction and the experimental data.

Gait impairment-related axonal degeneration in Parkinson's disease by neurite orientation dispersion and density imaging.

Microstructural alterations in the brain networks of Parkinson's disease (PD) patients are correlated with gait impairments. Evaluate microstructural alterations in the white matter (WM) fiber bundle tracts using neurite orientation dispersion and density imaging (NODDI) technique in PD versus healthy controls (HC). In this study, 24 PD patients and 29 HC were recruited. NODDI and high-resolution 3D structural images were acquired for each participant. The NODDI indicators, including the intracellular neurite density index (NDI), orientation dispersion index (ODI), and isotropic volume fraction (ISO), were compared between the two groups. Diffusion-weighted (DW) images were preprocessed using MRtrix 3.0 software and the orientation distribution function to trace the main nerve fiber tracts in PD patients. Quantitative gait and clinical assessment scales were used to compare the medication "ON" and "OFF" states of PD patients. The NDI, ODI, and ISO values of the WM fiber bundles were significantly higher in PD patients compared to HC. Fiber bundles, including the anterior thalamic radiation, corticospinal tract, superior longitudinal fasciculus, forceps major, cingulum, and inferior longitudinal fasciculus, were found to be significantly affected in PD. The NDI changes of PD patients were well correlated with stride lengths in the "ON" state; ODI changes were correlated with the stride time in the "ON" and "OFF" states and ISO changes were correlated with the stride time and cadence in the "ON" state. In conclusion, combination of NODDI technique and gait parameters can help detect gait impairment in PD patients early and accurately.