Unsupervised Learning for Efficient Texture Estimation From Limited Discrete Orientation Data

The estimation of orientation distribution functions (ODFs) from discrete orientation data, as produced by electron backscatter diffraction or crystal plasticity micromechanical simulations, is typically achieved via techniques such as the Williams–Imhof–Matthies–Vinel (WIMV) algorithm or generalized spherical harmonic expansions, which were originally developed for computing an ODF from pole figures measured by X-ray or neutron diffraction. These techniques rely on ad-hoc methods for choosing parameters, such as smoothing half-width and bandwidth, and for enforcing positivity constraints and appropriate normalization. In general, such approaches provide little or no information-theoretic guarantees as to their optimality in describing the given dataset. In the current study, an unsupervised learning algorithm is proposed which uses a finite mixture of Bingham distributions for the estimation of ODFs from discrete orientation data. The Bingham distribution is an antipodally-symmetric, max-entropy distribution on the unit quaternion hypersphere. The proposed algorithm also introduces a minimum message length criterion, a common tool in information theory for balancing data likelihood with model complexity, to determine the number of components in the Bingham mixture. This criterion leads to ODFs which are less likely to overfit (or underfit) the data, eliminating the need for a priori parameter choices.     

Gradient-based microstructure reconstructions from distributions using fast Fourier transforms

Reconstructions are an important step in analyzing the statistics of local state distributions in the internal structure of heterogeneous material systems and in estimating their effective properties using deterministic models. In this paper, we demonstrate the use of fast Fourier transforms (FFTs) and gradient-based algorithms for the reconstruction of microstructure realizations from 2-point statistics. The FFT method greatly improves the computational efficiency of the algorithm, facilitating use of the full set of 2-point statistics in the reconstruction. This approach introduces periodic boundary conditions naturally into the model. The reconstruction of several two-phase 2D structures is demonstrated, resulting in exact replicas of the original microstructures. The limitations of the technique, especially for more complex structures, are also discussed.     

Application of composites to impact energy absorption

The sleeve, conical simple composite elements and polymer foam filled composite conical element behaviour during failure are presented and discussed. The impact energy in these elements is absorbed in progressive fracture process. Possibilities of energy absorption panels – the great structures made from simple elements in a certain military and civilian field are demonstrated.     

Effect of reinforcement size on the scratch resistance and crystallinity of HVOF sprayed nylon-11/ceramic composite coatings

The high-velocity oxyfuel (HVOF) combustion spraying of dry ball-milled nylon-11/ceramic composite powders is an effective, economical, and environmentally sound method for producing semicrystalline micron and nanoscale reinforced polymer coatings. Composite coatings reinforced with multiple scales of ceramic particulate material are expected to exhibit improved load transfer between the reinforcing phase and the matrix due to interactions between large and small ceramic particles. An important step in developing multiscale composite coatings and load transfer theory is determining the effect of reinforcement size on the distribution of the reinforcement and the properties of the composite coating. Composite feedstock powders were produced by dry ball-milling nylon-11 together with 7, 20, and 40 nm fumed silica particles, 50 and 150 nm fumed alumina particles, and 350 nm, 1, 2, 5, 10, 20, 25, and 50 μm white calcined alumina at 10 vol.% overall ceramic phase loadings. The effectiveness of the ball-milling process as a function of reinforcement size was qualitatively evaluated by scanning electron microscopy+energy dispersive x-ray spectroscopy (SEM+EDS) microanalysis and by characterizing the behavior of the powder during HVOF spraying. The microstructures of the sprayed coatings were characterized by optical microscopy, SEM, EDS, and x-ray diffraction (XRD). The reinforcement particles were found to be concentrated at the splat boundaries in the coatings, forming a series of interconnected lamellar sheets with good three-dimensional distribution. The scratch resistance of the coatings improved consistently and logarithmically as a function of decreasing reinforcement size and compared with those of HVOF sprayed pure nylon-11. This article was originally published inBuilding on 100 Years of Success, Proceedings of the 2006 International Thermal Spray Conference (Seattle, WA), May 15–18, 2006, B.R. Marple, M.M. Hyland, Y.-Ch. Lau, R.S. Lima, and J. Voyer, Ed., ASM International, Materials Park, OH, 2006.     

Introducing Grain Boundary Influenced Stochastic Effects into Constitutive Models

Twinning is an important deformation mechanism in hexagonal close-packed (hcp) metals such as Mg, Zr, Ti, and Be. Twinning in hcp materials is a multiscale process that depends on microstructural and mechanical response details at the mesoscale, microscale, and atomic scales. Twinning can generally be understood as a two-step process, a nucleation step followed by propagation. The nucleation of twins is governed by both material details such as the defect configurations at potential nucleation sites within grain boundaries, as well as the highly local mechanical field near grain boundaries. These two factors, the material and mechanical, must align for a successful nucleation event. In this article, we present a stochastic constitutive law for nucleation of twins and describe its implementation into a homogenized crystal plasticity simulation. Twin nucleation relies on the dissociation of grain boundary defects under stress into the required twinning partials. This dissociation is considered to follow a Poisson process where the parameters of the Poisson distribution are related to the properties of the grain boundaries. The rate of the process is a direct function of the local stress concentration at the grain boundary. These stress concentrations are randomly sampled from a distribution calibrated to full-field crystal plasticity simulations.     

Applications of the Phase-Coded Generalized Hough Transform to Feature Detection,Analysis, and Segmentation of Digital Microstructures

The generalized Hough transform is a common technique for feature detection in image processing. In this paper, we develop a size invariant Hough framework for the detection of arbitrary shapes in three dimensional digital microstructure datasets. The Hough transform is efficiently implemented via kernel convolution with complex Hough filters, where shape is captured in the magnitude of the filter and scale in the complex phase. In this paper, we further generalize the concept of a Hough filter by encoding other parameters of interest (e.g. orientation of plate or fiber constituents) in the complex phase, broadening the applicability of Hough transform techniques. We demonstrate the application of these techniques to feature detection in micrographs (2-D) and three-dimensional (3-D) microstructure datasets, and explore their utility to the closely related applications of feature based image segmentation and calculation of 3-D microstructure metrics.     

Development of the Cube Component $$ \left( {\left\{ 001 \right\}\left\langle {100} \right\rangle } \right) $$ During Plane Strain Compression of Copper and Its Importance in Recrystallization Nucleation

Metallurgical and Materials Transactions A - The origin of cube texture during recrystallization of medium to high stacking-fault energy FCC metals has been debated for several decades. However,...     

Spatially resolved in situ strain measurements from an interior twinned grain in bulk polycrystalline AZ31 alloy

In this paper, we report for the first time, to our knowledge, spatially resolved measurements of strain gradients across a grain containing twins, located in the bulk of a polycrystalline Mg AZ31 sample. We also report orientation mapping on three parallel sections from the bulk of the sample. We use for such purpose the technique of differential-aperture X-ray microscopy (DAXM) based on synchrotron X-rays. The DAXM technique allows us to map crystallographic strains with sub-micron-sized spatial resolution. The results of this experiment confirm indirect evidence from previous experiments having less spatial resolution that important stress gradients exist in the vicinity of twin boundaries. Such a result is relevant to understanding twin growth and de-twinning, since both mechanisms are affected by stress-driven twin dislocations at the interface.