Stephen R. Niezgoda

Microstructure sensitive design for performance optimization

Abstract The accelerating rate at which new materials are appearing, and transforming the engineering world, only serves to emphasize the vast potential for novel material structure, and related performance. Microstructure-sensitive design (MSD) aims at providing inverse design methodologies that facilitate design of material internal structure for performance optimization. Spectral methods are applied across the structure, property and processing design spaces in order to compress the computational requirements for linkages between the spaces and enable inverse design. Research has focused mainly on anisotropic, polycrystalline materials, where control of local crystal orientation can result in a broad range of property combinations. This review presents the MSD framework in the context of both the engineering advances that have led to its creation, and those that complement or provide alternative methods for design of materials (meaning ‘optimization of material structure’ in this context). A variety of definitions for the structure of materials are presented, with an emphasis on correlation functions; and spectral methods are introduced for compact descriptions and efficient computations. The microstructure hull is defined as the design space for structure in the spectral framework. Reconstruction methods provide invertible links between statistical descriptions of structure, and deterministic instantiations. Subsequently, structure–property relations are reviewed, and again subjected to representation via spectral methods. The concept of a property closure is introduced as the design space for performance optimization, and methods for moving between the closures and hulls are presented as the basis for the subsequent discussion on microstructure design. Finally, the spectral framework is applied to deformation processes, and methodologies that facilitate process design are reviewed.

Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data

The study of microstructure and its relation to properties and performance is the defining concept in the field of materials science and engineering. Despite the paramount importance of microstructure to the field, a rigorous systematic framework for the quantitative comparison of microstructures from different material classes has yet to be adopted. In this paper, the authors develop and present a novel microstructure quantification framework that facilitates the visualization of complex microstructure relationships, both within a material class and across multiple material classes. This framework, based on the stochastic process representation of microstructure, serves as a natural environment for developing relational statistical analyses, for establishing quantitative microstructure descriptors. In addition, it will be shown that this new framework can be used to link microstructure visualizations with properties to develop reduced-order microstructure-property linkages and performance models.

An integrated full-field model of concurrent plastic deformation and microstructure evolution: Application to 3D simulation of dynamic recrystallization in polycrystalline copper

Abstract Many time-dependent deformation processes at elevated temperatures produce significant concurrent microstructure changes that can alter the mechanical properties in a profound manner. Such microstructure evolution is usually absent in mesoscale deformation models and simulations. Here we present an integrated full-field modeling scheme that couples the mechanical response with the underlying microstructure evolution. As a first demonstration, we integrate a fast Fourier transform-based elasto-viscoplastic (FFT-EVP) model with a phase-field (PF) recrystallization model, and carry out three-dimensional simulations of dynamic recrystallization (DRX) in polycrystalline copper. A physics-based coupling between FFT-EVP and PF is achieved by (1) adopting a dislocation-based constitutive model in FFT-EVP, which allows the predicted dislocation density distribution to be converted to a stored energy distribution and passed to PF, and (2) implementing a stochastic nucleation model for DRX. Calibrated with the experimental DRX stress–strain curves, the integrated model is able to deliver full-field mechanical and microstructural information, from which quantitative description and analysis of DRX can be achieved. It is suggested that the initiation of DRX occurs significantly earlier than previous predictions, due to heterogeneous deformation. DRX grains are revealed to form at both grain boundaries and junctions (e.g., quadruple junctions) and tend to grow in a wedge-like fashion to maintain a triple line (not necessarily in equilibrium) with old grains. The resulting stress redistribution due to strain compatibility is found to have a profound influence on the subsequent dislocation evolution and softening.

Analysis of traction‐free assumption in high‐resolution EBSD measurements

The effects of using a traction‐free (plane‐stress) assumption to obtain the full distortion tensor from high‐resolution EBSD measurements are analyzed. Equations are derived which bound the traction‐free error arising from angular misorientation of the sample surface; the error in recovered distortion is shown to be quadratic with respect to that misorientation, and the maximum ‘safe’ angular misorientation is shown to be 2.7 degrees. The effects of localized stress fields on the traction‐free assumption are then examined by a numerical case study, which uses the Boussinesq formalism to model stress fields near a free surface. Except in cases where localized stress field sources occur very close to sample points, the traction‐free assumption appears to be admirably robust.

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.

Demonstration of near Field High Energy X-Ray Diffraction Microscopy on High-Z Ceramic Nuclear Fuel Material

Near-field high energy x-ray diffraction microscopy (nf-HEDM) and high energy x-ray micro-tomography (μT) have been utilized to characterize the pore structure and grain morphology in sintered ceramic UO2 nuclear fuel material. μT successfully images pores to 2-3μm diameters and is analyzed to produce a pore size distribution. It is apparent that the largest number of pores and pore volume in the sintered ceramic are below the current resolution of the technique, which might be more appropriate to image cracks in the same ceramics. Grain orientation maps of slices determined by nf-HEDM at 25 μm intervals are presented and analyzed in terms of grain boundary misorientation angle. The benefit of these two techniques is that they are non-destructive and thus could be performed before and after processes (such as time at temperature or in-reactor) or even in-situ.

Efficient computation of the angularly resolved chord length distributions and lineal path functions in large microstructure datasets

Chord length distributions (CLDs) and lineal path functions (LPFs) have been successfully utilized in prior literature as measures of the size and shape distributions of the important microscale constituents in the material system. Typically, these functions are parameterized only by line lengths, and thus calculated and derived independent of the angular orientation of the chord or line segment. We describe in this paper computationally efficient methods for estimating chord length distributions and lineal path functions for 2D (two dimensional) and 3D microstructure images defined on any number of arbitrary chord orientations. These so called fully angularly resolved distributions can be computed for over 1000 orientations on large microstructure images (5003 voxels) in minutes on modest hardware. We present these methods as new tools for characterizing microstructures in a statistically meaningful way.

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.

Symmetrized Bingham distribution for representing texture: parameter estimation with respect to crystal and sample symmetries

The quaternion Bingham distribution has been used to model preferred crystallographic orientation, or crystallographic texture, in polycrystalline materials in the materials science and geological communities. A primary difficulty in applying the Bingham distribution has been the lack of an efficient method for fitting the distribution parameters with respect to the materials underlying crystallographic symmetry or any statistical sample symmetry due to processing. In this paper we present a symmetrized distribution, based on the quaternion Bingham, which can account for any general combination of crystallographic or sample symmetries. We also introduce a numerical scheme for estimating the parameters of the symmetrized distribution based on the well known expectation maximization algorithm.

Shear Banding in Bulk Metallic Glass Matrix Composites with Dendrite Reinforcements

Bulk metallic glass matrix composites (BMGMCs) with metallic dendrite reinforcements combine the excellent strength, hardness, and elastic strain limit of amorphous metallic glass with a ductile crystalline phase to achieve extraordinary toughness with minimal degradation in strength. In order to explore the mechanical interactions between the amorphous and crystalline phases a full-field micromechanical model, which couples a free volume based constitutive model for the matrix with crystal plasticity, has been implemented in an elastic-viscoplastic Fast-Fourier Transform (FFT) solver. The findings indicate that in BMGMCs, local inhomogeneities in the glass phase are less influential on the mechanical performance than the contrast in individual phase properties. Due to the strong contrast in mechanical properties, heterogenous stress fields develop, contributing to regionally confined free volume generation, localized flow and softening in the glass. In these softened regions, plastic flow rapidly localizes into shear bands.