View Video Presentation: https://doi.org/10.2514/6.2023-1087.vid The goal of this study is to characterize and validate the texture and grain topology of additively-manufactured anisotropic 3D polycrystalline microstructures. The special focus is on developing methodologies to compare the grain shapes and orientations of 2D and 3D microstructure representations using the same metric. To generate statistical data, synthetic microstructures are reconstructed from experimental data using Markov Random Field (MRF). The statistical similarity between the experimental and synthetic microstructures is verified by comparing their grain topologies. A universal measure to compare 2D and 3D grains is portrayed through the concept of image moments that are invariant to shape transformations. The graphical plots developed based on moment invariants to compare the 2D and 3D grains are used to verify the synthetic model.

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

A data-driven framework is developed and examined for creating spatially-varying crystallographic textures over component-scale Computer-Aided Design (CAD) models. Here, a set of three orthogonal 2D micrographs of an Additively-Manufactured (AM) specimen are first obtained experimentally through Electron Backscatter Diffraction (EBSD) and subsequently converted to a 3D representative unit cell using the Markov Random Field (MRF) technique. Features such as grain size, crystallographic orientation, and grain boundary misorientation distributions are used to validate the reconstructed 3D microstructure against input experimental EBSD images. The variations of microstructural features during a powder-based additive manufacturing process are subsequently modeled by merging patches from the 3D snapshot of AM microstructural unit cell in a part-scale geometry using a tensor-based optimization process. The optimization algorithm repeatedly pastes microstructural elements from the reconstructed MRF unit cell onto the geometrical CAD domain until it is entirely covered. Here, through a simple Graphical User Interface (GUI), the user specifies a tensor field over the volumetric CAD model, defining the local control over grain-scale, anisotropy, and crystal growth orientation. This new approach provides a workflow for reconstructing global maps of AM microstructures in real-time by embedding site-specific images based on known AM microstructural patterns seen in experimental characterization techniques. The numerical results are helpful specifically for the visualization of process–microstructure relationships in metal additive manufacturing techniques.

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities ( e.g., fracture and crack propagation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the weak integral formulation in non-local approximations of the deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor- based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero- energy mode oscillations in all of the numerical examples.

The present work uses Markov Random Field (MRF) algorithm to construct large-scale and statistically -equivalent samples from small-scale experimental data of metallic microstructures. While the MRF method can build such digital material representations in large computational domains, its algorithmic stochasticity (epistemic uncertainty) causes variations in the resulting microstructural features, such as the texture and grain topology. This work addresses the effects of the epistemic uncertainty on homogenized mechanical properties by characterizing the variations in the microstructural features using a shape descriptor based on the concept of moment invariants. In particular, 2D and 3D synthetic microstructure data for Titanium-7wt%Aluminum (Ti-7Al) alloy is generated with the MRF method using smaller-scale 2D experimental data. To quantify the uncertainty of the reconstructed synthetic samples, a graphical method and five different metrics of statistical variability are developed. Next, the propagation of the microstructural uncertainty on homogenized properties is studied using an analytical uncertainty quantification (UQ) algorithm and Gaussian Process Regression (GPR).

A three-dimensional (3D) peridynamics (PD) model of crystal plasticity (CP) is presented for predicting the fine-scale localization in polycrystalline microstructures undergoing elastoplastic deformation. Microscale data from electron microscopy and digital image correlation have indicated that slip localizations arise early in deformation and act as precursors to mechanical failure and fracture. However, classical numerical approaches such as crystal plasticity finite element methods (CPFEM) are generally unable to predict the emergence and distribution of such localizations. Alternatively, the PD formulation has attracted significant attention for its unique treatment of deformation in the presence of high strain gradient fields. In this paper, a mesh-free non-ordinary state-based PD technique is developed for simulating the elasto-plastic deformation of 3D polycrystalline aggregates of a magnesium alloy. This work presents the details of 3D polycrystal plasticity modeling using PD theory with experimental and CPFEM comparisons. The results from this model are validated against published experimental data for the stress-strain response and texture evolution. The crystal plasticity peridynamic (CPPD) models are successful in simulating grain averaged strains seen in the experiment and depict well-resolved regions of strain localization.

Measurement and analysis of microstructures is an essential aspect of materials design and structural performance. In the case of surface experimental measurements such as digital image correlation (DIC), it is beneficial to know the subsurface microstructure to interpret the surface observations accurately. However, subsurface microstructures are expensive to obtain through three-dimensional (3D) tomography. Hence, it is of interest to generate these structures computationally. In this work, a generalized inverse Voronoi problem is used to grow an approximate representation of the 3D microstructure from a surface electron backscatter diffraction (EBSD) image. The novelty of the approach is that the surface microstructure is retained during the simulation. This technique is employed for the reconstruction of a recrystallized magnesium alloy microstructure. Crystal plasticity finite element modeling (CPFEM) was employed for comparing the predicted surface strains in the reconstructed 3D microstructures against experimentally measured data. It is observed that the surface strains of different 3D reconstructions are qualitatively similar to the experiment. However, strong basal slip activation in some subsurface grains can influence the choice of activated slip systems on surface microstructures. The results show the implications of performing a full 3D crystal plasticity analysis of measured surface data as compared to only analyzing a two-dimensional extruded microstructure.

A new numerical method is presented for reconstructing three-dimensional (3D) microstructures from two-dimensional (2D) sections, imaged on orthogonal planes, by exploiting the complete red–green–blue (RGB) color space. The algorithm reconstructs 3D models through sampling voxel neighborhoods to representative 2D micrographs, based upon a Markovian assumption. The sampling is followed by an optimization procedure, ensuring smoothness across the orthogonal sections of the synthesized voxels. Previous 3D Markov random field (MRF) microstructure reconstruction techniques were restricted to traditional grayscale images only. This method now enables the use of the entire RGB spectrum, employing a histogram matching step. This paper examines the algorithm’s accurate representation of orientations and morphologies, encompassing a variety of micrographs from electron backscatter diffraction (EBSD) and polarized light microscopy.