Michael A. Groeber

DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D

This paper presents a software environment for processing, segmenting, quantifying, representing and manipulating digital microstructure data. The paper discusses the approach to building a generalized representation strategy for digital microstructures and the barriers encountered when trying to integrate a set of existing software tools to create an expandable codebase.

Modeling Cyclic Deformation of HSLA Steels Using Crystal Plasticity

High strength low alloy (HSLA) steels, used in a wide variety of applications as structural components are subjected to cyclic loading during their service lives. Understanding the cyclic deformation behavior of HSLA steels is of importance, since it affects the fatigue life of components. This paper combines experiments with finite element based simulations to develop a crystal plasticity model for prediction of the cyclic deformation behavior of HSLA-50 steels. The experiments involve orientation imaging microscopy (OIM) for microstructural characterization and mechanical testing under uniaxial and stress-strain controlled cyclic loading. The computational models incorporate crystallographic orientation distributions from the OIM data. The crystal plasticity model for bcc materials uses a thermally activated energy theory for plastic flow, sell and latent hardening, kinematic hardening, as well as yield point phenomena. Material parameters are calibrated from experiments using a genetic algorithm based minimization process. The computational model is validated with experiments on stress and strain controlled cyclic loading. The effect of grain orientation distributions and overall loading conditions on the evolution of microstructural stresses and strains are investigated.

CAD-based reconstruction of 3D polycrystalline alloy microstructures from FIB generated serial sections

This paper develops a robust CAD-based methodology for simulating 3D microstructures of polycrystalline metals using crystallographic input data on sections created by a focused ion beam (FIB)-scanning electron microscopy (SEM) system. The method is able to construct consistent polycrystalline microstructures with control on the resolution necessary for meaningful computational analysis in microstructure-property estimation. The microstructure simulation methodology is based on a hierarchical geometrical representation using primitives used in CAD modeling. It involves steps of data cleanup, interface point identification, polynomial and NURBS function-based parametric surface segments construction, generalized cell decomposition, geometric defeaturing, and gap and overlap removal. The implementation of the entire procedure described above is performed with the aid of user-programming facilities of a commercial CAD package Unigraphics NX3. The microstructure simulation algorithm is validated using various error criteria and measures for an extracted microstructure of a nickel superalloy.

The influence of microstructure on surface strain distributions in a nickel micro-tension specimen

This work presents an integrated experimental and modeling approach for examining the deformation of a pure nickel polycrystal utilizing micro-mechanical testing and a crystal-based elasto-viscoplastic finite-element model (CPFEM). The objective is to study the influence of microstructure on the heterogeneous deformation in polycrystalline materials, and to utilize a modeling framework to explore aspects of the deformation that are difficult or impossible to measure experimentally. To accomplish this, a micro-tension specimen containing 259 grains was created from a pure nickel foil material and deformed in uniaxial tension. After the deformation, the specimen was destructively serial sectioned in concert with electron back scattering diffraction, and these data were used to instantiate a CPFEM simulation. The material parameters in the CPFEM model were calibrated by matching the experimental macroscopic stress-strain response of the micro-tension specimen, and then the simulation results were compared with experimental surface deformations measured with digital image correlation. After validating the simulation results by comparing measured and predicted surface strain distributions, a parametric study of the influence of both crystallographic texture and grain morphology is presented to better understand the influence of microstructure on the development of heterogeneous deformation in the pure nickel polycrystalline material.

Tail Departure of Log-Normal Grain Size Distributions in Synthetic Three-Dimensional Microstructures

Polycrystalline materials are generally thought to have grain size distributions that correspond to log-normal. Statistical volume elements can use such geometric shape distributions to simulate single-phase polycrystals. When the log-normal distribution is used for grain size, however, it can give rise to nonphysical large grains that cannot be practically accommodated in finite simulation volumes. The application of other distributions that afford better control of the upper tails, e.g., truncated distributions, resolves the problem and allows more representative distributions to be generated. These points are illustrated with an example of generation of a synthetic three-dimensional (3-D) microstructure to represent the nickel-based superalloy Inconel 100, which exhibits significant upper tail departure from log-normal. Twin insertion, to represent annealing twins, will also be discussed.

Experimental measurement of surface strains and local lattice rotations combined with 3D microstructure reconstruction from deformed polycrystalline ensembles at the micro-scale

This article describes a new approach to characterize the deformation response of polycrystalline metals using a combination of novel micro-scale experimental methodologies. An in-situ scanning electron microscope (SEM)-based tension testing system was used to deform micro-scale polycrystalline samples to modest and moderate plastic strains. These tests included measurement of the local displacement field with nm-scale resolution at the sample surface. After testing, focused ion beam serial sectioning experiments that incorporated electron backscatter diffraction mapping were performed to characterize both the internal 3D grain structure and local lattice rotations that developed within the deformed micro-scale test samples. This combination of experiments enables the local surface displacements and internal lattice rotations to be directly correlated with the underlying 3D polycrystalline microstructure, and such information can be used to validate and guide further development of modeling and simulation methods that predict the local plastic deformation response of polycrystalline ensembles.

An Automated Multi-Modal Serial Sectioning System for Characterization of Grain-Scale Microstructures in Engineering Materials

This paper describes the development of a new serial sectioning system that has been designed to collect microstructural, crystallographic, and chemical information from volumes in excess of 1 mm3. The system integrates a robotic multi-platen mechanical polishing system with a modern SEM that enables the acquisition of multi-modal data—scanning electron images, EBSD and hyperspectral EDS map—at each section. Selected details of the system construction as well as an initial demonstration of the system capabilities are presented.

h5ebsd: an archival data format for electron back-scatter diffraction data sets

We present an archival format for electron back-scatter diffraction (EBSD) data based on the HDF5 scientific file format. We discuss the differences between archival and data work flow file formats, and present details of the archival file layout for the implementation of h5ebsd, a vendor-neutral EBSD-HDF5 format. Information on sample and external reference frames can be included in the archival file, so that the data is internally consistent and complete. We describe how the format can be extended to include additional experimental modalities, and present some thoughts on the interactions between working files and archival files. The complete file specification as well as an example h5ebsd formatted data set are made available to the reader.

A Supervised Learning Approach for Dynamic Sampling.

Sparse sampling schemes have the potential to reduce image acquisition time by reconstructing a desired image from a sparse subset of measured pixels. Moreover, dynamic sparse sampling methods have the greatest potential because each new pixel is selected based on information obtained from previous samples. However, existing dynamic sampling methods tend to be computationally expensive and therefore too slow for practical application. In this paper, we present a supervised learning based algorithm for dynamic sampling (SLADS) that uses machine-learning techniques to select the location of each new pixel measurement. SLADS is fast enough to be used in practical imaging applications because each new pixel location is selected using a simple regression algorithm. In addition, SLADS is accurate because the machine learning algorithm is trained using a total reduction in distortion metric which accounts for distortion in a neighborhood of the pixel being sampled. We present results on both computationally-generated synthetic data and experimentallycollected data that demonstrate substantial improvement relative to state-of-the-art static sampling methods. Introduction In conventional point-wise image acquisition, all pixels in a rectilinear grid are measured. However, in many imaging applications, a high-fidelity pixel measurement could take up to 1 second. Examples of such methods include electron back scatter diffraction (EBSD) microscopy and Raman spectroscopy, which are of great importance in material science and chemistry [1]. Then, acquiring a complete set of high-resolution measurements on these imaging applications becomes impractical. Sparse sampling offers the potential to dramatically reduce the time required to acquire an image. In this approach, a sparse set of pixels is measured, and the full resolution image is reconstructed from the set of sparse measurements. In addition to speeding image acquisition, sparse sampling methods also hold the potential to reduce the exposure of the object being imaged to destructive radiation. This is of critical importance when imaging biological samples using X-rays, electrons, or even optical photons [2, 3]. Sparse sampling approaches fall into two main categories: static and dynamic. In static sampling, pixels are measured in a pre-defined order. Examples of static sparse sampling methods include random sampling strategies such as in [4], and lowdiscrepancy sampling [5]. As a result some samples from these methods may not be very informative, as they do not take into account the object being scanned. There are static sampling methods based on an a priori knowledge of the object geometry and sparsity such as [6, 7]. However a priori knowledge is not always available for general imaging applications On the other hand, dynamic sampling (DS) methods adaptively determine new measurement locations based on the information obtained from previous measurements. This is a very powerful technique since in real applications previous measurements can tell one a great deal about the object being scanned and also about the best locations for future measurements Therefore, dynamic sampling has the potential to dramatically reduce the total number of samples required to achieve a particular level of distortion in the reconstructed image. An example of a dynamic sampling method was proposed in [8] by Kovačević et al. Here initially an object is measured with a sparse grid. Then, if the intensity of a pixel is above a certain threshold, the vicinity of that pixel is measured in higher resolution. However, the threshold was empirically chosen for the specific scanner and thus this method cannot be generalized for different imaging modalities. For general applications, a set of DS methods has been proposed in previous literature where an objective function is designed and the measurements are chosen to optimize that objective function. For instance, dynamic compressive sensing methods [9–11] find the next measurements that maximally reduces the differential entropy. However, dynamic compressive sensing methods use an unconstrained projection as a measurement and therefore are not suitable for point-wise measurements where the measurement is constrained. Apart from these methods, application specific DS methods that optimize an objective function to find the next measurement have been developed. One example is [12], where the authors modify the optimal experimental design [13] framework to incorporate dynamic measurement selection in a biochemical network. Seeger et al. in [14] also finds the measurement that reduces the differential entropy the most but now to select optimal K-space spiral and line measurements for magnetic resonance imaging (MRI). In addition, Batenburg et al. [15] propose a DS method for binary computed tomography in which the measurement that maximizes the information gain is selected. Even though these measurements are constrained they are application specific and therefore not applicable to general point-wise measurements. In [16] Godaliyadda et al. propose a DS algorithm for general point-wise measurements. Here, the authors use a MonteCarlo simulation method to approximate the conditional variance at every unmeasured location, given previous measurements, and select the pixel with largest conditional variance. However, Monte-Carlo simulation methods such as the Metropolis-Hastings method are very slow and therefore this method is infeasible for real-time applications. Furthermore, the objective function in this method does not account for the change of conditional variance in ©2016 Society for Imaging Science and Technology DOI: 10.2352/ISSN.2470-1173.2016.19.COIMG-153 IS&T International Symposium on Electronic Imaging 2016 Computational Imaging XIV COIMG-153.1 the entire image with a new measurement. In this paper, we propose a new DS algorithm for point-wise measurements named supervised learning approach for dynamic sampling (SLADS). The objective of SLADS is to select a new pixel so as to maximally reduce the conditional expectation of the reduction in distortion (ERD) in the entire reconstructed image. In SLADS, we compute the reduction in distortion for each pixel in a training data set, and then find the relationship between the ERD and a local feature vector through a regression algorithm. Since we use a supervised learning approach, we can very rapidly estimate the ERD at each pixel in the unknown testing image. Moreover, we introduce a measure that approximates the distortion reduction in the training dataset so that it accounts for the distortion reduction in the pixel and its neighbors. Since computing the distortion reduction for each pixel during training can be intractable, particularly for large images, this approximation is vital to make the training procedure feasible. Experimental results on sampling a computationally-generated synthetic EBSD image and an experimentally-collected image have shown that SLADS can compute a new sample locations very quickly (in the range of 5 500 ms), and can achieve the same reconstruction distortion as static sampling methods with dramatically fewer samples (2-4 times fewer). Dynamic Sampling Framework The objective in sparse sampling is to measure a sparse set of pixels in an image and then reconstruct the full resolution image from those sparse samples. Moreover, with sparse dynamic sampling, the location for each new pixel to measure will be informed by all the previous pixel measurements. To formulate the problem, we denote the image we would like to measure as X ∈ RN , where Xr is a pixel at location r ∈ Ω. Furthermore, let us assume that k pixels have been measured at a set of locations S = {s(1), · · · ,s(k)}, and that the corresponding measured values and locations are represented by the k×2 matrix Y (k) =  s,Xs(1) .. s,Xs(k)  . Then from Y (k), we can reconstruct an image X̂ (k), which is our best estimate of X given the first k measurements. Now, if we select Xs as our next pixel to measure, then presumably we can reconstruct a better estimate of the image, which we will denote by X̂ (k;s). So then X̂ (k;s) is our best estimate of X given both Y (k) and Xs. So at this point, our goal is to select the next location s(k+1) that results in the greatest decrease in reconstruction distortion. In order to formulate this problem, let D(Xr, X̂r) denote the distortion measure between a pixel Xr and its estimate X̂r, and let D(X , X̂) = ∑ r∈Ω D(Xr, X̂r) , (1) denote the total distortion between the image X and its estimate X̂ . Then using this notation, we may define R r to be the local reduction in distortion at pixel r that would result from the measurement of the pixel Xs. R r = D(Xr, X̂ (k) r )−D(Xr, X̂ (k;s) r ) (2) Importantly, the measurement of the pixel Xs does not only reduce distortion at that pixel. It also reduces the distortion at neighboring pixels. So in order to represent the total reduction in distortion, we must sum over all pixels r ∈Ω. R(k;s) = ∑ r∈Ω R r (3) = D(X , X̂ (k))−D(X , X̂ (k;s)) . (4) Now of course, we do not know what the value of Xs until it is measured; so we also do not know the value R(k;s). Therefore, we must make our selection of the next pixel based on the conditional expectation of reduction in distortion which we will refer to as the ERD given by R̄(k;s) = E [ R(k;s)|Y (k) ] . (5) So with this notation, our goal is to efficiently compute the next pixel to sample, s(k+1), as the solution to the following optimization. s(k+1) = arg max s∈{Ω\S } ( R̄(k;s) ) (6) Once we measure the location Xs(k+1) , then we form the new measurement vector Y (k+1) = [ Y (k) s,Xs(k+1) ]

Automated detection and characterization of microstructural features: application to eutectic particles in single crystal Ni-based superalloys

Serial sectioning methods continue to produce an abundant amount of image data for quantifying the three-dimensional nature of material microstructures. Here, we discuss a methodology to automate detecting and characterizing eutectic particles taken from serial images of a production turbine blade made of a heat-treated single crystal Ni-based superalloy (PWA 1484). This method includes two important steps for unassisted eutectic particle characterization: automatically identifying a seed point within each particle and segmenting the particle using a region growing algorithm with an automated stop point. Once detected, the segmented eutectic particles are used to calculate microstructural statistics for characterizing and reconstructing statistically representative synthetic microstructures for single crystal Ni-based superalloys. The significance of this work is its ability to automate characterization for analysing the 3D nature of eutectic particles.