C. M. Hefferan

Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy

The evolution of the crystallographic orientation field in a polycrystalline sample of copper is mapped in three dimensions as tensile strain is applied. Using forward-modeling analysis of high-energy X-ray diffraction microscopy data collected at the Advanced Photon Source, the ability to track intragranular orientation variations is demonstrated on an ∼2 µm length scale with ∼0.1° orientation precision. Lattice rotations within grains are tracked between states with ∼1° precision. Detailed analysis is presented for a sample cross section before and after ∼6% strain. The voxel-based (0.625 µm triangular mesh) reconstructed structure is used to calculate kernel-averaged misorientation maps, which exhibit complex patterns. Simulated scattering from the reconstructed orientation field is shown to reproduce complex scattering patterns generated by the defected microstructure. Spatial variation of a goodness-of-fit or confidence metric associated with the optimized orientation field indicates regions of relatively high or low orientational disorder. An alignment procedure is used to match sample cross sections in the different strain states. The data and analysis methods point toward the ability to perform detailed comparisons between polycrystal plasticity computational model predictions and experimental observations of macroscopic volumes of material.

Probing Microstructure Dynamics With X-Ray Diffraction Microscopy

We describe our recent work on developing X-ray diffraction microscopy as a tool for studying three dimensional microstructure dynamics. This is a measurement technique that is demanding of experimental hardware and presents a challenging computational problem to reconstruct the sample microstructure. A dedicated apparatus exists at beamline 1-ID of the Advanced Photon Source for performing these measurements. Submicron mechanical precision is combined with focusing optics that yield ≈2 μm high × 1.3 mm wide line focused beam at 50 keV. Our forward modeling analysis approach generates diffraction from a simulated two dimensional triangular mesh. Each mesh element is assigned an independent orientation by optimizing the fit to experimental data. The method is computationally demanding but is adaptable to parallel computation. We illustrate the state of development by measuring and reconstructing a planar section of an aluminum polycrystal microstructure. An orientation map of ∼90 grains is obtained along with a map showing the spatial variation in the quality of the fit to the data. Sensitivity to orientation variations within grains is on the order of 0.1 deg. Volumetric studies of the response of microstructures to thermal or mechanical treatment will soon become practical. It should be possible to incorporate explicit treatment of defect distributions and to observe their evolution.

Implementation and verification of a microstructure-based capability for modeling microcrack nucleation in LSHR at room temperature

A microstructure-based capability for forecasting microcrack nucleation in the nickel-based superalloy LSHR is proposed, implemented, and partially verified. Specifically, gradient crystal plasticity is applied to finite-element models of the experimentally measured, 3D microstructure wherein a microcrack is known to have nucleated along a coherent Σ3 boundary. The framework is used to analyze this particular nucleation event and conduct an extensive grain boundary analysis study, the results of which underpin the importance that elastic anisotropy and coherency have in the localization of plastic slip.

Tests of microstructure reconstruction by forward modeling of high energy X-ray diffraction microscopy data

Verification tests of the forward modeling technique for near-field high energy X-ray diffraction microscopy are conducted using two simulated microstructures containing uniformly distributed orientations. Comparison between the simulated and reconstructed microstructures is examined with consideration to both crystallographic orientation and spatial geometric accuracy. To probe the dependence of results on experimental parameters, simulated data sets use two different detector configurations and different simulated experimental protocols; in each case, the parameters mimic the experimental geometry used at Advanced Photon Source beamline 1-ID. Results indicate that element orientations are distinguishable to less than 0.1°, while spatial geometric accuracy is limited by the detector resolution.

Simulation domain size requirements for elastic response of 3D polycrystalline materials

A fast Fourier transform (FFT) based spectral algorithm is used to compute the full field mechanical response of polycrystalline microstructures. The field distributions in a specific region are used to determine the sensitivity of the method to the number of surrounding grains through quantification of the divergence of the field values from the largest simulation domain, as successively smaller surrounding volumes are included in the simulation. The analysis considers a mapped 3D structure where the location of interest is taken to be a particular pair of surface grains that enclose a small fatigue crack, and synthetically created statistically representative microstructures to further investigate the effect of anisotropy, loading condition, loading direction, and texture. The synthetic structures are generated via DREAM3D and the measured material is a cyclically loaded, Ni-based, low solvus high refractory (LSHR) superalloy that was characterized via 3D high energy x-ray diffraction microscopy (HEDM). Point-wise comparison of distributions in the grain pairs shows that, in order to obtain a Pearson correlation coefficient larger than 99%, the domain must extend to at least the third nearest neighbor. For an elastic FFT calculation, the stress–strain distributions are not sensitive to the shape of the domain. The main result is that convergence can be specified in terms of the number of grains surrounding a region of interest.

Quantifying Damage Accumulation Using State-of-the-Art FFT Method

A 3D microstructure, measured by high-energy x-ray diffraction microscopy, is used as an input to a parallelized viscoplastic Fast Fourier Transform code (VPFFT) to simulate a tensile test. Distributions of strain, damage accumulation, neighbor interactions, and Schmid factor mismatch throughout the microstructure are calculated. These results will form the basis of a direct comparison to microstructure maps that track plastic deformation in the real sample.

In Situ Observation of Recovery and Grain Growth in High Purity Aluminum

We have used high energy x-ray diffraction microscopy (HEDM) to study annealing behavior in high purity aluminum. In-situ measurements were carried out at Sector 1 of the Advanced Photon Source. The microstructure in a small sub-volume of a 1 mm diameter wire was mapped in the as-received state and after two differential anneals. Forward modeling analysis reveals three dimensional grain structures and internal orientation distributions inside grains. The analysis demonstrates increased ordering with annealing as well as persistent low angle internal boundaries. Grains that grow from disordered regions are resolution limited single crystals. Together with this recovery behavior, we observe subtle motions of some grain boundaries due to annealing.

Image processing in experiments on, and simulations of plastic deformation of polycrystals

Comparisons between experiments and simulations of deformation of polycrystalline materials reveal some interesting challenges [1]. Addressing first the image processing issues, electron back-scatter diffraction (EBSD) [2] relies heavily on image transformations of electron diffraction patterns. High energy diffraction microscopy (HEDM) [3] also relies on thresholding of the diffractograms for peak identification [4]. By contrast to the standard finite element method, an image-based approach [5] that relies on the Fast Fourier Transform (FFT) has started to be used for simulating plastic deformation because it offers a more efficient solution of the same equations (e.g. mechanical equilibrium). It is possible, for example, to import directly a measured 3D image from HEDM into the FFT simulation code and simulate with no need for the time-consuming step of creating a 3D mesh. Common filters applied to orientation maps in particular, include grain average strain, Kernel Average Misorientation (KAM), Grain Orientation Spread (GOS), Intragranular Grain Misorientation (IGM).