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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Measuring residual stress in Ti-6Al-4V with HR-EBSD, using reference patterns from annealed material

In this study, elastic strain and residual stress values in an engineering material were determined by high-resolution EBSD (HR-EBSD) using reference patterns from annealed, recrystallized material. Specifically, rolled Ti-6Al-4V sheet was analyzed using HR EBSD in both an as-annealed and a strained state, the latter established via a static two-point bend fixture. The commercial software CrossCourt4 (CC4) was used to evaluate the relative intragranular strain tensor components of the alpha grains mapped by HR-EBSD. The intragranular reference patterns identified in each grain by the software were then replaced with similarly-oriented patterns from scans of the as-annealed, recrystallized material. The CC4 analysis was then repeated to provide calibrated strain and residual stress values. Elastic strains on the order of 10–3 were detected, with corresponding residual stress values on the order of 1 GPa. Subsequent analyses using high energy synchrotron x-ray diffraction showed good correlation with the elastic strains measured by HR-EBSD using the annealed reference patterns. Additionally, the maximum macroscopic stress analytically predicted for two-point bending was in agreement with the residual stress observed. Good repeatability of the methodology and insight into the state of individual grains were also observed. The findings provide encouraging evidence that accurate intragranular and long-range residual stress measurements of engineering significance can be made with HR-EBSD using a physical reference pattern library.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Micromechanical Fields Associated with Irregular Deformation Twins in Magnesium

Understanding and controlling the development of deformation twins is paramount for engineering strong and stable hexagonal close-packed (HCP) Mg alloys. Actual twins are often irregular in boundary morphology and twin crystallography, deviating from the classical picture commonly used in theory and simulation. In this work, the elastic strains and stresses around irregular twins are examined both experimentally and computationally to gain insight into how twins develop and the microstructural features that influence their development. A nanoprecession electron diffraction (N-PED) technique is used to measure the elastic strains within and around a $\left\{ {10\overline{1}2} \right\}$ tensile twin in AZ31B Mg alloy with nm scale resolution. A full-field elasto-viscoplastic fast Fourier transform (EVP-FFT) crystal plasticity model of the same sub-grain and irregular twin structure is employed to understand and interpret the measured elastic strain fields. The calculations predict spatially resolved elastic strain fields in good agreement with the measurement, as well as all the stress components and the dislocation density fields generated by the twin, which are not easily obtainable from the experiment. The model calculations find that neighboring twins, several twin thicknesses apart, have little influence on the twin-tip micromechanical fields. Furthermore, this work reveals that irregularity in the twin-tip shape has a negligible effect on the development of the elastic strains around and inside the twin. Importantly, the major contributor to these micromechanical fields is the alignment of the twinning shear direction with the twin boundary.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Part-scale evolution of fine-scale microstructural heterogeneity in solid-state additive manufacturing

Current solid-state additive manufacturing methods, refined through costly and time-consuming trial and error, have spurred interest in computational models that replicate material behavior under typical thermomechanical conditions (e.g., strain-rate ~ 102 s−1). These models, however, struggle to capture time-dependent microstructural evolution. In this work, Additive Friction-Stir Deposition (AFSD) is used as a representative case study for part-scale quantification of microstructure evolution at a fine spatial resolution (200 μm) by examining a liquid-nitrogen-cooled stop-action build via energy-dispersive X-ray diffraction coupled with a multi-channel detector. These results inform modeling efforts by linking process asymmetry to stored plastic strain, residual elastic strain, and texture development, and unlike current state-of-the-art characterization methods (e.g., EBSD or neutron diffraction), this approach provides both the spatial resolution and collection efficiency necessary to quantify fine-scale microstructural heterogeneity over large component volumes. As such, this technique provides essential validation data for computational models, e.g., crystal plasticity, enabling future prediction of heterogeneous behavior in AFSD and other additive manufacturing processes.

Franz, Cole [ORNL] (ORCID:0000000213465881)↗
DOE OSTI2020

Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Fifth-degree elastic energy for predictive continuum stress-strain relations and elastic instabilities under large strain and complex loading in silicon

Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

Levitas, Valery↗
DOE OSTI2025

Informed unsupervised machine learning analysis of dislocation microstructure from high-resolution differential aperture X-ray structural microscopy data

This study leverages high-resolution differential-aperture X-ray structural microscopy (DAXM) to probe the local dislocation structure in deformed 304L-stainless steel at small strain, by measuring the lattice rotation and deviatoric elastic strain with a sub-micron resolution. For a single grain in a polycrystalline specimen, the measured lattice rotation field over the measured volume exhibited a multimodal distribution while the deviatoric elastic strain showed a single-mode distribution. An unsupervised Cauchy mixture machine learning model was developed to resolve the multimodal distribution of the lattice rotation. By mapping the lattice rotation data associated with each Cauchy peak in the model back onto the measured volume, we identify contiguous regions of the crystal rotated near the average values corresponding to the peaks of the overall rotation distribution. These regions represent the grain subdivision in the microstructure. Finally, the dislocation density tensor was also computed and its norm was laid over the rotation field to detect the subgrain boundaries. This step provided a validation of the Cauchy mixture model for the analysis of the lattice rotation distribution. The current study highlights the integration of advanced X-ray microscopy techniques with data-driven analysis methods to uncover detailed microstructure scales in deformed crystals.

Machine learning; Lattice rotation; High-energy X-↗
DOE OSTI2021

A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity

Production of hydrocarbons and water from subsurface reservoirs are known to cause permanent deformation of the reservoir and seismicity along faults both of which are detrimental to sustainable development of natural resources. Most of the prior studies on understanding fluid flow-induced plasticity and seismicity have focused on one or the other phenomenon due to the numerical difficulty associated with simultaneous modeling of the two failure phenomena because stress and deformation evolve non-linearly in both plasticity and seismicity. However, in reservoirs undergoing long-term production, plastic failure can alter the stress paths of points on a fault such that the onset, location, and magnitude of actual seismic events can no longer be predicted by a poroelastic simulation due to inaccurate stress and deformation history. We present a computational framework for coupled multiphase flow, finite strain poroplastic deformation, and dynamic fault slip and use it to understand the impact of plastic deformation on the onset, location, and magnitude of induced fault slip events. We evaluate the impact of plasticity on reservoir pressure, deformation, induced stress, and fault slip by comparing infinitesimal strain elastic and finite strain poro-elastoplastic models. For real-world applications, we consider different scenarios where the reservoir is either mechanically weaker or stronger than the caprock. We analyze the stress evolution as a function of the change in reservoir pressure to understand the role of contrast in reservoir and caprock elastic moduli on geomechanical stability. The results show that the poroplastic reservoir exhibits larger vertical deformation and delayed slip than the poroelastic reservoir after the same amount of oil production. For the same amount of pressure drop, a reservoir with a smaller modulus than the caprock displays a larger vertical displacement and an earlier onset of both plastic failure and fault slip. For a reservoir with a larger modulus than the caprock, vertical displacement is larger on the reservoir top boundary and smaller on the ground surface, and a higher pressure drop is needed to induce plastic failure and fault slip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Phase-Field Model Incorporating Large Inelastic Strain with Application to the Oxidation of High-Temperature Coating Systems

Structural metallic and ceramic materials at high temperatures often suffer from creep, fatigue and oxidation, which typically involves local large inelastic strain. The large strain is usually approached by Lagrangian-description-based finite deformation theory. Here we develop an efficient, Eulerian-description-based, Incremental Realization of Inelastic Deformation (IRID) algorithm to deal with large inelastic strain with small elastic strain. We apply this algorithm to simulate high temperature oxidation with severe volume expansion using a phase-field approach. The oxidation and deformation of bond coat can lead to spallation and failure of the thermal barrier coatings (TBC) and environmental barrier coatings (EBC), which is a critical concern in design of these coatings. We simulate the growth of thermally grown oxide (TGO) in these coating systems, with phase transformations and microstructure evolution incorporated. The simulation results are compared with relevant experimental reports in the literature.

Cheng, Tianle↗
DOE OSTI2024

Multimodal 3D quantification of particle stimulated nucleation in industrially manufactured aluminium AA5182 sheet

Particle stimulated nucleation is a dominant recrystallisation mechanism observed in many industrially relevant aluminium alloys during thermomechanical processing. Here, in this work, we quantify particle stimulated nucleation in 3D in an aluminium AA5182 alloy sheet cold-rolled to 75% thickness reduction. Second phase particles and nuclei are mapped in the same sample volume by conventional laboratory absorption X-ray tomography and synchrotron X-ray Laue micro-diffraction. The large second phase particles are classified as Fe- and Mg-rich phases. It is found that 84% of the nuclei are particle stimulated and 40% of the particles stimulate nucleation. The critical particle diameter is found to be 4 μm. Deviatoric elastic strains are derived from micro-diffraction data and it is found that elastic strains are present in the recrystallised nuclei. The effects of the different particle types, particle clustering, particle size and aspect ratio as well as strain inheritance are discussed. This work provides a full 3D quantification of particle stimulated nucleation behaviour in AA5182 alloy sheet deformed to high strain.

Deviatoric strain↗
DOE OSTI2023

A reference-area-free strain mapping method using precession electron diffraction data

Here, in this work, we developed a method using precession electron diffraction data to map the residual elastic strain at the nano-scale. The diffraction pattern of each pixel was first collected and denoised. Template matching was then applied using the center spot as the mask to identify the positions of the diffraction disks. Statistics of distances between the selected diffracted disks enable the user to make an informed decision on the reference and to generate strain maps. Strain mapping on an unstrained single crystal sapphire shows the standard deviation of strain measurement is 0.5%. With this method, we were able to successfully measure and map the residual elastic strain in VO 2 on sapphire and martensite in a Ni 50.3 Ti 29.7 Hf 20 shape memory alloy. This approach does not require the user to select a “strain-free area” as a reference and can work on datasets even with the crystals oriented away from zone axes. This method is expected to provide a robust and more accessible alternative means of studying the residual strain of various material systems that complements the existing algorithms for strain mapping.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Rapid Nb 3 Sn film growth by sputtering Nb on hot bronze

Nb deposited by magnetron sputtering onto hot Cu-15 wt.%Sn bronze substrates at temperatures above 700 °C achieved Nb 3 Sn film growth at a rate of 33 nm min -1 , which was an order of magnitude faster than that achieved for deposition of Nb on bronze at low temperature followed by in situ post reaction at the same high temperatures. Tin content in the Nb 3 Sn films made on hot bronze was ~26.3%, which is significantly higher than ~24.5% obtained by post-reaction as well as for typical bulk reactions between Nb and α -bronze. The Nb 3 Sn lattice parameter was consistent with measured tin content and predicted elastic strain for both routes. Critical temperatures of 14 K–16 K, instead of 18 K, were consistent with elastic strain due to coefficient of thermal expansion mismatch between the Nb 3 Sn and bronze substrate and, for the hot-bronze samples, stress related to the growth mechanism. Films were fully coalesced and had surface roughness values <20 nm over a 100 μ m 2 scan. Grain structure of the Nb 3 Sn films produced by Nb sputtering on hot bronze resembles zone 2 in the Thornton structure-zone diagram, in contrast to the equiaxed grain structure reminiscent of microstructure observed in reacted Nb 3 Sn wires exhibited by the post-reaction route.

Physics↗
DOE OSTI2022

3D Bragg Coherent Diffraction Imaging of Extended Nanowires: Defect Formation in Highly Strained InGaAs Quantum Wells

InGaAs quantum wells embedded in GaAs nanowires can serve as compact near-infrared emitters for direct integration onto Si complementary metal oxide semiconductor technology. While the core–shell geometry in principle allows for a greater tuning of composition and emission, especially farther into the infrared, the practical limits of elastic strain accommodation in quantum wells on multifaceted nanowires have not been established. One barrier to progress is the difficulty of directly comparing the emission characteristics and the precise microstructure of a single nanowire. Here, in this study, we report an approach to correlating quantum well morphology, strain, defects, and emission to understand the limits of elastic strain accommodation in nanowire quantum wells specific to their geometry. We realize full 3D Bragg coherent diffraction imaging (BCDI) of intact quantum wells on vertically oriented epitaxial nanowires, which enables direct correlation with single-nanowire photoluminescence. By growing In 0.2 Ga 0.8 As quantum wells of distinct thicknesses on different facets of the same nanowire, we identified the critical thickness at which defects are nucleated. A correlation with a traditional transmission electron microscopy analysis confirms that BCDI can image the extended structure of defects. Finite element simulations of electron and hole states explain the emission characteristics arising from strained and partially relaxed regions. This approach, imaging the 3D strain and microstructure of intact nanowire core–shell structures with application-relevant dimensions, can aid the development of predictive models that enable the design of new compact infrared emitters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

In-situ high energy X-ray diffraction study of deformation behavior in Nb nanoparticle-martensitic NiTi composite wire

Here, this study investigated the deformation behavior in Nb nanoparticle-martensitic NiTi composite wire during tensile loading by means of in-situ high-energy X-ray diffraction. Compared to Nb nanowires, the dispersedly distributed Nb nanoparticles have little effect on the transformation and deformation behaviors of NiTi matrix, causing the absence of R phase transformation and the occurrence of deformation twinning in NiTi matrix. Meanwhile, the occurrence of deformation twinning in NiTi matrix can reduce the shape strain to be coordinated by the unfavorable orientated martensite variants, and thus decreases the internal stress among NiTi martensite variants generated during martensite reorientation process. In addition, TEM result proved that Nb nanoparticles can achieve exceptionally large elastic strain in B19'-NiTi matrix (~4%), just as Nb nanowires. However, this large elastic strain (stress) will be released with the occurrence of NiTi deformation twinning.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Local residual stresses and microstructure within recrystallizing grains in iron

The intragranular strains and the microstructure within recrystallizing grains in single phase pure iron have been systematically studied in 3D using synchrotron micro-diffraction. In contradiction to common knowledge we observe that residual elastic strains of up to 1–2 × 10 –3 are present in the recrystallizing grains. The local strain variations within individual grains can be similar in magnitude to those between different grains. The effects of processing parameters, including rolling reduction, recrystallized volume fraction, and cooling rate, as well as microstructural parameters, including grain size, orientation and internal misorientation, on the development of local residual elastic strains and microstructure have been quantified. It is suggested that the difference in local defect density between recrystallized grains and the surrounding deformed matrix, as well as the redistribution of medium to long-range residual stresses in the deformed grains, are the main reasons for the development of such strains in the recrystallized grains. The local residual stress levels are calculated and their possible impact on the mechanical properties and recrystallization processes are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Anisotropic structure and optical engineering of strontium titanate and zirconia responding to sequential hydrogen and helium irradiation

Unraveling the correlation between strain engineering with anisotropic optical properties via nanoscale defects gradually evolved into a strategy for fundamental studies and technological applications, yet it remains understudied in functional complex oxides compared to metals and semiconductors. Here, the methodology of strain engineering for the determination of the lattice parameters, parallel/normal to the sample surface, in the individual layers of single-crystalline superlattices is derived, which is based on analysis of high-angle X-ray diffraction measurements in combination with diffraction reciprocal space mapping. With modeling that takes into account the effect of elastic properties, two elastically anisotropic materials, SrTiO 3 and ZrO 2 , have been compared in terms of defect-induced elastic strain caused by individual and sequential H + and He 2+ irradiation. The anisotropic lattice swelling with corresponding refractive index, and obstructive behavior of elastic strain recovery are demonstrated in SrTiO 3 , while approaching strain behaviors accompanied by isotropic refractive index distribution in both orientations are confirmed in ZrO 2 . Under sequential He 2+ /H + irradiation, pre-existing He-vacancy complexes acted as vacancy traps, preferentially capturing H + clusters to induce lattice distortion and enhance absorption. Nanohardness increments (ΔH) calculated by the DBH model matched nanoindentation results, confirming that sequential irradiation generated higher indentation yield stress than individual irradiations.

Anisotropic expansion↗
DOE OSTI2025

Overcoming the Damping–Elasticity Paradox via 3D‐Printed NiTiSn Nanocomposite

Abstract Developing high damping alloys (HDAs) with large elastic strain has attracted growing attention due to the increasing demand for energy absorption with overload reliability and reusability. However, damping capacity inherently conflicts with elasticity, because the former requires a liable movement of crystal defects while the latter opposite. To deal with the damping‐elasticity paradox, the advantage of pseudobinary eutectic reaction and rapid cooling of laser powder bed fusion is taken to fabricate a bulk NiTiSn nanocomposite with a two‐level hierarchical structure. The first‐level architecture is composed of martensitic NiTi nanolamellae and reinforced Ti 3 Sn nanolamellae. In addition to lattice strain matching and lamellar boundary strengthening, a novel mechanism of martensite reorientation mediated by reversible stress‐induced detwinning‐twinning is activated to generate large elastic strain. A high density of nanotwins and nanodomains within NiTi nanolamellae constitute the second‐level architecture, which provides pronounced internal friction for high damping capacity. As a result, our NiTiSn nanocomposite exhibits a record‐high integration of damping capacity (tanδ > 0.10) and elastic strain (exceeding 4.5%), as well as superb stability under cyclic overload. This research not only represents a major breakthrough in achieving HDAs with outstanding damping and elastic strain but also offers a novel paradigm for high‐performance functional and structural materials.

Chemistry↗
DOE OSTI2021

Tuning magnetic antiskyrmion stability in tetragonal inverse Heusler alloys

The identification of materials supporting complex, tunable magnetic order at ambient temperatures is foundational to the development of new magnetic device architectures. In this work, we report the design of Mn 2 XY tetragonal inverse Heusler alloys that are capable of hosting magnetic antiskyrmions whose stability is sensitive to elastic strain. Here We first construct a universal magnetic Hamiltonian capturing the short- and long-range magnetic order which can be expected in these materials. This model reveals critical combinations of magnetic interactions that are necessary to approach a magnetic phase boundary, where the magnetic structure is highly susceptible to small perturbations such as elastic strain. We then computationally search for quaternary Mn 2 (X 1 , X 2 ) Y alloys where these critical interactions may be realized and which are likely to be synthesizable in the inverse Heusler structure. We identify the Mn 2 Pt 1–z X z Ga family of materials with X = Au, Ir, Ni as an ideal system for accessing all possible magnetic phases, with several critical compositions where magnetic phase transitions may be actuated mechanically.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗