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Dislocation-density evolution and pileups in bicrystalline systems
Here, a dislocation-density crystalline plasticity (DCP) framework based on total and partial dislocation densities interactions was used to investigate the behavior of Cu/Pb bicrystals with a focus on GB effects. The modeling predictions were validated with bicrystal compression micropillar experiments. A key new aspect of the modeling approach is to account for partial dislocation-densities. A GB formulation that is directly linked to GB energies was used to monitor GB transmission and blockages, such that pileups can be monitored and predicted at the GB interfaces for misorientations. The predictions indicate that pileups can form due to fully and partially blocked slip-rates and perfect and partial dislocation-densities. As the nominal strain increases from five to fifteen percent, dislocation-densities and pileups significantly increase by almost an order of magnitude. The proposed validated approach provides a microstructural scale predictive framework that accounts for a myriad of defects related to the interactions of partial and perfect dislocation densities that interact at highly misoriented GBs; it is these interactions that are critical to the formation and evolution of dislocation-density pileups that can lead to physically limiting stress accumulations in bicrystals.
Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg 4Al using in situ tensile testing in scanning electron microscope and HR-EBSD
In situ tensile testing in a scanning electron microscope (SEM) in conjunction with high-resolution electron backscatter diffraction (HR-EBSD) under load was used to characterize the evolution of geometrically necessary dislocation (GND) densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg—4Al alloy. The increase in GND density was investigated at plastic strains of 0 %, 0.6 %, 2.2 %, 3.3 % from the area including 76 grains and correlated with (i) geometric compatibility between slip systems across grain boundaries, and (ii) plastic incompatibility. We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility, from which uniaxial tensile stress-strain response of polycrystalline Mg—4Al are computed and compared with experimental measurement. The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.
Rules for the crystallite size and dislocation density evolution in phases during α-ω transformation in Zr under high-pressure and severe plastic flow
The first in-situ X-ray diffraction (XRD) study of the evolution of the crystallite size and dislocation density in phases during plastic strain-induced phase transformation (PT) is performed utilizing α-ω PT in strongly pre-deformed commercially pure Zr as an important example. Rough diamond anvils (rough-DA) are introduced to intensify all occurring processes during heterogeneous compression of Zr in a diamond anvil cell (DAC). The main rule is found that during α-ω PT the crystallite size and dislocation density in ω-Zr depend solely on the volume fraction of ω-Zr and are independent of pressure, plastic strain tensor, its path, and initial nanostructure. Crystallite size in ω-Zr increases from 10 to 60 nm during the PT, while dislocation density reduces from 1.83×10 15 /m 2 to 0.6×10 15 /m 2 . Rough-DA produce a steady nanostructure in α-Zr before PT with smaller crystallite size and larger dislocation density than smooth-DA, leading to a reduction of the minimum pressure for α-ω PT to a record value 0.67 GPa, 9 times smaller than under hydrostatic loading and 5.1 times lower than the phase equilibrium pressure. In addition to strain, the kinetics of strain-induced PT unexpectedly depends on time. Also, strain-controlled part of kinetics is zero order, in contrast to the first-order kinetics with smooth-DA. The obtained results open a new window for understanding the mutual effects of nanostructure evolution and PT during severe plastic flow in various technological and natural processes. In conclusion, they may bring up economic strategies of producing nanocomposites and single-phase nanostructured materials with optimal properties.
Simulation of dislocation evolution in microparticle impacts over a wide range of impact velocities
We report the dynamic loading environment created by high velocity microparticle impacts is very difficult to model. The extremely high strain rates, large deformations, and high temperatures affect the flow stress of the material in ways that standard flow stress models cannot capture. Plastic deformation and strain hardening in metals is controlled by the motion of dislocations. Dislocations can be nucleated, stored as forest dislocations, or be annihilated as loading progresses. A comprehensive accounting of dislocation density change is needed to accurately describe rate and temperature dependent dislocation glide and evolution across the wide rage of loading conditions present in microparticle impact problems. Therefore, we implement and apply a newly proposed flow stress model (Hunter and Preston, 2015, 2022) that is then coupled with mobile and immobile dislocation density evolution equations. This model is implemented in Los Alamos National Laboratory’s hydrodynamics code, FLAG, to model copper-on-copper microparticle impacts. This new strength model allows for accurate simulation of particle rebound and flattening across a wide range of impact velocities.
Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)
The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.
Deformation, dislocation evolution and the non-Schmid effect in body-centered-cubic single- and polycrystal tantalum
A physically-informed continuum crystal plasticity model is presented to elucidate deformation mechanisms, dislocation evolution and the non-Schmid effect in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show the unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10 -3 s -1 ) to extreme strain rates (5000 s -1 ) and at low (77 K) to high temperatures (873 K) at both single- and polycrystal levels. Here we also present predictive capabilities of the model for microstructural evolution in the material. To this end, we investigate the effects of dislocation interactions on slip activities, instability and the non-Schmid behavior at the single crystal level. Furthermore, ex situ measurements on crystallographic texture evolution and dislocation density growth are carried out for polycrystal tantalum specimens at increasing strains. Numerical simulation results also support that the modeling framework is capable of capturing the main features of the polycrystal behavior over a wide range of strains, strain rates and temperatures. The theoretical, experimental and numerical results at both single- and polycrystal levels provide critical insight into the underlying physical pictures for micro- and macroscopic responses and their relations in this important class of refractory bcc materials undergoing large inelastic deformations.
A data driven approach for cross-slip modelling in continuum dislocation dynamics
Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. Here, in this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.
Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact
This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. Here, the advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso-scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FEEPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.
In situ synchrotron investigation of tensile deformation and failure mechanisms in cold spray Cr-coated Zr-alloy system
Not Available
Phase-field modeling of stored-energy-driven grain growth with intra-granular variation in dislocation density
Abstract We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.
The Challenges of Modeling Defect Behavior and Plasticity across Spatial and Temporal Scales: A Case Study of Metal Bilayer Impact
Atomistic molecular dynamics (MD) and a microstructural dislocation density-based crystalline plasticity (DCP) framework were used together across time scales varying from picoseconds to nanoseconds and length scales spanning from angstroms to micrometers to model a buried copper–nickel interface subjected to high strain rates. The nucleation and evolution of defects, such as dislocations and stacking faults, as well as large inelastic strain accumulations and wave-induced stress reflections were physically represented in both approaches. Both methods showed similar qualitative behavior, such as defects originating along the impactor edges, a dominance of Shockley partial dislocations, and non-continuous dislocation distributions across the buried interface. The favorable comparison between methods justifies assumptions used in both, to model phenomena, such as the nucleation and interactions of single defects and partials with reflected tensile waves, based on MD predictions, which are consistent with the evolution of perfect and partial dislocation densities as predicted by DCP. This substantiates how the nanoscale as modeled by MD is representative of microstructural behavior as modeled by DCP.
Damage Accumulations Predictions for Boiler Components Via Microstructurally Informed Material Models
The goal of the project was to model material behavior and degradation during cyclic plasticity— with and without hold time—for nickel-based superalloys used in USC (ultra-super-critical) and A-USC (advanced-ultra-super-critical) boiler components. The study provided physically informed models, capturing the microstructural changes taking place in the industrial components under cyclic loading and long duration stress (up to 300,000 hours) and high temperature exposure (1100°F/593°C to 1400°F/760°C). The major developments were: 1) Qualitative and quantitative understanding of microstructure evolution (gamma prime precipitates), deformation (dislocation density), and damage mechanisms of Haynes ® 282 alloy. 2) Qualitative understanding of microstructural features generating local strain variations. 3) A continuum damage mechanics model (CDM) for Haynes ® 282 alloy at 1100°F to 1400°F capturing cyclic behavior with and without hold time. 4) Structural analysis for creep and LCF life predictions of an USC thick-wall Grade 91 superheater steel header and understanding life sensitivity to wall thickness of an AUSC Haynes ® 282 header.
Phase-field modeling of radiation-induced composition redistribution: An application to additively manufactured austenitic Fe–Cr–Ni
Multicomponent alloys undergoing irradiation damage develop radiation-induced composition redistribution at point defect sinks such as grain boundaries (GBs) and dislocations. Such redistribution results in undesired changes to their mechanical behavior and corrosion resistance. Additively manufactured alloys proposed for future nuclear applications are expected to demonstrate a distinct response to irradiation owing to their unique microstructure with as-solidified dislocation density and chemical microsegregation. To capture the composition redistribution in such systems, we develop a mesoscale model with coupled evolution of atomic and point defect components in the presence of dislocation density, dislocation heterogeneity, and thermodynamic interactions at the GB. The model is parameterized for an FCC Fe–Cr–Ni alloy as a representative system for austenitic stainless steels, and simulations are performed in 1D and 2D as a function of irradiation temperature, dose, dislocation density, and grain size. Radiation-induced segregation (RIS) characterized by Cr depletion and Ni enrichment is predicted at both the GB and the dislocation cell wall, with RIS being lower in magnitude but wider at the cell wall. Strongly biased absorption of self-interstitials by dislocations is found to suppress Ni enrichment but slightly enhance Cr depletion under certain conditions. Thermodynamic segregation at the GB is predicted to be narrower and opposite in sign to RIS for both Cr and Ni. Importantly, non-monotonic segregation is found to occur when both thermodynamic and RIS mechanisms are considered, providing a novel physical interpretation of experimental observations. The model is expected to serve as a key tool in accelerated qualification of irradiated materials.
Effect of loading path on grain misorientation and geometrically necessary dislocation density in polycrystalline aluminum under reciprocating shear
Solid phase processing (SPP) is a promising alloy fabrication technique to produce fine and homogeneous grain structures for high-performance alloys. However, there is very limited modeling capability to understand and predict the grain refinement during SPP. In this work, the crystal plasticity theory was used to study elastic-plastic deformation in polycrystalline aluminums under large shear deformation. Two approaches, kernel averaged misorientation (KAM) and grain reference orientation deviation (GROD), were used to assess the grain misorientations. The geometrically necessary dislocation (GND) density was computed with the plastic strain rate. The deformation simulations were carried out under two loading conditions to investigate the effect of loading paths on the evolutions of grain misorientation and GND density. The results show that the regions with high misorientation and GND density first appear near grain boundaries. These regions then extend toward interior grains. The loading path affects dislocation system activation and dislocation recovery, hence dislocation evolution and misorientation. In conclusion, both two- and three-dimensional simulations showed that the spatial and temporal evolutions of GROD, KAM, and GND density in are closely correlated, which indicates they all can be used as criteria of grain refinement or recrystallization.
Evolution of dislocations during the rapid solidification in additive manufacturing
Materials processed by fusion-based additive manufacturing (AM) typically exhibit relatively high dislocation densities, along with cellular structures and elemental segregation. This representative structural feature significantly influences material performance; however, post-mortem microstructure characterizations of AM materials cannot capture the dynamic evolution of dislocations during the manufacturing process, thereby offering limited mechanism-based guidance for further advancing AM techniques and facilitating the qualification and certification of AM products. In this study, we conduct operando high-energy synchrotron X-ray diffraction experiments on wire-laser directed energy deposition of 316 L stainless steel. Through a unique configuration, our operando synchrotron experiments semi-quantitatively probe the dislocation density in solid phases and their dynamic changes during solidification and subsequent cooling. By integrating this advanced synchrotron technique with multi-physics simulation, in-situ neutron diffraction, and multi-scale electron microscopy characterization, our mechanistic study aims to elucidate the effects of rapid cooling and subsequent thermal cycling on the dislocation generation and evolution.
The effect of heat treatment on the defect evolution in LPBF 316H stainless steel
This work investigates the effect of processing and heat treatment on defect evolution and irradiation response of laser powder bed fusion (LPBF) 316H stainless steel, with comparisons to LPBF 316L and wrought 316L/316H. Using in-situ and ex-situ ion irradiations across a wide parameter space—temperature (300–675 °C), dose (0.2–25 dpa), dose rate (10 -3 –10 -5 dpa/s), and helium co-implantation (20–2500 appm)—we correlated void swelling, dislocation loop evolution, and segregation behavior with pre-irradiation microstructures (as-built, stress-relieved, solution-annealed, and cold-worked). Results show that swelling is strongly controlled by dislocation density: intermediate densities maximize swelling, while solution annealing or cold working reduce susceptibility to levels comparable to wrought alloys. Low dose rates and helium both promote cavity nucleation and lower the incubation barrier, with helium suppressing the role of dislocation density and driving swelling behavior toward wrought-like response. Loop evolution in SA LPBF 316H resembles wrought 316L but shows localized denuded zones near low-angle grain boundaries. STEM-EDS mapping further revealed Ni segregation at voids and sparse Al-rich oxides, without evidence of Ni–Si precipitates. Collectively, these findings identify dislocation density, helium content, and dose rate as the factors governing swelling in LPBF 316H and provide mechanistic datasets for model validation, supporting LAIN and the qualification of AM austenitic steels for nuclear service.
Fundamental Study of Fatigue Crack Initiation at Grain and Twin Boundaries in Austentic Stainless Steel (Final Technical Report)
The overarching goal of this project was to understand the dislocation-based mechanisms driving fatigue crack initiation at grain and twin boundaries. The hypothesis of the work is that dislocation structures equivalent to persistent slip bands (PSBs) form in the boundaries, leading to local stress concentrations and fatigue crack initiation. The sub-goals associated with this work include: • Understanding the evolution of the dynamic stress state and dislocation density surrounding PSB/grain boundary interactions. This will require the development of new techniques that couple high resolution electron backscatter diffraction (HREBSD) with in situ scanning electron microscopy (SEM) deformation. • Uncover the mechanisms by which dislocations are accommodated in grain and twin boundaries during fatigue. The proposed approach here is to conduct in situ transmission electron microscopy (TEM) deformation experiments on fatigued samples. • Establish correlations between microstructure, deformation accommodation, and crack initiation across time and length scales. This work primarily focuses on understanding fatigue crack initiation in austenitic stainless steels, though promising work by an undergraduate researcher extended the work to high purity Al.