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Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics
Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.
Statistics of internal stress fluctuations in dislocated crystals and relevance to density-based dislocation dynamics models
A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. Finally, the implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.
Discrete stochastic model of point defect-dislocation interaction for simulating dislocation climb
Dislocation climb is an important high temperature process in metals plasticity, responsible for the phenomena such as creep, swelling, or hardening. Climb is defined by the ability of dislocations to leave their original glide plane by interacting with point defects. As such, dislocation climb is controlled by point defect diffusion/absorption/emission, all of which involve thermal activation. The existing thermodynamically consistent models for climb are generally formulated in a continuum framework, through the definition of effective defect fluxes and climb propensities in response to thermodynamic driving forces. However, the point-wise discrete nature of vacancies (and/or self-interstitials) confers a highly discrete nature to the climb dynamics, which is also strongly affected by elastic forces. The combination of discreteness, thermal activation, and elasticity makes this process too challenging for direct atomistic methods such as molecular dynamics. Here we develop a kinetic Monte Carlo model that captures vacancy generation and transport kinetics acting in conjuction with the evolving elastic fields provided by discrete dislocation dynamics simulations. The two models are coupled via the applied stresses and stress gradients generated by dislocation structures at vacancy locations. Our simulations reveal two surprising results. First that climb is dominated by vacancy emission even when the background vacancy concentration is much higher than the equilibrium one. And, second, that climb velocities might be much faster than otherwise believed when one uses the classical theories of climb. These effects are due to the locality of vacancy-dislocation processes, which are not captured in classical treatments that assume smooth vacancy fluxes and homogeneous concentrations. We apply the method to study elementary climb processes in body-centered cubic iron and furnish climb mobility functions to be used in parametric dislocation dynamics and/or crystal plasticity simulations. Here, we apply the technique to study non-conservative plastic bypass of spherical precipitates by edge dislocations and point out the differences between our discrete approach and existing continuum formulations.
Radiation Tolerant Interfaces: Influence of Local Stoichiometry at the Misfit Dislocation on Radiation Damage Resistance of Metal/Oxide Interfaces
To understand how variations in interface properties such as misfit-dislocation density and local chemistry affect radiation-induced defect absorption and recombination, we have explored a model system of CrxV1-x alloy epitaxial films deposited on MgO single crystals. By controlling film composition, the lattice mismatch with MgO was adjusted so that the misfit-dislocation density varies at the interface. These interfaces were exposed to irradiation and in situ results show that the film with a semi-coherent interface (Cr) withstands irradiation while V film, which has similar semi-coherent interface like Cr, showed the largest damage. Theoretical calculations indicate that, unlike at metal/metal interfaces, the misfit dislocation density does not dominate radiation damage tolerance at metal/oxide interfaces. Rather, the stoichiometry, and the precise location of the misfit-dislocation density relative to the interface, drives defect behavior. Together, these results demonstrate the sensitivity of defect recombination to interfacial chemistry and provide new avenues for engineering radiation-tolerant nanomaterials.
Molecular dynamics discovery of an extraordinary ionic migration mechanism in dislocation-containing TlBr crystals
TlBr can surpass CZT as the leading semiconductor for γ- and X-radiation detection. Unfortunately, the optimum properties of TlBr quickly decay when an operating electrical field is applied. Quantum mechanical studies indicated that if this property degradation comes from the conventional mechanism of ionic migration of vacancies, then an unrealistically high vacancy concentration is required to account for the rapid aging of TlBr seen in experiments. Here, we have applied large scale molecular dynamics simulations to study the effects of dislocations on ionic migration of TlBr crystals under electrical fields. We found that electrical fields can drive the motion of edge dislocations in both slip and climb directions. These combined motions eject enormous vacancies in the dislocation trail. Both dislocation motion and a high vacancy concentration can account for the rapid aging of the TlBr detectors. These findings suggest that strengthening methods to pin dislocations should be explored to increase the lifetimes of TlBr crystals.
Electrical current leakage and open-core threading dislocations in AlGaN-based deep ultraviolet light-emitting diodes
Electrical current transport through leakage paths in AlGaN-based deep ultraviolet (DUV) light-emitting diodes (LEDs) and their effect on LED performance are investigated. Open-core threading dislocations, or nanopipes, are found to conduct current through nominally insulating Al{sub 0.7}Ga{sub 0.3}N layers and limit the performance of DUV-LEDs. A defect-sensitive phosphoric acid etch reveals these open-core threading dislocations in the form of large, micron-scale hexagonal etch pits visible with optical microscopy, while closed-core screw-, edge-, and mixed-type threading dislocations are represented by smaller and more numerous nanometer-scale pits visible by atomic-force microscopy. The electrical and optical performances of DUV-LEDs fabricated on similar Si-doped Al{sub 0.7}Ga{sub 0.3}N templates are found to have a strong correlation to the density of these nanopipes, despite their small fraction (<0.1% in this study) of the total density of threading dislocations.
The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations
A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and, therefore, to the temperature of the material.
Enhanced mobility of dislocation network nodes and its effect on dislocation multiplication and strain hardening
Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been developed, but its lack of atomistic resolution leaves open the possibility that certain key mechanisms may be overlooked. Here, by comparing large-scale Molecular Dynamics (MD) with DDD simulations performed under identical conditions we uncover significant discrepancies in the predicted strength and microstructure evolution in BCC crystals under high-strain rate conditions. These are traced to unexpected behaviors of dislocation network nodes forming at dislocation intersections, that can move in ways not previously anticipated as revealed by MD. Once these newfound freedoms of nodal motion are incorporated, DDD simulations begin to closely match plastic evolution observed in MD. This additional mechanism of motion whereby non-screw dislocations can change their glide plane profoundly affects fundamental processes of dislocation multiplication, recovery and storage that define strength of metals.
Atomic-scale dynamics of edge dislocations in Ni and concentrated solid solution NiFe alloys
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Glide dislocation nucleation from dislocation nodes at semi-coherent {111} Cu–Ni interfaces
Using atomistic simulations and dislocation theory on a model system of semi-coherent {1 1 1} interfaces, we show that misfit dislocation nodes adopt multiple atomic arrangements corresponding to the creation and redistribution of excess volume at the nodes. We identified four distinctive node structures: volume-smeared nodes with (i) spiral or (ii) straight dislocation patterns, and volume-condensed nodes with (iii) triangular or (iv) hexagonal dislocation patterns. Volume-smeared nodes contain interfacial dislocations lying in the Cu–Ni interface but volume-condensed nodes contain two sets of interfacial dislocations in the two adjacent interfaces and jogs across the atomic layer between the two adjacent interfaces. Finally, under biaxial tension/compression applied parallel to the interface, we show that the nucleation of lattice dislocations is preferred at the nodes and is correlated with the reduction of excess volume at the nodes.
Dislocation nano-hydrides in nickel: Nucleation, evolution and effects on dislocation behaviors
Nano-hydrides have been predicted to precipitate at the core of edge dislocations in the Ni-H system, a mechanism that may promote hydrogen embrittlement. However, nano-hydride nucleation, growth, and effects on dislocation behavior have seldom been explored. This work combines molecular dynamics grand canonical Monte Carlo (MD-GCMC) simulations and continuum modeling to uncover a wide range of phenomena linked to dislocation nano-hydrides. Simulations reveal that nano-hydrides can be stabilized at dislocation cores with all character angles, including screw segments, due to the hydrostatic stresses around the cores of the Shockley partials. Nano-hydride nucleation takes place in these regions, and growth is dictated by the character angle θ of the perfect dislocation. The equilibrium stacking fault width d eq varies dynamically to increase the local hydrostatic stress field and facilitate the formation of the nano-hydride, forming a constriction-like feature and leading to three distinct behaviors: d eq decreases for θ > 30°, d eq remains unchanged for θ = 30°, and d eq increases for θ < 30°. Remote hydrostatic and Escaig stresses are also shown to influence the nucleation stage, implying stress concentrations such as those ahead of crack tips may facilitate nano-hydride precipitation. Moreover, we identify a new hydrogen-induced 60° dislocation reaction that emits a Shockley partial on a conjugate plane, with potential implications for twin nucleation. Testable predictions from this study are then used to reinterpret previous results from the literature. In conclusion, these findings provide a comprehensive framework to assess nano-hydride formation and evolution at dislocations in nickel and other face-centered cubic metals, with important implications to hydrogen embrittlement.
Solute-dislocation interaction in Mg from first-principles: and twinning dislocations with flexible boundary conditions
We relax the cores of $\langle c+a \rangle$ edge and screw dislocations, and $(10\overline{1}2)$ and $(10\overline{1}1)$ twinning dislocations in Mg using first-principles calculations with flexible boundary conditions (FBC). FBC couple highly distorted cores to a harmonic lattice through lattice Green functions (LGF), allowing dislocations to relax as isolated defects. Unlike previous FBC calculations using bulk LGFs, we use LGFs specifically for dislocated geometries. The optimized geometries provide sites for computing solute-dislocation interactions via direct substitution, as well as local strain and slip for input to computationally efficient geometric solute interaction models. The interactions are inputs for solid-solution strengthening models. We compute interactions between Al, Ca, Mn, Sn, and Zn and the dislocations, and predict corresponding changes in stress for dislocation motion. We compare the strengthening of each of these non-basal deformation modes to basal strengthening and examine implications for ductility in Mg alloys. Funding from DOE-USAMP Cooperative Agreement Number DE-EE0007756.
Dislocation density-based plasticity model from massive discrete dislocation dynamics database
In this work, we present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each slip system, and, equivalently, an exponential dependence of the plastic shear strain rate on the resolved shear stress. Hence the proposed generalized Taylor relation subsumes the Orowan relation for plastic flow. The DDD data also calls for a correction to the Kocks-Mecking model of dislocation multiplication to account for the increase of dislocation density on slip systems with negligible plastic shear strain rate. This is accomplished by allowing the multiplication rate on each slip system to include contributions from the plastic strain rates of the two coplanar slip systems. The resulting constitutive model successfully captures the strain hardening rate dependence on the loading orientation as predicted by the DDD simulations, which is also consistent with existing experiments.
Coupled effect of Cr and Al on interactions between a prismatic interstitial dislocation loop and an edge dislocation line in Fe-Cr-Al alloy
Segregation of alloying elements to a prismatic dislocation loop under irradiation is an important phenomenon in understanding the role of loops in radiation effects in alloys. In this work, various segregation sequences of Cr and Al atoms to a $\langle$100$\rangle$ and a 1/2 $\langle$111$\rangle$ prismatic dislocation loop in a Fe-Cr-Al alloy are explored using molecular dynamics method and ab initio energy calculation. Here, the results reveal that Cr can readily segregate to the loops while Al atoms cannot by themselves, but the segregated Cr atoms are able to promote Al segregation at the loops, defined as a coupled segregation of Cr and Al. After interacting with Cr and Al, a previously mobile 1/2 $\langle$111$\rangle$ loop becomes sessile. Al segregation through the coupled segregation process can further affect the pinning behavior of a dislocation loop to an edge dislocation motion. By varying the Al fraction in the segregated solutes, a nonlinear dependence of the pinning effect on dislocation motion is determined. At lower fractions, the pinning strength increases with the increasing Al fraction until Al fraction reaches a critical value of about 19%, above which the pinning strength decreases with further increase of Al fraction. All these results suggest that, in addition to the effect of Al on the surface resistance to oxidation, Al effect on the dislocation loop behavior is important to optimize the composition of Fe-Cr-Al alloys for their applications in accident tolerant fuel concepts.
A phase field dislocation dynamics model for a bicrystal interface system: An investigation into dislocation slip transmission across cube-on-cube interfaces
In this study, we present a phase field dislocation dynamics formulation designed to treat a system comprised of two materials differing in moduli and lattice parameters that meet at a common interface. We apply the model to calculate the critical stress τ crit required to transmit a perfect dislocation across the bimaterial interface with a cube-on-cube orientation relationship. The calculation of τ crit accounts for the effects of: 1) the lattice mismatch (misfit or coherency stresses), 2) the elastic moduli mismatch (Koehler forces or image stresses), and 3) the formation of the residual dislocation in the interface. Our results show that the value of τ crit associated with the transmission of a dislocation from material 1 to material 2 is not the same as that from material 2 to material 1. Dislocation transmission from the material with the lower shear modulus and larger lattice parameter tends to be easier than the reverse and this apparent asymmetry in τ crit generally increases with increases in either lattice or moduli mismatch or both. In efforts to clarify the roles of lattice and moduli mismatch, we construct an analytical model for τcrit based on the formation energy of the residual dislocation. We show that path dependence in this energetic barrier can explain the asymmetry seen in the calculated τ crit values.
Analytic model of the remobilization of pinned glide dislocations: Including dislocation drag from phonon wind
Here, we discuss the effect of a non-constant dislocation drag coefficient on the very high strain rate regime within an analytic model describing mobile-immobile dislocation intersections applicable to fcc polycrystals. Based on previous work on dislocation drag, we estimate its temperature and pressure dependence and its effects on stress–strain rate relations. In the high temperature regime, we show that drag can remain the dominating effect even down to intermediate strain rates. We also discuss the consequences of having a limiting dislocation velocity, a feature which is typically predicted by analytic models of dislocation drag, but which is somewhat under debate because a number of MD simulations predict supersonic dislocations.