A promising high-strength Fe – 17.7Mn – 4.7Cr – 0.48C – 10Ni – 5Al – 4Cu wt.% Austenitic steel was solutionized, then aged for 3 or 10 h at 580°C producing a pronounced precipitation hardening response primarily due to the formation nanoscale NiAl precipitates. Density functional theory (DFT), molecular dynamics (MD), and discrete dislocation dynamics (DDD) calculations were combined with microstructural data from atom-probe tomography (APT), informing theoretical strengthening models to predict yield strength at different stages of precipitation as a function of NiAl size, volume fraction, and composition. These yield strength predictions were compared with experimental microhardness measurements of the various ageing conditions, including the peak microhardness of 490 HV, which corresponds to an estimated alloy yield strength of 1200 MPa. Comparing MD calculations with theoretical models showed that anti-phase boundary (APB) formation was the predominant barrier to dislocation motion posed by the NiAl precipitates. Using single dislocation particle strengthening models with NiAl APB energies calculated from DFT, good agreement was observed between DDD calculations and the 10 h peak-aged experimental measurements, while agreement with the 3 h experimental measurements required reducing the NiAl APB energy. These results demonstrate the utility of the undertaken approach integrating simulations and experiments across multiple length-scales, particularly the presented coarse-grained DDD simulation method towards modeling materials strengthened by very fine precipitates. The results further suggest that the observed NiAl precipitates may adopt an alternate crystal structure early in their formation.

During additive manufacturing (AM), velocities of solid–liquid interfaces are on the order of 0.01−1m⋅s−1. Thus, local interfacial equilibrium may not be present. Molecular dynamics (MD) and Monte Carlo methods are employed to extract thermodynamic properties for a Fe–Cr binary alloy and the parameters that characterize the departure from interfacial equilibrium for velocities present during AM. The Gibbs free energies of the BCC, FCC, and liquid phases are determined and used in a partial-solute-drag model that self-consistently describes non-equilibrium solute trapping and solute-drag behavior. The partial-solute-drag model describes well the interfacial velocities as a function of supersaturation in the liquid and the velocity dependence of the partition coefficient. The maximum possible velocities, v0 of the solid/liquid interfaces are determined, with v0 of the stable BCC phase being higher than the metastable FCC phase, but both values are significantly lower than the reported speed of sound. Additionally, the partial-solute-drag model yields a trans-interface diffusivity much different from that of more classical models and very close to that measured in the MD simulations.

Solid solution strengthening remains the basis for many industrial alloys, yet chemical short-range order (CSRO) can also play a significant role in the strengthening of alloys with appreciable alloying additions, such as in Austenitic stainless steels. In this work, we study the evolution of CSRO under various annealing temperatures and its role on the mechanical strength of a ternary Fe–12Ni–18Cr (at.%) alloy using molecular dynamics (MD) and Monte Carlo atomistic simulations and experimental measurements from mechanical microindentation and atom-probe tomography (APT). A general model that incorporates the role of CSRO into a solute–solution strengthening model is proposed, based on a family of analytical models due to Varvenne et al. (2016) which takes into account dislocation-solute misfit interaction, and a more recent extension due to Nag and Curtin (2020) which incorporates the role of solute–solute interactions during dislocation slip. Predictions of the modified model are validated against MD shearing simulations using two commonly used embedded atom model (EAM) interatomic potentials for Austenitic stainless steel alloys, and mechanical microindentation experiments on cast alloys of the same composition. Our results suggest that, while significant CSRO is predicted in the simulations, there is little experimental evidence in cast and annealed alloys analyzed by APT.

We present first-principles density functional theory calculations of atomic properties relevant to the material strength of an austenitic (face-centered-cubic) steel alloy, ${\mathrm{Fe}}_{0.70}{\mathrm{Ni}}_{0.12}{\mathrm{Cr}}_{0.18}$. While alloys in this class appear nonmagnetic macroscopically because their local magnetic moments are disordered, significant deviation from experiment can result when calculating properties using nonmagnetic calculations or magnetically ordered calculations. To overcome these difficulties, in this paper we employ a magnetic sampling method with spin-polarized density functional theory to approximate magnetically disordered states by averaging over several static configurations. Using this approach, we calculate elastic and point defect properties, which are then used to evaluate the dominant solid-solution strengthening contribution to the yield strength. Moreover, since the local composition can interact with strain fields, whether externally applied or induced by dislocations, diffusion can give rise to local changes in mechanical properties. We therefore calculate contributions to the vacancy-mediated diffusivity from the formation and migration terms in the activation energy, and the harmonic-transition-state-theory prefactor which depends on the vibrational states of the initial and transition states. While the prefactor is very sensitive to noise and therefore only loosely constrained by our calculations, the activation energies and yield stress values obtained from paramagnetic calculations are in good agreement with available experimental results.

We present first-principles density functional theory calculations of atomic properties relevant to the material strength of an austenitic (face-centered-cubic) steel alloy, Fe0.70Ni0.12Cr0.18. While alloys in this class appear nonmagnetic macroscopically because their local magnetic moments are disordered, significant deviation from experiment can result when calculating properties using nonmagnetic calculations or magnetically ordered calculations. To overcome these difficulties, in this paper we employ a magnetic sampling method with spin-polarized density functional theory to approximate magnetically disordered states by averaging over several static configurations. Using this approach, we calculate elastic and point defect properties, which are then used to evaluate the dominant solid-solution strengthening contribution to the yield strength. Moreover, since the local composition can interact with strain fields, whether externally applied or induced by dislocations, diffusion can give rise to local changes in mechanical properties. We therefore calculate contributions to the vacancy-mediated diffusivity from the formation and migration terms in the activation energy, and the harmonic-transition-state-theory prefactor which depends on the vibrational states of the initial and transition states. While the prefactor is very sensitive to noise and therefore only loosely constrained by our calculations, the activation energies and yield stress values obtained from paramagnetic calculations are in good agreement with available experimental results.

Recent interest in chemically-complex solid-solution alloys has produced a number of new refractory BCC alloys with superior high-temperature properties. Preliminary atomistic studies show that, unlike simple BCC metals, these alloys produce equilibrium (screw) dislocations spread on varying glide planes along their length. This observation suggests that under load such defects produce kinks on different glide planes leading to a distribution of pinning points that significantly increases high-temperature strength. In order to validate this model a first-principle approach is developed to characterize these sub-nanoscale structures. We find significant spreading of the dislocation onto varying {110} planes (partial kinks) in NbTiZr and Nb17Ti33Zr50, while Nb50Ti33Zr17 produces a straight-compact dislocation as found in simple BCC metals. Chemical analysis around the dislocation indicate that the partial kinks form in response to increasing (decreasing) Ti and Zr (Nb) compositions. These results validate a growing body of work on understanding the hardening mechanisms in chemically-complex alloys.

Atomistic methods are used to anneal two body-centered cubic (BCC) chemically complex alloys (CCAs) in order to assess the effect of chemical short-range order on alloy strength. The two alloys, a model quaternary Co16.67Fe36.67Ni16.67Ti30 and ternary Nb33.33Ti33.33Zr33.33, are represented using simple Zhou interatomic potentials. Chemically random cells are annealed at temperatures 65% of the average melting temperature of the individual elements using a Monte Carlo approach, and the critical stress required to move a/2[111] screw dislocations in the initial and annealed cells are estimated using molecular dynamics simulations. It is shown that annealing leads to a softening of the BCC quaternary alloy relative to the random state, especially for deformation at low temperatures. On the other hand, short-range order has minimal effect on solid solution strengthening in the ternary alloy. These results are modeled using an extension of the Suzuki model of substitutional solid solution strengthening developed for BCC chemically complex alloys. Here the model is modified to account for the effects of chemical short-range order. Good agreement is shown between the model results and direct atomistic simulation data. The model presented should be useful in predicting BCC CCAs with adequate high temperature strength, which will accelerate development of high temperature, high strength BCC alloys for aerospace applications.

Building on our previously introduced multicell Monte Carlo (MC)^{2} method for modeling phase coexistence, this paper provides important improvements for efficient determination of phase equilibria in solids. The (MC)^{2} method uses multiple cells, representing possible phases. Mass transfer between cells is modeled virtually by solving the mass balance equation after the composition of each cell is changed arbitrarily. However, searching for the minimum free energy during this process poses a practical problem. The solution to the mass balance equation is not unique away from equilibrium, and consequently the algorithm is in risk of getting trapped in nonequilibrium solutions. Therefore, a proper stopping condition for (MC)^{2} is currently lacking. In this work, we introduce a consistency check via a predictor-corrector algorithm to penalize solutions that do not satisfy a necessary condition for equivalence of chemical potentials and steer the system toward finding equilibrium. The most general acceptance criteria for (MC)^{2} is derived starting from the isothermal-isobaric Gibbs ensemble for mixtures. Using this ensemble, translational MC moves are added to include vibrational excitations as well as volume MC moves to ensure the condition of constant pressure and temperature entirely with a MC approach, without relying on any other method for relaxation of these degrees of freedom. As a proof of concept the method is applied to two binary alloys with miscibility gaps and a model quaternary alloy, using classical interatomic potentials.

In order to understand the role of chemical short-range order on deformation mechanisms in FCC compositionally complex alloys, a random model alloy (Co30-Fe16.67-Ni36.67-Ti16.67) is annealed at various temperatures using Hybrid Molecular-dynamics/Monte-Carlo simulations. The simulations produce significant chemical short-range order (CSRO) that increases with decreasing annealing temperature. Annealing tends to homogenize regions of high enthalpy due to: (1) chemical species redistributing into more compact configurations, and (2) pairs of atoms forming chemical bonds that lower the overall energy of the system; the composition explored here shows significant amount of ordering in Ti-Fe pairs with respect to random distributions as described by pairwise (EAM) potentials due to Johnson and Zhou. An energy topology approach is used to assess the local strengthening behavior in random solid solutions and annealed systems, where an interesting interplay is observed between misfit components and chemical short-range order affecting the overall critical resolved shear stress. The role of short-range order on the critical yield stress is quantified and compared with current solid solution models. Finally, we propose and validate an extension to the Labusch-Varvenne class of high-concentration solid-solution analytic models that incorporates the effects of chemical short range order.

Solution hardening in body centered cubic alloys as a function of temperature can be well described by the Suzuki model. This model includes significant strengthening from the dragging of edge dislocation dipoles produced by kink collisions along the screw dislocations. However, the model does not consider diffusion-controlled processes. Here we estimate a critical temperature Tcr above which diffusional effects become important, resulting in the collapse of edge dipoles. Loss of edge dipoles leads to a significant decrease in yield strength above Tcr and marks the temperature limit for structural applications of these single phase body centered cubic alloys.

Large scale, atomistic simulations of the core structure and mobility of 1/2[111] screw, edge and mixed dislocations in ternary multicomponent alloys (e.g. High Entropy alloys), NbTiZr, Nb1.5TiZr0.5 and Nb0.5TiZr1.5, are presented. The core structure of %[111] screw dislocations continuously varies from compact to 3-fold with decreasing Nb content. The screw dislocation core structures in NbTiZr and Nb(1.5)TiZr(0.5.)are calculated using Embedded Atom Potentials (Johnson-Zhou) and compared with first-principles calculations of the screw dislocation in a quasi-random structure. In both simulations the dislocation core spreads on different (110) glide planes as the composition varies along the dislocation line in stoichiometric NbTiZr. The Nb-rich composition Nb1.5TiZr0.5 shows a compact core with very little core structure variation along the dislocation line in both First Principles and atomistic simulations. The screw dislocation deposits interstitial and vacancy dipole debris as it moves under stress. Average solute dislocation core interaction energies in NbTiZr, Nb1.5TiZr0.5 and Nb0.5TiZr1.5 are derived from the average interatomic potential derived for each of the three systems. The interaction energies are used to determine the critical stress for the motion of 1/2[111] screw dislocations in the three systems as a function of temperature using the Suzuki model of kink migration controlled mobility developed for concentrated BCC random alloys. This analysis shows that the relatively high barrier for kink migration caused by fluctuations in solute concentration along the screw dislocation line and the dipole dragging stress associated with the screw dislocation motion results in a shallow fall-off of critical stress with temperature in these alloys as compared to simple BCC metals. Finally, the screw dislocation to edge and mixed dislocation critical stress ratio in NbTiZr are shown to be low, similar to 2 at 5 K, in contrast to simple BCC metals, where it could be as high as 100-1000. (C) 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Current alloy development efforts in High Entropy Alloys call for a better understanding of solution hardening in high-concentration chemically-complex alloys. Here we propose a general scheme for assessing the overall solute-dislocation interaction, independent of concentration, stress, and temperature. While significant progress has been made in including solute-dislocation interactions in FCC metals (Leyson et al) there are open questions as to how to model more complex (solute-solute-dislocation) chemical interactions that arise in high concentration solid solutions. A method similar to Olmsted et al, is developed to quantify representative energy landscapes as a dislocation percolates through a field of solutes. This approach uses molecular dynamics under stress in order to estimate the strengthening parameters for a system over a wide range of solute concentrations and a moderate range of temperatures. While MD introduces additional complications to the simulation, due to coupling of temperature with the potential energy of the system, it also provides significant flexibility in terms of avoiding local minimum, assessing the effects of dislocation bowing and the effects of stress and temperature. Also, by avoiding the direct assessment of solute-solute bonding very complex systems can be evaluated efficiently. As proof of concept the method is applied to Al solutes in FCC Ni, where the system is known to be dominated by strong Al solute-solute interactions at high solute concentrations. Self-consistency of the method is shown by computing various strengthening parameters near critical percolation stress states at various system sizes, concentrations, and temperatures. We propose an extension to current solute-dislocation hardening models (i.e. Leyson et al.) to include solute-solute bonding and compare the scaling prediction and temperature dependence of solid solution models to the molecular dynamics results. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Room temperature strength of nine multi-principle element body-centered cubic alloys are predicted using atomistic potentials and a solution-hardening model. The complex solute dislocation interactions are estimated using Embedded Atom Method potentials. At least six of these alloys are known to form single-phase solid solutions on annealing. Assuming that strength is rate limited by screw motion by kink migration, the interaction energies are incorporated into Suzuki's model for kink-solute interactions and evaluated at room temperature. The method predicts room temperature yield strength across all the alloys with a standard error of 13%.

The fast loading rates associated with shockwaves in solids make molecular dynamics (MD) a particularly well-suited tool for their study. This chapter focuses on recent methods to study shock-induced chemistry using all-atom reactive MD and coarse-grained simulations and their application. We describe insight on the formation of hot spots formed following the shock-induced collapse of pores and their transition to a deflagration wave in high energy density materials obtained from large-scale MD simulations using the reactive force field ReaxFF. Experimental validation of such simulations is critical to assess the predictive capabilities of these methods to describe new materials and show how to extract observables from the simulations that can be directly contrasted with experiments. Such direct comparisons are not just critical for validation but also contribute to the interpretation of the experimental results. We also describe coarse-grained simulations to study the possibility and effectiveness of shock-induced, endothermic, volume-collapsing reactions; these simulations quantify how the various characteristics of the chemical reactions attenuate the propagating shockwave and provide key information to experimentalists designing and synthesizing such materials.

The strain hardening in FCC Ni was studied along low index directions using 3-dimensional discrete dislocation dynamics. Large (20 × 20 × 50 μm) Ni microcrystals were simulated using rectangular parallelepiped-cells loaded in tension along four low-index directions ([111], [001], [110] and [112]) to shear strains of ∼0.01–0.02. Loading was at a constant strain rate of 10/sec, and all surfaces of the cell are treated as free surfaces. The FCC dislocation mobility routines were modified to include thermally activated cross-slip processes, as a function of three different stress components, using the results of previous atomistic simulations. These include bulk cross slip (cross-slip at atomic jogs), intersection cross slip (attractive and repulsive) as well as surface cross slip. One of these, repulsive intersection cross-slip, has zero activation energy and is present at all simulated deformation temperatures. The simulations were performed for three different temperatures, 5, 150 and 300 K. The strain-hardening rate is independent of temperature and of the order of μ/200 – μ/400, in agreement with experimental data for the <111> and <001> orientations of deformation. For the [001] orientation, at 5 and 150 K, the strain hardening rate decreases considerably when repulsive intersection cross-slip is removed from the simulations. The [110] and [112] orientations exhibit single-slip glide and a very low strain-hardening rate (∼μ/3000). Heterogeneity of dislocation microstructure develops spontaneously at the higher temperatures as a result of increased cross slip. Even though the strain-hardening rate is independent of temperature, the increase in dislocation density with shear strain is larger at higher temperatures. It is proposed that higher temperatures deformation produces larger dislocation-microstructure heterogeneities, providing for higher average dislocation densities and regions of low density where deformation can proceed. Also, the strain hardening rate at 300 K is controlled by the rate of increase of forest dislocation density in these lean regions.

This chapter presents a review and tutorial on molecular dynamics (MD) simulation of shock loading of solids, under which materials are compressed at ultra-fast rates to extreme conditions of pressure and temperature. Due to the ultra-fast loading rates, shockwaves can reveal processes not accessible otherwise, including melting below the equilibrium melting temperature and chemical reactions away from equilibrium. The timescales involved in shock physics make MD an ideal tool for their study and these atomic-level simulations have and continue to play a critical role of our understanding of the physics and chemistry of materials under extreme mechanical loads. Such simulations, when done with care, have been particularly useful to resolve complex processes that occur at or right behind the shock front, where plasticity, phase transformations, and the initiation of chemical reactions are relevant. Flyer plate simulations, coarse grain dynamics, and shock-induced plasticity are also discussed.

We use molecular dynamics simulations to investigate how the energy input and distribution in contacts affect the thermal transport in silicon as described by the Stillinger-Webber potential. We create a temperature difference across a Si specimen by maintaining the temperature of two contacts (also made of Si) using widely used thermostats: the deterministic Nosé-Hoover approach and a stochastic Langevin bath. Quite surprisingly, the phonon thermal conductivity of the channel obtained using the two thermostats but under otherwise identical conditions can differ by a factor of up to three. The discrepancy between the two methods vanishes as the coupling strength between the thermostat and material is reduced and for long channels. A spectral analysis of the contacts and channel shows that increasing the coupling of the stochastic Langevin thermostat affects the spectral energy distribution in the contacts away from that based on the vibrational density of states, broadening peaks and smoothening the distribution. This results in contacts injecting phonons preferentially in low frequency modes and in transport through the channel away from local equilibrium. A comparison of the MD results with Boltzmann transport equation simulations provides an additional insight into the role of contacts on thermal transport in nanoscale specimens. These results stress the importance of contacts in nanoscale thermal transport in simulations and in the interpretation of experimental data.

We use large-scale molecular dynamics simulations to investigate the mechanisms responsible for plastic deformation in metal-organic framework-5 (MOF-5). Simulations of uniaxial compression along [001], [101], and [111] directions reveal that structural collapse of {001} planes is responsible for irreversible deformation. The process involves slip along either one of the two < 100 > directions on the collapsing plane; this local shear process is due to the flexibility of the connection between of Zn-O clusters and 1,4-benzenedicarboxylate ligands. Thus, the collapse is driven both by compressive and shear stresses, and this fact explains the anisotropy in the mechanical response of this cubic crystal. The development of shear-collapse bands follows a nucleation and growth process with nuclei elongated along the slip direction and their subsequent growth in the directions normal to the slip and at much slower rates. This process is reminiscent of the glide of screw dislocations. Compression along the [101] and [111] directions led to intersection of active shear-collapse bands and the activation of multiple < 001 >{100} systems. We also find that partially collapsed planes reduce the stiffness of the structures, an observation that can explain discrepancies between experimental and theoretical stiffness predictions.

We use a particle-based mesoscale model that incorporates chemical reactions at a coarse-grained level to study the response of materials that undergo volume-reducing chemical reactions under shockwave-loading conditions. We find that such chemical reactions can attenuate the shockwave and characterize how the parameters of the chemical model affect this behavior. The simulations show that the magnitude of the volume collapse and velocity at which the chemistry propagates are critical to weaken the shock, whereas the energetics in the reactions play only a minor role. Shock loading results in transient states where the material is away from local equilibrium and, interestingly, chemical reactions can nucleate under such non-equilibrium states. Thus, the timescales for equilibration between the various degrees of freedom in the material affect the shock-induced chemistry and its ability to attenuate the propagating shock.