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This study presents an approach to investigate the influence of intergranular stresses induced by equilibrium and non-equilibrium grain boundaries (GBs) on dislocation transmission via the discrete dislocation dynamics simulation method. First, a disclination-based construct is used to describe the equilibrium intergranular stress fields of two symmetric tilt GBs. Then, slip transfer through these GBs is simulated via an algorithm that predicts dislocation transmission considering geometric and plastic dissipation criteria. Results show that the locations for transmission and the glide of residual dislocations are strongly correlated with GB stresses. Next, ordered structural defects in the equilibrium GBs are modified using a new approach to simulate disruptions in GB structure caused by dislocation transmission, creating non-equilibrium GBs. Slip transmission preferentially occurs near the non-equilibrium defects, illustrating the effect of modified GB screening characteristics due to prior dislocation transmission. The present work provides a basis for physically representative modeling of GBs and dislocation-GB phenomena in mesoscale simulations of polycrystalline plasticity.

High entropy alloys (HEAs) have been the subject of significant research in recent years due in part to their excellent mechanical properties and unique microstructure. Chemical disorder in these alloys is thought to lead to a complex energetic environment that affects the nucleation and movement of dislocations. In this study the development of deformation substructures is assessed in the Cantor HEA (CoCrFeMnNi) due to quasistatic and dynamic compression. Scanning and transmission electron microscopy (SEM/TEM) techniques are used to image and quantify dislocation density. When increasing the strain rate from 10−3 s−1 to 5000 s−1 we observe an increase in the overall dislocation density which leads to the formation of deformation twins. Further at a rate of 8000 s−1, both deformation twins and microbands become operative plasticity modes, which are usually associated with different extremes of stacking fault energy. To relate this plastic response to chemical disorder, atomistic calculations are used to compute the generalized stacking fault energy curve and approximate the temperature dependence of the intrinsic stacking fault energy for the Cantor alloy, which reveals significant local variation in these critical energetic parameters associated with dislocation and twinning behaviors.

The mechanical properties of metallic systems at the nanoscale can be modified by varying their structure and composition. One example of a deformation-resistant structure is a core–shell nanostructure (CSN). In the present work, we use molecular dynamics simulations to perform nanoindentation and retractions to understand plastic deformation of core–shell nanostructures. The core consists of aluminum (Al), the shell is amorphous silicon (a-Si), and the substrate is either crystalline Al or a-Si. The unique aspect of this work is that we study the deformation behavior of CSNs that contain symmetric and asymmetric grain boundaries in the core with two different orientations; comparisons are made to deformation in a CSN with a single-crystal core. Nanoindentation on CSNs with 5 nm and 10 nm core radii shows that the elastic stiffness with and without a grain boundary is similar when the substrate material is the same. Five-nanometer-core-radius CSNs with a-Si and Al substrates and an asymmetric tilt grain boundary in the core show 100% recovery from dislocation plasticity, but damage within the core leads to reduction of ~ 50% of the atoms that no longer being identified as FCC crystal structure, which makes these CSNs non-deformation-resistant. CSNs with Al substrate (5 nm and 10 nm core radii) obtained 100% recovery from plasticity and retained its crystal structure after unloading when the core is single crystal or contains a symmetric tilt grain boundary. Moreover, a single-crystal core can withstand nanoindentation to 100% of the shell thickness, whereas a symmetric tilt grain boundary core can only withstand nanoindentation about 80% of the shell thickness and still have 100% recovery from plasticity. Therefore, CSNs with single-crystal core are more reliable for deformation-resistant behavior than those that contain grain boundaries.

Grain boundary (GB) migration and grain growth in nanocrystalline metals are major obstructions to exploit these materials to their fullest potential, thus limiting their utility as advanced structural materials. Here, we investigate the effect of Zr segregation to a Ni GB on migration and subsequent strengthening during shear deformation and high-temperature bending creep. Specifically, using molecular dynamics simulation, we simulate deformation of a Ni bicrystal specimen having a symmetric ∑5 grain boundary with and without segregated Zr. It is found that GB segregation up to 0.4 at.% pins the CSL boundary resulting in increased shear strength. Similar behavior is also observed in the case of bending creep deformation where the creep resistance increases only up to 0.4 at.%. This study indicates that larger amounts of GB segregation cause destabilization of the local atomic structure and consequently affect the GB stiffness. Moreover, we investigate the effect of Zr segregation on the interaction between the GB and a dislocation. We find that the preexisting dislocation is absorbed in the GB region for both clean and segregated specimens; however, the absorption path of the dislocation is different due to the change in GB stiffness caused by the Zr segregation.

The extent that non-Schmid stresses influence the mobility of dislocations in Al is studied using molecular dynamics (MD) simulations. Specifically, mobility laws for straight screw, 30°, 60° and edge dislocations are atomistically derived for different combinations of Escaig stress, τe, and stress normal to the (111) slip plane, σn. MD simulations show that the mobility of each dislocation is distinctly influenced by non-Schmid stresses. Furthermore, MD simulations of dislocation shear loop expansion show that mobility laws derived from straight dislocations are applicable to describe the more complex behavior of stress-state dependent expansion of a dislocation loop. Data describing the dislocation mobility laws are incorporated into discrete dislocation dynamics (DDD) simulations using a hierarchical multiscale approach. DDD simulations of isolated dislocation loop expansion show strong agreement with MD simulation results, validating the nonlinear multiscale implementation. DDD simulations of dislocation network evolution show that the use of stress state dependent dislocation mobility laws provides quantifiable changes to the plastic deformation path, which leads to different final microstructures. The results presented here demonstrate the key role that local stresses, experienced by the dislocation core, play on the evolution of a dislocation network during plastic deformation.

Non-destructive evaluation of plastically deformed metals is particularly valuable both for assessing dislocation microstructures and validating constitutive models. Among other methods, diffraction line profile analysis has been widely used to extract dislocation densities in deformed bulk single crystals and polycrystals. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study proposes and assesses the prospects of a data-driven approach to extract dislocation densities from experimentally gathered whole line diffraction profiles. A database of virtual diffraction whole line profiles of Ta single crystals containing varying dislocation densities is generated. The dislocation microstructures are synthesized using discrete dislocation dynamics, and two distinct strain-based virtual diffraction algorithms are used to generate diffraction profiles. Instrumental broadening is applied to the synthetic profiles. The databases inform two Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is applied to 11 experimentally obtained whole line diffraction profiles gathered from plastically deformed Ta polycrystals. Upon applying both surrogate models to the experimental data and using eCMWP as a point of comparison, it is found that data-driven predictions of dislocation density can clearly capture the evolution of dislocation density with applied strain. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.

Nanotexturing reduces the effective contact between surfaces in relative motion, which can result in a lower coefficient of friction. However, nanotextured surfaces lack structural integrity, resulting in permanent deformation even at moderate contact forces. Therefore, core–shell nanostructures (CSNs) have been developed to protect the structural integrity of nanotextured surfaces. These CSNs can withstand higher contact forces, might include some plastic deformation (dislocations), but during unloading there is no evidence of residual plastic deformation. Therefore, the CSN is deformation resistant. In the current study, molecular dynamics simulations are used to study the effect of core (aluminum) radius, shell (amorphous silicon) thickness, and the random atomic distribution in the amorphous shell, on mechanical properties of core–shell nanostructures. The results suggest that core radius does not have a significant influence on the initial plastic deformation of the CSN. The shell thickness should be chosen so that the core to shell ratio is less than two to have deformation resistant CSNs. Further we observe that with an increase in core radii or shell thickness, the ability of a CSN to fully recover decreases. These results will help in the design of deformation resistant surfaces for MEMS/NEMS applications.

Transient rheological properties of poly(ethylene glycol) diacrylate (PEGDA) hydrogels under Couette flow conditions are determined via molecular dynamics simulations and validated by high strain r...

With recent advances in computational modeling and in situ transmission electron microscopy (TEM) technologies, there have been increased efforts to apply these approaches to understand defect-based mechanisms dictating deformation mechanics. In situ TEM experiments and atomistic simulations each have their own unique limitations, including observable length and time scales and accessibility of information, motivating approaches that combine the two approaches. In this paper, we review recent studies that combine atomistic simulations and in situ TEM experiments to understand defect mechanisms associated with deformation of metals and alloys. In addition, we discuss ongoing developments in characterization and simulation capabilities that are expected to significantly advance the field of defect mechanics and allow greater integration between atomistic simulations and in situ TEM experiments.

Molecular dynamics modeling is used to study the mechanism of brittle fracture in multi-layer two-dimensional molybdenum disulfide ( MoS 2 ) with a center crack subjected to mode-I loading. The simulation data is used to verify the application of Griffith, Inglis and quantized fracture mechanics theories for the fracture of monolayer MoS2 sheets. Results show that the Griffith theory cannot accurately predict the fracture strength of cracked MoS2 sheets. Since tip radius is quantized at the nanoscale, Inglis and quantized fracture theory are examined for cracks with different tip radii. Inglis theory is valid for cracks with blunt tips but is not accurate if the crack tip radius is less than 1.15 nm. In comparison to Inglis theory, quantized fracture mechanics gives a better prediction for the fracture strength of MoS2 sheets when the crack tips are very sharp. The simulation results also predict that the structure of the initial crack highly influences the crack advancing path. While at the macroscale, cracks propagate along a straight line perpendicular to loading, at the microscale level cracks in MoS2 kink to grow along a zigzag direction. The toughness and strength of the MoS2 sheets are not significantly affected by an increase in the number of layers from one to three.

The simple shear response of soft polymers under large deformation (>50%) and strain rates spanning 10−3 – 103 s−1 is characterized by developing quasi-static and split-Hopkinson pressure bar based single-pulse dynamic simple shear experiments rooted in continuum mechanics fundamentals. Cross-linked polydimethylsiloxane (PDMS) is chosen as a model material. By examining the evolution of stress, strain and strain rate, the latter two parameters measured using two-dimensional digital image correlation (DIC), it is demonstrated that dynamic simple shear deformation consists of four distinct stages: momentum diffusion, inertia effect, steady-state material response, and strain rate decay. By isolating the unsteady and steady-state deformation stages, inertia-free material response is captured under a uniform strain rate. It is shown that the shear response of PDMS is nearly linear with a weakly rate-sensitive shear modulus in the investigated strain rate range. Further, by analyzing the DIC strain-field and comparing the kinematic experimental results with those predicted by classical continuum mechanics, it is demonstrated that the proposed experiments not only achieve a nearly theoretical simple shear state that is uniform across the specimen, but also allow for post-test validation of individual experiments based on these criteria.

A generalized thermodynamic stability criterion for isotropic finite elastic solids is derived using the fundamental balance laws and field equations of continuum mechanics, which is then used to formulate constitutive inequalities for the polynomial form of hyperelastic constitutive equations. Individual thermodynamic constitutive inequalities (called T-C inequalities) are derived for the neo-Hookean, Mooney Rivlin, and three-parameter generalized Rivlin models under three pure homogeneous deformation modes, namely, uniaxial compression, uniaxial tension and shear (simple and pure), and are compared against two commonly used adscititious inequalities, the Baker-Ericksen (B-E) and E-inequalities. The range of stable model constants as defined by the T-C inequalities is represented by a region in an N-dimensional coordinate space (N is the total number of model constants), which is defined as the Region of Stability (ROS). It is shown that the ROS is a function of material deformation and evolves with the limiting strain, shrinking from an initially large region representing the necessary condition of thermodynamic stability to a converged region under infinite limiting strain that is equivalent to the ROS defined by the E-inequalities. By investigating the evolution of the ROS under different deformation modes, the implication of T-C inequalities on the selection of experimental routines and filtering of erroneous test data and model constants is discussed. It is also demonstrated that while the E-inequalities are over-restrictive for hyperelastic materials with small to moderate limiting strains, an observation supported by recent experimental evidence, the B-E inequalities are inaccurate under moderate to large limiting strain conditions. The applicability of the proposed mathematical framework to other hyperelastic strain energy density forms, such as exponential/logarithmic functions, is demonstrated by investigating the thermodynamic stability of the Fung-Demiray model. It is shown that the commonly assumed restriction that the Fung-Demiray model constants must be positive can be relaxed so that some typical material behaviors under small to moderate limiting strains can also be modeled.

Shockwave propagation in polyethylene glycol diacrylate (PEGDA) hydrogels is simulated for the first time using nonequilibrium molecular dynamics simulations. PEGDA hydrogel models are built using the “perfect network” approach such that each crosslink junction is comprised of six chain connections. The influence of PEGDA concentration (20–70 wt%) on shock behavior is investigated for a range of particle velocities (200–1000 m/s). In agreement with reported experimental results in the literature on gels with similar densities, shock velocity and pressure in PEGDA hydrogels are found to increase with polymer concentration, within a range bounded by pure water and pure polymer behaviors. Nonlinear relationships are observed for shock pressure and shock front thickness as a function of concentration, and a logarithmic equation is proposed to describe this behavior. In addition, the relationship between pressure and shock front thickness is compared with hydrodynamic theory. Deviation from hydrodynamic predictions is observed at high particle velocities and this deviation is found to be related to viscosity changes. A power-law relationship between strain rate and pressure in PEGDA hydrogels is identified, similar to that of metals. However, a power-law exponent of 1.4 is computed for all gel concentrations, whereas an exponent of 4 is typically reported for metals.

Hydrogels exhibit a fluid-like viscous response under high shear strain rates with significant rate- and microstructure-dependent rheological properties. In this study, the transient shear response of poly(ethylene glycol) diacrylate (PEGDA) hydrogels is characterized by application of the power-law fluid model to incompressible Navier–Stokes equation of start-up planar Couette flow. To impart the necessary boundary conditions for model calibration, a split-Hopkinson pressure bar based single-pulse dynamic simple shear experiment is developed, in which unsteady momentum diffusion between two shear plates is measured using two-dimensional digital image correlation (DIC). The measured shear profiles and their characteristic self-similarity under these boundary conditions are utilized to calculate power-law exponent and transient-state viscosity via finite difference simulations.

An analytical model is developed to predict shockwave propagation and attenuation in hydrogels by combining the classical method of shock characteristics and a solution for the shock front structure. To guide the development of the model, molecular dynamics (MD) simulations are performed. Specifically, a one-dimensional shock pulse in poly(ethylene glycol) diacrylate (PEGDA) hydrogels is simulated with the nonequilibrium MD method. The role of polymer concentration on the shock response is evaluated by constructing hydrogels with 20, 35, and 50 wt% PEGDA concentrations in an idealized crosslinked network. Steady-state pressure-density and shock-particle velocity relationships are established using the Murnaghan equation of state. Shock front structure is characterized by a power-law equation that relates the shock front thickness with shock pressure. These results are used as critical input for the shock propagation and attenuation model. The model is then evaluated via comparison with the classical method of characteristics. It shows significant improvement in accuracy and successfully captures salient features of shockwave attenuation, including the shock pressure amplitude, the velocities of the shock and release waves, and the attenuation timeline. Hydrogels with higher polymer concentrations exhibit a shorter attenuation time at all particle velocities studied. This behavior is attributed to differences in bulk properties and shock front structure in hydrogels with different polymer/water concentrations.

The high strain rate behavior of nonideal poly(ethylene glycol) diacrylate hydrogels under uniaxial tension and transient-state shear deformations is investigated using molecular dynamics (MD) simulations. This work specifically focuses on the influence of first-order loop defects, including their effect on topological evolutions. Two approaches are proposed to systematically introduce first-order loops, allowing separate and controllable investigations of effective cross-link functionality and cross-link density. MD simulations confirm that first-order loop defects are elastically inactive, but the topological disruptions caused by the presence of loop defects influence mechanical behavior. For decreasing effective cross-link functionality but constant cross-link density, a weaker tensile stress-strain response and decreasing shear-thickening behavior are observed. This is due to nonaffine translation of cross-link junction positions during deformation. Hydrogels with lower cross-link density but constant effective functionality show a stronger stress-strain response and an earlier transition between entropic and enthalpic deformation regimes. This behavior is correlated to changes in mesh size caused by the introduction of loops within an elastically active network. However, the resulting range of cross-link densities is not sufficient to cause measurable changes in shear-thickening behavior. To conclude, reductions in effective cross-link functionality are more important to high strain rate behavior than reductions in cross-link density.

Graphical abstract, One of the limitations of atomistic simulations is that many of the computational tools used to extract structural information from atomic trajectories provide metrics that are not directly compatible with experiments for validation. In this work, to bridge between simulation and experiment, a method is presented to produce simulated Kikuchi diffraction patterns using data from atomistic simulations, without requiring a priori specification of the crystal structure or defect periodicity. The Kikuchi pattern simulation is based on the kinematic theory of diffraction, with Kikuchi line intensities computed via a discrete structure factor calculation. Reciprocal lattice points are mapped to Kikuchi lines using a geometric projection of the reciprocal space data. This method is validated using single crystal atomistic models, and the novelty of this approach is emphasized by simulating kinematic Kikuchi diffraction patterns from an atomistic model containing a nanoscale dislocation loop. Deviations in kinematic Kikuchi line intensities are explained considering the displacement field of the dislocation loop, as is done in diffraction contrast theory.

The effect of pressure applied normal to the {111} slip plane on the Peierls stress in Al is studied via atomistic simulations. Edge, screw, 30°, and 60° straight dislocations are created using the Volterra displacement fields for isotropic elasticity. For each dislocation character angle, the Peierls stress is calculated based on the change in the internal energy, which is an invariant measure of the dislocation driving force. It is found that the Peierls stress for dislocations under zero pressure is in general agreement with previous results. For screw and 60° dislocations, the Peierls stress versus pressure relationship has maximum values associated with stacking fault widths that are multiples of the Peierls period. For the edge dislocation, the Peierls stress decreases with increasing pressure from tension to compression. Compared with the Mendelev potential, the Peierls stress calculated from the Mishin potential is more sensitive to changes in pressure.

A coupled phase-field model is presented for simulating physical vapor deposition (PVD) of multi-phase materials, including the effects of phase nucleation. This model is utilized to study the role of initial substrate phase and temperature distributions, which are important experimental deposition parameters, on PVD of a generic allotropic metal with two stable phases. PVD simulations are performed for the deposition of a high temperature phase below its phase transition temperature, and for bicrystal and amorphous substrates with a Gaussian temperature distribution. Several general observations are made from these simulations. During the initial stages of PVD, the substrate phase distribution acts as a template for the growing phases. As the thin film continues to grow, the release of latent heat due to deposition creates a temperature gradient within the film, i.e., regions near the film surface become hotter than near the substrate. Additionally, a substrate with a defined temperature distribution that encompasses temperatures above and below the phase transition temperature, allows for distinguishable regions within the thin film where different phases are stable and continue to grow. Three-dimensional simulations provide additional insight into the role of substrate temperature and phase distribution on the resulting microstructure with different flux rates.

Dislocations in high entropy alloys (HEAs) are wavy and have natural pinning points due to the variable chemical and energetic landscape surrounding the dislocation core. This can influence the critical shear stress necessary to initiate dislocation motion and the details associated with sustained dislocation glide. The objective of this work is to determine the relationship between Schmid shear stress and dislocation velocity in single phase FCC FeNiCrCoCu HEAs using molecular dynamics simulations, with comparisons made to dislocation motion in homogeneous Ni and Cu. Simulations are performed for four different dislocation character angles: 0° (screw), 30°, 60° and 90° (edge). Several key differences are reported, compared to what is previously known about dislocation motion in homogeneous FCC metals. For example, the drag coefficient B in the phonon damping regime for HEAs has a nonlinear dependence on temperature, whereas this dependence is linear in Ni. Mobility relationships between different types of dislocations common in homogeneous FCC metals, such as the velocity of screw and 60° dislocations being lower than edge and 30° dislocations at the same shear stress, do not necessarily hold in HEAs. Dislocation waviness is measured and is found to correlate with the ability of dislocations to glide under an applied shear stress, including the temperature dependence of the drag coefficient B. These results confirm that the influence of HEA chemical complexity on dislocation motion is important and this data can be used to guide development of analytical or empirical models for dislocation mobility in HEAs.

A major obstacle in the accurate measurement of the dynamic tensile response of soft materials is the issue of obtaining material response under simultaneous stress equilibrium, stress uniaxiality and constant strain rate. To resolve this issue, a split-Hopkinson pressure bar (SHPB)-based dynamic tension experiment is developed in this study, which has sufficient fidelity to ensure temporal and spatial accuracy of the stress state, to investigate soft materials under large deformations and intermediate dynamic strain rates (100-102 s−1). Cross-linked polydimethylsiloxane (PDMS) elastomer is chosen as a model material. By examining the evolution of full-field strain and strain rate measured using digital image correlation (DIC) and employing analytical criteria for quantifying stress equilibrium and deformation uniaxiality, it is demonstrated that the proposed test method yields a true steady-state and inertia-free stress-strain material response when all three conditions of equilibrium, uniaxiality and strain rate constancy are satisfied. Quasi-static experiments at 10−3-10−1 s−1 strain rate are also conducted for comparison. By analyzing the quasi-static and dynamic stress-strain plots and the variation of uniaxial moduli in the investigated range of strain rates, it is shown that the tensile response of PDMS points to limiting chain extensibility and exhibits a weak nonlinear strain rate sensitivity. Finally, a visco-hyperelastic model based on the Gent strain energy density function and a recently proposed viscous dissipation potential is employed to capture the experimentally obtained response. It is shown that all the features of the rate-dependent stress-strain response are modeled with good fitting accuracy.

The shock response of Cu x Zr100−x (x = 30, 50 and 70) metallic glasses (MGs) is characterized using large-scale molecular dynamics simulations. A wide range of piston velocities U p = 0.125–2.5 km/s are simulated corresponding to shock pressures from 3 to 130 GPa. Independent of composition, the metallic glasses exhibit the following shock wave propagation regimes: (1) single elastic shock wave for U p 0.75 km/s. Within the split wave and overdriven regimes, the amplitude of the elastic precursor increases with increasing shock intensity, thereby indicating a pressure-dependent yield criterion. Hugoniot states are strongly dependent on the Cu content of the MG with Cu70Zr30 exhibiting a much higher resistance to plastic deformation than either Cu50Zr50 or Cu30Zr70.

All grain boundaries are not equal in their predisposition for fracture due to the complex coupling between lattice geometry, interfacial structure, and mechanical properties. The ability to understand these relationships is crucial to engineer materials resilient to grain boundary fracture. Here, a methodology is presented to isolate the role of grain boundary structure on interfacial fracture properties, such as the tensile strength and work of separation, using atomistic simulations. Instead of constructing sets of grain boundary models within the misorientation/structure space by simply varying the misorientation angle around a fixed misorientation axis, the proposed method creates sets of grain boundary models by means of isocurves associated with important fracture-related properties of the adjoining lattices. Such properties may include anisotropic elastic moduli, the Schmid factor for primary slip, and the propensity for simultaneous slip on multiple slip systems. This approach eliminates the effect of lattice properties from the comparative analysis of interfacial fracture properties and thus enables the identification of structure-property relationships for grain boundaries. As an example, this methodology is implemented to study crack propagation along Ni grain boundaries. Segregated H is used as a means to emphasize differences in the selected grain boundary structures while keeping lattice properties fixed.

Physical vapor deposition (PVD) simulations are performed using a phase-field model to study microstructure evolution in single-phase polycrystalline materials as a function of deposition conditions. Specifically, this work focuses on the influence of (i) polycrystalline substrate microstructure with low-angle and high-angle grain boundaries (GBs), (ii) incident vapor flux rate, and (iii) model parameters controlling grain evolution dynamics. Simulation results show that low-angle and high-angle GBs in the substrate promote the formation of low-angle and high-angle GBs within the deposited thin film, in qualitative agreement with experimental reports. Changing the vapor flux rate has a significant influence on the deposited microstructure. A relatively low flux rate is found to provide a thin film with no subsurface porosity, smoothed surface roughness, and a mixture of grain sizes. With an increased vapor flux rate, uniformly distributed surface columnar features are observed with subsurface porosity. The GBs migrate during growth to align with these surface features. At the largest flux rate studied, a dendritic style microstructure is formed where the GBs tend to align with and grow along the regions of low phase density within the thin film. Finally, a parametric study is performed on the phase-field model grain evolution parameters to elucidate their role on grain boundary thickness, internal grain variations and grain rotation during simulated PVD.

Twin nucleation and growth are prevalent plastic deformation mechanisms in hexagonal close-packed metals such as Mg. For twin growth to occur, the interfaces that border the twinned domain must migrate and the kinetics associated with this process are yet to be fully explained. Thus, the objective of this study is to characterize the relationship between the kinetics of the ${10\overline{1}2}$ twin boundary in pure Mg in the stress-driven regime, and the nucleation, growth, and coalescence of disconnection terraces that serve as the mechanisms for migration. This problem is addressed via atomistic simulations adopting both two- (2D) and three-dimensional (3D) simulation geometries, and a model for the velocity of the ${10\overline{1}2}$ twin boundary as a function of temperature and shear stress is proposed. This study shows that the kinetics of ${10\overline{1}2}$ twin boundary migration must be addressed using 3D models, as 2D simulations do not properly capture disconnection terrace nucleation and growth processes, demonstrated via differences in activation volumes and energies. Importantly, simulations reveal an autocatalytic terrace nucleation mechanism as playing a role in twin growth, where nucleation of a new terrace is dependent on the growth of existing terraces on the twin plane.

Grain boundaries in metallic materials can exist in a wide range of stable and metastable structures. In addition, the properties of a grain boundary may be altered through solute segregation. In this work, we present a formulation that combines the spectrum of embrittling potencies associated with solute segregation with site-occupancy statistics. As a prototype problem, we illustrate the relation between segregation and embrittlement in the case of S segregation to grain boundaries in Ni. To obtain a population of site segregation energies, we perform molecular statics calculations on 378 different symmetric-tilt grain boundaries and their free surface equivalents, using an embedded-atom method interatomic potential developed specifically for studying embrittlement. Our results show that it is important to consider both the energies associated with embrittlement and the probability of occupancy to describe the general embrittling nature of a grain boundary. When analyzed in isolation, certain grain boundaries show large embrittling potencies; however, that effect is diminished when the probability of S segregation to that grain boundary is considered within a polycrystal. We propose a new quantity, the embrittling estimator, which not only categorizes grain boundaries as embrittling or strengthening, but also considers site occupancy probabilities, so that the embrittlement behavior of grain boundaries within a network of grain boundaries can be compared. Finally, we examine the relationship between embrittlement behavior and innate grain boundary properties, such as the free volume, and find statistical evidence that the complex nature of embrittlement cannot be explained by linear correlations with excess volumes or energies. Ultimately, this combined approach provides a theoretical tool to assist grain boundary engineering of metastable alloys.

Two models are presented based on the phase-field methodology to simulate thin film growth during physical vapor deposition (PVD), including subsurface microstructure evolution, for isotropic single-phase polycrystalline materials. The first model couples previous phase-field modeling efforts on ballistic deposition of single-phase materials and grain orientation evolution in polycrystalline materials in a sequential simulation algorithm. The second model incorporates both PVD and grain evolution dynamics into a single free energy functional for use in a phase-field model. To illustrate the capability of the proposed models in capturing combined thin film growth and subsurface grain evolution, PVD simulations of a generic single-phase polycrystalline metal are performed on substrates with different grain sizes. In both models, when the initial substrate grain sizes are smaller than the expected surface features, the thin film grains coarsen via grain boundary (GB) migration until the GBs become aligned with the valleys between the columnar surface features. Thus, each columnar feature is associated with a distinct subsurface grain, in qualitative agreement with experimental observations. Differences between the models arise when initial substrate grain sizes are larger than the surface columnar features. For example, when using the single free energy functional approach, grains contain noticeable internal low-angle variations, which are not captured using the coupled model.

In isotropic linear elasticity, a constitutive model calibrated using a single deformation mode (e.g., compression or tension or shear) is sufficient to describe a complex three-dimensional (3D) stress state. Such an approach, however, is likely inadequate for modeling hydrogels, which exhibit a nonlinear stress-strain response that varies significantly between deformation modes and is also sensitive to microstructure via gel concentration. In this study, a combined experimental and constitutive modeling framework is proposed for the development and validation of concentration-dependent 3D hyperelastic models for hydrogels. Agarose hydrogel in a concentration range of 0.4–4% w/v is chosen as the model material. Uniaxial compression, uniaxial tension, and simple shear (three primary deformation modes) experiments are conducted. The small strain elastic modulus-gel concentration relationships obtained from experiments are compared with those predicted by the molecular theory of rigid polymer networks (Jones-Marques theory) to identify the concentration range in which entropic elastic (hyperelastic) response dominates. In this range (1.5–4% w/v), four hyperelastic constitutive models are fit to the combined compression-tension-shear stress-strain data: Mooney-Rivlin, three-parameter generalized Rivlin, Gent, and Gent-Gent models. It is demonstrated that the generalized Rivlin model offers the best overall accuracy, and the variation of its model parameters with gel concentration is consistent with the Jones-Marques theory. The resulting concentration-dependent Extended Generalized Rivlin model is employed in finite element simulations of the non-homogeneous 3D stress state of wedge indentation. Simulated load versus depth and strain field predictions show very good agreement with experimental wedge indentation results. Finally, it is shown that a hyperelastic model calibrated using only a single deformation mode yields poor results for other primary and 3D deformations, and thus multiple primary deformation modes (preferably all three) should be considered.

Twinning is an important plastic deformation mechanism in Mg. While computational and experimental efforts have studied the two-dimensional equilibrium structure of boundaries and facets that surround twin domains, little consideration has been given to three-dimensional nonequilibrium structures. Furthermore, the relationship between the structure of nonequilibrium facets and the kinetics of twinning is also not well understood. Thus, the objective of this work is to characterize the structure of three-dimensional defects on the { 10 1 ¯ 2 } twin boundary and to study the kinetics associated with motion of the facets that bound these three-dimensional defects. Atomistic simulations show that the three-dimensional defects are bounded by nonequilibrium facets with prismatic/basal and twist pyramidal/pyramidal interfaces. The three-dimensional defects are surrounded on the { 10 1 ¯ 2 } twin boundary by disconnection loops. The kinetics of the twin domain facets at finite temperature are analyzed by both molecular dynamics and a newly proposed anisotropic phase-field model. The latter allows the deconvolution of the competing role of interface energy, mobility and internal stress state. Molecular dynamics simulations show that inclined facets control the annihilation process; this behavior is captured in the phase-field model using mobility for the coherent twin boundary that is significantly lower than that of crater inclined facets. Furthermore, molecular dynamics simulation results are best matched via the introduction of facet orientation dependent excess energies.

Ni/Al nanolaminates are reactive materials with customizable combustion characteristics. A common approach to synthesize the repeating Ni and Al nanolayers is physical vapor deposition, which often results in columnar grains with ⟨ 111 ⟩ texture and grain diameters on the order of a single layer thickness. Changes in grain size have been reported to affect combustion rates, yet the role of individual grain boundaries (GBs) on this process is unclear. Thus, this work investigates the role of the GB structure on atomic diffusion/dissolution and the resulting combustion reaction via molecular dynamics simulations. Nanolaminate combustion is simulated in bicrystal models containing columnar symmetric tilt GBs with ⟨ 111 ⟩ misorientation axis perpendicular to the Ni/Al interface. A range of GB misorientation angles is studied, and combustion in a Ni/Al nanolaminate without GBs is simulated for comparison. Combustion in bicrystal models reveals a rise in temperature with an exponential form prior to complete Al melting, while the model without GBs shows a linear temperature increase. Diffusion coefficients are measured for each bicrystal model, and separate Arrhenius fits are used to identify the first three combustion stages. Models containing higher energy GBs generally have higher diffusion coefficients and lower activation energies prior to complete melting of Al, while the GB structure shows little effect on dissolution after the Al layer melts. Thus, the GB structure plays a key role in Ni/Al nanolaminate ignition sensitivity but does not impact runaway combustion.

This work proposes a data-analytics-based method to correlate diffraction peak broadening to dislocation density in relaxed dislocation networks. The model relies on two key developments: the generation of virtual diffraction signatures of dislocated crystals and the development of a surrogate model to predict dislocation density from diffraction profiles. First, two algorithms are introduced for the generation of diffraction profiles from discrete dislocation dynamics (DDD) simulations. Both algorithms leverage the full-field spectral computation of the elastic strain fields generated in the presence of dislocations. However, the two algorithms differ in their treatment of correlations in the elastic strain field; the impact of this difference on the shape of diffraction peaks is emphasized. A database containing 220 virtual diffraction profiles is generated from networks of dislocations in Al using the correlation-dependent algorithm. This dataset is employed to train and test a surrogate model. Predictions consistently yield dislocation densities within a 90% confidence interval of +30% to −41%, which is an improvement over prior dislocation density prediction methods. It is thus demonstrated that the simultaneous use of virtual diffraction and data analytics can yield alternative models for the analysis of diffraction line profiles in which uncertainty can be quantified for complex dislocation networks.

A novel viscous dissipation potential is proposed for the visco-hyperelastic constitutive modeling of short-time memory responses of soft materials, which can capture both linear and nonlinear large deformation behaviors over a wide range of strain rates. The proposed potential is compatible with objectivity and continuum thermodynamics principles, consists of physically motivated model parameters, and adds the capability of modeling strain rate sensitivity in the small strain regime, which is currently not possible with available external state variable driven viscous dissipation potentials. By combining the proposed viscous dissipation potential with the Mooney-Rivlin strain energy density function, a visco-hyperelastic relation is formulated and fit to the rate-dependent tensile stress-strain data of human patellar tendon, which was previously modeled using an existing viscous dissipation potential. It is demonstrated that the proposed model offers improvements in fitting accuracy and prevents possible thermodynamic instabilities in quasi-static hyperelastic models from corrupting the dynamic response. In addition, the uncomplicated mathematical form of the model and the accompanying multi-step multi-start optimization procedure helps prevent numerical instabilities. Multi-deformation mode fitting of human brain gray matter under all three primary deformation modes (compression, tension and shear) is also considered using a visco-hyperelastic model based on the proposed potential and the semi-empirical Gent-Gent strain energy density function. It is shown that visco-hyperelastic models based on the proposed viscous dissipation potential capture all the essential features of the stress-strain data with unique optimal model parameters, giving reasonable accuracy in both single and multiple deformation mode cases. Further, it is demonstrated that the proposed model is stable and robust with respect to both the choice of the hyperelastic strain energy density and the availability of data from multiple deformation modes.

A statistical approach combined with molecular dynamics simulations is used to study the influence of hydrogen on intergranular decohesion. This methodology is applied to a Ni Σ3(112)[ 1 1 ¯ 0 ] symmetric tilt grain boundary. Hydrogenated grain boundaries with different H concentrations are constructed using an energy minimization technique with initial H atom positions guided by Monte Carlo simulation results. Decohesion behavior is assessed through extraction of a traction–separation relationship during steady-state crack propagation in a statistically meaningful approach, building upon prior work employing atomistic cohesive zone volume elements (CZVEs). A sensitivity analysis is performed on the numerical approach used to extract the traction–separation relationships, clarifying the role of CZVE size, threshold parameters necessary to differentiate elastic and decohesion responses, and the numerical averaging technique. Results show that increasing H coverage at the Ni Σ3(112)[ 1 1 ¯ 0 ] grain boundary asymmetrically influences the crack tip velocity during propagation, leads to a general decrease in the work of separation required for crack propagation, and provides a reduction in the peak stress in the extracted traction–separation relationship. The present framework offers a meaningful vehicle to pass atomistically derived interfacial behavior to higher length scale formulations for intergranular fracture.

The molecular dynamics method is used to investigate the dependence of grain size and grain orientation on deformation in nanocrystalline Cu during shock. Particle velocities from 1.0 to 3.4 km/s are applied to nanocrystalline Cu samples with grain sizes from 6 to 26 nm. Results show that grain size does not significantly influence the temperature and pressure of the Hugoniot state. However, grain size, grain orientation, and particle velocity do influence the details by which Cu is uniaxially compressed into a BCC structure at pressures between 100 and 200 GPa behind the shock front. The computed atomic percentage of BCC structure ranges between 3.4% and 9.2% depending on grain diameter at a particle velocity of 1.5 km/s, reaches a maximum between 23.3% and 30.7% at a particle velocity of 2.4 km/s, and then decreases to approximately 0.0% at a particle velocity of 3.2 km/s. At a particle velocity of 2.4 km/s, the atomic percentage of BCC structure observed during shock increases with increasing grain size, while this trend is reversed at a particle velocity of 1.5 km/s. Moreover, the observation of BCC structure strongly depends on grain orientation; grains with 〈1 0 0〉 directions closely aligned with the shock loading direction show a higher percentage of BCC structure, implying a tetragonal transformation path (Bain path).

Virtual diffraction is a computational technique that enables a synergistic coupling between experiments and atomistic simulations, which can help to elucidate nanoscale structure–property relationships. The research objective herein is to highlight recent advances in the use of virtual diffraction as a method to study the geometry and structure of homophase grain boundaries and heterophase interfaces with direct experimental validation. Virtual selected area diffraction patterns for two types of boundaries—homophase Al twist grain boundaries and heterophase Al2O3/Al interfaces—are created without a priori assumption of the periodic interface structure by computing diffraction intensities across high-resolution, 3-D reciprocal space meshes. In this work, computed diffraction patterns clearly identify Al grain boundary misorientation angles, reveal subsidiary peaks created by the dislocation arrays within select Al grain boundaries, and allow experimental validation of the minimum energy orientation relationship for the Al2O3/Al interface. Due to its advanced implementation, virtual diffraction characterization used throughout this work can be easily extended providing routes for similar analysis and experimental validation of atomistic simulations.

The objective of this work is to elucidate the structure and energy of 12 homophase and heterophase alumina interfaces using atomistic simulations with the ReaxFF potential. First, the computational methods are validated by exploring a set of five α-Al 2 O 3 symmetric tilt twin interfaces. The interface structures and energies for most homophase α-Al 2 O 3 twins are in good agreement with prior atomistic studies; however, small deviations occur for select α-Al 2 O 3 interfaces due to the larger, more appropriate interface areas explored in this work. Next, select experimentally observed κ-Al 2 O 3 , γ-Al 2 O 3 , and θ-Al 2 O 3 homophase interfaces as well as heterophase α-Al 2 O 3 //γ-Al 2 O 3 and θ-Al 2 O 3 //γ-Al 2 O 3 interfaces are investigated for the first time using atomistic simulations to elucidate their atomic structure, including terminating plane(s) and relaxations, and to compute interface energies. ReaxFF predicts that the γ-Al 2 O 3 {1 1 1} twin and the θ-Al 2 O 3 {2 0 0} twin interfaces have energies of the same order as the lowest-energy α-Al 2 O 3 prismatic twin boundary and that the heterophase α-Al 2 O 3 (0 0 0 1)//γ-Al 2 O 3 (1 1 1) interface has the lowest energy of all interfaces studied. Lastly, virtual selected-area electron diffraction patterns of select interfaces are used to experimentally validate the predicted interface structures. Because a consistent computational method is implemented throughout this work, the computed interface energies can be incorporated in future predictive mesoscale simulations of polymorphic alumina.

The structures of select alumina surfaces are studied using molecular statics and molecular dynamics simulations and are characterized using virtual diffraction methods. First, bulk alumina simulations are performed to validate the transferability of the ReaxFF potential to model different alumina phases. Bulk alumina simulations accurately predict α-Al2O3 as the lowest energy crystalline phase; however, they unexpectedly predict an even lower-energy amorphous phase. At 0 K, virtual X-ray diffraction patterns of the bulk crystalline phases and select alumina surfaces are validated by experimental studies. Molecular statics simulations of select alumina surfaces are consistent with prior first-principles studies. However, molecular dynamics simulations show that many surfaces experience significant reconstructions at temperatures below what is expected from experiments. It is believed that premature surface reconstructions are biased by the predicted lower-energy amorphous phase and occur due to the extra degrees of freedom allowed by the free surfaces as well as the available thermal energy during dynamics. Discrete peaks appearing in virtual selected-area electron diffraction patterns indicate that the reconstructions are not fully amorphous due to lattice constraints imposed by the internal bulk structure. Bulk and surface energies are tabulated for each simulation to be used in future predictive mesoscale models of polymorphic alumina.

To fully understand the plastic deformation of metallic polycrystalline materials, the physical mechanisms by which a dislocation interacts with a grain boundary must be identified. Recent atomistic simulations have focused on the discrete atomic scale motions that lead to either dislocation obstruction, dislocation absorption into the grain boundary with subsequent emission at a different site along the grain boundary, or direct dislocation transmission through the grain boundary into the opposing lattice. These atomistic simulations, coupled with foundational experiments performed to study dislocation pile-ups and slip transfer through a grain boundary, have facilitated the development and refinement of a set of criteria for predicting if dislocation transmission will occur and which slip systems will be activated in the adjacent grain by the stress concentration resulting from the dislocation pile-up. This article provides a concise review of both experimental and atomistic simulation efforts focused on the details of slip transmission at grain boundaries in metallic materials and provides a discussion of outstanding challenges for atomistic simulations to advance this field.

The mechanisms associated with grain boundary motion induced by synthetic, crystal-orientation-dependent driving forces are investigated for a large-angle [0 0 1] Ni symmetric tilt grain boundary. The application of non-physical forces by this method brings legitimate concern that it could lead to non-physical results. This concern is especially relevant below the interface roughening transition temperature where there is a substantial drop in grain boundary mobility and large driving force dependence. Using slip-vector analysis and examining continuum metrics for microrotation and strain, this work shows that the application of synthetic-driving forces does not alter the fundamental mechanisms leading to grain boundary motion. Results in this work are compared directly to shear driven simulations which reveal that the path and deformation history of grain boundary motion is unbiased by the non-physical nature of the driving force acting on the boundary. Nudged elastic band calculations show that the transition path for grain boundary motion is independent of the driving force magnitude and the energy barriers for motion are not appreciably altered by the application of the synthetic driving force.

The objective of this work is to use molecular dynamics simulation with a reactive empirical bond order potential to study the mechanical deformation and failure of monolayer molybdenum disulphide under uniaxial and multiaxial tension. Multiaxial tension is generated via a nanoindentation procedure analogous to recent experiments. Analysis shows that a phase transformation occurs prior to fracture during both uniaxial and multiaxial tension. The force required for monolayer fracture is consistent with experimental results.