Scaling Laws in the Ductile Fracture of Metallic Crystals

We explore whether the continuum scaling behavior of the fracture energy of metals extends down to the atomistic level. We use an embedded atom method (EAM) model of Ni, thus bypassing the need to model strain-gradient plasticity at the continuum level. The calculations are performed with a number of different 3D periodic size cells using standard molecular dynamics (MD) techniques. A void nucleus of a single vacancy is placed in each cell and the cell is then expanded through repeated NVT MD increments. For each displacement, we then determine which cell size has the lowest energy. The optimal cell size and energy bear a power-law relation to the opening displacement that is consistent with continuum estimates based on strain-gradient plasticity (Fokoua et al., 2014, “Optimal Scaling in Solids Undergoing Ductile Fracture by Void Sheet Formation,” Arch. Ration. Mech. Anal. (in press); Fokoua et al., 2014, “Optimal Scaling Laws for Ductile Fracture Derived From Strain-Gradient Microplasticity,” J. Mech. Phys. Solids, 62, pp. 295–311). The persistence of power-law scaling of the fracture energy down to the atomistic level is remarkable

Non-clasical Nucleation in Supercooled Nickel

The dynamics of homogeneous nucleation and growth of crystalline nickel from the super-cooled melt is examined during rapid quenching using molecular dynamics and a modified embedded atom method potential. The character of the critical nuclei of the crystallization transition is examined using common neighbor analysis and visualization. At nucleation the saddle point droplet consists of randomly stacked planar structures with an in plane triangular order. These results are consistent with previous theoretical results that predict that the nucleation process in some metals is non-classical due to the presence of long-range forces and a spinodal.Comment: 4 pages, 5 figure

Atomistic simulations of the plasticity behavior of polycrystalline metals.

Recent advances in computers and atomistic modeling have made the realistic simulation of materials behavior possible. Two decades ago, modeling of materials at the atomic level used simple pair potentials. These potentials did not provide an accurate description of the elastic properties of materials or of the formation of free surfaces, a phenomenon critical in the fracture process. This paper will review the evolution of the Embedded Atom Method (EAM), a modern theory of metallic cohesion that was developed to overcome the limitations of pair potentials. The EAM includes many body effects that are necessary to describe such processes as bond weakening (or strengthening) by impurities. We examine the effects of deformation on polycrystalline FCC metals. We perform simple shear molecular dynamics simulations using the EAM on nickel samples of -10000 atoms to study yield and work hardening. It is found that the deformation is always inhomogeneous when a grain boundary or free surface is present. The atomistic simulations reveal that dislocations nucleating at grain boundaries or free surfaces are critical to causing yielding in pristine material as observed in experiment. Detailed investigation shows that the grain boundaries are significantly weaker than the bulk material and yield at a lower stress. Even so, the yield stress of the polycrystalline samples with either low angle and high angle grain boundaries are found to be similar and only slightly lower than the yield stress of single crystals with the same characteristic dimensions. The local yield stress at the boundaries if found to be significantly less than the average yield stress

Structural, elastic and thermal properties of cementite (Fe3_3C) calculated using Modified Embedded Atom Method

Structural, elastic and thermal properties of cementite (Fe$_3$C) were studied using a Modified Embedded Atom Method (MEAM) potential for iron-carbon (Fe-C) alloys. Previously developed Fe and C single element potentials were used to develop an Fe-C alloy MEAM potential, using a statistically-based optimization scheme to reproduce structural and elastic properties of cementite, the interstitial energies of C in bcc Fe as well as heat of formation of Fe-C alloys in L$_{12}$ and B$_1$ structures. The stability of cementite was investigated by molecular dynamics simulations at high temperatures. The nine single crystal elastic constants for cementite were obtained by computing total energies for strained cells. Polycrystalline elastic moduli for cementite were calculated from the single crystal elastic constants of cementite. The formation energies of (001), (010), and (100) surfaces of cementite were also calculated. The melting temperature and the variation of specific heat and volume with respect to temperature were investigated by performing a two-phase (solid/liquid) molecular dynamics simulation of cementite. The predictions of the potential are in good agreement with first-principles calculations and experiments.Comment: 12 pages, 9 figure

The influence of defects on magnetic properties of fcc-Pu

The influence of vacancies and interstitial atoms on magnetism in Pu has been considered in frames of the Density Functional Theory (DFT). The relaxation of crystal structure arising due to different types of defects was calculated using the molecular dynamic method with modified embedded atom model (MEAM). The LDA+U+SO (Local Density Approximation with explicit inclusion of Coulomb and spin-orbital interactions) method in matrix invariant form was applied to describe correlation effects in Pu with these types of defects. The calculations show that both vacancies and interstitials give rise to local moments in $f$-shell of Pu in good agreement with experimental data for annealed Pu. Magnetism appears due to destroying of delicate balance between spin-orbital and exchange interactions.Comment: 13 pages, 4 figure

Modified embedded-atom method interatomic potentials for the Mg-Al alloy system

We developed new modified embedded-atom method (MEAM) interatomic potentials for the Mg-Al alloy system using a first-principles method based on density functional theory (DFT). The materials parameters, such as the cohesive energy, equilibrium atomic volume, and bulk modulus, were used to determine the MEAM parameters. Face-centered cubic, hexagonal close packed, and cubic rock salt structures were used as the reference structures for Al, Mg, and MgAl, respectively. The applicability of the new MEAM potentials to atomistic simulations for investigating Mg-Al alloys was demonstrated by performing simulations on Mg and Al atoms in a variety of geometries. The new MEAM potentials were used to calculate the adsorption energies of Al and Mg atoms on Al (111) and Mg (0001) surfaces. The formation energies and geometries of various point defects, such as vacancies, interstitial defects and substitutional defects, were also calculated. We found that the new MEAM potentials give a better overall agreement with DFT calculations and experiments when compared against the previously published MEAM potentials.Comment: Fixed a referenc

Atomic interactions between plutonium and helium.

An essential issue in gallium (Ga)-stabilized fcc-phase plutonium ({delta}-Pu) is the formation of helium (He) voids and bubbles emanating from the radiolytic decay of the Pu. The rate of formation of He voids and bubbles is related to the He-defect formation energies and their associated migration barriers. The size and shape distributions of the bubbles are coupled to these critical migration processes. The values of the defect formation energies, internal pressure, and migration barriers can be estimated from atomistic calculations. Complicating this picture is the destruction of He-filled voids and bubbles by subsequent radiolytic decay events. The present study concerns the construction of the necessary potential energy surfaces for the Pu-He and He-He interactions within the modified embedded atom method (MEAM). Once fully tested, the potentials will be used to estimate the He-defect formation energies and barriers to the migration of these defects for both interstitial and substitutional He on an fcc Pu lattice. The He-He interactions are modeled from ab initio electronic structure calculations for the He{sub 2} dimer and the equilateral He, trimer. The experimental data and the electronic structure calculations on He{sub 2} agree very well. These data were fit to a Rose function fn{sub R}(x) = A P({alpha}x) exp(-{alpha}x), where P is a polynomial, x = R/R{sub 0}-1, R is the bond length, and R{sub 0} is its equilibrium value. The fits are very satisfactory. Both linear (P = 1+{alpha}x, zeroth-order Rose) and rational (P = 1+{alpha}x+a{sub 3} ({alpha}x){sup 3}/(1+x) first-order Rose) polynomials in the Rose function were tried. The more flexible rational form does improve the fit, but only marginally. Only the linear form was used thereafter. The resulting MEAM potential was used to predict the behavior of the linear trimer and the fcc cold compression curve. The results are shown in Fig. 2 and appear to be satisfactory. The compression regions of the curves are of particular interest for several reasons. First, an octahedral interstitial He atom in anfcc Pu lattice with a lattice constant of 4.64 {angstrom} has a nearest Pu neighbor distance of 2.32 {angstrom}. This distance is in the compressive region of the potential energy curve. Second, the compressive region will partially determine the internal pressure of He-filled voids and bubbles. Third, the shape of the He-filled voids will be influenced by the compression region of the potential. The Pu-He interactions are also modeled from ab initio electronic structure calculations, this time only for the PuHe dimer. The lowest-energy spin state of the dimer appears to be the S=7/2 state with a 'Stuttgart small-core RECP/6-31 g' basis. Two electronic structure methods were tried which would bound the extremes of the Pu-He interaction. One was the local density approximation (LDA), which tends to overestimate binding strength. It gives a well depth of 0.08 eV and a bond length of 3.6 {angstrom}. The other used the Becke-3-Lee-Yang-Parr (B3LYP) exchange-correlation energy functional, which tends to underestimate binding strength. It predicts no binding at any separation. For purposes of fitting to the Rose functional form, a well depth of 0.03 eV and bond length of 4.8 {angstrom} was used. The bond length exceeds the cutoff distance that will be used in future simulations to limit the maximum range of the atomic interactions and is effectively purely repulsive. Furthermore, the dimer information is sufficient to determine the painvise part of the Pu-He MEAM potential, but not the effective electron density that determines the many-body part of the potential, the embedding functions F{sub He} and F{sub Pu} in Fig. 3. The effective electron density, as well as determining which of the two dimer curves (LDA or B3LYP) is preferable, will be decided by comparing simulation results to known information about He bubble formation rates at elevated temperatures and estimates of Me bubble sizes. Initial simulations suggest that an interstitial He defect, based on either the LDA or the B3LYP dimer curve with a He:Pu density ratio of 0.04, will not remain at an octahedral site as in other fcc metals such as nickel. The He defect may also form a split interstitial with a Pu atom. The details remain to be determined

Increasing the fracture toughness of silicon by ion implantation

This study was motivated by some earlier indications that the fracture toughness of silicon could be increased by ion implantation. The location of fracture in hydrogen implanted silicon was found to change depending on the dose of implanted ions. For relatively low doses, fracture occurred at the center of the damage region created by implantation. However, for larger doses, the fracture location switched to the deeper edge of the implanted zone. This implied that the center of the implanted region experienced toughening due to ion implantation at the higher dose level. In addition, an initial increase in fracture toughness with radiation dose has been observed experimentally in some ceramics. After the initial increase, the fracture toughness reaches a peak and then decreases with further irradiation. The toughness increases found thus far are modest (25-100%). In attempts to explain the experimental results, several toughening mechanisms (such as deflection of the crack by the irradiated damage) have been proposed. However, the proposed mechanisms predict only a 40-80% increase in fracture toughness, which does not account for the highest levels of toughness observed. Our recent molecular dynamics (MD) calculations have found a previously unknown toughening mechanism acting in silicon, which can also explain the earlier experimental observations of toughening induced by irradiation. In our MD simulations, ion implantation produced clusters of disordered atoms. The presence of these clusters allowed silicon to deform plastically as a crack approached, blunting the crack tip and arresting crack growth. The MD calculations show a factor of 3 increase in fracture toughness. We have conducted experiments with silicon implanted with a small dose (ions/cm2) of alpha particles uniformly distributed to a depth of 25 pm. A 20% increase in fracture toughness is observed. Additional experiments with higher implantation doses are planned for the immediate future

Point-detect production and migration in plutonium metal at ambient conditions

Modeling thermodynamics and defect production in plutonium (Pu) metal and its alloys, has proven to be singularly difficult. The multiplicity of phases and the small changes in temperature, pressure, and/or stress that can induce phase changes lie at the heart of this difficulty, In terms of radiation damage, Pu metal represents a unique situation because of the large volume changes that accompany the phase changes. The most workable form of the metal is the fcc (6.) phase, which in practice the 6 phase is stabilized by addition of alloying elements such as Ga or AI. The thermodynamically stable phase at ambient conditions is the between monoclinic (a-) phase, which, however, is approximately 20 % lower in volume than the 6 phase. In stabilized Pu metal, there is an interplay between the natural swelling tendencies of fcc metals and the volume-contraction tendency of the underlying phase transformation to the thermodynamically stable phase. This study explores the point defect production and migration properties that are necessary to eventually model the long-term outcome of this interplay