J. Chem. Phys., Vol. 125, p. 164907, 2006.

Coarse grained model of entangled polymer melts

A. Rakshit, R. C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

A coarse graining procedure aimed at reproducing both the chain structure and dynamics in melts of linear monodisperse polymers is presented. The reference system is a bead-spring-type representation of the melt. The level of coarse graining is selected equal to the number of beads in the entanglement segment, Ne. The coarse model is still discrete and contains blobs each representing Ne consecutive beads in the fine scale model. The mapping is defined by the following conditions: the probability of given state of the coarse system is equal to that of all fine system states compatible with the respective coarse state, the dissipation per coarse grained object is similar in the two systems, constraints to the motion of a representative chain exist in the fine phase space, and the coarse phase space is adjusted such to represent them. Specifically, the chain inner blobs are constrained to move along the backbone of the coarse grained chain, while the end blobs move in the three-dimensional embedding space. The end blobs continuously redefine the diffusion path for the inner blobs. The input parameters governing the dynamics of the coarse grained system are calibrated based on the fine scale model behavior. Although the coarse model cannot reproduce the whole thermodynamics of the fine system, it ensures that the pair and end-to-end distribution functions, the rate of relaxation of segmental and end-to-end vectors, the Rouse modes, and the diffusion dynamics are properly represented.

 

Macromolecules, Vol. 39, p. 3098-3092, 2006

Adsorption and desorption dynamics of linear polymer chains to spherical nanoparticles: a Monte Carlo investigation

P.J. Dionne, R.C. Picu, R. Ozisik

Abstract

Dynamics of attachment/detachment processes of chains to/from spherical fillers in a polymer nanocomposite is investigated by means of numerical simulations using a chemistry-specific model for the polymer.The effects of polymer-particle interaction, chain length, chain-to-filler distance, and filler radius on the attachment/detachment processes are studied. It is found that the time a chain is in contact with a filler scales with the number of attached beads following a power law. Increasing the energetic interaction parameter between polymer and filler slows the detachment process, and the system average characteristic detachment time follows an Arrhenius law in which the activation energy is proportional to the polymer-particle energetic interaction parameter.

 

Model. Simul. Mat. Sci. Eng.., Vol. 14, p. 195-206, 2006

Dislocation-solute cluster interactions in Al-Mg binary alloys

Z. Xu, R.C. Picu

Abstract

The close-range interaction of dislocations and solute clusters in the Al-Mg binary system is studied by means of atomistic simulations. We evaluate the binding energy per unit length of dislocations to the thermodynamically stable solute atmospheres that form around their cores, at various temperatures and average solid solution concentrations. A measure of the cluster size that renders linear the relationship between the binding energy per unit length and the cluster size is identified. The variation of the interaction energy between a dislocation and a cluster residing at a finite distance from its core is evaluated and it is shown that the interaction is negligible once the separation is larger than approximately 15 Burgers vectors. The data are relevant for the dynamics of dislocation pinning during dynamic strain ageing in solid solution alloys and for static ageing.

 

J. Nanosci. Nanotech, Vol. 5, p. 1893-1897, 2005

Mechanical testing of isolated amorphous Si nanorods

C. Gaire, F. Tang, D.X. Ye, R.C. Picu, G.C. Wang, T.M. Lu

Abstract

Mechanical testing was performed on a new class of nanostructures-amorphous Si slanted nanorods of rectangular cross section, fixed at one end to the substrate. These nanorods were grown spatially well separated on nano-pillars under the oblique angle physical vapor deposition technique. Various samples with different dimensions and inclination angles were tested in bending using an atomic force microscope. The material response was elastic up to large stresses/deflections. The Young's modulus was calculated from the slope of the experimentally observed stiffness versus the geometrical factor common to all the samples and was found to be (94_14±10_21) GPa. No size effect of this parameter was observed within the accuracy of the present measurement.

 

Macromolecules, Vol. 38, p. 9351-9358, 2005

Structure and dynamics of polyethylene nanocomposites

P.J. Dionne, R. Ozisik, R.C. Picu

Abstract

The structure and dynamics of linear monodisperse polyethylene (PE) melts (C160H322 and C440H882) containing homogeneously distributed spherical nanoparticles were investigated. The PE chains were simulated using a coarse-grained model and a Monte Carlo algorithm. Two variables were considered: (i) the wall-to-wall distance between particles d and (ii) the interaction energy between monomers and particles. The various chain structures changed greatly with d while the monomer-particle interaction had little effect. The average size, shape, and orientation of PE chains did not differ significantly from those of a neat melt. Bridge segments were more stretched relative to segments in the neat melt, and the stretch increased with increasing d. However, the number of bridge segments decreased markedly with increasing d. The chain dynamics were monitored by computing the Rouse relaxation modes and the MSD. The dynamics were slowed by both geometric (confinement by fillers) and energetic (monomerparticle energetic interaction) effects

 

Rheologica Acta, Vol. 45, p. 132-141, 2005.

A frictional molecular model for the viscoelasticity of entangled polymer nanocomposite

A.S. Sarvestani and R.C. Picu

Abstract

The dynamics of polymer melts and concentrated solutions reinforced with nanoscale rigid spherical particles is analyzed. Nanocomposites with low filler volume fraction and strong polymer-filler interactions are considered. Entanglement effects are represented by requiring the diffusion in the chain contour direction to be more pronounced than in the direction transverse to the chain primitive path. Filler particles are treated as material points. They reduce the polymer mobility in both longitudinal and transverse tube directions due to short-range energetic filler-polymer interactions. Hence, the contribution to chain dynamics and stress production of both filler-polymer and polymer-polymer interactions is considered to be purely frictional in nature. In the model, the strain rate sensitivity is associated with the thermal motion of chains, with the convective relaxation of entanglement constrains and with the polymer-filler attachment/detachment process. The effect of model parameters is discussed and the predictions are compared with experimental data.

 

Scripta Mat., Vol. 54, p. 71-75, 2006.

Effect of solute clustering on the strain rate sensitivity of solid solutions

R.C. Picu, G. Vincze, J.J. Gracio, F. Barlat

Abstract

An experimental study is presented regarding the effect of pre-existing inhomogeneous solute distribution on the strain rate sensitivity of a non-heat treatable Al-Mg alloy (AA5182). Tests are performed with specimens heat treated to eliminate pre-existing solute structures within the material and with specimens equilibrated at room temperature. The rate sensitivity is significantly more pronounced in the equilibrated specimens, which indicates that solute structures that exist before the test play a role in determining the rate sensitivity of the material at low temperatures.

 

Phil. Mag. Lett., Vol. 79, p. 241-247, 1999.

Direct Observation of Surface Sublimation and Relaxation in CdTe {111} Films by High Resolution Electron Microscopy

R. C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

J. Rankin and A. F. Schwartzman
Division of Engineering, Brown University, Providence, RI 02912

Abstract

The sublimation of a CdTe {111} surface at 600°C is studied by High Resolution Electron Microscopy (HRTEM) in the profile-image geometry. The sublimation involves the simultaneous desorption of Cd and Te atoms of the outermost layer and occurs by a kink-step propagation mechanism. The rate of sublimation is found to be independent of the presence of twins in the film. Further, the surface relaxation in this system is investigated. It is found that the relaxation affects only the outermost atomic layer which finds its equilibrium position at a {111} inter-planar spacing 13 % bigger than the corresponding bulk value. Surface relaxation measurements have been performed at both room temperature and 600°C with similar results.

J. Computer-Aided Mat. Design., Vol. 7, p. 77-87, 2000.

Atomistic-continuum simulation of nano-indentation in Molybdenum

R. C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

Simulations of nano-indentation in bcc Molybdenum are performed using a coupled atomistic-continuum method and a multi-body interatomic potential which includes angular forces. The indenter is flat and rigid while the indented material is a single crystal having its <100> and <111> directions respectively parallel to the indentation direction, in separate simulations. Indentation is accommodated by elastic deformation of the surface, up to an indenter displacement of about 6 Å, and by nucleation of crystalline defects for deeper indents. When indented in the <100> direction, the crystal twins under the indenter, while indentation in the <111> direction produces dislocation nucleation from the stress concentration sites at the indenter edge. The critical loads for these events are computed and the nucleation mechanism is observed. The results are compared with available experimental data.

Materials Science and Engineering A, Vol. 326, p. 297-305, 2002.

Mechanical behavior of Ti 6%Al4%V at high and moderate temperatures;
Part I: Experimental results

A. Majorell
General Electric Corporate Research and Development Center, Niskayuna, NY 12309

S. Srivatsa
General Electric Aircraft Engines, Cincinnati, OH 45215

R.C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

This study investigates the plastic deformation of titanium alloy Ti-6Al-4V under low and moderate strain rates and various temperature conditions. Mechanical testing is performed in the temperature range 650 to 1340°K (710 to 1950°F) and under constant strain rate loading ranging from 0.001 to 10 per sec. The test results are correlated with the evolution of the microstructure and compared to published data. The flow stress of this alloy is strongly dependent on both temperature and deformation rate, with the temperature effect becoming negligible in the upper part of the temperature range investigated. At temperatures above 800°K (980°F) the flow stress decreases sharply with temperature. The effect of deformation rate on this transition is investigated and the possible mechanisms responsible for the behavior are discussed. Based on these experimental results, a physically-based constitutive law is developed in the sequel of this paper.

Materials Science and Engineering A, Vol. 326, p. 306-316, 2002.

Mechanical behavior of Ti 6%Al4%V at high and moderate temperatures;
Part II: Constitutive modeling

R. C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

and

A. Majorell
General Electric Corporate Research and Development Center, Niskayuna, NY 12309

Abstract

A physically-based model for the deformation of Ti 6%Al 4%V is proposed. The various deformation mechanisms active in this material over the whole range of temperatures of industrial interest are discussed, and a strategy by which the relevant strengthening effects are captured in the model is proposed. The flow stress contains a thermal and an athermal component. The thermally activated processes are modeled based on the Kocks-Mecking formalism, while the athermal processes are simulated using an internal state variable. The deformation of the a and b phases is captured separately. The model is calibrated based on experimental results obtained from tests performed in the temperature range (77 - 1400°K) and at strain rates between 0.001 and 10 per sec. The model predictions are extrapolated to strain rates as high as 2000 per sec. The experimental findings are presented in the companion paper.

J. Chem. Phys., Vol. 110, p. 4678-4685, 1999.

Towards a Unified View of Stress in Small-Molecular and in Macromolecular Liquids

R. C. Picu (1), G. Loriot (2) and J. H. Weinera (1)
(1) Division of Engineering, (2) Computing and Information Services,
Brown University, Providence, RI 02912

Abstract

Macromolecules, Vol. 32, p. 7319-7324, 1999.

Intrinsic Distribution and Atomic Level Stress in Polymeric Melts

R. C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The relationship between stress production and relaxation, and the local structure is studied in model polymeric melts by the use of equilibrium and non-equilibrium molecular dynamics. The analysis is performed in the intrinsic coordinate system - a mobile frame tied to the generic bond. The variation of the intrinsic distribution of interacting neighbors about a representative atom, g~, with density and temperature is investigated above and below the glass transition. It is shown that g~ captures close packing effects and the build-up of structure upon transition, similarly with the radial distribution function g(r). When computed from the nearest non-bonded neighbors, the intrinsic distribution is non-uniform due to steric shielding. Neighbors at distances larger than a covalent bond length from the representative atom however, lead to a uniform distribution g~. Thus, the steric shielding effect generates a non-zero intrinsic deviatoric stress in both equilibrium and non-equilibrium systems, while longer range interactions do not contribute to deviatoric stress production. Consequently, each intrinsic frame carries a non-hydrostatic stress (induced by both bonded and non-bonded interactions) which, upon rotation in the global coordinate system, contributes to the global stress in the melt. A preferential orientation of intrinsic frames (induced, for instance, by the deformation of the fluid) generates therefore a deviatoric global stress. In non-equilibrium simulations, the intrinsic distribution is seen to be independent of the deformation of the fluid. Furthermore, when computed from chain inner atoms, the intrinsic distribution is also chain length independent. This implies, in turn, that intrinsic stresses are deformation and chain length independent. The relevance of these observations to stress relaxation in polymeric melts is discussed.

Macromolecules, Vol. 34, p. 5023-5029, 2001.

The entropic character of the atomic level stress in polymeric melts

R.C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The entropic character of the atomic level stress in polymeric melts and the stress optical coefficient are studied in model systems by the use of equilibrium and nonequilibrium molecular dynamics. The atomic level stress is defined in intrinsic coordinates, a mobile frame tied to the generic bond. The global stress sigma is obtained in the global coordinate system by summing up the contribution due to the intrinsic stress corresponding to each atom in the population. The atom-based global stress is proportional to an average measure of bond orientation (P2), with the proportionality constant sigma/P2 being related to the macroscopic stress optical coefficient (SOC). The proportionality constant may be expressed in terms of intrinsic quantities which, in turn, are computable from equilibrium simulations. The model reproduces most experimentally observed properties of the SOC. The ratio sigma/P2 is chain length and deformation rate independent in the melt, and becomes rate dependent in the glassy state. The dependence of the global stress on temperature at imposed average bond orientation is therefore determined by the variation of the intrinsic stresses with temperature. The stress is purely entropic in the melt for all chain lengths. However, neither one of its components, that due to bonded and that due to non-bonded interactions, is purely entropic. The global stress sigma acquires an energetic component at high temperatures and at large deformations, when chains are significantly stretched. The entropic character of the atomic level stress is shown to be due to packing effects, similar to the situation encountered in simple fluids. These conclusions remain unchanged upon variation of the model parameters such as the stiffness of the non-bonded and bonded interatomic potential, the cut-off radius of the non-bonded potential, and the bond length.

Polymer Composites, Vol. 23, p. 110-119, 2002.

Elastic moduli of particulate composites with graded filler-matrix interfaces

M.S. Ozmusul and R.C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The elastic response of plane-array models of composites reinforced by particles or aligned fibers having graded interfaces with the matrix is analyzed. Such microstructure is representative for a new class of polymer matrix composite materials in which the filler is nanometer-sized. In such materials, the polymer chains in the matrix are preferentially oriented close to the interface with the relatively rigid fillers, this leading to a graded interfacial layer about each inclusion. The composite elastic moduli are determined based on the properties and geometry of the interfacial graded layer as well as on the moduli of the filler and the matrix, and the volume fraction of filler. Conversion curves are constructed allowing for an equivalence to be established between the present case and that of similar composites without graded interfaces. Based on these conversion curves, standard homogenization algorithms can be applied to determine the overall elastic properties of such composite. The fillers are considered to be stiffer than the matrix, both rigid and of finite stiffness. Results for both sliding and bonded interfaces are presented. The effect of anisotropic material properties in the graded region on the composite moduli is also investigated. The results of the model are compared with published experimental data.

J. Mech. Phys. Sol., Vol. 50, p. 717-735, 2002.

The Peierls Stress in Non-Local Elasticity

R. C. Picu
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The effect of non-locality on the Peierls stress of a dislocation, predicted within the framework of the Peierls-Nabarro model, is investigated. Both the integral formulation of non-local elasticity and the gradient elasticity model are considered. A modification of the non-local kernel of the integral formulation is proposed and its effect on the dislocation core shape and size, and on the Peierls stress are discussed. The new kernel is longer ranged and physically meaningful, improving therefore upon the existing Gaussian-like non-locality kernels. As in the original Peierls-Nabarro model, lattice trapping cannot be captured in the purely continuum non-local formulation and therefore, a semi-discrete framework is used. The constitutive law of the elastic continuum and that of the glide plane are considered both local and non-local in separate models. The major effect is obtained upon rendering non-local the constitutive law of the continuum, while non-locality in the rebound force law of the glide plane has a marginal effect. The Peierls stress is seen to increase with increasing the intrinsic length scale of the non-local formulation, while the core size decreases accordingly. The solution becomes unstable at intrinsic length scales larger than a critical value. Modifications of the rebound force law entail significant changes in the core configuration and critical stress. The discussion provides insight into the issue of internal length scale selection in non-local elasticity models.

J. Mech. Phys. Sol., Vol. 50, p. 1923-1939, 2002.

On the Functional Form of Non-Local Elasticity Kernels

R.C. Picu
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The functional form of non-local elasticity kernels is studied within the context of the integral formalism. The study is limited to linear isotropic elasticity. The kernels are derived analytically based on the discrete structure of the material at the atomic scale. Atomistic simulations are used to validate the results. Materials in which the interatomic interactions are represented by pair, as well as embedded atom-type potentials are considered. The derived kernels have a range which extends up to the cut-off radius of the interatomic potential, are positive at the origin, and become negative approximately one atomic distance away, thus departing from the commonly assumed Gaussian functional form. The functional form of the potential and the radial distribution function of interacting neighbors about a representative atom fully define their shape. This new continuum model involves two material length scales that are both derived from atomistics for a Morse solid and for Al. Two applications are considered in closure. It is shown that in strained superlattices, the non-local model predicts maximum stresses that are much larger than those obtained within the local theory. This observation has implications for defect nucleation in these structures. Furthermore, the new non-local model improves upon the Gaussian one by predicting a more realistic wave dispersion relationship, with essentially zero group velocity at the boundary of the Brillouin zone.

Macromolecules, Vol. 35, p. 1840-1847, 2002.

Fast relaxation modes in model polymeric systems

R.C. Picu and M.C. Pavel
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The fast stress relaxation modes in a model polymeric melt are investigated by means of non-equilibrium molecular dynamics simulations. The stress is computed on the atomic level by accounting for both bonded and non-bonded interatomic interactions. The system evolution is traced during the loading and the relaxation periods, and the mechanisms of stress production are identified. Stress relaxation takes place by several modes, each corresponding to specific atomic scale structural changes. The relaxation corresponds to the return to isotropy of the atomic distribution in the neighborhood of a representative atom, and encompasses a quasi-elastic mode, (1), and a slower mode (2). A diffusion-like process governs the 2 mode. The 1 mode is non-exponential and accounts for roughly 50% of the total atomic scale stress drop during relaxation. The 2 mode is exponential, leads to a smaller stress drop but takes longer to complete compared to 1. Both modes involve only local structural changes and their time constants are independent of the molecular weight of the chains. These are simple thermally activated processes which do not involve cooperative relaxations and whose temperature dependence may be described by an Arrhenius equation. Furthermore, it is shown that the time constant for the exponential mode, 2, may be derived from equilibrium simulations based on the fluctuation dissipation theorem and a continuum model of diffusion in the neighborhood of a representative atom. This shows that the non-equilibrium system is in the linear response regime during this relaxation regime.

Polymer, Vol. 43, p. 4657-4665, 2002.

Structure of polymers in the vicinity of curved impenetrable surfaces - the athermal case

M.S. Ozmusul and R.C. Picu
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The influence of the presence of a curved (convex) solid wall on the conformations of long, flexible polymer chains is studied in a dense polymer system and in the athermal limit by means of lattice Monte Carlo simulations. It is found that the chain conformation entropy drives a reduction of the density at the wall, similar to the flat wall case. The chain end density is higher next to the interface compared to the bulk polymer (segregation), with the difference increasing with chain length. The wall curvature does not significantly affect the segregation. The bonds are preferentially oriented in the direction tangential to the wall. The distance from the interface over which this effect is observed is about two bond lengths. Similar results are obtained when probing the preferential orientation of chain segments. In this case, the perturbed region has a thickness on the order of the considered probing chain segment length. This suggests that experimental results on the thickness of the "bonded layer" next to a wall depend on the wavelength of the radiation employed for probing. The chains are ellipsoidal in the bulk and rotate close to the surface with the large semi-axis of the ellipsoid normal to the line connecting their center of mass with the filler center. Since there is no energetic interaction with the filler, no adsorption transition is observed, but the chains tend to wrap around the filler once the gyration radius becomes comparable to the filler radius.

Journal of Chemical Physics, Vol. 118, p. 11239-11248, 2003.

Structure of linear polymeric chains confined between impenetrable spherical walls

R.C. Picu and M.S. Ozmusul
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The bond-scale and chain-scale structure of linear polymers located close to spherical impenetrable surfaces is studied in dense systems by means of lattice Monte Carlo simulations. The role of the various types of interactions (entropic, cohesive in the bulk polymer, attraction to filler surface) and that of the chain length, polymer density and wall curvature in defining the polymer structure is analyzed. The size effect of the spherical fillers is investigated by scaling the filler radius at constant filler volume fraction. On the bond scale, the chain ends segregate to the wall in all systems, with the effect being essentially independent of wall curvature. The bonds are preferentially oriented in the direction tangential to the wall. The distance from the wall over which these effects are observed is about one bond length in the athermal case, and about two chain gyration radii in the energetic case. On the chain scale, the ellipsoidal chains undergo a "docking" transition to the spherical fillers. The ellipsoids do not deform, rather rotate with their large semi-axis in the direction tangential to the filler as their centers of mass approach the wall. This configurational entropy-controlled situation remains valid when cohesive interactions are considered in the bulk polymer, and even with a hydrogen bond-strong attraction of the polymer to the wall. When the wall-to-wall distance between fillers decreases below two bulk gyration radii, the chain size decreases in the direction of its large semi-axis, effect essentially independent of the details of the energetic interactions in the system.

J. Multiscale Comput. Eng., Vol. 1, p. 23-32, 2003

A non-local formulation of rubber elasticity

R.C. Picu
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer
Polytechnic Institute, Troy, NY 12180

Abstract

A non-local formulation of rubber elasticity with applications to nanostructured materials is developed. In general, stress has an entropic and an energetic component. The energetic component is due to short range interactions of the representative atom with its neighbors, while the entropic component is due to chain conformation changes upon deformation. In rubbers, the entropic component is dominant. Both components are intrinsically non-local; stress at a point depends on the deformation in a whole neighborhood of that point. This property becomes important when the deformation field varies significantly over a distance comparable with the internal length scale of the material (large gradients). Here, non-local formulations are derived for both the energetic and the entropic components of stress for a system of polymeric chains. For small deformations, linear non-local elasticity may be used for the energetic component of stress and a kernel may be derived within the integral formalism of non-local elasticity. The entropic component is highly non-linear and no kernel may be separated. The implications of considering a non-local description for nanostructured materials in place of the conventional local one are discussed.

J. Appl. Phys., Vol. 93, p. 3535-3539, 2003

Strain and size effect on heat transport in nanostructures

R.C. Picu, T. Borca-Tasciuc and M.C. Pavel
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

The relative role of the residual strain and dimensional scaling on heat transport in nanostructures is investigated by molecular dynamics simulations of a model Lennard-Jones solid. It is observed that tensile (compressive) strains lead to a reduction (enhancement) of the lattice thermal conductivity. A non-hydrostatic strain induces thermal conductivity anisotropy in the material. This effect is due to the variation with strain of the stiffness tensor and lattice anharmonicity, and therefore of the phonon group velocity and phonon mean free path. The effect due to the lattice anharmonicity variation appears to be dominant. The size effect was studied separately in unstrained thin films. Phonon scattering on surfaces leads to a drastic reduction of the thermal conductivity, effect which is much more important than that due to strain in the bulk. It is suggested that strain may be used to tailor the phonon mean free path which offers an indirect method to control the size effect.

Macromolecules., Vol. 36, p. 9205-9215, 2003

Scale invariance of the stress production mechanism in polymeric systems

R.C. Picu and M.C. Pavel
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Abstract

Stress production in a model monodisperse polymeric material is investigated on multiple scales. The analysis is performed by means of equilibrium and non-equilibrium molecular dynamics. A family of mobile intrinsic coordinate systems is introduced, each system having one axis tied to the end-to-end vector of a generic chain segment of specified length. A similar mobile coordinate system tied to the large semiaxis of the ellipsoidal chains is defined on the chain scale. The atomic level stress is evaluated based on bonded and non-bonded interatomic interactions, and averaged in the global coordinate system, to result in the global, system level stress, and in the various intrinsic systems, to result in intrinsic stresses. It is observed that the deviatoric intrinsic stress is scale independent, a bond, a chain segment and the chain scale intrinsic frame carrying the same stress. The hydrostatic component of the stress tensor scales with the segment length. This concept extends the previously introduced Intrinsic Stress Framework, scale linking the bond and chain scales. During melt deformation, the chain segments stretch and rotate. Chains shorter than the entanglement length mainly rotate during an elongational deformation of limited amplitude, their size remaining essentially constant. Longer chains distort and rotate. Two regimes are evidenced during the return to isotropy of the orientation on multiple scales. The faster mode is associated with the return to equilibrium of the internal structure of the generic chain, while the slower mode is associated with chain rotation in the global coordinate system. The intrinsic deviatoric stress carried by a chain changes during the first mode, and is essentially constant during the second. The physical picture of stress production defined on the scale of a bond (Kuhn segment) in the Intrinsic Stress Framework translates to the chain scale during this late relaxation regime: each rotating chain carries a constant deviatoric intrinsic stress, the preferential chain orientation leading to a non-zero global deviatoric stress.

J. Nanosci. Nanotech., Vol. 3, p. 492-495, 2003

Mechanics of Patterned Helical Si Springs on Si Substrate

D. L. Liu°, D. X. Ye ¹ , F. Khan ², F. Tang ¹, B. K. Lim ³, R.C. Picu ², G. C. Wang ¹ & T. M. Lua*
¹ Department of Physics, Applied Physics, and Astronomy,
² Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
³ Department of Materials Engineering, Nanyang Technological University, Singapore
*Corresponding author: T.-M. Lu (e-mail: lut@rpi.edu))

Abstract

The elastic response, including the spring constant, of individual Si helical-shape sub-micron springs, was measured using a tip-cantilever assembly attached to a conventional atomic force microscope (AFM). The isolated, 4-turn Si springs were fabricated using oblique angle deposition with substrate rotation, also known as the glancing angle deposition, on a templated Si substrate. The response of the structures was modeled using finite elements and it was shown that the conventional formulae for the spring constant require modifications before could be used for the loading scheme employed in the present experiment.

Acta Materialia, Vol. 52, p. 161-171, 2004

Atomistic study of pipe diffusion in Al.Mg alloys

R. C. Picu, D. Zhang

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180

Abstract

Solute diffusion in an Al-rich binary Al .Mg alloy is studied by means of atomistic simulations.The activation energy for diffusion of Mg in the bulk is evaluated in the dilute solution limit for the nearest neighbor and the ring mechanisms. It is concluded that bulk diffusion at low and moderate temperatures must be assisted by vacancies. Further,disscusion of Mg along the core of edge, 60° and screw dislocations is studied.The activation energy for vacancy formation in the core and for vacancy-assisted Mg migration is evaluated for a large number of diffusion paths in the core region.It is observed that similar to the bulk, Mg diffusion in absence of vacancies is energetically prohibitive. The paths of minimum activation energy are identified for vacancy-assisted diffusion, for all three types of dislocations.The lowest energy path is found in the core of the 60o dislocation, its activation energy being 60% of the activation energy in the bulk. Most diffusion paths have activation energies larger than 75%of the equivalent bulk quantity. This analysis is relevant for the discussion on the mechanism of dynamic strain aging in these alloys. The data presented here show that pipe diffusion, which is currently considered as the leading mechanism responsible for dynamic strain aging is too slow in absence of excess vacancies.

Acta Materialia, Vol. 52, p. 3447-3458, 2004.,

A mechanism for the negative strain-rate sensitivity of dilute solid solutions

R. C. Picu

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180

Abstract

A new mechanism is proposed for dynamic strain ageing and the negative strain-rate sensitivity (SRS) exhibited by dilute solid solutions containing mobile solute atoms.The mechanism is based on the strength variation of dislocation junctions due to the presence of solute clusters on forest dislocations.The strength of a Lomer .Cottrell lock in which the mobile dislocation is free of solute,while the forest dislocation is clustered,is studied by using an orientation-dependent line tension model.It is shown that the junction strength increases with the size of the cluster on the forest dislocation (binding energy of the forest dislocation to its cluster). The cluster forms by lattice diffusion and its size depends on the time lapsed from the formation of the respective dislocation segment.Therefore,the average size of clusters on new forest dislocations is smaller the larger the imposed strain rate. Consequently,the average strength of junctions decreases (after a transient) upon an increase of the strain rate,which leads to negative SRS. A model including the results of the mesoscopic analysis is developed to capture this mechanism. The model reproduces qualitatively a number of key features observed experimentally at the macroscopic scale. The new mechanism does not require solute diffusion to take place sufficiently fast for clustering of mobile dislocations to happen during their arrest time at obstacles, as assumed in previous models of the phenomenon.

Modelling Simul. Mater. Sci. Eng., Vol. 11 p. 1-12

Solute clustering in Al-Mg binary alloys

D. Zhang, R. C. Picu

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180

Abstract

Clustering of Mg in Al-Mg binary alloys is studied by means of atomistic simulations. The phenomenon is analysed in the undistorted Al lattice, as well as in the presence of dislocations. In the undistorted lattice, Mg has a tendency to cluster in a coherent phase. The binding energy of this structure is rather low and it dissolves at room temperature, and only dynamic associations of doublets or triples of solute atoms are observed. Increasing the temperature above 100°C inhibits the formation of any solute short range order. The application of a homogeneous hydrostatic strain has no effect on clustering. In the presence of dislocations and at room temperature, Mg clusters at cores forming the coherent phase observed in the undistorted lattice at low temperatures. The cores of all types of dislocations are described. It is shown that the size, shape and structure of the cluster cannot be predicted using elementary calculations based on the pressure field generated by the unclustered dislocation. Furthermore, the field of the clustered dislocation is observed to differ from that of the unclustered defect, even at distances as large as 20 Burgers vectors from the core. The variation of the stacking fault due to clustering is determined by simply monitoring the distance between partials, which is observed to decrease upon clustering.

J. Multiscale Comput. Eng., Vol. 2, p. 401-420, 2004

Composite Grid Atomistic Continuum Method: An adaptive approach to bridge continuum with atomistic analysis

D.K. Datta, R.C. Picu and M.S. Shephard

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180

Abstract

The Composite Grid Atomistic Continuum Method (CACM), a method to couple continuum and atomistic models is proposed in a three dimensional setting. In this method, atomistic analysis is used only at places where it is needed in order to capture the intrinsically non-linear/non-local behavior of the material at the atomic scale, while continuum analysis is used elsewhere for efficiency. The atomistic model is defined on a separate grid that overlaps the continuum in selected regions. The atomistic and the smallest scale continuum model are connected by appropriately defined operators. The continuum model provides boundary conditions to the discrete model while the atomistic model returns correcting eigenstrains. The adaptive selection of the spatial regions where the atomistic correction is needed is made based on error indicators developed to capture the non-linearity and non-locality modeling errors. The method is applied to represent dislocation nucleation from crack tips and nanoindentation in aluminum.

Other Selected Papers:

1. R. C. Picu and V. Gupta, "Crack Nucleation in Polycrystalline Ice Due to Elastic Anisotropy and Grain Boundary Sliding," Acta Metall. Mater., Vol. 43, p. 3783-3790, 1995.

2. R. C. Picu and V. Gupta, "Observations of Crack Nucleation in Columnar Ice Due to Grain Boundary Sliding," Acta Metall. Mater., Vol. 43, p. 3791-3798, 1995.

3. R. C. Picu and V. Gupta, "Singularities at Grain Triple Junctions in Two Dimensional Polycrystals with Cubic and Orthotropic Grains," J. Appl. Mech., Vol. 63, p. 295-300, 1996.

4. R. C. Picu and V. Gupta, "Stress Singularities at Triple Junctions with Freely Sliding Grains," Int. J. Solids Struct., Vol. 33, p. 1535-1541, 1996.

5. R. C. Picu, "Stress Singularities at Vertices of Conical Inclusions with Freely Sliding Interfaces," Int. J. Solids Struct., Vol. 33, p. 2453-2457, 1996.

6. R. C. Picu, "Singularities of an Interface Crack Impinging on a Grain Triple Junction," Int. J. Solids Struct., Vol. 33, p. 1563-1573, 1996.

7. R. C. Picu, J. S. Bergstrom and V. Gupta, "Nucleation of Splitting Column Cracks in Freshwater Columnar Ice," Acta Mater., Vol. 45, p. 1411-1421, 1997.

8. R. C. Picu, J. S. Bergstrom and V. Gupta, "The Brittle Failure of Columnar Ice Under Off-Axis Loading," Scripta Mater., Vol. 36, p. 63-67, 1997.

9. R. C. Picu and V. Gupta, "Three Dimensional Stress Singularities at the Tip of a Grain Triple Junction Line Intersecting the Free Surface," J. Mech. Phys. Solids., Vol. 45, p. 1495-1520, 1997.

10. R. C. Picu, "Three-dimensional Stress Concentration at Grain Triple Junctions in Columnar Ice," Phil. Mag. Lett., Vol. 76, p. 159-166, 1997.

11. R. C. Picu and J. H. Weiner, "Structural Changes During Stress Relaxation in Simple Liquids," J. Chem. Phys.,Vol. 107, p. 7214-7222, 1998.

12. R. C. Picu and J. H. Weiner, "Stress Relaxation in a Diatomic Liquid," J. Chem. Phys., Vol. 108, p. 4984-4991, 1998.