Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
5
3-4
2007
Preface
vii-viii
Multiscale Simulations of Triblock Copolymers
167-179
Jan
Andzelm
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5069, USA
Frederick L.
Beyer
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5069, USA
James
Snyder
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5069, USA
Peter W.
Chung
University of Maryland
Triblock copolymers self-assemble into a rich spectrum of microphase separated morphologies such as lamellae and cylinders. These materials are utilized in numerous materials science applications such as in membranes for protective clothing, fuel cells, and batteries. Such mesoscale features of copolymers extend to hundreds of nanometers and form in microseconds or longer times. However, many interesting processes, such as diffusion, occur within these mesoscale phases much faster and depend on underlying atomistic structure of the polymer. Such structure, in turn, is a function of molecular interactions at the fundamental quantum level. Thus comprehensive simulations of copolymers require consideration of quantum, atomistic, and mesoscale phenomena, spanning vastly different time and length scales. These simulations can be accomplished through sequential multiscale modeling. In this article, we describe key concepts and discuss interdependence and accuracy at various stages of this multiscale approach. Results are presented for a poly (styrene-b-isobutylene-b-styrene) copolymer that, in its sulfonated form, was found to be useful as a membrane in protective garments.
Chemical Complexity in Mechanical Deformation of Metals
181-202
Dipanjan
Sen
Department of Materials Science and Engineering; and Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Markus J.
Buehler
Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Prediction of the deformation behavior of metals in the presence of environmentally embrittling species like water or hydrogen, or under presence of organic reactive chemicals, remains a critical challenge in materials modeling. Here we propose a combination of the first principles-based reactive force field ReaxFF and the embedded atom method (EAM) in a generic multi-scale modeling framework, the Computational Materials Design Facility (CMDF), that enables the treatment of large reactive metallic systems within a classical molecular dynamics framework. Our hybrid method is based on coupling multiple Hamiltonians by weighting functions, which allows accurate modeling of chemically active sites with the reactive force field, while other parts of the system are described with the computationally less expensive EAM potential. We apply our hybrid modeling scheme in a study of fracture of a nickel single crystal under the presence of oxygen molecules. We observe that the oxide formed on the crack surface produces numerous defects surrounding the crack, including dislocations, grain boundaries, and point defects. We show that the mode of crack propagation changes from brittle crack opening at the crack tip to void formation ahead of the crack and void coalescence for lll orientation of the crack. Our results illustrate the significance of considering oxidative processes in studying deformation of metals, an aspect largely neglected in most modeling work carried out with pure EAM potentials. Our hybrid method constitutes an alternative to existing methods that are based on coupling quantum mechanical methods, such as density functional theory, to empirical potentials.
Multiscale Modeling of Point and Line Defects in Cubic Lattices
203-226
John
Clayton
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
Peter W.
Chung
University of Maryland
A multilength scale method based on asymptotic expansion homogenization (AEH) is developed to compute minimum energy configurations of ensembles of atoms at the fine length scale and the corresponding mechanical response of the material at the coarse length scale. This multiscale theory explicitly captures heterogeneity in microscopic atomic motion in crystalline materials, attributed, for example, to the presence of various point and line lattice defects. The formulation accounts for large deformations of nominally hyperelastic, monocrystalline solids. Unit cell calculations are performed to determine minimum energy configurations of ensembles of atoms of body-centered cubic tungsten in the presence of periodic arrays of vacancies and screw dislocations of line orientations [111] or [100]. Results of the theory and numerical implementation are verified versus molecular statics calculations based on conjugate gradient minimization (CGM) and are also compared with predictions from the local Cauchy-Born rule. For vacancy defects, the AEH method predicts the lowest system energy among the three methods, while computed energies are comparable between AEH and CGM for screw dislocations. Computed strain energies and defect energies (e.g., energies arising from local internal stresses and strains near defects) are used to construct and evaluate continuum energy functions for defective crystals parameterized via the vacancy density, the dislocation density tensor, and the generally incompatible lattice deformation gradient. For crystals with vacancies, a defect energy increasing linearly with vacancy density and applied elastic deformation is suggested, while for crystals with screw dislocations, a defect energy linearly dependent on the dislocation density tensor appears more appropriate than the quadratic dependency often encountered in the continuum plasticity literature.
A Parametric Domain Map for Top Coat Damage Initiation and Propagation in EB-PVD Thermal Barrier Coatings
227-242
Himanshu
Bhatnagar
Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA
Mark E.
Walter
Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA
Somnath
Ghosh
Department of Civil Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
Despite providing superior protection of engine components from severe temperatures, thermal barrier coatings are susceptible to catastrophic failure due to large-scale interfacial delamination. Under operating conditions, interfacial waviness increases due to bond coat creep and the cyclic nature of the thermal loading. Recent analyses show that the top coat incurs cracks at the sites of interfacial undulation. The top coat cracks propagate and coalesce under cyclic thermal load, which leads to catastrophic interfacial delamination. In this article, a finite element model of the thermal barrier coating (TBC) system is developed in the commercial code ABAQUS to investigate dependencies on various parameters and to develop a simplified parametric understanding of the top coat crack initiation and propagation. A parametric domain map for assessing crack initiation and propagation is developed in terms of geometric parameters of the TBC. Thus the domain map identifies which TBC geometries yield a fail-safe
Plasticity in Monocrystals with Limited Active Slip Systems
243-248
M. A.
Grinfeld
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5069, USA
T. W.
Wright
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5069, USA
Two related effects are predicted for monocrystals with a single active slip system: (1) the appearance of surface corrugations due to the stress-driven rearrangement instability (SDRI) and (2) the increase of the yield threshold for small specimens. In addition, for the systems under study, we (1) establish the appropriate expression of a chemical potential and (2) establish the key quantitative formula to be verified in the suggested experiment on the SDRI.
Applications of the Gunther Problem in Multiscale Systems
249-260
Pavel
Grinfeld
Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA
Various problems of heterogeneous multiscale systems are analyzed from the variational point of view. Since many composite materials consist of different components, the optimal functions may experience discontinuities along internal interfaces. In many instances, the locations of the interfaces is not a priori known, but must instead be determined by the variation principle. One of the first attempts of analyzing such problems was presented by Gunther, which we advance in several directions. In the Gunther problem, the integrand q (x, w, Δw)depends on the spatial gradients of a scalar field w (x). For one of the simplest types of discontinuities sort, Gunther found the formula of the first variation and established the appropriate extension of the Weierstrass-Erdmann transversality conditions. We establish some explicit solutions of the boundary value problems associated with the Gunther problem and derive the expression for the second variation.
Integration of Microstructure-Sensitive Design with Finite Element Methods: Elastic-Plastic Case Studies in FCC Polycrystals
261-272
Joshua R.
Houskamp
Department of Materials Science and Engineering, Drexel University, Philadelphia, PA 19104, USA
Gwenaelle
Proust
Department of Materials Science and Engineering, Drexel University, Philadelphia, PA 19104, USA
Surya R.
Kalidindi
Department of Materials Science and Engineering, Drexel University, Philadelphia, PA 19104, USA
A new mathematical framework called microstructure-sensitive design (MSD) was recently developed and demonstrated to facilitate solutions to inverse problems in microstructure design, where the goal is to identify the complete set of relevant microstructures (defined as statistical distributions) that are theoretically predicted to satisfy a set of designer-specified criteria on anisotropic macroscale properties and/or performance. In this article, we describe our efforts to interface the MSD framework with the finite element (FE) modeling tools used typically by the designers. This new MSD-FE framework facilitates a rigorous consideration of microstructure in a broad class of mechanical problems involving elastic-plastic design and optimization. The main elements of this newly developed MSD-FE framework are presented in this article, and their viability is demonstrated through two design case studies involving structural components made from FCC polycrystalline metals. The microstructure design variable in both these case studies is the orientation distribution function (ODF). The first case study involves the minimization of the elastic J-integral in the design of a cylindrical pressure vessel. The second case study involves the maximization of the load-carrying capacity of a thin plate with a central circular hole and loaded in-plane tension, while avoiding plastic deformation. In both these case studies, elementary upper bound theories were utilized in obtaining the macroscale properties of textured polycrystalline metal. It was observed that the elastic and plastic anisotropy associated with crystallographic texture influenced strongly the overall performance of the components.
Action-Based Pathway Modeling for Atomic Surface Diffusion
273-286
Sung Youb
Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
In-Ho
Lee
Korea Research Institute of Standards and Science, Daejeon 305-600, Korea
Sukky
Jun
Department of Mechanical Engineering, University of Wyoming, Laramie, WY 82071, USA
Action-derived molecular dynamics is applied to the simulation of self-diffusion processes on copper substrates. By minimizing a modified action with an energy conservation constraint, the method enables effective computations of minimum energy paths and activation energy barriers for the broad range of multiple timescale problems, including infrequent events and slow-mode systems. Single-adatom diffusions of hopping and exchange moves are first presented to demonstrate its performance. More complex diffusion mechanisms are simulated for hopping and exchange motions across a double-layer step on the Cu(111) surface, which are very difficult to explore by conventional molecular dynamics. Strain effects on diffusion energy barriers are also investigated for a Cu(001)flat surface. Finally, we propose an algorithm to incorporate a multiple length scale scheme into the current method, i.e., the combination of the action-derived molecular dynamics with the nonlocal quasicontinuum method. This hybrid scheme is expected to provide an efficient route to the simultaneous coupling of multiple length and timescales within a single algorithmic framework.
Breakdown of Self-Similar Hardening Behavior in Au Nanopillar Microplasticity
287-294
Jaime
Marian
Chemistry, Materials, and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
Jaroslaw
Knap
Chemistry, Materials, and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
This article is concerned with the study of scale effects in Au nanopillars under compression. We propose that plastic yielding in these nanostructures is characterized by a critical length scale at which a transition from volumetric to surface-dominated plasticity takes place. This transition effectively sets a lower bound on the self-similar behavior commonly assumed in nanostrength models. Using quasi-continuum simulations, we study the subcritical regime and find that plasticity at these scales is governed by dislocation emission at surface irregularities.
Nonlocal Gradient-Dependent Thermodynamics for Modeling Scale-Dependent Plasticity
295-323
George
Voyiadjis
Louisiana State University
Rashid K. Abu
Al-Rub
Department of Civil Engineering, Catholic University of America, Washington, DC 20064, USA
This article is concerned with formulating the thermodynamics of nonlocal gradient-dependent plasticity based on the nonlocality energy residual introduced by Eringen and Edelen (1972). A thermodynamic based theory for small strain gradient plasticity is developed by introducing gradients for variables associated with kinematic and isotropic hardening. This theory is a three-nonlocal-parameter theory that takes into consideration large variations in the plastic strain, large variations in the accumulated plastic strain, and accumulation of plastic strain gradients. It is shown that the presence of higher-order gradients in the plastic strain enforces the presence of a corresponding history variable brought by the accumulation of the plastic strain gradients. Gradients in the plastic strain introduce anisotropy in the form of kinematic hardening and are attributed to the net Burgers vector, whereas gradients in the accumulation of the plastic strain introduce isotropic hardening attributed to the additional storage of geometrically necessary dislocations. The equilibrium, or so-called microforce balance, between the internal Cauchy stress and the microstresses that are conjugates to the higher-order gradients turns out to be the yield criterion, which can be simply retrieved from the principle of virtual power. The classical macroscopic boundary conditions are supplemented by nonclassical microscopic boundary conditions associated with plastic flow. The developed nonlocal theory preserves the classical assumption of the local plasticity theory such that the plastic flow direction is governed by the deviatoric Cauchy stress. However, it is also argued here that plastic flow direction is the same as if it is governed by the nonlocal microstress. This is not in line with Gurtin (2003), who argued that the plastic flow direction is governed by a microstress and not the deviatoric Cauchy stress. Some generalities and the utility of this theory are discussed, and comparisons with other gradient theories are given. Applications of the proposed theory for size effects in thin films are presented.
Adiabatic Shear Band Localizations in BCC Metals at High Strain Rates and Various Initial Temperatures
325-349
Farid H.
Abed
Department of Civil Engineering and Construction, Bradley University, Peoria, IL 61625, USA
George
Voyiadjis
Louisiana State University
In general, metal structures display a strong rate and temperature dependence when deformed nonuniformly into the inelastic range. This effect has important implications for an increasing number of applications in structural and engineering mechanics. The mechanical behavior of these applications cannot be characterized by classical (rate-independent) continuum theories because they incorporate no material length scales. It is therefore necessary to develop a rate-dependent (viscoplasticity) continuum theory bridging the gap between the classical continuum theories and the microstructure simulations. A finite strain hypoelastoviscoplastic framework is developed for body-centered cubic metals using the corotational formulation approach. Material length scales are implicitly introduced into the governing equations through material rate dependency (viscosity). An implicit objective stress update, which is an efficient algorithm for the type of nonlinear problems considered here, is employed. The effectiveness of the present approach is tested by studying strain localizations in a simple tensile plane strain problem and in a cylindrical hat-shaped sample over a wide range of initial temperatures and strain rates. The finite element simulations of material instability problems converge to meaningful results on further refinement of the finite element mesh. Comparisons of the simulation results of adiabatic shear localizations are also made, with experimental results conducted by different authors. Results indicate an excellent performance of the present framework in describing the strain localization problem for niobium, vanadium, and tantalum.