Combined Research-Curriculum Development:
Computer Simulation of Material Behavior -
From Atomistic to The Continuum Level

NSF Grant: EED-9700815

Ronald D. Kriz, PI
Principal Contact
Department of Engineering Science and Mechanics
Virginia Tech (VPI&SU)
Blacksburg, Virginia 24061-0219
voice: 703-231-4386
fax: 703-231-9187

Romesh C. Batra, CoPI
Department of Engineering Science and Mechanics
Virginia Tech
voice: 703-231-6051
fax: 703-231-4574

John K. Burton, CoPI
Department of Instructional Systems Development
voice: 703-231-5587
FAX: 703-231-3717

Willam A. Curtin, CoPI
Department of Engineering Science and Mechanics and
Department of Material Science and Engineering
Virginia Tech
Moved to Brown University
Mechanics of Solids and Structures

Diana Farkas, CoPI
Department of Material Science and Engineering
Virginia Tech
voice: 703-231-4742
fax: 703-231-8919

This proposal:

  1. Project Summary
  2. Results from Prior NSF Supported Research
  3. CRCD Project Description
  4. References


Computing has had a tremendous impact on research in materials engineering and engineering mechanics during the last decade, but much of this knowledge remains to be transferred into the classroom. Access to supercomputing has led to the development of new numerical models, simulation-visualization tools, and potentially useful material systems. A sequence of two courses - one for seniors and the other for first year graduate students - is proposed in which state-of-the-art computer hardware and software will be used to teach the concepts and techniques of modern material performance simulation. The focus will be on the range of computer simulations covering and linking the physical length scales necessary for taking a material from the laboratory to the marketplace. These courses will bring into the classroom, research in materials engineering that the Principal Investigators and others have been conducting over the last six years, with an emphasis on computational methods applied to the study of deformation and fracture processes from the atomistic scale to the macroscopic scale. Subjects will be introduced and taught using advanced visual tools and interactive computing in the classroom, and will prepare students for designing complex material systems for the 21st century. Topics to be covered include effect of dislocations, grain boundaries and crystal orientations on material response; dependence of macroscopic behavior upon that of the constituents; localization of the deformation into narrow bands of intense plastic deformation; effects of material anisotropy; crack initiation and propagation in metals and ceramics; performance of advanced composites; modeling of heterogeneous materials; and wave propagation in anisotropic media. An interdisciplinary team of material scientists and engineering mechanicians will develop and teach the courses. The courses will also emphasize design of material systems and thus enhance the capstone design component of the existing engineering curriculum.

The courses will have Web-Java based modules on specific topics in atomistic aspects of Materials Science and Micromechanics. The modules will stress the way in which macroscopic materials properties are controlled by phenomena at the atomistic and microstructural levels. Advanced computational and scientific visualization techniques will be used to incorporate research into the modules. The National Center for Supercomputer Applications (NCSA) will work with Virginia Tech as part of NCSA's new Partnership in Advanced Computational Infrastructure (PACI) proposal (pending). Together researchers will create modules that will access NCSA computing resources and provide visual interpretation of simulation results both in real-time on the Web and by Java enabled batch jobs submitted to remote supercomputers both at Virginia Tech and NCSA. Access can then also be extended to PACI industrial partners and other Universities. Virginia Tech has also been funded by NSF (CDA-9601874) to build a CAVE virtual environment in partnership with NCSA. The virtual immersive CAVE environment will be used to demonstrate complex structure property relationships.

Educational pedagogy will follow the current research methodology on notions of learning higher level problem solving skills, and the requisite knowledge necessary to operationalize them, in contexts which are as realistic as possible. For example, useable knowledge is situated in the environment in which it is needed. Knowledge and skills learned in the classroom are situated in the classroom and, as a result, best remembered in the classroom. Conversely, knowledge and skills learned in the problem solving context are most usable in that context as well. A critical evaluation component will then be used to measure the transfer of what is learned to novel, realistic contexts. Visualization, by providing a more context rich set of stimuli, should produce the most "portable" knowledge. An evaluation team will consist of: 1. Industry: Drs. Buddy Poe (NASA-Langley ); Dr. Vijay Stokes (General Electric Co.), 2. Virginia Tech: Dr. R. E. Denton, Jr., Head of Communication Studies and one faculty member from the Mechanics and Materials Sceince Departments; 3. Other Universities: 1. D.J. Srolovitz (Univ. of Michigan), D.M. Barnett (Stanford), A. Gilat (Ohio State Univ.), R. Talreja (Georgia Tech), G.J. Weng (Rugers), P.K. Law (Univ. Tennessee), and Elias Aifantis (Michigan Technological Univ.). Together these individauls will formulate and evaluate the course content in anticipation of needs of the materials engineers in industry. Some of these individuals have volunteered to participate in the creation of courseware.

The course contents, philosophy, modules, and the feedback received from various segments of the scientific and industrial community, will be disseminated to the engineering community at large through presentation of the work at suitable conferences, workshops, short courses, seminars, the Web, and educational journals.

Results from Prior NSF Supported Research

NSF-SUCCEED: Virginia Tech is also a member of the Southeastern Universities and Colleges Coalition for Engineering Education (SUCCEED), funded by the NSF under Cooperative Agreement EID-9109853 for the period March 1992 through February 1997. Total NSF funding for SUCCEED is $15M, and there is an additional $15M in university and industry cost-sharing.Prof. Kriz ($75,354), together with Georgia Tech, is participating in the project "Development and Implementation of Interactive Multimedia in Basic Engineering Education Courses." This work has led to the development of CD-ROM multimedia course material on beam theory with ten publications and conference proceedings.

The mission of SUCCEED is to conduct a program of educational and curricular research, development and implementation. R.D. Kriz has received funding to study topics related to the activities in the Center for Technology and Communication. The Center's goals are: 1) Implement a demonstration of electronic connectivity for education delivery and interaction between (a) SUCCEED institutions, and (b) SUCCEED campuses and community colleges and 2) Demonstrate multimedia technology insertion into teaching/learning situations comprised of four or more engineering courses and one or more pre-university engineering courses.

Modelling and Characterization of Materials for Dynamic Metal Working Processes, Prof. R. Batra, CMS 9121279, August 1991 - January 1995, $110,000: This was a joint project with Dr. A. Gilat of the Ohio State University with the goal of developing a constitutive relation for a metal/alloy used in a hot working process. Researchers analyized by experimental tests and finite element tests the forging characteristics of SAE 1151 steel - one of the alloys being used for forging.The microstructure of the tested specimens was found to be strongly dependent upon the strain-rate used to deform the specimens. Dr. Batra formulated a constitutivc relation and used it to simulate the experimental torsion tests. Upon obtaining a good agreemcnt between the computed and the experimental stress-strain curves, the material modcl was implemented in the large scale explicit three-dimensioal finite element code DYNA3D. This information was useful in optimizing the steps used to forge a connecting rod. The Ford Motor Co. has established a group designated to simulate numerically different forging processes.

This research has resulted in three Ph.Ds, one M.S., and 13 publications. As a result of this research Professor Batra also organized three Symposia. Computer codes resulting from this research are now being used by researchers at U.S. Army Weapons & Materials Technology Directorate and U.S. Naval Academy.

NSF-FAW: Professor D. Farkas: The work on the atomistic structure of defects in alloys is sponsored by NSF through an award in the FAW program. The award started in November 1992 and is for a total of 250,000 $ duringfive years.

The most recent research concentrated on the Embedded Atom atomistic simulation of defect structures in a series of intermetallic compounds with the same crystal structure in order to identify trends that will help model mechanical behavior. The series used for the B2 structure is FeAl-NiAl-CoAl. We are comparing dislocation core structures, dislocation mobilities and grain boundary energetics in this series of compounds. We are also computing dislocation core structures in TiAl. Work on the development of interatomic potentials included potentials for ternary alloys in the Nb-Al-Ti system. Studies began in the area of the interaction of point defects with grain boundaries and dislocations in these materials.

Significant results were achieved during the last three years in the area of development of interatomic potentials for the atomistic simulations including non-central interactions. During that period a study of grain boundaries in hexagonal materials was completed, as well as studies on dislocation core structure and motion in various alloys. Fifteen publications were written during this period acknowledging the award, including two chapters in a review book on Intermetallic Alloys, recently published by J. Wiley.

Other activities included a a symposium on atomistic mechanisms of deformation that was organized in 1995. In 1993-1994 a course on Computer Simulation in Materials Science was taught as part of a Fulbright grant and our international cooperation program. The cooperative program is also funded by NSF, division of International Programs. Six graduate Students were advised during the year. Two at the M.S. level and four at the Ph. D. level.


2.1 Introduction

The rapidly expanding field of materials research and development has now progressed to the point where new materials are being designed and/or their behavior understood with the critical assistance of various computer simulation technologies. The near future will see an even faster expansion of the use of numerical techniques to complement not only materials development, but also material processing and rapid prototyping of components, be they structural or electronic. The goal of this Combined Research-Curriculum Development program is to bring the current concepts of computer simulation and visualization, and their applications to a broad spectrum of materials problems into the classroom at the Senior/First Year Graduate Student level. We will introduce students to current computer simulation work at the atomic level, microstructural scale (e.g. grains in polycrystals), and continuum level. The issues of 1) which material problems need to be addressed at which length scales, and 2) the coupling of atomic and microscopic behavior to macroscopic component performance, will be key physical concepts transferred to the students. The emphasis of the program will be on deformation and fracture behavior of materials, encompassing metals, ceramics, polymers, and composites, and will draw upon our expertise in computer simulations of the mechanical performance.

Computer visualization techniques will be used to "observe" deformation and fracture processes. This is the modern equivalent of the "observational" basis used for decades in science: we observe a phenomenon in the laboratory and then develop both the concepts to understand and the means to control the observed phenomenon.

Students pursuing the proposed curriculum in tandem with more traditional analytical and experimental studies will be well-prepared to adopt and/or adapt computer simulation and visualization technologies into their future work, whether directly related to the topics emphasized here or to other areas of materials development and processing.

2.2 Modeling Description

The research to be integrated into the proposed curriculum encompasses state-of-the-art work in atomistic, micromechanical, and continuum level computational work in the areas of material deformation and fracture, wave propagation, and visualization.

2.2.1 Atomistic Modelling

At the atomistic level, embedded atom methods (EAM) [1] combined with molecular statics and dynamics techniques have been utilized to understand dislocation core structures and dislocation motion.

We have been working in the computer simulation of the structure of defects in alloys since 1984. The initial work dealt with grain boundary structures and we have studied grain boundaries in a variety of materials [2]. We have also studied the structures of point defects [3] and planar defects, such as free surfaces and stacking faults. Our recent research work also dealt with theoretical studies of the structure and mobility of dislocation cores [4] and other extended defects in high temperature intermetallic materials in order to contribute to the understanding of the correlations among the dislocation core structure, mobility, and alloy mechanical behavior.

We have obtained detailed dislocation core structure and mobility for the cores of various dislocations in several materials, as well as studied the effects of alloy stoichiometry on the core structure and mobility of these dislocations. Research efforts also concentrated on the development of interatomic potentials for the study of various materials. Interatomic potentials are also necessary for the study of the effects of impurities on dislocation cores in these materials. A large effort has been devoted to the development of these potentials and we have been successful in a series of compounds, such as the intermetallics series FeAl-NiAl-CoAl. We compared dislocation core structures, dislocation mobility and grain boundary energetics in this series of compounds. We also computed dislocation core structures in TiAl. Work on the development of interatomic potentials included potentials for ternary alloys such as the Nb-Al-Ti system [5] and a detailed study of the B2 phase in this ternary alloy. We propose to incorporate the results of this research into the curriculum in the form of modules dealing with various defects in materials and their microscopic relaxation behavior.

Figure 1. Atomistic structure of a propagating crack in intermetallic CoAl.

The current research deals with the atomistic simulation of crack structures (Fig. 1) and propagation in metallic and intermetallic alloys. The overall goal of research in this area is to understand the mechanical behavior of these materials and relate the results to the structures of dislocations and grain boundaries studied previously. The study of crack propagation is of great value for the general background of engineering students regarding the fracture behavior of various materials.

We use molecular statics [6] to find the low energy interface configurations of a stressed material including a crack, grain boundary, dislocation, stacking fault or other planar defects [4]. We model internal cracks, without cutting the bonds across the crack in order to study their nucleation and propagation. The initial configuration and boundary conditions are those of an equivalent distribution of dislocations. We carry out simulations for cracks of various lengths with different orientations of the crack plane and the crack front.

The interatomic potentials to be used in these simulations are of the embedded atom type [1], in some cases with the addition of an angular dependent term [7]. These potentials are derived based on experimental data available for the particular materials considered and, when experimental data are not available they are derived from first principle calculations [8]. Our goal is to improve existing many-body potentials and to apply these models to the simulation of extended defects, and more importantly in the context of this proposal, to the simulation and understanding of the local atomistic structure of defects in intermetallic alloys. These defects include complex grain boundaries and multiple dislocations and the results of their interaction with point defects such as vacancies, antisites and impurities. The resulting trends in defect structures have to be compared with experimental observations of mechanical behavior of the alloys.

Embedded atom simulation data are linked to experimental data concerning the mechanical behavior of intermetallics. Simulation data have proven valuable in both the visualization of defect structures and in comparison to high-resolution transmission electron micrographs (HRTEM) of corresponding real materials. Actually, it is in comparison of simulated results to HRTEM that greater insight in the interpretation of experimental results has been obtained. Such understanding of the local atomistic structure of complex grain boundaries and dislocations has implications for alloy behavior and design.

The connection between theory and experiment that is seen at the atomistic level will be of great value for students, since they will be able to see cases where we have been able to successfully predict the material structure at the atomic level through the comparison of simulated and observed HRTEM results. Another essential connection is the fact that the development of interatomic potentials is often based on properties calculated by first principles techniques and the agreement among these results and the embedded atom predictions helps establish confidence in the potentials derived. The potentials can then be applied to larger scale simulations comparable to experimental situations. Thus, first principle calculations and experimental data may be linked.

2.2.2 Microstructural Modelling

At the microstructural level, atomistic and continuum techniques are being adapted to investigate the role of microstructure in material performance. In particular, crack propagation behavior in polycrystalline materials has been studied to elucidate the role of residual stresses, and thermal anisotropy on microcracking formation and subsequent microcrack toughening [9,10]. The qualitative effects of grain boundary toughness variations and thermal residual stress distributions on material strength and toughness in particulate composites have also been investigated [10,11]. In all cases above, interesting and often non-intuitive behavior is observed in the regime of large disorder, or heterogeneity. For materials with broad distributions of thermal stress, the material undergoes extensive distributed damage evolution prior to the onset of global failure and is largely flaw-insensitive. The toughness of polycrystals with variations in grain boundary or crystallite toughness is found to be either below or above the classic Griffith value, depending on the nature of the toughness variations, and interesting crack growth behavior is observed [12]. Crack propagation in composites explicitly toughened by "crack bridges" has been found to depend sensitively on the spatial distribution of the bridges, and continuum models which ignore the intrinsic heterogeneity of the microstructure generally overestimate the toughness and the reliability [13]. In addition, new numerical techniques for modeling the evolution of damage in fiber-reinforced composites have just been developed to predict the strength and toughness of such composite materials as a function of the underlying constituent material properties [14,15]. The full spectrum of problems attackable using these new models is only just getting started, and is the subject of current research. Much of our current research in these areas is also directed toward the understanding of time-dependent failure in "composite" materials (polycrystals, particulate and fiber-reinforced composites) caused by creep, creep damage, and environmental corrosion.

A key aspect of all of this research is the stochastic nature of damage evolution at the microstructural (grain, particle, fiber) scale. Stochastic damage accumulation culminates in the formation of a critical damage region which leads to a rapidly propagating crack and failure, but the formation of the critical damage is dependent on the physical volume of material and the nature of the microstructure. To thus capture the expected behavior at a truly macroscopic length scale requires large scale simulations to provide insight into the failure process and the volume-scaling, and for development of quantitative predictive theories which can be scaled up to macroscopic lengths/volumes. Visualization of these processes also becomes very important as a means to quickly and physically identify the complex damage evolution processes underlying failure, and the variations from "pictures" one might ideally imagine to occur in "continuum" or non-heterogeneous materials. Figure 2 shows an example of the fracture surface predicted for a fiber-reinforced ceramic composite after tensile loading, and as observed in a real material. The ability to accurately predict the detailed "pullout" length distributions measured experimentally provides insight into the failure process in this type of composite.

Figure 2. Experimental, simulated fibber fracture pullout of ceramic matrix composities.

These microstructural studies in fiber composites are now also providing continuum constitutive relations and failure criteria to be utilized in continuum-level modeling of components or sub-elements of components, and are also providing guidance on the length scale limitations over which such "continuum" relations can actually be employed. In general, an understanding of the importance of stochastic aspects of failure, aspects that are absent from continuum modelling, is critical to the accurate assessment of component failure and reliability at the macroscopic level.

2.2.3 Continuum Modelling

At a continuum level we have simulated [16,17] penetration experiments into Titanium (Ti) [18], Ti-alloy [19,20] and aluminum plates [21], and are now simulating high strain-rate torsional experiments on AISI 1018 CR (cold rolled) steel [22], HY-100 steel [23], and AISI 4340 VAR (vacuum arc remelted) steel [24]. These studies have revealed that the fracture occurred by a process of void nucleation and coalescence; no cleavage

was observed on any surface, including the most brittle of the steels tested. In AISI 1018 CR steel, microcracks were found to initiate by the decohesion of phase boundaries between the ferrite and pearlite, by the fracture of pearlite, and possibly by the separation of ferrite grain boundaries. In HY-100 steel, manganese sulfide (MnS), which exists in the form of stringers and globular particles, provided initiation sites for voids within the shear bands. Coalescence of these voids preceded the final fracture. Fine carbide particles in AISI 4340 VAR steel were found to serve as nucleation sites for voids. In all of these materials, the nucleation of voids was generally preceded by the formation of shear bands, which are narrow regions, a few micrometers wide, of intense plastic deformation. The plastic deformation of the material surrounding the shear band is negligible as compared to that of the material within the shear band. Cho et al. [23] found that cracks formed by the linkage of voids, and microcracks generally appeared in the three steels listed above when the shear strain within the band equaled almost 20. A review of the literature on adiabatic shear bands will take considerable space; it should suffice to mention that three recent symposia proceedings [25-27] and the book by Bai and Dodd [28], provide references to most of the relevant works. We now describe briefly some research work that we will bring into the classroom.

At the continuum level, finite-element techniques are being extended into the realm of dynamic fracture in metals, with a particular emphasis on adiabatic shear band formation, propagation, and initiation of cracks from these bands. We have developed robust and efficient finite element codes to analyze dynamic shear bands in thermoviscoplastic materials. The finite element mesh is refined adaptively so as to concentrate smaller elements in severely deforming regions and coarse elements elsewhere with great care taken to grade the mesh properly. Such meshes for the analysis of a shear band in plane strain tension, as studied by Batra and Jin [26], are shown in Fig. 3.

Figure 3. Plane strain deformations in a porous thermoviscoplastic steel block with adaptive meshs.

Using these techniques, we have delineated the effect of material parameters, loading conditions, defect shape and size, the distribution of defects, crystal orientations, misalignment among crystallographic planes and other factors upon the initiation, and growth of adiabatic shear bands. Our current work is focused on determining the energy required to drive a shear band, which factors reach critical values at the shear band tip before it propagates, and the interaction between cracks and shear bands. The numerical techniques, i.e., the finite element method, adaptive mesh refinement, and the solvers for stiff equations, are general enough to be applicable to a wide class of problems. Also, the research elucidates upon the interaction between mechanical and thermal effects; such interactions among different aspects of the problem are common place in real world problems and engineers of the 21st century need to learn these. Often, the coupled effects escape intuition and because of the nonlinearities involved, the effects are not additive. The computer visualization and simulation techniques will be employed to elucidate upon the sensitivity of the initiation and propagation of this mode of ductile failure to different parameters, and students introduced to the concepts of optimization, compromise, and iterative processes in the design of material systems.

2.2.4 Application of Visualization Tools

In all of the above problems, which range over the full spectrum of physical length scales, computer simulations are a necessary tool because of the highly non-linear nature of the phenomena studied, and because of the heterogeneity of the material structure. The mechanics of failure in heterogeneous materials is extremely challenging, and when coupled with non-linear phenomena (dislocation formation, shear-banding, ductility, time-dependent damage formation, stochastic fracture, etc.) becomes prohibitively difficult. Computational simulations together with visualization have provided insight, and a basis of understanding in all of these areas.

As a means of providing insight, an important aspect of all of these programs has been the application of computer visualization techniques to interpret the wealth of data obtained from the simulations. Visualization of these non-linear heterogeneous problems in both 2 and 3 dimensions has been absolutely invaluable to our development of the computer codes themselves as well as in gaining a physical picture of the phenomenon of interest, a picture which subsequently guided development of physical understanding. The observation of atomic displacements around a dislocation core, the strains around a crack tip, the damage distribution in a fiber composite, and shear band development have all been essential to our own understandings, and just as importantly are critical to transferring that understanding and insight to non-experts.

The use of computer visualization techniques in research and teaching is the recent thrust of the Virginia Tech Laboratory for Scientific Visual Analysis [30]. The on-going, successful application of visualization to so many areas to date, and to other problems in the future, strongly indicates that computer simulation techniques with visualization can and should be brought out of the laboratory and into the classroom in an integrated and coherent manner. Our Curriculum Development Program to accomplish this is discussed below.

2.3 Curriculum Development

2.3.1 Senior-level Course Content

At the Senior level, the course will emphasize the basic concepts of simulation techniques at the atomic and microstructural levels, and introduce computer visualization techniques. The course will start with the relationship between atomic interactions and macroscopic behavior. The emphasis will be on the most basic physics aspects of atomic interactions, and aimed to get the students to a level where they can run their own simulations and "measure" macroscopic properties from the details of the microscope atomic potentials. Problems to be studied will include elastic constants, vacancies, thermal expansion, dislocations, crack tips, and diffusion.

We will start with simple pair potential models for the interactions between atoms in a monatomic material, and the molecular dynamics technique will be introduced. Since this is basically application of Newton's Laws at a microscopic level, the needed skills have already been developed by the students. Visualization of various phenomena will be emphasized. First, simple crystals will be studied and boundary conditions adjusted to measure macroscopic elastic properties. Relaxation around vacancies will also be investigated, as well as structure around impurities, all with reference to the continuum concepts students have already learned. Diffusion in simple systems will then be investigated. Dislocation structures will be created and understood visually. Microcracks will then be introduced and the central concept of fracture mechanics, the Griffith condition for failure under tensile load, will be demonstrated microscopically. Following this, dislocation emission from a crack tip and brittle/ductile transitions will be studied as a function of the interatomic potential. The embedded atom method (EAM) will then be introduced as a tractable approach to studying realistic atoms, and the students will experiment with EAM models on problems similar to those stated above and investigate important similarities and differences. At all stages, visualization of the dynamics of the atomic motion will be used to understand the local atomic arrangements and how the large deformations therein preclude the explicit use of continuum concepts at the atomic level.

Microstructural-scale problems will then be investigated, using conceptually similar numerical techniques. The microscopic properties obtained in the first part of the course will be utilized as input constitutive relations at this next length scale to simulate performance of polycrystalline materials, materials with grain boundaries, internal/precipitate phase-transformations, and composites. Emphasis will be on the translation of the microscopic behavior to the macrostructural scale, and then on the quantitative differences in behavior that arise macroscopically due to the microstructural features. Issues such as thermal mismatch stresses, microcracking, crack propagation, and measurement of elastic properties by wave propagation will be studied. Subsequently, concepts for improving macroscopic elastic and fracture behavior through microstructural-scale modifications (composites, microstructure control) will be studied. As a lead in to the continuum-scale simulations to be covered fully in the graduate level course, the issue of when homogenization concepts are appropriate and when they are not will be carefully discussed. This is a critical issue in making the transition from a heterogeneous material to an effectively homogeneous material.

Students completing this course in a fall semester Senior year will then have the option to pursue Capstone Design projects in the area of computer simulation of materials as a Senior Design Project under the guidance of one of the faculty in the final spring semester. It will be an outstanding course for undergraduate mechanics students who are familiar with continuum level concepts but who have only been exposed to the microscopic aspects at a sophomore level, and it will complement and supplement the knowledge already gained by students in the materials course. Delivery

We presently have the hardware and the software to run real time simulations in the class and project results on the screen. As a new concept is introduced, a simple problem to illustrate and reinforce it will be run and the results exhibited in class. Students will be involved in the learning process by seeking "what if" type of questions from them, encouraging them to predict the outcome and then explain the differences, if any, between their answers and those obtained from numerical simulations. The recently created Scientific Modeling and Visualization Classroom funded by Virginia Tech, Sun Microsystems and Visual Numerics includes 9 Sun Sparc 20 and Ultra workstations that are particularly well suited for the simulation and visualization activities discussed in this proposal.

Extensions of concepts covered in the class will be assigned as homework problems to a team of students; the team members will be free to divide the work among themselves. They will be encouraged to explore "what if" aspects of the project as part of the problem solving model. This approach capitalizes on two widely accepted notions: that knowledge is situated in contexts, and that meaning is constructed from interactions with others. In the first case, the use of simulation and visualization, means that the knowledge and skills learned should be remembered in similar contexts. Lave's [31] landmark studies of South American boys who could perform complex computations in their heads while bargaining in the market place, constantly figuring profit margin per unit, but could not perform the same arithmetic at all in the classroom, are good examples of how knowledge is grounded. Basing knowledge on direct experience and application will decrease less-related classroom learning. In the second case, when learning in a group, meaning is constructed from social interactions. This is obvious from researchers such as Skinner. Notions of what pain is, for example, highlight the problem. No one teaches pain. Everyone has different notions at what is painful, yet we all understand. All abstract meanings are learned in this manner, although they may be memorized.

In order to maintain continuity of thought process and use a consistent set of notations, the PIs will participate throughout the two courses either by lecturing or by attending the classes. We realize that a change in notations and/or the delivery mode can throw off some students; these will be avoided or at least minimized. Self-standing Modules

The Senior course will be designed so that sections of the course can be extracted and modified to become self-standing "modules" for application in other undergraduate classes, with an emphasis on the visualization aspects. For instance, work on dislocation and vacancy structures will be brought into our Sophomore-level materials class that is required by most departments in the College of Engineering. Work on atomistics of fracture, and microstructure features, will be brought into the Junior-level course in Structure-Property relationships. Microstructural aspects of particulate composites can be used in the Senior-level course in advanced composites. The emphasis here is on self-contained modules which will help to demonstrate the physical behavior to a broader range of students, with only a minor discussion of the simulation methods used to generate the visual paradigms. The students in these courses will already be familiar, through the specific work of each course, with the physics of the phenomenon under study. This unique aspect of the present proposal leverages the specific course development effort by bringing the knowledge to a very broad cross-section of our undergraduate engineers.

Each of the simulation modules will consist of a multimedia interactive presentation of the results of computer simulation in the particular area addressed by the module. The format to be used will be compatible with the World Wide Web (WWW or "the Web"), including text, figures and movies. The results of the simulations will be put in formats that can be read by commercial visualization packages (i.e., AVS, CERIUS) for the students to analyze. We have been working with several companies producing this type of software as industrial partners in the present project where students can submit batch jobs to supercomputers at Virginia Tech and to the NCSA supercomputer center. Letters of support from Visual Numerics and NCSA are attached. All the modules will be linked through hypertext, for the students to explore. The modules will be primarily research-based results obtained at the Atomistic Computer Simulation Lab at Virginia Tech [32], visualized at the Visualization Lab [30] also at Virginia Tech. However, they will also contain hypertext references to results obtained by other computer simulation research groups that might be available on the Web. As an example, we point to a Web site for Visualizations in Materials Science [33]. This site has a series of movies designed to aid in the understanding of basic materials science concepts, such as crystal structures. We also point to a number of sites that are specific to materials theory and simulation that contain results that we may be able to incorporate in our modules; e.g., the Web site of the Materials Theory Center at NIST [34], or the Center for Materials Simulation and Processes at Cal Tech [35].

NCSA and Visual Numerics will participate with Virginia Tech researchers in the creation of educational modules that will access supercomputing resources and provide simulation results to be visually interpreted on the web. NCSA, Visual Numerics and Virginia Tech are pioneers in creating and implementing visual and computational tools. In the last five years Virginia Tech has developed extensive expertise in the use of simulation models and visualization of model results as an NCSA Academic Affiliate and most recently as a partner in the NSF Partnership in Advanced Computational Infrastructure proposal, pending. When working with complex structures, students will take advantage of the immersive computer virtual environment (CAVE) which was recently funded by NSF-ARI in collaboration with NCSA. The industrial partnership with VNI and industries associated with the NCSA Industrial Affiliates Program will be prepared to take the next step in applying the use of real-time simulation visualization and Web tools distributed across the network.

A number of the modules related to atomistic and continuum behavior of materials are summarized below.

Module 1: Interatomic potentials, various crystal structures and lattice stability. This module will concentrate on the predictions of computer simulation regarding phase stability. The module will be useful in the teaching of basic features of crystal chemistry as it relates to bonding.

Module 2: Relaxation around point defects and diffusion. This module will demonstrate simulation results for a variety of point defects in various metals and alloys [3]. The module will incorporate our results for the relaxed structure of these defects as well as new results that we are now obtaining regarding the mobility of these defects. In this new research we are calculating the activation energy for diffusion in various metals. This module will be linked to modules that treat the diffusion problem at longer length scales. An example of such a module on diffusion has already being initiated by Kriz [36].

Module 3: Structure of grain boundaries. This module will incorporate the results that we have obtained over the last ten years on the atomistic structure of grain boundaries [2]. The grain boundaries will be visualized using MSI's CERIUS and they will be animated for better viewing by the students, as well as to enable visualizing them in three dimensions.

Module 4: Dislocation structures and motion. This module will incorporate research results on dislocation core structures. We will start with dislocation in simple bcc metals. We will then include dislocation core studies in various intermetallics [4]. We will use various techniques to visualize the dislocation s[4].

Module 5: Interaction of point defects and a dislocation. We will incorporate here some of our latest results that deal with the interaction of point defects with dislocations, which model the hardening phenomena introduced by impurities or deviations from stoichiometry.

Module 6: Simulation of fracture processes in pure metals. In this module, we will address the basic question of whether a pure material is inherently ductile or brittle at low temperatures. For this purpose we will use the various interatomic potentials available in the literature to simulate cracks in fcc and bcc phases. This research is being carried out currently and we show some of our latest results in Figure 1. This module will include the effects of impurities on deformation and fracture behavior in steels. We have found that the addition of Cr in Fe changes the shape of dislocation cores losing the three-fold symmetry typical of the cores in pure bcc metals. Cr stabilizes [111] {110} slip as opposed to [111] {112} slip. The Peierls stress of 1/2[111] screw dislocations in Fe is increased by the addition of Cr.

Module 7: Simulation of adiabatic shear bands at high strain rates. We will exhibit the effect of various material and geometric parameters and loading conditions on the initiation and propagation of shear bands. Shear bands initiating from a notch tip, and other material and geometric defects in a thermoviscoplastic body will be modeled.

Module 8: Simulation of fracture in unidirectionally-reinforced composites. Simulation of fracture in unidirectionally-reinforced ceramic and metal composites, including slip at the fiber/matrix interfaces, load transfer among fibers, stochastic fiber strength distributions, and observation of localization and final failure, followed by fiber pullout. Stress-stratin curves up to failure versus key microstructural parameters can be "measured" and observed.

2.3.2 Graduate-level Course

The Graduate Level Course will consider all three length scales (atomistic, microstructural, and continuum), and in more depth than can be achieved at the undergraduate level. In particular, the thermodynamics of temperature-dependent behavior will be discussed in more detail, and applications of elasticity theory and simple fracture mechanics will be utilized to address more complicated problems. At the atomistic scale, problems such as grain boundary structures and grain boundary cracks will be studied. At the microstructural level, we will consider both particulate and fiber-reinforced composites and damage evolution both with stress and with time. These highly non-linear phenomena in heterogeneous materials are the subject of some of our current research. At the macroscopic level, we will emphasize calculation of strain-energy release rates for crack growth, evolution of toughening in transformation-toughened ceramics, and response of materials to rapid loading. The phenomenon of shear strain localization, i.e. the initiation and development of shear bands, will be discussed in detail. We note that these shear bands precede fracture in ductile materials under dynamic loads. The dependence of the width of these bands upon microstructural parameters is currently being investigated and students will be introduced using the most recent information available on this topic. To better understand the transition of deformation from the atom scale to the continuum, we will introduce the idea of deformation over a wavelength as it transitions from atomic spacing through the microstructure dimension and onto the continuum in the long wavelength limit. With simple wave propagation models we can also introduce the idea of material anisotropy for a continuum.

As in the Senior level course, visualization of all of these phenomena will be a crucial addition to the learning / teaching process. In fact, with the increased complexity of coupled non-linear phenomena it is more critical at this level to work in tandem with visualization techniques. To this end we will encourage interested undergraduate students to take the visualization class ESM5984 [37] who will continue into the graduate program and take the proposed graduate level course (see student projects [38]). Also, the material used in this course will be extracted and modified to form independent modules which can be adapted into other existing courses. For instance, the simulation work on diffusion clearly applies to the existing graduate course in diffusion, the composite simulations will complement the analytic development in an existing graduate course in composite mechanics, and the examples at the continuum level can be inserted as sophisticated extensions of the FEM into our graduate FEM courses.

2.3.3 General Aspects of Course Development

We envision the development of the two new Computer Simulation in Materials courses not as a separate thrust or in competition with other courses, but rather to complement those courses and to help students gain further insight into a wide range of materials problems with the help of computer simulations and visualization. The use of modules in other classes will extend the impact of this curriculum beyond the specific classes. Overall, many students in the entire College of Engineering will be exposed, in various degrees, to the capabilities and advantages of simulation techniques. In order to estimate the number of students these courses will impact, we add that the College of Engineering at Virginia Tech is among the top ten producers of graduates at the Bachelor and Masters level, and the largest producer of graduates in Engineering Mechanics at the doctoral level in the country. The enrollment in most of the first year graduate level and senior year courses varies between 40 and 50. We anticipate that each one of the proposed courses will attract about 40 students. Students taking the proposed courses will develop the detailed level of understanding and more general familiarity needed for them to consider the simulation approach as yet another tool for problem solving in the future. The content of these new courses has been carefully planned to integrate into the overall curriculum.

Both courses will be "Team Taught" by the PIs as appropriate for the areas to be covered. This accomplishes several goals: (i) it maximizes the student exposure to faculty, which assists students in the development of design projects with those faculty, and (ii) provides each faculty member the opportunity to emphasize the important physical aspects of problems at each scale, but maintains a continuity across subjects because of the interdisciplinary nature of work by each of the Pls separately. "Team" teaching has proven successful in ESM5984 [37] class on Scientific Visual Analysis and Multimedia and the MSE "Core" class required of all incoming MSE graduate students. All CoPIs have experience in team teaching.

The courses will also have an explicit "Computer Laboratory" component in which students will develop small-scale simulation codes to get a feel for the numerical issues and approaches used, rather than simply adapting "canned" programs. In-class and out-of-class use of computers will use the Web to display lectures and simulations will facilitate the associated module development. Both of these hands-on and eyes-on experiences will help students learn the physics and mechanics of complex behavior better than via the blackboard/textbook approach. The visualization component is particularly important, as it is now recognized that many people do learn better visually than aurally. The frequent introductions of "what if" concepts will enable students to investigate various aspects of a problem. The visualization of results will enable them to appreciate the effect of different parameters and prepare them better as materials designers. To this end we will use the immersive environment of the CAVE, a recently funded NSF-ARI proposal, where students can view and interact with complex structures that result from their simulation calculations. The optimum use of materials in the design of components will inevitably enhance the competitive position of U.S. industries when these education modules are distributed by open access through the Web to our industrial partners associated with the NCSA PACI proposal, pending.

2.4 Personnel

2.4.1 Faculty Team

The faculty involved in this research program are in the Materials Science and Engineering, Engineering Science and Mechanics, or Education Departments at Virginia Tech. However, the spectrum of disciplines and training of the faculty are rather broader, encompassing materials science, mechanics, physics, education pedagogy and computing. All faculty are involved in research on computational aspects of materials science, as described earlier, and the proposed emphasis on fracture and deformation represents our cumulative areas of expertise. Besides being active researchers, these faculty members have consistently received excellent teaching evaluations from students and are deeply involved in bringing new material into the classroom. They have been teaching regularly both undergraduate and graduate courses, and four of the five Pls have been involved in Team Teaching.

2.4.2 Undergraduate and Graduate Students

We propose to involve both undergraduate and graduate students in this program as follows. We will provide summer research assistant positions to well-qualified undergraduate students with an interest in computers and simulations to assist in the development of modules to be used in other courses. We have already successfully involved undergraduates in a team project [36] where they created a Web module on diffusion that included a numerical model to solve a variety of boundary problems in diffusion. A graduate research assistant will be employed in the development of visualization techniques, and this will constitute a part of their dissertation.

2.4.3 Non-Academic Personnel and Collaborators

We are currently working, in our research, with a number of Industrial and National laboratory partners, such as NCSA, NASA, NIST, Naval Research Laboratory, Visual Numerics, Ingersoll-Rand Co., Pratt & Whitney, Army Research Laboratory in Aberdeen Proving Ground, and DOE-Oak Ridge National Laboratory. It is our intent to take the modules developed within this program out to these partners in the form of on-site Short Courses to initially disseminate the concepts and results of computational materials science. This education and training component of this proposal can also be extended to the industrial partners of the recently proposed NSF PACI proposal. This educational experience can be continued through access to our WWW modules. We have planned several collaborative activities for the duration of the proposed work. Regarding the development of interatomic potentials we will collaborate with the group headed by Dr. Papaconstantopoulos at NRL doing first principle calculations of alloy properties. Regarding the basic fracture behavior of pure metals, we plan collaborations with Dr. Rob Thomson at NIST and Dr. Anders Carlson at Washington University. We will work with Mr. Robert J. Garrett Jr. of the Naval Warfare Center on failure of welded joints. Finally, we plan to develop a strong collaboration with Dr. S.J. Zhou at LANL. The collaboration will be particularly beneficial since Dr. Zhou has access to multi-million atom simulation capabilities. In general, the development of visualization techniques in the area of failure of fiber composites has been well-received by the technical community at-large. The module on wave propagation in a heterogeneous medium (e.g. rocks) is of great interest to Ingersoll-Rand Co.

Ongoing collaboration with scientists at the above-mentioned establishments will be continued to further develop atomistic methods and visualization of fracture. To this end we will also form a partnership with NCSA for access to supercomputers resources used for model simulations. Two of the PIs have received a significant amount of CPU time on these supercomputers. Material scientists/engineers from some of the above organizations will also serve on the evaluation team. NCSA will work with Virginia Tech as one of the partners in NCSA's NSF-PACI proposal. Members of this research effort will be included in the working groups we establish in applications development, user support, training, documentation and the integration of technical environments. This will provide opportunities for increased collaboration in software development and optimization, benchmarking, distributed computing and educational activities.

2.5 Project Evaluation/Assessment/Dissemination

The course material and the course modules will be evaluated by a team consisting of materials engineers from the industry, national research laboratories, a faculty member from each of the ESM, MSE and the Communication Studies departments, and two senior doctoral level students who have completed all requirements for their degree except for the dissertation defense. Dr. Buddy Poe, a research scientist at NASA Langley and chairman of the ESM Departmental Industrial Advisory Committee, Dr. Vijay Stokes, a research engineer at the GE Co., Schenectady, NY and chairman of the ASME Materials Division, and Dr. R.E. Denton, Jr., Head of Virginia Tech's Department of Communication Studies will also serve on this committee. The lectures will be videotaped and tapes will be shared with the committee members who will be requested to suggest improvements in both the contents and the delivery of the material.

Each course module will employ a set of questions to delineate how well the basic concepts have been transferred to the students. This survey will seek student input on difficulties encountered in grasping these concepts, and request suggestions to improve upon the presentation mode. The senior year course will be taught in Fall 1997 and the graduate level course in the following spring semester. In 1998 summer, the committee will look at the feedback received from students who took the course, and also solicit input from material designers in the industry and federal organizations; these suggestions will be used to improve upon the course. Formal steps to incorporate the course into the undergraduate curriculum will be initiated. A similar procedure will be followed for the graduate level course. The sequence of courses will be repeated starting Fall 1998. These course modules will be shared with interested colleagues at other Universities (see next section). The input received from their students will be invaluabe in improving these modules.

After having successfully taught the sequence of two course, their availability and the experience gained will be disseminated to the engineering community at large by presenting results at the ASEE Conference, conducting a short course/workshop, posting it on the Web, and publishing in ASEE's journal PRISM and other suitable publications. The course modules of interest to our industrial partners and other industries will be shared with them.

2.6 Participation by Other Universities

Several universities have commited to evaluating the proposed modules by introducing appropriate modules into existing classes, see attached letters of support. An evaluation team from other universities will consist of: 1. D.J. Srolovitz (Univ. of Michigan), D.M. Barnett (Stanford), A. Gilat (Ohio State Univ.), R. Talreja (Georgia Tech), G.J. Weng (Rugers), P.K. Law (Univ. Tennessee), and Elias Aifantis (Michigan Technological Univ.). Together these individauls will formulate and evaluate the course content in anticipation of needs of the materials engineers in industry. Professors David Barnett from Stanford and David Srolovitz from the University of Michigan have requested to participate in the the creation of these modules.

2.7 Preliminary Effort

With the support of the NSF funds, the PIs are advising three undergraduate research assistants on research projects in materials engineering involving some of the topics delineated above. For example, one student is analyzing the response of a prenotched plate subjected to impact loading and is fascinated with the pictures depicting the closure and re-opening of the crack. The goal here is to ascertain the range of impact speeds which result in the transition of the failure mode at the crack tip. She will be presenting her research findings at the Society of Engineering Science Meeting, Tempe, Arizona Obtober 20-23, 1996. Another undergraduate is exploring the reliability of ceramics toughened by "bridging" inclusions, and the time-dependent crack growth in such systems. One of the PIs working with Visual Numerics, Sun Javasoft, and Netscape has already developed Java-Web based modules for submitting batch jobs to supercomputers and visual analysis and display of the simulation results using VRML.

2.8 Cost Sharing

As detailed on the sheet following the summary budget page, Virginia Tech will release each of the Pls 5% during the academic year to work on the project; the PIs' man-months supported by the Institution essentially equal that requested to be funded by the NSF. The dollar amount contributed by the University equals $84,509, or 38% of that requested from the NSF. The University, College of Engineering and Departments of Materials Science and Engineering (MSE) and Engineering Science and Mechanics (ESM) have collectively committed to cost share an additional $53,000 for new computer workstations and visualization software that was purchased from last years budget when this proposal was submitted last year.

As indicated in the supporting letters from the Dean of Engineering, the College of Engineering is committed to bringing computer technology to the classroom and will facilitate the development of the proposed two courses in every way possible.

2.9 Facilities

The university Computing Center and ESM and MSE Departments maintain a large array of hardware ranging in size from PCs and workstations to an array of parallel computers on campus. A list of computing resources is given in the NSF FORM 1363: Facilities, Equipment & Other Resources, H.1.

3.0 References

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  4. R. Pasianot. Z. Xie, D. Farkas, and E.J. Savino. Computer simulation of (100) dislocation core structure in NiAl. Modelling and Simulation in Materials Science and Engineering, 2(3):383-394, 1991.

  5. D. Farkas and C. Jones, "Interatomic potentials for ternary Nb-Ti-Al alloys, Modeling Simul. Mater. Sci. Eng. 4, 23-32, 1996.

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  7. D. Farkas. Interatomic potentials for Ti A with and without angular forces. Modelling and Simulation in Materials Science and Engineering, 2(5):975-984, 1994.

  8. C.L. Fu and M.H. Yoo. Deformation behavior of B2 type aluminides: FeAl and NiAl. Acta Metallurgica et Materialia, 40(4):703-711, 1992.

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  10. W. A. Curtin and K. Futamura, "Microcrack Toughening?", Acta Met. Mater. 38, 2051, 1990.

  11. W. A. Curtin and H. Scher, "Brittle Fracture in Disordered Materials: A Spring Network Model", J. Matls. Res. 5, 535, 1990.

  12. W. A. Curtin, "Disorder-induced Toughness", Subm. to Phys. Rev. B

  13. W. A. Curtin, "Toughening by Crack-Bridging in Heterogeneous Ceramics", J. Am. Cer. Soc. 78, 13/3, 1995.

  14. W. A. Curtin, "Fiber Pullout and Strain Localization in Brittle Matrix Composites", J. Mech. Phys. Solids 41, 35, 1993.

Ronald D. Kriz