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Collaborative Proposal: The Role of Grain Boundaries in Non-Nano Polycrystal Deformation Robert H. Wagoner, The Ohio State University (OSU), PI Brent L. Adams, Brigham Young University (OSU), PI Elizabeth A. Holm, Sandia National Laboratories (SNL), Principal Advisor (These are shown on a separate page to show the page limit for the Project Summary.) PROJECT SUMMARY (next page) 1 Grain size is a critical aspect determining the strength of polycrystalline metals. Grain size reduction alone can increase the strength of steels by a factor of 3 for “normal” (non-nano) grain sizes (>1 m). In spite of its identification more than 50 years ago (Hall-Petch Effect [1,2]) and its undisputed practical importance, its origins are poorly understood and quantitative predictions have been elusive. Intellectual Merit - PI’s Adams and Wagoner have been developing ways to simulate and measure the interactions of large numbers of dislocations (1014/m2) with grain boundaries. Recently, through an NSF EAGER award, two breakthroughs were made: 1) A multi-scale simulation scheme was demonstrated. It predicted quantitatively, for the first time, the Hall-Petch effect. 2) New EBSD techniques were developed, thus enabling the resolution of dislocation densities and characters for typical densities in annealed polycrystals (i.e. about two orders of magnitude lower than were previously resolvable). Both of these rely on knowing the grain boundary obstacle strength, τobs. The proposed work capitalizes on these advances to measure and verify τobs, thus solving a long-standing challenge in metallurgical science and enabling a new phase of polycrystalline material design. A “Critical Experiment” will be carried out by the three collaborating groups. It involves the insitu loading and deformation of an Fe bicrystal, simulation using atomistic and the multi-scale methods, and the high-resolution measurement of dislocation tensor distributions within the specimen. Each of these aspects requires new, novel techniques to be developed. The result will be a verified value of τobs and its variation with boundary character and strain. Broader Impacts – New capabilities in computational metal plasticity and its characterization will enable material design, a benefit to society. The methods developed will bridge longstanding length-scale gaps between single-dislocation behavior and continuum plasticity without introducing arbitrary unknowns and fitting parameters. Benefits will include design of higher strength / higher ductility structural materials, improved processing routes, and new multi-scale measurement techniques. EBSD, already widely used, will be extended to recover detailed tensor dislocation content at previously unimaginable resolutions (HR-EBSD), a contribution to enhanced infrastructure. The multi-scale model predicts polycrystal properties and interpretation of collective dislocation characterization corresponding to measurements from HR-EBSD. For the first time, the full lattice distortion can be predicted and measured for any array of dislocations and with any boundary conditions. This capability allows critical probing of long-held assumptions of the links between single-dislocation / atomistic methods and large-scale constitutive models. Each investigator is committed to wide dissemination of results: publicationin peer-reviewed journals, graduate theses/dissertations, and reporting at national/international meetings. For example, output from two recently-completed NSF grants to Wagoner and Adams included 53 publications 10 invited/plenary presentations, and 4 book chapters. The collaboration of two universities and a government laboratory will provide exciting learning opportunities for the three funded Ph.D. students, for undergraduate students to be funded separately by REU proposals, and for the senior researchers. Periodic meetings and summer internships will deepen the interactions. All of the investigators are committed to broadened participation by under-represented groups. 10 of the 44 graduate students advised by Wagoner to completion of their degrees are women. Adams currently mentors 3 undergraduate women in materials design. 2 SPECIAL NOTES TO REVIEWERS Two unusual aspects of this proposal need clarification The first relates to the structure of the proposal, which is dictated by the unusual history of the prior work. The second clarifies the key, unfunded role of the Sandia National Laboratory personnel. History of Collaboration. A significant part of this proposal focuses on two recent research advances made as part of a current NSF EAGER award. These enabling advances have not all appeared in print yet, so significant space is devoted to introducing them, and links are provided to manuscripts for more detail. The “Past Results” section of this proposal is thus longer and more detailed than usual. It reflects many years of work although the EAGER funding has been in place for only one year, as explained by the brief history below. The PIs, during a discussion at a chance professional meeting in 2004, identified the following “grand challenge:” understand and predict, without unrealistic models or arbitrary length scales, the Hall-Petch Effect. An unfunded collaboration was begun that continues today. New, promising approaches were developed but two major problems were uncovered that appeared unsolvable until very recently: 1) A new idea for a multi-scale simulation technique treating the interactions of many dislocations with grain boundaries showed good numerical characteristics and practical computation times, but did not properly link strain with the motion of dislocation populations. It predicted Hall-Petch slopes 20-50 times smaller than those measured. 2) The most accurate EBSD techniques developed to resolve dislocation tensor content were only suitable for high dislocation densities, typically greater than 1014/m2, such as are found only near grain boundaries or in highly-strain-hardened states. Thus, the critical grain-scale spatial distributions of dislocation density throughout grain interiors predicted by the multi-scale could not be compared with sufficient precision. A series of 4 “Hall-Petch” proposals were declined by NSF between 2004 to 2008. The reviews grew progressively more positive as the unfunded research progressed. The last proposal received reviews of Excellent and Very Good, but was declined for budgetary reasons. Part of that proposal was revived by new Program Director Ardell as an EAGER award, thus making possible the advances outlined in the Past Results section. The main criticisms of the Hall-Petch proposals related to two issues: 1) Unlikely to succeed; simulation method untried and unproven, and 2) Not based on nano-scale experiments and theory In answer to the first of these, the results in the Prior Results section (and in links provided) demonstrate the validity of the simulation and experimental approach. In answer to the second criticism, atomistic simulation of a key parameter, the obstacle stress, is a key focus in the current project, however, the target microstructural scale (“non-nano”) remains as before. Non-nanograined materials have overwhelming importance for structural applications, and it is clear that distinct mechanisms operate in nano and non-nano grains.. Role of Sandia National Laboratory (SNL). The PI’s have insufficient experience in atomistic simulation to carry out an essential part of the proposed project. Fortunately, Elizabeth A. Holm, Stephen Foiles, and Christopher R. Weinberger of the Computational Materials Science and Engineering group at SNL volunteered to assist the project in the following immediate ways: 1) Train and advise a graduate student at OSU on atomistic methods 2) Provide summer internships to accelerate and improve the training 3) Host and/or attend annual project review meetings 3 4) Provide access to state-of-the-art computation facilities at SNL Furthermore, Dr. Holm will apply for internal SNL funding to allow direct performance of simulations and developments by Holm, Foiles, and Weinberger. The success of that application cannot be guaranteed, but funding from NSF would make it more probable. TECHNICAL BACKGROUND Hall-Petch Models. The widely accepted and experimentally verified Hall-Petch equation [1, 2] relates the strength of polycrystalline metals, y , to the grain size, D, as follows: y 0 ky D1/2 (1) where σ0 and ky are material constants usually referred to as the friction stress and the Hall-Petch slope, respectively. For FCC materials, ky values are generally less than 0.3 MN/m3/2 while those for BCC materials are higher by a factor of 2 to 3, the origin of the large difference being unclear. The sole quantitatively predictive model is the original one of Hall and Petch. Dislocations on a slip plane pile-up until a obstacle stress is exceeded at the head of the pile-up, the length of which is taken to be half of the grain diameter, giving a Hall-Petch slope as follows: b obs ky M k 1/2 (2) where M is the Taylor factor, µ is the shear modulus, b is the Burgers vector, and k=1 for screw dislocations and k=1-ν for edge dislocations. While an attractive, predictive model, pile-ups are seldom seen in deformed polycrystals, particularly BCC ones, where the effect of grain size is most pronounced. When seen (at very small strains and in very thin specimens of FCC materials), pile-ups do not extend across a sizable fraction of a grain but instead are local to a grain boundary [6-8]. Furthermore, the value of k y computed for iron using Eq. 2 (with one of the few measured values of obs ) is approximately an order of magnitude smaller than measured. Alternative models of the Hall-Petch effect are phenomenologically fit to the macroscopically observed behavior. The composite model, for example, envisions a strong grain boundary “phase” of constant width [11-13]. The width is fit to macroscopic behavior. More recent straingradient models introduce an arbitrary material length scale to adjust dislocation density [14-19] or introduce a similar term directly into a continuum constitutive description [20-27]. The physical origin of the new length scale is murky or unmeasurable, and its relationship to grain boundary character is not addressed. Progress has been made for mechanisms for nano-scaled grains, including dislocation dynamic simulations [28-33] and nanoindentation near a grain boundary [34-36] but the nano-scale mechanisms are generally recognized as distinct from “normal”grain sizes, and yield different slopes. Grain Boundary Obstacle Stress, obs. The only known experimental determinations of obs utilize TEM observations of pile-up spacings in stainless steel. Shen, Wagoner, and Clark [37] found that a simple geometric criterion [37] reproduced observed emitted slip systems across a boundary from a pile-up: N L1 Li g1 gi (3) 4 where L1 and Li are the intersection lines between grain boundary and slip planes and g1 and gi are the slip directions of incoming and emitted dislocations, respectively. The transmissivity, N, ranges from 0 to 1 representing maximum and minimum obstacle stress, respectively. Eq. 3 was recently used to prepose a quantitative relationship for the obstacle stress for any grain boundary as follows [REF]: obs (1 N ) * (4) where * is the maximum grain boundary strength. Shen et al. [35] calculated a lower-bound value * equal to 5 times the macroscopic yield stress for 304 stainless steel. Atomistic simulation to obtain obs for specific interfaces or grain boundaries for FCC metals have appeared [38-41] but their accuracy for BCC metals, for which interatomic potentials are less satisfactory, has not been tested. This aspect is a key part of the proposed work. RESULTS FROM PRIOR NSF SUPPORT DMR-0936349: EAGER/ Interactions between dislocations and grain boundaries in BCC metals: Hall-Petch effect, R. H. Wagoner, B. L. Adams, Sep.09- Aug. 11, $155,462 OSU, $139,841 BYU. This project was intended to predict the strengthening effect of grain boundaries (Hall-Petch effect) in metallic polycrystals in a physically consistent way, and without invoking arbitrary length scales. In the first year of the two-year project (and after many unfunded years of prior developments) two major advances have been made: 1. A multi-scale method to treat the interactions of large numbers of dislocations with grain boundaries predictively has been developed, implemented, and tested successfully. 2. High-resolution EBSD methods (HR-EBSD) based on cross-correlation techniques have proven capable of resolving the tensor character of dislocation densities as low as 1012/m2, two orders of magnitude lower than is possible for traditional Hough-based methods. These advances, summarized in this section, lend optimism to the overall goal of predicting the mechanical properties of a non-nano-scale polycrystal based on the grain / grain-boundary structure. The two advances are summarized in the remainder of this section of the proposal. Multi-scale Model. Two simulation scales are sequentially iterated in the model. At the first scale, a standard finite-element model of a polycrystal (up to 100 grains currently) [3-7] uses a new, dislocation-based constitutive equation for single crystals [8]. The single-crystal constitutive model represents measured single-crystal behavior. (In contrast, typical singlecrystal constitutive models are inferred from fitting textured polycrystals using simulations that ignore grain size, shape, and character.) The new constitutive equations represent real singlecrystal stress-strain response by a factor of two better overall than conventional PAN (Peirce, Asaro, Needleman [9]) models back-fit from texture simulations. An example comparison is shown in Fig. 1. 5 120 100 Cu single crystal Fit to multiple slip 100 y= 81 MPa std.dev.=22.6 MPa 80 Taylor Model (SCCE-D) [001] Measured 80 [123] Prediction (PAN) [001] Fitted 60 y (MPa) Eng. Stress (MPa) Taylor Model (SCCE-T) Sample 1 PAN model 40 [123] prediction (Two-scale model) 40 y= 80 MPa std. dev.=18.6 MPa 60 y= 83 MPa std.dev.=19.8 MPa Two-scale model 20 20 y= 72 MPa std. dev.=4.6 MPa Measured y= 86 MPa [123] Measured 0 0.00 0.02 0.04 0.06 Eng. Strain (a) 0.08 0.10 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Eng. Strain (b) Figure 1: Comparison of predicted stress-strain curves with the measurement for (a) copper single crystal [8], and (b) Fe multi-crystal. [10] (Fix reference number?) At the second scale, dislocation densities demanded by the first scale simulation are lumped into superdislocations on each slip system at the center of each finite element. The dislocation population is distributed at each time step in order to be consistent with the plastic strain throughout the polycrystal, and the dislocation configuration is used to compute the associated inter-dislocation back stress. Finally, the second scale simulation enforces local slip transmission criteria at grain boundaries, i.e. so slip across a boundary is blocked until the total stress acting on a single dislocation near the boundary exceeds a critical obstacle stress (characteristic of the slip systems involved, the boundary orientation and grain-to-grain misorientation). Only three arbitrary parameters are used in the multi-scale model, all related to the strain hardening of single crystals. Comparisons of preliminary tests of the new method and experiments revealed the following: 1) It is practical, taking only 5% more CPU time compared with a standard elastic-plastic FE model of a polycrystal. 2) It reproduces solutions consistent with results for analytical solution of simple single pileups. 3) It predicts Hall-Petch slopes for iron of 1.2 ± 0.3 MN/m3/2 and 1.5 ± 0.3 MN/m3/2, in agreement with the measured value of 0.9 ± 0.1 MN/m3/2. 4) It predicts the tensile response of an Fe multicrystal (9 to 39 grains) 2-4 times more accurately than by standard CP-FEM or Taylor-type texture models. 5) It predicts the magnitude of lattice curvature near grain boundaries of deformed Fe-3% Si multicrystals within the experimental scatter, Fig. 2. (The techniques for measuring lower lattice curvature or dislocation content were not available at the time this work was done. See below for the promising new developments in that area.) 5) It predicts the dislocation content and character at a scale represented by the finite elements. Examples of predictions for an idealized single crystal within a crystal are shown in Fig. 3. 6 G1 G2 B A G4 G3 (b) Initial mesh (a) Initial grain orientations (OIM) rad/μm rad/um 0.004 0.002 0 (d) Lattice Curvature (Predicted) (c) Lattice Curvature (Measured) (a) (b) Figure 2: Deformed Fe-3% Si specimen images after 8% strain, (a) measured lattice curvature (b) predicted lattice curvature using the multi-scale mode (m2 ) (m2 ) (m2 ) e=0.01 e=0.05 e=0.10 (b) (m2 ) (m2 ) 21 1 1 11 1 12 111 (c) Figure 3: First predicted dislocation densities for cylindrical grain within a grain tensile specimen:. (a) evolution of total dislocation density distribution with deformation, and (b) dislocation densities for two slip systems at the same deformation state. High-Resolution-EBSD. A key experimental challenge to verifying any dislocation-based model of metal deformation lies in the resolution and characterization of large populations of dislocations, not only in scalar form but in tensor form. (For small numbers of isolated dislocations, as for example in nano structures, TEM and other methods can resolve all aspects of individual dislocations.) Standard EBSD using Hough-based indexing of EBSD patterns is limited to 0.5 in angular resolution of lattice orientation, corresponding to greater than 1014 m-2 of dislocation density. New HR-EBSD methods, based upon cross-correlation techniques [11, 12] can now resolve lattice orientations and dislocation densities of ~ 0.005, and 1012 m-2, respectively. [13-16]. These double-order-of-magnitude improvements allow mapping of incredible detail of dislocation densities, as shown in Figure 4, where even cell formation and other such complex dislocation arrangements are imaged. While polishing techniques for Ni (as shown 7 in Fig. 4) are well established, the ones for softer steels have been developed at BYU and are still being improved. Figure 4. GND dislocation density estimates for a wedge indented Ni sample, at a step size of 100nm[17]. An equally important advance promises to allow recovery of the complete field of the elastic displacement gradient tensor, e(x), and the complete elastic incompatibility, curle(x), which is Nye’s geometrically-necessary dislocation (GND) tensor, (x) [18-22]. HR-EBSD methods enable direct, partial recoveries of these tensor fields. Cross correlation is insensitive to the spherical components of e; but given the near-surface nature of EBSD, if the local elastic properties are known, the traction free surface condition can be exploited to recover the missing spherical component [11, 15]. The stress equilibrium relation (div = 0) can be exploited to recover estimates of the additional components of the dislocation tensor, as long as the elastic properties of the local material are known. Only 5 components of the 9 component dislocation tensor can be measured; however the form of the solution to the equilibrium relation suggests that additional information can be recovered by solving a large system of linear equations. This approach has now been verified by recovering the four missing, and previously unretrievable components of a simulated dislocation distribution; these recoveries were for a W grain, selected for its isotropic elastic simplicity, Fig. 5. The ability to recover the principal features of the simulated dislocation field is evident. Figure 5. Demonstration of principle of recovery of the complete dislocation tensor for a single grain of Tungsten, of 6.26 m2. 8 Human Resources Developed. Hojun Lim received his Ph. D. in Spring 2010; is now Postdoctoral researcher. .Ji Hoon Kim was post-doc, now is Research Scientist, Korea Institute of Materials Science. Publications 1) Lim, H., Lee, M. G., Kim, J. H., Adams, B. L., Wagoner, R. H., (2010). "Simulation of Polycrystal Deformation with Grain and Grain Boundary Effects", Int. J. Plast. (submitted). LINK (to be added): 2) Lee, M. G., Lim, H., Adams, B. L., Hirth, J.P., Wagoner, R. H., (2010). "A dislocation density-based single crystal constitutive equation." International Journal of Plasticity 26: 925-938. LINK (to be added): 3) Lim, H., Lee, M. G., Kim, J. H., Hirth, J. P., Adams, B. L., Wagoner, R. H., (2010). "Prediction of Polycrystal Deformation with a Novel Multi-scale Approach", 1st Conf. Adv. Interaction & Multiscale Mech. (AIMM'10). Eds. C.-K., Choi, Y. -B. Yang, Techno-Press, pp.1164-1192 4) BRENT – CAN YOU CONTRIBUTE SOMETHING HERE, SUBMITTED OR IN PREPARATION? [YOUR REFERENCE 5] A CRITICAL EXPERIMENT This section outlines, in a condensed and simplified way, the core of the proposed work: a “Critical Experiment” aimed at measuring the stress to push1 a dislocation through a grain boundary, obs . A value for obs has seldom been measured and is poorly understood. Its determination is an important scientific advance in its own right; it is the key to understanding the mechanical behavior of non-nano-scale polycrystals (i.e. virtually all structural alloys). It is also needed to enable effective material design, the eventual technical and societal benefit of the work proposed here. The goal is not only to measure a single value of τobs, but more importantly its dependence on grain boundary character, grain misorientation, and orientation of slip systems on both sides of the grain boundary. Only through such knowledge can the varying properties depending on grain boundary character (not only texture) be understood. The open question of whether τobs depends on the magnitude of slip transmitted will also be answered. For the moment, the developments required to carry out the “experiment” will be ignored. These will be addressed subsequently. In its simplest presentation, the experiment consists of the physical in-situ deformation and simultaneous EBSD characterization of a bcc bicrystal, and at least two kinds of corresponding simulation, as portrayed schematically in Fig. 6. The simulations will be conducted at two widely removed length scales: meso and atomistic. The experiment will be repeated for various combinations of active slip systems and grain/ground boundary orientations. The critical importance of obs for understanding macroscopic grain boundary behavior was revealed in the Past Results section. Accurate prediction of the Hall-Petch slope and the More formally, obs is the local stress required to propagate plastic slip across a boundary obstacle. The detailed mechanisms are not of immediate concern at the meso scale, except as they affect the effective obstacle strength. Thus, obs may be determined by the nucleation of a new dislocation on the outgoing side of the boundary, or other mechanisms involving cross-slip, absorption and emission events. The proposed atomistic scale simulations will probe these detailed mechanisms automatically as they simulate the grain boundary resistance to slip transmission. 1 9 dislocation distribution within the grains required one main critical parameter, obs . The other parameters inherent in the multi-scale simulation are either well-known and standard (elastic constants, slip system orientations, burgers vectors, for example), or are readily determined (3 strain hardening parameters, obtainable from single crystal tensile tests), or have little effect on the model predictions (for example, the proportion of edge and screw dislocation character). In preparation of this proposal, simulations were performed to probe the sensitivity of the Hall-Petch slope by changing each parameter by a factor of ½ and 2. The change of Hall-Petch slope for the various parameters is as follows: obs: +/-80%, o (initial dislocation density): +/-15%, all others: maximum of 3%. Figure 6: Conceptual views of a bicrystal “critical experiment” including EBSD measurement of tensor dislocation density distributions and two two kinds of interpretative simulations: multi-scale model of the overall configuration and atomistic simulation of a small region of the physical boundary. The values of obs for various grain boundaries were obtained using Eq. 4 and a value of the maximum obstacle stress, * , 375 MPa, inferred from TEM measurements of dislocation pile-up spacings in thin films. There are many possible sources of error in this procedure, but there have been few alternative schemes for determining obs or * (as reviewed in the Background Section). It is unclear, for example, whether the obstacle strength varies with slip passage, with the crystal structure, or with the magnitude of slip transmitted. The Basic Physical Experiment. The Critical Experiment, in its simplest form, Fig. 7, consists of the following steps : 10 1) Prepare a columnar bi-crystal tensile specimen oriented for single slip in a planar direction. Materials: originally very coarse grained Fe or Fe-3%Si for which singlecrystal constitutive behavior has already been measured and equations have been verified. The specimen size will depend on the grain size achievable, but will be suitable for insitu deformation in an EBSD-equipped SEM. (The procedures for obtaining large grains and tensile specimens are in place. They were used to obtain the Past Results.) 2) Specimens will be polished using techniques for Fe developed at BYU. (Already developed.) 3) Specimens will be OIM scanned to obtain initial crystallographic orientations and dislocation densities near the grain boundary. New HR-EBSD techniques will be employed. 4) Fiducial marks will be applied to each sample to determine the local extension. 5) A pre-set extension will be applied using special micro-tensile stage developed for in-situ SEM2. Load and extension will be recorded, and the shape of the specimen and the grain boundary. 5) Full components of dislocation tensors will be measured and recovered using HR-EBSD and special analysis. The dislocation content will be obtained at locations throughout the specimen with a focus on locations approaching the grain boundary along the traces of the active slip planes. The step size will approximate the element size for two-scale modeling. 6) After EBSD in-situ testing is complete, the specimen will be sent to OSU for nanoindentation experiments similar to ones reported by Aifantis et al. [REF] These will provide a third route to the measurement of obs. Figure 7: Schematic of a tensile specimen for the “Critical “Experiment.” Analysis. In parallel with the physical EBSD bicrystal tensile experiment, meso-scale and atomistic simulations will be conducted using identical orientations of grains, grain boundary, and extension direction. The simplest analysis will compare the measured distribution of scalar dislocation density (function of distance from the grain boundary, (x)), the measured stress-strain response, and the 2 The tensile testing apparatus was designed by Luke Brewer and Brad Boyce at SNL, especially for use with EBSD capabilities. The design has been altered at BYU to accommodate the short (12mm) working distance on the available FEI-SFEG-based EBSD system. The modified system is currently under construction. 11 measured shape changes of grain boundaries and specimens with corresponding quantities from meso-scale simulations based on obs computed atomistically. If everything agrees within experimental and simulation scatter, the computed obs will have been confirmed. This would be the first such measurement and confirmation of a grain boundary obstacle stress. Assuming that the agreement is not perfect, a second layer of analysis will be initiated to recover the effective obs from the scalar dislocation distribution, (x), ignoring for the moment the value of obs simulated atomistically. This will be accomplished using an overall reverse analysis, i.e. computing (x) for several choices of obs, finding the best fit value, and then comparing details of the simulations and measurements to verify the consistency of the solution. The task will then be to determine why obs from meso-scale measurements and simulation do not agree with atomistic ones. Assuming that the nature of the discrepancy has not yet been revealed, the next step will be to look at detailed dislocation content in tensor form, and its gradient from one element or measurement to another. Discrepancies in these quantities may reveal detailed local mechanisms not considered in the meso-scale model, such as cross-slip, complex interactions among the longrange fields of among various types of slip systems, slip-affecting boundary conditions at free surfaces (currently treated as traction free only). These will guide future developments of the meso-scale model. Similarly, such analysis can also be used to guide the atomistic simulations and to probe the accuracy of the BCC potentials used. One particular phenemonen to look for in the experiments and measurement is the non-Schmid nature of slip in BCC crystals [REF]. This should appear automatically in the atomistic simulations if the potential is sufficiently accurate, and will need to be added in a continuum fashion [REF – Anand, others?] to the meso-scale simulation as guided by the atomistic results and EBSD experimental results. Extensions of the Basic Experiment. Two basic extensions are planned at the outset. Others will be guided by the results and the experimental difficulties that are encountered. The first planned extension involves stopping the deformation of the bicrystal at various extensions, then performing the measurements as shown for the basic experiment. The number of EBSD scans is limited by the time in the SEM chamber with voltage on, on the order of a few hours until the signal is degraded. Nonetheless, even obtaining three sets of (x), will allow determination of whether obs evolves with the magnitude of local slip passed through a boundary. Such a determination would be a first. If such scans cannot be performed in their entirety because of time limitations, coarser scans of smaller areas would be attempted to get the required variation with strain. The second planned extension involves testing a series of bicrystals with markedly different crystal misorientations and boundary orientation. It is hoped that 6-10 such configurations can be tested in order to verify or modify the simple rule for computing obs from a known value of the maximum ground boundary resistance () and geometric orientation information, Eqs. 3 and 4. Having a confirmed rule for general grain boundary character would also be the first result of its kind, although inferences for TEM of thin films at very small strain have tended to confirm relationships such as Eqs. 3 and 4. The remainder the extensions are conceived of, but will be guided by the results and by the practical limitations of cost, time, and equipment. A high priority is to use the basic method to 12 examine dislocation distributions (measured and simulated) around grain boundary triple junctions. If the results make sense, then the next step would be to test and analyze multicrystals. These configurations are shown schematically in Fig. 9. Figure 8 : Extended tests following the critical experiment. The last kind of extension envisaged is the testing of other materials, perhaps jumping to multicrystal configurations if results are good for bicrystals and multicrystals of Fe or Fe-Si. Testing other BCC materials, such as Ta or Ni, would test whether the relationships for obsand carry over. Ta is of particular interest because the SNL partners are working on it in a related project, and verified potentials are being developed. Ni would be a good target because it can readily be polished to a very fine surface finish, using procedures already developed [REF]. Finally, and particularly if difficulty understanding the results for BCC materials persists, it would helpful to test and simulate an FCC material for which the atomic potentials are known as well as the polishing procedures. Examples would include Cu and 304 stainless steel. In the remaining technical sections of this proposal, brief introductions to the methods and developments needed to carry out the Critical Experiment are outlined. EBSD TECHNIQUES AND CHALLENGES (BYU). The EBSD work (primarily conducted at BYU) has three key challenges and solutions: 1. Recover the complete intra-grain dislocation density fields using HR-EBSD for direct components and by applying stress equilibrium relation (div = 0) for the remaining components. These measurements are for comparison with, verification of, and improvement of the OSU multi-scale model. 2. Fine-scale HR-EBSD recoveries of the inter-grain elastic incompatibility (also known as the surface dislocation tensor). These will be compared with corresponding incompatibilities obtained by atomic-scale simulations. 3. If contributions 1 and 2 are successful, pursue methods for accelerating the HREBSD methods in order to facilitate characterizations at the multi-crystal and poly-crystal levels. The technical basis for each of these challenges/solutions is discussed briefly in this section. Each of these contributions of HR-EBSD to the critical experiment requires extension of current HR-EBSD methods. Key elements of the work include: 1. Completion and experimental verification of the methodology for recovering estimates of the complete GND tensor using Green’s function methods, as mentioned in the Prior Results section. 2. Develop methods for determining the elastic strain fields in loaded and unloaded samples. Using reference EBSD images taken far from the bi-crystal interface, in the unloaded condition, the elastic strain field will be recovered as close to the interface as possible. These recoveries will be used to make direct estimates of τobs. 13 3. Development of elastic incompatibility recoveries as proximate as possible to grain boundaries, and methodology for comparison with atomic-scale simulations. 4. Acceleration of HR-EBSD methods for characterization of multi-crystals and poly-crystals A brief description of these activities follows. Methodology for recovering complete GND tensor. This approach has been outlined briefly in the Prior Results section. Finite-difference solutions to the stress equilibrium equations with known or assumed boundary conditions provide additional constraints on GND fields. To verify consistency with measurements, Ni samples will first be prepared and tested because removal of polishing effects is much easier. The results will then be extended large-grain Fe, and Fe-Si steel. A Ni sample will be serially sectioned to measure directly the missing derivatives parallel to the sample normal direction. Relaxations corresponding to the new surface creation will occur, but this alteration does not significantly affect all components of the dislocation tensor; thus it will be possible to conduct a partial experimental validation of the new methodology. Fine Scale Recovery of Elastic Fields. Determination of local elastic strain requires knowing the PC very precisely [8] along with a reference strain-free EBSD pattern. The lattice orientation of the strain-free EBSD pattern must be within 20 of the field point, otherwise corrections for crosscorrelation must be made [9]. These techniques will be extended to the plastic regime by comparing the loaded and unloaded states. The presence and character of internally-equilibrated elastic strain fields will be compared between OSU simulations and BYU experimental characterizations. BYU has recently presented techniques related to full elastic characterization [5]. [Brent: Add link here or elsewhere.] Use of a reference strain-free EBSD pattern has been shown to allow measurement the tensor dislocation content of a grain boundary, although this is at the limit of HR-EBSD resolution. For boundaries subjected to large plastic deformation (slip transmission), the strength of incompatibility will increase, and HR-EBSD should be able to resolve the interaction of dislocations with particular boundaries by considering the changes in the surface dislocation tensor. Equally novel and interesting, measured incompatibilities can be compared with those predicted from equilibrated atomic positions obtained by molecular simulations of selected boundaries. Thus, the HR-EBSD results, which characterizes structure at ~ 100nm, will be compared with the multi-scale simulations of OSU at a length scale of ~ 1,000nm, and with atomistic simulations at ~ 10nm. Acceleration of HR-EBSD methods. Adaptive EBSD techniques [16,17] will be devloped to allow faster partial scans, i.e. focusing on finer length scales near grain boundaries and triple junctions. A coarse step size ~ d/10 (where d is the grain size) will used to scan the microstructure, where differences in adjacent lattice orientation identify the presence of one or more grain boundaries. The scan is subsequently and sequentially refined in the local neighborhood. A typical final step size might be ~ d/1000, leading to accelerations of ~100 in typical applications. Adaptive methods will become important in the proposed work as larger numbers of interfaces and grains are considered within the simulations and the corresponding experimental campaigns. Similarly, multiple scans will be required for a single sample stopped at several extensions for characterization. ATOMISTIC SIMULATION OF τOBS. (OSU, SNL). 14 The initial atomistic simulation work will be done by PI Wagoner and an OSU graduate student co-advised by the SNL group (Holm, Foiles, Weinberger). Later stages will depend on internal SNL funding to allow direct participation in large-scale simulations. Under both arrangements, SNL will make available large-scale computing facilities in addition to facilities at the Ohio Supercomputer Center (see supplementary information). SNL has a project in place to simulate the mechanical response of bcc Ta from the atomic to the continuum scales. SNL will supply computational methods and experimental data that will enable the measurement of the obstacle stress for Ta grain boundaries (and indirectly for Fe grain boundaries). The results will benefit the projects at SNL with improved constitutive and continuum models for Ta deformation. Technical Developments. The direct interaction of a dislocation and grain boundary occurs at distances less than 100 nm, in reference volumes making it suitable for atomistic simulation. In concept, the appropriate bicrystal is built, a dislocation is inserted, and the bicrystal stressed until slip passes through the boundary. However, each step requires special knowledge and techniques for which SNL has the needed expertise. SNL is the developer of the widely used LAMMPS code for molecular dynamics [1] and the inventor of the embedded atom method (EAM). It therefore has as unique capabilities in atomistic simulation. Dislocation motion in bcc materials such is highly sensitive to the Peierls stress, which is not accurately reproduced by EAM potentials. Current research programs at SNL are developing atomistic simulation methods for dislocations in Ta based on bond order potentials; this work will provide a platform for simulations required in this program. These potential will be directly applicable to Ta, but variations will likely be suitable for Fe. Fe represents an additional challenge because of ferromagnetic effects. These will be ignored in the original simulations. Building an atomic bicrystal with an equilibrated grain boundary structure is required [3]. SNL has developed an automated grain boundary construction method that provides well-minimized bicrystal structures with arbitrary grain boundary crystallography [4]. Ts technique will be used to build the required bicrystals. The magnitude of the applied stress needed to move a dislocation through a grain boundary can affect the structure of the dislocation and the grain boundary, and the stress is affected by the strain rate applied in the simulation. The solution is to decrease strain rate as much as possible by running very long simulations. SNL recently performed the longest MD simulation of polycrystalline grain growth to date [5], and can apply such simulations to this program. The large number of large-scale simulations required necessitates access to high performance computing resources, such as those that will be provided by SNL. An alternate method that might prevent the distortions caused by large applied stresses is the “synthetic driving force” MD method, recently developed at SNL [6-8]. This method has shown to simulate grain boundary motion identically to physical driving forces, but without the artifacts caused by the physical mechanism [8]. A similar development applied to dislocations might allow simulation of realistic dislocation motion while still avoiding long CPU times. SNL will investigate both low-rate conventional MD and synthetic driving force MD to determine the more appropriate method. Both the physical insights gained and the computational technique developed will be important outcomes from this program. Complexities are expected in the details of the simulated results. Dislocations may be absorbed by the grain boundary and disappear from the system, thus changing the boundary structure for the next slip event. After enough absorption events, the grain boundary structure may be modified sufficiently to then transmit a dislocation or to undergo a structural transformation [9]. 15 These sorts of changes will produce a changing τobs with regard to slip magnitude. Unrealistically high stresses might be required because thermally activated or assisted mechanisms are typically not amenable the MD time frame for complex problems such as this one. Nonetheless, MD simulations should predict the relative transmission strength of boundaries despite the influence of high stresses, and perhaps a small number of detailed simulations can be used to estimate τ* , such as appears in Eq. 4, thus effectively scaling the 0 K simulations for a variety of configurations. Investigating, understanding, and incorporating these effects into a model that can be applied on the continuum scale is the ultimate goal – and challenge – of the atomic scale simulation effort. Research Tasks and Approximate Schedule Develop a synthetic driving force MD method for dislocation motion and compare with conventional stress-driven MD. (Y01Q02) Define atomistic simulation platform, including accurate and appropriate interatomic potential for defects in Ta. (Y01Q04) Build a catalog of atomic scale Ta bicrystals containing dislocations. (Y02Q02) Measure obs for individual dislocations approaching bicrystal grain boundaries. (Y02Q04) Investigate the phase space of dislocation/boundary interactions, including multiple dislocation effects. (Y03Q02) Develop a model for obs that can be implemented in continuum deformation simulations. (Y03Q04) MULTI-SCALE MODELING AND MATERIAL PREPARATION (OSU) The OSU multi-scale model has been introduced in the Prior Results section along with various verifications to-date. More detailed information about its formulation and the dislocation-density-based single crystal constitutive equations which are utilized is available the respective links provided. No further detail will be provided here because of space limitations. Simulations performed using the multi-scale model (described in the XX section) showed that obs is the only parameter likely to be of critical importance in the accuracy of its predictions, thus many of the details of the formulation may not be of immediate significance. However, the original dislocation density (related to the yield stress of single crystals) has secondary importance, about 1/5 the sensitivity as for obs. The form of single-crystal constitutive models used so far was confirmed by single-crystal experiments for Fe and Cu appearing in the literature, with parameters set by limited experiments with small multi-crystal specimens of Fe and Fe-3%Si. Large columnar grains are attainable for these metals using strain annealing. One of the OSU tasks will focus on preparing single-crystal specimens as well as the bicrystals and mulit-crystals required for the critical experiment and extension. With single-crystal specimens of known orientation, and utilizing techniques similar to the critical experiment, the constitutive equations and initial dislocation densities will be verified. Extensions to other metals such as Ni and Ta will in any case require single-crystal measurements. If large single crystals can be obtained by thermo-mechanical treatments, similar 16 procedures will be followed. If attaining very large grains proves difficult, special micro tests being developed at OSU [1, 2], Figure 9. Figure 9: Hardening curve (left) of Rene 80 from a 6 m-diameter tensile specimen (right). [2] Research Tasks and Approximate Schedule Heat treatment of Fe to obtain large grain sizes/ fabricate single- and bi-crystal specimens oriented for various directions (Y01Q02) Formulate the multi-scale model in a form that can be parallelized to make larger-scale simulations (~100-1000 3-D grains) possible. (Y01Q04) Conduct tensile tests of single crystals, fit to two scale model to obtain best fit parameters (Y01Q04) Perform pileup analysis of bicrystals to obtain obs (Y02Q02) Simulate lattice curvature for more complicated grain structure, e.g. triple junctions (Y03Q04) Simulate Hall-Petch slope for 1000 3-D grains (Y04Q02) BROADER IMPACT (BYU, OSU) Benefits to Society – Fundamentally new capabilities in computational metal plasticity and its characterization will enable material design and improve applications such as metal forming. The methods developed bridge length-scale gaps between single-dislocation behavior, computational methods, and continuum plasticity for finite-strain applications without introducing arbitrary unknowns and fitting parameters. The methods will enable a range of new developments that cannot readily be envisaged at the moment, but will include higher strength / higher ductility structural materials, improved processing routes to obtain optimal grain structures, and new measurement techniques that rely on multi-scale simulation for interpretation. Enhanced Infrastructure – Orientation Imaging Microscopy, invented by PI Adams, is today widely used to investigate the structure and properties of a range of materials. The proposed collaborations in developing HROIM, and 3D EBSD techniques and software will allow direct measurement of deformation tensors and GND content. For metal applications, this ability provides a quantitative method to characterize the local dislocation density content that is otherwise unavailable and badly needed. 17 The multi-scale model developed at OSU allows both the prediction of polycrystal properties but also the interpretation of collective dislocation characterization such as is available with EBSD. For the first time, the full lattice distortion can be predicted for any array of dislocations and with any boundary conditions. This capability allows critical probing of long-held assumptions of the links between single-dislocation / atomistic methods and large-scale constitutive models. Dissemination of Results – Each investigator is committed to wide publication of results in peerreviewed journals, graduate theses/dissertations, and undergraduate project reports. This commitment is readily demonstrated by the most-recently completed NSF grants to Wagoner and Adams. For DMR 0139045 (Wagoner), 23 publications, 2 book chapters, 6 invited/international presentations, and numerous domestic presentations were made. For DMR 0079996 (Adams), 30 publications, 2 book chapters, 4 invited and plenary addresses and various domestic presentations were made. Teaching, Training, Learning – The collaboration of two universities and a government laboratory will provide exciting broadening opportunities for the three funded Ph.D. students, for undergraduate students to be funded separately by REU proposals, and for the senior researchers. Two meetings are planned per year to maintain close contact, in addition to weekly conference calls and e-mail exchanges. The summer internship opportunities at SNL will also be used to deepen and broaden the educational opportunities for the students. Educational modules will be developed presenting basic concepts of how microstructure influences properties, including the interpretation and simulation of OIM data. Wagoner will incorporate the modules into MSE 661: Ferrous Metallurg. Funds to Wagoner from a 5-year curriculum development grant from AISI and the AIST Foundation will leverage these developments. Adams is leading a group of 4 faculty from ME and Math developing a 2-year undergraduate capstone sequence. The modules will be incorporated into this sequence as well as project assignments for ME 500 Design and Materials Applications, and ME 503 Plasticity and Fracture.. Broadened Participation – All of the investigators are committed to advising graduate students from under-represented groups and mentoring undergraduate students through the transition to graduate education. 10 of the 44 graduate students advised by Wagoner to completion of their degrees are women who now work at a variety of places, including Honda of America, Idaho National Laboratory, British Petroleum R&D, and Daimler-Chrysler. Adams currently mentors 3 undergraduate women in materials design. 18 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. Hall, E.O., The deformation and ageing of mild steel. Proc. Roy. Soc. (London), 1951. B64: p. 747. Petch, N.J., The cleavage strength of polycrystals. J. Iron Stee. Inst., 1953. 174: p. 25-28. Peirce, D., Asaro, R. J., Needleman, A., Materials rate dependence and localized deformation in crystalline solids. Acta metall., 1983. 31: p. 1951-1976. Asaro, R.J., Needleman, A., Texture development and strain hardening in rate dependent polycrystals. Acta metall., 1985. 33: p. 923-953. Beaudoin, A.J., Dawson, P. R., Mathur, K. K., Kocks, U. F., Korzekwa, D. A., Application of polycrystal plasticity to sheet forming. Computer methods in applied mechanics and engineering, 1994. 117: p. 49-70. Sarma, G.B., Dawson, P. R., Effects of interactions among crystals on the inhomogeneous deformations of polycrystals. Acta Mater., 1996. 44(5): p. 19371953. Dawson, P.R., Mika, D.P., Barton, N.R., Finite element modeling of lattice misorientations in aluminum polycrystals. Scripta Mater, 2002. 47(10): p. 713717. Lee, M.G., Lim, H., Adams, B. L., Hirth, J.P., Wagoner, R. H.,, A dislocation density-based single crystal constitutive equation. International Journal of Plasticity, 2010. 26: p. 925-938. Peirce, D., Asaro, R. J., Needleman, A., An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall, 1982. 30: p. 1087. Lim, H., Lee, M. G., Kim, J. H., Adams, B. L., Wagoner, R. H., Simulation of polycrystal deformatiln with grain and grain boundary effects. International Journal of Plasticity, 2010. Submitted Wilkinson, A.J., Meaden, G., Dingley, D. J., High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity. Ultramicroscopy 2006. 106: p. 307. Villert, S., Maurice, C., Wyon, C, Fortunier, R. , Journal of Microscopy, 2009. 233: p. 290–301. Sun, S., Adams, B. L., King, W. E., Observation of lattice curvatue near the interface of a deformed aluminum bicrystals. Phil. Mag. A, 2000(80): p. 9. Kacher, J., Landon, C., Adams, B. L., Bragg’s Law Diffraction Simulations for Electron Backscatter Diffraction Analysis. Ultramicroscopy, 2009. 109(1148). Gardner, C.J., Adams, B.L., Basinger, J., Fullwood, D.T., EBSD-Based Continuum Dislocation Microscopy. International Journal of Plasticity, 2010. 26: p. 1234-1247. Kacher, J., Adams, B. L., EBSD-Based Microscopy: Resolution of Dislocation Density. Computers, Materials and Continua, 2009. 14: p. 185-196. Gardner, C.J., J. Kcher, Basinger, J., Adams B.L., Techniques and Applications of the Simulated Pattern Adaptation of Wilkinson's Method for Advanced Microstructure Analysis and Characterization of Plastic Deformation. Experimental Mechanics, 2010. Submitted. 19 18. 19. 20. 21. 22. Nye, J.F., Some gemetrical relations in dislocated crystals. Acta metall., 1953(1): p. 153. Kröner, E., Continuum theory of dislocations and self-stresses. Ergebnisse der Angewandten Mathematik. Vol. 5. 1958, Berlin: Springer-Verlag. Kröner, E., Initial Studies of a Plasticity Theory Based upon Statistical Mechanics. Materials Sciences and Engineering, ed. M.F.K.e. al. 1970, NY: McGraw Hill. Kröner, E., Benefits and Shortcomings of the Continuous Theory of Dislocations. Int. J. Solids and Struct., 2001. 38: p. 1115-1134. Pantleon, W., Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction. Scripta Materialia 2008. 58: p. 994-997. REFERENCES (BACKGROUND) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. Hall, E.O., The deformation and ageing of mild steel. Proc. Roy. Soc. (London), 1951. B64: p. 747. Petch, N.J., The cleavage strength of polycrystals. J. Iron Stee. Inst., 1953. 174: p. 25-28. Leibfried, G., Z. Phys., 1951. 130: p. 214. Hirth, J.P., Lothe, J., Theory of Dislocations. 1969: McGraw-Hill, New York. Eshelby, J.D., Frank, F. C., Nabarro, F. R. N, The equilibrium of linear arrays of dislocations. Phil. Mag. , 1951. 42: p. 351. Feaugas, X., Haddou, H, On the origin of the tensile flow stress in the stainless steel AISI 316L at 300K: back stress and effective stress. Acta Mater., 1999. 47: p. 3617. Feaugas, X., Haddou, H, Grain-size effects on tensile behavior of nicke and AISI 316L strainless steel. Met. Trans. A, 2003. 34: p. 2329. Saada, G., From the single crystal to the nanocrystal. Phil. Mag., 2005. 85(26-27): p. 3003-3018. Hull, D., Effect of grain size and temperature on slip twinning and fracture in 3% silicon iron. Acta. Met. , 1975. 9(191). Li, J.C.M., Chou, Y. T. The Role of Dislocations in the Flow Stress-Grain Size Relationships. in Proceedings of the Symposium on the Deformation and Strength of Polycrystals, Met.Trans. 1970. Kocks, U.F., The relation between polycrystal deformation and single crystal deformation. Metall. Trans., 1970. 1: p. 1121-1143. Hirth, J.P., Influence of grain boundaries on mechancal properties. Met. Trans., 1972. 3: p. 3047. Meyers, M.A., Ashworth, E, A model for the effect of grain size on the yield stress of metals. Phil. Mag. A, 1982. 46(5): p. 737-759. Taylor, G.I., The mechanism of plastic deformation of crystals. Proc. R. Soc., 1934. A165: p. 362. Cottrell, A.H., Dislocations and plastic flow in crystals. 1953: Oxford University Press, London. 18. Conrad, H., Electron Microscopy and Strength of Crystals, ed. G. Thames, Washburn, J. 1961: Interscience, New York. 299-300. Conrad, H., Ultrafine-Grain Metals, ed. J. Burke, Weiss, V. 1970: Syracuse University Press, Syracuse, New York. 213-229. Li, J.C.M., Petch relation and grain boundary sources. Trans. metall. Soc. A.I. M. E., 1963. 227: p. 239. 20 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. Ashby, M.F., The deformation of plastically non-homogeneous alloys. Philosophical Magazine, 1970. 21: p. 399-424. Fleck, N.A., Muller, G. M., Ashby, M. F., Hutchinson, J. W., Strain gradient plasticity, theory and experiment. Acta Metall. Mater., 1994(42): p. 475. Fleck, N.A., Hutchinson, J. W., Strain gradient plasticity. Adv. Appl. Mech., 1997(33): p. 295. Nix, W.D., Gao, H., Indentation size effects in crytalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids, 1998. 46: p. 411-425. Gurtin, M.E., On the plasticity of single crystals, free energy, microforces, plastic strain gradients. J. Mech. Phys. Solids, 2000(48): p. 989. Gurtin, M.E., A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids, 2002(50): p. 5. Gao, H., Huang, Y., Nix, W.D., Hutchinson, J.W., Mechanism-based strain gradient plasticity. I: Theory. J. Mech. Phys. Solids, 1999. 47: p. 1239-1263. Huang, Y., Gao, H., Nix, W.D., Hutchinson, J.W., Mechanism-based strain gradient plasticity. II: Analysis. J. Mech. Phys. Solids, 2000. 48: p. 99-128. Abu Al-Rub, R.K., Voyiadijus, G. Z, A physically based gradient plasticity theory. International Journal of Plasticity, 2006. 22: p. 654-684. Biner, S.B., Morris, J. R., The effects of grain size and dislocation source density on the strengthening behaviour of polycrystals: a two dimensional discrete dislocation simulation. Phil. Mag., 2003. 83: p. 3677-3690. Lefebvre, S., Devincre, B., Hoc, T., Yield stress strengthening in ultrafine-grained metals: A two dimensional simulation of dislocation dynamics. J. Mech. Phys. Solids, 2007. 55: p. 788-802. Lefebvre, S., Devincre, B., Hoc, T., Simulation of the Hall-Petch effect in ultra-fine grained copper. Mater. Sci. Eng. A, 2005. 400-401: p. 150-153. Ohashi, T., Kawamukai, M., Zbib, H., A multiscale approach for modeling scaledependent yield stress in polycrystalline metals. International Journal of Plasticity, 2007. 23: p. 897-914. Balint, D.S., Deshpande, V. S., Needleman, A., Van der Giessen, E., A discrete dislocation plasticity analysis of grain size strengthening. Mater Sci Eng A, 2005. 400401: p. 186-190. Balint, D.S., Deshpande, V. S., Needleman, A., Van der Giessen, E., Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals. International Journal of Plasticity, 2008. 24: p. 2149-2172. Soer, W.A., Aifantis, K. E., De Hosson, J. Th. M., Incipient plasticity during nanoindentation at grain boundaries in body-centered cubic metals. Acta Mater., 2005. 53: p. 4665-4676. Soer, W.A., De Hosson, J. Th. M, Detection of grain-boundary resistance to slip transfer using nanoindentation. Materias Letters, 2005. 59: p. 3192-3195. Aifantis, K.E., Soer, W.A., De Hosson, J.T.M., Willis, J.R., Interfaces within straingradient plasticity: theory and experiments. Acta. Mater., 2006. 54: p. 5077-5085. Shen, Z., Wagoner, R. H., Clark, W. A. T., Dislocation pile-up and grain boundary interactions in 304 stainless steel. Scripta Metall., 1986. 20: p. 921. Hoagland, R.G., Kurtz, R. J., The relation between grain-boundary structure and sliding resistance. Philos. Mag., 2002. 82(6): p. 1073-1092. Hoagland, R.G., Kurtz, R. J., Henager Jr., C. H., Slip resistance of interfaces and the strength of metallic multilayer composites. Scripta Materialia, 2004. 50: p. 775-779. Hoagland, R.G., Mitchell, T. E., Hirth, J. P., Kung, H., On the strengthening effects of interfaces in multilayer fcc metallic composites. Philos. Mag., 2002. 82(4): p. 643-664. 21 41. de Koning, M., Kurtz, R. J., Bulatov, V. V., Henager, C. H., Hoagland, R. G., Cai, W., Nomura, M., Modeling of dislocation-grain boundary interactions in FCC metals. Journal of Nuclear Materials, 2003. 323: p. 281-289. SNL References 1. 2. 3. 4. 5. 6. 7. 8. 9. Plimpton, S.J., LAMMPS: Large-scale Atomic/Molecular Massively Parallel Simulator, 2007, Sandia National Laboratories. Daw, M.S., S. Foiles, and M.I. Baskes, The Embedded-Atom Method - A Review of Theory and Applications. Materials Science Reports, 1993. 9(7-8): p. 251-310. Wolf, D., Structure-energy correlation for grain boundaries in silicon. Philosophical Magazine A, 1989. 60: p. 545-53. Olmsted, D., S.M. Foiles, and E.A. Holm, Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Materialia, 2009. 57(13): p. 3694-3703. Holm, E.A. and S.M. Foiles, How Grain Growth Stops: A Mechanism for Grain-Growth Stagnation in Pure Materials. Science, 2010. 328(5982): p. 1138-1141. Janssens, K.G.F., et al., Computing the mobility of grain boundaries. Nature Materials, 2006. 5: p. 124-127. Olmsted, D., E. Holm, and S. Foiles, Survey of computed grain boundary properties in face-centered cubic metals-II: Grain boundary mobility. Acta Materialia, 2009. 57(13): p. 3704-3713. Olmsted, D.L., S.M. Foiles, and E.A. Holm, Grain boundary interface roughening transition and its effect on grain boundary mobility for non-faceting boundaries. Scripta Materialia, 2007. 57: p. 1161-1164. Medlin, D.L., S.M. Foiles, and D. Cohen, A dislocation-based description of grain boundary dissociation: Application to a 90 degrees < 110 > tilt boundary in gold. Acta Materialia, 2001. 49(18): p. 3689-3697. OSU REFERENCES (micro-pillar) [1] M.D. Uchic, D. M. Dimiduk, R. Wheeler, P. A. Shade, H. L. Fraser: Application of Micro0- Sample Testing to Study Fundamental Aspects of Plastic Flow, Scripta Metall., 2005, vol. 54. pp. 759-764. [2] R.Wheeler, P. Shade, M. Uchic, R. Kerns, A. Shively, F. Scheltens, H. Fraser, and D. Sergison: Development of an In-Situ Mechanical Test System for Micron-Size Samples, unpublished research. 22