Symposium Organizers
Peter M. Derlet Paul Scherrer Institut
Daniel Weygand Universität Karlsruhe, izbs
Ju Li University of Pennsylvania
Mike D. Uchic Air Force Research Laboratory
Eric Le Bourhis Université de Poitiers
GG1: Plasticity of Small-Scale Systems - Experiment
Session Chairs
Eric Le Bourhis
Andrew Minor
Monday PM, November 30, 2009
Room 300 (Hynes)
9:30 AM - **GG1.1
Size Effects Resulting from Interactions of Material and Specimen Length Scales in Micropillar Compression and Nanoindentation.
H. Bei 1 , S. Shim 2 , J. Morris 1 3 , G. Pharr 3 1 , E. George 1 3
1 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States, 2 Steel Structure Research Laboratory, Research Institute of Industrial Science and Technology, Gyounggi Korea (the Republic of), 3 Materials Science and Engineering Department, University of Tennessee, Knoxville, Tennessee, United States
Show AbstractInteresting size effects are manifested when a material length scale, defined by the average dislocation spacing, becomes comparable to the geometric length scale, determined by the volume of material tested. We investigated these size effects in single crystals using two complementary techniques, micropillar compression and nanoindentation. Controlled pre-straining was used to vary the dislocation density (internal length scale). Pillar size and indenter radius were varied to alter the effective specimen volume (geometrical length scale). In both sets of experiments, pillar compression and nanoindentation, the yield strengths approach theoretical values, when the probed volume is small (compared to the average dislocation spacing), and bulk values when the probed volume is large. The transition between these two extremes is inherently statistical and depends on factors such as the distribution of dislocations and their pinning strengths. Although pillar compression has the advantage that its stress state is simpler, indentation offers better statistics since it is easier to make hundreds of nominally identical indents than it is to compress hundreds of nominally identical pillars. Preliminary results are presented for a simple statistical model that incorporates dislocations having varying pinning strengths distributed within the volume tested, and comparisons are made with the experimental results.Research sponsored by the Division of Materials Sciences and Engineering, U.S. Department of Energy.
10:00 AM - GG1.2
Experimental Investigation of Geometrically Necessary Dislocations Beneath Small Indents of Different Depths using EBSD Tomography.
Dierk Raabe 1 , Eralp Demir 1 , Stefan Zaefferer 1
1 , Max Planck institute, Dusseldorf Germany
Show AbstractIn this work we study the link between the indentation size effect and the density of geometrically necessary dislocations (GNDs) through the following approach: Four indents with different indentation depth and hardness were placed in a Cu single crystal using a conical indenter with spherical tip. The deformation-induced lattice rotations were monitored in 3D below the indents at 50 nm resolution using a tomographic electron back scatter orientation microscope in conjunction with a focused ion beam instrument for serial sectioning (3D EBSD). From the EBSD data we calculated the first order gradients of strain and from these the GND densities below the four indents. This approach allows us to directly quantify in one set of experiments both the mechanical parameters (depth, hardness) and the lattice defects (GNDs) that are held responsible for the indentation size effect. The main result of the analysis is that the density of the GNDs does not increase with decreasing indentation depth but it drops instead. More precisely, while the hardness increases from 2.08 GPa for the largest indent (1230 nm depth) to 2.45 GPa for the smallest one (460 nm depth) the GND density decreases from 2.34 x 10^15 m^2 (largest indent) to 1.85 x 10^15 m^2 (smallest indent).
10:15 AM - GG1.3
Micro Structural Evolution in Un-Tapered Ni Pillars.
Robert Maass 3 , Steven Van Petegem 1 , Michael Uchic 2 , Helena Van Swygenhoven 1
3 , Swiss Federal Institute of Technology (ETHZ), Zurich Switzerland, 1 NUM/ASQ, PSI, Villigen Switzerland, 2 , Air Force Research Labs RXLM, Wright-Patterson AFB, Ohio, United States
Show AbstractCompression of micron sized pillars has evidenced an enhanced flow stress and strain hardening strengthening with decreasing pillar diameter. To provide further understanding of the mechanistic background for such size affected plasticity an in-situ setup combining both micro-compression and Laue micro-diffraction has been developed [Phys. Rev. Lett. 99, 145505 (2007)], and shown to provide detailed insight into the microstructure during deformation [Appl. Phys. Lett. 92, 071905 (2008)].In this work we study the deformation behaviour of un-tapered single crystal Ni pillars. The results demonstrate that some of the pillars investigated contain small rotational gradients in the as-prepared state. Upon compression local plastic processes, such as the build-up of plastic strain gradients or dislocation wall formation eventually leading to a crystallographic orientation distribution and substructure evolution, are not only occurring during the flow regime but already during the initial loading portion of the stress-strain curve. The diffraction signal is indicative for conventional strain hardening processes including a clear increase in dislocation density and shows the occurrence of plastic processes prior to the break away slip, which is understood as the moment when the stress on the formed dislocation structure is high enough to trigger a dislocation avalanche passing through the formed dislocation structure. 2D mapping of the pillars microstructure completes the information gained during in-situ testing, evidencing the localized nature of the rotational gradients within the pillars.
10:30 AM - **GG1.4
An Experimental Investigation of Intermittent Flow and Strain Burst Scaling Behavior in LiF Crystals During Microcompression Testing.
Dennis Dimiduk 1 , Ed Nadgorny 2 , Chris Woodward 1 , Michael Uchic 1 , Paul Shade 3 1
1 AFRL/RXLM Bldg 655, Air Force Wright Rresearch Laboratory, Wright-Patterson AFB, Ohio, United States, 2 Department of Physics, Michigan Technological University, Houghton, Michigan, United States, 3 , UTC, Inc., Dayton, Ohio, United States
Show AbstractCurrent research seeks methods for coarse graining the ensemble dislocation response. However, the physical understanding of intermittency micromechanisms is still lacking, thus limiting developments in this field. This paper reports on the first comprehensive experimental statistical study of plastic deformation of LiF microscopic samples having low initial dislocation densities, in both as-grown and gamma-irradiated conditions. The investigations used the microcompression testing method. Data sets were evaluated independently for the loading and flow deformation stages for each material. Investigations examined evolution of the strain-burst response in both the spatial and temporal domains. A new technique (described in detail) provided advances in quantitative evaluations of the statistical data relative to previous studies. The findings showed that specimen-size-dependent strengthening might be tied to differences between dislocation nucleation and multiplication conditions. Platen displacement event cumulative probability distributions exhibited both Gaussian regimes at small displacements and power law regimes for event displacement, duration and average velocity at larger sizes. However, the observed event size scaling exponents did not follow the expectation from mean-field theory, revealing scaling exponents in the range from 1.9 – 2.8. Additionally, extraordinarily large displacements events were observed that exceeded the sizes of those found in previous studies by at least ten times. Quantitative clarification of the power-law exponent values and their dependence on deforming sample conditions demands both further experimental studies with larger numbers of samples and a wider range of sample conditions. Such studies would benefit from better matching of the time scales of dislocation processes and observation.
11:30 AM - GG1.5
Microcompression Experiments on bcc Metals.
Daniel Kaufmann 1 , Reiner Moenig 1 , Andreas Schneider 3 , Cynthia Volkert 2 , Oliver Kraft 1
1 IMF 2, Forschungszentrum Karlsruhe, Eggenstein-Leopoldshafen Germany, 3 , Max-Planck-Institut für Metallforschung, Stuttgart Germany, 2 Institut für Materialphysik, Georg-August-Universität , Göttingen Germany
Show AbstractSize effects can cause a significant increase in the strength of a metal. In the past this effect has been extensively investigated for fcc metals but until today only limited knowledge exists on the size dependent behaviour of bcc metals. Bcc metals are used in many applications and therefore knowledge of their size scaling is of technological importance. Size effects in bcc metals are also interesting from a fundamental point of view, since new insights into underlying dislocation processes and their interaction with sample size can be obtained. The fundamental dislocation processes of bcc metals differ from those of fcc metals. In contrast to fcc metals, where screw and edge dislocations have similar mobilities with little or no temperature dependence, the mobility of screw dislocations in bcc metals is strongly temperature dependent. In bcc metals screw dislocations move by thermally activated kink pair nucleation and motion. Below the material dependent athermal temperature, their mobility is lower than that of edge dislocations. In this work the deformation of Ta and α-Fe micropillars has been studied using microcompression experiments. Pillars were produced using a focused ion beam microscope and were compressed in a nanoindenter using a flattened tip. The data shows that there is a pronounced size effect in bcc metals. The size effect of α-Fe is similar to the one found in typical fcc metals. It is more pronounced than the one found in Ta. A combination of this data with data obtained on several other bcc metals indicates that the size dependence of bcc metals is temperature dependent. Concepts that can explain the observed behaviour will be discussed and experiments that support the importance of screw dislocation motion for the deformation of small bcc metals will be presented.
11:45 AM - GG1.6
A Microcompression Study of Mg Single Crystal.
Erica Lilleodden 1 , Gyu Seok Kim 1 2
1 Institute of Materials Research, GKSS Research Center, Geesthacht Germany, 2 Science et Ingénierie des Materiaux et Procédés (SIMaP-GPM2) , Grenoble Institute of Technology, Grenoble France
Show AbstractThere is considerable need to develop mechanism-based material models for the deformation of Mg, due to its strong anisotropy and its importance in the development of lightweight structural materials. Unfortunately constitutive inputs for such models are critically lacking; fundamental studies of the critical stresses and strains and associated deformation mechanisms are needed. Employing the recently exploited method of microcompression testing, we have investigated the deformation behavior of Mg single-crystals. The main advantage of the microcompression method over conventional mechanical testing techniques is the ability to localize single crystalline volumes free of preexisting twins. However, it is found that the small geometric scale leads to the widely observed size effect in which the flow stress increases with decreasing column diameter. In this presentation, the results from microcompression testing will be discussed in terms of orientation-dependent slip and twinning mechanisms, and the role of geometric scale in the associated strain-strain relations.
12:00 PM - GG1.7
Size Dependent Brittle to Ductile Transition in Semiconductors.
Rudy Ghisleni 1 , Fredrik Ostlund 1 , Philip Howie 2 , Sandra Korte 2 , William Clegg 2 , Johann Michler 1
1 Laboratory for Mechanics and Nanostructures, EMPA - Swiss Federal Laboratories for Materials Testing and Research, Thun Switzerland, 2 Gordon Laboratory, Department of Materials Science and Metallurgy, Cambridge University, Cambridge United Kingdom
Show AbstractRecently it has been shown that micropillars of materials normally considered as brittle can be deformed plastically [Michler et al., App. Phys. Lett. 90, 043123 (2007)]. In this paper we have studied how the deformation behaviour varies with micropillar diameter, d, in particular the transition from brittle to ductile behaviour as the diameter is decreased. Single crystal silicon, gallium arsenide, and indium phosphide micropillars with diameters from 0.2 to 10 μm with an aspect ratio of three were fabricated by a focused ion beam (FIB) milling and uniaxially compressed with a diamond flat punch using a custom-made in-situ SEM nanoindenter. Si and GaAs pillars formed by lithography were also tested to substantiate the results and evaluate FIB damage.The results show that all the semiconductors investigated deform by slip band formation at room temperature under uniaxial compression. All the InP pillars in the size range tested deformed plastically, while Si and GaAs specimens presented size-dependent failure modes: 1) plastic flow for d < dcrit, and 2) compression splitting where d > dcrit. Splitting was initiated by plastic deformation (nucleation of partial dislocations/twinning), causing dislocation intersection and pile-ups, as suggested by Cottrell [Phil. Mag. 43, 645 (1952)]. Approximate estimates for dcrit are obtained by adapting an analysis/model for compression splitting and predicts that splitting should not occur at pillar diameters less than 1 μm for Si and GaAs and 20 μm for InP, consistent with the observed behaviour.
12:15 PM - GG1.8
Insights from In situ Compression Testing of Vanadium Nanopillars in a Transmission Electron Microscope.
Daniel Kiener 1 , Jia Ye 1 , Patric Gruber 2 , Andreas Schneider 3 , Claire Chisholm 4 , Andrew Minor 1 4
1 National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California, United States, 2 Institut fuer Materialforschung II , Forschungszentrum Karlsruhe GmbH , Karlsruhe Germany, 3 , Max Planck Institute for Metals Research, Stuttgart Germany, 4 Department of Materials Science and Engineering, University of California, Berkeley, California, United States
Show AbstractIn recent years, significant experimental and numerical research has addressed the mechanical properties of face centered cubic (fcc) micro- and nano-compression samples [1].A rational of the dislocation mechanisms governing the increased strength in these small dimensions was put forward by 3D discrete dislocation dynamics simulations [2] and in situ transmission electron microscope (TEM) observations [3, 4]. However, up to date few experimental studies dealt with body centered cubic (bcc) materials (see e.g. [5, 6]), and no direct in situ observations of the actual dislocation mechanisms operating in the nanopillars are available.Here we present results from nano-compression tests performed on single crystal V samples inside the TEM. Specimens were oriented for either single slip or multiple slip and were prepared from the same macroscopic bulk V single crystal. Compression samples were fabricated using a focused ion beam (FIB) workstation operated at 30 keV. Subsequent low energy ion milling techniques were also employed to minimize the FIB induced material damage and their effect will be discussed. Loading of the samples was performed in situ in a TEM [7], allowing for direct observation of the dislocation processes.The dislocation mechanisms and their relation to strength and hardening are examined for the different slip orientations and surface conditions. This will be discussed with respect to observations from FIB fabricated fcc materials that were tested using in situ TEM [3, 4], the existing ex situ studies on FIB fabricated bcc materials [5, 6, 8], and to initially defect free bcc whiskers [9]. Lastly, the in situ TEM experiments will be compared with ongoing micro-Laue investigations of the same material for what is anticipated to be highly complementary information about the deformation behavior of the bcc nanopillars.[1] Uchic MD, Shade PA, Dimiduk D. Ann. Rev. Mater. Res. 2009;39.[2] Rao SI, Dimiduk DM, Parthasarathy TA, Uchic MD, Tang M, Woodward C. Acta Mater. 2008;56:3245.[3] Shan ZW, Mishra RK, Asif SAS, Warren OL, Minor AM. Nat. Mater. 2008;73:115.[4] Oh SH, Legros M, Kiener D, Dehm G. Nat. Mater. 2009;8:95.[5] Greer JR, Weinberger CR, Cai W. Mater. Sci. Eng. A 2008;493:21.[6] Schneider AS, Clark BG, Frick CP, Gruber PA, Arzt E. Mater. Sci. Eng. A 2009;508:241.[7] Minor AM, Asif SAS, Shan ZW, Stach EA, Cyrankowski E, Wyrobek TJ, Warren OL. Nat. Mater. 2006;5:697.[8] Kim J-Y, Jang D, Greer JR. Scripta Mater. 2009;61:300.[9] Bei H, Shim S, George EP, Miller MK, Herbert EG, Pharr GM. Scripta Mater. 2007;57:397.
12:30 PM - **GG1.9
Confined Dislocation Plasticity: Nucleation, Kinetics, and the Size Effect.
William Gerberich 1 , Aaron Beaber 1 , Douglas Stauffer 1 , Andre Mkhoyan 1 , Ozan Ugurlu 2
1 Chem. Engng. and Mat. Sci., U of Minnesota, Minneapolis, Minnesota, United States, 2 Charcterization Facility, U of Minnesota, Minneapolis, Minnesota, United States
Show AbstractTwo critical questions for plasticity in confined volumes are addressed. Both of these concern dislocation plasticity in the absence of twinning or phase transformations. First it will be proposed that in initially dislocation-free, confined volumes, that the nucleation and velocities of dislocations are intimately correlated. Additionally, the ability to measure dislocation velocities in confined volumes while also measuring stress will be demonstrated. Thus, the question: “Is plasticity best described by nucleation or kinetic theory or are both required? This is clearly critical to atomistic simulations which still have temporal constraints. As there are four types of confinement which we designate as external, internal, crystallographic, and geometric, what is (are) the critical confinement feature(s) which control(s) plasticity. As this is mostly unknown, we address here only the size effect. Thus, the second question: Is the activation volume for plasticity only controlled by size effects on yield or flow strength, or is there an independent contribution of size? Preliminary experiments on Ni, Si, and Al may or may not give definitive answers.
GG2: Plasticity of Small-Scale Systems - Simulation
Session Chairs
Peter Derlet
Daniel Weygand
Monday PM, November 30, 2009
Room 300 (Hynes)
2:30 PM - **GG2.1
Comparison of 3-D Discrete Dislocation Dynamics Simulations and in-situ Experiments: Monotonic and Cyclic Micro Bending Tests.
Christian Motz 1 2 , Jochen Senger 2 , Daniel Weygand 2 , Peter Gumbsch 2 3 , Reinhard Pippan 1
1 Erich Schmid Institute, Austrian Academy of Sciences, Leoben Austria, 2 IZBS, University of Karlsruhe (TH), 76131 Karlsruhe Germany, 3 IWM, Fraunhofer Institut fuer Werkstoffmechanik, 79108 Freiburg Germany
Show AbstractThe ongoing miniaturization in many areas of modern technologies, e.g. medical devices, microelectronics, etc., requires material properties in small dimensions. Size effects in mechanical properties prevent the usage of macroscopic material properties. In the last years, it was generally found that there is a specimen size effect on plasticity, i.e. smaller is stronger, if the typical size is reduced to the micrometer regime or below. The mechanisms causing this size effect are still under debate.For the understanding of these mechanisms both, in-situ experiments and discrete dislocation dynamics simulations are crucial. In the current presentation in-situ micro bending tests within the scanning electron microscope under monotonic and cyclic loading are compared with the results of 3-D discrete dislocation dynamics simulations (DDD). The experiments are carried out on single crystalline copper beams with typical thicknesses from 1 µm to 8 µm, lengths from 10 to 30 µm and widths from 5 to 15 µm. During the in-situ tests the load vs. displacement response as well as the deformation behaviour are recorded. Along with the experiments 3-D DDD simulations on bending beams with thicknesses from 0.5 µm to 3 µm and an aspect ratio of thickness:length:width of 1:3:1 were performed. For monotonic loading both, the experiments and simulations, show a strong size effect where the normalized bending moment (flow stress) increases with decreasing beam thickness. This strong size effect is attributed to a dislocation pile-up around the neutral plane of the beam, which can be quantified in the 3-D DDD simulations. For cyclic loading, a strong Bauschinger effect is found in experiments and simulations. No cyclic hardening is evident in the experimental tests, whereas a change in the active glide planes can be observed. This behaviour can be also found in first 3-D DDD simulations, where also no cyclic hardening is observed while a cyclic increase in dislocation density and a change in slip system activity is evident. Finally, dislocation mechanisms that may cause size effects in mechanical properties are discussed including the effect of more complex loading conditions.
3:00 PM - GG2.2
Deformation Mechanism Models in Nanoporous Metals.
Brian Derby 1 , Rui Dou 1
1 School of Materials, University of Manchester, Manchester United Kingdom
Show AbstractIn order to model the plastic deformation and collapse of nanoporous metals it is common practice to use the models for macroscopic foam behavior developed by Gibson and Ashby.1 This assumes that the deformation is concentrated at plastic hinges located at the nodes where ligaments intersect. If this is the case there could be a significant contribution of strain gradient hardening to the strength of these materials. However, it is also possible that nanoporous metals do not deform by the same mechanisms as are found in macroscopic foams (possibly because they have higher relative densities) and instead the strengthening observed in nanoporous metals arises from the same mechanisms as are found with the deformation of metal micropillars of similar dimensions to that of the ligaments in nanoporous metals.Here we explore the micromechanics of deformation of nanoporous metals to consider three possible relationships between the strength of nanoporous metals and metal micropillars: 1) Nanoporous metals deforms by a strain gradient hardening mechanism and there is no "intrinsic strengthening" mechanism related to ligament diameter.2) Nanoporous metals deform without plastic hinges through ligament shear and any size effect is identical tio that found in micropillar compression.3) Nanoporous metals display both mechanisms 1) and 2) above, acting in parallel.In all three cases it is possible to predict the behaviour of the nanoporous metal as a function of both ligament diameter and foam relative density and in case (3) it is possible to produce a mechanism map to predict the transition from strain gradient to shear-dominated behavior. These models are used to demonstrate that the influence of strain gradients cannot be ignored, at least in the case of low relative density foams. [1] L.J. Gibson and M.F. Ashby,Cellular Solids: Structure and Properties. 2 edn, (Cambridge University Press, 1997).
3:15 PM - GG2.3
Size Effects in the Deformation of Sub-micron Specimens: Heterogeneous Deformation and Dislocation Dynamics.
Hussein Zbib 1 , Sreekanth Akarapu 1 , David Bahr 1
1 School of Mechanical and Materials Engineering, Washington State University, Pullman, Washington, United States
Show AbstractThe size dependent deformation of Cu single crystal submicron size specimens, micropillars under compressions and thin films under tension, with thickness ranging from 0.1 to 2.5 micrometer is investigated using a Multi-scale Discrete Dislocation Plasticity (MDDP) approach. MDDP is a hybrid elasto-visco plastic simulation model which couples discrete dislocation dynamics at the micro-scale (micro3d) with the macroscopic plastic deformation. Our results show that the deformation field in these specimens is heterogeneous from the onset of plastic flow and is confined to a few deformation bands, leading to the formation of ledges and stress concentrations at the surface of the specimen. Furthermore, the simulation yields a serrated stress-strain behavior consisting of discrete strain bursts that correlates well with experimental observations. The intermittent operation and stagnation of discrete dislocation arms is identified as the prominent mechanism that causes heterogeneous deformation and results in the observed macroscopic strain bursts. We show that the critical stress to bow a dislocation arm, whose length changes during deformation due to pinning events, is responsible for the observed size dependent response of the single crystals. We also reveal that hardening rates, similar to that shown experimentally, occur under relatively constant dislocation densities and are linked to dislocation stagnation due to the formation of entangled dislocation configuration and pinning sites. The scaling behavior of the sub-micron specimens can be described by a model relating yield stress to both the strength of the primary dislocations source modified to account for pinning effects, and to the back stress resulting form the formation of ledges.
3:30 PM - **GG2.4
Distribution of Dislocation Source Length and Size-dependent Plasticity in Freestanding Thin Films.
Erik Van der Giessen 1 , Siamak Soleymani Shishvan 2
1 Zernike Institute for Advanced Materials, University of Groningen, Groningen Netherlands, 2 Dept. of Structural Engineering, University of Tehran, Tehran Iran (the Islamic Republic of)
Show AbstractPlasticity in thin metallic films exhibits two classes of size effects: dependence on grain size (the Hall-Petch effect in bulk materials) and dependence on film thickness. Experimental and simulation studies over recent years have revealed that the two effects are coupled, but in a way that is not fully understood. Nicola et al. [1] showed two-dimensional discrete dislocation computations that are able to capture these size effects on the yield strength seen in Cu films under plane-strain tension. The origin of the size dependence according to that study lies in the restricted mean-free dislocation path and the piling-up of dislocations against grain boudnaries. Von Blanckenhagen et al. [2], on the other hand, have emphasized the importance of dimensional constraints on the operation of Frank-Read sources.In this work, we present an innovation to the discrete dislocation framework as used in [1] by introducing Frank-Read sources whose size, strength and activation time are dependent on the film characteristics. Motivated by the activation of a Frank-Read source in a three-dimensional confined volume, we propose a log-normal distribution of the source strengh, which is bounded by the theoretical strenght of the material and by a minimum strength depending on the film thickness and grain size. The approach leaves a single fit parameter, in addition to the density of sources, which is to be determined from an experimental stress-strain curve of a film with some film thickness. We demonstrate the procedure and then proceed to simulate the stress-strain curves for films of the same material but different film thickness and grain size. This is done for two independent sets of Cu films [3,4] and excellent agreement with experimental results is found in terms of initial yield strength as well as hardening rate.Having thus demonstrated the power of the proposed strength distribution, it is shown that the mode of this distribution governs the most effective source strength. This is then used to propose a method to estimate the yield strength of thin films as a function of film and grain size. Simple maps are presented that are in very good in agreement with recent experimental results for Cu thin films.
[1] Nicola L, Xiang Y, Vlassak JJ, Van der Giessen E, Needleman A. J Mech Phys Solids 2006;54:2089. [2] von Blanckenhagen B, Gumbsch P, Arzt E. Philos Mag Lett 2003;83:1.[3] Xiang Y, Vlassak JJ. Acta Mater 2006;54:5449.[4] Gruber PA, Bohm J, Onuseit F, Wanner A, Spolenak R, Arzt E. Acta Mater 2008;56:2318.
4:30 PM - **GG2.5
Indentation Crystal Plasticity : Experiments and Multiscale Simulations.
Marc Verdier 1 , Hyung-Jun Chang 1 , Marc Fivel 1 , Laurent Tabourot 2
1 , SIMaP-CNRS, St Martin d Heres France, 2 Symme, Polytech Savoie, Annecy France
Show AbstractThis work aims at a quantitative understanding of instrumented indentation test based on physics of crystal plasticity. Such a triaxial mechanical test provides a benchmark for elastic confinement and size effects in an anisotropic medium such as Cu single crystals.For large scale indentation (micron size), a 3D numerical simulation using finite element crystal plasticity (FEM) is setup and quantitatively compared to experimental results using critical constraints: the load/stiffness-displacement curves and the surface displacement. it shows the dominant effect of initial dislocation density and slip system interactions. For smaller depth (maximum 100 nm), Dislocation Dynamics (DD) coupled to FEM are setup. Since this method does not provide defects nucleation rules, several strategies are tested: fitting on Molecular Dynamics (MD) load-depth curve for spherical tip, or automatic generation of geometric necessary dislocation (GND) for conical tip for example.Size effects show up in the modification of the dislocation structures with depth through critical expansion of dislocation loops and junctions. The bridge between these methods and their limits are discussed as well as perspectives of new experimental techniques to investigate this mechanical test.
5:00 PM - GG2.6
Evolution of Identical Initial Dislocation Microstructures under Different Loading Conditions Simulated with 3-D Discrete Dislocation Dynamics.
Jochen Senger 1 , Daniel Weygand 1 , Christian Motz 1 2 , Peter Gumbsch 1 3 , Oliver Kraft 1 4
1 , IZBS, Universität Karlsruhe (TH), Karlsruhe Germany, 2 , Erich Schmid Institute, Leoben Austria, 3 , IWM, Freiburg Germany, 4 , IMF II, Forschungszentrum, Karlsruhe Germany
Show AbstractMiniaturization in technical devices requires a more detailed comprehension of mechanics of materials at small scales. Compared to bulk materials, mechanical properties in micrometer-sized single crystalline metallic samples are different. Experimental results of tension and compression tests have shown increasing flow stresses with decreasing sample size and external boundary constraints, e.g. due to aspect ratio in a tensile test specimen, influence strongly the flow stress and also the hardening. The size effect can not be attributed to strain gradient plasticity as these specimens are expected to be free of strain gradients. It was confirmed by discrete dislocation dynamics simulations that multiplication mechanisms of dislocations depend on the available volume, leading to larger and therefore weaker sources in samples with a wider diameter. A different aspect, which cannot be excluded in experiments are undesired misalignments between sample and loading gadget, leading to more complex and multi-axial stress states superimposed on the nominally uni-axial deformation mode. It is the aim of this study to elucidate the influence of these experimental shortcomings on the dislocation microstructure and flow behavior at small scale.A three-dimensional discrete dislocation dynamics tool is used to analyze the role of several loading conditions set up to mimic possible imperfections. First, tension tests with a laterally compliant as well as a stiff sample end are conducted. These Al samples have diameters from 0.5 to 2.0 µm. The same samples are then deformed with superimposed torsion to mimic a non-ideal tensile loading. Additionally, the influence of sample geometry is discussed on the basis of the two aspect ratios 1:1.5 and 1:3. Using the identical initial dislocation microstructure enables a direct comparison between the different boundary conditions and the influence of strain gradients. On the one hand, very different dislocation microstructures are created for the different loading conditions, including high forest-dislocation density due to superimposed torsion moments. On the other hand, the flow stresses at 0.2% plastic strain are found to be similar for all the different conditions. However, increasing the torsion angle leads to lower initial yielding (measure at 0,01% plastic strain). In summary, it is shown that the aspect ratio of the columns has a much stronger effect on the measured flow stresses and the hardening behavior than the boundary conditions investigated.
5:15 PM - GG2.7
Modeling the Role of Pre-existing Defects on the Statistical Behavior of Nanoscale Plasticity.
James Morris 1 2 , Hongbin Bei 1 , George Pharr 2 1 , Easo George 1 2
1 Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States, 2 Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee, United States
Show AbstractThe strengths of metals and alloys at small length scales can approach theoretical values, due to the absence of defects in the probed volumes. These strengths may be more than an order of magnitude larger than those measured in the bulk, where many defects are present. Strength values between these two extremes are inherently statistical: when the probed volume contains few dislocations or other defects, their actual number, arrangement, and potency can dramatically affect the mechanical properties. As a result, there is a wide variation in the yield and flow behavior, due to the variation in defect number and arrangement. This has been shown in both nanoindentation and micropillar compression experiments, where the probed volumes are small and the dislocation density is controlled by pre-straining the samples. In this presentation, a statistical model is presented to capture the change in behavior from the defect-free case to the bulk limit, with a focus on capturing the wide variability of the intermediate regime. The model will be compared directly to both nanoindentation and pillar experiments. In this model, defects are modeled as distinct points, with a distribution of defect strengths. Salient differences between pillar compression and nanoindentation will be discussed. We will also present large scale molecular dynamics simulations which examine the effects of pre-existing dislocation networks on the subsequent plastic behavior.
This research was sponsored by the Division of Materials Sciences and Engineering, U.S. Department of Energy.
5:30 PM - GG2.8
Transformation-Induced Plasticity in Pseudoelastic, Single-Crystal NiTi Micropillars.
Peter Anderson 1 , Sivom Manchiraju 1 , David Norfleet 2 , Peter Sarosi 3 , Michael Mills 1 , Michael Uchic 4
1 Department of Material Science and Engineering, The ohio state university, Columbus, Ohio, United States, 2 , Engineering Systems Inc, Aurora, Illinois, United States, 3 , GM Research and Development Center, Warren, Michigan, United States, 4 , Air Force Research Laboratory, Materials & Manufacturing Directorate, Wright-Patterson AFB, Ohio, United States
Show AbstractNiTi undergoes a stress-induced phase transformation from B2 austenite to B19 martensite at room temperature, leading to large recoverable strains termed``pseudoelasticity.” Compression testing of 5 micron diameter NiTi micropillars produced by FIB machining have been performed to study the interaction between phase transformation and plasticity, which can lead to non-recoverable strains during stress cycling. After stress cycling, detailed TEM analyses of the pillars show intricate dislocation structure on a slip-systems that are not favored by the external stress, thus pointing to transformation induced plasticity. Two computational models at different length scales are used to understand this transformation induced plasticity. At a length of individual variants of martensite, potential variants consistent with the TEM images are identified and a Fourier transform based micromechanical model is used to calculate the stress field around the martensite variants. The calculations show spatial distributions in the net resolved-shear stress (applied plus transformation-induced stresses) that may explain the observed dislocation structures. Further, the stress from the individual variants within the plate is shown to favor activation of the observed slip system. At micron length-scales, a finite element (FE) based computational model that includes the phase transformation and crystalline plasticity is used to study the macroscopic behavior of the pillar. The FEM results show the austenite transforming into martensite plates which are consistent with the TEM observations. The smeared out spatial distribution of slip-system activities are also consistent with the TEM results. Further, some generic but important issues such as the effect of sample misorientation, sample misalignment and the effect of stress concentrators in the micropillar tests are analyzed. It is found that all these factors can significantly alter the spatial distribution of the transformation zone and the dislocation activity, though the macroscopic response might remain relatively similar.
5:45 PM - GG2.9
Breakdown of Self-Similar Hardening Behavior in Au Nanopillar Microplasticity.
Jaime Marian 1 , Jaroslaw Knap 2
1 , Lawrence Livermore National Laboratory, Livermore, California, United States, 2 , Army Research Laboratory, Aberdeen Proving Ground, Maryland, United States
Show AbstractIn this work, we study scale effects in Au nanopillars under compression. We propose that plastic yielding in these nanostructures is characterized by a critical length scale at which a transition from volumetric to surface-dominated plasticity takes place. This transition effectively sets a lower bound on the self-similar behavior commonly assumed innanostrength models. Using Quasicontinuum simulations, we study the subcritical regime and find that plasticity at these scales is governed by dislocation emission at surface irregularities.
Symposium Organizers
Peter M. Derlet Paul Scherrer Institut
Daniel Weygand Universität Karlsruhe, izbs
Ju Li University of Pennsylvania
Mike D. Uchic Air Force Research Laboratory
Eric Le Bourhis Université de Poitiers
GG3: <i>In-situ</i> Studies of Plasticity & Novel Experimental Methods
Session Chairs
Tuesday AM, December 01, 2009
Room 300 (Hynes)
9:30 AM - **GG3.1
Probing the Mechanical Properties of Nanostructures in the TEM.
Andrew Minor 1 , Jia Ye 1 , Daniel Kiener 1 , Claire Chisholm 1 , Raj Mishra 2 , Zhiwei Shan 3 , Oden Warren 3
1 , UC Berkeley & LBL, Berkeley, California, United States, 2 , General Motors R&D Center, Warren, Michigan, United States, 3 , Hysitron, Inc., Minneapolis, Minnesota, United States
Show AbstractIn situ transmission electron microscopy (TEM) provides dynamic observations of the physical behavior of materials in response to external stimuli such as temperature, environment, stress, and applied fields. In many cases, research is driven by the development of novel instrumentation and testing methodologies. Over the last few years we have used a quantitative in situ TEM mechanical testing device to probe the mechanical properties of different nanostructured volumes inside a TEM. By correlating the measurement of the imposed forces with a particular deformation event, we can improve our understanding of the data for both in situ and ex situ testing. Recent progress in both in situ and ex situ small-scale mechanical testing methods has greatly improved our understanding of mechanical size effects in volumes from a few nanometers to a few microns. Besides the important results related to the effect of size on the strength of small structures, the ability to systematically measure the mechanical properties of small volumes through mechanical probing allows us to test samples that cannot easily be processed in bulk form, such as a specific grain boundary or a single crystal. In the case of individual nanostructures, the need to address the nanostructure in a direct manner is even more acute, and in situ TEM in many cases makes this possible. This talk will demonstrate how individual nanostructures or individual microstructural features can be tested directly with mechanical probing techniques, allowing us to explore the fundamental origins of strength and ductility. Specifically, results will be presented from in situ nanocompression of microfabricated pillars, in situ nanocompression of individual nanoparticles and in situ tension tests of individual nanowires. In addition, progress on the development of new techniques for quantitative in situ tensile testing of individual nanostructures will also be presented, including a discussion of the advantages and disadvantages of the various techniques.
10:00 AM - GG3.2
Dislocation Nucleation in Confined Crystalline Volumes: In-situ TEM Observations and Micro-mechanical Tests on Submicron Al Fibers.
Marc Legros 1 , Frederic Mompiou 1 , Daniel Caillard 1 , Daniel Gianola 2 , Andreas Sedlmayr 4 , Oliver Kraft 4 , John Sharon 3 , Kevin Hemker 3
1 , CEMES-CNRS, toulouse France, 2 Dept. Mat. Sci. Eng., University of Pennsylvania, Philadelphia, Pennsylvania, United States, 4 Institute for Materials Research II, Forschungzentrum Karlsruhe, Karlsruhe Germany, 3 Dept. Mech. Eng., Johns Hopkins University, Baltimore, Maryland, United States
Show AbstractThe strength of metals and alloys depends intrinsically on the ability of their dislocations to multiply and travel over large distances inside the crystal structure. When reduced to very small dimensions such as in thin films, whiskers or micro-pillars, dislocations can escape more easily through free surfaces before interacting with others. For this reason, these small crystals do not harden easily when strained. Their initial resistance to deformation is however much larger than their bulk counterpart, and the physical explanations for this multiplied yield stress are still highly debated.One critical contribution lies in the nucleation of fresh dislocations, but this step is much less documented than dislocation-dislocation interactions, for instance. The limited knowledge of the nucleation process in small structures partly lies in the stochastic nature of sources (often single armed), and the interaction of the emitted segment with free surfaces. In the present work, we present an extensive in situ transmission electron microscope (TEM) study of dislocation multiplication and shearing processes in sub-micrometer Al fibers that were kept free of FIB (Focused Ion Beam) preparation. The size of operating sources and their production mode has been systematically analyzed and compared to the crystal dimensions. In addition to the source operating regime, a very low ductility plastic regime has been observed in fibers containing no preexisting dislocations. These plastic mechanisms have been correlated to stress and strain measurements obtained by micro-mechanical testing performed in a dual beam scanning electron microscope (SEM) and FIB. The measured mechanical response exhibits discrete load drops as a result of highly localized crystalline slip, and these events have been quantified and compared in the context of mechanisms observed from in situ TEM observations. Possible strengthening mechanisms and size effects on the mechanical properties will be discussed in the light of these results and confronted with recent results obtained in similar experiments [1].1. Oh, S.H., M. Legros, D. Kiener, and G. Dehm, Nature Materials, 2009. 8: p. 95-100.
10:15 AM - GG3.3
In-situ Laue Diffraction during Compression of Mo Pillars.
Julien Zimmermann 1 , Hongbin Bei 2 , Steven Van Petegem 1 , Easo George 2 3 , Helena Van Swygenhoven 1
1 NUM/ASQ, PSI, Villigen Switzerland, 2 Div. Mat. Sci. Technol., Oak Ridge Natl. Lab, Oak Ridge, Tennessee, United States, 3 Dept. Mat. Sci. Engn., University of Tennessee, Knoxville, Tennessee, United States
Show AbstractIn-situ microcompression during Laue diffraction is performed on single crystal Mo pillars obtained via directional solidification. Earlier in-situ experiments performed on fcc pillars synthesized using FIB have demonstrated the presence of strain gradients in the pillars prior to deformation (Scripta 59(2008)471), suggesting a possible role of the initial defect content on the “smaller is stronger” effect. Deformation of defect-free Mo pillars obtained via directional eutectic growth, showed a whisker type behaviour where the strength of the pillar approaches the theoretical shear strength and no particular size dependence is observed (Acta Mat 56(2008)4762). However, when these pillars are pre-deformed prior to compression, or FIB treated, the strength measured in a micro-compression test decreases and a large scatter is observed (Acta Mat 57(2008)503). To understand the role of the initial defect structure on the mechanical behaviour of metallic pillars, in-situ micro-compression Laue diffraction has been performed on as-prepared, pre-deformed and FIB surface treated Mo pillars. The experiments show that FIB surface treatment and pre-deformation introduce streaking of the diffraction peaks, whereas the as-prepared Mo pillars exhibit very narrow diffraction peaks as expected for perfect single crystals. In-situ compression experiments performed in load control as well as in displacement control allow the correlation of special characteristics of the stress-strain curves with plastic events and changes in the microstructure. The role of the defects introduced by FIB and pre-deformation on the mechanical behaviour of Mo pillars will be discussed.A portion of this research was sponsored by the Division of Materials Sciences and Engineering, U.S. Department of Energy and the Swiss National Research Foundation.
10:30 AM - GG3.4
3D X-Ray Microscopy Measurement of Mesoscale Deformation Microstructure in Micro-Compression Tested Ni-Superalloy Pillars.
Bennett Larson 1 , Jon Tischler 1 , Michael Uchic 2 , Dennis Dimiduk 2 , Wenjun Liu 3
1 Materials Science & Technology, ORNL, Oak Ridge, Tennessee, United States, 2 , Air Force Research Laboratory, Wright-Patterson AFB, Ohio, United States, 3 , Argonne National Laboratory, Argonne , Illinois, United States
Show AbstractCompression testing of micro-pillars fabricated by focused-ion-beam milling has provided insight into the role of sample size-effects in the deformation process – showing significant increases in flow stress compared to that of bulk materials. In this presentation we discuss submicron-resolution 3D x-ray microscopy measurements made at the Advanced Photon Source (APS) of the mesoscale deformation microstructure in a 10 micron diameter Ni base superalloy microcrystal (UM F19, an experimental Ru-containing alloy), which was compressed to an engineering strain of ~0.12 (M. D. Uchic and D. M. Dimiduk, Mat. Sci. and Eng. 400-401, 268 (2005)). As indicated by SEM observations of the external surface of the pillar following compression, multiple slip systems were activated during the test. Three-dimensional maps of the local misorientations and rotation gradients in the pillar and in the base will be presented and discussed in terms of geometrically necessary dislocation densities and compared with the size and location of external slip steps observed by SEM.*Research at ORNL supported by the DOE Basic Energy Sciences Division of materials Sciences and Engineering; the APS is supported by the DOE Office of Science; research at WPAFB supported by the Air Force Office of Scientific Research and AIM-DARPA.
10:45 AM - GG3.5
In-situ EBSD During Micropillar Compression.
William Mook 1 , Christoph Niederberger 1 , Xavier Maeder 1 , Johann Michler 1
1 Laboratory for Mechanics of Materials and Nanostructures, Empa - Swiss Federal Laboratories for Materials Testing and Research, Thun Switzerland
Show AbstractUniaxial compression testing has long been a method of choice for the determination of mechanical properties. In recent years, micropillar compression experiments have been realized both as stand-alone experiments and in combination with other characterization techniques such as electron microscopy. Since any deformation is limited to the volume of the pillar, such experiments are particularly suitable for the study of properties which are length scale-dependent. An SEM in-situ experiment enables observation of the micropillar during the experiment and thus provides information concerning relevant deformation and failure modes. The aim of the present contribution is to demonstrate the compression of a micropillar inside of an SEM while simultaneously mapping the pillar using electron backscatter diffraction (EBSD). The EBSD technique can identify the crystal orientation to better than 0.5° with a spatial resolution of 10 nm. Initial experiments on single crystal semiconductor pillars will be shown to quantify both elastic compression and bending in addition to plastic deformation modes.
11:30 AM - GG3.6
A New Criterion for Elasto-plastic Transition in Nanomaterials: Application to Size and Composite Effects on Cu–Nb Nanocomposite Wires.
Ludovic Thilly 1 , Pierre-Olivier Renault 1 , Steven Van Petegem 2 , Helena Van Swygenhoven 2 , Florence Lecouturier 3
1 PHYMAT, University of Poitiers, Futuroscope France, 2 , Paul Scherrer Institute, Villigen Switzerland, 3 , LNCMI, Toulouse France
Show AbstractNanocomposite wires composed of a multi-scale Cu matrix embedding Nb nanotubes are in situ cyclically deformed in tension under synchrotron radiation in order to follow the x-ray peak profiles (position and width) during mechanical testing. The evolution of elastic strains vs. applied stress suggests the presence of phase-specific elasto-plastic regimes in direct relation with size characteristics. The nature of the elasto-plastic transition is uncovered by the ‘‘tangent modulus” analysis and correlated to the microstructure of the Cu channels and the Nb nanotubes. Finally, a new criterion for the determination of the macroyield stress is given as the stress to which the macroscopic work hardening, θa = dσa / dε0, becomes smaller than one third of the macroscopic elastic modulus. This criterion appears to be valid to determine the transition from elasto-microplastic to macroplastic regimes in several nanocrystalline materials in contradiction to the traditional 0.2%-strain offset criterion [Acta Materialia 57 (2009) 3157–3169].
11:45 AM - GG3.7
Indentation Cracking as a Toughness Measurement Method at Small Scales.
Jinhaeng Lee 1 , Kurt Johanns 1 , Yanfei Gao 1 2 , George Pharr 1 3
1 Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee, United States, 2 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States, 3 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
Show AbstractMeasurement of fracture toughness by indentation methods is usually based on a long crack that propagates and arrests in a stabilizing stress field. Under this condition, if the driving force can be determined analytically, the toughness can be deduced by measuring the size of the crack. However, the driving force calculation is usually a nontrivial task for indentation induced cracks. In addition, crack initiation in brittle materials is sensitive to flaws since these materials do not have well defined R-curve during crack propagation. To this end, a finite element model has been developed to study the effects of indenter geometry, interface friction, and material properties on the initiation and propagation of the median/radial crack systems. Results are compared to nanoindentation experiments on Si and Ge using triangular pyramidal indenters with centerline-to-face angles varying from 35.3 to 75.0 degree. Insights on the toughness evaluation will be discussed.
12:00 PM - GG3.8
Development of a Biaxial Tensile Module at Synchrotron Beamline for the Study of Mechanical Properties of Nanostructured Films.
Eric Le Bourhis 1 , Baptiste Girault 1 , Pierre-Olivier Renault 1 , Philippe Goudeau 1 , Guillaume Geandier 2 , Dominique Thiaudiere 2 , Remy Chiron 3 , Olivier Castelnau 3
1 Laboratoire PHYMAT UMR 6630 CNRS, Universite de Poitiers, Futuroscope-chasseneuil Cedex France, 2 DIFFABS, Synchrotron SOLEIL, Gif sur Yvette France, 3 LPMTM – CNRS, Institut Galilee, Universite Paris 13, Villetaneuse France
Show AbstractIn the frame of an ANR project (Cmonano) we have developed a biaxial tensile module at SOLEIL DIFFABS beamline in order to study and model the mechanical behavior of nanostructured thin films. Indeed, the mechanical characterisation of such structures and the relationship with the microstructure required for further development of technological applications, are still poorly explored. The project encompasses the elaboration of thin films of controlled microstructure, the experimental characterisation of their mechanical response under biaxial loading and synchrotron X-ray diffraction, and the modelling of the observed mechanical behavior in view of the nanostructure. W thin films and non-miscible W/Cu multilayers are produced using PVD on polyimide substrates. The composites film-substrate are then deformed in situ in an X-ray goniometer. We vary the period of the stratification in order to explore structure and size effects on the elasticity and yield. The morphology and texture of the coatings are characterized using TEM and XRD respectively. The modelling using homogenization methods is developed and takes into account both the crystallographic texture and morphology of the metallic films.
12:15 PM - GG3.9
Fatigue Properties of Micro Molded Aluminum Bronze.
Tobias Kennerknecht 1 , Gundi Baumeister 2 , Chris Eberl 1
1 izbs, Universitaet Karlsruhe (TH), Karlsruhe Germany, 2 Fakultaet Maschinenbau, Hochschule fuer angewandte Wissenschaften Fachhochschule Coburg, Coburg Germany
Show AbstractMicro molding techniques allow manufacturing complex 3 dimensional micro specimens made of ceramics and metals. The incorporation of such materials into the micro manufacturing world allows new applications e.g. miniaturized fuel cells, miniaturized surgical tools for micro invasive treatments, micro fluidic devices for systems on a chip, small scale turbines or miniaturized sensors.The focus of this work lies on the fatigue behavior of micro molded samples having a cross section of 130 µm by 260 µm, made of aluminum bronze. During casting micro components cool down quickly due to their small volume and the large surface to volume ratio. This leads to a fine micro structure, similar to MEMS and coating materials. Scaling and size effects are expected to dominate reliability of micro molded components. Furthermore, these samples represent interesting items to analyze micro plasticity in the high and very high cycle fatigue regime.A custom built micro-sample fatigue setup was assembled in order to conduct life-time experiments. Cyclic loads up to 1 kHz can be applied using a piezo stack with a resolution down to 0.6 nm. Strain is determined by means of digital image correlation and displacement measurement. Therefore local plasticity and crack propagation can be detected and analyzed. Scanning Electron Microscopy and Focused Ion Beam microscopy will be used to characterize the microstructure and defect morphology in these samples. The experimental setup as well as results from fatigue experiments will be presented. The interpretation of these results will help to understand active fatigue mechanisms and their impact on sample geometry and frequency in micro molded specimens as well as in metallic MEMS and coating materials. We greatly acknowledge the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG) for sponsoring this work as part of the SFB499.
12:30 PM - **GG3.10
The Deformation Behavior of Nanocrystalline Metals: Insights from Strain Rate Sensitivity and in situ Synchrotron Testing.
Oliver Kraft 1
1 Institut für Materialforschung, Karlsruhe Institute of Technology, Karlsruhe Germany
Show AbstractIt has been shown that a reduction in grain size continues to strengthen a metallic material down to grain sizes of 20 nm and below. For this size regime, it is well accepted that dislocation networks are not developed and that deformation is carried by other mechanisms than motion of full dislocations. This is also supported by the observation that nanocrystalline metals exhibit much stronger strain rate sensitivity at low temperature, with small activation volume, compared to their coarse-grained counterparts. Suggested deformation mechanisms include nucleation and motion of partial dislocations, grain boundary sliding as well as grain rotation and growth. It is worth noting that some of these mechanisms do not leave a footprint after deformation and, therefore, strain hardening is reduced in nanocrystalline metals. In addition, it makes it difficult to study the mechanisms by post-testing analysis.In our work, we have studied nanocrystalline Pd and Pd-Au as a model system with grain sizes between a few and about 150 nm. We have applied nanoindentation to study the strain rate dependence as well as synchrotron-based in situ tensile testing. The experimental setup at the synchrotron allows for measuring the stress evolution in the sample as well as tracking the shape of several diffraction peaks as a function of applied strain. Experiments have been carried out in a temperature range from 173 to 353 K and strain rates ranging from 10-3 to 10-5 s-1. The activation volume is found to be of the order of a few atomic volumes and to increase with increasing grain size. For Pd-Au alloys, the stacking fault energy is reduced with respect to the Au content and is likely to affect deformation mechanisms. Preliminary results suggest that the addition of Au reduces the strain rate sensitivity at a given temperature. The synchrotron experiments revealed that micro- and macroplastic contributions can be clearly distinguished and directly correlated to the stress-strain behavior. Microplastic processes yield to strong variations in peak width which may be completely reversible depending on temperature and strain rate. In contrast, the increase in peak width is irreversible for macroplastic deformation indicating that remanent defects are formed. The results will be discussed in the light of suggested models for the deformation of nanocrystalline materials.
GG4: Bulk Metallic Glasses - Experiment & Simulation
Session Chairs
Michael Falk
Eric Le Bourhis
Tuesday PM, December 01, 2009
Room 300 (Hynes)
2:30 PM - GG4.1
Molecular Dynamics Simulation of Cavitation in Metallic Glass.
Shuo Lu 1 , Pavan Valavala 2 , Michael Falk 2 3 4
1 Materials Science and Engineering, Beihang University, Beijing China, 2 Materials Science and Engineering, Johns Hopkins University, Baltimore, Maryland, United States, 3 Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland, United States, 4 Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland, United States
Show AbstractIn order to predict the fracture toughness of amorphous solids such as metallic glasses it is necessary to understand the physics of the process zone. Theories of plastic deformation provide information about response to shear, but on their own these theories provide limited insight into the microscopic mechanisms that mediate the free surface generation critical to crack propagation. Previous molecular dynamics simulations indicate that cavitation likely plays this role. We have undertaken a series of molecular dynamics simulations of cavitation under hydrostatic tension in a binary metallic glass analog using pair-wise potentials. We compare the rate of cavity nucleation directly to homogeneous nucleation theory to extract the role of irreversible deformation in the cavitation process. The stress and strain fields around the cavity are analyzed in the context of perfect plasticity and the STZ model of amorphous plasticity.
2:45 PM - GG4.2
Avalanches, Size-effects, and Critical Behavior in Shared Model Metallic Glasses.
K. Michael Salerno 2 , Craig Maloney 1 , Mark Robbins 2
2 Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland, United States, 1 Civil and Environmental Engineering, CMU, Pittsburgh, Pennsylvania, United States
Show AbstractWe perform computer simulations of sheared binary Lennard-Jones glasses in 2D at zero temperature and in the limit of small strain rate. The strain energy is released in discrete bursts with a Gutenberg-Richter size distribution. The plastic strain is organized into lines of slip which accumulate during avalanches over a system-size dependent characteristic strain scale \delta\gamma_c. \delta\gamma_c should give rise to interplay between indentation rate and system size which may be observable in micro-pillar indentation experiments on metallic glasses. Furthermore, we show that the spatial organization of the plastic deformation has a novel kind of fractal geometry, with orientation-dependent scaling exponents. These results further suggest that micro-pillar indentation experiments performed on bulk-metallic glass samples should exhibit a kind of self-organized critical behavior similar to that observed in crystalline samples [1].[1] Dimiduk, DM , et al. Science 312 (5777). 1188-1190 (2006).
3:00 PM - GG4.3
Nanomechanics of Glasses and Supercooled Melts.
Stefan Mayr 1 2
1 , Leibniz-Institut für Oberflächenmodifizierung e.V., Leipzig Germany, 2 Fakultät für Physik und Geowissenschaften und Translationszentrum für Regenerative Medizin, Universität Leipzig, Leipzig Germany
Show AbstractMetallic glasses are characterized by a rather complex viscoelastic response and the occurrence of the glass transition, while the underlying atomistic origins are still poorly understood. Using a realistic CuTi model glass we employ global and local elasticity tensors for a thorough analysis of relaxation kinetics and mechanical stability at the nanoscale. We obtain strong indication [1] that i) α and β relaxation are closely related, presumably manifestations of a general relaxation scenario, ii) glasses reveal intrinsic mechanical instabilities at the nanoscale, which are closely connected to collective shear events within shear transformation zones and iii) the glass transition can be understood as a percolation transition of these mechanically unstable regions.[1] S.G. Mayr, Phys. Rev. B 79, 060201(R) (2009)
3:15 PM - GG4.4
Size Dependence of Flow Stress in Amorphous Nano-wires During Straining at Temperatures Near the Glass Transition.
Yujie Wei 1 2 , Allan Bower 2 , Huajian Gao 2
1 Mechanical Engineering, University of Alabama, Tuscaloosa, Alabama, United States, 2 , Brown University, Providence, Rhode Island, United States
Show AbstractMolecular dynamic simulations are used to predict the flow stress of amorphous metallic nanowires that are deformed at temperatures near the glass transition. The simulations show a strong size dependence of flow stress, and suggest that nano-wires with sufficiently small diameter, subjected to moderate stresses at elevated temperature and low deformation rates, can deform by continuous production of free volume in the interior of the wire, which subsequently diffuses to the wire surface. An analytical model is developed to estimate the critical wire dimensions where this diffusional mechanism is likely to replace viscous creep, and to estimate the resulting size dependence of flow stress. The stability of the diffusional deformation mode is also analyzed. Conditions are identified where the bulk deformation mode, in combination with externally applied stress, can delay or suppress the occurrence of necking in the wire by Rayleigh instability.
3:30 PM - **GG4.5
Shear Deformation of Hard-Sphere Colloidal Glasses.
Frans Spaepen 1
1 School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States
Show AbstractDense colloidal systems form phases similar to those formed by atoms: liquids, crystals and glasses. Hard-sphere colloidal glasses are useful for modeling a number of phenomena in metallic glasses with central pair potentials, since the transition state is often governed by repulsive steric interactions. Confocal microscopy makes it possible to track the colloidal particles in time and space during the shear deformation of the glass. Analysis of the local strains makes it possible to indentify the flow defects, or shear transformation zones, that govern the deformation. This allows determination of the size and strain of these zones, as well as the correlations between them and their relation to fluctuations in the local density. Possible implications of these observations for the size-dependence of the deformation of metallic glasses will be discussed.
4:30 PM - **GG4.6
Confined Plasticity in Metallic Glasses: Experiments and Simulations.
Christopher Schuh 1
1 Materials Science and Engineering, MIT, Cambridge, Massachusetts, United States
Show AbstractIn metallic glasses, plasticity is suppressed around local mechanical contacts because of the nature of yield in these materials, which requires cooperative motion of many atoms to form a local shear band. As a result, the elastic-plastic transition is nebulous, and substantial structural rearrangement can occur under nominally elastic loading. This talk will review our efforts at understanding local microplasticity near stress concentrations in metallic glasses. Experimentally, we use nanoindentation methods to both indirectly probe structural change and study the kinetic and kinematical issues behind it. We also employ meso-scale simulation methods to study the local activity of shear transformation zones around the contact point.
5:00 PM - GG4.7
Effect of Dilatation on the Elasto-plastic Response of Bulk Metallic Glasses under Indentation.
Anamika Prasad 1 , Ming Dao 1 , Upadrasta Ramamurty 2
1 , Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 2 Department of Materials Engineering, Indian Institute of Science, Bangalore India
Show AbstractUnlike metals, elasto-plastic response of bulk metallic glasses (BMGs) follow closely that of granular materials through pressure dependent (or normal stress) yield locus and shear stress induced material dilatation. These aspects of material behavior have been addressed in several recent studies; however, several issues and discrepancies remain to be addressed regarding the true mechanism and nature of plastic flow. In particular, while material dilatation is responsible for post yield stress softening and formation of localized shear bands, its influence on macro-scale flow and deformation is largely unknown. This effect cannot be ignored as new studies suggest a more diffused effect of dilatant behavior [Schuh et al, Acta Materilia,2007]. Thus, ignoring the effect of dilatation can cause underestimation of surface deformation, as observed recently in our work on the sliding response of Zr-based BMG. On the other hand, excessive dilatation via associated flow rule can lead to gross error in deduction of material parameters. Confined plastic flow such as that obtained through instrumented indentation provides a versatile tool for evaluating these aspects of the response of BMGs and forms the basis of our current study. Here, we have systematically analyzed the effect of material dilatation for Zr-based BMG using finite element simulation of frictional indentation analysis with Mohr-Coulomb and the Drucker-Prager yield criteria. The strengthening/softening effect of load-depth response and corresponding stress-strain profiles are presented in light of different elastic-plastic regimes under common indenters. The numerical results are compared and contrasted against existing experimental data, and important conclusion regarding the relevance of dilatation parameter in predicting the behavior for BMGs is discussed.
5:15 PM - GG4.8
Transition from Strong-yet-brittle to Stronger-and-ductile by Size Reduction in Metallic Glasses.
Dongchan Jang 1 , Julia Greer 1
1 Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, United States
Show AbstractA combination of high strength and extended deformability of materials is favorable for engineering applications, as the former assures optimal performance under extreme environments while the latter increases the reliability by protecting the system from a sudden breakdown. Unfortunately, these two attributes are nearly mutually exclusive as high-strength structural materials rarely show any notable plasticity while engineering materials capable of attaining substantial plastic strains generally sacrifice their strength. In this work we report the attainment of both high strength and superior deformability attained by Zr-based metallic glass by using sample dimensions as key property-controlling parameter. We report the emergence of two unique and useful properties: (1) a yield strength increase from 1.7 GPa to 2.6 GPa as the pillar diameter is reduced below ~1000 nm, remaining at that high value with subsequent diameter reduction and (2) once the lateral dimension is decreased to 100 nm, the formation of shear bands ceased, and the material shows significant homogeneous plasticity while maintaining its high strength. Furthermore, unlike in other engineering materials, we observe a distinct difference between the transition from lower, bulk-like strength to higher one and that from brittle to ductile deformation, as strength and ductility appear to be de-coupled in these metallic glass nano-pillars. We discuss these enhanced mechanical properties in terms of deformation mechanisms unique to confined volumes. We present a phenomenological model based on free enthalpy, where the relaxed outer layer presents an energy barrier to the propagation of an embryonic shear band.
5:30 PM - GG4.9
Understanding Extrinsic Ductility in Porous Bulk Metallic Glasses from Molecular Dynamics Simulations.
Yunfeng Shi 1
1 Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York, United States
Show AbstractBulk metallic glasses (BMGs) have excellent strength, processibility and resistance to corrosion for load-bearing applications. However, most monolithic BMGs are intrinsically brittle in unconfined loading conditions. One promising method for obtaining extrinsic ductility is to introduce porous microstructures into the BMGs, which is otherwise featureless above a few nanometers. The precise picture of the confinement effect of pores on shear band development is not yet clear. Here we present a simulation study focusing on the early-stage plasticity of porous BMGs. We will investigate the interplay between shear bands and porous microstructure and provide atomic understanding of how extrinsic ductility arises. A well-studied monatomic glass former is investigated here, which has been used in studying strain localization in systems that are either monolithic [1] or with embedded crystallites [2]. The porous microstructure is obtained by simulating the dissolution of inert gases in liquid phase at high pressure, phase separation at low pressure and subsequent cooling to a porous glassy state. The presence of the pores leads to the formation of mechanically distinct surface layers, redistribution of the stress field and, more importantly, the introduction of new length scales. We will investigate possible toughening mechanisms including proliferation of shear band initiation, blunting the sharp shear off-sets at the pore surfaces and restriction of the shear band propagation from pore confinement. The relevance of various mechanisms depends on the pore size, shape and spacing. This study will also shed lights on designing porous microstructure that optimize both the ductility and strength.[1] Y. F. Shi, M. L. Falk, "Atomic-scale simulations of strain localization in three-dimensional model amorphous solids", Physical Review B, 73, 214201 (2006) [2] Y. F. Shi, M. L. Falk, "A computational analysis of the deformation mechanisms of a nanocrystallite-metallic glass composites”, Acta Materialia, 56, 995-1000 (2007)
5:45 PM - GG4.10
Aging and Plastic Flow in Metallic Glasses: Monte Carlo Simulations Based on the Activation-Relaxation Technique.
David Rodney 1 2 , Christopher Schuh 2
1 Science et Ingenierie des Materiaux et Procedes, Grenoble Institute of Technology, Saint Martin d Heres France, 2 Materials Science and Engineering, Massachussetts Institute of Technology, Cambridge, Massachusetts, United States
Show AbstractThe yield stress in metallic glasses, as in all disordered solids, marks a transition between aging at low applied stresses and plastic flow at higher stresses. The transition involves thermally-activated processes that are difficult to account for at the atomic scale because they occur on timescales that can not be simulated by molecular dynamics. Here, we overcome this limitation through Monte Carlo simulations in which the elementary thermally-activated events are determined using the activation-relaxation technique. We show that aging increases the stability of the glass, both thermodynamically (the internal energy of the glass decreases during aging) and dynamically (the aged glass is surrounded by higher energy barriers than the initial quenched glass). By contrast, plastic flow brings the glass into a high internal energy state that is only marginally stable, being surrounded by a high density of low-energy barriers. The strong influence of plastic deformation on the glass state is also shown through a polarization of the microstructure, evidenced by an asymmetry of the distribution of thermally-activated plastic strains in glasses after simple shear deformation.
GG5: Poster Session: Plasticity in Confined Volumes
Session Chairs
Peter Derlet
Eric Le Bourhis
Ju Li
Mike Uchic
Daniel Weygand
Wednesday AM, December 02, 2009
Exhibit Hall D (Hynes)
9:00 PM - GG5.1
Disorder Induced Low Frequency Localized Vibrational Modes and their Role in Initiating Diffusion and Local Plasticity.
Peter Derlet 1
1 NUM - Condensed Matter Theory Group, Paul Scherrer Institut, PSI-Villigen Switzerland
Show AbstractUnder an applied load atomic disorder can lead to local structural transformations that result in either diffusion or irreversible shear stress relief and plasticity. Such disorder also induces low frequency localized resonant vibrational modes that are manifested as a Bose peak in the vibrational density of states and as anomalous bulk thermal properties. Using a combination of standard harmonic analysis and inter-site Green function techniques, the present work investigates the relationship between these phenomena for two and three dimensional disordered systems and how this may be exploited in atomistic simulations of driven systems.
9:00 PM - GG5.12
Effect of Surface Roughness on Determination of Creep Parameter using Impression Creep Technique.
Wuzhu Yan 1 , Bin Zhao 1 , Zhufeng Yue 1
1 , Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an, PR China, Xi'an, Shan'xi, China
Show Abstract The indentation creep test, especially the impression creep, which is carried out using a flat cylindrical punch owing to a constant contact area during test, exhibits a magic appealing in the determination of creep properties of small structures in industry, such as integrated circuit systems (ICs), for its simplicity, efficiency and non-destruction merits. Most of previous researches of indentation or impression creep neglect the effect of surface roughness of materials, which plays a crucial role in extracting creep properties of materials. In the present study, the cosine surface profile is employed to simulate fractal behavior of real surface. The Kachanov-Rabothov (K-R) creep damage law is implemented into the finite element (FE) code ‘ABAQUS’ as a user subroutine ‘CREEP’ to investigate the effect of surface roughness as well as magnitude of load on damage evolution, which has a dramatic influence on the determination of creep stress exponent using impression creep technique. The results showed that the exponent of impression creep stress is decreased under a small load due to the ‘Tuning’ effect of asperities. However, this effect can be neglected under a big load (P>150MPa in the present study) because of the reach of flat surface as well as the steady-state impression creep stage. Moreover, the punch size has no influence on derivation of the exponent of impression creep stress with the presence of a certain surface roughness. The conclusions drawn in the present study provide an important guidance on experiment results amendment for impression creep technique.
9:00 PM - GG5.15
MD Simulation of Dislocation Dynamics in Copper Nanoparticles.
Yoshiaki Kogure 1 , Toshio Kosugi 1 , Tadatoshi Nozaki 1 , Masao Doyama 1
1 , Teikyo University of Science and Technology, Uenohara, Yamanashi, Japan
Show AbstractDynamical properties of edge dislocation in copper nanoparticles are investigated by means of molecular dynamics simulation. The embedded atom method potential for copper is used in the simulation. Numbers of atoms consisting nanoparticles are 30000 and 140000. An edge dislocation is introduced along [112] direction near the center of nanoparticles. The dislocation split to two partials after the initial relaxation. Configuration and motion of split dislocations in a slip plane are graphically demonstrated in a 3-dimentional model by highlighting the atoms with larger potential energy. Wavy motion of partial dislocations on a {111} plane are observed under the applied stress. Initially the partial dislocation on left side of crystal moved towards left by the applied stress, afterwards it was pushed back by the mirror force due to the fixed boundary. These motions were repeated. A period of the dislocation oscillation was about 10 ps, which was about 100 times of the period of thermal lattice vibration. Many kinks seem to be present on the Peierls hills. Dislocations are always confined in one of the atomic plane, namely, the clime motion is not observed in the present simulation. Change of mean potential energy during the dislocation motion is calculated, and the Peierls potential for the dislocation is evaluated. From the results of simulation at elevated temperatures a role of phonons on the dislocation motion is also investigated
9:00 PM - GG5.16
Line Tension Simulation of Solid Solution Hardening by Obstacles of Different Kinds.
Yi Dong 1 , Curtin William 1 , Thomas Nogaret 1
1 Division of Engineering, Brown University, Providence, Rhode Island, United States
Show AbstractParticle strengthening material usually contains two or more types of second-phase particles. Yet the strengthening effect of multiple second-phase particles is still an open problem both in experimental and theoretical study. To formulate the solid-solution hardened by second-phase particles, numerical calculation for dislocation line gliding through a field of different types of impenetrable weak particles is performed based on line tension model. The numerical result shows that an ad hoc superposition law with single parameter α is suitable for describing the particle strengthening accompanied with pre-existed solid solution strengthening matrix. The calculation also shows there exists a transition for the superposition law from linear addition rule to Pythagorean rule. The transition of superposition law is defined by the relative value of the average space of different strengthening particles.
9:00 PM - GG5.17
Effect of Surface Energy on the Plastic Deformation of Nanocontacts.
Milca Aponte-Roman 1 , Sandip Basu 1 , Adrian Mann 1
1 Materials Science & Eng, Rutgers University, Piscataway, New Jersey, United States
Show AbstractIt is well known that surface energy affects the elastic deformation of nanocontacts, but its affect on their plastic deformation is less clear. We have used self-assembled monolayer (SAM) systems that terminate in nonpolar groups to modify the surface energy of surfaces. The effect of the lower surface energy on plastic deformation has then been investigated using nanoindentation followed by atomic force microscopy (AFM) analysis of the deformed surface. SAMs have been used previously to reduce surface forces during nanoindentation tests and the tribological properties of SAMs have been studied with AFM and molecular dynamics (MD) simulations. Some of the prior work has demonstrated that the typical models for contact adhesion do not correctly describe contacts on SAMs. In our studies we have examined Au (111) nanofilms chemically modified with 1-decanethiol SAMs. Remarkably the SAMs, which are less than one nanometer thick, have a pronounced affect on nanoindentations over a hundred nanometers deep. That is, far beyond the depths and loads where contact adhesion or the SAM’s compliance would be expected to affect the mechanical deformation. Examination of load-displacement curves revealed that they were lower (less load for a given depth) on SAM covered surfaces. Using the standard analysis for nanoindentation data the reduced elastic modulus (E*) and hardness (H) were found. Even at large indentation depths E* decreased by 9% and H by 16% on the SAM covered surface. Analysis of the work of indentation showed that the SAM lowered the work of plastic deformation by 18%. AFM characterization of the residual nanoindentation impressions showed a substantial difference in the indent geometry between the Au with SAM and the Au alone. The surface area of pile-up around the nanoindents is much greater when a SAM is present. The volume of pile-up also shows an increase of up to 90% for the Au with SAM compared to Au alone. The greater pile-up suggests an increase in plastic deformation which is not seen in the work of indentation analysis. Intriguingly, the dependence of the pile-up on the SAM becomes more pronounced as the indents become deeper. In summary, SAM films on the Au seem to have several effects on the contact deformation depending on the depth of the contact. At shallow depths the effects of modified surface adhesion reduce the force on the surface and, hence, reduce the extent of plastic deformation. However, at larger depths the SAM lowers the energy required to create new surface (pile-up) and also lowers the friction between the indenter tip and the surface. Finite element modeling shows that lowering this friction increases pile-up in ductile materials. Thus, the effect of SAM films on the plastic deformation of nanocontacts shows a strong dependence on the contact depth with a transition from reducing plastic deformation at shallow depths to increasing it at larger depths.
9:00 PM - GG5.18
Bending of Single Crystal Copper Micro Cantilever Beams with Cube Orientation: Finite Element Simulation and Experiments.
Eralp Demir 1 , Franz Roters 1 , Dierk Raabe 1
1 , Max Planck Institute für Eisenforschung, Dusseldorf Germany
Show AbstractIn this study, single crystal micro cantilever beams with thicknesses of 5 m were manufactured by ion beam milling. Beams were deformed in an indenter device and subsequent ex-situ electron backscatter diffraction (EBSD) measurements were performed to track the microstructural changes after several increments of deformation. Localized shear bands along the slip plane traces and uniformly deformed regions were found in the beams by the EBSD maps. The amount of the shear localizations increased as the moment arm reduced and shearing became dominant compared to bending. A Single crystal plasticity model with phenomenological constitutive descriptions was implemented using the state integration method proposed by Maniatty and Dawson, ref.: A. M. Maniatty, P. R. Dawson, and Y.-S. Lee., Int. Jour. for Num. Met. in Eng. 35, 1565 (1992) [1]. Strain distributions similar to the EBSD image quality maps were produced by the model. The simulations showed the negligible effect of both the thickness variation along width of the beams and the friction between the indenter and the beam surface. The radius at which the beam was connected to the bulk had stronger influence on the force displacement curves.
9:00 PM - GG5.19
Size Dependence of Mechanical Strength Observed During Bending of Beams with Rectangular and Circular Cross Sections.
Eralp Demir 1 , Franz Roters 1 , Dierk Raabe 1
1 , Max Planck Institute, Dusseldorf Germany
Show AbstractBending is a mechanical testing method at micrometer length scale. It is advantageous because of its simpler deformation geometry compared to nanoindentation and its less strict precision requirements as in compression tests, i.e. alignment of two flat surfaces. For this reason, microsized copper cantilever beams with rectangular cross sections were manufactured by focused ion beam (FIB) milling and the beams were bent in an indenter device. Bending stress dependence of t-0.51 was found on the beam thickness. The shear strengths were estimated based on the geometrically necessary dislocation (GND) densities from electron backscatter diffraction (EBSD) maps of the bent beams after deformation. The shear strengths were found to be ~60% less than measured shear strengths at the end of loading and this difference was explained with the mean-field break-down theory. EBSD measurements showed the influence of the radius at which the beam was connected to the bulk. In addition, beams with round cross sections were manufactured by rotating the sample while milling with the ion beam. Size dependent flow stresses were also measured for the beams with circular cross sections.
9:00 PM - GG5.20
Lower Bound Geometrically Necessary Dislocation (GND) Densities with High Resolution EBSD Measurements.
Muin Oztop 1 , Jeffrey Kysar 1 , Brent Adams 2 , Josh Kacher 2
1 Mechanical Engineering , Columbia University, New York, New York, United States, 2 Mechanical Engineering, Brigham Young University, Provo, Utah, United States
Show AbstractThe size dependence of the mechanical behavior of elastic-plastic materials at the meso- and micro-scale is studied by investigating the deformation field associated with a wedge indentation in a face-centered single crystal; the resulting deformation field is two-dimensional in the sense that the only non-zero lattice rotation occurs in the plane. The lattice rotation was measured by high resolution electron backscatter diffraction (EBSD) analysis, which was capable of measuring lattice rotations and elastic strains at high resolution with a recently introduced method. The measurements were performed with 20 nm, 50 nm, mapping step size. The primary observation was the development of high lattice rotation gradient on a region beneath the indenter tip. This region was depicted as a discontinuity line in previous studies, however high resolution measurements showed the structure of the GND fields in this region much clearer. The Nye dislocation density tensor for plane strain deformation and the rigorous lower bound on GND densities were determined by the lattice rotation measurements. The GND densities determined in this region were of the order of 1016 m-2 which is higher than the density measurements reported with similar methods.
9:00 PM - GG5.21
Quantifying Near-Surface Machining Damage in High Yield Stress Materials.
Benjamin Groth 1 , Sandip Basu 1 , Adrian Mann 1
1 Materials Science and Engineering, Rutgers University, Piscataway, New Jersey, United States
Show AbstractMachining is a very harsh process for many materials frequently causing detrimental changes in microstructure (grain boundaries, twinning, dislocations and point defects), increases in residual stresses and the generation of sub-surface flaws. When machining a material one must consider all the factors and processes which can affect the extent of damage to the surface. These include very high contact pressures, large shear stresses, localized temperature increases, phase transformations and environmental (chemical) interactions. All of these are potentially taking place and influencing the final machined product. Here we report the results of a study on the effects of machining on a number of materials systems. In particular we have examined the combination of indentation testing and vibrational spectroscopy as tools for quantifying inhomogeneities in residual stresses and work hardening on machined surfaces. Analysis was done on hard ceramic and metallic samples using nanoindentation, microindentation and, for ceramics, micro-Raman. Nanoindentation data for the test samples has been analyzed using a variety of different methods to distinguish between hardening and residual stress effects. These methods include: the standard Oliver & Pharr analysis of unloading curves to find reduced elastic modulus (E*) and hardness (H); the ratio E*2/H which is independent of the contact geometry; work of indentation to find E*/H, and fitting to the loading curve to find E*/H. Microindentation (Knoop) was used to find hardness, though the ratio between the long and short axes was found to be a significantly better measure of residual stress. The data suggests that the combination of microindentation and nanoindentation can be used to distinguish between the macroscale effects of residual stress and work hardening. This is supported by finite element analysis of contacts on surfaces that are subject to residual stresses and work hardening. For ceramic systems micro-Raman in combination with nanoindentation has been found to be a powerful method for mapping and distinguishing local variations in residual stresses and work hardening. These methods also show promise for the quantification of sub-surface flaw distributions on machined samples.
9:00 PM - GG5.22
Super-hard Nanobuttons: Constraining Crystal Plasticity at the Nanoscale and Dealing with Extrinsic Effects.
Antonio Rinaldi 1 2 , Silvia Licoccia 1 , Enrico Traversa 1 , Pedro Peralta 2 , Cody Friesen 2 , Karl Sieradzki 2
1 NAST center and Department of Chemical Science and Technology, Univ Rome Tor Vergata, Rome Italy, 2 MAE, Arizona State University, Tempe, Arizona, United States
Show AbstractThe compressive plastic strength of nanosized single crystal metallic pillars is known to depend on their diameter D. Here, we analyze the role of pillar height h observing the suppression of generalized crystal plasticity below a critical value hCR that can be estimated a priori. Novel in-situ compression tests on regular pillars (D=300-900nm) as well as nanobuttons (i.e. very short pillars with h less than hCR, such as D=200nm and h<120nm in this case) show that the latter ones are exceedingly much harder, withstanding stresses greater than 2GPa. Such an h-lead transition in the structural behavior at the nanoscale is apparently reported here for the first time. A statistical model holding for both pillars and buttons can be formulated based on Extreme Value Theory. The findings render a more complete perspective of size-effect in crystal plasticity. The second part of the work concerns the extrinsic effects that naturally arise in the nanobuttons response when the Saint-Venant’s assumption ceases to be accurate. The bias related to such effects is identified and removed from test data when possible. This aspect is doomed to become increasingly crucial in nanomechanical testing, as materials become much harder and stiffer compared with fixtures when their size shrinks. Furthermore, we report "continuous hardening", that is observed to occur under increasing stress levels, in analogy to what reported for nanoparticles. Therefore, besides the intrinsic relevance to NEMS/MEMS design, the results bear significance by a metrological standpoint since expose some difficulties in nanoscale testing related to current methodology and technology when pushed to the limit.
9:00 PM - GG5.25
Modelling of Dislocation Self-ordering in Nanometric SiGe Islands Grown on Si(001) Substrate.
Anna Marzegalli 1 , Francesca Boioli 1 , Riccardo Gatti 1 , Vladimir Zinovyev 2 , Francesco Montalenti 1 , Leo Miglio 1
1 Material Science Department, Università degli studi di Milano Bicocca, Milano Italy, 2 , Institute of Semiconductor Physics, Novosibirsk Russian Federation
Show AbstractWhile in pseudomorphic heteroepitaxial films dislocations nucleate at random, giving rise to a disordered network whenever the critical thickness is exceeded, in SiGe islands grown on Si(001) a cyclic growth mechanism, involving serial nucleation of concentric dislocations at the interface between island and substrate is observed [1]. Selective etching of SiGe plus Atomic Force Microscopy analysis have recently shown [2] that, during the cyclic growth, a series of equally-spaced steps is carved in the Si substrate. The investigation of dislocation self-ordering when located in three-dimensional islands could highlight the peculiar mechanisms occurring therein, due to dislocation confinement in nanometric volumes, opening also the possibility of predicting and controlling defect positions in nanostructures.In the present work, we modelled dislocation rings at the interface, studying their thermodynamic equilibrium positions in a realistic island and supposing their dynamical evolution. In order to study dislocations and their strong interactions with island surfaces and interfaces, we use a joint model of classical dislocation theory [3] and numerical calculation, solved by Finite Element Methods (FEM), fully described in [4]. Our calculations give account for equally spaced dislocation rings. References:[1] A. Portavoce, R. Hull, M. C. Reuter, F. M. Ross,. Phys Rev B 76, 235301 (2007)[2] T. Merdzhanova, S. Kiravittaya, A. Rastelli, M. Stoffel, U. Denker, O. G. Schmidt, Phys. Rev. Lett. 96, 226103 (2006)[3] P. Hirth and J. Lothe, Theory of Dislocations (Krieger Publishing Company, Malabar 1992)[4] R.Gatti, A. Marzegalli, V. Zinovyev, F. Montalenti, Leo Miglio, Phys. Rev. B 78(18), 184104 (2008)
9:00 PM - GG5.26
First-Principles Study of the Bonding and Mechanical Properties of Grain Boundaries in Al and Cu.
Masanori Kohyama 1 , Shigeki Saitou 1 , Yoshinori Shiihara 2 , Ru-Zhi Wang 3 , Shingo Tanaka 1 , Tomoyuki Tamura 2 , Shoji Ishibashi 2
1 Research Institute for Ubiquitous Energy Devices, National Institute of Advanced Industrial Science and Technology, Ikeda, Osaka, Japan, 2 Research Institute for Computational Sciences, National Institute of Advanced Industrial Science and Technology, Tukuba, Ibaraki, Japan, 3 College of Materials Science and Engineering, Beijing University of Technology, Beijing China
Show AbstractGrain boundaries (GBs) have serious effects on the mechanical properties of metallic materials as barriers of dislocation transmission or as sources or sinks of dislocations. This feature is greatly enhanced in nano- or sub-micron grained metals formed by severe plastic deformation, exhibiting peculiar mechanical properties such as co-existence of hardness and ductility [1]. In such systems, GB regions dominate substantial volume ratio and there are only few movable dislocations inside grains. Thus the response of GB regions for applied stresses and the dislocation nucleation at GBs directly dominate the macroscopic mechanical behavior. The understanding of primary behavior of metallic GBs under various tensile or shear stresses is crucial. For this purpose, first-principles tensile or shear testing simulations of GBs [2] have made valuable contributions. On the other hand, it is desirable to deal with both the electronic and mechanical properties more directly. For this purpose, we have developed computational codes for the local energy and local stress densities [3] within the framework of the projector augmented wave (PAW) scheme in our original QMAS (Quantum MAterials Simulator) code [4]. In the present study, we examine the bonding and mechanical properties of GBs in fcc metals, Al and Cu, using the above theoretical schemes. First, we have examined the stability and interfacial bonding of tilt and twist GBs in Al and Cu [5] as well as stacking faults (SFs). We have found the covalent nature of Al leads to the reconstruction of interfacial bonds with peculiar charge redistribution at Al GBs. Second, we have applied the local energy-density and stress-density schemes to GBs and SFs in Al and Cu. It has been shown that the interface disordered regions indeed cause local energy increases, and that the different bonding nature results in different energy and stress distributions at GBs and SFs in Al and Cu. Third, we have applied first-principles tensile tests to Al and Cu GBs, where we have also observed the covalent nature at Al GBs. Fourth, we have examined the effects of Si and Mg impurities in first-principles tensile tests of Al GBs. We have observed that the tensile strength and bond breaking behavior at Al GBs are remarkably affected by the bonding nature change due to impurities. Results are consistent with experiments of Al samples containing Si or Mg formed by the accumulative roll bonding method [6]. [1] X. Huang, N. Hansen and N. Tsuji, Science 312 (2006) 249; [2] S. Ogata, Y. Umeno and M. Kohyama, Model. Simul. Mater. Sci. Eng. 17 (2009) 013001; [3] Y. Shiihara, M. Kohyama and S. Ishibashi, submitted; [4] http://www.qmas.jp; [5] R.Z. Wang et al., Mater. Trans. 50 (2009) 11; [6] D. Terada et al., Mater. Sci. Forum 584-586 (2008) 547.
9:00 PM - GG5.29
Dislocation Engineering in SiGe Heteroepitaxial Films on Nanopatterned Si (001) Substrates.
Riccardo Gatti 1 , Francesca Boioli 1 , Martyna Grydlik 2 , Moritz Brehm 2 , Anna Marzegalli 1 , Francesco Montalenti 1 , Thomas Fromherz 2 , Guenther Bauer 2 , Friedrich Schaffler 2 , Leo Miglio 1
1 L-NESS and Department of Materials Science, University of Milano-Bicocca, Milano Italy, 2 Institute of Semiconductor and Solid State Physics, Johannes Kepler University, Linz Austria
Show AbstractDislocations are heterogeneously nucleated in overcritical SiGe/Si(001) films, eventually providing a random network. However, for several micro and optoelectronic applications it would be highly desirable to obtain pre-determined regions free of dislocations (or threading arms, at least), as wide as few hundred nanometers at minimum. Here we show that a suitable nanopatterning of the Si substrate is able to confine the misfit segments into pits or trenches, providing the job with no need of oxide barriers. The optimal etching geometry and pattern was predicted by a synergic use of classical dislocation theory and Finite Element Methods (FEM) simulations, able to provide the full elastic field of dislocations interacting with surfaces and interfaces [1]. Our calculations reveal the subtle interplay of elastic and plastic relaxation in the SiGe film, as driven by submicron features carved in the substrate.Confirmation of the model predictions are provided by AFM analysis on several samples where thick layers (160 nm and 250 nm) of SiGe on Si(001) were grown by solid source molecular beam epitaxy. The pit and trenches pattern periods was varied between 500 nm and 5 μm as well as the Ge content in the epilayer (10% and 20%). We observed that the predicted pinning of dislocations bunches is obtained for a wide experimental parameter range.References: [1] R. Gatti, A. Marzegalli, V.A. Zinovyev, F. Montalenti, Leo Miglio, Phys. Rev. B 78(18), 184104 (2008).
9:00 PM - GG5.3
Towards a Virtual Laboratory for Grain Boundaries and Dislocations.
Sebastian Echeverri Restrepo 1 , Barend Thijsse 1
1 Materials Science and Engineering, Delft University of Technology, Delft Netherlands
Show AbstractIn order to perform a systematic study of the interaction between grain boundaries (GBs) and dislocations using molecular dynamics (MD), several tools need to be available. A combination of computational geometry and molecular dynamics was used to build the foundations of what we call a virtual laboratory.First, following the interface plane notation, an algorithm to generate GBs on FCC bicrystals was developed. Initially, two crystals with different orientations are placed together. Then, assuming that “real” GBs tend to have low energies, an energy minimization procedure is performed: for each combination of the five “macroscopic” degrees of freedom (DOFs), a set of three additional “microscopic” translations is found that result in a minimum energy configuration.Second, to classify the geometry of the GBs a local symmetry type (LST) describing the angular environment of each atom is calculated. It is found that for a given relaxed GB the number of atoms with different LSTs is not very large and that it is possible to find unique geometrical patterns in each GB. For instance, the LSTs of two GBs having the same macroscopical configuration but different microscopical DOFs can be dissimilar.Third, edge dislocations are introduced into the bicrystals. We see that full edge dislocations split into partials and that their presence modifies the geometry of the GBs. Finally, by loading the bicrystals with tensile and shear stresses the edge dislocations are put into motion.Various examples of dislocation-GB interactions in Al and Cu are presented.
9:00 PM - GG5.30
In-situ Deformation Analysis of as-quenched Martensite during Large Uniform Deformation.
Junya Inoue 1 , Masato Michiuchi 1 , Shoichi Nambu 1 , Toshihiko Koseki 1
1 Department of Materials Engineering, The University of Tokyo, Tokyo Japan
Show AbstractPlastic deformation behavior of as-quenched martensite of low carbon steel, which has a strong geometrical anisotropy, an average crystal width and length of around 200nm and 10μm, respectively, was studied in-situ by SEM equipped with EBSP analysis system.Since martensite is known to be the hardest phase of steel, it has been one of the candidates as a component of high-strength structural materials. However, since the plastic deformation behavior of martensite during large deformation has little been clarified, it is still difficult to make the best use of the phase. In this context, deformation behavior of as-quenched martensite of low carbon steel was studied in detail, through the in-situ measurement of both local strain distribution and crystal rotation behavior in each grain during uniform deformation up to about 30% strain. The extraordinarily high uniform elongation, up to 50% strain, was achieved through the application of the multilayered structure combining the phase with highly ductile austenitic steel. The strain measurement was conducted by the Digital Image Correlation (DIC) method for the elongation from 0 to10%, while the slip system operative in each grain during the plastic deformation was estimated through the crystal rotation behavior obtained by EBSP analysis. From the strain measurement, it was clarified that, up until the strain less than 4%, strain distributes uniformly, while it will quickly localize into blocks with relatively high Schmid factor in the in-lath-plane slip systems as the deformation proceeds. In the meantime, the blocks with relatively low Schmid factor in the in-lath-plane slip system exhibited very small deformation, even though the Schmid factor in the out-of-lath-plane slip system is very high. Furthermore, from the EBSP analysis, the constraint in the activation of slip systems was also confirmed up to about 20% elongation. These results clearly demonstrate the unusual activation priority of slip systems in martensite steel.
9:00 PM - GG5.4
Effect of Obstacle Spacing on the Fracture Resistance of High Strength Alloys.
Srinath Chakravarthy 1 , William Curtin 2
1 Engineering, Brown University, Providence, Rhode Island, United States, 2 Engineering, Brown University, Providence, Rhode Island, United States
Show AbstractIn many high strength alloys the internal length scale controlling flow is the strength and spacing of obstacles such as precipitates and for problems such as crack growth the plastic zone is confined to a small volume surrounding the tip. The influence of obstacle spacing and cohesive strength on crack growth in high strength metal alloys and alloy/ceramic interfaces is examined using the 2D discrete dislocation dynamics (DD) framework. The macroscopic flow stress is held fixed while the internal material parameters such as the obstacle strength, obstacle spacing and average source strength are systematically varied. The numerical procedure uses a new moving mesh algorithm, where the fine mesh in the vicinity of the crack tip moves as the crack advances. DD computations are compared with recent strain gradient plasticity calculations of Mode I crack growth along Ni/Al2O3 interface.
9:00 PM - GG5.6
Compressive Behavior of Small Metallic Glass Pillars from Micrometers to Nanometers.
Xiaolei Wu 1 , Brian Schuster 2 , Yazhou Guo 3 , Kaliat Ramesh 4 , Qiuming Wei 3
1 , Institute of Mechanics, CAS, Beijing, Beijing, China, 2 , US Army Research Lab, Aberdeen Proving Ground, Maryland, United States, 3 Mechanical Engineering, University of North Carolinat at Charlotte, Charlotte, North Carolina, United States, 4 Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland, United States
Show AbstractStrong size effects have been widely reported in single crystal metals, and the notion of “the smaller the stronger” has been substantiated both experimentally and theoretically. Such size effects can be due to the strain gradient plasticity, or be related to dislocation source mechanism in the absence of strain gradient. Such observations, and the advent of micro-compression technique first used by Uchic and his co-workers, have triggered great interest in exploring size effect in metallic glass systems of various chemistries. As a result, many papers have appeared in this area in the past five years. However, the conclusions drawn by different investigators are at great variance, to say the least. On the one hand, for example, some investigators have claimed strong specimen size effect of the compressive behavior of small pillars of bulk metallic glasses. Both enhanced uniform compressive plastic flow, or even complete suppression of shear banding, and increased strength with decreased pillar size have been reported. On the other hand, size-independent mechanical behavior has been observed. In this work, we have carefully measured the mechanical properties in terms of strength and plastic deformation of two representative bulk metallic glasses: the Pd-based system and the Zr-based Vit 1. The pillar sizes range from a few micrometers to as small as 150 nm. The pillars were fabricated using focused ion beam (FIB). We used both micro-compression with an instrumented nanoindentation system and in situ TEM nano-compression to evaluate the stress-strain behavior of the pillars. Both in situ TEM observations and post-loading imaging reveal strong evidence of localized shear banding in the pillars. The carefully recorded load-displacement curves exhibit either discrete displacement bursts (under load control) or load dips (under displacement control), again pointing to the occurrence of shear banding events. Such observations render us to believe that localized shear banding still prevails in BMGs with specimen size as small as ~100 nm.
9:00 PM - GG5.7
Numerical Simulations of the Nanoindentation and Recovery of a Platinum-based Metallic Glass.
David Henann 1 , Lallit Anand 1
1 Mechanical Engineering, MIT, Cambridge, Massachusetts, United States
Show AbstractThe unique mechanical properties of metallic glasses combined with their intrinsic homogeneity to the nanoscale (due to the absence of grain boundaries) make them ideal materials for a number of nano/micro-scale applications including MEMS and tools for nano/microimprinting of polymeric substrates for microfluidics. When a metallic glass is heated to temperatures above its glass transition temperature, a dramatic decrease in its strength and increase in its rate sensitivity are observed, such that the material may be easily formed in this temperature regime. Further, it has been observed in the literature that, at these temperatures, surface tension forces occurring around small surface features can drive recovery and subsequent flattening of these surfaces, sparking interest in utilizing this erasing capability for rewritable data storage. In this work, we (i) use a simple model for metallic glass plasticity above the glass transition temperature to model the nanoindentation of a Pt-based metallic glasses in this temperature range, (ii) develop a numerical method for accounting for the effects of surface tension in general three-dimensional situations, (iii) use this capability to extract quantitative estimates for the surface tension of this metallic glass, and (iv) apply this capability to predict the recovery behavior in various situations.The viscoplastic response of the material is described in our constitutive theory using a simple non-Newtonian viscosity model. The parameters appearing in the viscoplasticity model are determined over a small temperature range by fitting to load-displacement curves from nano-indentation experiments on a Pt-based metallic glass at high temperatures available in the literature. A model of this type is shown to capture the relevant features observed in the nano-indentation experiments. Using our numerical capability to model surface tension effects, we obtain quantitative estimates for the surface tension of the Pt-based metallic glass in this temperature range by fitting to the results of the accompanying recovery measurements. The capability is then applied to several geometries to study the erasing of nano/micro-scale features.
9:00 PM - GG5.8
Relaxation Dynamics in Locally Deformed Crystals of Peanut-Shaped Colloidal Particles.
Sharon Gerbode 1 , Chekesha Liddell 2 , Itai Cohen 1
1 Physics, Cornell University, Ithaca, New York, United States, 2 Materials Science, Cornell University, Ithaca, New York, United States
Show AbstractAt high area fractions, monolayers of colloidal “peanuts”, which consist of two connected spherical lobes, form a degenerate crystal (DC). In this structure, the peanut particle lobes order on a triangular lattice while the connections between lobe pairs are randomly oriented, uniformly populating the three crystalline directions of the underlying lattice. Utilizing real-time optical microscopy, we have directly observed the mechanisms for dislocation nucleation and propagation in DCs and have shown that obstacles formed by certain particle orientations severely limit the range over which dislocations can glide. Furthermore, we have observed that transport over longer distances can proceed through additional activated processes such as dislocation reactions, which switch the direction of propagation and allow dislocations to bypass such obstacles. While such mechanisms could theoretically transport any dislocation to an arbitrary position in a DC, the additional energetic cost and time required for such processes lead to novel defect relaxation dynamics. In an attempt to elucidate the relaxation process for dislocations in a perturbed DC, we have introduced an optically trapped “intruder” particle whose motion within the DC locally deforms the crystalline order and produces defects. Comparative studies of the recovery from such local deformations between crystals of spheres and DCs indicate that the geometric restrictions for dislocation glide in DCs lead to a marked slowing of the relaxation process.
9:00 PM - GG5.9
Length-scale and Temperature Dependence of Deformation Kinetics of Gold using Nanoindentation Technique.
Vineet Bhakhri 1 , Robert Klassen 1
1 Mechanical & Materials Engineering, The University of Western Ontario, London, Ontario, Canada
Show AbstractTwo stage indentation tests, involving a high strain-rate (loading) stage followed by a low strain-rate (creep) stage were performed on 99.99% purity annealed Au at 300K to 773K to investigate the effect of indentation depth and temperature on the plastic deformation process.Indentation data were analysed in terms of an obstacle-limited dislocation glide mechanism. Nanoindentation tests were performed in air at depths from 200nm to 2000nm at 300K, 473K, 623K, and 773K. Special measures were taken to characterize and control the thermal-drift of the indentation displacement signal by separately heating the specimen stage and the sapphire Berkovich indenter. The average thermal drift of the indenter displacement signal ranged from 0.02 nm/sec at 300K to 0.06 nm/sec at 773K.The stress dependence of the indentation strain-rate during the creep stage of the tests indicates that the activation energy ΔGo of the deformation process increases from about 0.16μb3 at 300K to 0.55μb3 at 773K. ΔGo is, however, relatively insensitive at a given temperature across the indentation depth range from 200nm to 2000nm. A Haasen plot activation analysis of the deformation process indicates that more mechanical work must be applied during the high strain-rate stage of the nanoindentation test, due to the predominance of work-hardening, compared to the low strain-rate stage where considerably more dislocation recovery occurs.TEM investigation of the dislocation sub-structure in the plastic zone around crept nanoindentations was performed on foils extracted from directly beneath nanoindentations using FIB-milling. The results clearly illustrate that the dislocation configuration in the nanoindentation plastic zone undergoes increasing reorganization into dense cell structures with increasing creep time and increasing temperature until dynamic recrystallization occurs beneath the nanoindentations at about 773K. These observations are consistent with our finding that ΔGo increases with the temperature.
Symposium Organizers
Peter M. Derlet Paul Scherrer Institut
Daniel Weygand Universität Karlsruhe, izbs
Ju Li University of Pennsylvania
Mike D. Uchic Air Force Research Laboratory
Eric Le Bourhis Université de Poitiers
GG6: Atomistic and Dislocation Dynamics Simulation Methods
Session Chairs
Wednesday AM, December 02, 2009
Room 300 (Hynes)
9:30 AM - **GG6.1
Studying Mechanical Behavior at the Nanoscale Using Accelerated Molecular Dynamics.
Arthur Voter 1
1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States
Show AbstractAtomistic simulation is a particularly appealing approach for studying mechanical behavior at the nanoscale. Molecular dynamics simulations can often be performed on a length scale that describes the entire nanoscale system, something that is not even remotely possible for macroscopic systems. Moreover, the behavior at the nano-scale, dominated by free surfaces and small volumes and cross-sections, sometimes involves thermally activated processes that have no macro-scale counterpart, so that exploration with full atomistic fidelity is desirable. However, direct molecular dynamics, which is limited to roughly one microsecond or less, typically cannot reach the time scales on which experiments are performed. In some cases, forcing the system to respond on shorter time scales (e.g., by increasing the driving rate or the temperature) can expose the key mechanisms from which useful models can be developed. However, it is also valuable to try to directly simulate the system behavior on the appropriate time scale, and sometimes there are important differences. Over the last decade or so, we have been developing a new class of methods, accelerated molecular dynamics, in which the known characteristics of infrequent-event systems are exploited to make reactive events take place more frequently, in a dynamically correct way. In many cases, this approach has been remarkably successful, offering a view of complex dynamical evolution of materials on time scales of microseconds, milliseconds, and sometimes beyond. I will present an introduction to these methods and discuss some of our recent results on ductility of metallic nanowires and friction at the atomic scale, in which we come much closer to experimental conditions than is possible with direct molecular dynamics.
10:00 AM - GG6.2
On the Formation of Dislocation Sources and Stability of Dislocation Structures in Small Volumes.
Daniel Weygand 1 , Christian Motz 2 , Jochen Senger 1 , Peter Gumbsch 1 3
1 izbs, University of Karlsruhe (TH), KIT, Karlsruhe Germany, 2 Erich Schmid Institute, Austrian Academy of Science, Leoben Austria, 3 IWM, Fraunhofer, Freiburg Germany
Show AbstractDiscrete dislocation dynamics simulations are nowadays often used for modelling the plastic flow of small scale samples, as classical continuum approaches fail to predict the size dependent plastic properties. The reason for this failure is that volume averaging over the dislocation microstructure, a fundamental assumption for the applicability of continuums descriptions, is no longer possible. It is known that discrete dislocation dynamics simulations need an initial dislocation microstructure or reasonable dislocation nucleation criteria and therefore the choice of this initial structure is often disputed, e.g the use of Frank Read sources stabilized by fixed pinning points, which cannot dissolve by reaction processes. In this contribution, dislocation networks are generated by relaxing pinning point free dislocation distributions. The analysis of the resulting dislocation network topology revealed different type of reactions points, where several dislocation originating from different glide planes intersect. The most surprising reaction point is a naturally occurring pinned node, involving three glide planes, which are always found to be end-points of Lomer reactions. A pinning point is connected to the Lomer reaction and a single freely moving dislocation located on a glide plane inclined with respect to the Lomer reation. This outgoing dislocation may act as a stable spiral source or if limited at both ends by the same type of node as Frank Read source. The consequences and frequency of these naturally occurring pinned or glissile nodes on the microstructure and mechanical properties of small-scale samples are discussed.
10:15 AM - GG6.3
Discrete Dynamical Simulation of Interacting Dislocations in Elastically-anisotropic Crystal Grains: Modelling Plasticity of Iron at High Temperatures.
Steve Fitzgerald 1 3 , Sylvie Aubry 2 , Wei Cai 2 , Zhongwen Yao 3 , Sergei Dudarev 1
1 Theory and Modelling, EURATOM/UKAEA Fusion Association, Abingdon, Oxfordshire, United Kingdom, 3 Materials, University of Oxford, Oxford, Oxfordshire, United Kingdom, 2 Mechanical Engineering, Stanford University, Stanford, California, United States
Show AbstractPlasticity of iron and ferritic steels, and changes in mechanical properties occurring as a result of irradiation, are largely controlled by the single-crystal microplasticity of individual grains. Furthermore, the experimental micromechanical techniques, presently being developed for investigating the elastic and plastic behaviour of ion-irradiated specimens, require that modelling methods capable of describing elasticity and plasticity on the micron scale be developed in parallel. Iron (and iron-chromium alloys) is the most elastically-anisotropic of all the bcc transition metals, and also the most technologically-important. The anisotropy of bcc iron is intimately related to its magnetic properties, and increases as the temperature approaches that of the α-γ phase transition at 912°C. Close to this point, the lattice becomes unstable to tetragonal shear, as manifested by the tetragonal shear modulus C’ = (C11 – C12)/2 falling nearly five-fold between room temperature and 900°C. At the same time, the trigonal shear modulus C44 falls much more gradually, by just 15% over the same temperature range. Anisotropic effects begin to dominate the crystal plasticity of iron from around 450°C. The effect of elastic anisotropy on interacting dislocations is particularly striking, and in this work we present the latest results obtained from discrete dislocation dynamics (DDD) simulations of single-crystal α-iron at high temperatures, paying particular attention to the interactions of ensembles of dislocations and the emergence of micron and sub-micron scale structures such as pile-ups and junctions. The simulations exhibit numerous features that cannot be understood within the isotropic elasticity approximation. Our transmission electron microscope observations of irradiated α-iron reveal microstructure highly characteristic of extreme anisotropy, underlining the inapplicability of the isotropic approximation, and the necessity of implementing full anisotropic elasticity theory in DDD simulations of microplasticity in iron. This work was partly supported by UK EPSRC and by EURATOM.
10:30 AM - GG6.4
Application of a 3D-Continuum Theory of Dislocations to Problems of Constrained Plastic Flow.
Stefan Sandfeld 1 3 , Thomas Hochrainer 1 2 , Michael Zaiser 3 , Peter Gumbsch 1 2
1 izbs, University Karlsruhe (TH), Karlsruhe Germany, 3 Institute for Materials and Processes, University Edinburgh, Edinburgh Germany, 2 IWM, Fraunhofer Institute for Mechanics of Materials, Freiburg Germany
Show AbstractThe growing demand for physically motivated continuum theories of plasticity led to an increased effort on field descriptions based on the averaged dynamics of dislocations. The line-like character of these defects, however, posed serious problems for the development ofcontinuum theories.
Only recently rigorous techniques have been developed for performing meaningful averages over systems of moving, curved dislocations. These techniques are used to define a generalization of the dislocation density tensor, the so-called dislocation density tensor of second order. This tensor can be envisaged as the analogue of the classical dislocation tensor in an extended space which includes the line orientation as an independent variable. With this higher dimensional tensorial description, the common distinction between geometrically necessary and statistically stored dislocations becomes dispensable.
We apply this extended continuum theory to study benchmark problems of constrained plastic flow in a single and double slip configuration: microbending and -shearing of a free-standing thin crystalline strip. These examples demonstrate e.g. that the evolution of dislocation density in the higher dimensional space is able to capture phenomenawhich are - in discrete simulations - governed by the rotation of line segments: the conversion from 'statistically stored' dislocation density to 'geometrically necessary' dislocation density which isneeded to acomodate strain gradients. The influence of dislocation density pileups on the size-effect obtained by our continuum theory will be discussed.
As a first application of the extended continuum theory towards the simulation of polycrystals we study a tricrystal under compression. We compare the results for the evolution of dislocation density and the behavior at grain boundaries with those obtained from a discretedislocation dynamics simulation.
10:45 AM - GG6.5
Modelling of the Non-Schmid Behavior in BCC Metals in a Three-dimensional Discrete Dislocation Dynamics Framework.
Kinshuk Srivastava 1 , Daniel Weygand 1 , Peter Gumbsch 1 2
1 Institut fuer Zuverlaessigkeit von Bauteilen und Systemen, University of Karlsruhe, Karlsruhe, Baden-Wuerttemberg, Germany, 2 IWM, Fraunhofer Institut fuer Werkstoffmechanik, Freiburg, Baden-Wuerttemberg, Germany
Show AbstractThe breakdown of Schmid’s law for the plastic flow behaviour of bcc metals is well known experimentally and confirmed by MD simulations. It is also known that plastic flow in bcc metals is controlled by 1/2<111> screw dislocations. Atomistic studies using Bond Order Potentials(BOP) for Molybdenum and Tungsten which take into account the directional nature of bonding typical of these transition metals, allowed to parametrize an yield criterion for a screw dislocation taking the entire stress tensor into account [Groeger et al. Acta Mater. 2008,56,5401/5412].The present work focuses on the implementation and validation of this type of yield-criteria in a three-dimensional Discrete Dislocation Dynamics framework. The motion of single dislocations and groups of dislocations in micrometer-sized pillars of Tungsten under uniaxial tension and compression loading is presented. The results suggest that the motion of grouped screw dislocations is enhanced compared to an isolated dislocation due to local stress fields of the dislocations. A comparison of this yield criteria with Schmid’s law is done. In our simulations, mobility of screw dislocations is governed by the well known thermally activated motion via kink-pair nucleation.
11:30 AM - **GG6.6
Nanomechanics of Plasticity in Ultra-Strength Materials.
Ting Zhu 1
1 Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States
Show AbstractRecent experiments on nanoscale and nanostructured materials, including nanowires, nanopillars, nanoparticles, nanolayers, and nanocrystals, have revealed a host of “ultra-strength” phenomena, defined by stresses in the material generally rising up to a significant fraction of the ideal strength—the highest achievable strength of a defect-free crystal. This talk describes the strength-controlling deformation mechanisms in ultra-strength materials with dislocation source-limited characteristics. Examples include the strength-ductility tradeoff in nanostructured metals, strength limit in nanopillars, and size effects in nanoindentation. A modeling framework is introduced to address the stochastic nature of dislocation nucleation. Such an approach bridges the timescale gap between atomistic modeling and laboratory experiments, enabling a quantitative understanding of the size, temperature, strain-rate dependence of ultrahigh strengths in materials with confined volumes.
12:00 PM - GG6.7
Temperature and Shape Dependence of Dislocation Nucleation.
Seunghwa Ryu 1 , Wei Cai 2
1 Physics, Stanford University, Stanford, California, United States, 2 Mechanical Engineering, Stanford University, Stanford, California, United States
Show AbstractDislocation nucleation is essential to the plastic deformation of small-volume crystalline material. Due to the limited time scale of molecular dynamics simulation, it has been studied under the framework of transition state theory with nudged elastic band (NEB) method or molecular simulations with a strain late much higher than experimentally achievable. However, NEB method may overestimate the nucleation rate significantly by ignoring entropy of activation complex and re-crossing of energy barrier. Also, high strain rate in MD simulation may cause artifacts. With the aid of an advanced sampling method, the forward flux sampling (FFS), we directly obtain the nucleation rate and free energy barrier at finite temperature. We find that nucleation rates are much lower than NEB predictions because of re-crossings of nucleation barrier. We observe the reduction of energy barrier due to free surface, which is found from both NEB and FFS simulations of 1D, 2D, and 3D structures.
12:15 PM - GG6.8
On-the-fly Analysis of Large-scale Molecular Dynamics Simulations: Calculating Lattice Rotation and Dislocation Density Tensors from Atomistic Data.
Alexander Hartmaier 1 , Jun Hua 1 , Christoph Begau 1
1 ICAMS, Ruhr-University Bochum, Bochum, NRW, Germany
Show AbstractLarge-scale molecular dynamics simulations have been widely used to investigate the mechanical behavior of materials. But complex datasets generated during the atomistic simulations involving the positions of many million atoms make quantitative data analysis quite a challenge. This paper presents a novel method to determine dislocations in the crystal and also quantifies the corresponding Burgers vectors. This is achieved by combining geometrical methods to determine the atoms lying in the dislocations cores, like for example the common neighbor analysis or the bond angle analysis, with the slip vector analysis. The first methods are used to filter out the atoms lying in undisturbed regions of the crystal; the latter method yields the relative slip of the remaining atoms and thus indicates the Burgers vector of those atoms lying in the dislocation cores. A topological simplification of atom positions in the dislocation cores into geometrical line segments allows us to calculate local lattice rotations as well as the Nye dislocation density tensor from atomistic data during the simulation. Large-scale atomistic simulations of nanoindentation reveal the full potential of this advanced analysis method. Based on the gained data, the density of geometrically necessary dislocations (GND) is evaluated and expressed as a function of the deformed volume, the indentation depth and the indenter size. Also the dislocation-grain boundary interaction can be investigated with a drastically improved precision. Hence, this method is expected to provide valuable input for multi-scale modeling schemes.
12:30 PM - GG6.9
Prediction of Dislocation Nucleation in Nanoindentation Using an Atomic-Scale Stability Criterion.
Terry Delph 1 , Jonathan Zimmerman 2
1 Dept. of Mechanical Engineering, Lehigh University, Bethlehem, Pennsylvania, United States, 2 Mechanics of Materials Department, Sandia National Laboratory, Livermore, California, United States
Show AbstractNumerous macroscale phenomena in the behavior of solids, e.g., plastic flow, fracture, and cavitation, are governed by the initiation of defects on the nanoscale. At the nanoscale it is possible to identify a few unifying features. In particular, each of these phenomena originates from a process in which a given atomic configuration becomes unstable and shifts into a stable, lower energy, configuration. This shift may involve the breaking and reforming of a relatively small number of interatomic bonds, as is the case in the nucleation of a single dislocation in a perfect crystal, or it may involve a large-scale change in atomic configuration, as with catastrophic brittle fracture. Viewed in this fashion, loss of stability of the atomic configuration becomes the general mechanism underlying a wide variety of macroscopic and microscopic features of great importance in the behavior of materials.We outline here a general technique for the prediction of defect nucleation in crystalline solids. This technique is based upon an atomic-scale stability criterion put forward by Wallace. In essence, this criterion states that a given equilibrium atomic configuration is stable if all possible infinitesimal displacements of a group of atoms leads to a higher system energy than that of the equilibrium state. By a judicious choice of this atomic grouping, it is possible to make accurate, numerically efficient predictions of defect nucleation. Computationally, this involves a consideration of the lowest real eigenvalue of a relatively small matrix, loss of stability being signaled by a change in sign in this quantity from positive to negative. We have recently applied this criterion to analyze the stability of FCC crystals under uniform triaxial extension and the transition of a Mode I crack from slow to rapid quasi-brittle growth.More recently, we have considered the nucleation of a dislocation under the action of a spherical nanoindenter acting on the (001) face of an Au crystal. Dislocation nucleation is difficult to predict using criteria based upon continuum mechanics, e.g., maximum resolved shear stress. Modeling the mechanical behavior of gold with an EAM interatomic potential, we have obtained excellent results using atomic groupings that are quite small with regard to the total atomic assemblages. As judged by the results of parallel molecular statics simulations, the Wallace criterion accurately predicts the indenter depth at which dislocation nucleation occurs. Moreover the eigenvector associated with the lowest eigenvalue locates the site of nucleation as the fifth atomic layer beneath the surface, in excellent agreement with the large-scale numerical predictions.Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
12:45 PM - GG6.10
Rate Processes in 3D Dislocation Ensembles.
Mamdouh Mohamed 1 , Jie Deng 1 , Anter El-Azab 1
1 Dept. of Scientific Computing, Florida State University, Tallahassee, Florida, United States
Show AbstractAs carriers of the plastic strain, modeling the collective behaviour of dislocations is the keystone to simulate the deformation mechanism in metals. Recent efforts in this field have led to formulations of density-based models of dislocation dynamics replacing the constitutive laws in crystal mechanics framework. In these models, the spatio-temporal evolution of the dislocation density is governed by kinetic equations in which the dislocation density evolution depends on the density net flow, a divergence term of the density multiplied by its average velocity, and source terms corresponding to the local dislocation density changes due to processes such as cross slip, annihilation and junction formation reactions. Solution of those kinetic equations requires the predetermination of both average velocity and rate coefficients associated with the source terms. The average dislocations velocity is evaluated based on the average resolved shear stress acting on them, and also the nature of their collective motion. Since some of the dislocations will not move accoring to the single dislocation mobility law, the average stress-velocity relation is different from that law, and accounts for those distinctive segments. Regarding the source terms, theoretical modeling and numerical analysis of temporal statistics of dynamical dislocation ensembles is important. Here, the time series of cross slip and short-range reactions are modeled as stochastic marked point process in time. The statistical properties of these processes, in both time and frequency domains, are analyzed in conjunction with dislocation dynamics simulation of copper crystals. The numerical calculation of autocorrelation function and spectral density provides the time scale and frequencies associated with cross slip and short-range reactions. This information determines the correlation time that approximates the coarse graining time scale, which, together with the dependence of these processes on dislocation density and line orientation, fixes the source terms in kinetic equations and provides insight into the temporal behavior of the solution of the dislocation kinetic equations. We present an overview of this topic and show several important numerical results in this direction.
GG7: Microstructural Dominated Plasticity: Experiment & Simulation
Session Chairs
Javier Gil Sevillano
Mike Uchic
Wednesday PM, December 02, 2009
Room 300 (Hynes)
2:30 PM - **GG7.1
Plasticity in Nanocrystalline Metals: A Knowledge Base Obtained from Experiments and Atomistic Simulations.
Helena Van Swygenhoven 1 , Ch. Brandl 1 , A. Elsener 1 , P. Derlet 1 , S. Van Petegem 1
1 NUM, PSI, Villigen Switzerland
Show AbstractMolecular dynamics deformation studies of nanocrystalline (nc) metals suggest dislocations are nucleated at grain boundaries (GB), travel through the grain being hindered by local GB stress intensities, to be finally absorbed in the surrounding GBs. Recent constant strain rate molecular dynamics simulations of nc Al demonstrate that dislocations can also exhibit cross-slip via the Fleischer mechanism (PRL 100(2008)235501, Phil. Mag 2009, in press). The GB is found to strongly influence when and where cross-slip occurs, allowing the dislocation to avoid local stress concentrations that otherwise can act as pinning sites for dislocation propagation. Of course some of the deformation mechanisms observed can be affected by the presence of oxygen in the GBs (Acta Mat 57(2009)1988).In this talk the latest suggestions from molecular dynamics are discussed in terms of the very high strain rates applied in MD, making it difficult to determine the experimentally relevant rate limiting mechanism (nucleation or propagation controlled). Furthermore the simulation results are assessed in terms of experiments performed on nc Ni involving strain rate sensitivity measurements (APL 89(2006)73102), stress dip tests, and in-situ tensile and compressive testing during X-ray diffraction (Scripta Mat 60(2009)297, Scripta Mat 58(2008)61) including comparisons with XRD profiles calculated from MD simulated configurations (Acta Mat 56(2008)165).
3:00 PM - GG7.2
Getting Rid of all the Atoms - Observing Dislocation Lines in Atomistic Simulations.
Alexander Stukowski 1 , Karsten Albe 1
1 Institute of Materials Science, University Darmstadt, Darmstadt Germany
Show AbstractWe present a new general method that allows to directly extract dislocation lines and their associated Burgers vectors from atomistic simulations. Our dislocation detection algorithm is based on an automated Burgers circuit analysis followed by a vectorization step, thereby achieving the transition from the atomistic system to a discrete dislocation representation. The dislocation lines are finally connected at node points if Burgers vector conservation is satisfied.With a fast and parallelized implementation of the algorithm the dislocation analysis can be performed on-the-fly during molecular dynamics simulations with a very high time resolution. This enables the investigation of rapid dislocation processes, whose observation is otherwise impeded by the huge amount of data produced by large-scale atomistic simulations. Our analysis method is able to reliably detect full, partial, and twinning dislocations. Dislocation density can now directly be derived from the total dislocation line length. In principle, more sophisticated data can be extracted from the dislocation analysis, including dislocation mobility, dislocation reactions, and twin boundary density and mobility.The new analysis method is applied to large-scale deformation simulations of face-centered cubic nanocrystalline materials to study the density and character of dislocations as a function of strain. Being able to directly visualize and measure dislocation activity gives new insights into the interplay of grain-boundary mediated processes and dislocation plasticity in such materials.
3:15 PM - GG7.3
Size Effect in the Shear-Coupled Migration of Grain Boundaries Pinned by Triple Junctions.
Javier Gil Sevillano 1 , Aitor Luque 1 , Javier Aldazabal 1 , Jose Martinez-Esnaola 1
1 Materials, CEIT and TECNUN, University of Navarra, San Sebastian Spain
Show AbstractIn stressed polycrystals, tilt boundaries under resolved shear stress experience a virtual pressure that promotes their shear strain-coupled migration, like similar tilt boundaries in bicrystals do. However, in polycristals the grain boundaries are constrained by their limiting triple junctions. The pinning effect of the junctions induces the bulging of migrating boundaries that cannot take place without elastoplastic accommodation by simultaneous dislocation emission or grain boundary sliding. Finite migration of the pinned boundaries a given rate and temperature needs to increase the applied shear stress above the threshold shear stress needed for the migration of a free-to-move flat boundary and such increase is dependent on the size of the boundary. This paper presents molecular dynamics simulations of shear-coupled migration of tilt boundaries pinned by triple junctions in a simple model structure of columnar grains of different sizes. Simulations are for copper at 300 K. The phenomenon is of interest as a possible explanation of the Hall-Petch relationship breakdown in nanograined polycrystals.Work supported by the Department of Industry, Commerce and Tourism of the Basque Country (project ETORTEK inanoGUNE) and Spanish Ministry of Science and Innovation, MICINN, and the European Social Fund (Torres Quevedo Programme, A. Luque).
3:30 PM - GG7.4
Influence of Microstructure on Thermo-mechanical Fatigue of Al Films on Substrates.
Walther Heinz 1 , Gerhard Dehm 1 2
1 , Erich Schmid Institut of Materials Science, Leoben Austria, 2 Department Materials Physics, Montanuniversity Leoben, Leoben Austria
Show AbstractAluminum thin films are used as metallization in numerous microelectronic devices and may fail due to thermo-mechanical fatigue caused by cyclic thermal loading. Due to the difference in thermal expansion coefficients between the Al film and its substrate, thermal stresses evolve in the films during thermal cycling. Upon heating, compressive film stresses arise while upon cooling tensile film stresses are induced. In this study the texture evolution and its impact on the damage evolution of the film is studied for polycrystalline and epitaxial Al films thermally cycled between 373 K and 723 K. The tests were performed for different film thicknesses ranging between 200 to 2000nm.Epitaxial Al films were sputter deposited on (0001) α-Al2O3 substrates and polycrystalline Al films on SiOx or SiNx passivated (100) Si substrates. The as-grown film microstructure was investigated by SEM and EBSD prior to thermal cycling and after 100, 1000, and 10000 thermal cycles. Thermal cycling by ΔT=350 K inducing thermal strains of ~0.6% was performed in a nitrogen flooded tube furnace with a heating rate of 30 K/s and a more sluggish cooling rate of about 3 K/s. For polycrystalline films a change in texture occurs from a (111) fibre texture towards a (112) fibre texture. This change in texture is accompanied by a severe roughening of the film surface. On the contrary, the epitaxial (111) oriented Al films consisting of four grain variants keep the same texture and reveal no surface roughening. The reasons for this difference in behaviour will be discussed.
4:15 PM - GG7.5
Nanoscale Cu/Ni Multilayer Micropillars: Cyclic and Strain Rate Effects.
John Carpenter 1 , Michael Uchic 2 , Amit Misra 3 , Peter Anderson 1
1 , Ohio State University, Columbus, Ohio, United States, 2 , USAF AFMC AFRL/RXLMD, Dayton, Ohio, United States, 3 , Los Alamos National Laboratory, Los Alamos, New Mexico, United States
Show Abstract This work reports on a recent effort to characterize metallic Cu/Ni multilayer thin films via uniaxial compression of micron-scale samples. This test geometry has been used to study the size-dependent response of single crystal samples. The present work is different in two ways: First, the micron-scale samples have an underlying nanoscale structure with numerous interfaces and polycrystalline layers. Second, the testing protocol is extended to include interrupted compression and also strain rate jump studies. Other benefits are that the test geometry removes the constraint and stress-induced effects imposed by the substrate and avoids necking/tearing instabilities associated with in-plane tension testing of thin films. Cylindrical micropillars 2 μm in diameter and 4.8 μm in height were fabricated from 20 nm/20 nm Cu/Ni multilayers using a lathing method with a focused ion beam and then tested using a modified Nanoindenter XP with a flat punch tip. The interrupted compression tests involved unloading and reloading the same sample at five different points during uniaxial compression test, ultimately reaching an engineering stress of -1.6 GPa and a nominal engineering strain of -5%. The initial unloading portions are consistent with an elastic modulus E ~ 120 GPa normal to the layers. A typical unloading trace showed a recoverable plastic strain εp(rec) ~ 0.25%, indicating a possible effect of the large confinement and internal stress present in such systems. Higher order polynomial fits to the stress-strain data permitted calculation of dεp/dσ during the loading and unloading portions. The results suggest that the barrier stress for forward vs. backward motion of dislocations is quite asymmetric. The strain rate jump tests involved repeated jumps in strain rate, cycling back and forth from 10-5/s, 10-4/s, 10-3/s, etc. for 200 s, 20 s, and 7 s, respectively, ultimately reaching a maximum engineering stress of -1.8 GPa and nominal engineering strain of -4%. Corresponding stress jumps were observed, from which the strain rate sensitivity m can be deduced. These observations are interpreted in terms of a dislocation-based view of isolated layer deformation via confined layer slip, followed by codeformation of the layers.
4:30 PM - GG7.6
Plastic Flow Stability of Nanotwinned Cu Foils.
Osman Anderoglu 1 , Amit Misra 2 , Jian Wang 2 , Richard Hoagland 2 , John Hirth 2 , Xinghang Zhang 1
1 , Texas A&M University, College Station, Texas, United States, 2 , Los Alamos National Laboratory, Los Alamos, New Mexico, United States
Show AbstractThe plastic flow stability of sputter deposited, self-supported, nanotwinned polycrystalline Cu foils was investigated via room temperature rolling. Nanotwinned polycrystalline Cu, with a very fine scale structure consisting of twin lamellae with an average thickness of 5 nm and high hardness of 3.5 GPa, exhibited stable plastic flow with no shear localization or fracture, even at thickness reduction up to 50%. The {111} fiber texture was retained after rolling indicating insignificant out-of-plane rotation of the columnar grains and is interpreted in terms of a symmetric slip model. No significant change in the average twin lamellae thickness was seen although the height of the columnar grains was reduced by a factor of two after rolling, suggesting that thin twin boundaries were annihilated during deformation. The annihilation of very thin twins is a consequence of migration of twin boundaries normal to the twin boundary plane due to the glide of twinning dislocations (disconnections) in the twin plane. The work hardening after rolling is correlated with the dislocation storage at twin boundaries.
4:45 PM - GG7.7
Size Effects on the Yielding and Plasticity of Nanotwinned Gold: From Bulk to Nanowires.
Frederic Sansoz 1 , Chuang Deng 1
1 School of Engineering, University of Vermont, Burlington, Vermont, United States
Show AbstractGold nanopillars and nanowires play a central role in a wide variety of molecular applications and nanodevices. It is now possible to use microstructural design to create fcc gold nanowires with large densities of (111) planar faults forming nanoscale twins. Strengthening effects due to nanoscale twins are well-known in bulk fcc metals, but twin boundary effects on the strength and plasticity of nanowires dominated by free surfaces have not been fully investigated. This presentation summarizes our recent progress in understanding the role of pre-existing twin boundaries on the slip activity of [111] oriented twinned Au nanowires with circular cross-section subjected to tensile loading using massively-parallel molecular dynamics simulations. We first present size effects, as a function of twin size (from 2.1 nm to 16.8 nm) and wire diameter (from 8 nm to 49 nm), that enable ultrahigh plastic flow and work hardening in twinned gold nanowires. We show that a fundamental transition in slip behavior occurs when the ratio of wire diameter to twin boundary spacing is larger than 2.14. Second, we describe in detail the synergistic effects of twin boundaries and free surfaces on the stress required for the nucleation of new dislocations from nanowires and bulk specimens. It is revealed that the addition of nanoscale twins to crystalline nanowires can act to either increase or decrease their resistance to slip in tension, depending on both sample diameter and number of twins per unit length.
5:00 PM - GG7.8
Fatigue in Al Thin Films Stressed at Ultra-High Frequencies.
Diana Courty 1 , Christoph Eberl 1 , Thomas Gnielka 1 , Werner Ruile 2 , Oliver Kraft 1 3
1 , University of Karlsruhe, izbs, Karlsruhe Germany, 2 , EPCOS AG, Munich Germany, 3 , IMF II, Forschungszentrum Karlsruhe, Karlsruhe Germany
Show AbstractAl thin film test devices, similar to frequency filters used for radio communication applications, can be used to study damage behavior of thin films fatigued in the GHz-regime. In such devices an electrical signal with ultra-high frequency is transduced to an acoustic wave. Designed as acoustic resonators these systems can respond with large deflection amplitudes at their resonance frequency. The high cyclic stresses induce fatigue damage in the patterned thin metal film. This results in a shift of the resonance frequency, which is used as lifetime criterion and is an easily accessible fatigue criterion. As the resonance frequency of such devices is usually in the GHz-regime, cycle numbers up to 1014 can be reached within one day.The damage formation in thin metal films for ultra-high cycle numbers can be correlated with the damage mechanisms and the dislocation behavior. In particular, the damage in the Al thin films is analyzed by Scanning Electron Microscopy (SEM), Focused Ion Beam microscopy (FIB) and Transmission Electron Microscopy (TEM). Extrusions and voids develop in the stressed films, leading to a change of the film stiffness and can be correlated to the frequency shift. TEM is used to study the possible role of dislocations and to determine the mean grain size, which is in the order of 100 nm. No long range dislocation structures were observed in the fine grained material. These observations give valuable input for discrete dislocation simulations evaluating the dislocation behavior at ultra-high frequencies.The mechanisms leading to damage formation are attributed to single dislocation motion in the model. Therein, a ratcheting mechanism leads to the glide and climb of individual dislocations. It will be shown that dislocation motion is possible at ultra-high frequencies and therefore, the focus lies on the possible explanation of the strong stress dependence of the lifetime that has been reported. A simple dislocation model is presented that allows motivating strong stress dependencies based on interacting dislocations and the activation of dislocation sources. Based on this model it is possible to show that the lifetime strongly depends on the grain size and grain size distribution. The mobility of dislocations interacting with grain boundaries obtained by atomistic simulations is included in this model.Our attempt to correlate details of the dislocation behavior with the damage formation at ultra-high cycle fatigue in thin metal films is of general importance for the reliability of micro devices operated at radio frequencies. Ultimately, a physical understanding of the damage mechanisms will allow for improving the fatigue resistance of fine-grained materials at ultra-high frequencies.
5:15 PM - GG7.9
Temperature-mediated Transition from Brittle Fracture to Dislocation Emission at a Single Crystal Silicon Crack Tip.
Dipanjan Sen 1 , Stella Schieffer 2 , Christian Thaulow 3 , Markus Buehler 2
1 Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 2 Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 3 Department of Engineering Design and Materials, The Norwegian University of Science and Technology, Trondheim Norway
Show AbstractAt low temperatures, silicon is a highly brittle material that fractures catastrophically once the applied load exceeds a threshold value. At elevated temperatures, however, the behavior of silicon is ductile. This brittle-to-ductile transition has been observed in several experimental studies of single crystals of silicon. However, the mechanisms that lead to this change in behavior are debatable, and the atomic-scale phenomena are unknown. Here we use large-scale atomistic simulation using the first principles based ReaxFF force field to directly observe the thermally-activated emission mechanism of a partial dislocation at a silicon crack tip. By solely raising the temperature in a computational experiment with otherwise identical boundary conditions, we show that the material response changes suddenly from brittle to ductile over a very small temperature range. We observe the phenomenon of fracture crack arrest and the formation of a nanoscale ledge at the crack tip, both events just prior to dislocation emission. We also observe the nucleation of a stable dislocation loop at the crack tip, imaged from atomistic results using the Zimmerman slip vector approach. We suggest this single-event dislocation nucleation plays an integral part in the BDT in low-defect single crystal silicon. Our simulations provides important insight into the atomistic-level mechanism of the brittle-to-ductile transition in silicon.
5:30 PM - GG7.10
Interaction of Internal and External Length Scales in the Torsion of Thin Wires: Theory and Experiment.
David Dunstan 1 , Andy Bushby 1
1 Centre for Materials Research, Queen Mary, University of London, London United Kingdom
Show AbstractThe strength of materials has been shown to be increased in confined volumes, whether this confinement comes from the size of the object (external) or the extent of a localised strain field, or the microstructure (internal). Such size effects are well-known in nanoindentation, the bending of thin foils, the torsion of thin wires and in uniform deformation such as micro-pillar compression and the Hall-Petch grain size effect. However, the interaction between external- and internal-length-scale effects in plasticity is less well-studied. Here we present experimental data that directly probes the interaction of grain size and structure size via the torsion of thin metal wires. Our methodology was designed to explore the full range of strain, with high resolution below and above the yield point and to plastic strains as high as unity. Wires of different diameter were carefully annealed to control the microstructure and loaded in torsion using a load-unload method. The dependence of both the elastic limit and strain-hardening behaviour on both wire diameter and grain size is revealed. Theoretical studies of the size effect in the strength of wires under torsion are reported and compared with the experimental data. We apply slip distance theory with Taylor (forest) strain-hardening, and introduce physically necessary modifications to the standard theory for the case of a finite structure size. Equilibrium critical thickness theory is solved rigorously and used to validate the geometrical critical thickness approximation in this context. This can readily be combined with strain-hardening to predict the behaviour for wires of different diameter and for wires of the same diameter but different grain size in excellent agreement with the experiment data. The results strongly imply that the physical principle of length scale plasticity, for the case where internal dislocation sources dominate, is the constraint that size puts on allowed dislocation curvature.
5:45 PM - GG7.11
Effects Of Point Defects On Near-Theoretical Strengths In Metals Observed During Nanoindentation Testing.
David Bahr 1 , Stefhanni Jennerjohn 1 , Marc Weber 2
1 Mechanical and Materials Engineering, Washington State University, Pullman, Washington, United States, 2 Physics, Washington State University, Pullman, Washington, United States
Show AbstractYield phenomena in metals at stresses near the theoretical shear strength is generally observed only when small volumes of materials are tested. Traditional methods of strengthening materials often focus on increasing the resistance to plastic deformation by decreasing dislocation mobility. In many of the rapidly developing metallic materials that exhibit enhanced strengths, such as multilayered metals and ultrafine grained metals, the limiting factor is likely the creation and multiplication of dislocations, rather than the motion of dislocations. The volumes tested may be on the order of 1000 nm (in the case of classical whisker testing), or as small as 10’s of nm’s in the case of very fine contact probes. In very fine volumes, the likelihood of encountering a dislocation is reduced, and instead the most likely defect of contact will be a vacancy in pure solids, or impurities in solution in less clean systems. In this presentation we will describe local nanoindentation experiments in Ni samples as a function point defect concentration. Indentations in (111) Ni single crystals with two different vacancy concentrations (approximately different by a factor of two as measured by positron porisometry) show the load (and stress) at which the yield point is statistically significant, approximately 50% higher on average for the lower vacancy concentration. However, the maximum shear stress in the distribution of defects in both materials is the same, as is the minimum, suggesting that the upper limit is based on the defect free material and the lower values are limited by spatial variations in the vacancy concentration. In addition, tests on polycrystalline Ni with variations in vacancy concentration suggest that these trends can be obscured by crystal orientation differences. In all cases the indentation stresses were based on finite element simulations of the exact tip used for the tests, and not the traditional Hertzian approximation, which leads to a difference of up to 40% in the maximum applied shear stresses.