Tantalum is a body-centered cubic crystal with high strength suitable for us under extreme conditions. In this talk we describe measurements of the lower bound on the total density of Geometrically Necessary Dislocations (GND) on individual slip systems of a tantalum crystal indented by a wedge. The GND content is measured by high-resolution electron backscatter diffraction (EBSD) with spatial resolutions of 2500 nm, 100 nm, and 20 nm. The multiple length scale measurements demonstrate that the GND density varies quasiperiodically, and the period of the GND variation is a characteristic length scale of crystal plasticity. The tantalum crystal deformed via twinning in the regions of the crystal that underwent the largest strain gradients. We interpret the deformation in this region from the context of a GND basis. The results give deep insight into the development of stress-strain constitutive relationships for elastic-plastic deformation in body-centered cubic metals.

In order to gain a deeper understanding of the mechanisms responsible for plastic deformation at the micron and sub-micron scale, the experimental investigation of the evolution of local strain fields and dislocation microstructure during deformation is of great interest. Therefore, specifically designed mechanical tests on single and oligocrystalline microsamples were performed and combined with SEM, EBSD, TEM and X-ray microdiffraction techniques. In the present work, microsamples were studied under different loading conditions: compression, bending, and torsion. The samples for bending and compression experiments were fabricated out of 1-4µm thick Ag thin films epitaxially grown onto Si wafer substrates. Via conventional cleanroom processing they were shaped into microbeams and micropillars. The size of the beams ranges from 10µm x 5µm up to 40µm x 20µm, whereas the pillars are 0,5µm up to 5µm in diameter. In both cases the load was applied using a nanoindenter system. Au wires having 15 to 60 µm in diameter were used for torsion experiments. In contrast to the compression and bending samples, the Au wires were polycrystalline and have been heat treated to form a pronounced bamboo microstructure.
To study the microstructural changes due to plastic deformation various methods with high lateral resolution were applied. The main tools for bending and compression in this context are EBSD and TEM. The micro-wires were cut by FIB at selected cross sections and the analyzed via micro Laue diffraction and EBSD. Comparative measurements of deformed an initial microstructures allowed both to display the distribution of the dislocation density and strain gradients and an estimation of their absolute values. The results will be discussed with respect to the influence of crystal orientation and loading condition on the evolution of local strain fields and dislocation microstructure.

Dislocations affect on electrical and optical properties of a semiconductor crystal and finally leads to detrimental degradation of devices. A great deal of efforts has been continued to understand details of electrical and optical properties of dislocations induced during growth process to achieve high yield and efficiency of devices. However, elucidation of intrinsic properties of dislocations, which can be introduced freshly by plastic deformation is far limited. Here, dynamic properties and related optical and electrical properties of dislocations in bulk GaN are summarized.
Dislocations in GaN are mobile at elevated temperatures higher than 1173K. An activation energy for dislocation motion was evaluated to be 2-2.7 eV in GaN. By plastic deformation, (a/3)[1120]-type dislocations on the (1100) prismatic plane were introduced.
Carriers were effectively passivated by plastic deformation. Near-band-edge (3.48eV) photoluminescence intensity decreased remarkably, which is attributed to the introduction of high-density non-radiative recombination centers. Induced fresh dislocations give rise to some luminescence peaks in 1.7-2.4eV, which implies formation of radiative recombination centers by the dislocations. Dislocation-related energetic levels were evaluated.
Optical absorption spectra of plastically deformed GaN show red-shift of the absorption edge, supporting a model of the Franz-Keldysh effect by the electric fields associated with charged dislocations (3e/c).
Local electrical conductivities along fresh dislocations were found in plastically deformed GaN. Scanning spreading resistance microscopy images showed many spots with high conductivity around the dislocations, showing that there is an electric conduction along dislocations. Current-voltage spectra evidenced a Frenkel-Poole mechanism for the conduction.

The collective dynamics of dislocations provides the physical foundation for plastic deformation processes in metals. Discrete Dislocation Dynamics (DDD) simulations are able to predict the evolution of the dislocation microstructure in great detail but are limited to small length scales, strains and/or dislocation densities, because their computational cost increases rapidly as systems enlarge.
To overcome this limitation, the Continuum Dislocation Dynamics (CDD) theory was developed which represents the kinematics of curved dislocation lines in terms of statistically averaged quantities (e.g. densities). In this approach the dislocation density is considered a function of the local dislocation line orientation - in case of dislocation motion by glide only, in each material point it becomes a function on the unit circle. CDD provides kinematically closed evolution equations for the densities and associated orientation distribution functions. To reduce the number of variables and arrive at a theory that is amenable to efficient numerical implementation it is, however, desirable to approximate the orientation distribution in terms of a finite number of moments, e.g. in terms of Fourier expansion coefficients or so-called alignment tensors. These define novel field variables for which CDD allows to derive a hierarchy of evolution equations. To relate the approach to more traditional classical ways of envisaging dislocation arrangements, we note that the lowest-order coefficient is the total dislocation density, the first-order coefficients contain the information about density and orientation of geometrically necessary excess dislocations, while the second-order coefficients embody information about preferred dislocation orientations (e.g. screw or edge or 60°) irrespective of sign.
CDD allows to derive, in a kinematically exact manner, an infinite hierarchy of equations for such field variables. In this paper, we discuss different approaches such as the maximum entropy method for condensing this hierarchy into a closed set of kinematic equations which are capable of characterizing the evolution of strongly anisotropic dislocation arrangements as encountered when dislocations pile up against extended obstacles (grain boundaries), in BCC metals deforming below the transition temperature, or in fatigue of FCC metals. We investigate numerically how CDD performs in these simulations and evaluate the consequences of different closure approximations by benchmarking the results of our numerical studies against data from DDD simulations.

In the dislocation plasticity of crystalline materials the interaction between dislocations and obstacles plays a main role in hardening. These obstacles may have different types, namely, obstacles of dislocation character, secondary phase precipitates and grain boundaries. We present here a review on the strengthening due to various obstacles such as nano-sized void, Cr precipitate, dislocation loop and compare it to the binary dislocation junction in bcc-Fe using molecular dynamics (MD) simulation. We then focus on detailing the formation and unzipping process and the strength of the <100> binary junction through interaction between two ½<111> dislocations of edge and screw character. It appears that under applied strain two intersecting ½<111> dislocations, one mobile edge and one immobile screw, form a <100> binary junction of mixed character in the glide plane of the mobile edge, while no constrain on the zipping direction is imposed from the three fold glide planes of the screw dislocation. The binary junction is then unzipped as the impinging edge dislocation bows around and moves away, which results in the formation of a screw dipole along its Burgers vector. The dipole eventually annihilates, which liberates the edge dislocation. Effects of temperature and strain rate on the unzipping of the junction are quantified by the critical release stress needed to detach the edge dislocation from the screw one. The critical stress decreases when the temperature increases from 10 to 300 K, whereas it increases with increasing applied strain rate, or dislocation speed. Comparison of the <100> binary junction strength with that of different nano-sized defects indicates that at low temperatures it is comparable to the coherent Cr precipitate, slightly softer than the void and much weaker than ½<111> and <100> dislocation loops. At the highest temperature considered, 300 K, all defects including the binary junction induce a similar hardening, within -0.1 to +0.1 (Gb/L).

In a large network, intersections of dislocations gliding on different slip planes can produce binary or multi-junctions. Depending on the material properties and active slip systems, dislocation junctions can influence strength and lead to blocking effects that may affect the overall plastic response. For hexagonal close-packed (hcp) crystals, the material-dependent c/a ratio (where c and a are the vertical and lateral lattice spacings, respectively) and the multiplicity of slip systems add even greater complexities in determining the junction properties. In this work, we develop an empirically-derived universal scaling parameter that can be used to predict the strength of junctions in any hcp crystal regardless of the differences in the initial junction configurations, slip systems, and material elasticity. First we examine the strengths of several representative binary junctions in stressed hcp crystals via a modified discrete dislocation dynamics simulator ParaDiS using linear dislocation mobility and isotropic elasticity. The different junctions are generated by intersecting dislocations along the edges of different primary and secondary slip planes including basal (0 0 0 1), prismatic {1 0 -1 0} and type I {1 -1 0 1} and type II {-2 1 1 2} pyramidal planes. Depending on the planes associated with the junction, pairs of Burgers vectors composing the junction are chosen from the set including =1/3<1 1 -2 0>, =<0 0 0 1>, and < a + c >=1/3<1 1 -2 -3>. The critical resolved stresses for breaking a junction are then determined by exposing the equilibrium junctions to an incrementally increasing applied stress field until the junctions are completely destroyed. Our results strongly suggest that the yield surfaces representing the junction strengths resemble those predicted by the classical line tension model with a universal scaling factor. This appears to hold true for all hcp crystals studied in this work. This implies that the contribution to the yield surface from elastic segment-segment interactions, which is not present in the line tension model, can be computed as a single scalar constant regardless of the differences in the initial junction configurations or the complex bowed-out shapes the dislocations take on just prior to the complete dissolution of the junction. We also found that junctions involving Burgers vectors with a component, such as type and type Burgers vectors, are significantly stronger than those involving only type Burgers vectors.

From the recent micro-pillar experiments, it is now known that the flow stress of metallic micro-pillars increases with decreasing sample size even in the absence of significant hardening by geometrically necessary dislocations or strain gradients. To understand size dependent plasticity, several models have been proposed, but the role of the dislocation sources in sub-micron sample is still under debate. In the present study, we make a three-dimensional, dislocation dynamics model to study collective dislocation behavior under compression in FCC micro-pillars. Following the molecular dynamics calculation on the dislocation nucleation rate, we consider the surface nucleation as a function of stress. Additionally, truncated dislocation sources can be observed to form through the collective dislocation interaction without any artificial pinning points. Following dislocation structure and stress-strain relation, we explore the governing mechanism for sample size effect for different sample size between the operation of truncated dislocation sources and dislocation nucleation at the surface. In addition, we study the size effects and the strain rate sensitivity on strength.

Dislocations move via the so-called Peierls mechanism with double kink formation and migration in tetrahedrally bonded semiconductors. Since first model proposed by Hirth and Lothe (1968), many theoretical and experimental studies of dislocation motion have been conducted macro- and microscopically, though even now there are some controversies on glide and shuffle set configuration, kink-collision and kink-collisionless regime, and energies for kink formation and migration. We investigated dislocation mobilities in Ge in terms of electrically active impurity effects on them.
Velocities of isolated 60-degree dislocations were evaluated in Ge doped with various kinds of impurities at elevated temperatures of the glide set regime. Donor impurity enhances and acceptor impurity retards dislocation velocity in motion. Neutral impurity has no effect on the velocity of the dislocations. The velocity of dislocations can be expressed by an empirically well-established equation as a function of stress and temperature.
The activation energy for dislocation motion varied dependent on the Fermi level given by the dopant type and its concentration and was highest in Ge doped heavily with an acceptor impurity as 1.95 eV for Ge heavily doped by Ga, 1.65 eV for undoped Ge, and 1.30 eV for Ge heavily doped by As. The results are attributed to the model that a kink of a dislocation has an acceptor level in the bandgap as Ev+0.15eV and the Fermi level governs that formation of a kink.

To make clear the origin of plastic deformation properties of Fe-Si alloy, it is essential to get a detailed understanding of interaction between single screw dislocation and a solute Si atom. Using atomistic modeling, we in this study investigated the interaction of a screw dislocation with a substitutional solute Si in Fe-Si alloy. First, we developed an embedded atom method (EAM) potential for Fe-Si interaction based on material properties obtained from the density functional theory calculations. Using the developed Fe-Si potential and a conventional Fe-Fe EAM potential, the interaction energy between the single screw dislocation and the solute Si atom in the bcc Fe-Si alloy was evaluated. The interaction is found to be attractive, and the interaction energy becomes larger as the Si atom approaches to the screw dislocation core. The attractive driving force acting between the screw dislocation and the Si atom means solid-solution resistance. Moreover, using nudged elastic band method, we also investigated the energy barrier for screw dislocation glide associated with double kink formation. It is found that a nearby existing Si atom facilitates double kink nucleation and, in consequence, reduces the energy barrier for screw dislocation glide when the screw dislocation approaches to the Si atom. The attractive interaction of screw dislocation with Si and the reduction of energy barrier for dislocation glide suggest that solute Si contributes to solid-solution hardening and softening in Fe-Si alloy.

Recent experimental studies of severely deformed pearlite reveal C concentrations in ferrite far above equilibrium values [1]. Apart from thermodynamic arguments [2], it was suggested that the accumulation of C in the ferritic layers is driven by the co-migration of C atoms with mobile dislocations [1]. However, possible atomistic processes are unknown so far.
In the present study, we use the nudged elastic band method and molecular static calculations based on a semi-empirical EAM potential to scan the energy surface of the effective migration barrier of a C atom in the vicinity of a screw dislocation in bcc Fe. We show that the diffusion along the dislocation line (i.e., pipe diffusion) is energetically unfavorable. Further, we reveal that an intermediate region between core and far-field exhibits very low diffusion barriers giving rise to fast C diffusion channels. These channels turn out to have only components aligned with glide directions suggesting an atomistic mechanism for carbon drag by mobile screw dislocations.
[1] Li, Y.J., et al., Acta Materialia, 2011. 59(10): p. 3965-3977.
[2] Nematollahi, G.A., et al., Acta Materialia, 2013. 61(5): p. 1773-1784.

The interactions between a specified numbers of ‘positive&’ / ‘negative&’ edge dislocations and Σ11symmetrical tilt grain boundaries in two bi-grain models of copper have been studied using the quasi-continuum method. The mechanisms of both interactions in representative loading stages are analyzed in terms of the evolution of grain boundary (GB) configurations and Burgers vector conservation. The pile-up of incoming dislocations has a remarkable influence on both “positive” and “negative” interactions, and can activate dislocation transmission at smaller external loadings. Critical stress analysis for relatively easier dislocation transmission in “negative” interactions reveals that they depend on the ratio of total shear stresses on the incoming and outgoing slip planes and the ratio of total normal and shear stresses on the outgoing slip plane. An analysis of the Burgers vectors of residuals produced from dislocation/GB interactions shows that GBs impeding dislocation motion have larger residual values.

We report on numerical calculations of the spatial structure
of the critical modes responsible for the initial dislocation
nucleation under nano-indentation of single crystal thin films
in two dimensions (2D). Previous work has shown that the
nucleation process is governed by vanishing of energy
associated with a single normal mode that exhibits a
lengthscale that scales in an anomalous way with the
geometrical loading parameters (indenter radius and film
thickness).Here, we show that these scalings that were
previously observed for a single particular crystallographic
orientation in a two dimensional Lennard-Jones system are
generic with respect to the lattice orientation and
interatomic potential.We also show nucleation of dislocation
dipoles in an idealized crystal with pure hookean springs between nearest neighbors follows the same scaling laws
as other non-linear interaction potential crystals. This shows
that the geometry of the lattice and indenter play much more
significant roles than the interatomic interactions in the
instability. We will also discuss our work on three
dimensional (3D) EAM models of Al.

Experimental observations of enhanced activity of the pyramidal screw dislocations in MgY alloys suggest that the pyramidal slip plays a key role for the enhanced ductility in these alloys. We investigate the stable core structure of the screw dislocation in Mg and its mobility in several slip directions, using first-principles calculations. We show that the core can spread in both (-1011) and (2-1-1-2) planes, and the Burgers vector of the partial dislocations are /2. The corresponding stacking fault energy in both cases are almost the same. We also show that the Peierls energy barrier for the partial dislocation slip is modestly low.

Electron backscatter diffraction (EBSD) and electron channelling contrast imaging (ECCI) are two complementary diffraction techniques used to characterize microstructures of crystalline materials in a scanning electron microscope (SEM). EBSD allows the accurate measurement and mapping of crystal orientations and crystallographic phases. ECCI in contrast, is applied to observe individual lattice defects like dislocations, stacking faults and nano twins in the same manner as in TEM dark field images. Furthermore, ECCI can be used to image elastic strain fields with high accuracy. As in TEM optimum lattice defect contrast is obtained only if the sample is oriented in so-called two-beam conditions, when only one set of crystal lattice planes is in Bragg position with respect to the primary electron beam. We call the resulting technique ‘ECCI under controlled diffraction conditions&’, cECCI. To obtain proper diffraction conditions one can either use electron channeling patterns (ECP) or one has to calculate the position from the orientation determined by EBSD. The first option is available only on very few modern microscopes and is strongly limited by the large spatial resolution of ECP. The second option is therefore the much more versatile selection. We use the computer program TOCA [1] to simulate, based on EBSD-measured orientations, ECPs for the position under observation. From the simulated patterns the correct tilt angles are determined and ECC can be observed [2]. Figure 1 shows the arrangement of the different techniques inside of the SEM. Since ECCI has a very high angular sensitivity (the backscattered electron intensity obtained from a given crystal position may change from maximum to minimum over 0.5° of lattice tilt) it is very important to control the tilt and rotation angles and observation position in a very accurate manner. To this end we constructed a small, highly accurate 5 axes sample stage with the following features (see figure 2 for a photo of the stage):
(i) Comprises x,y,z, eucentric tilt and rotation axes. The translation axes have an accuracy of 0.25 nm, the angular axes of 0.1°. The angular axes are encoded.
(ii) Enables operation under short working distance, down to approximately 7 mm.
(iii) Keeps the sample in perfect eucentric position, even at large tilt angles
(iv) Reaches tilt angles of up to ±90° and provides unlimited rotation.
This stage has been mounted in a Zeiss field emission gun SEM (XB1540) with Gemini column which, due to its small beam convergence at high beam current, is excellently suited for this technique. The sample can be easily and accurately moved between the EBSD position (sample at 70° tilt) and ECCI position (sample at up to ±25° tilt) whereby keeping the observation position well in focus. Figure 3 shows an ECCI image of dislocations in a steel sample obtained in the indicated manner before and after straining the sample in an ex-situ experiment.

Multiscale dislocation dynamics plasticity (MDDP) method is used to investigate the evolution of dislocation microstructure in copper single crystals subjected to low cycle fatigue loading. Fully reversed and alternating plastic strain simulations are carried out at strain amplitudes ranging from 1×10-4 to 5×10-3. The effect of number of cycles applied, loading history, strain amplitude and crystal orientation on the stress-strain characteristics and the evolution of the dislocation substructure are studied in detail. The analysis of the dislocation network reveal that: 1) dislocation dipoles are prominent elements of the microstructure in crystals oriented for single slip, at the early stages of low cycle fatigue and they are formed in a broad spectrum of dipole orientations, 2) dipoles undergo frequent zipping and unzipping during the first few cycles until they are trapped into a stable configuration characteristic of the dipole height and dipole orientation. The cyclic hardening curves show that the flow stress and hardening rate increases with the dislocation density stored in the material, in agreement with the literature data. The analysis of various dislocations interactions and the obstacles that are produced, have been carried out to understand dominant that control the flow stress during low cycle fatigue of single crystals.

The development of texture and orientation gradients is studied in copper and zirconium. Tensile tests were performed with 3D high energy diffraction microscopy (HEDM) and computed tomography, which permitted orientation maps to be acquired at different levels of strain up to a maximum of about 15%. Comparing the measured lattice reorientation in copper to that calculated with an FFT-based crystal plasticity model shows that more dispersion exists than can be accounted for by the interactions between grains. The development of orientation gradients is strongly heterogeneous. Some grains form large gradients, in part because some exhibit fragmentation. Gradients tend to be strong near boundaries at small strains. At larger strains, however, the correlation between gradients and boundaries becomes more complex. Crystal plasticity modeling can account for some of these developments but there are also significant divergences with experiments, as has been noted by others. Zirconium twins in addition to slip. Although some twins are clearly stress-driven (i.e. correspond to a high Schmid factor), others have such low (or negative) Schmid factors that they can only be the result of coupling to slip activity, perhaps across grain boundaries. Full field calculation of elastic stress shows a spread in resolved stress on any given (twin or slip) system but no re-ordering of expected twin variants. Finally, some ideas will be presented for how dislocation dynamics simulations might be feasible for polycrystals.

A polycrystalline alpha-iron sample was plastically deformed under uniaxial tensile stress at room temperature and a quasi-static strain rate. The microstructure of the deformed sample was analyzed using electron backscatter diffraction (EBSD). In addition, analysis employing a dislocation density based crystal plasticity finite element (CPFE) simulation was conducted using the initial measured sample texture. Both the experiment and the simulation results indicated localized plastic strain and dislocation patterning, which were controlled by the individual crystallite orientations and the grain boundary effects. The results also revealed that the level of concentrated stress at the grain boundaries depends on misorientation of the interface. Regions near grain boundaries and triple junctions had higher hardening effects than the grain interiors in general.

Plastic deformation processes in polycrystalline materials are complex. Discrete dislocations accommodate plastic strain and their movement is guided not only by resolved components of the macroscopic stress state (Type I), but also local effects between grains (Type II) and inside grains (Type III). The evolution of dislocation networks and stress perturbations is of great interest to understand mechanical performance and failure, especially in relation to interfaces such as grain boundaries. These dislocation networks continue to evolve as a function of plastic strain, in an incremental fashion guided by local back stresses from interfaces and other dislocation structures (i.e. internal Type III stresses). The generation of stored dislocation networks can be quantitatively and qualitatively characterised by examining resultant lattice curvatures mapped with high angular resolution electron backscatter diffraction (HR-EBSD). Dislocation content can be related to curvature through the Nye tensor [1].
We have assessed spatial patterning of dislocations in polycrystalline copper with increasing levels of uniaxial applied plastic strain (0, 6, 10, 25, 40%). The size and scope of the dislocation density data is statistical in nature, with respect to microstructural features. We observe patterning of dislocation density with hot spots of high dislocation density accumulating near some, but not all, grain boundaries. Dislocation density cold spots tend to remain towards the grain interiors. We have related stored dislocation densities with stress patterning, also measured with HR-EBSD, and note strong correlations of stress hot spots with some, but again not all, grain boundaries. We observe a strong correlation between stress hot spots and areas of high GND density. This data is clearly of interest to the modelling community and can be used to link between length scales and validate models (e.g. dislocation dynamics and crystal plasticity based finite element/spectral methods).
[1] J.F. Nye Acta Met (1953) vol. 1 issue 2

Formulating a predictive understanding of deformation in ductile materials represents a scientific grand challenge involving the statistical dynamics of dislocations and dislocation densities interacting and evolving through complex, heterogeneous microstructures on mesoscopic length scales. We have used submicron resolution (0.5 µm) 3D x-ray microscopy (3DXM) measurements of local lattice rotations over a ~25µm x 25µm x 10µm volume in 1% compression-deformed single-crystal Cu and discrete dislocation dynamics simulations of compression in a nominally 10µm x 10µm x 10µm volume of Cu to test the ability to predict initial-stage ductile deformation in Cu. Direct quantitative comparisons have been made between 3DXM measurements performed using the polychromatic 3D x-ray microscopy facility on the Sector 34-ID-E beamline at the Advanced Photon Source and discrete dislocation dynamics simulations using the microMegas discrete dynamics code, coarse-grained to the 0.5 µm resolution of the 3DXM experimental measurements. These absolute comparisons between experiment and simulation will be discussed in terms of the spatial distributions of local lattice rotations, spatially-resolved geometrically necessary dislocation densities, and spatial correlations of the geometrically necessary dislocation densities. Work perfomed in collaboration with J. Tischler (APS), M. Mohamed (present address: KAUST), and A. El-Azab (Purdue University). Research supported by the Department of Energy, Office of Science, Materials Science and Engineering Division and the Center for Defect Physics an Energy Frontier Research Center. The Advanced Photon Source is supported by the Department of Energy, Scientific Users Facility Division.

Coherent x-ray micro-diffraction was used to detect and count a limited number of phase defects (stacking faults, SFs, left in the crystal after the glide of partial dislocations) introduced by deformation on InSb single-crystalline micro-pillars in the early plastic regime. A series of diffraction patterns was recorded scanning the coherent x-ray micro-beam along the axis of the pillars: peak splitting is observed in the diffraction pattern associated to the top region in agreement with the presence of a few SFs that are located in the upper part of the deformed pillars. In order to interpret the experimental observations, simulations of coherent diffraction patterns were performed considering SFs randomly distributed in the whole illuminated volume or concentrated in its central region; they show that not only the number of defects but also the size of the defected volume influences the maximum intensity of the pattern.
Similar diffraction measurements were performed in-situ, during compression, in order to detect the first lattice defects and determine at which stress the first events of the plastic deformation appear in InSb micro-pillars.
This study opens new perspectives for the study of the plasticity in micro-objects and the associated size effects.
V.L.R. Jacques, S. Ravy, D. Le Bolloc&’h et al., Phys. Rev. Lett., 106, p065502 (2011)
L. Thilly, R. Ghisleni, C. Swistak, J. Michler, Phil. Mag., 92, p3315 (2012)

We have used cross-correlation-based analysis of EBSD patterns [1, 2] to map variations of elastic strain and lattice rotation tensors in a variety of deformed materials. Measurement of the crystal orientations and knowledge of the single crystal elastic constants enable calculations of stress, while the lattice rotations allow a lower bound estimation of the geometrically necessary dislocation content. A characteristic of all these stress maps is that they show localized single pixel spikes of extremely high stress values. Data quality metrics indicate that these points cannot simply be explained as errors in the analysis. We estimate the measurement volume as being approximately 20 nm wide by 60 nm long by 20 nm deep (1.2x10⁴ nm³) so that the diffracting volume is smaller than the expected average dislocation spacing. Thus we ascribe these intense stress peaks to discrete dislocations distributed within the material coupled with the highly localized nature of the EBSD measurement.
To test this hypothesis we have examined the form of the stress probability distributions. These show Gaussian like-central peaks but significantly depart from this at high stress where a stress to the minus third power asymptote is found. This is consistent with the one over distance squared dependence of the stress field near a dislocation line as demonstrated theoretically by Csikor and Groma [3] in their analysis for X-ray peak broadening. We make quantitative comparison between the 1/σ³ tails of the measured stress distributions and stresses expected for simple uniform distributions of dislocations at the spacing implied by the measured geometrically necessary dislocation density. Results from Cu strained in tension to different strains illustrate the increase in the strength of the tails to the stress distribution with increased dislocation content. Measurements from other systems including rolled steels and GaN extend the analysis to higher and lower dislocation densities.
[1] Wilkinson, A.J., G. Meaden, and D.J. Dingley, High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity. Ultramicroscopy, 2006. 106(4-5): p. 307-313.
[2] Britton, T.B. and A.J. Wilkinson, High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations. Ultramicroscopy, 2012. 114: p. 82-95.
[3] Csikor, F.F. and I. Groma, Probability distribution of internal stress in relaxed dislocation systems. Physical Review B, 2004. 70(6).

The MAX phases have been classified as kinking nonlinear elastic (KNE) solids because fully and spontaneously reversible stress-strain loops, that are strain rate independent, form on cyclic loading. The operative micromechanism believed to be responsible for KNE was postulated to be incipient kink bands (IKB). The latter are concentric dislocation loops that form parallel to the basal planes. Here we present, for the first time compelling experimental results obtained on textured coarse-grained Ti₂AlC in situ loaded with the basal planes either normal or parallel to the loading axis. Fully and spontaneously reversible microstrains loops as well as the width of some peaks where observed from the neutron diffraction measurements. Analysis of the results is not only totally consistent with the existence of IKBs but as important also sheds important light on their nucleation and growth. The implication of this work to the deformation of other KNE solids in general and layered solids in particular cannot be overemphasized and will be discussed in detail.

Recently, fully reversible dislocation motion was postulated to result in hysteretic nanoindentation load-displacement loops in plastically anisotropic solids. Since microcracking can also result in hysteretic loops, herein we define a new parameter, reversible displacement, RD, readily obtained from load-displacement curves that can differentiate between the two. For C-plane LiTaO₃ surfaces and 5 other plastically anisotropic solids, the RD values were found to either increase initially or remain constant with cycling. In contradistinction, for glass and A-plane ZnO, where energy dissipation is presumably due to microcracking and irreversible dislocation pileups, respectively, the RD values decreased continually with cycling.

With the advance of technology the characteristic size of the microstructure of crystalline materials reached the submicron level. As a consequence, the role of boundaries (sample surface, grain boundary, etc.) became even more important than earlier. So, to model the plastic response of submicron sized sample it is crucial to determine the dislocation distribution near the boundaries.
In the first part of the paper a continuum theory of the time evolution of an ensemble of parallel edge dislocations with uniform Burgers vectors is presented. Since the dislocation-dislocation interaction is scale free, apart from the dislocation spacing the phase field theory of an uniform edge dislocation system cannot contain any length scale parameter. It is argued, in a continuum theory dislocations this unique feature largely determines the possible terms caused by dislocation-dislocation correlation.
It is shown, to recover the dislocation distribution near boundary obtained by discrete dislocation
dynamics simulation one has to step beyond the simple gradient type "back stress" assumption commonly used in earlier models. One has to introduce appropriate higher order derivatives with corresponding boundary conditions.
In the second part it is discussed how to generalize the theory for 2D dislocation systems with more than one type of dislocations.

The occurrence of size-effects in small scale plasticity challenged classical constitutive equations of plasticity and stimulated the development of strain gradient theories during the late 1990s through the early 2000s. However, strain gradient theories themselves were soon challenged through the discovery of scale dependent effects in macroscopically homogeneous deformations, as, e.g., in uniaxial compression tests of micro-pillars. These effects are typically ascribed to dislocation source limitation or dislocation starvation, i.e., to essentially kinematic effects on the dislocation level. The representation of such effects in continuum plasticity therefore requires a theory based on the kinematics of evolving dislocation systems. Based on a higher dimensional approach [1] we recently adopted the concept of higher order alignment tensors for a more detailed representation of the dislocation state [2] and its evolution.
In the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order dislocation density tensor is a symmetric second order tensor characterizing the orientation distribution of the dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature [3]. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions [3] but handle line length changes and segment reorientation consistently. Additionally the equations conserve the number of dislocations as is inevitable for describing effects stemming from dislocation source limitation. Small numerical examples will highlight the effects captured by the current theory.
References
[1] T. Hochrainer, M. Zaiser and P. Gumbsch. A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation Philos. Mag., 87, 1261-1282 (2007)
[2] T. Hochrainer. Higher order alignment tensors for continuum dislocation dynamics. MRS Proceedings, 1535, mmm2012-a-0343 doi:10.1557/opl.2013.451. (2013)
[3] A. Arsenlis et al. On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals J. Mech. Phys. Solids 52, 1213-1246 (2004)

The great demand for advanced materials and well-defined microstructures has led to an increasing effort towards a proper description of the motion of dislocations as the cause of plastic deformation. In the last few years, several dislocation based continuum theories have been introduced. Only recently have rigorous techniques been developed for performing meaningful averages over systems of moving, curved dislocations, yielding evolution equations for a higher order dislocation density tensor, see [1]. A numerical implementation and some benchmark tests of a continuum theory for dislocation dynamics (CDD) are discussed in [2].
In order to reduce the computational complexity of the theory, a simplified theory (sCDD) has been developed, which more readily allows for numerical implementation, useful for describing larger systems of dislocations. In order to construct a self-consistent implementation, several issues have to be resolved including calculation of the stress field of a system of dislocations, coarse graining, and boundary conditions.
While accurate solutions have been found for one dimensional systems, fully two- and three-dimensional systems increase the complexity of the system. In order for the behavior of the continuum dislocation density evolution to be accurately predicted, the continuum density must be properly understood as an ensemble average over discrete distributions.
In this contribution, an overview of the one-dimensional results compared with both analytic solutions and discrete simulation is given. Then, the results for a distribution of one-dimensional glide planes in a two-dimensional elastic medium are presented and several aspects of numerical homogenization are analyzed. Using comparisons with Discrete Dislocation Dynamics (DDD) in a few simple systems, the multi-component stress field which must be considered for dislocation density motion is derived and discussed.
REFERENCES
[1] HOCHRAINER, T.; ZAISER, M.; GUMBSCH, P.: A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation. In: Phil. Mag. 87 (2007), S. 1261-1282
[2] SANDFELD, S.; HOCHRAINER, T.; GUMBSCH, P.; ZAISER, M.: Numerical Implementation of a 3D Continuum Theory of Dislocation Dynamics and Application to Microbending. In: Phil. Mag. 90 (2007), p. 3697-3728.

The purpose of the current work is the formulation of thermodynamic
models for the energetics and kinetics of dislocation flow and dynamics
at large deformation. In particular, this is carried out here in the context
of a split of the rate of inelastic local deformation into compatible and
incompatible parts. This induces in turn a split of the inelastic flow rule
and total dislocation flux into such parts. On this basis, the energetics
and kinetics of the compatible part are modeled as relaxational in nature,
resulting in a thermodynamic model of Allen-Cahn type for this part. On the
other hand, the incompatible part determines the evolution of dislocation
tensor through a corresponding transport relation for this tensor. In the
context of irreversible thermodynamics, a thermodynamic flux-force model
is formulated for the dislocation flux with the help of a generalized "chemical"
potential thermodynamically conjugate to the dislocation tensor. Together
with the transport relation, this results in a thermodynamic model of the
Cahn-Hilliard type for the dislocation tensor. Examples will be given.

Continuum dislocation dynamics(CDD) is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. The higher dimensional theory may be reformulated in an inifite hierarchy of evolution equations of symmetric traceless tensors, the components of which are obtained as Fourier coefficients of the density and the curvature density. Low order closure approximations are needed to arrive at tractable systems of equations per slip system. Already the lowest order closure approximation, which is based solely on the total dislocation density, the Kröner-Nye tensor and a total curvature density, is capable of describing source limitation, line length increase and dislocation fluxes.
The according evolution equations define a dislocation flux based crystal plasticity law, which we implement as a materials subroutine for a finite element program. Due to the flux terms this plasticity law is inherently non-local. Because the total curvature is a conserved quantity in the theory (its integral being the total number of dislocations on the slip system) the time integration requires using conservative numerical schemes. We present a discontinuous Galerkin method for integrating the time evolution of the dislocation state. The evolution of the dislocation state at the same time determines the current plastic slip rate via Orowan&’s law to be used in a crystal plasticity framework solved by FEM. We demonstrate that the theory reproduces effects of dislocation starvation and dislocation curvature which are beyond the scope of phenomenological non-local theories which neither satisfy source limitation nor consider dislocation curvature. The simulations are compared to according experiments and 3D discrete dislocation simulations of, e.g., micro-pillar compression tests and thin film deformation.

We present a continuum model for dislocation dynamics in one slip plane incorporating the operation of Frank-Read sources. At the continuum level, the distributions of dislocations and the plastic flow are described by an evolution equation of a coarse-grained disregistry function. The operation of Frank-Read sources, which is the major dislocation multiplication mechanism in the plastic deformation processes, is incorporated in the continuum framework by source terms of the evolution equation whose exact form is derived from the discrete dislocation dynamics model. The Peach-Koehler force for the motion of dislocations at the continuum level contains both the long-range force of dislocations and a local force due to the dislocation line tension effect, which are also derived accurately from the discrete dislocation dynamics model. Simulation results using our continuum model agree with results of theoretic predictions, analytical formulas, and discrete dislocation dynamics simulations for the operation of Frank-Read sources and dislocation loop pileups at grain boundaries in two dimensions. We also derive analytical formulas for the Hall-Petch relation in two dimensions without adjustable parameters for dislocation loop pileups within a rectangular grain with any aspect ratio. This obtained analytical formula is validated using our continuum model and discrete dislocation dynamics simulations.

The flow stress in plasticity of metals and alloys is defined by the interaction of dislocations with obstacles and with other dislocations. The various types of obstacles define the strengthening mechanisms that operate in such materials. An essential question when developing constitutive equations is how the contributions to the flow stress of the various mechanisms should be superimposed. This pertains to inferring both the flow stress and its rate sensitivity from the mechanism-level activation behavior and stress production. This talk will review results linking the motion of individual or groups of dislocations to the superposition rules. The discussion will refer to both the thermal and athermal components of stress.

Low ductility in Al alloys is a major barrier to their replacement of steels in automotive and other applications where failure by localization limits component design. Low ductility in Al-Mg alloys has long been associated with Dynamic Strain Aging - the material is stronger at lower strain rates, which encourages localization and instabilities - but no quantitative or predictive models exist. Here, we present a hierarchical, mechanistic, multiscale model that quantitatively predicts the ductility . The components of the model are:
(1) the atomic-scale mechanism of cross-core diffusion;
(2) the effect of solutes and cross-core diffusion on dislocation strengthening;
(3) a full thermokinetic model for the evolution of the plastic strain versus stress and time.
The model quantitatively explains the scope of steady-state flow behavior as a function of strain-rate, plastic strain, temperature, and alloy composition in Al-Mg alloys, with nearly all inputs coming from quantum, atomistic, or dislocation-level computations. The observed reduction in ductility of Al-Mg 5182 alloys at room temperature and strain rate of 10-3/s is predicted in very good agreement with experimental studies. The ductility reduction is thus tied directly to atomistic features of the material behavior. The model is then used to design new Al alloy compositions that have higher ductility but the same yield and hardening behavior of the currently used alloys.

Hydrogen embrittlement of vital structural materials, such as high strength steels and nickel-based alloys, is often characterized by grain boundary decohesion leading to low-toughness intergranular fracture. In this study, nanoindenation and scanning probe microscopy (SPM) were used to characterize slip transfer across high- and low-energy grain boundaries in nickel (a model system for engineering alloys) before and after hydrogen charging. Both random boundaries (high-energy) and recrystallization twins (low-energy) were identified for indentation using electron backscatter diffraction (EBSD). Nanoindentation induced local deformation along grain boundaries, producing material pile-up and slip steps; thermal hydrogen-charging alters the observed materials response to local deformation. Additional indentation within specifically oriented grains indicates that hydrogen charging reduces modulus and increases hardness. Coupled nanoindentation and SPM investigations provide a unique, local method for analyzing the effect of hydrogen on dislocation plasticity as a function of grain boundary type, which can be used to develop grain boundary engineered materials. Part of this work was supported by Sandia National Laboratories, a Lockheed Martin Company for USDOE NNSA under contract DE-AC04-94AL85000.

One outstanding technological problem yet to be solved is the localization and failure of high-strength steel alloys due to hydrogen embrittlement. Hydrogen atoms affect the dislocation core causing the plastic deformation to localize and thus to decrease the material capacity for plastic deformation. Better understanding of the role of hydrogen will lead to reliable computational models that incorporate hydrogen effects and diffusion through dislocation-densities evolution laws. Here we present large scale molecular dynamics simulations of the dislocation-density evolution and surface morphology in pillar like iron nano-crystals. Several nanopillar sizes are modeled. An initial dislocation network is introduced using the anisotropic displacement field of the dislocations. Hydrogen atoms with different concentrations are randomly distributed in the crystals. The interrelated effects of size, initial dislocation-density, loading direction are investigated relative to the hydrogen concentration. The effect of hydrogen concentration on yielding, retention of dislocations, and the morphology of surface slip is investigated.

It is know that hydrogen and helium atoms deteriorate mechanical properties of metallic materials and cause serious metal fatigue in some cases. The mechanical properties of materials strongly depend on the existence of dislocations and their motions. Thus the effects of hydrogens and heliums on dislocation motions are of importance for clarifying the hydrogen/helium effects on the mechanical properties. However, since hydrogens and heliums are small and mobile, it is not easy to observe their effects on dislocaitons directly in experiments. So simulation studies have been done, such as quantum mechanical (QM) studies using density functional theory and classical mechanical (MM) studies using molecular dynamics. But QM approachs have limitations of its computational cost and can not treat wide elastic field around dislocation, and it is difficult for the interatomic potentials used in MM studies to reproduce precise atomic configurations, etc. Therefore, we have adopted a QM/MM method which uses QM method to dislocation core and MM to surrounding regions. Using the nudged elastic band (NEB) method combined with the QM/MM method, we have evaluated the migration barriers of screw dislocation with or without hydrogen and helium on its migration path. We have concluded from the QM/MM resutls that hydrogens can enhance or diminish the dislocation migration depending on their position, and heliums act as pinning centers for screw dislocations.

Dislocations are a common type of defects that significantly influence many mechanical phenomena such as plastic deformation, crystal growth, morphology, or diffusion of materials. While dislocations have been well studied for simple crystalline structures such as pure metals, semi-conductors, ionic materials, and binary oxides, there is very limited knowledge on such defects in complex layered oxides. In this work, we study the mechanisms and the influences of screw dislocations in tobermorite mineral, which is a complex layered oxide material serving as a natural analog of Calcium-Silicate-Hydrate (C-S-H) gel. The latter is the principal source of strength and durability in concrete.
We use a cluster-based approach combined with atomistic simulations to investigate the screw dislocation along the interlayer direction of tobermorite. An analytical solution of the sextic theory regarding anisotropic materials was implemented to obtain the elastic displacement field. The nonlinear deformations around the core dislocation were accurately captured by atomistic simulations. The final core has a complex 3D structure involving dramatic spiral displacements as well as formation of defected silicate chains resulting from the screw dislocation. Dislocation displacement map (DDM) indicates an ellipsoid non-planar spreading of the dislocation core extending about in 40 Å the [100] direction and 20 Å in the [010] direction. This analysis illustrates a low mobility of [001] screw dislocation in tobermorite, since any potential movement will inevitably involve silicate chain breakage. After fitting the atomistic data to classical screw dislocation theories, the core radius is found to be 14.3 Å with a core energy of 53.7 eV/Å. This formation energy and the above observation could be used to compare and predict the prevalent defects along different directions in tobermorite, thus providing fundamental insights on deformation mechanisms governing the mechanical responses in C-S-H phases.

Commercial purity (CP) Ti alloys are an attractive class of materials for a range of engineering applications, owing to their excellent corrosion resistance, lightweight and formability. A characteristic feature of CP-Ti alloys is the large changes in mechanical properties that result from relatively small variations in impurity content. Two separate mechanisms have been proposed for the effect of oxygen impurities on the mechanical properties and deformation of Ti: (i) The first is associated with the short-range-ordered (SRO) oxygen clusters or precipitates. (ii) The second effect is associated with the change of dislocation core structure in Ti-O solid solution. Recently we have run a systematic series of in situ TEM mechanical tests on Ti materials with various oxygen concentrations, where we have quantitatively measured and characterized the slip behavior in solid solution and the interaction of dislocation with oxygen precipitates. Specifically, in situ tensile and compression tests were performed to investigate the precipitation hardening effect and solid solution strengthening effect separately. The change of dislocation core structure due to oxygen interstitials and SRO oxygen clusters was characterized by using high-resolution aberration-corrected STEM. It was found that while both hardening effects exist, the change in the solid solution strengthening effect with increasing oxygen concentration is much more significant.

Dislocations and metallic impurities are two of the principal performance-limiting defects in multicrystalline silicon (mc-Si) solar cells. In particular, their interaction - the decoration of dislocations with metallic impurities - has been found to convert clean, electrically inactive dislocations into highly recombination-active extended defects [1], therefore decreasing minority carrier lifetime. In addition, metal impurities in highly dislocated regions are not easily extracted from the wafer bulk during standard external gettering steps [2], thus material performance degradation has been observed in heavily dislocation regions after high-temperature processing [3].
In mc-Si solar cells, direct evidence of high concentrations of copper and iron at recombination-active dislocations was recently found through synchrotron-based spatially resolved nano-probe X-ray fluorescence microscopy (mu;-XRF) [4]. However, the chemical state of these metals remaining at recombination-active dislocations after solar cell processing - second-phase precipitate or high-concentration cloud of solute atoms - is still unknown.
In this contribution, we detect and identify the elemental nature of metals decorating recombination-active dislocations clusters in phosphorus-gettered mc-Si samples. We use synchrotron-based spatially resolved mu;-XRF to detect metal clusters and, subsequently, X-ray Absorption Near Edge Spectroscopy (XANES) is performed to identify the chemical state of the metals via comparison with reference spectra. The knowledge of the chemical state of the decorating metals in the solar cell will help determine the limitations of standard gettering processes in highly dislocated regions of mc-Si, guiding the development of advanced processing schemes to improve the extraction of metal impurities from these regions, thus improving solar-cell performance.
[1] Kveder et al., Physical Review B, 2001, 63, 11520
[2] Bentzen et al., Journal of Applied Physics, 2006, 99, 093509
[3] Geerligs et al., Journal of Applied Physics, AIP, 2007, 102, 093702-093702
[4] Bertoni et al., Energy & Environmental Science, 2011, 4, 4252-4257

The motion of dislocations controls crystalline plastic behaviour, and many other mechanical properties besides. In the absence of stochastic effects, dislocations with an edge component are topologically constrained to move in the glide plane, containing their Burgers vector and line direction. This is in spite of the fact that the mechanical (Peach-Koehler) force acting on the dislocation can have components both in and out of the plane. Motion perpendicular to the glide plane is known as climb, and proceeds by the absorption and emission of point defects. As such, it is strongly dependent on the local concentration of point defects, their migration behaviour, and temperature. Climb thus necessarily occurs on a longer timescale than glide, and impacts long-time, high-temperature phenomena such as creep. Climb is generally held to be mediated by vacancy bulk diffusion [1-3] -- as a vacancy&’s formation energy is considerably less than an interstitial&’s, one would expect the thermal vacancy concentration to be most significant. This assumption no longer holds under irradiation, where supersaturations of both vacancies and interstitials are created during the damage cascade.
In this work, we investigate the effects of irradiation on the climb of an edge dislocation. A stochastic simulation methodology based on Langevin dynamics [4,5] is developed, including the effects of both interstitials and vacancies, as appropriate for high-dose radiation environments. The situation is complicated by the fact that interstitials, particularly crowdions in bcc metals, diffuse in a very different manner from vacancies: they have extremely low migration barriers along the <111> directions [6], and as such exhibit fast, directional diffusion compared with the slow, isotropic behaviour of vacancies. Some consequences for the design of high performance steels for advanced nuclear applications are discussed.
[1] Hirth, J.P. and Lothe, J., “Theory of Dislocations” (R.E. Krieger, U.S., 1991).
[2] Mordehai, E. et al, “Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics”, Phil. Mag. 88 (6) 899 (2008)
[3] Bako, B. et al, Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion, Phil. Mag. 91 (23) 3173 (2011)
[4] Dudarev, S. L. et al, “Langevin model for real-time Brownian dynamics of interacting nanodefects in irradiated metals”, Phys. Rev. B 81 224107 (2010)
[5] Swinburne, T. D. et al, “Theory and simulation of the diffusion of kinks on dislocations in bcc metals” Phys. Rev. B 87, 064108 (2013)
[6] Fitzgerald, S.P and Nguyen-Manh, D. "Peierls potential for crowdions in the bcc transition metals", Phys. Rev. Lett. 101,115504 (2008)

Local hydride formation around dislocations induces stress-shielding effects and has been recently shown to be the underlying mechanism for hydrogen-enhanced local plasticity (HELP) [1]. The method employed in this study is a hybrid approach of Molecular Statics and Monte Carlo to correctly capture long-range elastic interactions. While this approach allowed a highly realistic description of the complexity of this mechanism, it is computational very demanding preventing a systematic study e.g. at different temperatures, H partial pressures or materials. We have therefore developed an analytical model that accurately reproduces all details of the atomistic calculations such as e.g. shape and size of the nano-hydrides but reduces the computational effort by 4 orders of magnitude. The proposed approach uses as input atomistic data only and uses a self-consistent approach to compute the binding energies of hydrogen around the dislocation. As an example, we discuss nano-hydride formation around fcc Ni edge dislocations. The onset of nano-hydride formation and with it the activation of the HELP mechanism is predicted through a parametric study of the hydride size as a function of temperature and bulk hydrogen concentration. Additionally, local hydride formation around dislocation loops are studied within the context of nano-indentation experiments. Our results show that hydrogen interaction substantially lowers the line energy of dislocation loops and leads to a decrease in the critical stress required for homogenous dislocation nucleation (HDN). Based on this model we are able to quantitatively predict the decrease in "pop-in" stress observed in nano-indentation experiments.
[1] Pezold J, Lymperakis L, Neugebauer J. Acta Mater 2011; 59:2969

Recent studies have highlighted the strong anisotropic behavior of Fe₃C cementite both in terms of elasticity and ultimate strength [1,2]. These are related to the low C44 value of the Fe₃C orthorhombic structure. Beside ultimate strength, plastic behavior is expected to follow the same trend.
In this study, we perform calculations of dislocation core structure in Fe₃C based on a generalized Peierls-Nabarro (PN) model. We compute the generalized stacking fault (GSF) energy landscape for (100), (010) and (001) planes using first-principles. The potential effect of carbon atoms in the structure have been highlighted by several GSF calculations. As expected, restoring forces (taken as the derivative of GSF energies) are found in good agreement with ISS calculations [1]. First results show the highest stacking fault energy in (100) plane. We also found a low energy path corresponding to a shear vector along [100] in (010) plane. Further PN model confirms that screw dislocation with a Burgers vector [100] spreads in (010) plane.
Finally, preliminary results of Peierls stress evaluation in Fe₃C cementite will be shown.
[1] N. Garvik, Ph. Carrez, P. Cordier, First-principles study of the ideal strength of Fe₃C cementite, Mat. Sci. Eng: A 572, 25-29 (2013)
[2] C. Jiang, S. G. Srinivasan, Unexpected strain-stiffening in crystalline solids, Nature 496, 339-342 (2013)

Ultra fine and nano crystalline metals show plastic strain recovery upon unloading and reverse plastic strain during cyclic loading. It has been suggested that these phenomena are related to the unbalance of the residual stresses in grains with different sizes. In contrast, transmission electron microscopy (TEM) experiments indicate that the reverse plastic strain observed during cyclic loading is originated by intragranular stress imbalance due to the formation of dislocation pile ups next to grain boundaries. Here we present dislocation dynamics simulations coupled to a kinetic Monte Carlo algorithm that are able to predict the two mechanisms. Our simulations show that both processes are related to the formation of dislocation pile ups and that grain size inhomogeneity creates a residual stress imbalance that increases the amount of plastic strain recovered.

In small volumes of metals it is very possible to have few, if any, dislocations. Point defects, including vacancies and stacking faults, can be more prevalent then dislocations and are likely to exist in these dislocation free zones after quenching. Atomistic simulations of small volumes of Cu have been carried out to determine the impact of loading conditions on the onset of plastic deformation in the presence of stacking fault tetrahedra (SFTs) on the resulting compression / tension (C/T) asymmetry. By comparing the mechanisms by which these point defects interact with stress fields a clear difference between tensile and compression has been noted. When compared to testing perfect crystals, the presence of SFTs decreases the C/T asymmetry in copper, corresponding closely to prior published experimental results. The reduction in yield stress in tension is less sensitive to defects than that in compression. These results will be compared to nanoindentation experiments as well as micro-tensile and micro-compression, demonstrating some of the variability in the literature could be ascribed to the C/T differences. Since the reduction in yield stress, versus the perfect crystal, is almost constant in tension for all orientations in the presence of defects, testing in this geometry is more efficient to determine the orientation dependence of the yield stress, while testing in compression is more likely to emphasize pre-existing defects. This was then compared to experimental nanoindentation experiments probing the yield and subsequent hardness in Pt after a variety of annealing treatments in an effort to explain the range of behavior which manifests as stochastic distributions, likely due to the complex nature of the non-uniform stress field in conjunction with a non-uniform distribution of defects.

Crystal defects play a critical role in determining macroscopic properties of solids, even when they are presented in small concentrations. Defects such us vacancies and nanovoids, modify the perfection of the crystal lattice and produce changes in different scales of length and time. The modification in the chemical core of the defect, modify the discrete lattice which also alter the elastic solution of the problem. Moreover, the presence of defects starts the plasticity of the material by dislocations emission from the defect. The plastic work generates a transport of material from the defect, but also generates a flux of heat. This exchange between mass transport and heat flux have place on multiple scale of time and length. As result, the study of this type of problem must to reproduce the coupled nature of the thermoelastic response of the material as well as the mustiscale nature of them.
One multiscale approach which enables us to simulate thermoelastic coupled problems such as void cavitation, crack tip opening, etc. is the HotQC method, which allows to simulate nonequilibrium thermodynamics systems. The method can simulate coupled thermoelastic phenomena thanks to the implementation of a variational principle for thermoelastic coupled problems. In addition, the method reduces the degrees of freedom of the system through the application of judicious kinematic constraints. Furthermore, we can simulate system in different thermodynamics states, varying the state from isothermal to adiabatic.
In this work we study the phenomenon of ductile failure in single FCC materials such as Cu and Al. In particular the onset of void cavitation by dislocations emission at finite temperature is presented using the HotQC method. Different materials and loading cases are going to be simulated, to understand the influence of the temperature and it evolution on the dislocations emission. Moreover, a detailed analysis of the dislocations emission, temperature evolution and void growth is going to be presented in detail. Finally, a quasi-static and dynamic simulation is presented to show the inertia effects on small enough voids.

This talk demonstrates similarities in dislocation plasticity of metals in two very different forms: (a) bulk, e.g. 2-3 mm diam., surface-film coated bcc metals deformed at low homologous temperatures; (b) small-diameter micro-pillars of various metals deformed at room temperature. Both materials are usually but not necessarily single crystals; the latter have diameters too small for effective operation of Frank-Read sources. Both materials exhibit appreciable softening - a reduction in flow stress - by dislocation injection processes. For bulk, coated bcc metals, dislocation injection involves generation of high-mobility edge dislocations from the film-substrate interface, sometimes complemented by dislocations introduced by high-temperature prestrain. For micro-pillars, dislocations introduced by prestrain are more exclusively responsible for the softening. The softening in both cases can be understood in terms of kinetic analyses based on Johnston-Gilman dislocation dynamics.

Dislocations and their interactions strongly influence many of the properties of materials, ranging from the strength of metals and alloys to the efficiency of light-emitting diodes and laser diodes. Although various experimental methods have been used to image dislocations in materials since 1956, a 3D technique for visualizing dislocations at atomic resolution has not previously been demonstrated. Here we report the development of atomic resolution electron tomography and achieve 3D imaging of dislocation core structures of a Pt nanoparticle at atomic resolution. Compared to conventional electron tomography, our atomic resolution imaging method incorporates three novel developments. First, the conventional alignment approach used in electron tomography either relies on fiducial markers or is based on the cross-correlation between neighboring projections. To our knowledge, neither of these alignment approaches can achieve atomic level precision. To overcome this limitation, we have developed a method based on the center of mass (CM), which is able to align the projections of a tilt series at atomic level accuracy. Second, we have implemented a data acquisition and tomographic reconstruction method, termed equally sloped tomography (EST). Compared to conventional tomography that reconstructs a 3D object from a tilt series of projections with constant angular increments, EST acquires a tilt series with equal slope increments, and can achieve much better 3D reconstructions from a limited number of projections with a missing wedge. Third, to enhance the signal to noise ratio in the reconstruction, we have developed a 3D Fourier filtering method and applied it to the EST reconstructions.
After incorporating these three novel developments, we achieve atomic resolution electron tomography and observe nearly all the atoms in a multiply-twinned Pt nanoparticle. We find the existence of atomic steps at 3D twin boundaries of the Pt nanoparticle. We also image, for the first time, the 3D core structure of edge and screw dislocations in the nanoparticle at atomic resolution. These dislocations and the atomic steps at the twin boundaries are hidden in conventional 2D projections, and appear to be a significant stress-relief mechanism. The ability to image 3D disordered structures such as dislocations at atomic resolution is expected to find application in materials sciences, nanoscience, solid state physics and chemistry.
1. C. -C. Chen, et. al., "Three- dimensional imaging of dislocations in nanoparticles at atomic resolution", Nature, 496, 74-77 (2013).
2. M. C. Scott, et. al., "Electron tomography at 2.4-angstrom resolution", Nature, 483, 444-447 (2012).

The fundamental aspects of the core structure and slip features of pyramidal dislocations that have very large Burgers vector (about twice that of basal dislocation) in Hexagonal-Closed-Pack (HCP) crystals, are still not well understood. For example, type-II pyramidal dislocations were experimentally observed in Mg, while only type-I pyramidal dislocations were reported from atomistic simulations. In addition, the dissociation and core structure of dislocations are still not well-determined.
In this talk we present atomistic simulations characterizing the nucleation and slip of pyramidal dislocations in single crystal Mg. The leading and trailing partial dislocations of type-I pyramidal dislocations are identified from large scale molecular dynamics simulations of c-axis compression of single crystal Mg. Straight infinite-long dislocation cores are then reproduced to quantitatively study their slip behavior. The theoretical athermal Peierls stresses for dislocation motion is calculated for dislocations with different characters, including pure screw, near-screw and near-edge dislocations. From large scale simulations of finite crystals we show for the first time the mechanisms of transition of dislocations from type-I to type-II pyramidal planes. Screw components of nucleated Type-I pyramidal dislocations near free surface transition to type-II pyramidal planes by surface-induced cross-slip. Subsequently at large strains, most dislocations remaining in the crystal are on type-II pyramidal planes, which is in agreement with the experiments. In addition, as dislocations glide under applied stress, edge-dislocation are observed to climb to adjacent type-I pyramidal planes even at very low temperatures, resulting in the formation of vacancies and interstitials on the original glide plane. This slip feature of type-I pyramidal dislocation is fundamentally different than in FCC and BCC crystals, in which climb of dislocations typically happens at very high temperature.

The mechanical behavior of hcp magnesium is highly anisotropic due to the presence of the primary slip system on the basal plane. Enhancement of the widespread plasticity is hindered by the lower symmetry of the hcp crystal structure, in particular, the deformation along the c-axis direction. The activation of non-basal dislocations on the prismatic and pyramidal planes is the key to overcome this difficulty. One way to achieve this is to induce the prevalent a-screw dislocations on the basal planes to non-basal planes by the cross-slip processes. Atomistic mechanisms of cross-slip processes have been studied by the molecular dynamics method and the critical stress was determined. Firstly, by applying purely the shear stress on the a-screw dislocation to cross-slip to the prismatic plane, we found the limiting applied stress by constricting a part of the extended dislocation. The effects of the obstacles, temperatures, and the strain rates have been studied and compared with reference to the limiting case. The glide of the dislocation in the presence of obstacles and the other dislocation on the basal and prismatic planes is also studied.

Recent studies [1] of 1/2<110> screw dislocation core in MgO showed a major influence of high-pressure (> 50 GPa) on the dislocation core spreading. Here we revisit these conclusions (based on generalized Peierls Nabarro model in [1]) using full atomistic first-principles calculations of periodic dipole arrangement for screw cores. Calculations are thus performed within the DFT framework under pressure (up to 100 GPa). Our results confirm that dislocation core evolves from a spreading in {110} (at low pressure) to a narrower configuration spread in {100} as pressure increases. The dipole method enables also to record the induced core energy variations. Further calculations relying on pairwise potentials show a remarkable agreement with DFT calculations regarding both core spreading and core energy. Therefore to overcome the limitation of cell dimensions in DFT calculations, pairwise calculations have been carried out to investigate the Peierls barrier for gliding in {110} and {100} planes as a function of pressure.
[1] Amodeo J., Carrez Ph. &Cordier P. (2012) Phil. Mag. 92.

A first-principles DFT study of the energetics of 1/2<111> screw dislocations has been performed in the following body-centered cubic (bcc) transition metals: V, Nb, Ta, Mo, W and Fe. We studied the core properties and energy of the easy, hard and split core configurations, as well as of the pathways between these configurations. These data served to construct 2D energy landscapes in the {111} plane (Peierls potential) perpendicular to the dislocation Burgers vector. In all investigated elements, the non-degenerate easy core is the minimum energy configuration, and the split core configuration, centered in the immediate vicinity of a <111> atomic column, has a very high energy, comparable or higher than that of the hard core, in contrast with the usual predictions of interatomic potentials. Fe is shown to have a specific and surprising behavior, with a low relative energy of the hard core, close to that of the saddle configuration between easy cores, resulting in a flat Peierls potential around the hard core position. The 2D energy landscapes so obtained are strikingly different with the usual landscapes and consequences on the dislocation behavior under stress (deviation from Schmid law and glide plane) will be discussed.

In a recent work, we described a reversible phase transformation process to convert coarse-grained polycrystalline cubic-Y2O3 directly into the nanocrystalline state. The process involves a forward transformation from cubic-to-monoclinic under a high pressure and a backward transformation from monoclinic-to-cubic under a lower pressure. An example was given of a reduction in grain size of cubic-Y2O3 from 300 µm to 0.1 µm via a pressure-induced reversible phase transformation at 1000C.
In the same processed material, we also observed a striking surface modification effect. Specifically, a surface-localized columnar grained structure was observed, which covered the entire sample surface when processing time is prolonged > 360 min. This work will describe its structure, defect content, and properties. Ina addition, the processed samples at high temperate/high pressure conditions showed a plastic deformation/superplasticity as it was evidently clear from the morphology of the deformed surface columnar grains. Detailed structural analysis at the atomic scale was conducted on the samples in order to study the defect density and stresses in the processed samples. High-resolution TEM imaging was used to estimate the dislocation density and to obtain atomic scale strain mapping.
Preliminary work indicates that the surface layer is composed of an yttrium oxy-carbonate phase, formed by interaction between the graphite heater and sample. A report in the literature indicates that this phase decomposes at ~550C. Hence, its formation at 1000C may be attributed to increased stability under high pressure. On-going research should resolve this issue.

The collective dynamics of dislocations is characterized by large spatio-temporal fluctuations of the dislocation fluxes (the local shear strain rates). Over the past decade, a significant effort has been devoted to characterizing these fluctuations in space and in time, using both simulations and experimental data. On the other hand, density-based continuum models of dislocation dynamics still work with averaged velocity fields that evolve smoothly in space and time. In this presentation, we discuss how such models might be generalized to account for the intrinsic spatio-temporal intermittency of dislocation motions, using the known properties of dislocation fluxes to construct stochastic models which describe the evolution of heterogeneous dislocation arrangements and the associated internal stress patterns in space and in time.
The proposed approach revisits an idea first put forward in the late 1990s, namely to replace the complex and high-dimensional dynamics of interacting discrete dislocations by appropriately constructed stochastic processes in order to predict the evolution of randomly heterogeneous dislocation patterns. At the time, both density based models of dislocation microstructure evolution and stochastic models of dislocation motion were formulated on a phenomenological basis, using a combination of general scaling arguments and ad-hoc assumptions. In the meantime, a significant body of data has accumulated which quantitatively characterize the statistical properties of dislocation fluxes and thus provide a sound statistical basis for the development of stochastic models. At the same time, rigorous methods have been developed which allow to derive density evolution equations without resorting to mere guesswork. We demonstrate how these advances can be used to set up stochastic simulations of spatio-temporal dislocation patterning, and how these simulations can be applied to model the spatio temporal patterns of dislocations, internal stresses, and lattice (mis)orientations that emerge during deformation of fcc single crystals at elevated strains.

The dislocation microstructure and its evolution under different loading conditions, which comprise uniaxial loading, bending and torsion is analysed and linked to the observed macroscopic plastic behaviour of the simulated single or oligocrystals.
An analysis of the dislocation structure and dislocation multiplication mechanisms is presented. In order to give more quantitative measures for the dislocation structures, the dislocation networks are characterized by e.g. their junction density, types and connectivity. Furthermore the role of imposed strain gradients under bending or torsion loading and the resulting hardening and size effect are discussed.

In bcc metals, dislocations often migrate through the kink mechanism, requiring GPa-level stresses to be seen on the timescales of molecular dynamics. However, many important microstructural changes, such as the transition from brittle to ductile fracture, occur under the influence of low, MPa, applied stresses.
To investigate the dynamics of kink-limited motion under very low applied stress we exploit special periodic boundary conditions to force isolated kinks to form on dislocations. Kinks are seen to move stochastically with a classical friction that is essentially temperature independent. This striking disagreement with decades of theoretical work on dislocation friction is investigated through extensive zero stress simulations of lattice defects and dislocations, providing a rare demonstration of the fluctuation-dissipation theorem.
A coarse grained Langevin dislocation line model, which crucially retains atomistic resolution, gives huge computational efficiencies whilst quantitatively reproducing all of the observed dynamics, enabling predictive modelling of kink mediated and thermally activated defect ensembles.

During plastic flow of crystalline solids with low lattice friction, dislocations self-organize in the form of patterns, with a wavelength that is inversely proportional to stress [1]. After four decades of investigations, the origin of this important property is still under discussion and the matter of many modeling investigations [2]. We show that realistic dislocation patterns, dynamically induced and verifying the principle of similitude can be obtained from 3D Dislocation Dynamics simulations. Two different examples of dislocation patterns reproduced in monotonic and cyclic loading are presented and compared with observations in Cu single crystals [3]. The physical mechanisms governing the bifurcation from uniform to ordered microstructures are analyzed.
[1] D. Kuhlmann-Wilsdorf, Metall. Trans. A 16A, 2091 (1985).
[2] M. Zaiser and A. Seeger. In Dislocations in Solids, volume 11, chapter 56, pages 1-100. Elsevier Science B.V., Amsterdam, (2002).
[3] M. Sauzay and L. P. Kubin. Progress in Materials Science, 56(6):725-784, 8 2011.

A wide range of dislocation structures, including cell structures and ordered patterns, have been observed in deformed metallic crystals. Understanding these patterns has been a major concern of the metal mechanics community for a number of decades. The 1980s witnessed the getting together of materials modellers and metallurgists with the mechanics community to tackle the dislocation patterning problem theoretically. Some limited-scope models were developed. In the late 1980s, however, the simulation technique known as dislocation dynamics method emerged. In the mid-1990s, the field of metal plasticity witnessed a significant rise by the generalization of this method to 3D. With a large computing power coming on board, there was a hope that the problems of strain hardening and dislocation patterning in metals can be finally tackled. But soon after, and due then unforeseen limitations of the simulation techniques, the field has been handed back to the continuum mechanics community who continued the phenomenological development of the field with no regard to the patterning process. More than a decade later, there seems to be a hope that, with the continuum formulation of dislocation dynamics, solutions might be on the horizon. The current generation of scientists working on these problems (the author included) are, however, less familiar with the original experimental motivation behind the quest for a dislocation-based theory of metal plasticity. Hence, a historical perspective on the data and early models, along with their successes and failures, is due. Motivated by the need for such a perspective, this presentation gives and a review of dislocation patterns in deformed metallic crystals. We will focus on the salient features of these patterns in connection with the type and level of mechanical loading. In parallel, we will give an assessment of current dislocation dynamics models, both discrete simulation and continuum approaches, from the viewpoint of predicting dislocation patterning and strain hardening. The predictive capability of these models will be assessed from both the theoretical and computational viewpoints. We will conclude the presentation by introducing a new modelling approach for dislocation dynamics that has a potential to predict the basic characteristics of the deformation of single crystals (dislocation patterning and strain hardening) and give some illustrative results. This work was supported by the U.S. DOE Office of Basic Energy Sciences, Division of Materials Science & Engineering via contract # DE-FG02-08ER46494 at Florida State University and by funding from the School of Nuclear Engineering at Purdue University.

Recent experimental and modeling evidence shows that micron-scale crystalline materials deform via intermittent abrupt strain bursts. These avalanches caused by the sudden collective motion of lattice dislocations make the deformation process unpredictable at this scale. It is, therefore, of high technological importance to give a deep understanding of the statistical properties of these dislocation avalanches.
It is known that the magnitude of the strain bursts follow a scale-free distribution, showing that the deformation process exhibits critical-like avalanche dynamics. Based on these observations it has been argued that this system belongs to the universality class of mean field depinning (MFD) of an elastic manifold. In this picture yield stress corresponds to the critical point of a continuous phase transition and the power-law exponent of the burst size distribution is tau;=1.5.
In this talk we explore the behavior of dislocation avalanches in terms of discrete dislocation dynamics (DDD). To this end, quasistatic stress-controlled simulations are conducted with three DDD methods differing in the spatiotemporal discretization and the dynamics assumed for individual dislocations. We find that each model exhibits identical avalanche dynamics with the following properties: (i) the avalanche exponent tau; is tau;asymp;1.0, which is significantly smaller than that of MFD and (ii) the avalanche cutoff diverges with increasing system size at any studied applied stress level. The latter property is inconsistent with cutoff scaling in depinning systems and with the existence of a critical yield point. We, therefore, conclude that dislocation systems belong to a different universality class than MFD.
Finally, based on the analysis of the spatial structure of avalanches, we elucidate the fundamental differences between dislocation plasticity and depinning systems. We also discuss the relation of our findings to previous experimental observations.

Dislocation networks within crystalline materials are extended defect
structures that control macroscopic plasticity and therefore material
strength and toughness. Due to their complexity dislocation dynamics
modelling has played a central role in developing our understanding of how
these structures respond and evolve in time to applied stress. Recent
understanding has viewed dislocation structures as being in a critical
configuration, and plasticity as an irreversible structural transformation
from one such critical configuration to another - a feature that dislocation
dynamics simulations are well able to model. Such self-organized
criticality is a universal phenomenon and should be insensitive to material
specific details, a perspective suggesting simplified models can describe
fundamental aspects of plasticity. Here a simple one dimensional dislocation
model is developed in which only mobile dislocations are treated explicitly,
with the remaining immobile component being treated via a static mean field
description (MSMSE 21, 035007 (2013)). Despite its simplicity, a diversity of
micro-plastic behaviour is admitted, involving intermittent plasticity in the
form of a scale-free avalanche phenomenon, with mean field exponents and
scaling-collapse for the strain-burst magnitude and dislocation velocity
distributions that is seen in experiment and more complex dislocation
dynamics simulations.

The deformation behavior of small crystals is characterized by large strain rate fluctuations (strain bursts) which are associated with localized dislocation motions and manifest themselves as serrations or plateaus in the stress strain curves. In this investigation we use DDD simulations of micropillars containing high dislocation densities in order to investigate the spatio-temporal statistics of local stress and strain fluctuations within the pillars (i,e,. below the specimen scale) . We investigate statistical properties of these fluctuations as a function of spatial resolution and establish scale-dependent scaling laws. In conclusion we discuss how our results might help to construct a renormalization theory of dislocation-mediated plastic flow.

At low homologous temperatures, plastic deformation of metals is
controlled by dislocation glide. At temperatures greater than about 1/3 of the melting
point, dislocation climb becomes important leading to phenomena such as creep.
Current discrete dislocation dynamics codes do not account for that. The modeling of
climb as a non-conservative motion requires the concurrent modeling of
dislocation motion and point defect diffusion into the cores of dislocations.
Here we report on a formulation of high-temperature discrete dislocation
plasticity in finite bodies, which accounts for the above couplings. An
adaptive multi-time stepping algorithm is used in the numerical
implementation of the theory. We then present a series of deformation analyses
at constant applied stress in single crystals. We show that two regimes of power-law
creep naturally emerge in the simulations, as affected by the applied stress and
test temperature. We also systematically quantify the power law exponent in
either regime.

Large scale flow in the Earth's mantle involve plastic deformations of rocks and their constitutive minerals. Due to the extremely slow strain rate conditions in the Earth's mantle, it is very challenging to identify the fundamental mechanisms controlling such process. Thus, the development of a multi-scale approach linking the atomic scale properties and the microscopic elementary mechanisms to the macroscopic behavior is needed [1]. Within this framework, we present a model to investigate the creep of olivine, one of the main constituent of the Earth's mantle, at the mesoscopic scale.
In the past years, it has been demonstrated that dislocations play an important role in the creep flow of rocks and minerals. However, the influence of the climb mechanism, which is expected to be dominant in high temperature plasticity, and extent of the glide versus climb process have not yet been clarified. To this aim, we performed 2.5D dislocation dynamics simulations coupling the climb with the glide dislocation motion. In particular, local rules are implemented to reproduce the relevant three-dimensional dislocation mechanisms, as originally proposed to model fcc metal plasticity [2]. Moreover, the transport of matter through vacancy diffusion is taken into account and directly related to the climb dislocation velocity, similarly to the approach proposed in Ref. [3]. The interplay between thermally activated glide and climb motion is discussed and the effect of climb on the creep strain rate is studied.
[1] P. Cordier et al., Nature 481, 177 (2012)
[2] D. Gomez-Garcia et al., Phys. Rev. Lett. 96, 125503 (2006)
[3] S. M. Keralavarma et al., Phys. Rev. Lett. 109, 265504 (2012)

Convection and plastic deformation in the Earth's lower mantle occur in extreme conditions of pressure and temperature, and at geological times that are reflected in the very low strain rates (10^-12 to 10^-16 s^-1). Although the MgSiO₃ perovskite represents more than 80% of the composition of the lower mantle, the mechanical properties of this phase, its microstructure and the mechanisms responsible for its plastic deformation are still a matter of debate: bulk and interfacial diffusion, grain boundary sliding, and dislocation creep. Both dislocation glide and climb are expected to contribute significantly to the plastic flow, however the activation energies and rates of these mechanisms are still to be determined.
In this study we utilize atomic-scale simulations to investigate the properties of dislocations in MgSiO₃ perovskite. The core structure of edge and screw dislocations are finely characterized, and their Peierls stresses for glide are evaluated in the range of pressures relevant to Earth's lower mantle. The formation and migration energy of intrinsic vacancies around the edge dislocations are determined, and dislocation-vacancy interactions are explicitely computed. These results give insight into the importance of dislocation activity in the rheology of the mantle.

Single-crystalline nanostructures with low or zero defect densities are ideal model materials for elucidating the atomistic origins of elasticity and plasticity. In the case of metal nanostructures, large elastic strains enabled by a dearth of defects allow access to extreme deviations from the equilibrium atomic separation where anharmonic effects play a substantial role. In addition, plastic deformation in such pristine structures is often governed by the nucleation of defects, which is expected to be thermally activated.
We performed nanoscale tensile testing on single-crystalline, nominally defect-free Pd nanowhiskers using a microelectromechanical (MEMS)-based platform for a range of diameters, strain rates and temperatures (100 to 500 K). In addition to characterizing nonlinear elasticity and size-dependences in elastic moduli, we investigated the thermal activation of dislocation nucleation. Our results show a weak size dependence of yield strength and highlight the need for a probabilistic description of strength mediated by dislocation nucleation. Strength is found to be temperature and strain-rate sensitive, and our measurements allow for comparison with recent atomistic models of surface nucleation in nanowires. Atomic layer deposition is used to modify the atomic bonding of the surface layer, and the results are discussed in the context of atomic coordination and local stiffness contrast in the surface-affected regions of the nanowhiskers.

At ambient temperature and pressure, most of the semiconductor materials are brittle. This is the case of the III-V compound semiconductor indium antimonide (InSb). Traditionally, use of confining pressure via indentation or a hydrostatic confining medium [1, 2] has been required to study the plasticity of such brittle materials. However, previous work has demonstrated that sample miniaturization can prevent the onset of cracking and allow plastic deformation [3]. This has been previously exploited using micro-pillar compression at ambient temperature to examine the size dependence and deformation mechanisms of InSb at small scales [4].
At elevated temperatures, InSb has been observed to undergo a brittle-to-ductile transition. Bulk techniques using elevated temperature compression in the Paterson press and indentation testing has elucidated the nature of the change in deformation [1]. In the brittle regime, 20°C < T < 150°C, the crystal deformation takes place via the nucleation and glide of dissociated perfect dislocations or only leading partials. In the ductile regime, T > 150°C, the crystal deforms via the nucleation and motion of perfect dislocations belonging to the glide set.
Recent advances in in-situ instrumentation have enabled micro-compression techniques to extract temperature- and time-dependent deformation parameters [5, 6]. Due to its well characterized ductile to brittle transition in with temperature for bulk deformation [2], InSb is a model system for determining whether thermally activated deformation mechanisms at the micro scale correspond to macro scale behaviour.
Here, strain rate jump micro-compressions at elevated temperature have been performed in situ in the SEM to measure and observe the deformation of InSb at the micro scale above and below the transformation temperature. Results show the flow stress follows similar trends to that observed in bulk testing with different confining media.
References
[1] B. Kedjar, L. Thilly, J.L. Demenet, J. Rabier, Acta Materialia, 58 (2010) 1426-1440.
[2] T. Suzuki, T. Yasutomi, T. Tokuoka, I. Yonenaga, Physica status solidi (a), 171 (1999) 47-52.
[3] J. Michler, K. Wasmer, S. Meier, F. Ostlund, K. Leifer, Applied Physics Letters, 90 (2007) 043123-043123.
[4] L. Thilly, R. Ghisleni, C. Swistak, J. Michler, Philos. Mag., (2012) 1-11.
[5] S. Korte, W.J. Clegg, Scripta Materialia, 60 (2009) 807-810.
[6] J.M. Wheeler, C. Niederberger, C. Tessarek, S. Christiansen, J. Michler, International Journal of Plasticity, 40 (2013) 140-151.

Nickel based superalloys are preferred materials in the high temperature components of gas turbines due to their excellent thermo-mechanical properties such as high tensile strength, superior creep resistance, and high resistance to fatigue crack growth. The current study aims to develop a micro-structurally informed crystal plasticity model for polycrystalline alloy Rene 88DT at a high temperature (above 1000F). For this purpose, single crystals with representative microstructures were created by the investment casting process, and mechanically tested under various orientations in tension and compression. The experiments were used to investigate various deformation mechanisms including activation of mixed octahedral and cubic slip systems, stacking-faults formation and precipitate shearing. These mechanisms were incorporated into a physics - based viscoplastic constitutive model. The model calibrated on single crystal data can be further used as the basis for each grain in the polycrystalline material to predict the macroscopic stress-strain response as well as heterogeneous local stress and strain fields. Thus, the current methodology may provide a superior alternative to traditional crystal plasticity models, which are usually calibrated based on the bulk stress-strain curve of the polycrystalline material.

Creep is one of the life limiting processes of single crystal Ni base superalloys that are used in the blades of hot gas turbines where they operate at elevated temperatures. While in-situ observation of dislocations evolution during the creep process is nontrivial, discrete dislocation dynamics simulation can provide further insight into the gamma/gamma' microstructure of single crystal superalloys at different creep strains. We focus on the early stages of creep, where dislocation plasticity is confined to narrow gamma channels. A hybrid glide-climb mobility model (S.M. Hafez Haghighat, G. Eggeler, D. Raabe, Acta Materialia 61 (2013) 3709) is used to conduct the interaction of dislocations with gamma' particle. The influence of misfit stress and loading direction on the low stress creep rate and its resulting microstructure is considered. It appears that the creep rate is limited when the crystal is loaded along the [111] direction. It is due to the small number of activated slip systems and low Schmid factor when compared to that of the [100] loading direction. In the latter case the creep strain increases monotonically due to the propagation of dislocations in the channel oriented perpendicular to the loading direction, where a dislocation network may form in agreement with experiments. The anisotropy of dislocations microstructure deposited along the gamma/gamma' interfaces is investigated in details for both the loading conditions.

In this talk recent advances in understanding plasticity and fracture of miniaturized materials will be presented. Examples include compression experiments of Cu micro-pillars containing individual grain boundaries, tensile testing and cyclic loading of micron-sized polycrystalline Cu structures. The experiments are performed in situ in the electron microscope or using in situ diffraction methods to resolve the underlying deformation mechanisms.

The activities and interactions between dislocations and structural boundaries including grain boundaries (GBs) and twin boundaries (TBs) are expected to dominate the mechanical performances and deformation behaviors of nanostructured materials, and have been widely studied. However, some proposed nanomechanics including the grain rotation- or GB sliding-induced softening of nanocrystalline (NC) materials as well as the dislocation retardation-yielded strengthening or the detwinning-induced softening of nanotwinned (NT) materials have not been completely verified. Thus in this study, single-crystalline (SC), chain-grain NC (grain size 50 nm) and single-grain NT (twin plane spacing 35 nm) Cu nanopillars (diameter less than 100 nm, [111] oriented along the longitudinal direction of the pillars) were prepared; the in-situ observations of nanoscopic deformations were performed under nanoindentation (compression) in a high-resolution transmission electron microscope to clarify the structure-to-mechanical response correlations of the differently-structured specimens. The stress-strain curves indicated that, at the early deformation stages, all the specimens behaved elastically with a modulus of about 114 GPa and yielded at about 0.3 GPa; upon yielding, dislocation activities began. Pure dislocation activities dominated the plastic deformation of the SC Cu, and dislocation accumulations conducted work hardening to an ultimate stress of about 0.6 GPa; sudden bursts of big dislocation clusters towards surface were observed to cause drastic stress drops. In comparison, GB sliding dominated the deformation of the NC Cu without obvious dislocation activities or work hardening; the stress decreased to and remained at only 0.1-0.2 GPa while GB sliding proceeded along the easiest direction (45°) with the maximum resolved shear stress. Compared to the large-range dislocation activities in SC Cu with a low work-hardening capacity, the uniform and confined small-range dislocation activities in the NT Cu were observed to yield a high strength of about 1.3 GPa. Dislocations emmitted from a TB were found to jump toward the next for a short distance and soon retarded/arrested by the next TB, therefore restricting the plastic deformation of the NT Cu. However, a slight reduction in pillar strain rate extraordinarily resulted in a markedly lowered work-hardening capacity of the NT Cu, with a strength drop of 0.3 GPa far beyond the decrease caused by a strain rate sensitivity effect, due to observed twin plane migration- and detwinning-induced softening. The twin plane spacing-dependent, strain rate-governed dislocation gliding speed is suggested to dominate the dislocation retardation-strengthening or detwinning-softening of the NT structures.

Although deformation processes in submicron-sized metallic crystals are well documented, the direct observation of deformation mechanisms in crystals with dimensions below the sub-10-nm range is currently lacking. Here, through in situ high-resolution transmission electron microscopy (HRTEM) observations, we show that (1) in sharp contrast to what happens in bulk materials, in which plasticity is mediated by dislocation emission from Frank-Read sources and multiplication, partial dislocations emitted from free surfaces dominate the deformation of gold (Au) nanocrystals; (2) the crystallographic orientation (Schmid factor) is not the only factor in determining the deformation mechanism of nanometre-sized Au; and (3) the Au nanocrystal exhibits a phase transformation from a face-centered cubic to a body-centered tetragonal structure after failure. These findings provide direct experimental evidence for the vast amount of theoretical modelling on the deformation mechanisms of nanomaterials that have appeared in recent years. The talk will be focused on in-situ TEM investigation on discrete plasticity in gold nanowires based on the publication: H. Zheng, Ajing Cao, C. Weinberger, J. Y. Huang, K. Du, J. Wang, Y. Xia, S. X. Mao, Nature Communication (2010).

Experimental studies show strong strengthening effects for micrometer-scale FCC as well as two-phase superalloy crystals, even at high initial dislocation densities. This talk shows results from large-scale 3-D discrete dislocation simulations (DDS) used to explicitly model the deformation behavior of FCC Ni as well as superalloy microcrystals under single-slip conditions. The study shows that two size-sensitive athermal hardening processes, beyond forest and precipitation hardening, are sufficient to develop the dimensional scaling of the flow stress, stochastic stress variation, flow intermittency and, high initial strain-hardening rates, similar to experimental observations for various materials. One mechanism, source-truncation hardening, is especially potent in micrometer-scale volumes. A second mechanism, termed exhaustion hardening, results from a break-down of the mean-field conditions for forest hardening in small volumes, thus biasing the statistics of ordinary dislocation processes. Effects of thermally activated and athermal cross-slip in the bulk, at surfaces and at intersections, whose rules are derived from large-scale atomistic simulations, on the stress-strain behavior of microcrystals of Ni is also discussed.

Yielding in nanomaterials (observed in nanoindentation or in defect-free pillar deformation) often occurs when the material is close to its theoretical strength, due to the absence of defects in the stressed volumes. For bulk materials, yielding occurs at a much lower stress, due to the typically large number of defects present in the system. An intermediate regime is observed, where there is a broad distribution of observed yielding. For nanoindentation, this is observed as a distribution of pop-in stresses for the same sample and loading conditions. We have shown that a simple statistical model can predict the experimentally observed distribution of stresses, and how this distribution changes with indenter size [1]. For plastically anisotropic materials, the model explains the observed dependence of this distribution on the surface orientation, where pop-in observed in “hard” directions has a significantly different distribution than for other orientations [2]. We extend this to the case of pillar deformation, and highlight important differences between this case and the case of nanoindentation.
This work was supported by the U.S. Department of Energy (DOE), Basic Energy Sciences, Materials Sciences and Engineering Division.
References
[1] J. R. Morris, H. Bei, G. M. Pharr, and E. P. George, Phys. Rev. Lett. 106, 165502 (2011).
[2] T. L. Li, H. Bei, J. R. Morris, E. P. George, and Y. F. Gao, Materials Science and Technology 28, 1055 (2012).

Contact between a sinusoidal surface and an elastic platen is investigated using discrete dislocation plasticity simulations [Van der Giessen, E., & Needleman, A. (1999)]. The focus of this study is on capturing possible size dependent responses when sinusoidal asperities are flattened. Our previous works involving flattening of a sinusoidal metal surface by a rigid platen [Sun, F., et al. (2012), Nicola, L., et al. (2007)] demonstrated two different size effects, i.e plasticity is a function of asperity size as well as spacing, when these lengths are in the micrometer range. However if the sinusoidal surface is flattened by an elastic instead of a rigid platen, these size effects are expected to be different. This study aims at pointing out the differences.
Contrary to our previous simulations, in which the effect of the rigid body on the metal crystal was modelled through boundary conditions directly applied to the metal surface, both bodies in contact are now modelled in these simulations. This is a major improvement because now, dislocations can leave the crystal through the contacted region, naturally leaving a displacement step on the metal surface.

The contact simulations will keep track of the mean as well as the local contact pressure, the evolution of the true contact area and the stress distribution in the subsurface region. Understanding the influence of the elastic platen on plastic deformation of the asperities and the accompanying plasticity size effects will bring us a step closer to understanding contact between bodies that can both plastically deform.

Nanoscale laminates have been shown by several researchers to exhibit superior mechanical properties including ultra high strength. Nevertheless, the details of the role of interfaces and dislocation mechanisms contributing to this strength are still not completely understood. In this work, molecular dynamics is used to study the plastic deformation of coherent cube-on-cube Cu/Ni system having different layer thicknesses under uniaxial loading. The simulations indicate that early stages of deformation involve the disassociation of misfit dislocations into Shockley partials and stair rods. Forest type interactions between Shockley dislocations lead to hardening in the early stages, which is more significant than that related to interface crossing. Stacking faults areas, which dominate the defect structure, and the formation of lock upon the reaction of the partials also act as barriers to dislocation propagation further hardening. At later stages of deformation, trailing dislocation nucleate lowering defect density and the hardening rate. Another interesting mechanism is the glide of lomer dislocations within the interface, which is not a traditional slip plane.

This work intends to develop better understanding of the deformation mechanisms in Cu thin films at the submicron length scale using multiscale dislocation dynamics plasticity (MDDP) model. The main focus of this research is primarily to investigate the role of dislocation interactions on the overall mechanical response of copper thin films for volumes beyond the capabilities of current atomistic simulations. In MDDP, criteria for the activation of several deformation mechanisms are implemented including: a-full dislocation slip, b- homogenous nucleation of dislocation loops inside the film or on free surfaces, c-partial dislocation emission from free surfaces or grain boundaries, d-formation of extended stacking faults ribbons. Our results show that the deformation field in thin films is heterogeneous and strongly dependent on the source size, film thickness, strain rate and type of loading. Competition between full dislocation slip and partial dislocation will be highlighted.

Grain boundaries play a very important role in the deformation of polycrystalline materials - especially on the nano-scale. They act as sources and sinks for dislocations, transmit deformation from grain to grain, are sites for void nucleation, and slide. I will quickly review some relevant observations from recent large scale MD simulations of the uniaxial deformation of polycrystalline nanowires/pillars. Most of this talk will present a discussion of how to incorporate grain boundaries into a general dislocation dynamics framework that allows for grain boundary sliding, slip transmission, and dislocation source and sink behavior - in addition to normal crystal plasticity. Extensions to plasticity induced grain boundary migration will also be discussed. The new approach is grain boundary structure-aware. I will show preliminary results where these new ideas are incorporated into 2d DD simulations.

Although nanolayered metals are of very high strength/hardness (about 1/2-1/3 theoretical strength) when the individual layer thickness of the materials approaches nanometer scale, the plastic deformation ability of the materials is very limited due to the prevailed development of shear bands (SBs) in the materials. In this talk, based on atomic scale observations, we show that severely localized deformation (the continuous thinning of the layers) within the indentation-induced SBs of the 25 nm Cu/25 nm Au nanolayers is essentially attributed to the large shear stress component along the interface, which can refresh the capability of the interface to absorb incoming dislocations through unlocking the product of the dislocation-interface reaction. The dislocation-interface interaction influenced by shear stress for plastic deformation within SBs will be discussed to understand the interface-mediated plasticity of nanostructured materials.

Plastic deformation of crystalline materials is the result of the collective movement of dislocations, in response of their mutual interactions and boundaries effects including the influence of free surfaces, interfaces and grain boundaries. The dislocation microstructures emerging from such dynamics are intrinsically heterogeneous and the way they affect the mechanical properties is a puzzling problem. Nowadays, the development of analytical and/or numerical models for this problem is one of the most challenging problems in materials science.
A reliable tool to investigate this complex problem is the Discrete-Continuum Model (DCM). The DCM is based on a coupling between 3D Dislocation Dynamics (DD) simulations and Finite Element (FE) method. In particular, the DD simulation code is in charge of the evolution of the dislocation microstructure and short-range dislocation-dislocation interactions, while the long-range mechanical fields, dislocation interactions with the boundaries and heterogeneous loading are handled by the FE simulation code.
The DCM, which was proposed first in 1999 [1], has been revised in the last two years. It is now possible to handle problems with very large number of dislocations (the efficiency of the DCM algorithm has been significantly improved), to use non-regular FE meshes, to precisely take into account the influence of image forces, to consider isotropic and anisotropic elasticity. In addition, a new important feature of the DCM is the latter ability to handle multidomains calculations including simultaneously Dislocation Dynamics and Crystal Plasticity approaches to model plastic deformation.
In this communication, the new capabilities of the DCM are presented and illustrated with recent calculations made for Cu polycrystalline micro-samples. Thanks to this example, we show how mesoscopic simulations of plastic deformation can be improved by mixing continuum and discrete models. In addition, the influence of detailed boundary conditions in polycrystalline calculation is highlighted. Finally, the attractive possibility, supplied by the DCM, of calculating X-Ray diffraction patterns accounting for the impact of dislocation microstructure is presented.
[1] C. Lemarchand, J. L. Chaboche, B. Devincre, and L. P. Kubin. Multiscale modelling of plastic deformation. J. Phys. IV, 9:271, 1999.

Size effects are a common phenomena observed in the plastic deformation of micro-specimen. In particular, one important contributing factor to this behavior of the mechanical response is the resistance of grain boundaries against plastic flow [1].
In order to account for these size effects a single-crystal strain gradient plasticity theory is presented. This includes an interface yield condition and the previously presented numerically efficient treatment by the gradient of an equivalent plastic strain in [2]. The 3D Finite Element model and its fit to experimental data of tensile tests on micro-wires with several grains in the cross-section [3] is discussed. The experimentally observed size effects are captured reasonably with one fixed set of parameters.
However, the resistance of the grain boundaries to plastic flow is, to some extent, influenced by the orientation misfit between adjacent grains. One possibility of a consideration of the orientation misfit in the phenomenological grain boundary yield criterion is discussed. This aims towards a further refinement of the presented model at hand.
[1] Hirth, J.: The influence of grain boundaries on mechanical properties. In: Metallurgical and Materials Transactions B 3 (12) (1972), 3047-3067
[2] Wulfinghoff, S., Boehlke, T.: Equivalent plastic strain gradient enhancement of single crystal plasticity: theory and numerics. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 468 (2145) (2012), 2682-2703
[3] Yang, B., Motz, C., Rester, M., Dehm, G.: Yield stress influenced by the ratio of wire diameter to grain size - a competition between the effects of specimen microstructure and dimension in micro-sized polycrystalline copper wires. In: Philosophical Magazine 92 (25-27) (2012), 3243-3256

In an effort to better understand the deformation mechanisms of magnesium alloys, we investigate the superplastic behavior of twin-roll cast AZ31 through modeling and experiments, using microstructural features such as texture and dislocation densities. We study a wide range of temperatures from room temperature to 450C and strain rates of 0.0001 s-1 to 0.1 s-1. A continuum dislocation dynamics model coupled with viscoplastic self consistent model is developed which accounts for deformation at high temperatures and grain boundary sliding (GBS). The rate effect and temperature effect from unified Langdon model are implemented into the polycrystalline deformation model and the results are compared to the experimental data with emphasis on the role of GBS in the evolving texture. The connection between the dislocation density evolution and GBS mechanism is discussed. The model allows simulation of deformation and the evolving texture over a wide range of deformation and temperature conditions.

In this study we carried out a serials of molecular dynamics (MD) simulations on two symmetric and four asymmetric sum;5 <100> grain boundaries (GBs) of Cu with embedded atom method (EAM) potential to investigate the mechanical properties and the relevant deformation mechanisms under uniaxial tensile and shear deformation. Firstly, the equilibrium 0K GB structures are generated by molecular statics simulation. The simulation results show that the four sum;5 asymmetric GBs with different inclination angles (phi;=11.31°, 18.43°, 26.57°, 30.96° ) in the <100> system are composed of only two structural units which corresponding to the two sum;5 symmetric tilt GBs (phi;=0° and phi;=45°). GB energies are calculated according to the simulation results and they are compared with the predicted energy values as a function of inclination angle based on faceting into the two symmetric boundaries. MD simulations are then conducted to investigate the mechanical response of different sum;5 boundaries. In uniaxial tension, the tensile strength of the symmetric GBs are higher than the asymmetric GBs, suggesting that the symmetric GBs may have a more stable boundary structures. Crack is prefer to initiate at the boundary plane which result in the sudden decrease of the maximum tensile stress and GBs can play a role as the partial dislocation sources accelerating crystal damage. In shear deformation, the critical shear stress of symmetric GBs are much lower than the asymmetric GBs, which can be attributed to the differences on their deformation mechanisms. GB-related atom shuffling is the predominant factor responsible for the decrease of boundary strength for the asymmetric boundaries, crystal plasticity is evidenced in the form of both GB diffusion and GB migration. While for the symmetric boundaries, GB migration is the only deformation mechanism. The migration of asymmetric GBs is seldom studied before and the migration mechanism is still unclear. In this paper, the migration of sum;5 asymmetric GBs is determined, but different from the migration of sum;5 symmetric GBs which is proved to be a stress-driven motion through collective transformation of structure units, it is a process that is confirmed to closely connected with the GB atoms diffusion. This work provided a better understanding of the relationship between GB structures, mechanical properties and the corresponding deformation mechanisms at atomic scale.

Disclinations may be formed during stress-driven grain boundary (GB) migration, which is one of the plastic deformation processes observed in nanocrystalline (NC) metals. We use atomistic simulations to study the formation of disclinations in NC metals, their effect on plasticity, and their interaction with cracks. We find that disclination formation gives rise to rapid kinematic hardening and—depending on microstructure—may either enhance or inhibit the extension of nanometer-scale cracks, thereby influencing the effective fracture toughness of NC metals. This work was funded by the BP Materials and Corrosion Center at MIT.