Oral contributions

abstract: 2.7
Dynamic strain aging : a coupled dislocation - solute dynamic model
C. FRESSENGEAS, Laboratoire de Physique et Mécanique des Matériaux, Université de Metz - CNRS, Ile du Saulcy, 57045 Metz Cedex France A.J. BEAUDOIN, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA M. LEBYODKIN, Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia. L.P. KUBIN, Laboratoire d'Etude des Microstructures, CNRS-ONERA, 29 Av. de la Division Leclerc, 92322 Châtillon Cedex, France. Y. ESTRIN, Institut für werkstoffkunde und werkstofftechnik, Technische Universität Clausthal, 38678 Clausthal - Zellerfeld, Germany.
Jerky flow or the Portevin-Le Chatelier (PLC) effect is observed in dilute alloys. It results from the dynamic interaction of mobile dislocations and solute atoms referred to as Dynamic Strain Aging (DSA). Mobile dislocations move by successive jerks between forest obstacles. Solute atoms diffuse to and age them while they are temporarily arrested at these obstacles. DSA leads to negative Strain Rate Sensitivity (SRS) of the flow stress when the two types of defects have comparable mobility. Then plastic flow is heterogeneous, with high plastic strain rate localized in narrow bands. Offsetting by low strain rates occurs in the rest of the sample.

We discuss here a "dynamized" Kubin - Estrin (KE) model [1], the objective being to capture the coupled dislocation - solute dynamics. The model is written as a local constitutive formulation. However, by using it for example at slip plane level and inserting polycrystal plasticity in finite element calculations, it can be used in a framework where spatial interactions are taken care of. The model is obtained by embedding the KE formulation in a dynamic system with "slow" and "fast" time scales where the KE model appears as the "slow manifold", i.e. the kernel obtained when fast evolution is cut off. The term "slow evolution" refers to the transformation of the dislocations microstructure over the sample loading time scale. "Fast variations" pertain to an immobilisation - break away cycle due to DSA. They occur through exchange of dislocations between mobile and forest populations, with the solute concentration level as a controlling parameter. "Slow evolution" of the solute concentration during some aging time is in the form due to Louat [2]. Its fast evolution is driven by relaxation of the aging time to the fast changing waiting time of dislocations on obstacles [3]. Features of jerky flow predicted by the KE model such as the negative SRS of the flow stress and critical strains for the occurrence of the PLC effect are retrieved. In addition, negative SRS of the threshold stress for instability is predicted. This result potentially allows to obtain a complete rendering of the spatio-temporal properties of jerky flow, including bandwidth and band average strain.

References
1. Kubin L.P. and Estrin, Y., Acta Metall., 1985, 33, 397; 1990, 38, 5, 697.
2. Louat N. Scripta Metall., 1981, 15, 1167.
3. McCormick, P.G., Acta Metall., 1988, 36, 3061.


abstract: 2.10
Finite strain dislocation plasticity
VIKRAM S. DESHPANDE, Cambridge University Engineering Dept., UK; ALAN NEEDLEMAN, Division of Engineering, Brown University, USA; ERIK VAN DER GIESSEN, Dept. of Applied Physcis, University of Groningen, Netherlands.
A framework for carrying out finite deformation discrete dislocation plasticity calculations is presented. The discrete dislocations are presumed to be adequately represented by the singular linear elastic fields so that the large deformations near dislocation cores are not modeled. The finite deformation effects accounted for are: (i) finite lattice rotations and (ii) shape changes due to slip. As a consequence of the nonlinearity, an iterative procedure is needed to solve boundary value problems. The general three dimensional framework is specialized to plane strain. The plane strain specialization is implemented in a finite element code assuming (i) slip and smeared out over the elements and thus the displacement fields are continuous and (ii) accounting for the displacement jumps across the slip segments. Numerical examples are given including uniaxial tension and bending are discussed and the capabilities and limitations of a finite element framework for this class of problems will be illustrated and discussed.


abstract: 2.12
Gradients of Geometrically Necessary Dislocations from White Beam Microdiffraction
ROSA I. BARABASH, GENE E. ICE, Oak Ridge National Laboratory, Oak Ridge, TN, USA.
Plastic strain gradients appear either because of loading geometry or because of inhomogeneous plasticity/elasticity. They cause varying in space gradients in the arrangement and density of geometrically necessary dislocation, GNDs and/or geometrically necessary boundaries, GNBs. Different models of geometrically necessary dislocations, GNDs, were recently used to describe the plastic strain gradient. Varying GNDs density results in gradients of local orientations with depth and redistributes the intensity around each Bragg reflection. Depending on the ratio between absorption coefficient and gradient of GNDs density with depth the maximum of the streak intensity displaces. Intensity distribution along the Laue streak becomes highly asymmetric with a strong maximum at one end of the streak and a long tail with gradually decreasing intensity. Different slip systems cause distinctly different Laue-pattern streaking. Experimental patterns are therefore sensitive to stored disocations and GNDs. We use a multiscale hierarchical framework similar to a cell-wall model, to extend the dislocation/disclination description for the length scales introduced in strain gradient-plasticity theory. We show that diffraction experiments give natural criteria for the aforementioned length scales. White beam diffraction analysis of several examples of deformation inhomogeneities in 2D and 3D systems are discussed.


abstract: 2.14
Noise in Deforming Systems
THOMSON ROBB M., 250 E. Alameda St. Apt. 515, Santa Fe, USA; MARISOL KOSLOWSKI, RICHARD LESAR, Theoretical Physics Div., Los Alamos National Laboratory, Los Alamos, NM, USA.
Since the demonstration by Hahner [1] that noise in deforming systems is substantial, and may play an important part in dislocation patterning, it has been important to confirm this proposition. We have developed, and will report on, a model of a wall of dislocations in kinetic equilibrium with a flux of dislocations, in which the equilibrium is established by an emission of new dislocations from the wall, and the annihilation of opposite pairs by recovery within the wall. Noise is a natural part of such a system, because the flux depends on the random populations of neighboring walls from which the flux is produced, and the noise is "multiplicative." In our case, the noise can be viewed as a pseudo temperature, and the wall "evaporates" at a critical value of the noise. This phenomenon can be viewed as a confirmation of Hahner's proposition. But in our model as well as Hahner's there is no energetics, and in Hahner's model, there is not even any explicit localization of the dislocations. Thus, one must view the prediction of the role of noise with caution, because one of the most important driving forces for the process of deformation is missing from the models. We are engaged in an investigation of simplified 2D models of deformation in which both energetics and noise play their natural roles, and will report on the interplay between noise and energetics, and to what extent noise can be said to have a dominant role in the formation of dislocation patterns.

References:
1. P. Hahner, Appl. Phys. A, Vol. 62 p473 (1996)


abstract: 2.17
Multiple slip in a statistical-mechanics based strain-gradient plasticity model
SERGE YEFIMOV, ERIK VAN DER GIESSEN, University of Groningenn, The Netherlands.
We have recently proposed a nonlocal continuum crystal plasticity theory for single slip, which is based on a statistical-mechanics description of the collective behavior of dislocations in two dimensions. In the present paper we address the problem of extending the theory from single slip to multiple slip. Continuum dislocation dynamics in multiple slip are derived and coupled to the small-strain framework of conventional continuum single crystal plasticity. Dislocation nucleation, the material resistance to dislocation glide and dislocation annihilation are included in the formulation. Nonlocal interactions between the dislocations of different slip systems are also taken into account.

Various interaction laws are considered on phenomenological grounds. To validate the theory in multiple slip we compare with the results of discrete dislocation simulations of two boundary value problems. One problem is bending of a single-crystal strip in plane strain with double slip. The bending moment versus rotation angle and the evolution of the dislocation structure are analyzed for different slip orientations, specimen sizes and slip system interaction laws. The other problem concerns the simple shearing of a crystalline strip constrained between two rigid and impenetrable walls. Key features are the formation of boundary layers and the size dependence of the material response in the case of symmetric double slip.


abstract: 2.22
Hall-Petch revisited
G. SAADA, LEM, CNRS-ONERA, FRANCE.
Since it was experimentally demonstrated more than fifty years ago, the Hall-Petch law has been checked many times. Its most interesting feature is that it applies to grain sizes varying from one micron up to one millimeter. The development of the study of nanocrystals, and more generally of nanostructured materials has triggered the publication of a wealth of papers trying to extend the former analyses to these new situations. In these latter materials, however, careful experiments have revealed the limited relevance of this approach, despite some successful attempts.

Our understanding of the mechanical behaviour of polycrystals of grain size larger than a few microns combines analyses of the intragranular plasticity with the effect of the locking of dislocations close to the grain boundaries. We shall therefore start by carefully revisiting the hypotheses which have been put forward in this case, and testing them at the light of recent available experimental results. We show that, whatever the grain size or shape, the pile ups models are more adapted to the description of the fracture mechanisms, than to the description of yielding. We shall therefore rather focus on analyses taking into account both the long range stress field of the dislocations blocked at the grain boundaries, and the build up of the intragranular dislocation network. Although the understanding of the development of the intragranular dislocation network needs a large amount of numerical calculations, we shall show, with the help of reasonable assumptions, some insight can be gained on the mechanisms controlling the yield stress, the strain hardening rate, and in some cases the ductility of polycrystals of various grain sizes. In doing this we were able to discard the effect of low angle boundaries on the Hall-Petch behaviour.

Extrapolation of these results to crystals of smaller size requires a detailed description of the effects which do not play a significant role in standard grain size materials : grain boundary volume, grain boundary sliding, strain localisation. A simple scaling analysis reveals the limits of the relevance of this extrapolation.


abstract: 2.25
The statistical origin of bulk mechanical properties and slip behavior in fcc metals
L. E. LEVINE, R. THOMSON, National Institute of Standards and Technology, USA.
Plastic stress-strain measurements of fcc metals exhibit a relatively simple and consistent behavior, requiring only a few internal state variables for reasonably accurate simulation. This is in stark contrast to the immensely complex dislocation behavior that underlies this process. Over the past several years, we have attempted to understand the origins of bulk mechanical properties through studies of a critical percolation model where dislocation cell walls act as both sources for mobile dislocations and as barriers to their motion. We will show that this process is controlled by the continuously evolving distribution of dislocation segment lengths within the walls and that a feedback mechanism keeps the system near its critical surface. A single physically-based assumption about this process leads to several direct predictions that are in agreement with experimental measurements. These include the magnitude of the flow stress for strained Al single crystals, the linear hardening law for stage II, the Voce hardening law for stage III, the formations of slip lines, the segregation of slip lines into slip bands, and the intermittent nature of the slip process. The macroscopic deformation behavior comes from the mean-field trajectory of the system on the critical surface and the microscopic slip behavior is associated with excursions away from this surface. The model also qualitatively explains the experimentally observed dependencies on time, temperature, applied stress, strain, and strain rate.


abstract: 2.28
Atomistic Simulation Studies of Size Effects in Plastic Deformation
ROBIN L. B. SELINGER, SCOTT WEINGARTEN, Catholic University, USA.
To study fundamental mechanisms associated with size effects in plasticity, we perform atomistic simulation studies of deformation in strain gradient geometries.

Using an idealized molecular dynamics model of a crystal under anti-plane deformation, we study the evolution of pure screw dislocations under a shear strain gradient. Looking at samples of different sizes, we observe that the mechanical response of the interior follows a simple constitutive law; however, a surface layer emerges whose mechanical response is harder than that of the interior. This surface layer, whose width varies with sample size and strain rate, produces an apparent size effect. This phenomenon can be explained by dislocation image interactions at the surface.

Next we consider an atomistic model of a two-dimensional crystal under bend in plane strain. The system equilibrates between bending increments via off-lattice Monte Carlo simulation at finite temperature. We examine the behavior of single crystalline, polycrystalline, and composite samples. Deformation occurs via nucleation and motion of pure edge dislocations. We examine the evolution of the sample's stress profile and bending moment. In preliminary results, we observe no obvious strain gradient effects in the interior of the sample, but we again observe emergence of a surface layer whose properties differ from those in the bulk.

If verified through further study, these results suggest that strain-gradient effects might be modeled by assuming that properties such as yield stress are depth-dependent.


abstract: 2.34
Structure of Newly Formed Dislocation Boundaries in Plastically Deformed Aluminum
SVETLANA BECKER, ISAAC GARBAR, Department of Materials Engineering, Ben Gurion University of the Negev, Israel; GUY MAKOV, ARIE VENKERT, ARIE VENKERT, Nuclear Research Center Negev, Israel; RONI Z. SHNECK, Department of Materials Engineering, Ben Gurion University of the Negev, Israel.

The internal structure of dislocation boundaries was studied in pure polycrystalline aluminum, following large plastic compression at room temperature. The boundaries are found to have surprisingly simple internal structures, consisting of one to three regularly spaced parallel dislocation arrays. The dislocations in each array share a common Burgers vector and are usually of mixed character. They do not have a simple crystallographic orientation. The majority of the boundaries are inclined 22-87 degrees to the slip planes of the dislocations. It is shown theoretically that parallel dislocation arrays may be states of stable equilibrium or unstable equilibrium, depending on their inclination to the slip plane. The simple internal structure persists to high strains. With increasing strain from 5% to 70% the fraction of two dislocation arrays increase in the boundaries and concurrently the density of the dislocations in each array increases from 12 to 48 dislocations in a micron. Different populations of boundaries with different densities can be discerned at the high strains.


abstract: 2.35
Modelling crystallite fragmentation as a function of friction stress and stacking fault energy
MARC SEEFELDT, PAUL VAN HOUTTE, DepaK.U. Leuven, Department of Metallurgy and Materials Engineering, Leuven (Heverlee), Belgium.

During cold deformation, f.c.c. crystallites subdivide into fragments. These fragments are separated from each other by deformation-induced dislocation rotation boundaries (DRBs) that accommodate the orientation mismatches. It is proposed to consider this fragmentation as a process of nucleation and growth of DRB segments. In this picture, the nuclei are groups of parallel excess dislocations on parallel slip planes.

The nucleation part, i.e. the formation of such groups, is proposed to be based on double cross-slip (DCS) of screw and/or vacancy-assisted climb of edge dislocation segments. Multiple DCS of screws and subsequent formation of Frank-Read sources can provide dislocation loops on parallel slip planes, and segments from these loops can get stopped at obstacles resulting into an excess dislocation group in the form of a DRB segment. Similarly, pile-up-like configurations of edges in front of obstacles could be transformed into an excess dislocation group by vacancy-assisted climb.

The growth part, i.e. the expansion of such groups, is proposed to be based on the capture of additional excess dislocations by the end stresses around the tips of the DRB segments. For these end stresses to be large enough, it is necessary that the misorientation across the nucleus be sufficiently large, i.e. that the distance between the excess dislocations in the nucleus be sufficiently small. This distance reflects the cross-slip distance covered in a DCS event or the climbing distance covered in a vacancy-assisted climb event.

Via these elementary processes, fragmentation can be studied as a function of parameters like friction stress, stacking fault energy, vacancy formation and migration enthalpies and temperature. The proposed model is worked out in terms of balance equations for defect densities. These equations include reaction terms based on mechanisms for the elementary processes. Parameters like the mean fragment size and misorientation can be derived from the defect densities.

The model is able to qualitatively reproduce the fragmentation behaviour of Cu, CuAl, CuMn during cold deformation as a function of the solid solute concentration. Defect densities as well as misorientations can be predicted in reasonable agreement with TEM measurements. Furthermore, applications to Al and AlMg will be discussed.


abstract: 2.36
IN SITU STUDIES OF PLASTIC DEFORMATION DURING NANOINDENTATION
ANDREW M. MINOR, national center for electrin microscopy, lawrence berkeley national laboratory, USA. MIAO JIN, Dept. materials science, univ. california, berkeley, USA. ERIC A. STACH, National center for electrin microscopy, Lawrence berkeley national laboratory, USA. JOHN W. MORRIS, dept. materials science, univ. california, berkeley, USA.

The authors have developed and implemented an in situ stage for a high-resolution transmission electron microscope that incorporates a diamond-tipped nanoindenter and permits observation of the nanoindentation process in real time. The observations achieved by this technique provide unique insight into mechanical behavior in conventional instrumented nanoindentation tests, and microstructural-level understanding of the mechanics of ultra-small volumes. Research to date includes indentation experiments on aluminum, steel, silicon and hard coatings of various types. Most of the current data is in the form of tapes of nanoindentations that show the formation and motion of dislocations and the motions of grain boundaries and interfaces in the various materials studied. This talk will present examples of the nanoindentation experiments and discuss new results concerning the initiation of deformation in Al and Fe, the mechanisms by which deformation is transmitted across grain boundaries or interfaces, deformation-induced coarsening of nanograins, low-temperature dislocation plasticity in Si and plastic deformation of diamond films, among other subjects.

abstract: 2.41
Influence of lattice friction on junctions in HCP and BCC metals: dislocation dynamics simulations
G. MONNET, EDF-Renardieres, France; B. DEVINCRE, LEM, CNRS-ONERA, France.

Lattice friction plays an important role in low-temperature plastic deformation of BCC and HCP materials. Under usual deformation conditions, lattice friction reduces strongly the probability of formation of junctions by reducing the spatial interaction region between close dislocations. Lattice friction affects also the stability of preexisting junctions. Due to the strong anisotropy of the Peierls valleys, the movement of the junction arms depends on the orientation of the junction orientation compared to the orientation of the Burgers vectors. Dislocation dynamics simulations are used to investigate this complex effect of lattice friction in different configurations including different interacting slip systems in HCP and BCC. In addition to interaction mapping, DD simulations are powerful tool for the investigation of large number on interacting dislocations, which is necessary to provide realistic prediction of the hardening induced by junction formation. Since the mobility of dislocations is thermally activated, the effect of the deformation temperature is also investigated. Interaction coefficients were found to vary with temperature and strain rate. The reason is that the formation and destruction of junctions are controlled by the thermally activated dislocation mobility. It is shown that interaction coefficients converge to those of FCC metals when temperature approaches the athermal temperature of the material.


abstract: 2.42
Quantitative dislocation microstructure analysis coupling micromechanical tools and X-ray diffraction line-broadening
BOUGRAB HAKIM, INAL KARIM, SABAR HAFID, BERVEILLER MARCEL, Laboratoire de Physique et Mécanique des Matériaux, LPMM-UMR CNRS 7554, Ecole Nationale Supérieure d'Arts et Métiers, 4, rue Augustin Fresnel, 57078 Metz Cedex 3, FRANCE.

An inverse approach for the dislocation microstructure analysis was developed. The aim is to determine the character of the activated dislocations, the range of the distortion field and the dislocation density. Such a problem is particularly complex, this is why, a tool allowing to analyze the diffraction line-broadening due to the dislocations is necessary. This analysis is possible by coupling the continuous micromechanical theory of dislocations, which provided the distortion field in each lattice spatial positions, with Fourier coefficients of X-ray diffraction (XRD) line.

The lattice distortion formulation is based on two tensors, the first is the dislocation density tensor which expresses the incompatibility of the microstructure and the second one is the Green's function. This last characterizes the interaction phenomena between lattice spatial positions. With a deterministic way, cases of a crystal filled with single dislocation and with periodic dislocation distributions were examined by (Bougrab et. al., 2004).

In this paper, an inverse approach is proposed in order to confront the numerical simulations with X-ray diffraction measurements. For that, an analysis of the dislocation character and the activated slip systems on duplex steel (casted and aged), under loading was carried out. It should be noted that the ferrite activates more screw dislocations and the austenite edge ones.

Finally, a quantitative coupling between X-ray high resolution measurements and our numerical simulations was examined in rolled copper multicrystal. In one grain of the specimen, the average distance H between dislocations was identified as 290Å and the dislocation density is equal to 1,8.1015m-2. These results are in good agreement with those given by (Monnet, 1999).

References:
Bougrab H., Inal K., Sabar H., Berveiller M., (2004). J. Appl. Crys., in press (V. 37, Part 2).
Monnet G. Phd thesis (1999), LPMTM-Ensam Paris.


abstract: 2.45
The strain hardening properties of fcc single crystals: simulations and modelling
B. DEVINCRE, LADISLAS KUBIN, LEM, CNRS-ONERA, BP 72, Chatillon 92322, France. T. HOC, Ecole Centrale Paris, France.
The strain hardening properties of fcc crystals can be modelled accurately by introducing dislocation-based crystalline models in finite element codes. The objective of the present work is to obtain a constitutive formulation containing a minimum number of free parameters and having a predictive value. For this purpose, a combination of numerical modelling and various data on dislocation properties available in the literature has been used in order to establish the constitutive model. The latter derives from the one proposed by Teodosiu and coworkers, which is an expanded form of the scalar Kocks-Mecking model. The key constitutive element in this framework is the hardening matrix, in which the matrix describing the interactions between slip systems plays a major role. This contribution is focused on the determination of the coefficients of the interaction matrix by dislocation dynamics (DD) simulations and their analysis. The method consists in measuring the applied stress associated with the interaction of mobile segments with a forest of given density, exclusively containing segments leading to one of the six different types of interactions available in fcc crystals. Care has been taken to ensure that the mean-free path of the dislocations in the DD simulations is not limited by artificial recombinations resulting from the use of periodic boundary conditions. Two main results were obtained. The hierarchy of the different types of interactions shows the major role played by the collinear interaction, whose strength is about fifteen times that of the Lomer lock (1). The apparent interaction coefficients depend on forest density, due to line tension effects not properly accounted for in the Taylor relation. A correction is then made in order to describe the variations of the interaction coefficients up to large strains. Finally, after a short description of the full model, some examples of predicted single crystal stress-strain behaviour, in single (three-stage curves) or multiple slip will be shown and compared to experimental data. The reason why such a model, which is based on uniform dislocation densities, can reproduce single crystal behaviour in monotonic deformation will be discussed.

1. R. Madec et al. , Science, 301 (2003) 1879.


abstract: 2.49
Evolution of the statistical properties of dislocation ensembles
ISTVAN GROMA, FERENC SZéKELY, Department of General Physics, Eötvös University Budapest, Hungary.
X ray line profile analysis is an efficient non-destructive technique to determine some key statistical properties of dislocation structures developing during plastic deformation. At the first part of the talk recent developments on describing the asymptotic behavior of the line profiles is outlined. A new evaluation method is presented to determine the average dislocation density and its spatial variation. The method is demonstrated on measurements obtained on compressed Cu single crystals. After this, it is shown that the relative dislocation density fluctuation exhibits a large sharp maximum at stage II-III transition. Finally, a simple model is outlined to explain the experimental evidences. The results give a new insight into the dislocation phenomena taking place during stage III deformation regime.