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Poster contributions

abstract: 2.1
Spatio-temporal dynamics of the Portevin-Le Chatelier effect
G. ANANTHAKRISHNA, Materials Research Centre, Indian Institute of Science, Bangalore, Karnataka, India.
Here we show that an extension of the Ananthakrishna's model to include spatial degrees of freedom explains all the important spatio-temporal features of the Portevin-Le Chatelier effect including the recently discovered crossover in the dynamics from a low dimensional chaotic regime at low and medium strain rates to an infinite dimensional power law regime of stress drops at high strain rates (1,2). The stress drop exponent turns out to be the same as for the experimental time series. Using a simple geometrical realization, we show that while a large proportion of dislocations are in the pinned state in the chaotic regime, most of them are pushed to the threshold of unpinning in the scaling regime, thus providing an insight into the mechanism of crossover. We also show that this model qualitatively reproduces the different types of deformation bands seen in experiments. At high strain rates where propagating bands are seen, the model equations can be reduced to the Fisher-Kolmogorov equation for propagative fronts. Marginal stability analysis shows that the velocity of the propagating of the bands varies linearly with the strain rate and inversely with the dislocation density. These results are consistent with the known experimental results. The analysis demonstrates that this simple dynamical model captures the complex spatio-temporal features of the PLC effect.

References :
1. M. S. Bharathi and G. Ananthakrishna, Europhys. Lett., 60, 234 (2002).
2. M. S. Bharathi and G. Ananthakrishna, Phys. Rev., 67, 065104 (R), (2003).
3. M. S. Bharathi, S. Rajesh and G. Ananthakrishna, Script Materialia, 48, 1355 (2003).

abstract: 2.2
Elastic wave propagation through a distribution of dislocations
A. MAUREL, LOA/ESPCI, 10 rue Vauquelin, Paris 75005 - France. V. PAGNEUX, LAUM, Université du Mans, Av. Olivier Messaien, Le Mans 72095 - France. D. BOYER, Departamiento de Fisica, UNAM, Mexico - Mexique. F. LUND, CIMAT/ Universidad de Chile, Santiago du Chili - Chili.
Our study concerns the coherent propagation of elastic waves through an elastic medium filled with randomly located scatterers. These scatterer are either 2D dislocations lines (edge or screw) or segment of aggregated dislocations that mimics a grain boundary.

Our motivation for this study is to explore possible new non-intrusive methods to study the properties of dislocations in materials. There are of course many situations of interest in the study of the mechanical properties of materials where crystal defects play a crucial role and transmission electron microscopy (TEM) appears to be the only technique of choice to characterise such defects in the bulk. Would it be possible to develop new tools ? Our results suggest acoustic waves could be used as a sensitive probe of dislocation structure. Such a tool would be useful to study plastic deformation or to understand the brittle-to-ductile transition and the role played by dislocations in continuous melting.

The basic mechanism for the scattering of an elastic wave by a line defect is simple: An elastic wave will hit each individual dislocation, causing it to oscillate in response. The ensuing oscillatory motion will generate outgoing (from the dislocation position) elastic waves. When many dislocations are present, the resulting wave behaviour can be quite involved because of multiple scattering. However, under some circumstances, there may exist a coherent wave propagating with an effective wave velocity, its amplitude being attenuated because of the energy being scattered away from the direction of propagation. This is the subject of the present research, in the case of a two dimensional continuum. There are two cases of interest: the anti-plane case, which corresponds to a scalar wave equation for the elastic wave in interaction with screw dislocations, and the in-plane case, which corresponds to a vector wave equation for the in-plane waves in interaction with edge dislocations. The vectorial nature translates into these waves being a superposition of longitudinal (acoustic) and shear waves.

abstract: 2.5
Dislocation Density Based Work Hardening Model
V.S.S. PRASAD GURLA, M. GOERDELER, G. GOTTSTEIN, Institut für Metallkunde und Metallphysik, RWTH Aachen, Germany.
The work hardening theory presented here, is a variant of the 3IVM (3 internal variables model) originally developed by Roters et. al [1]. It is a micro-structural model utilising the micro-structural state variables to describe the plastic flow behavior of cell forming metals and alloys. The internal variables in the present model (4IVM) are the four categories of dislocation densities; the immobile edge and screw dislocation densities in the cell walls $(\rho_e^w,\rho_s^w)$ and the immobile dislocation densities in the cell interiors $(\rho_e^i,\rho_s^i)$ . Unlike the original model which considers only edge dislocations, the present model includes both edge and screw dislocations, hence can be used in both high and low temperature ranges for a wide range of strain rates. The inclusion of screw dislocations and their ability to cross slip contributes to enhanced dynamic recovery, particularly at low temperatures and high strain rates. Along with the introduction of the model, a few illustrative results will be presented here, on how the model can be used to calculate the stress strain curves for various temperatures and strain rates. For the same set of optimizing parameters, the predicted flow curves for a variety of strain rates and temperatures are in good agreement with experiments. An advantage of the flow stress model presented here is that, the model results in output, which can be directly used as input for subsequent recovery and recrystallisation models.

References :
1. F. Roters, D. Raabe and G. Gottstein, Acta mater., 2000, 48, 4181- 4189.

abstract: 2.6
Electronic Drag of Dislocations and Work Hardening in Superconductors
V.V PUSTOVALOV, I.N. KUZMENKO, N.V.ISAEV, V.S.FOMENKO, S.E.SHUMILIN, B.I.Verkin Institute for Low Temperature Physics and Engineering, NAS of Ukraine, 61103, Lenin Ave., Ukraine.
The N-S transition in metals and alloys below $T_{c}$ entails appreciable changes in their plasticity: the flow stress decreases, the relaxation rates of stress and creep increase. Several theoretical models were proposed to explain these phenomena which are sometimes called softening at the NS transition. The models allow for an increase in the dislocation mobility due to the attenuation of the electron drag force in the superconducting phase. Recently, attention has been focused on the NS transition effect upon work hardening, which goes beyond the scope of only softening in the superconducting state. This has stimulated a detailed investigation of work hardening in the normal and superconducting states. The objects were single crystals of $(99.999\%)$ and $Pb-5 at.\% In$ alloy. The single crystals were tensiled at the constant rate $1.1 \times 10^{-5}s^{-1}$ at . The tasks of the experiments were to obtain the work hardening coefficients $\theta$ of the sample deformed: i) in the normal or superconductive state only; ii) at cyclically changed electronic states imposed by the magnetic field of the solenoid. The $Pb-5 at.\% In$ single crystal oriented for the easy-glide was tensiled at the strain rate $1.1 \times 10^{-5}s^{-1}$ . Simultaneously with the deformation, the sample was slowly heated in the vicinity of $T_{c}=7.05-7.1$ to estimate $\theta$ above and below $T_{c}$ on the same sample. It was show that except the NS transition-induced decrease in the flow stress, the plastic deformation in the superconducting state is characterized by a higher work-hardening coefficient as compared to that in the normal state, i.e. $\theta S > \theta N$ . This means that the superconducting transition lead to the additional work hardening of the crystal. It may be concluded that the actual model of low temperature work hardening should include the electron drag of dislocations which changes at the superconducting transition.

abstract: 2.9
Dipole heights in cyclically deformed polycrystalline AISI 316L stainless steel
STéPHANE CATALAO, Laboratoire de Conception des Systèmes Innovants (LCSI), CEA-Cadarache, France; XAVIER FEAUGAS, Laboratoire d?Étude des Matériaux en Milieux Agressifs (LEMMA), Université de La Rochelle, France; PHILIPPE PILVIN, Laboratoire Génie Mécanique et Matériaux (LG2M), Université de Bretagne Sud-Lorient, France. MARIE-THéRèSE CABRILLAT, Laboratoire de Conception des Systèmes Innovants (LCSI), CEA-Cadarache, France.
Cyclic deformation of f.c.c. metals leads in certain range of plastic strain amplitude to a localisation of plastic strain which can be recognized by a special dislocation microstructure so-called persistent slip bands (PSBs) surrounding by matrix (vein and channel). For a descriptions of microstructural mechanisms at the origin of these heterogeneous dislocation distribution and mechanical behaviour of this one, a knowledge of quantitative microstructural parameters is necessary. The main dimensional parameters, generally measured : wall tickness (e) and boundaries spacing (?) has been extensively used on a composite scheme to evaluate long-range internal stresses [1-3]. However poor information has been obtained on the evolution of the internal stress state. A measure of dipole height offers a good evaluation of the dislocation rate trapped in walls. Edge dipoles are a characteristic feature observed on walls, channels and veins substructures under cyclic loading. The investigations of dipole heights has been provided on metal which present a medium (copper, [4]) or high stacking fault energy (aluminium, [5] and nickel [6]). However there are remarkably few investigations in low stacking fault energy alloys [3]. The purpose of this work is to investigate the frequency distributions of heights of edge dipoles of a cyclically deformed polycrystalline AISI 316L stainless steel in the temperature range 300K to 873K. The effect of grain orientation, temperature and plastic strain rate on dislocations microstructure are discussed in term of the dipole annihilation distance ( $h_{min}$ ), the critical dipole height ( $h_{max}$ ), the mean dipole height and the variance $\sigma^{2}$ of the frequency distributions of heights. The dipole annihilation distance ( $h_{min}$ ) do not depend on plastic strain rate, increases as a function of temperature and as a function of stacking fault energy. If grain orientation do not affect dipole annihilation distance, the frequency distributions of heights is clearly dependent on the grain considered without scaling relation. In a similar way that in nickel an increase of can be related as a function of temperature. However, in 316L an anomaly is clearly demonstrated on $h_{max}$ vs T in temperature range where DSA is related in these alloys.

References:
1. Mughrabi H., Acta metall mater, 31 (1983) 1367.
2. X. Feaugas, Acta Mater., 47, (1999), 3632.
3. G.Gaudin, X. Feaugas, Mat. Sci. and Eng. A, A209-310, (2001), 382.
4. J.G. Antonopoulos, A.T. Winter, Phil. Mag., 33, (1976), 87.
5. M.E. Kassner, M.A. Wall, Met. Trans. A, 30A, (1999), 777.
6. B. Tippelt, J. Bretschneider, P. Hähner, Phys. Stat. Sol. (a), 163, (1997), 11.

abstract: 2.11
Atomistic mechanism of large plastic deformation of amorphous covalent bonded materials studied with molecular dynamics method
S. MUTO, Department of Materials, Physics and Energy Engineering, Division of Quantum Science and Energy Engineering, Nagoya University, Nagoya University, Nagoya 464-8603, Japan; T. TANABE, Department of Energy Engineering and Science, Division of Energy Materials and Device Engineering, Nagoya University, Nagoya University, Nagoya 464-8603, Japan.
Covalent bonded materials such as semiconductors and ceramics are generally brittle for plastic deformation, though they can exhibit a large plastic deformation, as is the case for superplasticity of sintered polycrystalline ceramic or blistering in gas-ion-irradiated group IV semiconductors. A key issue is that the structure bearing the large plastic deformations is amorphous, the mechanism of which of course is not ascribed to dislocation motion. In the present study, we propose an atomistic mechanism of such a large plastic flow of covalent bonded amorphous materials with the tetrahedral coordination, base on classical molecular dynamics (MD) simulations, using a semiempirical interatomic potential.

The simulation was conducted for a model system containing 1,000 silicon atoms with the Tersoff potential applied. An amorphous structure was first built by melting the system at 4,000 K, followed by rapidly cooling down to 300 K at a rate of 10 K/ps. Then a uniaxial stress of 1-2 Gpa was applied to the system at 298 K under the three-dimensional periodic boundary condition. The simulation condition was also imposed on crystalline silicon.

The crystal MD cell exhibited Poisson type strains proportional to the magnitude of the applied stress and the strain is recovered by release of the applied stress. By contrast, the amorphous cell kept plastically deformed (expanded) in the direction of the applied stress throughout the simulation. The deformation process of the amorphous cell could be classified into two regimes: pseudo-plasticity and super-plasticity regimes. In the former regime the local atomic configurations are relaxed to accommodate the applied stress, and in the latter regime the MD cell is gradually deformed so that the local atom configurations (bond lengths and coordination numbers) and hence the total energy should remain almost unchanged. Such large deformations are realized by collective atom motions of a quasi-static process. The effect of hydrogen termination of dangling bonds is also discussed, based on the experimentally obtained results on surface blistering induced by hydrogen ion implantation.

abstract: 2.13
On the plasticity of AlCuFe quasicrystals
MICHAEL TEXIER, JOËL BONNEVILLE, HONZA FIKAR, ANNE PROULT, Université de Poitiers - LMP - Chasseneuil Futuroscope - France; PIERRE GUYOT, Institut National Polytechnique - LTPCM - Grenoble - France.
In the present work, a detailed study has been performed to characterise the plastic behaviour of AlCuFe poly-quasicrystals. A variety of experimental techniques have been used: deformation tests at constant strain-rates, creep and stress relaxation experiments. Creep experiments were performed for various time intervals after interrupting constant strain-rate tests at different stress levels. After creep, plastic flow was again investigated at constant strain-rate. Cottrell-Stokes type experiments have been undertaken to determine the reversible part of the flow stress. Low temperature down to room temperature plasticity has been examined using both micro-indentation and confining pressure deformation techniques. At such temperatures, which is far below the brittle-to-ductile transition , dynamic recovery can be reasonably assumed to be negligible. The corresponding deformation microstructures have been examined by transmission electron microscopy., prior to and after deformation. Depending on deformation temperature, tweed-like background contrasts together with dislocations and/or platelet-like contrasts are predominantly observed. Direct proof of dislocation activity can not be firmly established from transmission electron microscopy observations. The flow stress is found to be fully temperature reversible, if one accounts for cumulated plastic strains, while creep and relaxation experiments indicate that significant structural changes do occur during plastic deformation. Measured activation parameters support a deformation mechanism that would be controlled by dislocation movement. The results are consistently explained in the frame of the constitutive model first proposed by Guyot and Canova [Phil. Mag A 79 (1999) 281], which strain dependent friction stress has been refined to account for time dependent processes specific to quasiperiodic lattice. Mechanical data as well as microstructural observations will be presented and the values of the physical parameters involved in the model will be discussed.

abstract: 2.15
DISLOCATION DYNAMICS SIMULATIONS IN BCC METALS
RONAN MADEC, CEA DAM-IdF, Département de Physique Théorique et Appliquée, FRANCE; LADISLAS KUBIN, Laboratoire d'Etudes des Microstructures, CNRS-ONERA, FRANCE.
Dislocation dynamics simulations have now reached a stage where they are able to tackle such questions as dislocation microstructures and forest hardening in bulk single cristals. The effective connection between the mesoscopic and continuum approaches of plasticity is based on the concept of interaction matrix between slip systems, from which a hardening matrix can be derived. As this connection is less advanced for BCC metals than for FCC metals, the purpose of the present work is to establish this link for BCC metals, using a dislocation dynamics simulation that will be described briefly. Emphasis will be put on the determination of the interaction matrix in the high temperature regime, above the so-called "athermal temperature" at which lattice friction vanishes. Preliminary results on forest hardening in the low temperature regime will also be discussed.

abstract: 2.16
Cyclically induced softening due to low-angle boundary annihilation in a martensitic steel
MAXIME SAUZAY, HELENE BRILLET, ISABELLE MONNET, MICHEL MOTTOT, FRANCOISE BARCELO, CEA, DEN-DMN-SRMA, FRANCE; ANDRé PINEAU, ensmp, centre des materiaux, FRANCE.
Martensitic 9Cr1Mo steel is used for high temperature applications. Several scales are involved in its microstructure. First, blocks are about 4mm, second laths inside a block are elongated and their thickness is about 0.7mm and third subgrains along the laths are equiaxed and their diameter is about 0.7mm. Between blocks, the misorientations can be high but the misorientations inside a block are smaller than 5°.

Low-cycle fatigue tests under strain control condition are carried out including various temperatures, strain levels and hold times. During cycling a significant softening is observed that is the peak stress decreases cycle by cycle. Hysteresis stress-strain curve study shows that the softening is mainly due to a backstress decrease (long-range athermal stress).

Transmission Electron Microscopy observations are carried out, on the initial condition, after cycling with or without hold time and after ageing. A large number of lath and subgrain boundaries disappear during cycling. Only low-angle boundaries seem to annihilate that is the block boundaries have not disappeared during lifetime. Ageing is not the driving force because the aged specimen microstructure is similar to the initial condition ones. Using these experimental data and observations, softening mechanism and modelling are proposed:

- mobile dislocations and dislocations of the low-angle boundaries (modelled as Read and Shockley tilt boundaries or similar boundaries) are supposed to interact. If the distance between a mobile edge (screw) dislocation and a low-angle boundary edge (screw) dislocation of opposite sign is smaller than the edge (screw) annihilation distance, both dislocations annihilate. Because of cyclic slip and random cross-slip, the boundary dislocation densities and the misorientations are decreasing cycle by cycle.

- a part of the backstress is induced by a Hall-Petch type (grain size) effect. Following Li computation (1963), the backstress corresponding to a tilt boundary depends on both the misorientation and grain size. In the calculation, the grain size is supposed to be associated to the smallest ones that is the sub-grain size.

Quantitative predictions of microstructure size and backstress cyclic evolutions are compared to the experimental results. Finally, the generalisation of these mechanism and modelling to the cyclic softening of polycrystals with a (sub)microcrystalline grain size is discussed.

abstract: 2.18
Size dependent yield strength and surface energies of thin films
P. FREDRIKSSON, P. GUDMUNDSON, KTH Royal Institute of Technology, Sweden.
Strain gradient plasticity theories have been developed especially during the last decade with the purpose of describing the plastic behaviour of materials on the micron scale. In the present paper the plastic strain rates are assumed to be colinear with a certain micro stress, instead of the usually applied stress deviator. The micro stress is conjugate to the plastic strain and it coincides with the stress deviator for vanishing plastic strain gradients. A third order moment stress tensor is also introduced. It is conjugate to, and colinear with the gradient of plastic strain. Through the consideration of plastic strain gradients, the effect of geometrically necessary dislocations is implicitly included. In the present paper a viscoplastic formulation is applied. A thin film on a thick elastic substrate is analysed for two simple load cases, biaxial loading and pure shear. Boundary conditions for the film - substrate interface are treated with special care. Since the interface will serve as an obstacle for dislocation movement, the dislocation constraint is formulated as a surface energy that depends on the plastic strain state at the interface. The surface energy contains a length scale parameter which is needed for dimensional consistency. FE-results show a strong dependence on the surface energy. If the surface energy is small, no size effects appear. On the other hand, if a stiff interface is simulated, corresponding to a large surface energy, a thickness dependence of the yield strength is found. For not too small thicknesses, the yield strength is inversely proportional to the film thickness. The application of several alternative strain gradient models would predict a thickness dependent hardening, but strictly not a size dependence of the yield strength. The presently predicted thickness dependence on yield strength and hardening is supported by experimental results.

abstract: 2.19
Fragmentation, Structural Saturation and Dynamic Effects during Severe Plastic Deformation
REINHARD PIPPAN, Erich Schmid Institute of Materials Science, Leoben, Austria. ANDREAS VORHAUER, FLORIAN WETSCHER, CD-Laboratory for Local Analysis of Deformation and Fracture, Leoben, Austria. MARIO FALESCHINI, Erich Schmid Institute of Materials Science, Leoben, Austria. HEIN PETER STüWE, Institute of Metal Physics, University Leoben, Austria. JOZEF KECKES, Erich Schmid Institute of Materials Science, Leoben, Austria.
Severe Plastic Deformation has been systematically applied to different pure metals, Al, Cu, Fe, W, Cr and different types of alloys. Shear strain and temperature have been varied over a wide range (shear strain between 1 and 1000, homologous deformation temperature between 0.1 and 0.4). Most deformation experiments were performed by high pressure torsion, in selected cases also other techniques, cyclic channel die compression and equal channel angular extrusion, have been applied. The microstructure were investigated by backscattered electron imaging, orientation image microscopy and in some cases by transmission electron microscopy.

The paper will give at first a short overview about the resulting microstructure after severe plastic deformation and then the reasons for fragmentation, the structural saturation and possible underlying mechanism will be discussed.

abstract: 2.20
THE EFFECT OF PEIERLS RELIEF ON THE KINETIKS OF LOW TEMPERATURE PLASTIC DEFORMATION OF ALPHA-TITANIUM
VLADYSLAV A. MOSKALENKO, VASYL' D. NATSIK, VIRA M. KOVALEVA, B.Verkin Institute for Low Temperature Physics & Engineering, NASU, Kharkiv, Ukraine.
Within the problem concerned with the physical mechanisms of plastic deformation of crystals, the results obtained for transition hcp metals of IVA group (Ti, Zr, Hf) appear to be most contradictory. According to calculation for Ti, the covalent component of the bonding can influence significantly the lattice friction of dislocation in these metals. It is known also that in alpha-titanium the dislocation core is spread, which should induce considerable Peierls stress and affect the low temperature plasticity. However, like in the bcc metals, the high sensitivity of the deforming stress, its temperature and strain-rate dependences to the interstitial impurities hampers separation of the contributions made by the Peierls barriers and the impurities. This calls for more detailed investigations of the plasticity mechanisms in higher purity titanium at low temperatures. To verify and ascertain the previous concepts of the potential Peierls relief effect on the plasticity of pure IVA group metals, the authors investigated thoroughly the kinetics of plastic deformation of higher purity titanium (0.06 at.% interstitial impurity) between 1.7 and 448 K. It is found that the yield strength and the strain-rate sensitivity of the deforming stress are proportional to the temperature factor T to the power four over five, which agrees with the results of the theoretical analysis of the dislocation mobility in the Peierls relief at low temperatures. The activation volume vs. stress dependence has also been obtained. The good agreement of theory and experiment has permitted us to find empiric values of the whole set of parameters for string model of a dislocation: linear tension, linear effective mass density and Peierls relief characteristics. It is show that the Peierls relief effect upon the kinetics of plastic deformation of polycrystalline higher purity titanium is the determining factor at 7 ? 150 K. Below 7 K the temperature dependences of the plasticity parameters deviate from the typical regularities of the thermally activated process. Further investigations are needed to elucidate the mechanism of plastic deformation of this material at T < 7 K and T > 150 K.

abstract: 2.21
Dislocation patterning and the deformation of metals
MARISOL KOSLOWSKI, RICHARD LESAR, ROBB THOMSON, Los Alamos National Laboratory, USA.
One of the central, and long-standing, issues in metals is the phenomenon of strain hardening, in which the complex interrelationship between evolving dislocation microstructures and the deformation response of the material plays the key role. We present results from a simplified computer simulation of dislocation motion and evolution that, for the first time, yields quantitative predictions of both the deformation properties of face-centered cubic metals as well as key descriptors of the evolving microstructure over a wide range of stress and strain.

We are able to describe the microstructure evolution of a single crystal and its correspondent macroscopic response over a wide range of deformation with its principals features: plastic flow (Stage I), forest hardening (Stage II), and recovery (Stage III). As the deformation proceeds, a partially ordered cellular dislocation structure develops. We obtain a stress dependent fractal exponent which characterizes the cell size distribution of the dislocation structure in agreement with experimental observation.

The average dislocation density and the average dislocation density fluctuation are also investigated. We find that during the transition from stage II to III, the dislocation density increases monotonically while the dislocation density fluctuation exhibits a maximum which is observed in X-ray diffraction experiments.

abstract: 2.23
Mechanical properties of C60 single crystals
L.S. FOMENKO, S.V. LUBENETS, B.Verkin Institute for Low Temperature Physics & Engineering, National Academy of Sciences of Ukraine; A.N. IZOTOV, R.K. NIKOLAEV, N.S. SIDOROV, Institute of Solid State Physics, Russian Academy of Sciences, Russia.
The Vickers microhardness HV of 60 single crystals grown from the vapour phase in vacuum has been measured in the temperature range 77-300K. The temperature dependence of HV manifests two distinct features, namely, the step-wise variation of microhardness by approximately 30% in the region of the fcc-sc transition temperature Tc $\approx$ 260K and the kink on the HV(T) dependence at T $\approx$ 180K. The latter is associated with the interaction of dislocations with the system of pentagonal and hexagonal configurations of C60 molecules whose equilibrium is violated by moving dislocations. The influence of structural defects, storage in air, illumination, polishing, annealing in air and in vacuum, and gaseous impurities intercalation on the value and the peculiarities of the temperature dependence of HV are investigated.

The stress-strain curves have been obtained on large (h $\approx$ 4 mm, S $\approx$ 6 sq mm) C60 crystals loaded in compression along at a constant strain rate at room temperature. The crystals revealed high brittleness, so their deformation occured not only by slip but also by the nucleation and growth of cracks. Moreover, the fracture of the samples under deformation occurred by cleaving along some crystallographic planes. It was shown that cleavage planes in C60 crystals are $\{111\}$ . The Vickers microhardness was measured on a fresh cleavage plane: HV = 130 MPa. The chemical etching showed dislocation rossette around the impression characteristic of $\{111\}$ planes.

abstract: 2.24
UNIVERSALITY OF AMPLITUDE AND FREQUENCY DEPENDENCES OF HARDENING AND SOFTENING IN MATERIALS
NELLY S. KISSEL, VALERY P. KISEL , Institute of Solid State Physics, 142 432 Chernogolovka, Moscow district, Russia.
This work concerns with the effect of applied compressive-extension stresses (the inter-rupted loadings are included), S (S = 0.6Sy to 95Sy, Sy is the resolved yield stress), stress rates, SR (SR = 10 to 106 MPa/s) and temperature range T = (4 10-3 to 0.945) Tmelt (Tmelt is the melting point) on the dislocation mean path lengths l(S, SR, T) and the mean number of mobile dislocations n(S, SR, T) in nominally pure ionic NaCl and semicon-ductor InSb single crystals. The general damping character of unpinning, motion and multiplication of dislocations appears in the ultimate lult and nult ,which corresponds to a macroscopic work-hardening of crystals (WH) [1]. Dislocation motion in slip lines and glide bands has a still more pronounced attenuation. The first interesting finding is that after the polishing of the near-surface layer with the thickness h = 5 to 35 microns the dislocations stopped by previous loadings began to move and multiplicate discontinu-ously down to their next or full stop (this microscopic work-hardening - softening is in line with macroscopic Ioffe effect in NaCl). Only the higher values of stress start their regular moving and multiplying and make dislocation motion more uniform on the same scale of observation. The second finding is that after the loading of NaCl and InSb cry-stals a definite fraction of mobile dislocations usually shifts under the action of back forces (due to dislocation line tension after the Orowan bowing of obstacles) in the direc-tion reverse to the acting force [2]. All their properties are common: under the first and low stress (magnetic field [3], etc.) loadings the reverse dislocation motion is usually more intensive than in the direct direction, the l, n(S, SR, T) are increased with the ap-plied S, SR, T, then they decelerate with an increase of the number of loadings (micro-scopic Bauschinger effect [2]). The next important finding of this work is that the WH generally varies non-monotonically to crystal softening according to the pulse length, amplitude and strain rate (times of leading and trailing edges of the pulse), the length of unloading pulse (restore time, frequency of loading) and their total number, predeforma-tion, temperature, etc. It is worth stressing that these V-shaped frequency dependences are universal for micro- and macrodeformation as well as for nanostructured crystals [4], magneto- and electroplastic effects, various physical-chemical effects (the effects of ultralow doses of chemicals, electromagnetic fields and particle irradiation, etc. are in-cluded) on solids, liquids, melts, glasses and biological tissues [5]. All the above data are irrefutably explained by the key role of dislocation micromechanisms of deformati-on in crystals [1,2,5]. The same effects for the melts, liquids, glasses and biological tis-sues demonstrate the universality of plastic flow mechanisms in various materials [5].
1.Kissel, N.S. and Kisel, V.P. Mater. Sci. Eng. A, 309-310 (2001) 97-101.
2.Kisel, V.P. et al. Philos. Mag. A, 67 (1993) 343-360.
3.Darinskaya, E.V. et al. Pis'ma v ZhETF, 70, No 4 (1999) 298-302.
4.Kisel,V.P.NanoSPD2 (Int.Conf.on Nanomaterials),9-13.12.2003,Vienna,Abstr.P-3.11.
5.Kisel, V.P. In: Untraditional natural resources, innovation technologies and products Collected Scientific Works. Issue 10. Moscow, 2003, 183-196 (in Russian).

abstract: 2.29
The Complexity of Dislocation Nucleation under Combined Normal and Shear Stress across the Slip Plane
GUANSHUI XU, DARREN SEGALL, CHENGZHI LI, University of California, Riverside, USA.

Dislocation nucleation under simple shear stress has been previously studied based on both continuum elastic dislocation theory and the Peierls-Nabarro model. Dislocation nucleation under a combined normal and shear stress across the slip plane, however, has received little attention. Unlike dislocation motion in which the normal stress can not be possibly too high to play any noticeable role on lattice resistance, the normal component of the stress which shear component is capable of nucleating a dislocation in perfect crystals can be as high as in the order of the theoretical strength such as in the case of dislocation nucleation in nanoindentation and strained heteroepitaxial thin films. Understanding the effect of the normal stress across the slip plane on dislocation nucleation therefore not only is scientifically important but also has significant implications on technological applications.

We will present our recent study of this subject based on a combined atomistic and continuum approach in which the ab initio calculation based interatomic layer potential is incorporated into the generalized variational boundary integral formulation of the Peierls-Nabarro model. We will report probably for the first time, to our best knowledge, how the large compressive stress can considerably change the landscape of interatomic layer potentials for certain crystal such as Tantalum. The significant implication of the complexity of this phenomenon on critical configurations of dislocation nucleation and possibly also disassociation will be elaborated. We shall also further attempt to reveal several competing dislocation nucleation mechanisms in nanoindentation. Understanding of these mechanisms appears to be essential for better understanding of the strong length-scale dependent mechanical behavior of crystals from atomistic to microstructural length-scales.

abstract: 2.30
Discrete Dislocation Simulations of Plasticity in Polycrystalline Materials
GUD. S. BALINT, V. S. DESHPANDE, Department of Engineering, Cambridge University, UK; A. NEEDLEMAN, Division of Engineering, Brown University, USA; E. VAN DER GIESSEN, Department of Applied Physics, University of Groningen, Netherlands.

The effect of grain size on the shear strength of a polycrystalline material subjected to doubly periodic pure shear is investigated using a framework that models plastic flow using large numbers of discrete dislocations. Frank-Read sources are distributed throughout initially dislocation-free grains on designated slip systems. Obstacles, annihilations and grain boundaries are accounted for through a set of constitutive laws. Materials used in the simulations are made by translating and rotating a square grain that has slip planes at +60, -60 and 0 degrees. The results are discussed in the context of the Hall-Petch effect, which is the observation that shear strength is inversely proportional to the square root of the grain size. In a second set of simulations, Mode I crack growth in a polycrystalline solid under monotonic loading is simulated. Fracture properties are embedded in a cohesive surface constitutive relation. Comparisons are made between crack-tip stress fields predicted by the simulations and the well-known HRR fields for isotropic solids, as well as theoretical predictions for fields in an ideally plastic single-crystal. While a strong dependence of grain size on shear strength was observed, no significant effect of grain size on crack growth resistance was seen.

abstract: 2.31
Atomistic simulations of screw and edge dislocations motion in BCC materials
BOUSSAD AMAROUCHENE, VASSILIS PONTIKIS, CECM/CNRS, Vitry-sur-Seine, France.
Using a N-body central-force phenomelogical potential which satisfactorily reproduces static and dynamical properties of body centred cubic iron, we have performed a series of molecular dynamics simulations to investigate, in detail, the structure, the energy and the Peierls stress to move ideal straight $1/2 <111>\{110\}$ edge dislocation, $1/2 <111>\{112\}$ edge dislocation and $1/2 <111>\{110\}$ screw dislocation.

Further, many related behaviours were revealed, especially, force-distance plots, trajectories of dislocations motion, trapping effect of dislocations on point defects (vacancy and self-interstitial) and influence of the trapping effect on dislocations trajectories.

Additionally, other simulations were performed for molybdenum (using another N-body central-force phenomelogical potential) in order to establish a comparison between iron and molybdenum edge/screw dislocation velocity ratios.

abstract: 2.32
A dislocation density-based plasticity model explicitly incorporating the frequency distribution of dislocation dipole heights
P. EISENLOHR, W. BLUM, Institut für Werkstoffwissenschaften, LS 1, Universität Erlangen-Nürnberg, Martensstraße 5, 91058 Erlangen, Germany.

Owing to their nature of being borderlines of dislocated area, dislocations annihilate by coalescence of equally slipped areas. A premise for such coalescence is the formation of dipolar configurations which need to be stable against the locally acting stress. Thus, not the total dislocation density but only the density of dislocations in dipolar configuration is relevant in modelling the static as well as dynamic annihilation of dislocations. In the present study a statistical, dislocation density-based, plasticity model is set up. Spatial homogeneity as well as equipartition on slip systems is assumed for the dislocation density. The total density is elementary discriminated into the two essential categories of dislocation dipoles and (residuary) "single" dislocations. Annihilation is modelled in terms of logging the frequency distribution of dislocation dipole heights, i.e. $\approx$ separation of dipole constituents. Next to dynamic dislocation reactions (in the course of plastic slip) this frequency distribution is constantly altered (with respect to time) based on climb of edge dislocations. The constitutive model is exemplarily complemented by a dislocation kinetics taking thermally activated splitting of junctions, formed with forest dislocations, as rate-controlling process. After fitting model parameters to pure Al, the plastic deformation behavior at various temperatures and loading conditions is evaluated. At high stress, the stationary deformation resistance exhibits a break-down of power-law behavior associated with annihilation turning purely glide-controlled. At low stress, the predicted stationary deformation resistance falls short of experimental reference (by 2-3 orders of magnitude in strain rate). Since the present model disregards spatially heterogeneous glide activity, geometrically necessary dislocations (GNDs) are not accounted for. The discrepancy at low stress is discussed in terms of hardening caused by subgrain boundaries constituted from GNDs. Interactions between individual dislocations and low-angle (sub)grain boundaries are noticed as relevant problem for further microscale modelling.

abstract: 2.38
Internal stress and work hardening of GNDs in continuum plasticity
ANISH ROY, AMIT ACHARYA, Carnegie Mellon University, USA.

We discuss existing gradient plasticity proposals that are intended to represent internal (back) stress effects of dislocation distributions, and show by a common and simple example that all such proposals overestimate the strain energy or stress of a dislocated medium by the introduced phenomenology. Based on the above observation, we propose a model of plasticity that does not have the above defect. The model phenomenologically accounts for short-range interactions through a gradient-enhanced strength-based Voce law model due to Acharya and Beaudoin (2000), and calculates the long-range stress and evolution of so-called geometrically necessary dislocation distributions, at the desired scale of resolution, in a mechanically rigorous manner based on field dislocation mechanics (Acharya, 2001; 2003; 2004). The gradient enhancement of the Voce law model requires only one extra material parameter. The further combination of field dislocation mechanics and the gradient hardening model requires no additional material parameters. We present finite element based computational results that demonstrate the prediction of

1) size effect

2) development of microstructure from homogeneous initial conditions under boundary conditions for homogeneous deformation in the conventional theory

3) development of back stress

4) distinct stages of hardening in average stress strain response.

abstract: 2.44
A dislocation distribution model based on concentration change of vacancy type defects in surface nano-structured materials produced by severe plastic deformation
XIAOGUANG LIU, XIAOWEI WANG, LIANGYUE XIONG, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 10016, China P. R.
The nano-structured surface layers were successfully created on several metallic materials by severe plastic deformation of surface. A great number of vacancy type defects mainly including vacancy and dislocation occur in the surface plastic zone (SPZ) and a super-saturation status of defects concentration was found in positron annihilation experiment. However the distribution of dislocation in the SPZ will not be homogeneous if the effect of surface is involved. In this work, a dislocation distribution model is given to explain the distinctness of dislocation distribution in SPZ . Considering the interaction between the dislocations, the dislocation density at different depth along the surface is determined by the image force of dislocation and the frictional stress against the dislocation motion in the distribution equation of dislocation. The calculation result shows that the distribution of dislocation is related to the distance from the surface. The maximum of dislocation density is not located at surface but in certain depth from surface. The result is agreed with the distribution characteristic of vacancy type defects in the experimental result of positron annihilation lifetime spectroscopy[1].

References
1. Xiaowei WANG, Jingyang WANG, Liangyue XIONG and Gang LIU, Materials Science Forum VOLs. 445-446 (2004) pp210-212..

abstract: 2.46
The fluctuation of short range order evidenced by dislocations
FLORENCE PETTINARI-STURMEL, ARMAND COUJOU, NICOLE CLéMENT, CEMES / CNRS Toulouse, France.
The analysis of the distribution of moving dislocations is used to obtain quantitative information about short-range order present in a complex industrial superalloy. We have already used static TEM observations of the collective behaviour of dislocations to evidence the evolution of SRO as a function of temperature. This determination was found to be in agreement with diffuse neutron scattering results [1]. Then, as the deformation is controlled by the short-range order degree which can be quantified by the diffuse antiphase boundary energy [2], the evaluation of this energy is of great interest [3].

This paper is aimed to evidence its spatial fluctuations in the gamma-phase of a nickel base superalloy. This determination uses a recent study where the method for the determination of this diffuse antiphase boundary energy has been carried out taking into account the thin foils effects [4]. In this work, the measurement of the position of dislocations during their propagation in the sample over few micrometers allows to calculate precisely this energy at different spatial points. A clear spatial fluctuation by a factor 2 or 3 of the diffuse antiphase boundary energy is evidenced over several micrometers. For the first time, the non-uniformity of SRO is illustrated and quantified in a complex solid solution. This distribution of SRO induces soft and hard regions. As a consequence, the activated sources of dislocations are nucleated and in the soft regions [5]. The precise knowledge of the spatial distribution of SRO is thus an explanation for the observed heterogeneous deformation.

References :
1. F. Pettinari, M. Prem, G. Krexner, P. Caron, A. Coujou, H.O.K Kirchner, and N. Clément, Acta Mater., (2001), 49, 2549-2556.
div 2. P. Schwander, B. Schönfeld, G. Kostorz, Phys. Stat. Sol.(b) 172 (1992) 73-85.
3. F. Pettinari, doctoral thesis (1999).
4. G. Saada, J. Douin, F. Pettinari-Sturmel, A. Coujou, N. Clément, Phil. Mag., 84 (2004) 807-824.
5. F. Pettinari-Sturmel, C. Coupeau, N. Clément and A. Coujou, Mat. Sci. Eng. accepted.

abstract: 2.47
Incorporating the influence of the temperature into a mesoscopic continuum description of dislocation systems
BOTOND BAKÓ, ISTVáN GROMA, Eötvös University Budapest, Faculty of Science, Dept. of General Physics, Budapest, Hungary; E. C. AIFANTIS, Aristotle University, Laboratory of Mechanics and Materials, GR 54124, Thessaloniki, Greece.
During plastic flow of crystalline materials dislocations, the carriers of plastic deformation tend to form nonuniform, highly organized structures. A commonly applied approach for describing the collective behavior of many individual dislocations is the so-called continuum description in which the dislocation system is described by continuous functions of the space coordinates. Starting from the exact evaluation of the -dislocation probability density distribution function, a Fokker-Planck type equation is derived by taking into consideration the influence of the temperature and dislocation climb. The results are discussed in terms of their general implications for dislocation patterning.

abstract: 2.48
Stress distribution in relaxed dislocation systems
FERENC F. CSIKOR, ISTVáN GROMA, Eötvös University Budapest, Faculty of Science, Dept. of General Physics, Budapest, Hungary.
The study of the probability distribution of the internal stress created by dislocation systems is motivated by two reasons. Stochastic methods can significantly accelerate the most computation intensive part of dislocation dynamics simulations, the calculation of pair interactions. Besides that, X-ray line profile analysis is an effective method for characterizing dislocation arrangements by direct measurement of the strain distribution.

The already known asymptotic properties of the stress distribution function are determined only by the 1/r decay of the stress field of individual dislocations. The central part of the distribution function is known to be determined by the correlation properties of the dislocation assembly. The topic of this contribution is the determination of the analytical form of this central part. The special case of relaxed dislocation configurations is investigated. At typical deformation rates the correlation properties do not change significantly so the results can be used in dynamics simulations as well.

Random, single slip configurations of straight, parallel edge dislocations were relaxed with ordinary dislocation dynamics simulations. The well-known development of dislocation dipoles and walls was observed. The stress distribution function of dipoles and walls was computed analytically. From these, a model stress distribution function was constructed for relaxed systems. Comparing our model to the numerically computed stress distribution function shows that pair correlations describe the central part of the stress distribution function satisfactorily. Using the same stress distribution model, a preliminary analysis of the time evolution of the relaxation process is performed.

abstract: 2.51
On the change of the characteristic length scale of the microstructure of tensile deformed copper single crystals
A. BORBÉLY, Eötvös University Budapest, Faculty of Science, Dept. of General Physics, Budapest, Hungary. P. J. SZABó, Budapest University of Technology and Economics, Department of Materials Science and Engineering, H-1111 Budapest, Goldmann sq. 3, V2/153. I. GROMA, Eötvös University Budapest, Faculty of Science, Dept. of General Physics, Budapest, Hungary.
Copper single crystals oriented for single slip were deformed in tension and the resulting microstructure was investigated by Electron Backscattering Diffraction (EBSD). Scans of 150 x 120 $\mu m^{2}$ were measured on samples corresponding to four deformation states situated at the middle of stage II, at the transition point between stages II-III, and at other two points in stage III of work hardening. Disorientation maps show a significant increase in the characteristic length of the deformed microstructure at the transition point, which is about 3-4 times larger than the characteristic lengths corresponding to stages II and III. At the transition point large regions of about 50 x 50 $\mu m^{2}$ develop, which are characterized by a high spatial correlation of the crystallographic orientation. It was found that the probability to find two points, separated by a given distance r < 10 $\mu m$ , and which have a disorientation smaller than 0.75° is the largest in these highly correlated regions of the transition point. The "correlation length" of the disorientation angle of 0.75° is about 12 $\mu m$ at the transition point, compared to 7 $\mu m$ in stage II and about 2-3 $\mu m$ in stage III. These experimental results emphasize the statistical behavior of the dislocation ensemble suggesting that the transition between stages II and III of work hardening is similar to a phase transformation. The EBSD results are compared with previous transmission electron microscopy data, available in the literature.

abstract: 2.52
Paradigm Shift in Plastic Deformation Studies due to Minimum Entropy Production Analysis
S. SAIMOTO, Materials and Metallurgical Engineering, Queen's University, Kingston, ON. K7L3N6, CANADA.
Plastic deformation first came under scientific scrutiny when heat was generated during the boring of cannons. However in the 20th century with the discovery of single crystal production and the Schmid law, the emphasis has been to determine the evolution of the dislocated structure as a deviation from the perfect crystalline state as a form of storing minimum enthalpy. In this manner, Stage I, II and III deformation modes and its evolution is well described (Brown, Metall. Trans. 1991). On the other hand, continuum-crystal plasticity approaches were developed to interpret or to make the plastic potential more predictive. This approach inherently assumes a polycrystalline aggregate which undergoes uniform macroscopic strain. In order that each crystallite deform in a compatible manner to meet this geometric stipulation, a slip-system selection rule must be invoked. It turns out that the current Asaro-Needleman (Acta metall. 1985) rule of constant strain rate sensitivity is limited to cases where no dynamic recovery takes place, although it conforms to the minimum entropy production principle (Saimoto, Phil. Mag. 2004). The latter principle is more powerful in that it can encompass dynamic recovery. Consideration of the means to dissipate power rather than to focus on dislocation arrays which comprise the stored work suggests that different modes of grain break-up are a result of how efficiently dislocations are annihilated. From this viewpoint, the specific dislocated arrays come about due to the inherent mobility of dislocations depending first on the crystal structure but also depending strongly on the presence of solutes of varying solubilities. A characterization method is suggested from the theory to determine which evolving arrays will enhance greater ductility. Examples comparing fcc and bcc metal crystal structures will be given.

abstract: 2.53
Fokker-Planck equation for the internal stress distribution functions
BENEDEK KOCSIS, ISTVáN GROMA, Eötvös University, Dept. of General Physics, Hungary.
The time evolution of internal stress distribution function in computeristic discrete dislocation relaxation experiments was recorded. Fokker-Planck equation was built for describing the time evolution of internal stress distribution functions and the solution of this equation was compared to the computer simulation results.

abstract: 2.54
Scaling of dislocation cells in GaAs crystals by global numeric simulation and their restraints by in situ control of stoichiometry
PETER RUDOLPH, CHRISTIANE FRANK-ROTSCH, UTA JUDA, FRANK-MICHAEL KIESSLING, Institute of Crystal Growth, Max-Born-Str.2, 12489 Berlin, Germany.

In contrast to metals dislocation structures in semiconductor compounds are not yet intensively studied. As-grown GaAs crystals show characteristic dislocation cell arrays evoking undesirable mesoscopic inhomogeneities of the wafer parameters. The dislocation densities are orders of magnitude lower than in metals and are typically $10^{3}$ - $10^{3}$ cm $^{-2}$ in undoped GaAs depending on growth methods and crystal diameters. Therefore, the mean cell sizes are much larger and are in the range of 0.1 - 2 mm. The correlation between cell diameter d and dislocation density $\rho$ , taken from crystals grown variously, obeys the Taylor relation d = 10 $\rho^{-1/2}$ . In order to scale the cell dimension with the flow stress $\tau$ that acts during the growth in the high-temperature region global computer simulation of the thermo-mechanical stress field was carried out. All obtainable material, geometrical and growth parameters of the given experimental set up were carefully considered. The calculations are based on the time-dependent crystal geometry in strong correlation to the real position of the crystallized fractions where the wafers for cell structure analysis were taken from.

First, the temperature distribution within the whole liquid encapsulated Czochralski growth arrangement was calculated. Then the axis-symmetric radial stress distribution was modelled by solving the stress-strain relation for an anisotropic body. The tensorial stress components were converted into the resolved shear stress for the twelve $\{111\}<110>$ slip systems. The mean cell diameter distributions along the and directions of the real wafers were correlated with the computed shear stress courses. Additionally, transversal von Mises stress field calculations were included in the scaling analysis. Despite of some uncertainties the results meets the principle of similitude d = K Gb/ $\tau$ quite well, whereas , G - shear modulus, and b - Burgers vector.

First successful attempts to restrain the cellular structure in GaAs crystals grown in a vapour pressure controlled Czochralski arrangement without boric oxide encapsulant with in situ control of the stoichiometry will be presented. It will be shown, that the spatial cell formation can be depressed effectively by minimizing the intrinsic point defect content and, hence, dislocation climbing.

abstract: 2.55
Coupling of elementary dislocation processes during high temperature and low stress creep of super alloy single crystals
GUNTHER EGGELER, Ruhr-Universität Bochum, Germany.
Super alloy single crystals are characterized by their well known gamma/ gamma prime microstructure where 70 volume percent of gamma prime cubes (0.5 $\mu$ m; L12) are separated by thin (0.1 $\mu$ m; fcc) gamma channels. High temperature plasticity of super alloy single crystals is governed by dislocation glide and climb processes and while there is a good understanding of intermediate temperature/high stress plasticity of single crystal super alloys the coupling of elementary dislocation processes with microstructural softening processes (rafting) during high temperature and low stress creep is less well understood. We first consider the role of coherency stresses and dislocation stress fields on dislocation plasticity. Both, channel filling by dislocations and early rafting govern the strong decrease of creep rate during primary creep [1]. As long as rafting is not yet completed, gamma prime corners (at gamma channel crossings) represent locations where dislocations of opposite sign can mutually annihilate. The onset of secondary creep corresponds to a local steady state dislocation density with counteracting strain hardening (dislocations enter thin gamma channels) and time softening processes (annihilation of dislocations at gamma prime corners). A steady state dislocation net work spacing reflects this dynamic equilibrium; the results of a simple discrete dislocation model are shown to agree with experimental findings [1]. When rafting is completed, the annihilation of dislocations at gamma prime corners no longer can account for dynamic recovery. Now a new recovery process takes over which has recently been identified [2,3]. Pairwise cutting of the gamma prime phase by gamma channel dislocations with different Burgers vectors is observed. And it is shown how these two dislocations can move by a coupled process of glide and climb. The objective of the present paper is to show how this type of cutting process can interact with the well known rafting process and how this coupling of elementary microstructural processes can account for the stress and temperature dependence of creep.

References:
1. M. Probst-Hein, A.Dlouhy, G.Eggeler, Acta Mater., 47 (1999) p. 2497
2. G.Eggeler, A.Dlouhy, Acta Mater., 45 (1997) p. 4251
3. R. Srinivasan, G.Eggeler, M.J.Mills, Acta Mater., 48 (2000) p. 4867

abstract: 2.56
Cosserat modeling of grain size effect in polycrystals: application to ferritic steels
ASMAHANA ZEGHADI, SAMUEL FOREST, ANNE-FRANçOISE GOURGUES, Centre des Matériaux, Ecole des Mines de Paris, Evry, France. OLIVIER BOUAZIZ, IRSID, ARCELOR, Maizières-les-Metz, France.
The aim of this work is the continuum modeling of the grain size effect on the mechanical behaviour of multi-phased metallic materials, as experimentally observed. In order to predict macroscopic mechanical response of a heterogeneous medium, different homogenization methods are used in the literature. Most of them are so-called 'mean fields models', and don't take into account the absolute size of heterogeneities. Weng [1] introduce explicitly the grain size d into a pre-existing homogenization model (self-consistent). Such an approach remains purely phenomenological, and thus can not be really relied on, especially in the case of complex morphologies. Alternative approach, chosen here, is based on Cosserat continuum mechanics [2]. Plasticity models based on generalized continuum mechanic are an interesting issue because they include an internal length. The Cosserat approach introduces additional hardening associated with the lattice curvature which is directly linked with the density of geometrically necessary dislocations [3].

The model parameters are identified from tensile tests on a ferritic steel for grain sizes varying from 120 mu m to 5 mu m. Classical hardening parameters are identified from literature and from the tensile curve for large grains polycrystals. The three parameters of the additional hardening law are deduced from the tensile curves with the smallest grain size. three-dimensional finite element simulations of polycrystalline aggregates will be shown. Several aggregates containing ten to twenty grains are simulated using periodic boundary conditions. They provide us with intra-granular plastic strain fields and overall tensile curves. A detail analysis of the lattice curvature field close to grain boundaries as a function of grain size will be presented.

The first stage of the work lies in identifying constitutive equations parameters with an inverse method. Bi an tri-dimension simulations are realized on periodic aggregates for grain sizes varying between 120 mu m and 5 mu m, in the one hand with a classical approach and in the other hand with a Cosserat model. Many supplementary hardening laws were tested into the Cosserat approach. Results are at least compared to experimental tensile tests on various grain sizes IF ferritic steels. The grain size effect is clearly confirmed. Bi-dimension simulations allows us to understand physical phenomenon implied.

References:
1. Weng, G.J. (1983). A micro-mechanical theory of grain-size dependence in metal plasticity. J. Mech. Phys. Solids,vol. 31, pp 193-203.
2. Forest, S., Pradel, F., Sab, K. (2001). Asymptotic analysis of heterogeneous Cosserat media. Int. J. Solids Structures, vol. 38, pp +4585-4608.
3. Ashby, M.F. (1970). The deformation of plastically non-homogeneous alloys. Phil. Mag., vol. 21, pp 399-424.

abstract: 2.58
Modelling of the low temperature behavior in low alloy steels
MAXIMILIEN LIBERT, MSSMAT ECP, Chatenay Malabry, France and CEA DEN/SAC/DMN/SRMA, Gif sur Yvette, France; COLETTE REY, MSSMAT ECP, Chatenay Malabry, France: BERNARD MARINI, CEA DEN/SAC/DMN/SRMA, Gif sur Yvette, France.
Low alloy steels show a transition between a brittle behavior at low temperatures and a ductile behavior which leads to a strong increase of toughness at higher temperatures. The evolution of plasticity mechanisms with temperature is often considered as one of the possible causes to this ductile / brittle transition.

Above a temperature T0, the plastic behavior of B.C.C. metals is governed by forest hardening, whereas below this temperature, the thermally activated mobility of screw dislocations tend to become preponderant. The first stage of this study is to define a crystalline model which takes into account the plastic behavior below T0.

We use a crystalline approach in which the dislocation densities on each slip system are the state variables governing plasticity. In order to take into account the thermally activated mechanisms (such as double kink mechanism), a new flow rule is chosen. Further modifications of the hardening law are studied.

The model parameters are identified with an inverse method from tensile tests carried out in the temperature range 25°C / -195°C. The next stage consists in modelling a crystalline aggregate in which the microstructure (orientation and position of the grains in the aggregate) is determined by EBSD technique. This crystalline approach allows us to calculate the mechanical local field heterogeneities evolution in the ductile / brittle transition temperature range, where a change in the plasticity mechanisms is assumed.

abstract: 2.59
Finite Size Effects in Dislocation Glide: Simulations based on the Line Tension Model
THOMAS NOGARET, DAVID RODNEY, GPM2/INPG, Grenoble, France.
Recent Molecular Dynamics simulations of the glide of an edge dislocation in a random Ni(Al) solid solution [1] showed finite size effects: the yield stress decreases when the length of the dislocation between the two periodic boundary conditions increases, while it increases when the glide distance increases. In order to extrapolate the results of these simulations to scales representative of grains in polycrystals, we must understand quantitatively this size effect. Molecular Dynamics cannot be used, because they are too time consuming.

Instead, we employed simulations based on the isotropic line tension model. The use of this local model is justified by the fact that the MD simulations showed that the obstacles are short-ranged Al atoms brought in positions of strong mutual repulsion in the course of dislocation glide.

Results confirm that the yield stress depends on the size of the simulation cell. For example, in the case of a square box, the smaller the box, the higher the yield stress. This effect is stronger for weak obstacles. We found two governing scaled parameters: the average number of obstacles on the dislocation line, $n_{w} = \mathrm{Width} \times \beta^{0.5}/d$ , and the glide distance scaled by the height of the bending dislocations, $n_h = \mathrm{Height} / \beta^{0.5}/d$ , where $\beta=cos(\Phi_c/2)$ is the obstacle resistance and , the average distance between obstacles.

In a multiscale approach, we discuss how to combine the present simulations and MD simulations to predict the yield stress in large scale grains.

References:
1. E. Rodary, D. Rodney, L. Proville, Y. Bréchet and G. Martin, accepted to Phys. Rev. B (2004).

abstract: 2.60
Parallel algorithm for Discrete Dislocation Dynamics on distributed memory machines
CHANSUN SHIN, MARC FIVEL, GPM2, 101 rue de la Physique, 38402 Saint Martin d'Hères, France; MARC VERDIER, LTPCM, 1130 rue de la Piscine, 38402 Saint Martin d'Hères, France.
Dislocation dynamics (DD) simulations are computationally demanding due to the fact that the stress field of a dislocation segment is long-ranged and that it needs to inspect possible interactions for segment motion. This imposes certain limits on the problem size of DD simulations. To enhance the computing efficiency, a DDD code has been parallelized using the standard Message Passing Interface (MPI). Both stresses and segment motion have been parallelized using domain decomposition method, or ``Box method''. The box method with 213 boxes gives a speed-up of 30 for 20,000 segments. Performance test on IBM p690 architecture shows that the parallel scheme adds up a speed-up factor of nearly 20 using 36 processors. Thus the DD code presented here is about 600 times faster than the previous code. We present a parallel algorithm for highly complex dependencies in segment motion and performance test results in detail in this study.

Next: Dislocations in specific structured Up: Collective behavior of dislocations Previous: Oral contributions Index

Benoit Devincre 2004-09-09