Investigation of the statistical properties of dislocation ensembles

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Details of project

Identifier

43519

Type

Principal investigator

Groma, István

Title in Hungarian

Diszlokáció rendszerek statisztikus tulajdonságainak vizsgálata

Title in English

Investigation of the statistical properties of dislocation ensembles

Panel

Physics

Department or equivalent

Department of Materials Physics (Eötvös Loránd University)

Participants

Borbély, András
Csikor F., Ferenc
Székely, Ferenc
Vörös, György

Starting date

2003-01-01

Closing date

2006-12-31

Funding (in million HUF)

11.322

FTE (full time equivalent)

0.00

state

closed project

Final report

Results in Hungarian

A pályázat célkitűzéseinek megfelelően diszlokációk kollektív tulajdonságait vizsgáltuk mint elméletileg mind kísérletileg. Analitikus számításokkal és numerikus szimulációval vizsgáltuk a diszlokációk következtében kialakuló belső feszültségeloszlás tulajdonságait. Megállapítottuk, hogy az eloszlás központi része Lorentz eloszlású, míg a lecsengő tartományban a feszültség köbével fordítottan arányos. Továbbá kimutattuk, hogy a külső feszültség hatására egy a feszültség 4. hatványával leeső aszimmetrikus tag jelenik meg. Megmutattuk, hogy egy 2D diszlokációrendszer relaxációja során a különböző fizikai mennyiségek az idő hatványfüggvényeként csengenek le. Kimutattuk, hogy a diszlokáció climb bekapcsolása jól definiált cellaszerkezet kialakulásához vezet.. A korábban mikroszkopikus meggondolásokkal kidolgozott diszlokáció kontinuum elméletet sikerült egy variációs elvből származtatni. Ez lehetővé tette az elmélet általánosítását többszörös csúszásra ill. oldott atomok hatásának beépítését is. Az elmélet segítségével részletesen megvizsgáltuk egy extra hozzáadott diszlokáció terének árnyékolását a többi diszlokáció átrendeződése következtében (Debye screening) . A kísérleti munka során nanoindentációval Cu egykristályokon meghatároztuk a mikrokeménység relatív fluktuációját. Az irodalomban először megállapítottuk, hogy a diszlokációsűrűséghez hasonlóan ez is az alkalmazott feszültség függvényében egy éles maximumot mutat.

Results in English

According to the proposal the collective properties of dislocations were investigated both by theoretical and experimental methods. The properties of the internal stress distribution generated by dislocations were investigated by analytical calculations and computer simulations. It was found that the central part of the distribution is Loretzian while its tail decays with the invers cube of the stress. If external stress is applied the distribution becomes asymmetric. The antisymmetric part decaying with the invers fourth power of the stress. Numerical studies show that during the relaxation of the dislocation ensemble the different macroscopic quantities decay with some power of the time. Beside this, it is obtained that the dislocation climb leads to the the formation of cell structure. The continuum theory of dislocations derived earlier from microscopic considerations was reformulated into a phase field theory. This allowed us to extend the theory to multiple slip and study the influence of solute atoms. With this framework the Debye screening of the stress field of an extra dislocation was analysed in details . The relative fluctuation of microhardness (RFM) was determined by nanoindentation performed on deformed Cu single crystals. It was found that like the fluctuation of the dislocation density the RFM alo exhibits a sharp maximum as a function of applied stress.

Full text

http://real.mtak.hu/1112/

Decision

Yes

List of publications

I. Groma: Gradient terms in a continuum theory of dislocations, Multiscale Modeling of Strength Fracture, Workshor, Berkeley CA, 2004

I. Groma A. Borbely: X-ray Peak Broadening due to Inhomogeneus Dislocation Distribution, Diffraction Analysis of the Microstructure of Materials, E.J. Mittermeier, P. Scardi, 2004, 2004

Yefimov S, Groma I, van der Giessen E: A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 52 (2): 279-300, 2004

Csikor FF, Groma I: Probability distribution of internal stress in relaxed dislocation systems, PHYSICAL REVIEW B 70 (6): Art. No. 064106, 2004

Yefimov S, Van der Giessen E, Groma I: Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations, MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 12 (6): 1069-1086, 2004

I. Groma: From discrete to continuum dislocation dynamics, 5th EUROMEC Solid Mechanics Conference, 2003

I. Groma: From Discrete Dislocation Dinamics to Continuum Theory of Plasticity, ICSMA-13 Budapest, 2003

I. Groma M. Zaiser, A. El_Azab: The continuum representation of dislocation dynamics, MMM II UCLA Los Angeles, 2004

I. Groma: Linking micro to meso scale, A discussion meeting on Discrete Dislocation Plasticity, Cambridge, 2004

I. Groma f. Szekely A. Borbely and K. Mathis: Evolution of the statistical properties of dislocation ensembles, Dislocation 2004 �La Colle-sur-Loup\'', Meudon, France, 2004

Csikor FF, Kocsis B, Bako B, Groma I: Numerical characterisation of the relaxation of dislocation systems, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 400: 214-217 JUL 25 2005, 2005

Bako B, Groma I, Avlonitis M, Aifantis EC: Incorporating the influence of the temperature into a mesoscopic continuum description of dislocation systems, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 400: 218-221 JUL 25 2005, 2005

Groma I, Borbely A, Szekely F, Mathis K: Evolution of the statistical properties of dislocation ensembles, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 400: 206-209 JUL 25 2005, 2005

Borbely A, Szabo NJ, Groma I: Orientation correlation in tensile deformed [011] Cu single crystals, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 400: 132-135 JUL 25 2005, 2005

I. Groma: Statistical physics approach to describe the collective properties of dislocations, in Multi Scale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics, Ed. by P. Gumbsch and R. Pippan, in press, 2005

Bako B, Groma I, Mastorakos I, Aifantis EC: Investigation of dislocation patterning by stochastic integration of dislocation trajectories, MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 13 (5): 671-681 JUL 2005, 2005

I. Groma: Consequences of slow dislocation relaxation: Size-dependent Material Properties, Size-dependent Material Properties, Lorentz Center, February 27- Marc 4, 2005., 2005

I. Groma: Statistical Physics of Dislocations properties of dislocations, Multi Scale Modelling of Plasticity, Advanced School, CISM, Udine, July 4-8, 2005, 2005

I. Groma: Microscopic origin of gradient terms, McMat 2005, Baton Rouge, Louisiana, June 1-3, 2005 Lorentz Center, February 27- Marc 4, 2005., 2005

I. Groma: Derivation of the evolution equation of dislocations from the maximum entropy principle properties of dislocations, International Conference on the Statistical Mechanics of Plasticity and Related Instabilities, Bangalore, India, Aug. 29 - Sept. 2. 2005, 2005

I. Groma F. Szekely: Evolution of the dislocation microstructure: A model based on X-ray line profile measurements, Scripta Materialia, 54 753-757, 2006

B. Bako, I. Groma, G. Gyorgyi, and G. Zimanyi: Dislocation patterning: the role of climb in meso-scale simulations, Computational Materials Science, 2005

Groma I, Gyorgyi G, Kocsis B: Debye screening of dislocations, PHYSICAL REVIEW LETTERS 96 (16): Art. No. 165503, 2006

Borbely A, Revesz A, Groma I: Momentum method applied to evaluation of size and strain in ball-milled iron, ZEITSCHRIFT FUR KRISTALLOGRAPHIE : 87-92 Part 1 Suppl. 23, 2006

Bako B, Groma I, Gyorgyi G, G. Zimanyi: Dislocation patterning: The role of climb in meso-scale simulations, COMPUTATIONAL MATERIALS SCIENCE 38 (1): 22-28, 2006

Bako B, Groma I, Gyorgyi G, Zimanyi G: Dislocation Glasses, Ageing during Relaxation and Coarsening, Physical Review Letters, 98 075701, 2007

Groma I, Gyorgyi G, Kocsis B: Dynamics of coarse grained dislocation densities form an effective free energy, PHILOSOPHICAL MAGAZINE, 87, 1185-1199, 2007

Groma I, Gyorgyi G, Kocsis B: Dynamics of Coarse Grained Dislocation Densities from an Effectiv Free Energy, Proc. MMM3, Freiburgh 18-22 Sept. 2006, 2006

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