Crystalmechanics Introduction

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Multiscale Models of Crystals D. Raabe, F. Roters, S. Zaefferer, P. Eisenlohr Department of Microstructure Physics and Metal Forming WWW.MPIE.DE [email protected] 02. May 2010

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Transcript of Crystalmechanics Introduction

Page 1: Crystalmechanics Introduction

Multiscale Models of Crystals

D. Raabe, F. Roters, S. Zaefferer, P. Eisenlohr

Department of Microstructure Physics and Metal Forming

WWW.MPIE.DE

[email protected]

02. May 2010

http://www.mpie.de/
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Scientific Board

Shareholder:

Max-Planck-Society, German Steel Institute

Scientific Board Trustees Board

MPIE

Strategy Board

MPIE Departments

Microstructure

Physics

and Metal

Forming

Dierk

Raabe

Interface

Chemistry

and

Surface

Engineering

Martin

Stratmann

Administration

Herbert

Wilk

Computational

Materials

Design

Jörg

Neugebauer

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Multiscale Crystal Plasticity FEM

Overview

Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Materi.58 (2010)

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4Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

Multiscale crystal plasticity FEM

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dyadic flow law based on dislocation rate theorydyadic flow law based on dislocation rate theory

Physics-based constitutive laws: mean field theory

plastic gradients, size scale and orientation gradients (implicit)

plastic gradients, size scale and orientation gradients (implicit)

1

1. set internalvariables

2

grain boundariesgrain boundaries3

2. set internalvariables

3. set internalvariables

T

T

T

T

T

T

T

T

Taylor, Kocks, Mecking, Estrin, Kubin,...

Nye, Ashby, Kröner,....

activation concept:energy of formation upon slip penetration: conservation law

Ma, Roters, Raabe: Acta Mater. 54 (2006) 2169; Ma, Roters, Raabe: Acta Mater. 54 (2006) 2181; Ma, Roters, Raabe: Intern. J Sol. Struct. 43 (2006) 7287

Roters et al.: Acta Mater. (2010)

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From local misorientations to GNDs

misorientation

orientation gradient(spacing d from EBSD scan)

Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

orientation difference

misorientation angle

0°

20°

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From local misorientations to GNDs

distortion(sym, a-sym)

dislocation tensor (GND)

J. F. Nye. Some geometrical relations in dislocated crystals. Acta Metall. 1:153, 1953.E. Kröner. Kontinuumstheorie der Versetzungen und Eigenspannungen (in German). Springer, Berlin, 1958.E. Kröner. Physics of defects, chapter Continuum theory of defects, p.217. North-Holland Publishing, Amsterdam, Netherlands, 1981.

Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

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From local misorientations to GNDs

Frank loop through area r

DDT in terms of 18 b,t combinations

DDT in terms of 9 b,t combinations

Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

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Extract geometrically necessary dislocations

Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

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Size effect sas a mean-field break down phenomenon

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SSD

experiment

CPFEM:viscoplasticphenomen.model

CPFEM:dislocation-based model;g.b. model

von Misesstrain [1]

10% 20% 30% 40% 50%

Ma, Roters, Raabe: Acta Mater. 54 (2006) 2169 and 2181

10% 20% 30% 40% 50%

Al Bicrystals, low angle g.b. [112] 7.4°, v Mises strain

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3% 8%

15%Sachtleber, Zhao, Raabe: Mater. Sc. Engin. A 336 (2002) 81

Homogeneity and boundary conditions at grain scale

Raabe et al. Acta Mater. 49 (2001) 3433

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1mm

21mm

8mm

5mm

5mm

FE mesh

exp., grain orientation, side A exp., grain orientation, side B

equivalent strain

equivalent strain

Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe : Intern. J. Plast. 24 (2008)

Crystal plasticity FEM, grain scale mechanics (3D Al)

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T

T

Texture component crystal plasticity FEM for large scale forming

Zhao, Mao, Roters, Raabe: Acta Mater. 52 (2004) 1003

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0 15 30 45 60 75 900,95

0,96

0,97

0,98

0,99

1,00

1,01

1,02

1,03

1,04

1,05

Simulation

Experiment

rela

tive e

ar

hig

ht

[1]

angle to rolling direction [°]

Texture component crystal plasticity FEM for large scale forming

D. Raabe and F. Roters: Intern. J. Plast. 20 (2004) 339 15

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Numerical Laboratory: From CPFEM to yield surface (engineering)

Kraska, Doig, Tikhomirov, Raabe, Roters, Comp. Mater. Sc. 46 (2009) 383 16

Multiscale crystal plasticity FEM for large scale forming

DC04 study with Mercedes, Volkswagen, Audi, Inpro


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