Small scale deformation studied via experiments and dislocation-based crystal plasticity FE simulation

D. Raabe, F. Roters, P. Eisenlohr, N. Zaafarani, E. Demir

20. May 2010, ECCM, Paris

Düsseldorf, Germany

WWW.MPIE.DEd.raabe@mpie.de

large scale pillar small scale pillar

Overview

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

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

3Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

Multiscale crystal plasticity FEM

4

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-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)

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

Overview

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

6

* GND: geometrically necessary dislocations (accomodate curvature)

[-110][111

]

[11-2]

Zaafarani et al. Acta Mat. 54 (2006) 1707; Wang et al. Acta Mat. 52 (2004) 2229

Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN

Hardness and GND* in one experiment

Higher GND density at smaller scales?

[-110]

[11-

2]

[111]

Nanoindentation (smaller is stronger): 3D EBSD and CPFEM

7

* GND: geometrically necessary dislocations (accomodate curvature)

[-110][111

]

[11-2]

Misorientation angle

0°

20°

Zaafarani et al. Acta Mat. 54 (2006) 1707; Wang et al. Acta Mat. 52 (2004) 2229

Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN

Nanoindentation (smaller is stronger): 3D EBSD and CPFEM

8

Comparison, crystal rotations (absolute, about [11-2] axis)

CPFEM, viscoplastic experiment CPFEM, dislocation-based

0

5°

10°

15°

20°

25°Absolute rotations

<11-2> rotations

expe

rim

ent

sim

ulat

ion

[-110][111

]

[11-2]

Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

CPFEM, viscoplastic experiment CPFEM, dislocation-based

[-110][111

]

[11-2]

+ --+

+-

9

Simplify, strain path

Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

10Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

Overview

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

11

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

Crystal Mechanics FEM, grain scale mechanics (2D)

Experiment (DIC, EBSD)v Mises strain

Simulation (CP-FEM)

v Mises strain

Sachtleber et al. Mater. Sc. Eng. A 336 (2002) 81; Raabe et al. Acta Mat. 49 (2001)

13

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)

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

Overview

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

15

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°

16

From local misorientations to GNDs

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

17

From local misorientations to GNDs

Frank loop through area r

18 b,t combinations

9 b,t combinations

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

T TT

18

Extract geometrically necessary dislocations

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

19

Size effect as a mean-field break down phenomenon

Demir, Raabe, Roters: Acta Mater. 58 (2010) Pages 1876

1. Mean field break-down: source size dependence

)2/(source dGb

2. Schmid law break down: from Peierls to source mechanism

ss

sijij

s m

sourcecrit

source is NOT identical on systems with the same index

20Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

Overview

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

21

Microscale Bauschinger* effect in beam bending

* Bauschinger effect: flow stress asymmetry upon load path change

Kernal average misorientation orientation map

orientation map

Kernal average misorientation

bending (forward)

straightening (backward)

22Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

Overview

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

23

24

Example of patterning phenomena: plastic laminates in bicrystals

Zaefferer et al. Acta Mater. 51 (2003) 4719

Kuo et al., Adv. Eng. Mater.5 (2003)563

Simplify: plastic laminates in single crystals

together withO. Dmitrieva,P. Dondl,S. Müller

Dmitrieva et al., Acta Mater 57 (2009) 3439

26Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

Overview

Multiscale Crystal Plasticity FEM

Examples at small scalesIndentation

Grain boundaries in CPFEM

Challenges and limitsSize effects, source limitation

Bauschinger effects

Lamination and plastic patterning

Conclusions

27Roters et al. Acta Mater.58 (2010)

Conclusions

Multiscale Crystal Plasticity FEM is a versatile method for boundary condition treatment in crystal mechanics

Include phenomenological or dislocation-based hardening laws

Good at predicting stresses, strains, shapes, contact, texture

One-to-one comparison to experiments

Limits: constitutive aspects where DDD is better suited (limits of statistical and mean field models): size effects, source limitations, bursts, localization, Bauschinger effect, patterning and laminates