Download - E C C M Paris Conference
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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
large scale pillar small scale pillar
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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
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3Raabe, 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)
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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)
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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
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* 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
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* 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
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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]
+ --+
+-
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Simplify, strain path
Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31
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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
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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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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)
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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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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
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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
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
18 b,t combinations
9 b,t combinations
Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559
T TT
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Extract geometrically necessary dislocations
Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559
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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
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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
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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)
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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
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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
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Simplify: plastic laminates in single crystals
together withO. Dmitrieva,P. Dondl,S. Müller
Dmitrieva et al., Acta Mater 57 (2009) 3439
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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
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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