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1
Analysis of nanoindentation size effectbased on
Crystal Plasticity and Dislocation Dynamics
Hyung–Jun CHANG
9th October, 2009
Supervisors
Marc Fivel, Marc Verdier (Grenoble INP)
Laurent Tabourot (Univ. de Savoie)
Heung Nam Han, Kyu Hwan Oh (Seoul Natl’ Univ.)
Samuel Forest (Centre des matériaux)
2 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Principle of indentation
hf
∞∞
Specimen
Indenter
Pile upSink in
∞∞
h
P
Loading state
Unloading state
Measurement
1. Continuous measure : Force, Depth, Stiffness
2. Post measurement : surface imprint (contact area)
Objective : Obtain material property using the measurements
Macro scale Micro scale
3 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Work done by L. Charleux (ideal case) For - Isotropic material : amorphous or poly crystal with fine grain
- Self symmetric indenter : conical or pyramidal
Mechanical parametersIndentation testModel analysis (2D FEM)
Surface imprint
P
0 h
S
Indentation curve
L. Charleux, ph.D thesis, Grenoble INP (2006)
E
ε
σy
00 εy
σ
Mechanical parametersy and E Hardness
H
0 h
Obtain - two mechanical parameters - stable hardness
4 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Indentation with single crystal metal
Surface imprint Mesured hardness
Y.Y. Lim and M. M. Chaudhri, Philosophical Magazine A (1999) Work done by M. Verdier (2007)
: Anisotropic slip line : Indentation size effect
Need 3D modeling for anisotropic behavior and indentation size effect
With Self symmetric indenter : conical or pyramidal
5 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Simulation model for indentation
Isotropic model (2D, axisymmetric)
anisotropic model (3D,continuum)
: Only for ideal (isotropic) indentation
: Constitutive law for anisotropy crystal plasticity model
anisotropic model (3D,discrete)
: Dislocation dynamics coupled with FEM
6 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Reproducing experiment(single crystal, CPFEM)Reproducing experiment(single crystal, CPFEM)
Theoretical analysis (size effect, DD&CPFEM)
Sphere
Cone
Pyramidal, cube
Single crystal
Scale of indentation
Simulation(analysis tool)
Indentation
Scale
Experiment Micro-Indentation Nano-Indentationmm m nm Å
Indenters Sphere
Cone
Specimen Poly crystal
Single crystal (Copper)
FEM (isotropy)
FEM (anisotropy)
FEM (size effect)
DD
MD
FEM (anisotropy)
Multiscale method ( DD base )
FEM (size effect)
Nano-Indentation
Theoretical analysis (ideal, FEM)
Theoretical analysis (initiation, MD)
Vickers Berkovich Cone
sphere
MD
Theoretical analysis (initiation+evolution, DD)
7 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
8 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
Continuum modeling
9 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Nanoindentation procedure
Tip
4 Specimens
Loading condition
Tip
radi
us =
3.3
m
hsphere=200 nm
4 Cu single crystals
Experiment
Tip angle = 71.2o
Sapphire sphero-conical tip
5mm × 5mm
Strain rate control
sec/105 2
FEM
1400 nm
Indentation depth
Rigid body tip (identical)
5m × 5m
Velocity control
Crystal plasticity theory
• Objective : To check– Orientation effect
– Dislocation density effect
• Mean – Force, Stiffness, Contact area and
Hardness – Surface displacement
(symmetry, pile-up height)
Nanoindentation procedure (EXP)
- Experiment
10 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Sample preparation for experiment
(110), (001), (111) surface orientation
(123), (111low) surface orientation
Grown from high purity Cu using Bridgman technique
(001)
(12-3)
(-541)
(111 low)
Cut by spark erosion from bulk single crystal (high ini)
(low ini)
- 4 surface orientations
- Experiment
(111)(110)
- 2 initial dislocation densities on (111) orientation
11 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Quantitative results (EXP)
Strong effect of initial dislocation density & Weak effect of orientation
S
- Experiment
12 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Surface morphologies (AFM)
5m
m
5m
m
m5m
m
5m
m
5m
(001) Surface (110) Surface (123) Surface
(111) Surface (highini) (111) Surface (lowini)
Surface orientation
Surface morphology strongly affected by
To check by FEM modelling
- Experiment
13 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Nanoindentation procedure
Tip
4 Specimens
Loading condition
Tip
radi
us =
3.3
m
hsphere=200 nm
4 Cu single crystals
Experiment
Tip angle = 71.2o
Sapphire conical tip
5mm × 5mm
Strain rate control
sec/105 2
FEM
1400 nm
Indentation depth
Rigid body tip (identical)
5mm × 5mm
Velocity control
Crystal plasticity theory
FEM
1400 nm
Indentation depth
Rigid body tip (identical)
5mm × 5mm
Velocity control
Crystal plasticity theory
• Ingredient : Physical constitutive equations
– Dislocation density based model of crystal plasticity
• Procedure :– Inverse method to find the
best set of parameters
Nanoindentation procedure (FEM)
- CP model
14 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Crystal plasticity theory
Plasticity = activation of many slip systems
1 21 2
x x
x1 x2
01(C1) 02(C3) 03(C5) 04(A2) 05(A3) 06(A6)
(1 1 -1) [0 1 1] (1 1 -1) [1 0 1] (1 1 -1) [1 -1 0] (1 -1 -1) [0 1 -1] (1 -1 -1) [1 0 1] (1 -1 -1) [1 1 0]
07(D1) 08(D4) 09(D6) 10(B2) 11(B4) 12(B5)
(1 -1 1) [0 1 1] (1 -1 1) [1 0 -1] (1 -1 1) [1 1 0] (1 1 1) [0 1 -1] (1 1 1) [1 0 -1] (1 1 1) [1 -1 0]
12 slip systems for Copper single crystal
- CP model
15 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Constitutive law for crystal plasticity
L. Tabourot, M. Fivel, E. Rauch, Mater. Sci. Eng. A (1997)
*E* ECT Elastic
Equations Key variable
CE
ini , sp
asp, Kg
+Surface
orientation
sm
s
sss sign
r
1
0 s0
* μT :sFlow law
12
1p
ps b spα
ssc
g
p
p
s yKb
21
12
1
spa
Hardening law
gK
spa
spα
- CP model
Evolution law
16 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Obtaining variables
Surface Orientation
FWHM (111)( scan °)
Relative disl. density
Initial density(total)
(011) 1.35 6 ~ 8 1.56×1014/m2
(111) 0.57 3 ~ 4 1.20×1014/m2
(001) 0.56 3 ~ 4 1.20×1014/m2
(123) 0.2 1 3.00×1013/m2
(111low) 0.08 0.2 ~ 0.3 6.00×1012/m2
Initial dislocation density and
Surface orientation
From X-ray results
C11 168.4 GPa
C12 121.4 GPa
C44 75.4 GPa
b 2.56×10-10 m yc 1.43×10-9 m
1~6
Taylor (0.09, 0.09, 0.09, 0.09, 0.09, 0.09)
Hetero (0.122, 0.122, 0.07, 0.137, 0.122,0.625)
a1~6
K
Normal (0.01, 0.4, 0.4, 0.75, 1.0, 0.4), K=36
Same a1-6 same as 1~6 , K=36
High K (0.01, 0.4, 0.4, 0.75, 1.0, 0.4), K=100
Elastic properties for
From literatures
Hardening parameters
From DD theory
L. Kubin, B. Devincre and T. Hoc, Acta Mater., (2008)M. Fivel, PhD These, (1997)
*E* ECT
Unknown
- CP model
17 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Implementation in ABAQUS (UMAT / VUMAT) & Validation
Well know three stage curve reproduced
(Taylor / normal)
- CP model
18 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Application to nanoindentation Effect of orientation
5m 5m
5m 5m
(001) Surface (110) Surface
(123) Surface(111) Surface
3%
(Hetero / Same)
Strong effect on surface displacement
ini= 1.2×1013/m2)
- CP FEM
Weak effect on loading curve
19 / 49
Introduction Macro scale Micro scale Discussion & Prospective
m(111) Surface (high ini)
5m
m(111) Surface (low ini)
5m
Effect of dislocation density for (111) orientation
Optimized initial dislocation density
(Hetero / Same)
ini= 6.0×1012/m2 for (111low)
ini= 1.2×1014/m2 for (111high)
What about the other orientations ?
- CP FEM
Strong effect on surface shape
Strong effect on loading curve
20 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Comparison of quantitative results (hetero / same)
Optimizedinitial densities
(011) 1.56×1014/m2 (123) 3.00×1013/m2
(111) 1.20×1014/m2 (111low) 6.00×1012/m2
(001) 1.20×1014/m2
- CP FEM
ini= 1.56×1014/m2 (110)
ini= 1.20×1014/m2 (111)
ini= 1.20×1014/m2 (001)
ini= 3.00×1013/m2 (123)
ini= 6.00×1012/m2 (111low)
21 / 49
Introduction Macro scale Micro scale Discussion & Prospective
m
5m 5m
m
5m 5m
m
5m 5m
Taylor Hetero
Normal
Same
High K
Effect of hardening parametersfor (111) orientation
Influence surface morphology
Obtained hardening parameter
Hetero + Same
5m
mEXP
Need to check for other orientation
- CP FEM
Weak effect on loading curve
22 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Comparison of Surface morphologyFEM EXP FEM EXP
m
m
m
m
m
5m 5m
5m 5m
5m 5m
5m 5m
5m5m
(001) Surface
(110) Surface
(123) Surface
(111) Surface (high ini)
(111) Surface (low ini)
b 2.56×10-10 m yc 1.43×10-9 m
1~6 Hetero (0.122, 0.122, 0.07, 0.137, 0.122,0.625)
a1~6
KSame same as a1~6 , K=36
(hetero / same)
Confirmed hardening parameter
- CP FEM
23 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Comparison of pile up morphology
111 (lowini)
001 110 123
111 (highini)
(hetero / same)
The hardening parameter (hetero/Same) is confirmed quantitatively
- CP FEM
24 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Conclusion : best set of parameters
Initial dislocation density and
Surface orientation
C11 168.4 GPa
C12 121.4 GPa
C44 75.4 GPa
b 2.56×10-10 m yc 1.43×10-9 m
1~6 Hetero (0.122, 0.122, 0.07, 0.137, 0.122,0.625)
a1~6
KSame same as a1~6 , K=36
L. Kubin, B. Devincre and T. Hoc, Acta Mater., (2008)
*E* ECT
Hardening
Elastic
- CP FEM
Surface Orientation
Relative disl. Density
(from X-ray)
Initial density(from FEM)
(011) 6 ~ 8 1.56×1014/m2
(111) 3 ~ 4 1.20×1014/m2
(001) 3 ~ 4 1.20×1014/m2
(123) 1 3.00×1013/m2
(111low) 0.2 ~ 0.3 6.00×1012/m2
25 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Summary of EXP and FEM studies
• Effect of key variables– Orientation
• Weak effect to Force displacement curve• Strong effect on surface morphology (imprint symmetry)
– Initial dislocation density• Strong effect on Force displacement curve• Effect to pile up height
– Hardening parameters • Weak effect to Force displacement curve • Effect to details of surface morphology and pile up height
• Comparison between EXP and FEM with best parameter set Reasonable both qualitatively and quantitatively
• Limits– No size effect Dislocation dynamics
26 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
Discretemodeling
27 / 49
Introduction Macro scale Micro scale Discussion & Prospective
= +
FS
FTOT= FFEM+ FDD
FDD
FFEM SFEM SDD
DDDDE =DTOTDTOT
Bulk Bulk Infinite region
Virtual indenter
DTOT : Total indenting depthDDD : depth from dislocation fieldDE : depth from Elastic fieldSFEM : Elastic stress field
FTOT : Total applied loadFDD : Load from dislocation fieldFFEM : Load from Elastic fieldFS : Surface load from dislocation field
Coupling (Superposition) method
= +
FS-FS
FTOT= FFEM+ FDD
FDD
FFEM SFEM SDD
DDDDE =DTOT-DDD DTOT
Bulk Bulk Infinite region
Virtual indenter
DTOT : Total indenting depthDDD : depth from dislocation fieldDE : depth from Elastic fieldSFEM : Elastic stress field
FTOT : Total applied loadFDD : Load from dislocation fieldFFEM : Load from Elastic fieldFS : Surface load from dislocation field
100nm 100nm 100nm
Coupled FEM DD
E. van-der-Giessen, A. Needleman, Mater. Sci. Eng. , (1995)
- Simulation method
28 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Algorithm of the coupled simulation
Dislocation dynamics (TRIDIS)
Finite Element Method (CASTEM)
Nucleate ?
Yes
No
Get dDD, dFEM, FS,DD from previous step
Impose B.C. at top Surface
Solve an elastic FEM problem
Update dDD, FS,DD
Nucleation (it could be failed)
Dislocation Dynamics Steps
Equilibrium ?
Over constraint ?
START CALCULATION
END CALCULATION
Yes
No
Yes
No
Nucleate ?
No
Yes Recalculate FEM ?
Yes
No
Update dDD, FS,DD
Remove over constraints
Need a criterion !
What (shape) ?When (condition) ?
Dislocation dynamics
- dislocation multiplication- dislocation nucleation ?
- Simulation method
MD simulations
29 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Nucleation criterion #1 : MD global criterion
First Generation of Dislocation loops
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0
F [m
N]
depth [nm]
Ni1Ni2Ni3Ni4Ni6Ni8
Master curve (MD,111)Shape of Nucleation (MD,111)
When : Global criterion (Master curve)
Good : criterion without any experimental resultsWeak : MD cannot tell the force for deeper indentation depth
Need a nucleation criterion without master curve
What : 3 Prismatic loops
- Simulation method
30 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Nucleation criterion #2 : GND criterion
Dislocation dynamics (TRIDIS)
Finite Element Method (CASTEM)
Nucleation(it could be failed)
Impose B.C. at top Surface
Solve an elastic FEM problem
Update dDD, FS,DD
Dislocation Dynamics Steps
Equilibrium ?
Over constraint ?
START CALCULATION
END CALCULATION
Yes
No
Yes
No
Remove over constraints
Get dDD, dFEM, FS,DD from previous step
Deformation and GND
Flow Chart
xindxDD,Nucle
nucleationDDind xx ,
W. D. Nix, H. Gao, J. Mech. Phys. Solids, (1998)
Nucleation imposed by indentation depth
Good : without any experimental results Good : without any master curves
- Simulation method
31 / 49
Introduction Macro scale Micro scale Discussion & Prospective
50nm 50
nm
Cone (angle = 71.2o)
Copper single crystal (111 surface)
Sphere (r=150nm)
Calculation Parameters
Tip geometries
Cross-slip probability PL
L
t
t kT VIII
0 0
exp/
*
EasyMPaHardMPanoIII 32,640,
Specimen
- Simulation method
Nucleation method Master curve from MD (sphere) or Exp (cone)
1. Global criterion : Force controlled Nucleation
2. GND criterion : Depth controlled Nucleation
: For indentation ?
32 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
Discretemodeling
- Spherical indentation (111)
33 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Dislocation evolution (MD global crit. + no cross-slip)
(1 0- 1)
(1-2 1)
(1 1 1)
(1-2 1) 150nm
10nm depth5nm depth
(1 0- 1)
(1-2 1)
(1 1 1)
(1-2 1) 150nm
Nucleation only (similar to MD)
Nucleation andFrank-Read source
230nm
(1 0- 1)
(1-2 1)
(1 1 1)
(1-2 1)
60nm depth
Frank-Read source only
Loop Length ↑Line tension ↓
Contact area ↑ loop length ↑
> line tension
F-R source
No space to nucleation
- Spherical indentation (111)
34 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Force displacement curveMD global crit. + no cross-slip GND crit. + no cross-slip
MD global crit. + Cross-slip condition
Cross-slip Deviation delayed
Nucleation allow
Nucleation forbidden
- Spherical indentation (111)
MD master curve
MD master curve
GND crit. closer to MD prediction
MD global crit.
GND crit.
MD master curve
35 / 49
Introduction Macro scale Micro scale Discussion & Prospective
100nm 100nm 100nm
No cross-slip Hard cross-slip Easy cross-slip
Cross-slip effect (30nm depth)
150nm
(1 1 1)
(1-2 1)
(1 0 -1)
(1-2 1)
150nm
(1 1 1)
(1-2 1)
(1 0 -1)
(1-2 1)
150nm
(1 1 1)
(1-2 1)
(1 0 -1)
(1-2 1)
Cross-slip↑ def. homogeneous ↑, Glissile loops ↓, Plastic zone size ↑
- Spherical indentation (111)
36 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Cross-slip effect after unloading
230nm
(1 0- 1)
(1-2 1)
230nm
(1 0- 1)
(1-2 1)
230nm(1 0- 1)
(1-2 1)
Before unloading (60nm depth)
After unloading (60nm depth)
No cross-slip Hard cross-slip Easy cross-slip
230nm230nm
230nm
Cross-slip↑ more irreversible micro structure
- Spherical indentation (111)
37 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
Discretemodeling
- Conical indentation (111)
38 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Nucleation criterion for conical indentation
Total Force Hardness
MD global crit. GND crit.
Exp. global crit. single behavior ( linear response)
Hardness : Drop down Stable
MD master c
urve, sphere
Exp. master curve, Berkovich
- Conical indentation (111)
Two phase behavior ( linear to parabolic)
Exp. global crit. long range decreasing
39 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Dislocation Structure (60nm depth)
GND crit. MD global crit. Exp. global crit.
230nm
230nm
(1 1 1)
(1-2 1)
(1 0- 1)
(1-2 1)
230nm
230nm
(1 1 1)
(1-2 1)
(1 0- 1)
(1-2 1)
230nm
230nm
(1 1 1)
(1-2 1)
(1 0- 1)
(1-2 1)
Prismatic loops & Glissile loops Prismatic loops & Junctions
- Conical indentation (111)
40 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Coplanar Junction : unexpected behavior !!
321 bbb
230nm
b3=(1 -1 0)
(1 1 2)
(1 -1 0)
b2=(1 0 1)b1=(0 1 1)
b1- b2
b3
3111 b
21,//111 bb
- Activate dislocations
perpendicular to loading direction
- Mobile dislocations
Immobile dislocations
- Conical indentation (111)
Coplanar Junctions
41 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Summary of DD results
• Dislocation evolution source : Size effect– Nucleation in size effect phase– Frank-Read source in no size effect phase– Cross slip– Coplanar junction (>50nm, Conical indenter with Exp. global crit.)
• Dislocation structures– Prismatic loops
• Increase by nucleation
– Glissile loops • Increase by Frank Read source• Decrease by Cross slip, Coplanar junction, Unloading
42 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
43 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Problem of CPFEM model :Size effect
Force curve of (111) Surface
Curvature of EXP < Curvature of FEM
FEM(ini)
EXP
FEM(lower ini)
- FEM modeling (Size effect)
Problem !!! : Different ini for deeper indentation depth
Solution : Fit the curvature
How ? : Using Generalized plasticity theory (Ex. Strain gradient theory)
Access to size effect
44 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Simplified strain gradient theory
Extra stress extra ↓ if indentation depth ↑
localpglobalavgp
SSD
SSDtotalL
Kb ,_,
12
- FEM modeling (Size effect)
Usual internal stress
- No extra parameter and extra degree of freedom- Easy to implement in FEM
= =
strain gradient theorydislocation theory
PROBLEM !! Very high calculation cost
Simplified theory (proposed)
: GND: SSD
45 / 49
Introduction Macro scale Micro scale Discussion & Prospective
First FEM results of simplified model
- reproduce indentation size effect, qualitatively- Need detailed verification
- FEM modeling (Size effect)
(001) Surface orientation
46 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Origin of Size effect (Microscale)
• Dislocation structures beneath indenter– Size effect phase : Prismatic loops dominant– Stable hardening phase : Glissile loops dominant
Prismatic loops dominant Glissile loops dominant
(1 1 1)
(1-2 1) 150nm 230nm
(1 1 1)
(1-2 1)
Dislocation dynamics can help understanding size effect
- DD modeling (Size effect)
47 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Link between size effect and local rotation
• Local rotation with scale (Simulation)– Microscale DD :
– Size effect theory :
– Crystal plasticity :
• Local rotation with scale (Experimental, EBSD)
κ : lattice torsion curvature
x
ffext
oldEnew GFG1
curlItrtl Tdd bα
M. Rester, C. Motz, R. Pippan, Acta Mater., (2008)
- DD modeling (local rotation)
ANR CATSIZE project with Samuel Forest (CMR) : Connenction bet. Cosserat & DD
48 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Thank you for your attention
49 / 49
Introduction Macro scale Micro scale Discussion & Prospective
Contents
• Part 0 : Introduction
• Part I : macro scale : experiments and FEM– Experiments– Crystal plasticity modeling– Finite element simulations
• Part II : micro scale : DD simulation– Simulation method– DD simulation of spherical indentation– DD simulation of conical indentation
• Discussion & prospective– FEM modeling (size effect)– DD modeling (Size effect, local rotation)
Analysis of nanoindentation size effect based on Crystal Plasticity and Dislocation Dynamics