MD-157
Prof. Dr. Siegfried SchmauderIMWF, Universität Stuttgart
• Interaction between dislocations and phase boundaries
• Inverse Hall-Petch effect
• Solid solution hardening
Molecular Dynamics (Part II)
MD-158
Progress in used Software
Aim:Looking into the effects of
- interaction of particles- influence of differently sized particles
MD-159
Strength Increase in Cu-alloyed Steels due to Precipitates after Anealing (57000h, 340°C)
MD-Simulation
0
100
200
300
400
500
600
700
800
0.00 0.05 0.10 0.15 0.20 0.25Strain / m/m
A111A112
A113
Material 15 NiCuMoNb 5States E60A and E60B B111B112
B113T= 90°C
Zustand E60A
Zustand E60B
Stre
ss
/ MPa
Stress-Strain-Curces of Cu-Alloyed Steels
MD-160
Characterization of a Precipitate by APFIM / TAP
MD-161
Characterization of a Precipitate by APFIM / TAP
MD-162
Atom Probe Field Ion Microscope / Topographic Atom Probe
Research Group R. Kirchheim / T. Al-Kassab, University of Göttingen, Germany
APFIM / TAP
MD-163
„Cu“-Precipitates: More Realistic Model
Cu
Mn
Ni
Con
cent
ratio
n
Distance (center of gravity, nm)
MD-164
Temperature Dependence ofCritical Resolved Shear Stress
MD-165
Cu-Precipitates
• Size of precipitate (radius)• Distance between precipitates (box length)• Shape (spherical, ellipsoidal)• Position of glide plane (central, marginal)• Composition (Fe atoms)
Free parameters:
MD-166
Different Radii and Distancesof Spherical Precipitates
Lc1
Spherical Precipitates
MD-167
Precipitates of Different Shape: Ellipsoids
2.5 nm
2b
Ellipsoidal Precipitates
bCu [nm]
MD-168
Different Positions of Glide Plane
2.5 nm
Different Positions of Glide Plane
MD-169
Repulsion
+: Positive Pressure-: Negative Pressure
Repulsion and Attraction of Dislocations
+
-
+Attraction
++
-
MD-170
24 MPa
80 MPa
Repulsion and Attraction of Dislocations
MD-171
Different Cu Concentrations
Influence of Cu-Concentration
MD-172
Cu/Ni-Precipitates
• Radius (Ni, CuNi)• Composition (Fe, Cu atoms)• Ni precipitates with Cu core
Free parameters:
Cu/Ni-Precipitates
MD-173
Important Physical Data for Fe, Cu, Ni
Fe Cu Nibcc fcc bcc fcc bcc
a0 2.866 Å 3.615 Å 2.881 Å 3.520 Å 2.812 ÅEcoh 4.28 eV 3.54 eV 3.49 eV 4.45 eV 4.37 eVBulk
modulus179.97 GPa 141.03 GPa 127.29 GPa 180.19 GPa 143.73 GPa
c11 243.73 GPa 179.34 GPa 109.43 GPa 244.01 GPa 101.62 GPac12 148.10 GPa 123.23 GPa 136.22 GPa 148.29 GPa 164.79 GPac44 113.65 GPa 81.02 GPa 92.32 GPa 125.53 GPa 135.50 GPa
ShearModulus
G[111]
69.76 GPa 21.84 GPa 24.110 GPa
Derived from nanosimulation
Important Physical Data for Fe, Cu, Ni
MD-174
Spherical Cu and Ni Precipitates of Different Radii
Spherical Cu and Ni Precipitates
MD-175
Different Fe-Concentrations
Different Fe-Concentrations
MD-176
Spherical Cu/Ni-Precipitates
Ordered Cu/Ni-precipitate
B2-structure
NiCu
Ordered and Random Spherical Cu/Ni-Precipitates
MD-177
Spherical Cu-Precipitates with Ni-Shell
NiCu
Cu-Precipitates with Ni-Shell
MD-178
Maximal density
Zero density
Minimal density
Burgers Vector Density within Glide Plane
12.5 Å Ni 12.5 Å Ni / 4 Å Cu 12.5 Å Ni / 6 Å Cu
12.5 Å Ni / 10 Å Cu 12.5 Å Cu
MD-179
NiCu
Spherical Cu-Precipitates with Ni-Shell
MD-180
Critical Resolved Shear Stress:from idealized Model to Reality
Overview on the numerical correction factors of the critical resolved shear stress versus the idealized simulation configuration:
1.) Temperature: temperature of mechanical exp. 90°C vs. 0K (in basic simulation):Reduction by ca. 33%
2.) Nickel-shell (chemical inhomogeneity): Reduction by ca. 55%3.) Presence of iron in the precipitate: Reduction by ca. 5%4.) Scatter of precipitate position parallel to dislocation movement:
Reduction by ca. 50%5.) Scatter of precipitate sizes: Reduction by ca. 20%6.) Scatter of precipitate distances: Reduction by ca. 20%
Idealized simulation result for precipitates, aligned on linear chains, withidentical distances and sizes according to the mean sizes and distances: Critical resolved shear stress: 300 MPaTaking into account the reducing effecs ( 1 to 6 ), 300 MPa shrink to 35 MPa. The critical tensile stress is calculated from the critical shear stress byMultiplying with the Schmid factor (~ 3.05), resulting in an increase in tensile tress by
100 MPaIn agreement with the experimental observation due to thermal load.
MD-181Interaction of a Dislocation with a Fe/Cu-Interface
Molecular Dynamics Simulation
MD-182
Dislocation Movement underexternal Shear Loading
• Ni3Al-Precipitate in Ni• System size: 24.8 nm x 9.75 nm x 14.7 nm (325 000 Atoms)• Diameter of precipitate: 5 nm• Maximal Shear deformation: = 0.95 %• Real Time: 37.5 ps
Partial Dislocations
Stacking faultAlNi
Glide Plane ofDislocation
MD-183
Inverse Hall-Petch Effect
Simulating nanocrystalline copper The smallest grain sizes. Larger grains. Flow stress: an optimal grain size. Dislocation structure.
Conclusions.
MD-184
Dislocations and Grain Boundaries
Dislocations carry the plastic deformation.
Grain boundaries hinder the motion of dislocations.
MD-185
Dislocations carry the plastic deformation.
Grain boundaries hinder the motion of dislocations.
When grains become smaller, the material becomes harder(Hall-Petch effect)
y
d1
Hall (1952)
Dislocations and Grain Boundaries
MD-186
Dislocations carry the plastic deformation.
Grain boundaries hinder the motion of dislocations.
When grains become smaller, the material becomes harder(Hall-Petch effect)
dk
yy ,
d1
Dislocations and Grain Boundaries
MD-187
The Hardness of N.C. Metals
S. Takeuchi, Scripta Mater. 44, 1483 (2001).
MD-188
Simulations of N.C. Copper
Set up the system in the computer. Do Molecular Dynamics while
deforming the sample. Interpret the results.
MD-189
Set up the system in the computer. Do Molecular Dynamics while
deforming the sample. Interpret the results.
Material: copper. No texture. Strain rate: 5108 s-1. Temperature: 300 K.
Simulations of N.C. Copper
MD-190
Results – Small Grains
380000 atoms – 7 nm grains
Structure:
Blue atoms: f.c.c. structure, this is inside the grains.
Yellow atoms: h.c.p. structure, this is stacking faults etc.
Red atoms: irregular structure, this is grain boundaries and dislocation cores.
MD-191
380000 atoms – 7 nm grains
Plastic deformation:
The dislocation activity cannot account for the observed plastic deformation.
Something else is happening, perhaps the grain boundaries.
Results – Small Grains
MD-192
Deformation Map, Small Grains
The main deformation is in the grain boundaries. Little “conventional” dislocation activity.
380000 atoms – 7 nm grains
MD-193
Stress vs. Strain, Small Grains
The hardness increases with the grain size.(reverse Hall-Petch effect)
• Nature 391, 561 (1998).• Phys. Rev. B 60, 11971 (1999).
MD-194
Deformation Map, Large Grains
The main deformation is inside the grains. Dislocations carry the deformation.
101 million atoms – 49 nm grains
MD-195
What happens in the Grains?
50 million atoms.20 grains.Grain size: 39 nm.
Blue atoms:perfect crystal
Yellow atoms:stacking faults
Red atoms:grain boundariesdislocation cores
MD-196
A Change in Deformation Mode
Small grains (d < 10 nm) Deformation is in the grain boundaries. Smaller grains more grain boundaries
easier deformation.
Larger grains (d > 15 nm) Dislocations carry the deformation. Grain boundaries hinder the dislocation motion. Smaller grains more grain boundaries
harder material.
MD-197
An optimal Grain Size
For small grains the strength increase with increasing grain size.
For large grains the strength decrease with increasing grain size.
MD-198
What happens inside the Grains?
MD-199
Dislocation Structures (pile-ups)
Dislocations queued up on the same glide plane.
Pressed towards a grain boundary by the external stress.
Held apart by their mutual repulsion.
The stress concentration from the pile-up cause dislocation activity in the next grain.
MD-200
Summary – Optimal Grain Size
Using parallel computers, molecular dynamics simulations (MD) with 107 – 108 atoms are possible with realistic interatomic forces. It is possible to simulate the plastic deformation of
polycrystalline metals with realistic grain sizes.
Nanocrystalline copper has an optimal grain size at 10 – 15 nm, where the hardness is maximal. In smaller grains, grain boundary sliding is the dominant
deformation mechanism, and a reverse Hall-Petch effect is seen.
In larger grains, dislocations carry the deformation. Grain boundaries cause pile-ups. The Hall-Petch effect is seen.
MD-201
dissolved atoms
initial configuration
-Fe/C
experiment(literature)
Concentration / %
Moleculardynamic (MD)-Simulation is adequate to simulate the solid solution hardening in Fe (and other metals). For this purpose, foreign atoms are distributed statistically in a simulation box and their resistance against the movement of an edge dislocation on a low level energetic glide system is calculated.
Solid Solution Hardening
Fe/
Experiment (Literature)
Concentration / %
Crit
ical
she
arst
ress
c
/ MP
a
MD-202
dislocation and dissolved atoms
dissolved atoms
initial configuration
experimental resultssimulation
Concent / %
Incr
ease
inYi
eld
stre
ss /
MP
a
Fe/
Experiment (Literature)
Concentration / %
Crit
ical
str
ess c
/ MPa
Solid Solution Hardening
MM-203
Macro(Mechanics)
Electrons(Bonding)
Atoms(Interaction)
Microstructure(Localisation)
Specimen(Controlled Failure)
Component(Integrity)
Micro(FEM)
Nano(MD)
Femto(ab initio)
Macro(FEM)
Materials Science(bottom-up-approach)
Conclusion
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