molecular dynamics (part ii) - lecture 4.pdf · using parallel computers, molecular dynamics...

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



When grains become smaller, the material becomes harder(Hall-Petch effect)

y

d1

Hall (1952)


MD-186



When grains become smaller, the material becomes harder(Hall-Petch effect)

dk

yy ,

d1


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


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.


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

molecular dynamics (part ii) - lecture 4.pdf · using parallel computers, molecular dynamics...

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