mechanical failure in sic bicrystals
TRANSCRIPT
1Department of Materials Science and Engineering
University of Arizona
November 14, 2014 S. Bringuier, MS&T 2013 1
Stefan Bringuier1 V.R. Manga1 , P.A. Deymier1 ,K. Runge1
and K. Muralidharan1
Mechanical failure in SiC Bicrystals And The Effect of Graphene
Elevator Pitch ( Going Up)
November 14, 2014 S. Bringuier, MS&T 2013 2
Nature of failure (Intra- vs. Inter-granular) is grain
boundary misorientation dependent.
High angle GB
Inter-granular failure
Low angle GB
Intra-granular failure
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Graphene at GB influences tensile failure in low angle GB
Graphene mitigates shear failure at GB
Why β-SiC Bicrystals?
• Understanding interfaces and the effect of
additives provides valuable insight into
mechanical properties.
• Molecular dynamics provides a fundamental
understanding of the phenomenology.
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• Symmetric tilt grain boundaries (STGB) only two
DOF tilt axis and tilt angle.
Adapted from:
V. Randle, The Measurement of Grain
Boundary Geometry (IOP Publishing Ltd, Great
Britian, Lodon, 1993).
Talk given by Dr. Erica Corral
Slicon Nitride-graphene Composites with improved Strength
and Toughness Processed From Low Concentrations of Few
Layer Graphene Using SPS
November 14, 2014 S. Bringuier, MS&T 2013 5
Minimization Procedure
[3] M. Wojdyr, S. Khalil, Y. Liu, and I. Szlufarska, Modelling
Simul. Mater. Sci. Eng. 18, 075009 (2010).
• LAMMPS MD package 1
• Potential: SiC Tersoff 1989 Si-Si cutoff
modified to 2.85 Å
• Minimization procedure to find lowest energy
interface (Adapted from M. Wojdyr et al.)2 :
1. Generate GB; choose deletion criteria.
2. Displace Grain 1 relative to Grain 2
3. Anneal under NVT conditions for 400 ps
4. Minimize using Conjugate Gradient method
[2] S. Plimpton, Journal of Computational Physics 117, 1 (1995).
Generation of STGB
• Using Coincidence site lattice (CSL)
model to generate STGB.3
• Choice of the rotation axis is <001> and
boundary plane (110)
• Constructed under periodic boundary
conditions in 3D.
• Maintain overall stoichiometry.
November 14, 2014 S. Bringuier, MS&T 2013 6
[3] A. Sutton and R. Balluffi, Interfaces in Crystalline Materials (Clarendon Press, 1995).
Adapted from:
V. Randle, The Measurement of Grain
Boundary Geometry (IOP Publishing Ltd, Great
Britian, Lodon, 1993).
Example of interpenetrating lattices
Removing Lattice 2 in
Lattice 1 and visa versa Translational shift
GB Energy vs. Misorientation
November 14, 2014 S. Bringuier, MS&T 2013 7
GB Angle
(Degree
s)
Σ365 4.242
Σ145 6.733
Σ85 8.797
Σ61 10.389
Σ41 12.680
Σ25 16.26
Σ13 22.610
Σ17 28.072
Σ5 36.870
Σ is the coincident site density
•Low angle GBs show
considerable agreement
with Read-Shockley
behavior.
• Fairly good agreement in
parameters when assuming
isotropic behavior
𝑮 ⋅ 𝒃
𝟏 − 𝝂
𝜶
Calculated: 66.41 +/- 2.42
Literature : 63.00
3.001 +/-0.621
GB Energy Surfaces
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•Lower angle grain boundaries
shows dips.
•High angle grain boundaries
are fairly flat.
Σ365 – Low Angle
Σ25 – High Angle
Typical system size
~60,000 atoms
lx ~ 176 Å
ly ~ 174 Å
lz ~ 21.5 Å
𝐸𝐺𝐵 =𝐸𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒 − 𝐸𝑆𝑇𝐺𝐵
2 ∗ 𝐴𝑟𝑒𝑎𝐺𝐵
GB Structure
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Free-Volume is a
results of generation
method.
Free volume
Depends on
criteria used
to remove
atoms from
GB
Introducing Strain
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•Initially equilibrate system.
•Use non-periodic boundary conditions
and prescribe velocity (strain-rate) to
one end.
• 3 runs to gather statistics.
Example of ┴ strain
Values for elastic constants of single crystal SiC
Elastic
Constants (GPa)
This
work
Tersoff 1989
C11 436 420
C12 117 120
C44 257 260
Uniaxial Strain
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Intra-Granular Failure
•Nucleation of
void at GB causes
instability.
•Crack initiates
along void but
fails chaotically.
•Intragranular
failure
ε = 0.238 ε = 0.239
ε = 0.240 ε = 0.241
Cleavage
beginning
Initial void most
likely due to free
volume from
generating GB
Strain-rate : 1e9 s-1
Inter-Granular Failure
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• Rings break and form
amorphous regions
• Crack propagates
along GB. Inter-
granular failure
Voids forming
and coalescing
ε = 0.242
ε = 0.243 ε = 0.244
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Graphene Impacts Failure
Σ 365 – Low angle
• Transition from intra-granular to
inter-granular for low angle STGB.
• No difference in high angle STGB.
Σ 25 – High angle
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Shearing Of STGB
•Applied shear causes rigid body slip breaking symmetry
across GB.
• Low angle and high angle STGB show no significant
difference in response to shear.
Σ 365 – Low Angle Σ 25 – High Angle
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Graphene To The Rescue
• The addition of graphene nanoribbon perpendicular to
the GB prevents rigid body slip at GB.
.
Σ 365 – Low Angle Σ 25 – High Angle
Elevator Pitch (Coming Down)
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• Nature of failure (Intra- vs. Inter-granular) is grain boundary
misorientation dependent.
• Addition of graphene mitigates GB slip in shear.High angle GB
Inter-granular failure
Low angle GB
Intra-granular failure
Graphene at GB influences failure in low angle GB
Low angle GB
No slip
Further question please contact:
Stefan Bringuier
Email: [email protected]
Website: www.u.arizona.edu/~stefanb
November 14, 2014 S. Bringuier, MS&T 2013 17
• Other STGB systems
• Multi-layered graphene platelets.
• Hall-Petch effect in nanocrystalline SiC with graphene.
Future Work
Thank You!Software used:
LAMMPS – MD http://lammps.sandia.gov/index.html
OVITO4 – Visualization http://ovito.org
[4] A. Stukowski, Modelling and Simulation in Materials Science
and Engineering 18, 015012 (2010).
November 14, 2014 S. Bringuier, MS&T 2013 18
• Nonlinear elastic stress-strain
response. Result of Tersoff potential.
• Higher than experimental stresses and
strains can be attributed to limitations
in MD.
Σ365:
Fracture Stress:
77.134 +/- 0.598 GPa
Young’s Modulus:
301.521 +/- 2.645 GPa
Σ 25:
Fracture Stress:
73.771 +/- 0.770 GPa
Young’s Modulus:
287.990 +/- 3.592 GPa
Uniaxial Tension Of STGB
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SiC With Graphene ||
Fig. : Stress-Strain relationship with low and
high angle grain boundaries including single
layer graphene (SLG) parallel to the GB for a
strain-rate of 1*109 s-1 .
Considerable weakening due to
graphene.
Free volume acts as
stress concentrator
Σ 365
Σ 25
Σ365:
Fracture Stress:
44.036 +/- 1.99
Young’s Modulus:
317.009 +/- 4.10
Σ 25:
Fracture Stress:
41.778 +/- 2.102
Young’s Modulus:
359.578 +/- 4.83
November 14, 2014 S. Bringuier, MS&T 2013 20
Fig. : Stress-Strain relationship with low and
high angle grain boundaries including single
layer graphene (SLG) perpendicular to the GB
for a strain-rate of 1*109 s-1 .
Failure transitions for low angle
grain boundary (Σ 365) from
intragranular to intergranular
when SLG is included
SiC With Graphene ┴
Σ365:
Fracture Stress:
75.025 +/- 0.442
Young’s Modulus:
305.425 +/- 1.988
Σ 25:
Fracture Stress:
67.606 +/- 0.634
Young’s Modulus:
286.575 +/- 2.301
Σ 365
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Shear Of STGB
365
Shear flow stress :18.796 GPa
Shear Modulus: 194.882 GPa
25
Shear flow stress : 18.405 GPa
Shear Modulus : 159.928 GPa
365 Graphene Perp
Shear flow stress :20.199 GPa
Shear Modulus: 181.586 GPa
November 14, 2014 S. Bringuier, MS&T 2013 23
Strain Type Youngs Modulus
(GPa)
Fracture
stress(GPa)
┴ GB, 108 285.35 69.65
┴ GB, 109 291.39 72.96
|| GB, 108 255.28 73.54
|| GB, 109 285.43 73.01
Σ25
Strain Type Youngs Modulus
(GPa)
Fracture
stress(GPa)
┴ GB, 108 300.68 75.08
┴ GB, 109 312.81 80.73
|| GB, 108 389.30 117.14
|| GB, 109 370.63 116.01
Σ365