Mechanical failure in SiC Bicrystals

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)


Nature of failure (Intra- vs. Inter-granular) is grain

boundary misorientation dependent.

High angle GB

Inter-granular failure

Low angle GB

Intra-granular failure


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.


• 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


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.


[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


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


•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


Free-Volume is a

results of generation

method.

Free volume

Depends on

criteria used

to remove

atoms from

GB

Introducing Strain


•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


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


• 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


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


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


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)


• 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


• 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).

http://lammps.sandia.gov/index.html

http://ovito.org/


• 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


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


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


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

Intentionally Blank



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


But Not Always

Σ 365 – Low Angle

Σ 25 – High Angle

• Graphene sheet causes

significant weakening at GB.

• Failure is “atomically clean”.

Free volume acts as

stress concentrator

Mechanical failure in SiC Bicrystals

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Mechanical failure in SiC Bicrystals