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A primer on selecting grain boundary sets for comparison of interfacial fracture properties in MD simulations

2017 LAMMPS Workshop & SymposiumAugust 1st - August 3rd, Albuquerque NM

Rémi DingrevilleSandia National Laboratories

Doruk Aksoy, Douglas E. SpearotDepartment of Mechanical and Aerospace Engineering

University of FloridaSAND2017-7867 C

2

LAMMPS random fact of the day:

[Source: Google scholar as a 8/3/2017]

Fundamentals of fracture processes influenced by interfacial structure

3

§ Interfacial attributes of importance:

§ Elastic mismatch§ Degree of symmetry§ Interfacial coherency (structure)

(physical and the chemical nature between both phases)

[Wuttiphan, 1996, JAmCeramSoc]

Crack resistant glass/ceramic

[Pan, 1996, ActaMater]

GB effects on intergranular SCCSCC in alloy X-750

Fracture stress in Mo bicrystals

[Watanabe, 1999, ActaMater]

✏ =1

2⇡ln

✓1� �1 + �

◆, � =

µ1 (k2 � 1)� µ2 (k1 � 1)µ1 (k2 + 1) + µ2 (k1 + 1)

� (r, ✓) =Re

�Kri✏

�p2⇡r

�̂I (✓) +Im

�Kri✏

�p2⇡r

�̂II (✓) +KIIIp2⇡r

�̂III (✓)

4

✏ =1

2⇡ln

✓1� �1 + �

◆, � =

µ1 (k2 � 1)� µ2 (k1 � 1)µ1 (k2 + 1) + µ2 (k1 + 1)

� (r, ✓) =Re

�Kri✏

�p2⇡r

�̂I (✓) +Im

�Kri✏

�p2⇡r

�̂II (✓) +KIIIp2⇡r

�̂III (✓)

How do we isolate (decouple) the role of the interface structure on interfacial fracture?

§ Create grain boundaries with matching important fracture-related properties of adjoining lattices:§ Anisotropic elastic moduli§ Schmid factor§ Slip mode

Misorientation space Fracture properties space

Criterion: Elastic Anisotropy

5

�����

�����

�����

�����

§ Orientation dependent Young’s modulus:

§ Difference in elastic anisotropy lead to localization effects at GB but also a contributing factor for SIF (Dundur’s parameters)

1

E

�!X

=C11 + C12

(C11 � C12) (C11 + 2C12)+

✓1

C44� 2 1C11 � C12

◆x

21x

22 + x

22x

23 + x

21x

23

||�!X ||4

Criterion: Schmid factor for primary slip

6

Slip directionSlip plane

Normal to slip planeTraction axis

⌧↵ = µ↵ · � ,with µ↵ = cos� cos ✓

§ Largest resolved shear stress on any slip system defines the primary slip system to be activated upon plasticity activity.

Criterion: Slide mode

7

Rµ =µ1µ2

§ Slip mode and potential for second slip system to be activated with respect to first activated slip system:

§ Single versus multi-slip

µ↵ =

2

6666664

µ1

µ2

µ3

··µn

3

7777775

Eliminating role of selected lattice attributesin comparative analysis of interfacial fracture:

8

§ Matching of lattice attributes:§ Directional Young’s modulus and Schmid factor for primary slip

§ Importance of elastic/plastic transition§ Directional Young’s modulus and slip mode

§ Importance of partitioning of dislocation activities§ Schmid factor for primary slip and slip mode

§ Importance of elastic anisotropy/elastic impedance

9

E+ Schmid Factor + Slip Mode

E = 220 GPaSF = 0.45R = 1.25% error from target values

Grouping orientations

Case study

10

Simulating steady-state fracture

11

Step 1Build grain boundary structure

Step 2Equilibrate

system under pre-tension

Step 3Introduce atomically

sharp crack

Step 4Allow crack

growth under pre-tension

Step 5Averaging to

extract decohesion form

Primary GB

Secondary GB

Secondary GB

{415} {213}

[Yamakov et al., 2006, JMPS][Barrows et al., 2016, MSEA]

Simulating steady-state fracture

11

Step 1Build grain boundary structure

Step 2Equilibrate

system under pre-tension

Step 3Introduce atomically

sharp crack

Step 4Allow crack

growth under pre-tension

Step 5Averaging to

extract decohesion form

§ Avoids having to artificially impose a boundary velocity

Simulating steady-state fracture

11

Step 1Build grain boundary structure

Step 2Equilibrate

system under pre-tension

Step 3Introduce atomically

sharp crack

Step 4Allow crack

growth under pre-tension

Step 5Averaging to

extract decohesion form

§ Statistical mechanics rather than a deterministic approachC ra c k o p e n in g (Å )

0 2 4 6 8 1 0 1 2 1 4

Av

era

ge

Str

es

s s

yy (

GP

a)

0

2

4

6

8

1 0

1 2

1 4S c re e n e d d a ta D e c o h e s io n d a ta

Mechanistically similar fracture behavior

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Plasticity similar for both {213} and {415} as generally expected from Schmid Factor

Crack propagation:{213} STGB + 0 H/nm2

Crack propagation:{415} STGB + 0 H/nm2

15 nm

Mechanistically similar fracture behavior

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Using H segregation at GB as a surrogate for change in interfacial structure

14

� =1

A

"X

NNi

�ENNi � EbulkNNi

�+

X

NH

�ENH � EbulkNH

�#

−4

−3

−2

−1

0

1

2

3

4

0 0.01 0.02 0.03 0.04 0.05

Dis

tanc

e fr

om g

rain

bou

ndar

y [Å

]

H atom density, ρH [H/nm2]

{213}{415}

−4

−3

−2

−1

0

1

2

3

4

0 0.05 0.1 0.15 0.2

Dis

tanc

e fr

om g

rain

bou

ndar

y [Å

]

H atom density, ρH [H/nm2]

{213}{415}

GB plane

1H/nm2 20H/nm2

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

0 5 10 15 20

Inte

rfac

ial e

xces

s en

ergy

, γG

B [

J/m

2 ]

Average H coverage, 〈ρH〉 [H/nm2]

{213}{415}

Isolating the role of the interface (1/2)

15

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35

Trac

tion,

σyy

[GPa

]

Crack opening displacement, λ [Å]

0H/nm21H/nm25H/nm2

10 H/nm220H/nm2

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35

Trac

tion,

σyy

[GPa

]

Crack opening displacement, λ [Å]

0H/nm21H/nm25H/nm2

10 H/nm220H/nm2

0

2

4

6

8

10

0 5 10 15 20 25 30 35 40

Trac

tion,

σyy

[GPa

]

Crack opening displacement, λ [Å]

Decohesion data 1H/nm2 (run #1)Decohesion data 1H/nm2 (run #2)Decohesion data 1H/nm2 (run #3)

fit 1H/nm2

{213}(left crack tip)

{415}(left crack tip)

Region 4Region 3Region 2

Isolating the role of the interface (2/2)

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§ In this example, structure of interface directly influence driving force for crack propagation!

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.75 0.8 0.85 0.9 0.95 1

γ f/γ

f 0

γGB/γGB0

{213} γf - Left tip{213} γf - Right tip

{415} γf - Left tip{415} γf - Right tip

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.75 0.8 0.85 0.9 0.95 1σ

max

/σm

ax0

γGB/γGB0

{213} σmax - Left tip{213} σmax - Right tip

{415} σmax - Left tip{415} σmax - Right tip

Fracture energy Peak stress

Methodology toisolate role of GB structure

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§ Pathway for identifying general GB predisposition to resist fracture

§ Create sets of GBs using isocurves associated with identical lattice properties (E, 𝜇𝛼, R𝜇)

§ Enable identification of structure-property relationships

§ High-throughput simulations underway

[Dingreville, Aksoy and Spearot, in press Sci. Reports, 2017]@: rdingre@sandia.gov