Prediction of intergranular micro-crack initiation induced by the impingement of persistent slip bands on grain boundaries

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Prediction of intergranular micro-crack initiation induced by the impingement of persistent slip bands on

grain boundaries

J. Hazan, M. Sauzay

To cite this version:

J. Hazan, M. Sauzay. Prediction of intergranular micro-crack initiation induced by the impingement of persistent slip bands on grain boundaries. TMS 2018, Mar 2018, Phoenix, United States. �cea-02339080�

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PREDICTION OF INTERGRANULAR

MICRO-CRACK INITIATION INDUCED

BY THE IMPINGEMENT OF

PERSISTENT SLIP BANDS ON

GRAIN BOUNDARIES

TMS 2018 - MARS 12TH 2018

Jérôme HAZAN, Maxime SAUZAY

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CONTENTS

• CONTEXT & GOALS

• METHODS • RESULTS

• CONCLUSIONS & WORK IN PROGRESS

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CONTEXT

Cyclic deformation induces localization of plastic slip within Persistent Slip Bands (PSBs) for grains oriented for

single slip

 Formation of a two phase microstructure (if 𝜏_𝑝 = 𝜏_𝑃𝑆𝐵) : - Elastic matrix - Elastic-plastic bands (PSBs) | 3 [Man et al. 2002] [Mughrabi 1979] Poor channels(~1013_m-2₎ rich walls(~1015_m-2_{) :}

Ladder like structure

[Weidner et al. 2010] Copper single crystal 316L SS polycrystal Nickel polycrystal TMS 2018 | MARS 12th 2018

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CONTEXT

The extrusion of PSBs is due to the production of vacancies during

cyclic deformation 12 MARS 2018 | 4 Extr u si o n h ei g h t, h [n m] Number of cycles, N*103 [Man et al. 2003] Almost constant growth rate of PSBs

during cycling [Polák & Sauzay 2009]

Type A

Type B

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Aim of the present work: Predicting micro-cracks initiation due to the impingement of PSBs on grain boundaries

 Prediction of GB extrusions and GB stress fields

Transgranular initiation treated by [Liu & Sauzay 2014]

CONTEXT

Slip localization in PSBs leads to microcrack initiation (in LCF):

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Transgranular (type B):

[Polák et al. 2009] [Zhang et al. 1999]

Grain Boundaries (type A):

5 µm

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CONTEXT: EXISTING MODELS

Reference models mostly based on dislocations pile-up at GB : - Tanaka & Mura 1981

- Sangid et al. 2011 (Molecular Dynamics input for dislocation absorption and nucleation at GB)

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𝑁𝑖 = 8 µ 𝛾𝑒𝑓𝑓

2 𝜋 1 − ν 𝑎 (∆𝜏 − 2𝜏_𝑓)²

Our aim: Possibility of predicting GB micro-crack initiation through PSB cyclic plasticity and vacancy production ?

TMS 2018 | MARS 12th 2018

Cyclic deformation causes ratcheting of dislocations at grain boundaries Homogeneous slip within PSBs PSB containing Pile-up h = N.b t t [Weidner et al 2006] h = γ_p.t

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CONTENTS

• CONTEXT & GOAL

• METHODS

• Elastic-plastic model and behavior

• Cohesive zone model • RESULTS

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METHOD : ELASTIC-PLASTIC MODEL AND BEHAVIOR

| PAGE 8 TMS 2018 | MARS 12th 2018

Finite Element Calculations based on:

Elastic-Plastic behavior for PSBs

 Armstrong-Fredericks non-linear kinematic hardening

 Plateau behavior

2 Mixture rule of Winter:

𝛾_{𝑐𝑟𝑦𝑠𝑡}𝑝 = 𝛾_𝑀𝑎𝑡𝑝 𝑓_𝑣_𝑀𝑎𝑡 + 𝛾_𝑃𝑆𝐵𝑝 𝑓_𝑣_𝑃𝑆𝐵 𝛾_𝑀𝑎𝑡𝑝 _{≈ 1 100} 𝛾_𝑃𝑆𝐵𝑝  𝛾_{𝑐𝑟𝑦𝑠𝑡}𝑝 = 𝛾_𝑃𝑆𝐵𝑝 𝑓_𝑣_𝑃𝑆𝐵  Localisation of slip in PSBs 1 0 10 20 30 -0,01 -0,005 0 0,005 0,01 Sh ear str ess (M Pa ) Shear strain

Experiment - Single crystal behavior Experiment - PSB behavior

Fit Armstrong-Fredericks

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METHOD

Production of vacancies inducing the free dilatation of persistent slip bands

 Resistivity measurements on copper single crystals cycled at 4K [Polák 1987]

 Determination of the vacancy production term

[Polák & Sauzay 2009] p = 3.1 10-7 _{for Copper}

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3 𝜀_{𝑣𝑎𝑐𝑎𝑛𝑐𝑦}∗ = 𝑁_{𝑐𝑦𝑐𝑙𝑒𝑠} ∗ 𝑝 TMS 2018 | MARS 12th 2018 Grain size, L Slip band thickness, t 𝒃 Grain boundary impinged by the slip band

Elastic matrix 𝒃 : Burgers vector Grain 1, orientation 1 Grain 2, orientation 2 PSB Matrix c_v x Diffusion of vacancies toward matrix

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10 20 30 40 50 60 S h e a r s tr e s s ( M P a )

Plastic shear strain amplitude

Experiment [001] Gong et al 1997 Experiment [011] Li et al 1998 Experiment [-111] Lepistö et al 1986 Experiment [-149] Mughrabi 1978 10-5 ₁₀-4 ₁₀-3 ₁₀-2 ₁₀-1 METHOD

Elastic-plastic behavior of neighbor grain impinged by the PSB

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4

TMS 2018 | MARS 12th 2018

Assumptions for the calculations:

 Elastic-Plastic behavior of PSBs & production, annihilation of vacancies within PSBs

and diffusion toward the matrix

 Elastic-Plastic behavior of neighbor grain

 Elastic matrix

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CONTENTS

• CONTEXT & GOAL

• METHODS

• Elastic-plastic model and behavior

• Cohesive zone model

• RESULTS

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Evaluation of three parameters:

- GB Young modulus E_GB

- Fracture energy of the interface 𝛾_{𝑓𝑟𝑎𝑐𝑡} = 2𝛾_𝑠 − 𝛾_𝐺𝐵

- Critical stress

Output: Opening of the interface, δ => δ/δ_c = 1 : Complete separation

METHOD : COHESIVE ZONE MODELING

GB obeys a non linear cohesive law: 2 criteria for crack initiation :

- Critical stress (UBER model) [Rice & Wang, 1989] [Rose et al. 1981] - Critical energy released by the

cracked interface [Griffith]

12 MARS 2018 TMS 2018 | MARS 12th 2018 | PAGE 12

GB PSB 𝜎_{𝑐𝑟𝑖𝑡} = 𝐸 𝑑𝐺𝐵 ∗ 𝛾𝑓𝑟𝑎𝑐𝑡 𝑒 Grain 1 Grain 2 0 5 10 15 0 1 2 3 N o rm al s tr e ss (GPa ) Opening displacement, δ (Å) σ_crit γ_Griffith δ = δ_c See [Barbé et al 2018]

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CONTENTS

• CONTEXT & GOAL • METHODS

• RESULTS

• GB extrusions and stress-fields

• Prediction of crack initiation • CONCLUSIONS & WORK IN PROGRESS

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0 2 4 6 8 0 20 40 60 80 100 S h e a r s tr e s s ( G P a )

Distance to grain boudary / slip band interface (nm), r 1500 cycles 10500 cycles 20500 cycles 30000 cycles 0 2 4 6 8 0 20 40 60 80 100 N o rm a l s tr e s s ( G P a )

Distance to grain boudary / slip band interface (nm), r

1500 cycles 10500 cycles 20500 cycles 30000 cycles

RESULTS : PREDICTION OF MECHANICAL FIELDS

Copper | PSB thickness = 1 µm | Grain size = 50 µm | 30 000 cycles

| 14 TMS 2018 | MARS 12th 2018

GB

b

σ_nn

τ_nm _{Height of grain boundary} extruded by the PSB impingement 0 20 40 60 80 100 0 5 10 15 20 G ra in b o u n d a ry e x tr u s io n ( n m )

Position along grain boundary (µm)

1500 cycles 10500 cycles 20500 cycles 30000 cycles Isotropic elastic grain r + 30000 cycles

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RESULTS: PREDICTION OF MECHANICAL FIELDS

Influence of the persistent slip band characteristic lengths:

=> grain boundary extrusion

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Influence of slip band thickness, t Influence of grain size, L

Φ = 10 µm

Combined effect of the slip band thickness and grain size on the grain boundary extrusion : Higher damage expected

y = 1,7182x0,2348 y = 5,1967x0,2357 0 2 4 6 8 10 12 14 16 18 20 0 50 100 150 200 250 Gr ai n b o u n d ar y extr u si o n h ei g h t (n m) Grain size (µm) 10 000 cycles 30 000 cycles 𝒉 (𝑵) = 𝟎, 𝟓𝟔 . 𝒑. 𝑵. 𝒕𝟎,𝟕𝟕 ∗ 𝑳(𝟏−𝟎,𝟕𝟕) y = 0,0149x0,7652 y = 0,0455x0,7643 0 1 2 3 4 5 6 7 8 9 10 0 200 400 600 800 1000 Gr ai n b o u n d ar y extr u si o n h ei g h t (n m)

Slip band thickness (nm)

10 000 cycles 30 000 cycles

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Influence of neighbor grain crystallographic orientation ?

| 16 High increase in the grain boundary extrusion due to plasticity in the

neighbor grain TMS 2018 | MARS 12th 2018

[Li et al 2010]

8 active systems 4 active systems 6 active systems 1 active system 0 2 4 6 8 10 0 200 400 600 800 1000 G ra in b o u n d a ry e x tr u s io n ( n m )

Slip band thickness (nm)

SSO - 5 degree rotation SSO - 10 degree rotation SSO - 15 degree rotation SSO + 5 degree rotation SSO + 10 degree rotation SSO + 15 degree rotation Isotropic elastic 0 2 4 6 8 10 12 14 16 35 36 37 38 39 40 G ra in b o u n d a ry e x tr u s io n (n m )

Position along grain boundary (µm)

[100] [110] [111]

SSO + 15 degree rotation Isotropic Elastic

Grain size = 10µm

Grain size = 200µm

Slip band thickness = 1µm Neighbor grain :

Neighbor grain :

SSO : Single slip orientation

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Influence of neighbor grain crystallographic orientation ?

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Expected decrease of GB stress fields due to plasticity in the neighbor grain TMS 2018 | MARS 12th 2018

[Li et al 2010]

8 active systems 4 active systems 6 active systems 1 active system 0 0,5 1 1,5 0 20 40 60 80 100 Norma l s tres s (GPa )

Distance to grain boundary / slip band interface (nm), r [100]

[110] [111]

SSO + 15 degree rotation Isotropic Elastic -0,5 0 0,5 1 1,5 0 20 40 60 80 100 S he a r s tre s s (GP a )

Distance to grain boundary / slip band interface (nm), r [100]

[110]

[111]

SSO + 15 degree rotation Isotropic Elastic

Grain size = 200µm

Slip band thickness = 1µm Neighbor grain :

Neighbor grain : Grain size = 10µm

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| 18 TMS 2018 | MARS 12th 2018 Comparison of the prediction to experimental data from literature :

Impact of PSB thickness on GB extrusion height ?

[Zhang & Wang]

[Weidner et al. 2010]

Exponents adjusted using experimental data in reasonable agreement with the exponents provided by

the FE computations ~0.7 y = 0,2309x0,6845 R² = 0,6506 0 0,5 1 1,5 2 2,5 0 10 20 30 G ra in b o u n d a ry e x tr u s io n ( µ m )

Slip band thickness (µm) y = 0,3175x0,973 R² = 0,7208 0 0,2 0,4 0,6 0,8 1 0 1 2 3 G ra in b o u n d a ry e x tr u s io n ( µ m )

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CONTENTS

• RESULTS

• GB extrusions and stress-fields

• Prediction of crack initiation

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Prediction: Stronger influence of PSB thickness than grain size Order of magnitude in agreement with experimental observation ?

RESULTS: PREDICTION OF MICRO-CRACK INITIATION

Preliminary results: influence of PSBs characteristic lengths on GB micro-crack initiation : Copper, elastic neighbor

| 20 t (nm) L (µm) Ni (cycles) 50 10 60k 100 10 45k 200 10 25k 500 10 15k 1000 10 13k 1000 20 13k 1000 50 11k 1000 100 10k 1000 200 9k TMS 2018 | MARS 12th 2018 0 0,2 0,4 0,6 0,8 1 100 1000 10000 100000 δ /δ c Number of cycles t = 50 nm | L = 10µm t = 100 nm | L = 10µm t = 200 nm | L = 10µm t = 500 nm | L = 10µm t = 1000 nm | L = 20µm t = 1000 nm | L = 50µm t = 1000 nm | L = 100µm t = 1000 nm | L = 200µm

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RESULTS: PREDICTION OF MICRO-CRACK INITIATION

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Observations of intergranular initiation published in literature (RT, air environment):

TMS 2018 | MARS 12th 2018 Material Δε_p/2 t (µm) L (µm) Ni Reference 316L - polycristal 10 -3 _{≈0,45 µm <30>} <5000 (20%Nr) [Mineur et al. 2000] 316L - polycristal 10 -3 _{≈0,45 µm <47>} <10000 (20%Nr) [Blochwitz et Richter 1999] 316L - polycristal 2.5 10 -4 _{≈0,45 µm <47>} <40000 (20%Nr) [Blochwitz et Richter 1999] Ni - polycristal 2.5 10 -4 _{≈1 µm} _<24> <145000 (66% Nr) [Morrison et Moosbrugger 1997] Ni - polycristal 2.5 10 -3 _{≈1 µm} _{<290> <200 (4% Nr)} [Morrison et Moosbrugger 1997] Ni - polycristal 2.5 10 -4 _{≈1 µm} _<290> _<17000 [Morrison et Moosbrugger 1997] Ni - polycristal 2.5 10 -3 _{≈1 µm} _<24> <1200 (19% Nr) [Morrison et Moosbrugger 1997] Ni – polycristal 3 10

-4 _{≈1 µm} _<150> ₁₈₀₀₀ _{[Dorr & Blochwitz 1987]}

Cu -

polycristal 10

-3 _{≈1 µm} _<100> <10000

(25%Nr) [Liu et al 1992] Cu - bicrystal 2 10-3 ≈1 µm ~5 mm <10000 [Zhang et Wang 2002]

Cu - bicrystal 5 10-4 ≈1 µm ~5 mm <20000 [Zhang Wang Hu 1999] First prediction are in the good order of magnitude

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CONTENTS

• RESULTS

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CONCLUSIONS & WORK IN PROGRESS

Conclusions :

• Simulation based on basic physical assumptions

• Prediction of stress-fields induced by impingement of PSBs at GB for different crystallographic orientations of the neighbor grains • Analytical formulas of GB extrusion heights (elastic neighbor) Work in progress :

• Prediction of intergranular initiation introducing atomistic

considerations in the calculations as M.Sangid did [Sangid et al. 2011]

• GB type, environment, material, etc.

• Interrupted fatigue test carried out on two 316L SS containing (i) very large grains and (ii) small grains

• EBSD scan + SEM observations of crack-initiations

 Comparison of predictions to real cases microstructures

• Analytical model for the prediction of intergranular, transgranular and twin boundaries microcrack initiation _{TMS 2018 | MARS 12th 2018}_{| 23}

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WORK IN PROGRESS

Interrupted fatigue test :

316L SS, 2000 cycles, <200 µm>, Δε_p/2 = 10-3

12 MARS 2018 TMS 2018 | MARS 12th 2018 | 24

=> Microstructure informed FE computations based on EBSD data and post-FIB cutting (3D information)

In ter granul ar i ni tiatio n Tw in bo un dary i ni tiatio n

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Nuclear Energy Division Nuclear Material Department

Section for Applied Metallurgy Research Materials Mechanical Analysis Laboratory

French Alternative Energies and Atomic Energy Commission Saclay Center| 91191 Gif-sur-Yvette Cedex

T. +33 (0)1 69 08 17 05 jerome.hazan@cea.fr | PAGE 25

Many thanks for your attention

Any question ?

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WORK IN PROGRESS

=> Case of HCF & VHCF

Same methodology applicable for twin boundary cracking

12 MARS 2018 | 26

[Li et al. 2014]

[Man et al. 2012]

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TRANSGRANULAR OR INTERGRANULAR INITIATION ?

12 MARS 2018 TMS 2018 | MARS 12th 2018 | SLIDE 27

[Obrtlik et al, 1997]

Cylindrical Copper single crystal cyclically deformed : - Each peak is offset by 180°

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NUMBER OF GRAINS CONTAINING PSBS

12 MARS 2018 TMS 2018 | MARS 12th 2018 | SLIDE 28 [Sauzay 2006]

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VALIDITY DOMAIN ?

12 MARS 2018 | 29

Element size = 3,33 nm

Compression test on Ni micropillar [Legros 2014]

1013_m-2< ρ

Matrix < 1015 m-2

N_{dislocation, max} = 3.33*10-10 _{x 3.33*10}-10 _{x 10}15_{= 1.1*10}-4 ≈ 0 dislocation Why matrix is supposed to be elastic ?

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ENVIRONMENT EFFECT ON MICRO-CRACK INITIATION

12 MARS 2018 | 30

Air, RT, Δε_p/2 = 2.10-3 Vacuum, RT, Δε

p/2 = 2.10-3

Mostly transgranular initiation Mostly intergranular initiation

TMS 2018 | MARS 12th 2018

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METHOD : COHESIVE ZONE MODEL

12 MARS 2018 TMS 2018 | MARS 12th 2018 | PAGE 31

GB , CZM PSB Grain 1 Grain 2 Copper Nickel 316 SS Young modulus (Pa) 1.3 10 11 _{1.8 10}11 _{1.9 10}11 EGB min (Pa) 5.9 1010 8.1 1010 8.6 1010 EGB max (Pa) 1.3 1011 1.8 1011 1.9 1011 dGB min (Å) 3 3 3 dGB max (Å) 7 7 7 γsurf min (J/m²) 1.9 2 2 γsurf max (J/m²) 2.2 2.4 3 γGB min (J/m²) 0.3 0.45 0.48 γGB max (J/m²) 1 1.4 1.6 γfrac (J/m²) min 2.8 2.6 2.4 γfrac (J/m²) max 4.1 4.4 5.5 σc min (GPa) 5.6 6.4 6.3 σc max (GPa) 15 19 22

References : [Latapie & Farkas 2003] [Shen et al 1994], [Barbé et al 2018] [Tschopp & McDowell 2007] [Vitos 1998], [Holm et al 2010]

𝜎_{𝑐𝑟𝑖𝑡} = 𝐸 𝑑𝐺𝐵 ∗ 𝛾𝑓𝑟𝑎𝑐𝑡

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METHOD : COHESIVE ZONE MODEL

Many experimental and simulation efforts have been carried out to better understand grain boundaries role :

| 32 TMS 2018 | MARS 12th 2018 Influence of the Coincident Site Lattice Grains misorientation and GB characteristics GB energy, GB thickness Influence of Grain Size Influence of environment

[Lim & Raj 1984] [Shenyang group] [Liu et al 1992]

[Tschopp & McDowell 2007]

[Yamakov et al 2006] [Morrison & Moosbrugger _1997] [Taira et al 1979]