Precipitation and abnormal grain growth in low alloy steels

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Mohammad Razzak

To cite this version:

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CHIMIE

CHIMIE DE LYON

http://www.edchimie-lyon.fr

Insa : R. GOURDON

M. Jean Marc LANCELIN

Université de Lyon – Collège Doctoral Bât ESCPE 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cedex Tél : 04.72.43 13 95 [email protected] E.E.A. ELECTRONIQUE, ELECTROTECHNIQUE, AUTOMATIQUE http://edeea.ec-lyon.fr Secrétariat : M.C. HAVGOUDOUKIAN [email protected] M. Gérard SCORLETTI

Ecole Centrale de Lyon 36 avenue Guy de Collongue 69134 ECULLY Tél : 04.72.18 65 55 Fax : 04 78 43 37 17 [email protected] E2M2 EVOLUTION, ECOSYSTEME, MICROBIOLOGIE, MODELISATION http://e2m2.universite-lyon.fr Insa : H. CHARLES

Mme Gudrun BORNETTE

CNRS UMR 5023 LEHNA

Université Claude Bernard Lyon 1 Bât Forel 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cédex Tél : 06.07.53.89.13 e2m2@ univ-lyon1.fr EDISS INTERDISCIPLINAIRE SCIENCES-SANTE http://www.ediss-lyon.fr

Sec : Samia VUILLERMOZ Insa : M. LAGARDE

M. Didier REVEL Hôpital Louis Pradel Bâtiment Central 28 Avenue Doyen Lépine 69677 BRON Tél : 04.72.68.49.09 Fax :04 72 68 49 16 [email protected] INFOMATHS INFORMATIQUE ET MATHEMATIQUES http://infomaths.univ-lyon1.fr

Sec :Renée EL MELHEM

Mme Sylvie CALABRETTO

Université Claude Bernard Lyon 1 INFOMATHS Bâtiment Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cedex Tél : 04.72. 44.82.94 Fax 04 72 43 16 87 [email protected] Matériaux MATERIAUX DE LYON http://ed34.universite-lyon.fr Secrétariat : M. LABOUNE PM : 71.70 –Fax : 87.12 Bat. Saint Exupéry [email protected]

M. Jean-Yves BUFFIERE

INSA de Lyon MATEIS

Bâtiment Saint Exupéry 7 avenue Jean Capelle 69621 VILLEURBANNE Cedex

Tél : 04.72.43 83 18 Fax 04 72 43 85 28 [email protected]

MEGA

MECANIQUE, ENERGETIQUE, GENIE CIVIL, ACOUSTIQUE

http://mega.ec-lyon.fr

Secrétariat : M. LABOUNE PM : 71.70 –Fax : 87.12 Bat. Saint Exupéry [email protected]

M. Philippe BOISSE

INSA de Lyon Laboratoire LAMCOS Bâtiment Jacquard 25 bis avenue Jean Capelle 69621 VILLEURBANNE Cedex Tél :04.72 .43.71.70 Fax : 04 72 43 72 37 [email protected] ScSo ScSo* http://recherche.univ-lyon2.fr/scso/

Sec : Viviane POLSINELLI Brigitte DUBOIS Insa : J.Y. TOUSSAINT

M. OBADIA Lionel Université Lyon 2 86 rue Pasteur 69365 LYON Cedex 07 Tél : 04.78.77.23.86 Fax : 04.37.28.04.48 [email protected]

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Materials micro properties Precipitation state Grain growth Thermo-mechanical treatment Grain size evolution Grain growth type: AGG/NGG Volume fraction Precipitate modeling Coupled modeling Materials by design Volume fraction Precipitate size distribution & chemistry Grain growth modeling Materials macro properties Induction coupled plasma analysis Precipitate chemistry Precipitate size distribution

Picric acid etching + image analysis

Development required

Need further improvement or modification

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� �� v ol ume fr actio n �� 1 2 3 � ��_≈ � � 0 0.1 0.2 0.3 0.4 0 0.5 1 1.5 2 2.5 3 0E+00 3E+08 5E+08 8E+08 1E+09 �/�� − 1 1 2 3 �� Increasing pinning ❋✐❣✉r❡ ✷✳✺✿ ❙✉♣❡r✐♠♣♦s✐t✐♦♥ ♦❢ ❆●● ❝♦♥❞✐t✐♦♥ (d/dt(Dab/Dn) > 0) ❝♦♥s✐❞❡r✐♥❣ ❞✐✛❡r❡♥t ♣✐♥♥✐♥❣ ❝♦♥❞✐t✐♦♥ ♦♥ ❛ ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥✳ d/dt(Dab/Dn) ❝❛♥ r❛♥❣❡ ❜❡t✇❡❡♥ Dn ❛♥❞ ➀ ♦r ➁ ♦r ➂✳ ❍❡r❡✱ ✐t ✐s ❛ss✉♠❡❞ t❤❛t M = 1✳ ♦❢ ❆●● ✐♥✐t✐❛t✐♦♥✳ ■♥ ❝❛s❡ ✸ ✱ t❤❡ ❧❛r❣❡st ❣r❛✐♥s ✐♥ t❤❡ ♠✐❝r♦str✉❝t✉r❡ ❝❛♥ ❣r♦✇ r❡❧❛t✐✈❡❧② ❢❛st❡r t❤❛♥ t❤❡ ♠❡❛♥ s✐③❡❞ ♦♥❡s✳ ■♥ ❝❛s❡s ✶ ❛♥❞ ✷ ❣r❛✐♥ s✐③❡s ✈❡r② ❝❧♦s❡ t♦ t❤❡ ♠❡❛♥ s✐③❡❞ ♦♥❡ ❣r♦✇ ❢❛st❡r ✇❤✐❝❤ ✐♥ ❢❛❝t ❢❛❝✐❧✐t❛t❡s ❛ q✉❛s✐✲st❛t✐♦♥❛r② ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥ ❡✈♦❧✉t✐♦♥ ✭♥♦r♠❛❧ ❣r❛✐♥ ❣r♦✇t❤✮✳ ❋r♦♠ ✜❣✉r❡✷✳✺✱ ✐t ❝❛♥ ❜❡ ❝♦♥❝❧✉❞❡❞ t❤❛t Dmax ab ♠✉st ❜❡ ❛t ❧❡❛st ✷ t✐♠❡s ♦❢ Dn ✐♥ ♦r❞❡r ❢♦r ❆●● t♦ ♦❝❝✉r✳ ❙♦✱ ❛ r❡❛❧✐st✐❝ q✉❛❧✐t❛t✐✈❡ ✐❞❡♥t✐✜❡r ♦❢ ❆●● ❛♥❞ ◆●● ❝❛♥ ❜❡ ❡①♣r❡ss❡❞ ❛s ❢♦❧❧♦✇s✿ Dmax

ab /Dn> 2 Probable grain growth condition : ❆●● Dmaxab /Dn< 2 Probable grain growth condition : ◆●●

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5 10 15 20 25 30 5 10 15 20 25 30 1e+006 1e+007 1e+008 1e+009 1e+010 d/dt(D_ab/D_n)(s-1) D_n(µm) D_ab/D_n d/dt(D_ab/D_n)(s-1) 0 5e+008 1e+009 1.5e+009 2e+009 2.5e+009 3e+009 3.5e+009 4e+009 4.5e+009 5e+009 ❋✐❣✉r❡ ✷✳✾✿ ❊✛❡❝ts ♦❢ ♠❡❛♥ ❣r❛✐♥ s✐③❡ ✭Dn✮ ♦♥ ❛❜♥♦r♠❛❧ ❣r❛✐♥ ❣r♦✇t❤ ❝♦♥❞✐t✐♦♥ ✭d/dt(Dab/Dn)✮✳ ❍❡r❡✱ t❤❡ ♣r❡❝✐♣✐t❛t❡ ✈♦❧✉♠❡ ❢r❛❝t✐♦♥ fv = 0.00033 ❛♥❞ t❤❡ ♠❡❛♥ r❛❞✐✉s ¯r = 26♥♠✳ ❆●● ♠♦❞❡❧ ♣❛r❛♠❡t❡r µ = 0.56 ❛♥❞ λ = 0.6✳ d/dt(Dab/Dn) ✈❛❧✉❡ ✐s s❤♦✇♥ ♦♥ t❤❡ ①✲② ♣❧❛♥❡ ♠❛r❦❡❞ ❜② t❤❡ r✐❣❤t ❤❛♥❞ s✐❞❡ s❝❛❧❡✳ st❛t❡✱ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♠❡❛♥ ❣r❛✐♥ ❞✐❛♠❡t❡r ✐♥❝r❡❛s❡s t❤❡ ♠❛①✐♠✉♠ r❛♥❣❡ ♦❢ ❣r❛✐♥ s✐③❡s ✭Dmin

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Start

Read input data

Read parameters

�� = �� (initialize, i=0) �∗_calculation

� = ��

� �

_,

�

� = ��

�

_,

� �

1.

� �

_��

2. �

� �

/��

��/�� > 2

i=i+1

�

= �

�

+ ∆�

� ≤ � �� N��

yes

no

yes

Data

�� Precipitate size distribution Austenite grains size, �_�

�

∗

_{> �}

��

�

��

�

= �

��

�

= �

��

�

��

no

yes

no

i: Index of class, iϵ[1,N].

��: Radius of precipitate class i. ��: Number of precipitate in class i. �∗_{: Number of corner points.}

N_{: Number of precipitate classes.}

� : Corner point pinning pressure. � : Zener pinning pressure.

��: Mean grain diameter. ��: Abnormal grain size. AGG: Abnormal grain growth. NGG: Normal or no grain growth.

❋✐❣✉r❡ ✷✳✶✹✿ ❆ s❝❤❡♠❛t✐❝ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❆●● ♠♦❞❡❧ ❝❛❧❝✉❧❛t✐♦♥ ♣r♦❝❡❞✉r❡✳

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❢♦❧❧♦✇✐♥❣✿











dR dt

A

=

Dm A R Xm A−X I A(R) ψXP −XAI(R) dR dt

B

=

Dm B R Xm B−X I B(R) ψXP −XBI(R)

X

I A

X

BI

= K

s

exp

_R ◦ R

✭✸✳✷✶✮

❍❡r❡✱ XI _{✐s t❤❡ ❡q✉✐❧✐❜r✐✉♠ ❛t♦♠✐❝ ❝♦♥❝❡♥tr❛t✐♦♥ ♦❢ s♦❧✉t❡ ❛t♦♠s ❛t t❤❡ ♣r❡❝✐♣✐t❛t❡✲} ♠❛tr✐① ✐♥t❡r❢❛❝❡ ❛♥❞ Dm i r❡❢❡rs t♦ s♦❧✉t❡ s♣❡❝✐❡ i ❞✐✛✉s✐♦♥ r❛t❡ ✐♥ t❤❡ ♠❛tr✐①✳ ■♥ ❛ s♦❧✐❞ s♦❧✉t✐♦♥✱ ✐♥t❡rst✐t✐❛❧ s♦❧✉t❡ ❛t♦♠s ❞✐✛✉s✐♦♥ r❛t❡ ✐s ♠✉❝❤ ❢❛st❡r t❤❛♥ t❤❡ s✉❜st✐t✉t✐♦♥❛❧ ♦♥❡ ✭Dm B ≫ DmA✮✳ ❚❤✉s t❤❡ ♣r❡❝✐♣✐t❛t❡ ❣r♦✇t❤ r❛t❡ ✐s ❝♦♥tr♦❧❧❡❞ ❜② t❤❡ s✉❜st✐t✉t✐♦♥❛❧ ❛t♦♠✬s ❞✐✛✉s✐♦♥ ✐♥ t❤❡ ♠❛tr✐①✳ ❈♦♥s✐❞❡r✐♥❣ t❤❡ ❢❛❝t t❤❛t t❤❡ ♣r❡❝✐♣✐t❛t❡ ✭AxBy✮ ❣r♦✇t❤ r❛t❡ ✐s s♦❧❡❧② ❝♦♥tr♦❧❧❡❞ ❜② t❤❡ ❞✐✛✉s✐♦♥ ♦❢ A s♦❧✉t❡ ❛t♦♠s✱ t❤❡ ❢♦❧❧♦✇✐♥❣ s✐♠♣❧✐✜❝❛t✐♦♥ ❝❛♥ ❜❡ ✐♥tr♦❞✉❝❡❞✳ XI B(R) = X m B where, X m

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0 0.5 1 1.5 2 2.5 0 10 20 30 40 50 60 70 80 90 100

Mean grain diameter, ��

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Start

Read input data Read parameters t=0, initialize Calculate: �∗& �_� Precipitate nucleation: �∗ _�_� & dN/dt � > �∗ ��= ��+d�_dt� ∗ ∆� ��= ��+d�_dt� ∗ ∆� i=i+1 � ≤ � � ≤ � ��

_End

yes no yes no yes _no t=t+Δt �_��_� & Mean grain diameter: �_�

�∗_{: Number of corner points.} �: Number of class.

��

�� : Precipitate growth rate in grain boundary.

��

�� : Precipitate growth rate in the matrix.

i_{: Class index.}

❋✐❣✉r❡ ✸✳✺✿ ❆ s❝❤❡♠❛t✐❝ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣r❡❝✐♣✐t❛t✐♦♥ ♠♦❞❡❧ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ✐♥❝❧✉❞✐♥❣ ❜♦t❤ ❤♦♠♦❣❡♥❡♦✉s ❛♥❞ ❤❡t❡r♦❣❡♥❡♦✉s ❣r♦✇t❤ ♦❢ ♣r❡❝✐♣✐t❛t❡s✳

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r❛❞✐✐ ♦❢ t❤❡ ❝❧❛ss ❛♥❞ t♦t❛❧ ♥✉♠❜❡r ❞❡♥s✐t② ♦❢ ❛❧❧ ♣r❡❝✐♣✐t❛t❡ t②♣❡✳ ❆t ❡❛❝❤ t✐♠❡ st❡♣✱ t❤❡ ♣r❡❝✐♣✐t❛t❡ r❛❞✐✉s ❡✈♦❧✉t✐♦♥ ❛♥❞ ♥✉♠❜❡r ♦❢ ♣r❡❝✐♣✐t❛t❡ ✐♥ ❛ ♥❡✇ ❝❧❛ss ✐s ❝❛❧❝✉❧❛t❡❞ ✉s✐♥❣ ❢♦❧❧♦✇✐♥❣ t❤❡ ❡q✉❛t✐♦♥s ✸✳✺✶✱ ✸✳✺✷ ❛♥❞ ✸✳✺✸✳ Ri(t + ∆t) = Ri(t) + dRm i dt ∆t, Precipitate in matrix ✭✸✳✺✶✮ Ri(t + ∆t) = Ri(t) + dRb i

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❚❛❜❧❡ ✸✳✷✿ ❈♦♠♣♦s✐t✐♦♥ ♦❢ ✐♥❞✉str✐❛❧ st❡❡❧✲❆ ❛❧❧♦② ✐♥ ❛t♦♠✐❝ ✪ ❈ ❙✐ ▼♥ ◆✐ ❈r ❱ ❚✐ ❆❧ ◆❜ ◆ ✵✳✼✵✷ ✵✳✹✵✼ ✵✳✹✺✺ ✶✳✷✷ ✶✳✹✼ ✵✳✵✵✻✾✻ ✵✳✵✵✶✾✹ ✵✳✵✺✹✾ ✵✳✵✵✶✼✶ ✵✳✵✺✾✽ ❚❛❜❧❡ ✸✳✸✿ ❈♦♠♣♦s✐t✐♦♥ ♦❢ st❡❡❧✲❇ ✐♥ ❛t♦♠✐❝ ✪ ❈ ❙✐ ▼♥ ◆✐ ❈r ❆❧ ◆❜ ◆ ✵✳✵✾✻✸ ✵✳✸✺✷ ✶✳✷✷ ✵✳✶✸✸ ✶✳✷✸ ✵✳✵✼✵✶ ✵✳✵✷✷✶ ✵✳✵✾✷✾ Time T emp er atur e Hot rolling 875°C, 1hr 680°C, 2hr Slow cooling Slow cooling Water quench

As rolled state (AR)

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Precipitation model (t,T) Thermodynamic data Initial (�_��_�) �� < � � AGG model (t,T) �� Zener pinning: � Corner pinning: � �� & �� < � � �� >2 AGG NGG

��: Number of precipitate in class i.

��: Radius of precipitate in class i.

��: Precipitate volume fraction.

� : Precipitate mean radius.

�� : Max time limit of simulation.

��: ��ℎ time.

��0: Initial mean austenite grain size.

��: Abnormal grain size.

��: Normal grain size.

AGG: Abnormal grain growth. NGG: Normal or no grain growth.

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Time T empe ratur e Ac3 Ac1 Time T empe ratur e Ac3 Ac1 �0 �1 �0 �1

(a) Isothermal heat treatment setup (b) Heating rate simulation setup

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� �� v ol ume fr actio n �� 1 2 3 � �� _≈ � �

0

0.1

0.2

0.3

0.4

0

0.5

1

1.5

2

2.5

3 0E+00

3E+08

5E+08

8E+08

1E+09

�/�

� � �� − 1 1 2 3 �� Increasing pinning ❋✐❣✉r❡ ✹✳✸✿ ❙✉♣❡r✐♠♣♦s✐t✐♦♥ ❆●● ❝♦♥❞✐t✐♦♥ (d/dt(Dab/Dn) > 0) ♦♥ ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥✳ d/dt(Dab/Dn) ❝❛♥ r❛♥❣❡ ❜❡t✇❡❡♥ Dn ❛♥❞ ➀ ♦r ➁ ♦r ➂✳ ❍❡r❡✱ ✐t ✐s ❛ss✉♠❡❞ t❤❛t M = 1✳ ♣r♦❜❛❜✐❧✐t② ♦❢ ❆●● ✐♥✐t✐❛t✐♦♥✳ ■♥ ✸ ✱ t❤❡ ❧❛r❣❡st ❣r❛✐♥s ✐♥ t❤❡ ♠✐❝r♦str✉❝t✉r❡ ❝❛♥ ❣r♦✇ r❡❧❛t✐✈❡❧② ❢❛st❡r t❤❛♥ t❤❡ ♠❡❛♥✳ ■♥ t❤❡ ❝❛s❡ ♦❢✱ ✶ ❛♥❞ ✷ ❣r❛✐♥ s✐③❡s ❝❧♦s❡ t♦ t❤❡ ♠❡❛♥ s✐③❡❞ ♦♥❡ ❣r♦✇ ❢❛st❡r ✇❤✐❝❤ ❢❛❝✐❧✐t❛t❡ ❛ q✉❛s✐✲st❛t✐♦♥❛r② ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥ ❡✈♦❧✉t✐♦♥ ✭♥♦r♠❛❧ ❣r❛✐♥ ❣r♦✇t❤✮✳ ❋r♦♠ ✜❣✉r❡✹✳✸✱ ✐t ❝❛♥ ❜❡ ❝♦♥❝❧✉❞❡❞ t❤❛t Dmax ab ♠✉st ❜❡ ❛t ❧❡❛st ✷ t✐♠❡s ♦❢ Dn ✐♥ ♦r❞❡r ❢♦r ❆●● t♦ ♦❝❝✉r✳ ❙♦✱ ❛ r❡❛❧✐st✐❝ q✉❛❧✐t❛t✐✈❡ ✐❞❡♥t✐✜❡r ♦❢ ❆●● ❛♥❞ ◆●● ❝❛♥ ❜❡ ❡①♣r❡ss❡❞ ❛s ❢♦❧❧♦✇s✿ Dmax

ab /Dn> 2 Probable grain growth condition : ❆●● Dmax

ab /Dn< 2 Probable grain growth condition : ◆●●

(96)

m − 3

(a)

(b)

(c)

0 2E+17 4E+17 6E+17 8E+17 0.01 0.015 0.02 0.025 0.03

1E-01 1E+02 1E+05 1E+08

V olume fr a ct ion% Time(second) Volume fraction% Number density 0 50 100 150 200 250 300

1E-01 1E+02 1E+05 1E+08

Me a n ra dius(nm) Time(second) 1 1.5 2 2.5 3

1E-01 1E+02 1E+05 1E+08

(97)

(98)

(a)

(b)

(c)

0 2E+17 4E+17 6E+17 8E+17 0 0.01 0.02 0.03 0.04

1E-02 1E+00 1E+02 1E+04 1E+06

V olume fr a ct ion% Time(second) Volume fraction% Number density m − 3 0 10 20 30 40 50 60 70 80

1E-02 1E+00 1E+02 1E+04 1E+06

Me a n ra dius(nm) Time(second) 1 1.5 2 2.5 3 3.5

(99)

(a)

(b)

(c)

0 5E+17 1E+18 1.5E+18 2E+18 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

1E-02 1E+00 1E+02 1E+04 1E+06

Me a n ra dius(nm) Time(second) 1 1.5 2 2.5 3

(100)

(101)

❚❛❜❧❡ ✹✳✶✿ ❈♦♠♣♦s✐t✐♦♥ ♦❢ t❤❡ ✐♥❞✉str✐❛❧ ❛❧❧♦② st❡❡❧✲❆ ✐♥ ❛t♦♠✐❝ ✪ ❈ ❙✐ ▼♥ ◆✐ ❈r ❱ ❚✐ ❆❧ ◆❜ ◆ ✵✳✼✵✷ ✵✳✹✵✼ ✵✳✹✺✺ ✶✳✷✷ ✶✳✹✼ ✵✳✵✵✻✾✻ ✵✳✵✵✶✾✹ ✵✳✵✺✹✾ ✵✳✵✵✶✼✶ ✵✳✵✺✾✽ Time T e mper a tur e Hot rolling 875°C, 1hr 680°C, 2hr Slow cooling Slow cooling Water quench

As rolled state (AR)

(102)

(103)

(104)

(105)

(106)

(107)

(108)

(109)

(110)

(111)

(112)

0 0.5 1 1.5 2 2.5 3 3.5 4 0.01 0.1 1 10 100 1000 10000 Time(second)

AR-900°C-model AR-1050°C-model AR-1200°C-model NT-900°C-model NT-1050°C-model NT-1200°C-model

(113)

(114)

(115)

(116)

(117)

(118)

(119)

(120)

(121)

(122)

(123)

Precipitation model (t,T) Thermodynamic data Initial (�_��_�) �� AGG model (t,T) Zener pinning: � Corner pinning: � �� & �� < � � � � �� > AGG NGG

��: Number of precipitate in class i.

��: Radius of precipitate in class i.

�� : Max time limit of simulation.

��: ��ℎ time.

��0: Initial mean austenite grain size.

��: Abnormal grain size.(between �� and ∞)

��: Mean grain size.

AGG: Abnormal grain growth. NGG: Normal or no grain growth.

yes _no �� = ��+ ∆� �� , � = ��−�+��_{�� }� ❋✐❣✉r❡ ✺✳✶✿ ❙❝❤❡♠❛t✐❝ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❞②♥❛♠✐❝ ❝♦✉♣❧✐♥❣ ❜❡t✇❡❡♥ ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ ❛❜♥♦r♠❛❧ ❣r❛✐♥ ❣r♦✇t❤ ♠♦❞❡❧✳ Time T empe ratur e Ac3 Ac1 Time T empe ratur e Ac3 Ac1 �0 �1 �0 �1

(a) Isothermal heat treatment setup (b) Heating rate simulation setup

❋✐❣✉r❡ ✺✳✷✿ ❙❝❤❡♠❛t✐❝ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ s✐♠✉❧❛t✐♦♥ s❡t✉♣✿ ✭❛✮ ✐s♦t❤❡r♠❛❧ ❤❡❛t tr❡❛t✲ ♠❡♥t s❡t✉♣ ❛♥❞ ✭❜✮ ❤❡❛t✐♥❣ r❛t❡ s✐♠✉❧❛t✐♦♥ s❡t✉♣✳

(124)

(125)

� �� v ol ume fr actio n �� 1 2 3 � �� _≈ � �

0

0.1

0.2

0.3

0.4

0

0.5

1

1.5

2

2.5

3 0E+00

3E+08

5E+08

8E+08

1E+09

�/�

� � �� − 1 1 2 3 �� Increasing pinning ❋✐❣✉r❡ ✺✳✸✿ ❙✉♣❡r✐♠♣♦s✐t✐♦♥ ❆●● ❝♦♥❞✐t✐♦♥ (d/dt(Dab/Dn) > 0) ♦♥ ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥✳ d/dt(Dab/Dn) ❝❛♥ r❛♥❣❡ ❜❡t✇❡❡♥ Dn ❛♥❞ ➀ ♦r ➁ ♦r ➂✳ ❍❡r❡✱ ✐t ✐s ❛ss✉♠❡❞ t❤❛t M = 1✳ ✇❤✐❝❤ ❝❛♥ ❣r♦✇ ❝♦♠♣❛r❛t✐✈❡❧② ❢❛st❡r t❤❛♥ t❤❡ ♠❡❛♥ s✐③❡ ❣r❛✐♥s✳ ■♥ ❛ ③❡r♦ ♣✐♥♥✐♥❣ ❝♦♥❞✐t✐♦♥ ✭♥♦ ♣r❡❝✐♣✐t❛t❡✮✱ ❢♦r µ = 0.56 ❛♥❞ λ = 0.6✱ ✐t ❝❛♥ ❜❡ ❢♦✉♥❞ t❤❛t ❆●● ❝♦♥❞✐t✐♦♥ ✐s ✈❛❧✐❞ ❜❡t✇❡❡♥✱ Dmin ab /Dn≈ 1.26 ❛♥❞ Dabmax/Dn≈ 1.43✳ ■♥ t❤❡ ✜❣✉r❡ ✺✳✸✱ d/dt(Dab/Dn) ♦❜t❛✐♥❡❞ ❢♦r ✐♥❝r❡❛s✐♥❣ ♣✐♥♥✐♥❣ ❝♦♥❞✐t✐♦♥s ❛r❡ s✉♣❡r✐♠♣♦s❡❞ ♦♥ ❛ ♥♦r♠❛❧ ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥✳ ❆s s❤♦✇♥ ✐♥ t❤❡ ✜❣✉r❡✺✳✸✱ Dmax ab ❝❛♥ ❜❡ ✇✐t❤✐♥ t❤❡ ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥ ❛♥❞ ✈❡r② ❝❧♦s❡ t♦ t❤❡ ♠❡❛♥ s✐③❡❞ ❣r❛✐♥ ✶ ♦r ❝❧♦s❡ ❜✉t s♠❛❧❧❡r t❤❛♥ t❤❡ ❧❛r❣❡st ❣r❛✐♥ s✐③❡ ✷ ♦r ❧❛r❣❡r t❤❛♥ t❤❡ ♠❛①✐♠✉♠ ❣r❛✐♥ s✐③❡ ✐♥ t❤❡ ❞✐str✐❜✉t✐♦♥ ✸ ✳ ❆♠♦♥❣ t❤❡s❡ t❤r❡❡ s✐t✉❛t✐♦♥s ♦♥❧② ✸ ❜❡❛r✐♥❣ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❆●● ✐♥✐t✐❛t✐♦♥✳ ■♥ t❤❡ ✸ ✱ t❤❡ ❧❛r❣❡st ❣r❛✐♥s ✐♥ t❤❡ ♠✐❝r♦str✉❝t✉r❡ ❝❛♥ ❣r♦✇ r❡❧❛t✐✈❡❧② ❢❛st❡r t❤❛♥ t❤❡ ♠❡❛♥✳ ■♥ t❤❡ ❝❛s❡ ♦❢✱ ✶ ❛♥❞ ✷ ❣r❛✐♥ s✐③❡s ❝❧♦s❡ t♦ t❤❡ ♠❡❛♥ s✐③❡❞ ♦♥❡ ❣r♦✇ ❢❛st❡r ✇❤✐❝❤ ❢❛❝✐❧✐t❛t❡ ❛ q✉❛s✐✲st❛t✐♦♥❛r② ❣r❛✐♥ s✐③❡ ❞✐str✐❜✉t✐♦♥ ❡✈♦❧✉t✐♦♥ ✭♥♦r♠❛❧ ❣r❛✐♥ ❣r♦✇t❤✮✳ ❋r♦♠ ✜❣✉r❡✺✳✸✱ ✐t ❝❛♥ ❜❡ ❝♦♥❝❧✉❞❡❞ t❤❛t Dmax ab ♠✉st ❜❡ ❛t ❧❡❛st ✷ t✐♠❡s ♦❢ Dn ✐♥ ♦r❞❡r ❢♦r ❆●● t♦ ♦❝❝✉r✳ ❙♦✱ ❛ r❡❛❧✐st✐❝ q✉❛❧✐t❛t✐✈❡ ✐❞❡♥t✐✜❡r ♦❢ ❆●● ❛♥❞ ◆●● ❝❛♥ ❜❡ ❡①♣r❡ss❡❞ ❛s ❢♦❧❧♦✇s✿ Dmax

ab /Dn> 2 Probable grain growth condition : ❆●● Dmaxab /Dn< 2 Probable grain growth condition : ◆●●

(126)

(127)

(a) (b) 0 20 40 60 80 100 120 140

1E-01 1E+02 1E+05 1E+08

Time(second) Dn=1μm Dn=3μm Dn=5μm Dn=7μm �� μm (c) (d) m − 3 0 5 10 15 20 25 30

1E-01 1E+02 1E+05 1E+08

Me a n ra dius(nm) Time(second) 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

1E-01 1E+02 1E+05 1E+08

Time(second) Dn=1μm Dn=3_μm Dn=5μm Dn=7μm �� /�� Risk of AGG 0E+00 2E+17 3E+17 5E+17 6E+17 8E+17 0 0.005 0.01 0.015 0.02 0.025 0.03

1E-01 1E+02 1E+05 1E+08

(128)

(a) (b) 0E+00 2E+17 3E+17 5E+17 6E+17 8E+17 9E+17 0 0.005 0.01 0.015 0.02 0.025 0.03

1E-02 1E+00 1E+02 1E+04 1E+06

V olume fr a ct ion% Time(second) Volume fraction% Number density m − 3 0 20 40 60 80 100 120 140

1E-02 1E+00 1E+02 1E+04 1E+06

Me a n ra dius(nm) Time(second) 0 10 20 30 40

1E-02 1E+00 1E+02 1E+04 1E+06 Time(second) Dn=1μm Dn=3μm Dn=5μm Dn=7μm �� (μm ) 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

(129)

(130)

(a) (b) 0 10 20 30 40 50 60 70

1E-02 1E+00 1E+02 1E+04 1E+06

Me an rad iu s(nm) Time(second) m − 3 0 2 4 6 8 10 12 14 16 18

1E-02 1E+00 1E+02 1E+04 1E+06 Time(second) Dn=1μm Dn=3μm Dn=5μm Dn=7μm 0 0.5 1 1.5 2 2.5 3 3.5 4

1E-02 1E+00 1E+02 1E+04 1E+06 Time(second) Dn=1μm Dn=3μm Dn=5μm Dn=7μm �� μm �� /�� (c) (d) Risk of AGG 0E+00 2E+17 3E+17 5E+17 6E+17 8E+17 9E+17 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

1E-02 1E+00 1E+02 1E+04 1E+06

(131)

(132)

(a) (b) 0 10 20 30 40 50 60 70 80

1E-02 1E+00 1E+02 1E+04 1E+06

Me a n ra dius(nm) Time(second) 0 3E+17 6E+17 9E+17 1.2E+18 1.5E+18 1.8E+18 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

1E-02 1E+00 1E+02 1E+04 1E+06

1E-02 1E+00 1E+02 1E+04 1E+06 Time(second) Dn=1μm Dn=3μm Dn=5μm Dn=7μm �� μm 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

(133)

(134)

Time T emp er atur e Hot rolling 875°C, 1hr 680°C, 2hr Slow cooling Slow cooling Water quench

As rolled state (AR)

(135)

(136)

(137)

(138)

(139)

(140)

(a) (b) (c) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.01 0.1 1 10 100 1000 10000 V olume fr a cion% Time(second)

AR-900°C-model AR-1050°C-model AR-1200°C-model

AR-900°C(exp) AR-1050°C(exp) AR-1200°C(exp)

NT-900°C-model NT-1050°C-model NT-1200°C-model

NT-900°C(exp) NT-1050°C(exp) NT-1050°C(exp)

0 10 20 30 40 50 60 70 80 0.01 0.1 1 10 100 1000 10000 Me a n ra dius(nm) Time(second)

�� 0 10 20 30 40 50 60 70 0.01 0.1 1 10 100 1000 10000 Time(second)

❋✐❣✉r❡ ✺✳✶✷✿ ❙t❡❡❧✲❆✿ ❆❘ ❛♥❞ ◆❚ st❛t❡✬s ✭❛✮ ♣r❡❝✐♣✐t❛t❡ ✈♦❧✉♠❡ ❢r❛❝t✐♦♥✱ ✭❜✮ ♣r❡❝✐♣✲ ✐t❛t❡ ♠❡❛♥ r❛❞✐✉s ❛♥❞ ✭❝✮ ♠❡❛♥ ❣r❛✐♥ s✐③❡ ✭Dn✮ ❡✈♦❧✉t✐♦♥ ❛t ❞✐✛❡r❡♥t t❡♠♣❡r❛t✉r❡s ❛r❡ s❤♦✇♥✳

(141)

0 0.5 1 1.5 2 2.5 3 3.5 4 0.01 0.1 1 10 100 1000 10000 Time(second)

AR-900°C-model AR-1050°C-model AR-1200°C-model NT-900°C-model NT-1050°C-model NT-1200°C-model

(142)

(143)

(a) (b) 800 850 900 950 1000 1050 1100 0.01 1 100 10000 T empe ra tur e( °C) Time(second) 0.1 °C/min 0.5 °C/min 1.0 °C/min 0.01 0.02 0.03 0.04 0.01 1 100 10000 V olume fr a ct ion (% ) Time(second)

Exp-AR-1050°C(1hr) AR- 0.1 °C/min AR- 0.5 °C/min AR- 1.0 °C/min

(144)

0 0.5 1 1.5 2 2.5 3 3.5 4 0.01 0.1 1 10 100 1000 10000 Time(second)

AR- 0.1 °C/min AR- 1.0 °C/min AR- 0.5 °C/min

NT 0.1 °C/min NT 0.5 °C/min NT 1 °C/min

(145)

❚❛❜❧❡ ✺✳✸✿ ❙t❡❡❧✲❆✿ s✉♠♠❛r② ♦❢ ♠♦❞❡❧ ♣r❡❞✐❝t✐♦♥ ❛♥❞ ❡①♣❡r✐♠❡♥t❛❧ ♦❜s❡r✈❛t✐♦♥ ♦❢ ❣r❛✐♥ ❣r♦✇t❤ ❝♦♥❞✐t✐♦♥ ✐♥ s❛♠♣❧❡s s✉❜❥❡❝t❡❞ t♦ ❞✐✛❡r❡♥t ❤❡❛t✐♥❣ r❛t❡s✳ ❙t❛t❡ ▼♦❞❡❧ ♣r❡❞✐❝t✐♦♥ ❊①♣❡r✐♠❡♥t❛❧ ♦❜s❡r✈❛t✐♦♥ ❆❘✲✵✳✶◦❈✴♠✐♥ ◆●● ◆●● ❆❘✲✵✳✺◦❈✴♠✐♥ ◆●● ◆●● ❆❘✲✶✳✵◦❈✴♠✐♥ ◆●● ◆●● ◆❚✲✵✳✶◦❈✴♠✐♥ ❆●● ❆●● ◆❚✲✵✳✺◦❈✴♠✐♥ ❆●● ❆●● ◆❚✲✶✳✵◦❈✴♠✐♥ ❆●● ◆●● (b) (a) 800 850 900 950 1000 1050 1100 1150 1200 1250 1300

1E-02 1E+00 1E+02 1E+04 1E+06

T empe ra tur e( °C) Time(second) Steel-A: As rolled state(AR)

900°C Exp(NGG) Model(AGG) 800 850 900 950 1000 1050 1100 1150 1200 1250 1300

1E-01 1E+01 1E+03 1E+05

T empe ra tur e( °C) Time(second) Steel-A: Normalized tempered(NT)

(146)

(147)

(148)

(149)

(150)

(a) (b) 800 850 900 950 1000 1050 1100 1150

1E-02 1E+00 1E+02 1E+04 1E+06 1E+08

T empe ra tur e( °C) Time(second) Steel-B: As rolled state(AR)

900°C Exp(NGG) Exp(AGG) Model(AGG) 800 850 900 950 1000 1050 1100 1150

1E-02 1E+00 1E+02 1E+04 1E+06 1E+08

T empe ra tur e( °C) Time(second) Steel-B: Isothermally heat treated (ISO)

(151)

(152)

(153)

(154)

(155)

(156)

(157)

(158)

(159)

(160)

(161)

(162)

(163)

♦❢ ♠❡❛s✉r❡♠❡♥ts ❛r❡ r❡q✉✐r❡❞ t♦ ❜✉✐❧❞ ❛ r❡♣r❡s❡♥t❛t✐✈❡ ♣✐❝t✉r❡ ♦❢ t❤❡ ❣r❛✐♥ s✐③❡s ✐♥ t❤❡ s❛♠♣❧❡✳

(164)

(165)

❆ ▼♦♥t❡✲❈❛r❧♦ st✉❞② ♦❢ t❤❡

❝♦♠♣❛❝t ❡✣❝✐❡♥❝② ❢❛❝t♦r µ

1 2 3 4 5 6 7 8 �� 4 1 3 6 8 2 5

4 – Random primary selection 1 2 5 8 6 3

Random secondary selections Sample grains from a normal grain size distribution in increasing diameter

Available surface area, ��= 4 r4

Surface area covered by surrouding grains projected area, ��= r1+ r + r + r8+ r + r3

Compact efficiency factor, � = 4

(166)

(167)

(168)

(169)

(170)

(171)

(172)

(173)

Precipitation and abnormal grain growth in low alloy steels

HAL Id: tel-01015867

https://tel.archives-ouvertes.fr/tel-01015867

Mohammad Razzak

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