PHASE DIAGRAM · PDF file 2013. 11. 27. · L: 35wt%Ni α: 46wt%Ni C L: 35wt%Ni...

Click here to load reader

  • date post

    25-Jan-2021
  • Category

    Documents

  • view

    0
  • download

    0

Embed Size (px)

Transcript of PHASE DIAGRAM · PDF file 2013. 11. 27. · L: 35wt%Ni α: 46wt%Ni C L: 35wt%Ni...

  • BY

    PHASE DIAGRAM

    BY

    ENGR. MS TAYYABA BANO

  • Cu-Ni System

    • 2 phases: L (liquid) α (FCC solid solution)

    • 3 phase fields: 1400

    1500

    1600 T(°C)

    L (liquid)

    • 3 phase fields:

    L

    L + α α

    wt% Ni20 40 60 80 1000 1000

    1100

    1200

    1300

    1400

    α (FCC solid solution)

    L +

    α liq ui du s

    so lid us

  • • Rule 1: If we know T and Co, then we know:

    the # and types of phases present# and types of phases present# and types of phases present# and types of phases present.

    • Examples:

    1500

    1600 T(°C)

    L (liquid)

    liq ui du s

    (1 2 5 0 ,3 5 ) Cu-Ni

    phase

    A(1100, 60): 1 phase: α

    PHASE DIAGRAMS: # and types of phases

    wt% Ni20 40 60 80 1000 1000

    1100

    1200

    1300

    1400

    α (FCC solid solution)

    L +

    α

    liq ui du s

    so lid us

    A(1100,60) B (1 2 5 0 ,3 5 )

    phase

    diagram B(1250, 35): 2 phases: L + α

  • Rule 2: If we know T and Co, then we

    know: the composition of each phase.

    • Examples:

    1300

    T(°C)

    L (liquid) liq uid

    us

    sol idu

    s

    TA A

    TB B

    tie line

    L + α

    Cu-Ni

    system

    At TA:

    Only Liquid (L) C = C ( = 35wt% Ni)

    Co = 35wt%Ni

    PHASE DIAGRAMS: composition of phases

    wt% Ni

    20

    1200

    α (solid)L +

    α

    sol idu

    s

    30 40 50

    D TD

    TB B

    433532 CoCL Cα

    CL = Co ( = 35wt% Ni)

    At TB:

    Both α and L CL = Cliquidus ( = 32wt% Ni here)

    Cα = Csolidus ( = 43wt% Ni here)

    At TD:

    Only Solid (α) Cα = Co ( = 35wt% Ni)

  • Rule 3: If we know T and Co, then we know:

    the amount of each phase (given in wt%). Cu-Ni

    system• Examples:

    At TA: Only Liquid (L)

    WL = 100wt%, Wα = 0 At TD: Only Solid (α)

    Co = 35wt%Ni

    1300

    T(°C)

    L (liquid) liq uid

    us

    sol idu

    s

    TA A

    TB B

    tie line

    L + α

    PHASE DIAGRAMS: weight fractions of phases

    At TB: Both α and L

    At TD: Only Solid (α) WL = 0, Wα = 100wt%

    WL = S

    R +S

    Wα = R

    R +S

    %73 3243

    35430 wt CC

    CC

    L

    = − −=

    − −=

    α

    α

    = 27wt%

    wt% Ni

    20

    1200 α

    (solid) L +

    α

    sol idu

    s

    30 40 50

    D TD

    TB B

    433532 CoCL Cα

    R S

    %27wt CC

    CC

    L

    o = − −=

    α

    α

  • • Sum of weight fractions:

    • Conservation of mass (Ni):

    • Combine above equations:

    WL + Wα = 1

    Co = WLCL + WαCα

    = R R +S

    Wα = Co −CL Cα −CL

    = S R+ S

    WL = Cα −Co Cα −CL

    THE LEVER RULE: A PROOF

    R S Cα −CLR SCα CL

    • A geometric interpretation:

    Co

    R S

    WαWL

    CL Cα moment equilibrium:

    1−Wα solving gives Lever Rule

    WLR = WαS

  • • Phase diagram:• Phase diagram:• Phase diagram:• Phase diagram:

    CuCuCuCu----Ni system.Ni system.Ni system.Ni system.

    • System is:• System is:• System is:• System is:

    --------binarybinarybinarybinary i.e.i.e.i.e.i.e., 2 components:, 2 components:, 2 components:, 2 components: Cu and Ni.Cu and Ni.Cu and Ni.Cu and Ni.

    --------isomorphousisomorphousisomorphousisomorphous

    1300

    L (liquid)

    L +

    α

    T(°C)

    A

    D

    B

    L: 35wt%Ni

    α: 46wt%Ni C

    L: 35wt%Ni

    46

    43 32

    24

    35

    L: 32wt%Ni

    Cu-Ni

    system

    COOLING IN A Cu-Ni BINARY

    --------isomorphousisomorphousisomorphousisomorphous i.e., completei.e., completei.e., completei.e., complete

    solubility of onesolubility of onesolubility of onesolubility of one

    component incomponent incomponent incomponent in

    another; another; another; another; αααα phasephasephasephase field extends fromfield extends fromfield extends fromfield extends from

    0 to 100wt% Ni.0 to 100wt% Ni.0 to 100wt% Ni.0 to 100wt% Ni.

    wt% Ni 20

    1200

    30 40 50 1100

    α (solid)

    L +

    α D

    35 Co

    E

    24 36

    α: 43wt%Ni

    L: 32wt%Ni

    L: 24wt%Ni

    α: 36wt%Ni

    • Consider

    Co = 35wt%Ni.

  • 2 components has a special composition

    with a min. melting T.

    • 3 single phase regions

    (L, α, β) • Limited solubility:

    α: mostly Cu

    Ex.: Cu-Ag system

    L (liquid)

    α L + α L+β β

    1200 T(°C)

    800

    1000

    TE 779°C

    Cu-Ag

    system

    BINARY-EUTECTIC SYSTEMS

    α: mostly Cu β: mostly Ni • TE: No liquid below TE

    • CE: Min. melting T

    composition

    L+β β

    α + β

    Co, wt% Ag 20 40 60 80 100 0

    200

    400

    600

    800

    CE

    TE 8.0 71.9 91.2 779°C

  • L (liquid)

    α L + α L+β β

    120 0 T(°C)

    800

    1000

    TE 8.0 71.9 91.2 779°C

    α + β

    Co, wt% Ag 20 40 60 80 100 0

    200

    400

    600

    CE

  • IRON-CARBON/ SYSTEM/ PHASE DIAGRAMPHASE DIAGRAM

  • • 2 important points

    -Eutectic (A):

    -Eutectoid (B):

    L⇒ γ +Fe3C

    γ ⇒ α +Fe3C

    C ( c e m e n ti te )

    1600

    1400

    1200

    1000

    800

    L

    γ (austenite)

    γ+L

    γ+Fe3Cα +γ

    L+Fe3C

    δ

    727°C = Teutectoid

    1148°C

    T(°C)

    A

    B

    SR

    γ γ γγ

    α

    IRON-CARBON (Fe-C) PHASE DIAGRAM

    Result: Pearlite = alternating layers of α and Fe3C phases.

    120µm

    F e 3 C ( c e m e n ti te )

    800

    600

    400 0 1 2 3 4 5 6 6.7

    α+Fe3C

    (Fe) Co, wt% C 0.77 4.30

    727°C = TeutectoidB R S

    Fe3C (cementite-hard)

    α (ferrite-soft)

    α C e u te c to id

  • DEVELOPMENT OF MICROSTRUCTURESDEVELOPMENT OF MICROSTRUCTURES

    � Austenite precipitates Fe3C at Eutectoid Transformation Temperature (727°C).

    γγγγ αααα + Fe3C Cooling

    Heating

    � When cooled slowly, forms Pearlite, which is a micro-contituent made of ferrite (αααα) and Cementite (Fe3C),

    Heating

  • HYPOEUTECTOID STEEL

    (Fe-C System)

    C ( c e m e n ti te )

    1600

    1400

    1200

    1000

    L

    γ (austenite)

    γ+L

    γ+Fe3C

    L+Fe3C

    δ

    1148°C

    T(°C)

    γ γ γγ

    γγ γ γ

    α

    Adapted from

    Fig. 9.27,Callister 6e. (Fig. 9.27 courtesy Republic Steel Corporation.)

    Co

    F e 3 C ( c e m e n ti te )

    800

    600

    400 0 1 2 3 4 5 6 6.7

    α+Fe3C

    Co, wt% C0 .7 7

    727°C

    R Sα γ γ γ

    γ r s

    wα =s/(r+s) wγ =(1-wα)

    wα =S/(R+S) wFe3C =(1-wα)

    wpearlite = wγ

    α αα

    α α

    α pearlite

    100µm Hypoeutectoid steel

  • HYPOHYPO--EUTECTOIDEUTECTOID

    “Proeutectoid” means it formed ABOVE or BEFORE the Eutectoid Temperature!

  • How to calculate the relative amounts of proeutectoid

    phase (α or Fe3C) and pearlite? Eutectoid ,0.76% C Eutectoid ,0.76% C

    2.14

    HypoEutectoid HyperEutectoid

    2.14

  • � Fraction of pearlite:

    74.0

    022.0'

    022.076.0

    022.0' −= − −=

    + = CoCo

    UT

    T Wp 74.0022.076.0

    = −

    = +

    = UT

    Wp

  • � Fraction of Proeutectoid :

    74.0

    '76.0

    022.076.0

    '76.0 CoCo

    UT

    U W

    −= − −=

    + =α

  • � Fraction of pearlite: (for Hypereutectoid alloys)

    94.5

    '170.6

    76.070.6

    '170.6 CC

    XV

    X Wp

    −= − −=

    + =

    94.576.070.6XV Wp =−

    = +

    =

  • � Fraction proeutectoid cementite: (Hypereutectoid)

    76.0'176.0'1 −=−== CCVW 94.576.070.63

    = −

    = +

    = XV

    W CFe

  • (Fe-C System)

    C ( c e m e n ti te )

    1600

    1400

    1200

    1000

    L

    γ (austenite)

    γ+L

    γ+Fe3C

    L+Fe3C

    δ

    1148°C

    T(°C)

    γ γ γγ

    γγ γ γ

    Fe3C

    HYPEREUTECTOID STEEL

    Co

    F e 3 C ( c e m e n ti te )

    800

    600

    400 0 1 2 3 4 5 6 6.7

    α+Fe3C

    Co, wt% C0 .7 7

    R Sα s

    wFe3C =r/(r+s) wγ =(1-wFe3C)

    wα =S/(R+S) wFe3C =(1-wα)

    wpearlite =