I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

304
! " # $ % # & # !

Transcript of I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

Page 1: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

!

"

# $ % # &

# ! '

Page 2: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

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& ' "

) * + ,

& $

&

Page 3: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

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.................... .. ........... ..................... .......... ...!" ..........

# $ $ . ........... ............ ............ ........% $. ........... ..

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4

.................... !" # .....................&....................!" ..............# ................" '....$"% .........

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Page 4: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

4

222/6 ..22226 .......................$"% .().....& '" .....20//& ...............20/2#............( )*'...........

202/+ .2022+ $ .....................( )'.........200/+$ ......................( )".............+( % '"

( !*+ +, %

+-* ' " %

22/ 222 220 221 789

-1

-(-542404(4-4450

55-

/3//30/31/34//0

//0

//////(//4//5

Page 5: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

5

................... ................., ..........

*..

"..0/2/6 ..............0/22" ......0/20" ...............0/21".............,......... " .....

. " ....022/" ............02226 ..............2220".............0221".........,)............... '"..

00//# ....00/26 ...00/0, .................. ........

002/! .............00229 ..00209 .!'" ........!'" *............

/23/23

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/0/(3/(3/(2/-/-4/-5

$...................% ..........-..........

/4//40

Page 6: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/3

. ............ ........ ..........!. ...#/ /")*.......

/"0.........1(2/+.......1(22+........

/4/4-/50/5(/5-/54233233230

$.................... # .......! )..............!,' $0 .......+( %...+- '

.................

!1 $0 21&"3..+' ..............+# ...+( .........

! 1 ' ) 2+3 .....................+' ..............

+ # %

"'!! 23 ++' ..............++ ...............++&** ' ...++

......................

!# $ .......

2//2//2/22/2

22222122122-225

202202

20(

21021021(20

22(/

Page 7: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//

+' ..............+1 .............+( ...........&+4')

2(/2(02(4

2--

253

Page 8: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/2

Page 9: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/0

&'()(

'%*+,(-.&'(/&(('.(0('

!

#

% $ % : + 9 ; <

" $ &

, &

Page 10: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/1

$ ' ; <

=

% $ # τ τ3

τ>τ3

?@"6? AB@A

& $ # ;/30$/31 < $ ; <

9 $ C 9 ) &

Page 11: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/

6 ! 9 DE'

( )$,$

2 3 ,

// 0

/ 0

/ 0@

@

@=

−∆

;//<

':/$F$ F"$F6$F:$ F7$& F∆D$

&

!

4 3

= + +∫ ∫/ 23

;/2<

'? $

F$

63$6;0<F$

6$6;0<F

Page 12: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(

∆D$ ;1<,

/ & $ 2

= # '

$ 33°!;'=9! 8<F

$ 33°!/333°!;'&,=&<F

$ /333°!/33°!;'!&7!,<F

$ /33°!;'!8D6G,<

%

# $ $ !!$!E

! #$9'

[ ]- 5 5' '⋅ = ⋅( 2 @ ;/0<

&

) '

Page 13: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-

[ ]-

5 5' ' = ⋅-/

@ ;/1<

#

'

= + + 2 ;/<

= + + −H 2 ;/(<

I

! A7

=

∑∑

;/-<

'$ $F!$

! , % $ &

Page 14: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/4

3°!'

$ ∼/341AB@A$∼(12AB@A$∼/300AB@A$∼-0AB@A=

/

= !79 & ,

% $ 9$ //

C//:

Page 15: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/5

% $ # '

α∂∂

∂∂&

& &

6

2

2 = ;/4<

3≤E≤J;< '

α∂∂

∂∂ &

6

2

2 = ;/5<

J;<≤E≤∞ '

αα$ FJ;<$ $

! /4/5'6>6E>3≥36>6E→∞ ≥36>6E>E>3

'

6>6>6E>J;<# J;<

J;< $

:

∆D ρ!

'

Page 16: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

23

λ ∂∂ λ ∂

∂ ρ

&&

&

6

63

7

− = ∆

; <

;//3<

∆D>3 7

; << 3

#

'

*

3

7

&

&&; <

; </ ν λ ∂

∂ ρ− − = ∆ ;///<

'$ Fλ$ F6$ F6$

=;/4<;/5< '

- 8 6

6 7 & &= +

≤ ≤/ / 2

3α ; <

;//2<

- 8 6

7 6 = +

≤ ≤ ∞2 2 2α ; <

;//0<

&/ &2 K/ K2 ;//3<

C ; <

Page 17: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/

& /333

= # /3L 2$03L

%$:7;M/J/8/.MJ8< A ;A<% ; / 2< φ;/$2<N/O'

( ) ( ). 5

=>∑ ;//1<

' >;M J 8 <F > $

>∑ $ 7;7$/<@2

& %

9 ;A<

)

Page 18: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

22

9 8N/1O'

94

2

5

*

2

= −

20

π

;//<

'$FAD$K9PF6$F

4 5

.

5

5

=−∫ ; <

;//(<

9 8 C

9;A< N//2O'

: 5 9=

;//-<

#

45

.

5

5

; <

; <

=

;//4<

9

;A<#

7 , N5051//1O 7#

Page 19: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

20

;"<;//<;//(<'

95

*;

2

=

20

π

;//5<

;

.

5

=−∫ ; <

;/23<

+ ;"< C ;"< /2 :

C/2"

#

/2 " ;//5< ;/2/< N/(O'

Page 20: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

21

;< F 7;<@2

95

*

.

5

2

=

−20 3

π ν

; <

;/2/<

; $< ; <

! B ) $B N51O φ<= # QR QR$9 S φ; $ < # φ φ; $ < % 9 /0

9

,/0

Page 21: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2

C/0:

+

φ<= ) $B'

( ) ( ) ( )[ ]φ ε = −1 /2 (@ @ ;/22<

'$ Fε$ /0

9 $ φ<=

: ;>;<>3<

9 ε ) ;<;/23<'

Page 22: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2(

( ) ( ) ( );

.

5

. .

5

=− −

−∫ ;/20<

: ∆T'

( )∆1 25*

5

2.

= − +0

0

222

σ

π

;/21<

':$F;< $

Fσ$

)

) /$2L& 0$L

" ' D T K + T = =

: -

Page 23: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2-

: '

ρ>ρ$

;/2<

ρ °!

% '

ρ>ρN/$;$<O ;/2(<

'ρ$ F$

9 # '

ρ ρ

==

∑/

;/2-<

'ρ$ F$RR ρ$ QR

% $

Page 24: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

24

C

C

) $ $ $F &

C/1"

$

# '

r

"/ = 3

"2≥3

Page 25: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

25

"0<"1>""(≥3&

& /3$/3(

! CP =

# & ,

, N21O'

C>$ )>σ Ω ;/24<'

C$F ) $

F Ω$Fσ$

Page 26: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

03

, σ B@27@@2 E@!T=

# & 6 #

) "

6

) # T = T : T

Page 27: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

0/

T %

: '

1 & # $

H H H H H H H= − + +=

∑µ/

;/25<

1 & # $

U U U U U U U= − + +=

∑µ/

;/03<

=6:9$µ$

9 T :I> :II>3'

1 &

= − +=

∑µ/

;/0/<

'&$Fµ$QRF$ QRF$

=$

& '

1 1 1 1

& & & &

-

-

= − −

= − −

H U

H U

: : : :

-

-

= − −

= − −

H UH U

Page 28: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

02

1 & 1

-- - -

-

-

-

= − +

+

=

∑∂∂ µ

/

;/02<

: & :

-- - -

-

-

-

= − +

+

=

∑∂∂ µ

/

;/00<

T&C&

∂∂ σ1

-

-

-

=

∂∂ σ:

-

-

-

=

T

T 6 9 & '

11

-- #

#

=

∂∂

;/01<

∂∂ σ σ

1

-1

#

= =

% = ; 4< D! K ! =: # >

Page 29: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

00

& &

6 $

:

# σ@ < 3 % σ@ >3

: " N0(O

= , ;< Q R;<Q R

= 9 %

Page 30: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

01

) 6

# ;/00< '

1 - -

-

= +=

∑σ µ/

;/0<

)

1 - - -

-

-

= + + + == =

∑ ∑σ σ µ µ/ /

3 ;/0(<

# '

-

-

σ µ µ= − ==

∑ ∑/

Γ ;/0-<

6Γ T

QR

#;/0-<

9 <</ T'

Γ

$

,

V

= −

σ

;/04<

Page 31: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

0

'$ F"$F6$

;/04< σ@

% T'

Γ = −

,

σ

;/05<

9 ΓV

∆σ ∆= σ σ > ;< / 2. & σ@

T T & σ σσ' σ>σ$σ ;/13<

)σ≅σ

σ>3σ >σ " ;< & $ $

Page 32: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

0(

$

9 T 8 P=#N/0O'

( ) ( )σ/2 3 3 3 3= − + −∑ ∑. . . . H H H H U U U U ;/1/<

'

III$

F

I II $

FIII$

FI II $

) $

3II F

∆I 6>3 )3'

( )σ α?

9

9 ?3

3/

3/ 2= +∆

;/12<

'∆8$

8 F3

/ $ / 2 6F

α$ " ∆8@8

) @ ∆I>>∆II 3I$

II≅;2@0<3

I'

Page 33: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

0-

σ σα&? ?

?

?

5

9 9= + +

3

3

/

/ 2/

(∆ @

;/10<

# 6>3 σ)>σ)

3$6'

σ σσ

α&? ?

?

?

?

5

9 9= + + −

3

/(

2

∆ @

;/11<

'σ=)$ $

F)$ F> σ@ 6$ FA$ F

$

$=∆

9 $

'α9

9

= =3 322 3 2/- ∆

A≥1;/11< '

σ σσ&? ?

?

?

?5= + +

3

3 5(

(

;/1<

! ;/1< $

@! $

7WN//2O $ $

( )( )σσ σ

σ σ&?

&$ ?$

&$ ?$5=

/ 2 / 2

/ 2/

@ @

@ ;/1(<

Page 34: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

04

9 #E N/22O $ )N/2/O'

( ) ( )[ ]( )

σ σ λω

ω ω&? &?

/ /

/

$

/ .

.

.

$

/ .

/

$ / /

,

-(

-

-

-

= + + − −

− +

− −

2 2

2 H

;/1-<

'ω,$ >8Nε,$ $ ;ε,$,$ε$<@2O $

,$Fε,$ ε,$, ε$ $

,$,,$$F8>λX2$ Fλ$ F$ F,

$

F,

: : $

F&$F"$FI>

" ;/1-<

! '

3.

/

$

.

$

/

=

"6

;/14<

∆D

Page 35: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

05

C/"

%$ ' ;)< ;=<

;T<J'

σ σ σ θ&? &1 ?1= − ;/15<

' + σ=) σ=T σ)T $ $ $ θ $ $ ! θ>3°θ>/ σ=)>σ=T$σ)T θ>πθ>−/ σ=)>σ=TXσ)T %3YZθZ π −/ Z θ Z / #θ>3°σ=)>σ=T−σ)T3°π@2'σ)T;/−θ<[3 ;/3< θ > πσ=) >σ=T Xσ)Tπ@2π'

Page 36: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

13

σ)T;/Xθ<[3 ;//<

C & N21O'

* '

$

?1= +2

2

σρ θ π

;/2<

'$Fρ$ F$F:$

% $θ>π@2θ>3 :>3 >3#3°ZθZπ@2[3 π@2ZθZπZ3$ $

# '

?1=2σ θ

;/0<

#E'

5

?1=

2σ θη δ

;/1<

Page 37: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

1/

'A$ Fη$ Fδ$

:

9 ! $

:

C/(: δ

C

E # 7\'

τ η6

6= −

;/<

Page 38: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

12

'τ6$ E F

F

6$

η$ )7\

% \

: =+N7@2O!T= @>/9>/33!9 %'

##

2/333/3/

2==

]

9 $

] ηρ ν=

ρ$ : 2@>/=

/P>/3$12@]

% A

& ν # 'K9=! =&

Page 39: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

10

^ '86:!C,!:

! ! # 6

%

& #T $ E '

η η= -

. ,@ ;/(<

'&$ Fη$

& '

η = −-

8

;/-<

&K % /-

& ^ % /4 &$8

Page 40: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

11

C/-+

C/4: &$8

Page 41: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

1

! , %

, 9

: &$7 /5/0A #7&72&070&

C/5+ &$7;[/5/0A<

Page 42: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

1(

# $"$

# ) _ $ $ % 7\ \

!" ##6

%

! $ &

!

%

Page 43: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

1-

6

! $ 6/62 δ$=C'

4

= ⋅−ν δ

/ 2 ;/4<

λ G@A ! !

% G $C$)'

?5 =ν

;/5<

')$)N;<2;A<$2OFA$ NΩ$/$/OF6$NAOFν$ NG$/A$/O

C E'

;

66 = −ν∂∂

;/(3<

'; = − ∇ν ;/(/<

Page 44: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

14

'∂∂

6$ E

∇ = + +

6

"

∂∂

∂∂

∂∂

# '

α∂∂∇ =2

;/(2<

'

αν

ρ=

$ 2$/

∇ = + +22

2

2

2

2

2

6

"

∂∂

∂∂

∂∂

;/(2< ρ !

!

,

" 7\ !

Page 45: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

15

'

4 * & = ⋅ −; < ;/(0<

'$ G@2AF=$ 2F66$ A

! 25$25G@2A 43$433G@2A 4$253G@2A /-12$433G@2A N/4O

C '

$ F $ F $ F$

! =/ =2 6/ 62 =$K '

4 & = ⋅ −−

/24

/1

21/3 ; < ;/(1<

'!$ F=/2>/2=/>2/=2$ F/22/$

Page 46: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

3

! !>(-G@2A1 εN/1-O'

= =+ −

+ −

33

//2

22//

//

//

ε

ε ε

;/(<

ε/ε2 ;ε&>331$32233$(33°!Fε>3-33°!<

# +

%

! =6/ 62 '

?>?X?>=;6/$62<X!`=/2`/3$4;6/

1−621< ;/((<

#=/2>=

;/((<'

?>=;6/$62<NX!`/3$4;6/2−62

2<;6/X62<O ;/(-<#'

Page 47: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/

α>!`/3$4 ;6/2 − 62

2< ;6/ X 62< $ α>Xα $ ; < '

?>α=;6/$62< ;/(4<

6

@ # '

; * * & & & &= − = − = −/ / / / 2 2 2 2; < ; < ; <νδ

;/(5<

'/2$ /2Fν$ F6/62$

Fδ $

F6=/ 6=2 $ /

29 6=/ 6=2

'

;

* *

&=−

+ +

; </ /

/ 2

/ /δν

;/-3<

Page 48: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2

/

/ /

/ 2* *

5

+ +=δ

ν

$ $#'

; 5 = −; </ 2 ;/-/< $='

4 5& = −; </ 2 ;/-2<

$#%6

a/3$23L =

! '

$ F $F $ F $F $ F $;<F $ F$

Page 49: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

0

+ # $ $ ! N/14O $ N//5O

"

! & 9 @

9 '

$ $ F $F $ F $ F $ F $F $F

Page 50: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

1

$ F$ #

, # #

^

! /319 =$ /31 9 /32 9 %

% ≥ /31 9 )

Page 51: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

% '

; 5

=

× −α

2-0

2

/ 2

/ 2

@

; < ;/-0<

'

α =−

U H

H/

$

F

6I$ F6II$F6/$ F62$F

5/

= ⋅ ⋅ + −

−/1- /3 //

2γγ

$

F,$F

γ =

F

!$ F!$

% /329 33 °!

%

Page 52: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(

%

! $ δ

6 % /3$29

% 23 ) 3D$ /D 3D E

+ # δ

! δ '

ν

;

2/

/2 3+ =

;/-1<

%

'

22

22 3=

;/-<

Page 53: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-

'6/$δ°!F62$°!Fλ$ G@AFρ $ δ

G@0&

/>3'

ν ε

BC

/3

1

/33

=

=

;/-(<

'6$NAOFB$ NB@AOFG$ NA@2OFε$ F!$ NG@2AO

= N/25O '

; *

*BC

*= + −

− ⋅3

31

/33

δν

εν ν

;/--<

'$ F6$

# δ N/4O'

;

= ∇ +αρ

2 ;/-4<

'

Page 54: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

4

6

" 6 "= + + +∂∂

∂∂

∂∂

∂∂

αν

ρ=

$ F

$F!$Fρ$

;/-4<

!

7

&$) # & ) & ) &$)

'68K67

Page 55: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

5

) ^

:

)

# : &

&

6 !

! 6 =

Page 56: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(3

) =

)

+

) N/24O /2$/4 /3$/2 -

! 9 6^2 ; <

6 $ $

C ) $

6

Page 57: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(/

) , # # ;/3$2 9<

#

6 N/(O

6 53L $ N((O

6 $N42O 6(&1:

!

9 7 ! % ] 8 6 6^2

Page 58: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(2

+ 6

6 &

! '6867 ) N/24O'

−+∆

−+=

//

/

;/-5<

'! $

NLOF! $

NLOF∆!$

NLOF∆! $

NLOF$ NLO

# '

= + ∆ ;/43<

%

! >!'

Page 59: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(0

( )

∆+∆

−=−=∆

/

;/4/<

%

'

( )∆ ∆ ∆, , ,

, , = − =

−+

/

;/42<

# ∆ " X ∆ " > A

'

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5 = −

−⋅

/

;/40<

% '

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= −+ +

− − −/ / 2 2

/ 2/

;/41<

'" $

7@2F" $

7@2F/2.$ LFA/A2.$

!

Page 60: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(1

C

'

, & 733°!

# 03L

+

Page 61: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(

&'()('%-'!1/((2'/&(('

.(0(','%&

!" #

# # $ ' '

Page 62: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

((

( ) ( )

D

&

$

D!

D!

&

$

= − =+

−δ

δ

;2/<

'P$ @F=$2F:$ 0F $

@0F $

@0F$ FP$ 2@F#$ 2@Fδ$

% '

( ) D = −ρ

/33

;22<

'ρ$ @0F $

LF$ @2

% CP'

"

!

= − = + −−

ρ ρ δ H /3

;20<

'

Page 63: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(-

$ F $ $

LFδI$ F $ L

F $ L

=

C

!

<C # $, /1$/L ! ) %

< C & =

<C ! %

Page 64: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(4

!

< ! =$ =

#

% $

& '7!!, & '6 K 8 K ! ) , ) &

) &$) /3$/L ;< ) ) & &$)9

Page 65: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

(5

&2^0 ) 233$033°!

^ $&

% % " & #

& ' # K $ % $

) #

Page 66: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-3

:

] ) /3$2 9

#

% ^ $ $ %

&

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9

Page 67: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-/

) $

! ;/3/0`/3 7@2<

, N/1 25O (

:

9 '

∆1 , °= − ;21< $ !$!E'

3

$ $

=−

∆; <

;2<

'$ F"$F::$ F∆D$

) ∆D '

Page 68: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-2

-

3

,=

;2(<

&$ % !$!E

'

3

,

=∆

2 ;2-<

'

,

3

+∆−=

;24<

G $&'

-

8= − +

;25<

% ∆D

A'

∆ ∆ ∆

3 3 = + ∫3 3 ;2/3<

'

∆ ∆∆ ∆

3

2 0

2 0∫ = + + + ;2//<

∆D3$ 3A

# ;2//< ;2/3< ;24< ;2/2<

Page 69: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-0

3

,

,

,

, (

= − + + + +∆ ∆ ∆ ∆3 2

2 (

;2/2<

'+ $ $

:

#'

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3 = − H

;2/0<

'$ P@2FD$F$ 67@2FI $

7@2FA$

9 '

( )

3

=− H

;2/1<

≈≈3#

7 '

2

3

,=−/

0

;2/<

7I

Page 70: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-1

2

#H=/

2

;2/(<

'$ F $ F/

0 $ $

F

3

,−∆

$ KF

$ F9$ F$F

%

9 6 /D-(3D/2

$"%

%

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222/6

Page 71: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-

%$ 9

! 2/

C2/:

+ 22

Page 72: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-(

C22:

!

'

$'

-

-

- 8

8

8

- 8

= =

+ +

/33 /33 ;2/-<

$ '

E /

/ /E

/

/ /-

- -

- - 8 8

8

8 8

- - 8 8

=+

=+

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# $

22226

Page 73: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

--

! "

2

-

-

-

8

−=

;2/5<

2- -

-= ;223<

'-

$ &F-$ F

2

-

-

- 8

=+

$&F

-$ 8$

# 20

C20:

Page 74: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-4

C21:

%21

) "

γ ! γZ/ "%

& γ[/ ! %

% 2 2(

Page 75: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

-5

C2+ '

$ "$ "

!

"'9$,K$6&$&'9$! =$! 9$89$=

)

C2(:

"$F$

Page 76: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

43

& '

:

220$"% C

' = + +/ 2 0 ;22/<

'$F/$ F2$ F0$

# " /0

C '

$Z/3$27@2F$ /[[/3$27@2F$≈/7@2!$

)

/

,

/

= =α

π233400 NP@2O

;222<

Page 77: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

4/

'$F/$ Fα$)

9 6 N(1/32O)'

/

= 3 3400 γ NP@2O;220<

'

γ$ F$F$ F,$

) T$9E

#

$

$ '

=; <

; <

/

;221<

$,

'; < = ;

<'

; <; <

$

,

3

/

3= − ;22<

':;<$ F9$F3$ F$

Page 78: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

42

%$'

# $

,

= 3

; <

;22(<

9$;<

#

% '

$F$ F$;<F$ F$

:

&

& ]

:

9

Page 79: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

40

(%))

&

'D272^2D2^;<!^!^2=^2!D%$

= ;< $

, # '

& '"

=

!

% 2- 24

Page 80: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

41

C2-: 7

'

,

4

&−

= ;22-<'

=$F!$ F?$ B@F"$B@`

C24:

$ DE

Page 81: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

4

'

N O& 5# = ;224<

'A $

F$/@2 /

#

D272 =

& 5 #= ;225<

#

'Π Π1 1'; < N O= ;203<

# '

T22NTOX∆D' 5

1

1=

N O2

2

#'Π ∆1 1'

, 1 1 , ; <

N O= = +23 2

∆1 , 5

3 = − '

, 1 ,

5

1

N O

2

2

= ;202<

Page 82: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

4(

" ='

N O N O& 1 5 1= = 2 ;200<

+

'

N O & 5 = +/

2 ;201<

#&'

5-

8= + '

N O & -

8= + +

/

2 ;20<

9

20//& &

#

&

Page 83: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

4-

= : G & '

$F$ F$ ;/$1A@<%

&

% : 9 '

$F$ F$ ; A@<

20/2#T

CP'

6

!- −= ;20(<

!

6τ=

2

2 ;20-<

Page 84: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

44

' $

&;2< F#$ 2@F

6$ F

E$ Fτ$

;20(< ;20-< '

!,

2 =

/

(π η

;204<

'">/04/3$20B@ $F7>(320/320$& Fη$: 7@2F$

# '

! ! .

,=−

3 ;205<

'

! 5 = ;213<

'#3$ 6 F $ FA$

#

Page 85: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

45

( )*'

D -3$/33L

, %

+ 25

) '

$ $F

$ F$

C25#

$ F$ F/$F2$

Page 86: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

53

C $

'

( )( )

B-

!

6

!

5

3

6

= = −

= − =

= −=

/

;21/<

'&$F$ F$F#$ F!$ F!$ FA $

9 '

5!-

$ =/

2 0 δ ;212<

%

'

5!

* =

2

2 0

22 π

;210<

,'

Page 87: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

5/

( )B!

* 3 = −2

22π

;211<

'$F$F$ F:$

& % 2/3 2//

% &$, (L , & &2(1L6 2140D2@/33 &L8110D2@/33& ,$&$8 /1 /- 0D2@/33 ,$& 2$0L & N/25O

C2/3+

Page 88: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

52

C2//+

K 24 0D2@/33

240D2@/33 210D2@/33

+ 2/2

C2/2+

Page 89: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

50

#

/-2- °!

) /133$/33°!

'

2N&OX0bD2^c>N&2^0OX(NDO ;21<

, $ ;3$/33AB<D 133 $ 13 °! $ (33 $-33°!]9866:676) 'T&=K=6 %&+! 6

, !&C!7,!&9

202/+

&

$

& 330- 0 D2@/33 3- $ 24 0 D2@/33 ((3 $ 533°!=

Page 90: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

51

&2^0% -33$/333°! '

&

= − +233

2 (2 ;21(<

=

'7,C!,)!668^

, 133°! &-(3°!1/0D2@/33,

: '

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2

+=

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3

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Page 91: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

5

8 82D 8D8D2

= 8α8β /33°!

7 33°! 7D345

= 7 7 7D7D27D1 = 7 ) % F/33°! 1/(0D2@/33

2022+ $

!

% &$, 250@/33 &$6&$8 '20@/33 2-L6110@/33 L8& &$) %

2&X0D2^>&2^0X(D ;214<

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1)XD2^>2)DX)2^ ;215<

Page 92: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

5(

#

#

:

&-

3= − +

/

2 2 ;23<

% &2^0 6 $ # 3/3 0@/33

& (30@/33! & '68! ) J ! D 8D/52443°!6D//0(13°!

+

Page 93: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

5-

^

% 9 "$

+ $

) 7$! 7$: $ 6 '

7^XD2>7XD2^;< ;2/<

7XD2^>7^X2NDO ;22<

'

07X!D1>70!X1NDO ;20<

K

= "

( )'

Page 94: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

54

^

2,XE^2>2,^EX? ;21<!

! 2/0

! ∆1 ,

= 2

/3/0⋅/37@2

C2/0

Page 95: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

55

,

& G ',! : K

C '

% "

! + $ & +,^ 0$/3µ ) &2^0 /33$233&°% &2^0 3$/33µ &2^0 ) 7^

%

# '

F F

Page 96: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/33

, '&,89=! # & & 8!, !7, ,^⋅&2^00!^⋅&2^072^⋅&2^0

#

, '!7&68:76,G6] ,$,^ ) # $ ;,/<'

/

2 2 /F F /= L @ @ ;2<

$ ;,/$,2<'

/

2 2 / 2F F / /=

−LN O

;2(<

'

( )5

#F F / /= = ⋅

3

2/ /

γ LN O ;2-<

'

Page 97: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/3/

( )5

#F F / / / /= = ⋅

− −

3

2/ 2 / 2

γ LN O ;24<

!

,/'A>A

( )γ FF

F/ /

/

/ // 2

/

/ 2

=LN O

LN O

;25<

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$F$Fγ$ FLNFO$

! $

) )

#

^ & & 9

Page 98: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/32

200/+$

,

$ ;'&,687< ;' 7 ! 6 8 , G 7 < # & ,^ 6^2 8^2

$ & 6 8 7 6 ^

# ' 6^2 62^0 6^8^282^08^7^,^

= & 32L

+

= $

Page 99: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/30

&

) &$) 9

) ! 9

( )"%

%

;<

Page 100: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/31

C2/1+

& !=8! &&9TK

& ;&7533°!,072 <) -33$-3°!

, '68:76,G $') ! K ! ] 2/1

+( % '"

Page 101: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/3

T'!^!^2D2^;<=^27^2D2=7D0!D %

!^ , ',&688= !^'

,;<Xb!c>,^X! ;2(3<

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& !^

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&'7!:,6G,6

6 ) ;2(/< !^

) T !^

!^2 %

Page 102: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/3(

'&!9K! !^2'

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!^ ,^ , !^2

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]

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% $ ;2(1< D2^;<

=^2 ;'<;'

Page 103: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/3-

< #

] ' 8 , ! =^2'

0,X=^2>2,^X,= ;2(<

$

& '&9=K'

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;2(-< % =^2

"=^2 & ! ) =^2

), =^2 ,=,^

7^2 # 7^2

Page 104: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/34

9 % '

,XD2=>,=X2NDO ;2(4<

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# =^2

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$

(!

# # '

$ $ =^2F $$ !^,^F

$$ &2^0# '

Page 105: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/35

$ 53L =^2 /(33$/-33°!F $ $ 3$-3L =^2 03$3L&2^0/(53$/-53°!F

$ $ ($4L =^2 /2$24L&2^0/(3$/-/3°!# ' $ 53L ,^ 2333°!F $ $ -3L ,^ 4$/2L!2^0 2333°!F $$3L,^23L!2^0 2333 °! F $ -L,^ L&2^0 2333°! F

$$ -3L,^ 4$/2L !2^0 2333 °! #

' $($-3L&2^0 /-53$/423°!F $ $ 43$4L &2^0 /43$/443°!F

$ 50$54L&2^0 /523$/5(3°!^ F $ F $ ; <F

$

Page 106: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//3

9 =!!

! # ; θ[[53°< , & !9

+ $

"'"^X,;<>,^XN"O ;2-/<

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$ F$ ;2-/< & $

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=^2X2,;<>2,^XN=O ;2-2<=^2X1,;<>2,^XN,2=O ;2-0<

& =^2

Page 107: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

///

) =^2 '

0=^2X1&;<>2&2^0X0N=O ;2-1<!2^0X2&;<>&2^0X2N!O ;2-<0C^X2&;<>&2^0X0NCO

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+

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Page 108: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//2

133°! "

& ;86 , K< #

+ % & ' 72!^0 7C AC !C2 $

! 03$13L % '768,& ; < ! & 8 9 C ! =!

9 %

Page 109: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//0

! $ & 68,G76

*+ +, %

C

$

! ; <

C

+

% % '

Page 110: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//1

$ F

$ F$

9

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C + ++$ +++$ C

] ' ! ) 6 $

7!A! θ Z 53° # C

Page 111: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//

' 70&C( & 9 & 0$

7C7C$&C0$&2^0 70&C($&2^0

$,C2 !C2 KC2 !

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+-* ' " %

%

6

%

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#

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Page 112: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//(

9 ;2-(<;2--< !^2;2-4<'

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Page 113: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//-

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C & K 6 8 6 : , G

Page 114: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//4

' K&0 6&0 8&0:&06&0 ,&0 G&/2 & !$ 6 6 6&0 6&0

C # $

) '7C,$2&&C,$&$-

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C /3$/2LK!2/LK2^0# ,^

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Page 115: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//5

% 8&

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Page 116: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/23

% 9

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,

% ' &

. *

&

9

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% $

Page 117: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/2/

& $ ; <

= +'

< ^

2N+OXEN^2O>2;+^E< ;0/<

5

( F

(

F

6

6

=⋅

; <

N O

2

2

2

6

# ;< : ) @

<^

N+OXEN^O>;+^E< ;02<

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F(

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⋅=

Page 118: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/22

!

<^ ! '

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^

'

EN,^OXN+OEN,OX;+^E< ;01<

5

/

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( F

/F

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=

; < ; <

N O N O

, N,O≈+F ;+^E< ;+^E<≈/"'

5

5

5(

/F

6 N O

H

N O@

H@= =

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#

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C & 9

Page 119: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/20

# + '

# #

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π π

/F (F62 2N O N O>

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2 2N O N O= ;0-<

9 '

2 22 /

2

22

N O b c N ON O

N O; <

/ F /F 5/F

/ /F

+ = =⋅

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2

22

N O b c N O; <

N O; <

( F (F 5(F

( (F

+ = =⋅

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#N O

N O

; <

N O

/F

5 /

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5 (

2

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Page 120: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/21

[ ] [ ] ( )[ ]2

22

2

/2

/F

(F/

5

5( =

;0//<

!

N,^O ;+^<

[ ] [ ] ( )[ ] /

22

22

2

5

55

/5

(F/(

==

;0/2<

!

( )5 5 ,

= ⋅

∆ # 5'

∆ ∆ ∆1 1 1 , 5

(F

/F

= − = −

;0/0<

5 ,

1 1

,

/F

(F

= ⋅−

; < ∆∆ ∆

;0/1<

^

) + : ;<

. "

Page 121: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/2

0/2/6 "

C 9 '2L72=^123L7!1L!=^1 /3L 72K1^- 13L 72K1^- 13L 7! 23L K=^19 ' !2^ 72!^0 A2!^0 72=^1 7! A!72K1^-

) % ' 2L A! 2L 7! 3L ,!2 ' 13LA! 13L7! 23L&C0 13L 7!13LA!23L72=C(

C ;7CAC,C2!C2KC2< ;,!2A!)!!)27!< $ ! 8J7!

0/22" ,

!

Page 122: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/2(

%

^ & NC& C2& &4, ;, C<&O 9 '

6 , "

0/20" =

# & &!7

9

Page 123: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/2-

2/21"

,+ '

# ; 13$3 µ< ;/3µ<

. "

$ 9 % ;<

Page 124: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/24

# '

EN,^OXN#O>;#^E<XEN,O ;0/<

5

! F /

6

/F

6

!

6

=⋅

! DE

# "! F 6

≈ /

5/

F !

/

6 6

F

6 6

!

=⋅

⋅ ⋅

γγ γ

NL O

NL O NL O

#

,

NL ONL O

NL O!

/

5 F

/

6 6

F

6 6

!

= ⋅⋅ ⋅

γγ γ

/

;0/(<

=

$

. "

Page 125: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/25

,

, '

022/" &

' C C& C#

( ): : '- ' − = −1

00π ρ ρ

C

'

: -$

'

= µ ρ2

;0/-<

'µ$ F&$F:$Fρ$ F$

! µ "E /3$0Z7"Z2'

Page 126: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/03

µ =21

2"

;0/4<

# "E ' 2$

" =2 ρ

η

'&>π2 =P'

C>(πη: ;0/5<

% 'C&$C>C

( )1

0(0π ρ ρ πη ' $ − =

( )$ '

=

−2

52

ρ ρη

;023<

:

) ) $$= ; < & @ @

02226

Page 127: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/0/

C

;< % 9 # % $'

9 6 @ ! θZ53° @ $ ] !$!$>/4/&° C$ > /0/ &° # '

82+ = 30/ &°2+ = 355&°

/'2+ = 3(&° 82+ = /0&°

^

Page 128: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/02

&2^0X270&C(>2N&OX0b72^cX2;&C0< ;02/<

&

9 % 9 ^

2220""

C

C C $ #

Page 129: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/00

C 9

C @

C N45O+ # 0/

C0/= C

C

$ = -$53L 9 02

Page 130: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/01

C02= C

# '

( )'

ρρ

η−=

/4

2

;022<

'

( ):

'

= −π

ρ ρ0 2

0

;020<

\ '

E

!

'

8

=2 ∆

;021<

Page 131: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/0

=P$

!5

8

=0π η

;02<

'GG'$ FρGρ$ F>@ε$ F$ Fε$FE $ F∆$ E Fη$ F6$ FA$KF#K$

"'$ F$ F$

F$ F$: GF$ :

N44O'∆T>σ$$σ$$σ$ ;02(<

σ$σ$σ$$$$

#σ$>σ$Xσ$ ;02-<

Page 132: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/0(

σ$σ$$$

" '

σ$Xσ$Zσ$Xσ$ ;024<#σ

τ N1O'

5

στ =

;025<

'A$F!$

9A

5 5

= −

σ

;003<

'A$Fσ$

# N/25O'

( )

( )

/

/

/

/

=

+ −

σ ε φ θ η

φη σ ε φ θ η

;00/<

Page 133: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/0-

QR φ θ η '

θ ε η φ= = =

?

9

?

5 ?

F F ;002<

'ε$F$ F$ F)$F8$

% σσ

→ 3 ( )

σ ε φ θ η− → 3

;00/< '

5 ?

= =−

−φη ;000<

'!$ F!$ " η'

?5

3

/−

−=−

;001<

#5

= λ '

η λ= −

−/ ? ;00<

Page 134: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/04

# A

# N/-O'

&

&

= ⋅/33 L ;00(<

'=$F=$F$

# ;001< ;00(< '

λ = − −/

/?

.; < ;00-<

% N5O N/O N/-O N1O

N4O N54O

Page 135: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/05

C00+ $ /$ F2$ F0$ F

1$F$ F($ F-$ F4$ F5 $ 9$9"F/3 $ F//$ F/2$

^ $

00 $

% 01 $

% N44O'

4

-

$

-

=

+

∆ηε

α ;004<

Page 136: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/13

C01+

/$ F2$F0$ F1$F$ F($F-$ F4$

F5$

'∆$ F&$F$ Fα$F$F

901

0221")

Page 137: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/1/

9 53°

!

Σ>XσX ;005<

'$ F$ Fσ$F$

'

ΣC>CXCσXC ;013<#ΣC[3CC'

C>$ ;01/< '

$F$

C

∆>σ9T$σ9) ;012<

9 J'

Page 138: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/12

σ9T>σ9)Xσ)Tθ ;010<'

∆>σ)Tθ ;011<9'

∆>&σ)Tθ ;01<

:.

-

?1

σ

σ θ= =∆2 2

;01(<

'&$F$

# '

$'Cσ>;(π2</@0;@ρ<

/@0σ)Tθ ;01-<$'

Cσ>;@ρ</@0σ)Tθ ;014<

$'

Cσ>A=;@ρ</@0σ)Tθ ;015<

'A=$ Fρ$

CC'

: $ ' : ' ? ?

#

= =ρρρ

;03<

':$Fρ)$

Page 139: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/10

C'

: ' 5?

#&

#?1= −

+

∑ ρ

ρ ρ σ θ/

/

0

;0/<

# ΣC [ 3

# ΣC Z 3

9 ΣC [ 3 ΣCZ 3 C ΣC

:

," ?1= −

2π σ θ

;02<

"

2 /

/

0

π σ θ ρρ

ρ σ θ

,'

5

?1?

#

&#

?1

> −

+

+

;00<

#

θ9 θ>53°

'

Page 140: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/11

σπ

ρ ρρ?1

? #

#

'

,

, > ⋅

−⋅

2

;01<

9

; $ <

,)C $

$ ++$ % ' ;<

'"

6

$ &

9 '

Page 141: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/1

$ F

$ F

$ F

$ F

$ F

$ $

+ $ :

7

9 '

' * ' * " "> + + + +/ 22σ ρ ρ

;0<

'/$ F

Page 142: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/1(

2$ Fσ$ $F$ Fρ$ Fρ$ Fρρ$ F$ F$

9 N/(2O'

# 4

#

#= − +

//4 / /

2

/

2

;0(<

'?$ F6/$F62$ F9/$F92$ F9$

9 N/4O

( ) −

=−⋅ σπρρπ3

0

(''

;0-<

' $ F $ Fρρ$

" "E 33

Page 143: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/1-

C '

σ = (0

4

'

;04<

) "E

332/33& 9 '

σ= ⋅ ⋅( - 3 10 3/0 ;05<

'σ$ @F$0@F $

# '

2 = ⋅ ⋅3 24( 3 3 00 "

;0(3<

7""E

00//# C

#

Page 144: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/14

& "E

2

" =

ρη

;0(/<

'7"$"E F$ F $ Fρη$

K 2 "E 7"≤2 =P'

( ) = −/

/4

2 '

ρ ρ ;0(2<

K2Z Z1"E 2Z7Z133

$ 3L =P

K Z Z5133Z7"Z333

K [/3 7" [ 333 '

= 2 2( ;0(0<

Page 145: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/15

# D9'

9>9XρD ;0(1<

'

>$ρ ;0(<

#

':>: ;0((<

: :

) ;0(0<

$

=π 0

('

$ = 2 3 /(- ;0(-<

#

$ = = 2 3 /(-

;0(4<

#;0(/<;0(2<;0(0<'

$

'

= −

2

3 /(-

ρ

;0(5<

Page 146: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/3

# D '

>3 >3>D >'

( )( )

'3

' $

=− −

//(- //(-

3 /(-2 25

ρρ

;0-3<

00/26 !

'

( )B 5 &

- - = − =

/

;0-/<

'!-G$& F!-G$ $F=$ $FA >#&@δ$ F#&$ &Fδ$ $F

$

!DE !-G'

!-G>A& '

&$& FA$

Page 147: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

//

# $

9&>Xρ;D$< ;0-2<

'$ FD$ $F$

Fρ$

# $!-G'

!-G>ANXρ;D$<O ;0-0<9

='

! > AH N X O&

/

2ρ ' 3 ; <− ;0-1<

)

9&:>"6

':$ F$

:

'

Page 148: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/2

+=

$

$

,

--

/

;0-<

#$

$

$

= ⋅ =

;0-(<

=

#;0-<;0-(<'

−==

$

,

$

$ -

-

νν

//

;0--<

# > ⋅

;0-2<'

( )[ ]

' 3 '- = + − = −ρ ρ

;0-4<

C ;0-/<;0-2<;0-0<;0-4<;0--<

'

( )

( )

$

5 ,&

' 3 5

'$

' 3

-

= + − −

+

+ + −

ρρρ

;0-5<

#

φ

=>φ:2@0

Page 149: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/0

!

;0-5< '

:>: >39 ;0-5<

00/0,

T

# ] # '

$ F

$ F$ F$

F$

Page 150: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/1

C '

# # '

$ F

$ F

$ F

$ = /

$ 2 : / Z Z 2 Z / : $ /2 δ ++$ CP '

δδ

δδ

δδ

!

= +

2

2/

/ZZ2! : '

NTOXNTO>bT2c

'

Page 151: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/

( ) ( )

5 5 = − − = − −/

2 2 2 2 2π ;043<

'$ T2FA/$ FA$

F!$F! $

#

δδ π

2δ : / δ'

( )

5 = − −π δ2 2 2

;04/<

% > /

1= −

/

2

;042<

1

BT /

B&

!

1

1

= − = −

=

/

/

δδ

;040<

Page 152: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(

=>2π/δ

#;042<;040<'

!

= −

=

π δ δδ/

/

;041<

9;04/<;041<'

( )δδ

5

!

= −= /

2

/

2 2 ;04<

9;0-4< '

!>!>3 ;04(< '

( )δδ

5

!

= −

2

/

2 2 >/;04-<

δδ

= 3 >2

;044<

9 '

$'

=−−

≤ ≤ 3 /

$'τ τ= < < ∞!

22 3

Page 153: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-

$ '

= ≤ ≤

23 /

= ;0-4< ;04(< ;04-<;044<'

δδ τ

δδ

δδ β

= + ≤ ≤

2

2/

/

;045<

[ ]δδ α β

2 !− + = =3

;053<

δδ

= =3 /

;05/<

= =/ 3 τ ;052<

'

β =

/

2 ;050<α =

2

;051<

( )

2 5

!!

=−

22

/;05<

'β$

Fα$ F7#$

# 7#

97#

Page 154: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/4

7#

= ;045< ;052< β $ 7#%0αβ7#

, # βZ3-)β

#

Page 155: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/5

C0! αβ7#<α>300Fβ>3/F

<α>300Fβ>32F<α>300Fβ>3

4

= =(

;05(<

'

ν$ @F$@F4$ 0@

002/! :

3°!9 % & /00⋅/3$1902 ⋅/3/3@0& $ 7 '^2D2 9/3$0$/3$1

Page 156: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(3

% /3/⋅/39/3$19 2⋅/3192⋅/3$19N/2-O

: & # '

$ F$

F$ F$ #

0(!

Page 157: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(/

C0(#

00229 )

% $ ' D2 ^2 72 =

Page 158: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(2

= ;<$

# ;<

DE

N=O>A9 ;05-<

'=$FA $

F

=/

2

# ' D2 72 ^2 ='

& 5 #= ;054<

)

= ^ # N/25/(3O

Page 159: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(0

N^OX2NDO>bD2^c

;055<

N^OXN!O>b!^c ;0/33<!'

N O N OF 3 5 3 F 3 F

⋅ = ⋅2

2 2

;0/3/<

N^O⋅N!O>A!^⋅!^ ;0/32<# D2^;<

!^ = $N/(/O

,^XN!O>N,OXb!^c

;0/30<

,^X2NDO>N,OXbD2^c ;0/31</ 34 %

'$

F$

F$

F$ F

Page 160: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(1

$

C0-=

!$ F!$F$ !F$

F$% 0-

$

<6 6

# ;< ; < )

Page 161: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(

%

( ) ( )B!

5 = − = −δ ;0/3<

'#$ Fδ$FA $ F!$ F!$

C :&'

B$

-

= ⋅

; <

;0/3(<

9 '

( )

-

$5

; <= −

;0/3-<

#'

-

$5

−= −

;0/34<

!

% 04

Page 162: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/((

C04:$

9 '

B-

= ⋅

/

;0/35<

9 04 '

( ) = −/

;0//3<

( )

= −/

2

δ

;0///<

9;0/3<;0/35<;0///<'

Page 163: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(-

!δδ=

2

;0//2<

'

δ = 2 ! ;0//0<

: δ

'

δ != ;0//1<

#

9

,'

( )B !

*- - -

-= −

2

22

/

2

π

;0//<

<6 ,

'

'

'

'

'

'

''

5

5

5

5

5

5

−−−

6

=

6

Page 164: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(4

C05"

# 05

! !

( )

5 = −

;0//(<

) A A'

Page 165: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/(5

5 5

'

' '= − + ;0//-<

'$ F!$

&'

( ) ( )

5

5

,

'

'

' ''

' = − − = − ;0//4<

'A

$ F!$F$F$F"$

" >"6

)

'= 3

5

5

?

'

'

= = ;0//5<

'!$ F)$ ^\

! ^\

# 8'

9

'=

;0/23<

Page 166: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-3

#;0//(<$;0/23<'

?

5 95 95

'

'

=−

+ +

/

/ / /

;0/2/<

5

?

'

= −

/

;0/22<

/ / / /

5 5 95 95 '= + +

;0/20<

A

9A

7 )

,

,

/

'

= −ε

π2

;0/21<

'

$ !F

6 $ F

Page 167: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-/

ε $ F

"$!

8'

5

5

9

9

/ //

= =

@

9;0/21<'

5 ,

,

/

'

9

= −

ε

π/

/

2

;0/2<

9

5 ,

,

/

9

9

= −

−ε

π

/

2

;0/2(<

5

5 ,

,

/9

9

=−ε

π

/

/ 2

;0/2-<

#!→ 3

/

95

%

! A/'

5

,

9 9

9

'/ = =

Page 168: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-2

?

'

=

5 ?

,

9 9

/

/

=−

5?

,

/

π2

;0/24<

,

/5'

2π=

9

5?5

'=ε

;0/25<

#

'

/ / /

5 5 9 5 '= +

ε

;0/03<

#

?

5 5 ?

5

5'

'

ε

ε<< <<

/

Page 169: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-0

! ;0/3< # ε ZZ /

%

C0/3: #

'$ F$ # $

N/(/O'

Page 170: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-1

( )* '= −/3

γ

;0/0/<

'

γ$ 7@ 0⋅/3$(F $

DF$D

% %

00209 :

: % ;0//< ( N/25O

Page 171: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-

C0//# )

,

: N/4OC C '

# '*

# >> + +ρσ2

;0/02<

'9$ F

Page 172: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-(

ρ$ F$ Fσ$F$F9$

: !

: ) $

$ #/

3400= ⋅3 ;0/00<

'9$

6DF,$: /3$

/$/3$2 9 # '

( ) # /

= −3 3400 / ;0/01<

/ 9 %

Page 173: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/--

0/2(

C0/2

9

9

6 N(1O N/32O )'

$ /

= 3 3400 γ ;0/0<

P@2'γ$ F$F$ F,$

%

Page 174: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-4

!'"

=

NΨ;<>3>3OK $ : 9 ' ! !

:

# '$F$!

;/3<& & &

Page 175: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/-5

!'" *

# ' 6!1

,!2 &!0 8!2 ! 9

0=!1X1N&O>1b&!0cX0N=O

)

2NDOXN!O>;!D2<2NDOX2N!OXN^O>;!^<X;!D2<NDOXN)O>;)D<

&

1NDOX^2>2bD2^c

9

Page 176: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/43

&'()($

%'(*/&(('.(0('

=

&

= $

% &

9

) 1/! 1/ 1/% $

Page 177: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/4/

C1/,

< F< ; F

F<F<

8

^ # &

, #

= % + %

Page 178: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/42

6 C

-%

&

#

) 6Z6$ ∆6>6$6= 6 6

# 6 $ 9 = 6 &

&

Page 179: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/40

% " T

C126

'

σ=)>σT=Xσ)Tθ ;1/<'

σ=)$ $ FσT=$$ Fσ)T$ $Fθ$

= θ > 3° Tθ→3° %3°ZθZπ@2

Page 180: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/41

) !

. &

#

% C

% $ @$ &

C $ T % $ % $ : #

Page 181: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/4

! ! #

# $

C10"

#

. %] !)

!= 11

Page 182: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/4(

%

# $ δ K !)

C11# 6

$ K! K !) &

: $ 1

Page 183: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/4-

C1: $ δ$

%

= $

% # ;1(<

Page 184: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/44

C1(= $

/$ F2$

9 1-

$ & ;1-<

! $ '

( )!

, ?

?

? &=

= − −=3

;12<

'#)$ F

Page 185: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/45

" $ ; <F

?

=3

$

C1-=

/$F2$

T

?

?

?

=

= =3 3

;10<

=

Page 186: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/53

1

??

=3

;11<

#

'

1

??

=3

( )1

!, ? ?

?

?

?? &≥

≥ − −=3

1

,

D

!

? ? ?

?

≥− −; </

;1<

D

&

?

=

# 9 K

% $ /L ] $ 9$= 14

% $ 7$ C $ +

Page 187: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/5/

;15<

C14=$

C15=

/$ F2$

Page 188: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/52

) $ * = T)@"

. %% α

β ) α K β & # α & β K;1/3<

= ∆6# '

∆6#>6$6)>);!$!)< ;1(<

'6!$F)$ F!)$ $α

# '

∆6>6$6>∆6$∆6# ;1-<

Page 189: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/50

C1/3=

'

∆6 > 6) $ 6) >σρ

3

.

$

F6) $

F6) $

Fσ$ $ F

Page 190: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/51

6$Fρ=$ FD$ F$ $

) " λ% '

∆ -,8

= +λ λ ;14<

&K

, ; < " T)

] &$= T)") T) 9 T)@" ) α& = $ α& # &$= !

% T)@" ) T)@" %

Page 191: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/5

T)@"

. % 6

C1//= /3L=

%

$ C

Page 192: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/5(

1// =

9 α P⋅!) /0L = -54 °! ) -54 °! β α

!/ %,

@

) #

, $ C

/")*

Page 193: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/5-

% = '

<, + % &

< , ++$ & C , ++$

9 :A=P $ '

"

=

;15<

F$F$F$

, 7A"K C &

Page 194: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/54

<, +++$

# '$&$ F$K$ #

'$/$

F$2$ F$0$ ! "

+ & ++$ &@K

C & & ;6K8<+&/ , ++K2

, + 9 $ $ π@2! $

Page 195: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

/55

)

! & ^ N/((O !

/"&

9 '

1(2/+)

" = & >;< ^

' Ψ; <

= ⋅ −

ω

Page 196: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

233

= −

ω ω

;1/3<

G

'

C

= = ⋅ ⋅ −

/

2

/

22 2 2 2ω

;1//<

:

ρ>@'

C

= ⋅ ⋅ −

/

22 2 2ρω

;1/2<

:

2

2'

C = ⋅/

12 2ρω

;1/0<

'

C C C = + = ⋅/

22 2ρω

;1/1<

#ω>2πσ'

C = ⋅ ⋅ρπ σ2 2 2 ;1/<

Page 197: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

23/

"

) & N52O )

& 9 θ )K'

#

= +

ω θ ρ

2 ;1/(<

!

9 C 7 $

" ) $

Page 198: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

232

# N52O ] 6PE & &^/541BN/((O

'

1(22++ /40/

C E

% /501 $ = $ / $

& ' ! ;&< D &;T< & T ;C< 6 ;7< ' &=&;= <"^6)!!8]=+"=+#;C<#!E+;=]&<KK!&=&K\K\ +!,

Page 199: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

230

# $N/31O'

$ F

$ ; <F

$ F

$ F$ F$F$

F$ F$ F$

!

&

^ ]

9

Page 200: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

231

# ρ ν

7$=PN/11O'

( ) '#'

+−∆=+∂∂ ρρρ

;1/-<

'

$F9$F∆$)

%

;;<33<7$=P33 '

32

2

=+∂∂−

#

"

ρ

;1/4<

3=+∂∂− ""

#

;1/5<

#1/5'

# " " # "= +; < ; </ ;123<%;123<;1/4<9/;<

9/;< > 93;< X 9/ 93 9/ #;1/4< '

ρ

"#

2

2 = − ;12/<

Page 201: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

23

##

=∂∂

9 1/2 9 > 3 ;<'

;3<>3

" "→∞

= 3 ;122<

C1/2"#'

B

"

=+

/

2 /

2

2

2α µ ε

σδ

;120<

'

"

= ⋅

−2

δ ;121<

'$>3FB$ F

Page 202: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

23(

εω µ σα

= 2 $"E F

δ$ F

απ

ττ= $ F

µ$Fσ$

;12/< ;122<'

( )

−= −

"

"

δ

ρσδ 22

/1

;12<

: '

( ) ρσδ

1

2

""

==

∞→

;12(<

;/$2<⋅δ

9 B αεδ τ 6 δ

,

, 1/0

Page 203: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

23-

% ;12/<93'

;3<>3;<>3 ""

; <33∫ =

;12-<

C1/0,

,

=;12/< ;12-< B τ ) & >3 [ @2 )

Page 204: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

234

, C N/(-O

& N1O %

" $ N--O ^

C &=& 3$/ @ + τ>/$/ >32$/D N/2O & = #

& $

Page 205: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

235

! 9 & Q$\R $ =

Page 206: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/3

&'()($

'*%(*(2'(0('

)9

N/-O

+ /3$1$/3$9

9 '

$ F

$ F

$ F

$ 'F

Page 207: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2//

$ F

$

,'%#0+( %9

9 ')E $DBP T! ) T!&$! =]& &=& = K )

! /1

+ )E $D+= ! +=T 2 ' ; < 9 +=9

6 $ ; < ; < " +

Page 208: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/2

% " = # /3$1$/3$9 2333 Y!

, 9$9/0L" 903L"$9(L" 913L"$923L"+/3L"$+(3L" /-33Y!/43Y! 2/33 Y! 9 0333Y!

+ /$4 AD 6 ! 6:

) ;/33A< , ! BPN/14O/

Page 209: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/0

C/!

/$ F2$ F0$

!

' =

&

! 2 $ N/3O

] 0

Page 210: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/1

+ +=)E $D /2 P N/1O

C2+

/$ F2$ F0$F1$ F$ F($ F-$F

4$ F5$F/3$ F//$ F/2$ F/0$ F

/1$F/$ + 3@43P

!) =]& ) @ $ %1 N/(/O

Page 211: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/

C0=

/$ F2$ F0$F1$ F$ F($

#(3&F-$""]:&!G&23F4$ #+0333F5$

Page 212: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/(

C1= 3@43P !)

/$ 3@43PF2$ F0$

F1$ F$F($ F-$F4$ F

5$ F/3$F//$F/2$ F/0$ F/1$ F/$

F/($^

$ ] )E $D+=T3 =

Page 213: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/-

C= +=T3N/1O

/$ F2$ F0$ F1$ F$ F($;<

C )E $D

++=T/3:5 /

%

+ +=T33:0 1 ! $ + 3 D 6

Page 214: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/4

$

! ($4

C(+ +=T-33://

/$ F2$ F0$ F1$ F$ F($ F-$ F4$

++=T-33://

Page 215: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/5

C( N/0O

++=T/133:( (/2 ! % - N/(/O

C-= +=T/133:(

/$ F2$ F0$ F1$ F$ F($ F-$

F4$ F5$F/3$

+ +=T /533 : / # #

Page 216: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

223

%4 N/0O

C4: +=T/533:

/$ F2$ F0$ F1$F$ F($

F-$,CF4$

+- '

Page 217: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

22/

'

$ F$ F$F$F$ 9

9

^ /3$296 Q R &

" /3$2$/3$09

= ) # !^ & & 333/$333L /$23 %

Page 218: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

222

'

# !^!C2 43$5L 3332$3330L

) ^

] ;' , ! !< ;F6&6,G7<

# $ =

, '

$ F$ F$

F$ !

) ;/(333$23333 @< &

Page 219: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

220

; < N/(0O

# '$F$F$ F$ =

!

1%#021& 3+' 9 "&:

\ ; <

& % \

! 5 "&: $

9 $

Page 220: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

221

C5= "&:

/$ F2$ F0$ F1$ F$ F($ F-$F4$

9

$ & 6 9

# =

Page 221: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

22

9 233$033Y!

/3$2 9 = /0@/33 333$3334L 03$3L= = ) #

= =

+#

!

9 N/(2O'

Page 222: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

22(

5 (= /β P@A&⋅ ;/<

A/ β

^ 6 &:

( )* 5

!( = −2

α

;2<

( )$ 5 ! ( = −0α ;0<

'A2>/1FA0>4Fα>3(F $ F#$ F$ #

# /3

Page 223: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

22-

C/3# "&: +

= ;'!^< 9

%

: @# @# " @# '

Page 224: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

224

(

!

(=

2

2

2ρ π@

;1<

'+$ &Fρ$ +(

$

$ P ;< 9 ' )E $D T ! ) =]& =$ //3 24 /33 (

%// "&:)0339/ )E $DN/14O

, 9

Page 225: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

225

C//= "&:/$ F2$ F0$ F1$ F$ F($

F-$ F4$ F5$ F/3$ $F//$

F/2$ $F/0$ F/1$ F/$

F/($ F/-$ F/4$

F/5$ F23$ F2/$6:F22$ F20$

F21$ F2$F2($

Page 226: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

203

" ! $

+ A&

=

C/2!$"&:+

9 $ /2 %

Page 227: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

20/

9 "&: ;23337@2<

, +7!^-/0!+,&"$,102"d 43 ] &E GE ] 7 7 # 433$/333 7@2 -33$433 Y!

1 ' ) 2 +3

%+'

6

B$) $ ! '

?>"+2 ;<#

= /0

Page 228: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

202

C/0=

/$ F2$ F0$F1$F$F($F-$

, : 9 &

9 $

Page 229: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

200

$

! 43L $ $N/2(O

= % /1 $

/1! "8

#

+ ;< /0 $ ;1< ;< ;2<

Page 230: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

201

;/< ! % ' &

C/=

$ &

%/

Page 231: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

20

!

) (4L!C2/(LA7^0/(L /@/ &, 9 !C2 23$2L ) ! + $ B$)

9 2$/33L ;'/233$2333A\@<

+#% "'

9

C

N00O'

8.

∂∂−=

;(<

B8 = ;-<

'

8 $ 6F

Page 232: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

20(

. $:@F

B $ &@2Fµ$D@F$

9 N00/4O'

∂∂ α α

λ ρ

.= ∇ +2

2

;4<

'6$AF

α λγ=

$ G@2A

$ B@AAFρ$Ω.Fγ$ 7@ 0Fλ$ G@AF

∇ = + +

6

"

∂∂

∂∂

∂∂

2

2

2

2

2

2 $)

6αλ ρ.2

%

'

α λ ∂∂= −

=

;5<

'

Page 233: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

20-

6$ AF

$ %

'

!

.= ∇ +α α

λ ρ2

2

;/3<

'!

6

" 6 "= + + +∂∂

∂∂

∂∂

∂∂

;//<

E

# '

α σ λ ∂∂= − −

=

,

1 1 ;5<

"$Fε$ Fσ$=$KG@2A1F6$AF6$A

# % & ;<

Page 234: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

204

% / N20O

= !C2 !2X C$ 6^2X=^1

1$;=^02$<&0^-

$ %/( !^ $ !C2 $ &2^0 N/2(O

= '!^$,^$&2^0F!C2$,^$&2^0F!C2$!^$=^2F!C2$!^$,^

^ 033$133°!

C '

N=OX^2$→=2$XN^O

Page 235: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

205

C/(# !^$!C2$&2^0

"

] ^

: ' @ N/24O: N/(/O'

Page 236: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

213

> X > X "' !; @ <0

'$ F$ F $ F#$ ;<

# )

?H

(

-=ρ

;/0<

')$ F&$ $ 2Fρ$ΩF]$:F+$&

% & ]@+ $ 6 #

% 03$04L /$0 3332$3330L 300$/0-L ; 2$0 < N2O = =

Page 237: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

21/

9$ "8 %$ '

$ F

$ F

$

9 $ 3$033 N/3O /2$23 N/2(O& # ' 233$23 533$/333!

% "8 & ] ;/4L! /L! 1L6 L,7< (L -L 2-L

" ; 6^2 67< 03L

% DE;/3L7 23L! 3LG !< $

Page 238: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

212

9 ' "8 '

$ F

$ F

$ "8 F

$

"% 2%3++' 9

;"B< ;7,G6:<

9 N/4/2-O'

$ F

$ F

$ F

Page 239: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

210

$ /3$29F$ ;

/32$/35G@2<F$ F$

9

N/4/2-O'$

2333PG@F$ #

)E $D /33$/3L

% 6 $

%

?>?X?NBO ;/1<

?>?X?NBO ;/<

?>?X?X?NBO ;/(< '

?$ BF?$ BF

Page 240: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

211

?$ M BF

?$BF

? $ B

9 M; <

8 '

>31X2⋅/3$08 ;/-<

# ;! 7<

/L

# $ '

δ = 5-

9$ 2 µ

;/4<

'A$F&$Fρ$ 7@ 0F:$ :F8$

:ρµN/24O'7$34&$243!$//3G$314!$3449$34/

Page 241: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

21

9 ;/-<

C/-9

++ 6

# $ $ ' C /423/5

Page 242: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

21(

C/46

$ F$ F$

,

9 ; 0$A:23$13A:<

.

H= =

2

2

;/5<

'$F$;3/(323(/3$/4!<F$@F]$ :

9 '

Page 243: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

21-

C .

H (H= = =τ τ

;23<

τ$F$ F

(= τ $ &

C/56

/$ F2$ F0$ F1$ =

23

C ;/< \ ;2<& :

Page 244: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

214

C23=

/$ F2$ F0$ F1$F/2/1$ F($ F-45$

F/3//$F/0$;<F/$ F/($ F

! ;0<

/2/1 1 / )

Page 245: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

215

/( 6" $#'

B>&62;$:@A6< ;2/<

'B$ &@2F6$AF:$ :F&$ FA$K;/043/320B@A<

9\'&>43:>14:B>52-/3$-&@2/02-°!'&>(3:>1/2:B>5//3$(&@2

C2/#

#

Page 246: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

23

/3$2&@2# \ 2/

^ 22 N/2-O

6

] $

C22#

& Q R

=$6 ,! =]& # /4 $ \ %

Page 247: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2/

C20=

/$ F2$; <F0$ F1$

F$#

;/3$29<

++&** '

Page 248: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

22

9

$ 9 '

C221=

/$F2$ F0$F1$

F$$

;921<F

$ ;921<F

Page 249: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

20

$ ; D 21<F

$ /43° ;D21 <

6 21 2

C22:

$F$$&

% \

= $

Page 250: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

21

" '

$ F

$ F

$

#

++

, $

$2(2-

! ) #

Page 251: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2

C2(+

/$F2$ F0$F1$F$F($

?!>A=!X_! ;22< '

_$ 0@F!$ F!$ FA$ @F=$ 2

'

#

5

+=/3

Page 252: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2(

#;

&= @

C2-+

/$F2$ F0$ F1$

F$%'

5

#

= +

=

∏ //

;20<

#

'

5

#

= +

/

;21<

Page 253: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2-

9 '

=>=9>9# →∞'

#

5

#

5

=

+=

∞→/3

;2<

C24# !@! A@9

"

5

#

=

24

% !

Page 254: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

24

C25=

/$ F2$ F0$F1$F$

%

%

+ % 25 03

Page 255: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

25

C03=

/$;<F2$F0$ F1$F$

%

N/1-O

!"%#+'

Page 256: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2(3

9

6 /520 ) C 6 /3(A 2333$23333A /3$1A 6 N-2O 0/

9 $ /233$/033A@ /14$223@

Page 257: I.carcea Bazele Elaborarii Metalelor,Aliajelor, Superaliajelor

2(/

C0/:$ ;<;<

, '$

F

$F

$ #E

9 N/24O'$

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, T g 6 6K/540

(# + $ = $ ,5/544105

-9 ++ $ C * K/54/

4# ^ + ! $ ] & K/540

5, ,: $ , 6K/5((

(3, T=$ " ,,P/540

(/# , $ = ,0/54/

(29 7 9 , $ " ,5/541(-

(06 ) $ 7 +7+#K/54(

(1+,$6 ,/2/544(2

(P D , B $ & " ! , C 9 " $ C !9 /544=]&

((&&$] $ $,/3/5-444

(-& # $ C , , " EC$#]E9 /54=]&

(4#,$, 6K/544(5! ! ! : $ 6

6K/5-1

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-3& ) $ = 7 ! ,/54420(

-/*C $# ,2/544

-2D ^ $ , $ ,///54-25

-0 :& $ 6 6K/543

-1#!$! $,2/5--(2

-# T $ ] $ ,/2/5--(4

-(! ! $! ,2/5-442

--9 C $ + , 1/5-4213

-49 6 $ & ,//55320

-5*#)&$6 $ # 9 K/540

43* #, " C $ A T$$_ )_ $$ 69,$!= , , ! E 9 "$6,,i,=E/553

4/T =9,$, # 9 K/540

426 , $ ! $ ,/54/212

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032

40! \P!& $ % KC E/54(511(

41+ A$9 "B$6^)9/54(-21-;B<

4+, $, ,4/54504

4(! 7 $ 6 , /2 /544 1-

4-!)$6 ,/2/544(2

44K : $ & ,5$/2/5441-5

45K : $ " ,/55324

53MMM $ + &/54(-144

5/APT+$6 )9 /54(/2/0

52* C $ ! ,//55311

50=j$, ,//553/-

51K: $! , /3/54514

5& ) $ ! ,/3/5451--

5(+, $, ,4/54504

5-6P = $ 9 $ B5$/-(534 /30/54(

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54+ , , 9 $ " ,(/54524-

559 :9 $ + )9 (25

/33T P,+ $6 )9 4/5410

/3/9 69 $ 6 ),5$/3/54//2&

/32, 9 9 7 $ ! &$,&$8 ,1/545

/30& , $ ! $ Q!I K" ,$!+6C0/55325

/31T,$9 +=+B+B//553/

/3&6$,C$\C!9 =]&/544

/3(K: $& K+9K,/545K

/3-)_ T $ 9 DE$= " ,$!+6C/3/543-4/

/34) G $ ] B C_C/3/54/25

/35C B$= #^+#/54((

//3=PBP=$] =AC==6+&//54(01

///# D B = $ & _d dd I C $C I I41/545C

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031

//27&G T "B D !B = ,B $ ! +=(52/5-125/$032

//0=\ C 8 B&]& ! /1 /52(-5/(2/52-03//4//52500F2/0/5000/3

//19K]D,D50/512214

//T = = CD $ ! " = K &$- 9 =$= ! , ,!,6&20& /55200(5$00-(

//(! =, $ , = 6 +&0/54-00

//-6, $9 B 1$420-/ 203//54/ "B2/540/22/

//4=P+$" D & P & ,E &](/545/54

//5&P"6!$= , ,C&124/5-21-

/239D$9 , ,C&125/5-

/2/)D= 6,+=P6$6 GE ! &E !C+=]+25///54552($502

/22#E " 9 + K & #D $ =6 & T !) ) ;/5((</5

/20K "" &T^ $" ! ,//54505

/21999$B6C-/51-(14/2?PT$&9E/0/4(4(2/

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/2(= ) $ 9 # 9 K/543

/2-= ! + ,= # ) $ 6 # 9 K/54(

/24+,, 9 97K, $ # 9 K/54

/25+,, 9 97K, $ # 9 K/542

/03C J $ G , \ W & , 9$]"^,&6k45

/0/" B D , D , $ # \!G K9 9=E= =E & , 9 $ ]"^,&6I45

/02) ! $ ) , + ! & , 9$]"^,&6I45

/00,E$="6PE+]/(/52-/01A,=E= $&7\9 ,=$

= , 9 $ &E ! E=KK\ ,!C! B/5521-$-

/08 P=7#,9$+&P 7P===",//5(45/$5

/0(,TG$D6,$^:\& , 9$]"^,&6k45

/0-T 6K $ 6 =E $ 9 = C9& , 9$]"^,&6k45

/049 = +! $ & , 6_ E& , 9$]"^,&6k45

/05=lK$TP/3/54/0/4/13:T $8

6K/545

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/1/= ) * #, : ! $ C 6K/5-4

/12T = 9 , 9 7 $ & $ *K/544

/10T\ B $ 6P E\ PE\A"8G97+!+,6&)++I=6^9^GG\/541

/11C : $ +9K/545

/1" 7 K K $ & & K/545

/1(^ C $ 9 6K/5-1

/1-=&"T!$] # 9 K/543

/14* ! = ) $ % 6/54(

/15= ) $ # 9 K/5-

/3T =T7,7^C$, 6K/542

//*!!+$6 6K/54/

/2C : $ 9 6K/54(

/0=)!+= ,$6 6K/540

/1A&, 9$] # 9 K/543

/, 9 $ 6 # 9 K/5-5

/(*=: ,87$, ="!/54/

/-K G$7P &E D\ ) 6/541

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/4^ C $ 6 # 9 K/541

/5=)K:K!$K # 9 K/543

/(36 + 9 ! $ # 6K/54/

/(/6 + 9 ! $ " 6K/541

/(2:=$ 6K/543

/(0# 7 $ ] 6K/542

/(1=\E , $ : # & &E , , 4 G C E ! !\ $/@/5=/55/

/(!!!!$)\C_E:+= 7&E4G C E!!\$/@/5=/55/

/((&^$= =$:/54-/(-K:K!$6

$+9K/54

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