A Sur v e y of Cr yst allin e Def ect s
O u t lin e – Def ect s
• 0 D D ef ect s
• V acanc i es & I n t er st i t i a l s
• 1 D De f e c ts ( D islo c a tio n s )
• 2 D D ef ect s
• G r a i n & t w i n bounda r i e s
• 3 D D ef ect s
• C ohe r e nt vs . i nc ohe r e nt
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inc lus ions , p re c ipi ta te s
S i ngl e c r y s t a l o f Mn S , spa c e gr o up Fm 3 � m , F C C c r y s t a l s tru c tu r e
Cr yst allin e S o lid s
h t tp: / / w w w . w e be l e m e n ts .c o m / c a l c i um / c r y s t a l _ s t r uc t ur e .h tm l
• Pe ri odi c , l ong - ra nge orde re d st ruc t ure s
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F a ce ce n t e r e d cu b i c c a l ci u m cr y s t a l s t r u ct u r e
S i n g l e cr y s t a l s o f c a l ci u m m e t a l u n d e r k e r o s e n e
For m Fol l ows S tr uc tur e
h t tp: / / w w w .zk g .de / e n/ a r ti k e l / bi l dpo pup_ e n_ 1698578.h tm l ? i m a g e = 5
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P y r i t e ( F eS 2 ) , s i m pl e
G o l d ( Au) , f a ce cen t er e d reserved.
cubi c ( F CC) G y p s um , m o no cl i ni c
cubi c ( S C) h t tp: / / w w w .pa l a m i ne r a l s .c o m h t t p :/ / w w w . g a lle r ie s . c o m / m in e r a ls / W i k i med i a C o mmo n s / ne w s _ 2007_ v 2.php s y m m e tr y / m o no c l i n.h tm
G r ain vs. Cr yst al St r u ct u r e
• W hy do gra i ns l ook m ore sphe ri c a l , w he n c ryst a l
st ruc t ure s a re c ubi c ?
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cr y s t a l s t r u ct u r e (l e f t ), m i cr o g r a p h
o f F e - 12Cr - 2 S i (r i g h t )
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G r ain vs. Cr yst al St r u ct u r e
{ 1 1 1 }
{ 0 0 1 }
• Wu l f f c r y s ta ls d e s c r ib e
l o wes t en er g y s u r f aces
• E xposi ng cl o s e p a cked pl ane s l ow e rs s urfa c e en er g y
This image is in the public domain.
h t tp: / / w w w .c t c m s .ni s t . g o v / w ul f f m a n/ e x a m pl e s .h tm l
G r ain vs. Cr yst al St r u ct u r e
• W e s ee 2 D s l i ces o f Wu l f f c ryst a l s a s gra i ns!
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h t tp: / / w w w .c t c m s .ni s t . g o v / w ul f f m a n/ e x a m pl e s .h tm l
P o in t Def ect s ( 0D) – V acan cies
W as , p . 1 6 3
[ Was, Gary S. Fundamentals of Radiation Materials Science , p. 163. ISBN: 9783540494713.] removed due to copyright restrictions.
P o in t Def ect s ( 0D) – M u lt ip le V acan cies
W as , p . 1 6 3
[ Was, Gary S. Fundamentals of Radiation Materials Science , p. 163. ISBN: 9783540494713.] removed due to copyright restrictions.
P o in t Def ect s ( 0D) – In t er st it ials
• E x tr a a to m s sh o v e d in to th e c r y s ta l la ttic e
W a s , p . 157
O ct a h ed r o n
T e t r a he dr o n
Oc t a h e d r a l in t e r s titia l in B C C T e tr a h e d r a l in t e r s titia l in B C C la t tic e la t tic e
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P o in t Def ect s ( 0D) – S p lit In t er st it ials
W a s , p . 159
• D um bbe l l s a re oft e n l ow e r e ne r gy c onfi gura t i ons
• A l so m uc h e a s i e r t o di f fuse
• O ne i nt e r s t i t i a l c a n “ knoc k” t he ot he r in t he ir c o m m on di re c tion
• L ow e r di s t a nc e t o m ove m e nt
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P o in t Def ect E n er g ies
W a s , p . 160
Ha r d e r t o m a k e , e a s i e r t o m ov e
E a s i e r t o m a k e , h a r d e r t o m ov e
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P o in t Def ect E n er g et ics
• H ow m uc h e ne r gy t o m ak e a v acan cy ?
R e mo v e an a t o m b y br ea k i ng bo nds ( + )
L e t o th e r a t o m s re l a x i n w a rd ( - )
P o in t Def ect E n er g et ics
• H ow m uc h e ne r gy t o m a ke a v a c a n c y ?
• Fe - Fe bond di s s oc i a t i on e ne r gy:
R e mo v e an a t o m b y b r e ak i n g b o n d s ( + )
118 𝑘𝐽
𝑚 𝑜𝑙
= 1 . 22𝑒 𝑉 [1 ]
• Fe - F e cl u st er cal cu l at i o n s g i v e 0. 64e V [ 2]
• Z= 8 i n B C C Fe : 5 . 12 − 9 . 76𝑒 𝑉
[1 ] Y - R Luo. “ B ond D i s s oc i at i on E ner g i es . ” C R C H andbo o k ( 2009)
[2 ] T . N ak az aw a , T . Ig a r a s h i , T . Ts u r u , Y . K a ji , C om p. M at er . S c i . , 46( 2) : 36 7 - 375 ( 2009)
P o in t Def ect E n er g et ics
• Z=8 i n BCC F e:
5. 12 2 − 9. 76 1 𝑒𝑉
• M ol e c ul a r dyna m i c s (M D ) c a lc u la tio n s [ 3 ] s h o w :
𝐸 𝑉 𝑎 𝑐 𝑎 𝑛 𝑐 𝑦 = 1. 83𝑒 𝑉
• D i f fe re nc e due t o c rys t a l r el ax at i o n
L e t o th e r a t o m s r e l a x i n wa r d ( - )
[1 ] Y - R Luo. “ B ond D i s s oc i at i on E ner g i es . ” C R C H andbo o k ( 2009)
[2 ] T . N ak az aw a , T . Ig a r a s h i , T . Ts u r u , Y . K a ji , C om p. M at er . S c i . , 46( 2) : 36 7 - 375 ( 2009)
[3 ] B . D . W i r th e t a l . J. Nu c l . M a te r . , 244: 18 5: 1 9 4 ( 1997)
P o in t Def ect E n er g et ics
• W h ic h in te r stitia l is m o st sta b le ?
Courtesy of Elsevier, Inc., http://www.sciencedirect.com . Used with permission. Source: Wirth, B. D., et al . " Energetics of Formation and Migration of Self-interstitials and Self-interstitial Clusters in α-iron ." Journal of Nuclear Materials 244, no. 3 (1997): 185-94.
I n t e r s titia l
D um bbel l
B . D. W i r th e t a l . J. Nu cl . M a te r . , 244: 18 5 : 1 94 ( 1997)
P o in t Def ect E n er g et ics
• W h ic h in te r stitia l is m o st sta b le ?
Courtesy of Elsevier, Inc., http://www.sciencedirect.com . Used with permission. Source: Wirth, B. D., et al . " Energetics of Formation and Migration of Self-interstitials and Self-interstitial Clusters in α-iron ." Journal of Nuclear Materials 244, no. 3 (1997): 185-94.
I n t e r s titia l
D um bbel l
• D o e s it m a tte r ? B . D. W i r th e t a l . J. Nu cl . M a te r . , 244: 18 5 : 1 94 ( 1997)
Dir ect M easu r em en t o f
• Pos i t r on a nni hi l a t i on sp ectr o sco p y ( P A S )
• S hoot pos i t r ons i nt o m a te r ia l, th e y a n n ih ila te v e r y q u ic k ly w ith lo c a l el ect r o n s
• P os i t r ons c a n bi nd t o v acan c y , wh i ch h as a r ed u ced el ect r o n cl o u d
𝑒𝒆𝒆
𝐶
1𝑉
M ehr e r , p . 7 8
Me a n p o s itr o n lif e tim e in a lu m in u m
• L ast s l o n g er ! © Springer. All rights reserved. This content is excluded from our Creative Commons license. For more information,
1𝑉
Dir ect M easu r em en t o f 𝐶 𝑒𝒆𝒆
A. K h e lla f et al . , M at er . T r an s. 43( 2) : 18 6 ( 2002 )
• Q u e n c h in g re s i s t a n c e m e a s u re m e n ts
• Heat m at er i al t o h i g h t em p er at u r e, q u en ch , m easu r e r esi st i v i t y
• R e s is tiv ity d ir e c tly pr opor t i ona l t o va c a nc y co n cen t r at i o n
• M easu r ed at l i q u i d - He
t em p er at u r e R e s i s t i vi t y o f al u mi n u m v s . q u e n c h i n g t e mp e r a t u r e
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Dislo cat io n s ( 1D)
W as , p . 2 6 8
• E xt ra ha l f - pl a ne of a t om s s hove d i nt o t he l a t t i c e
• T w o ty p e s : E dge & S cr ew
[ Fig. 7.2 in p. 268 from Was, Gary S. Fundamentals of Radiation Materials Science , ISBN: 9783540494713 ] removed due to copyright restrictions.
Dislo cat io n s ( 1D)
W as , p . 2 6 8
• E xt ra ha l f - pl a ne of a t om s s hove d i nt o t he l a t t i c e
• T w o t ype s: E dge & S cr ew
[ Fig. 7. 3 in p. 268 from Was, Gary S. Fundamentals of Radiation Materials Science , ISBN: 9783540494713 ] removed due to copyright restrictions.
E d g e vs. S cr ew Dislo cat io n s
P as s c h i e r an d T r ou w , “M i c r ot e c t on i c s ,” p . 33 ( 2005)
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E d g e vs. S cr ew Dislo cat io n s
P as s c h i e r an d T r ou w , “M i c r ot e c t on i c s ,” p . 33 ( 2005)
• B u rg e rs v e c t o rs
• D islo c a t io n c o r e s
b s
b s
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The B ur ge r s V e c tor
• S t ar t at o n e at o m , m ak e a c i rc l e a round t he di sl oc a t i on c ore
• Th e Bu r g er s V ect o r is t he di re c t i on you m ove t o re a c h your st a rt i ng poi nt
• Ex am p l e: Ed g e di sl oc .
W a s , p . 275
D islo c
c o r
D islo c a t io n c o r e lin e
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Dislo cat io n G lid e
• M ove m e nt one pl a ne a t a t i m e a l ong t he s l i p d ir e c tio n
W as , p . 2 7 2
[ Fig. 7. 8 in p. 2 72 from Was, Gary S. Fundamentals of Radiation Materials Science , ISBN: 9783540494713 ] removed due to copyright restrictions.
E d g e Dislo cat io n G lid e
A video is played in class to demonstrate the concept.
Dislo cat io n G lid e
• M ove m e nt one pl a ne a t a t i m e a l ong t he s l i p d ir e c tio n
[ Fig. 7. 9 from Was, Gary S. Fundamentals of Radiation Materials Science.
ISBN: 9783540494713 ] removed due to copyright restrictions.
Dislo cat io n Clim b
• V a c a nc y di f fusi on t o di s l oc a t i on c ore
W as , p . 2 7 3
• V acan ci es ar e at t r act ed t o t h e co m p r essi v e st r ess at co r e
[ Fig. 7. 1 2 in p. 2 73 from Was, Gary S. Fundamentals of Radiation Materials Science , ISBN: 9783540494713 ] removed due to copyright restrictions.
Dislo cat io n Kin ks, Jo g s
A lle n , “ K in e tic s o f Ma t e ria ls , ” p . 1 1 6
• D i s l oc a t i ons p re fe re nt i a l l y m ove on s l i p syst e m s
• C er t ai n d i r ect i o ns o f easi er m ove m ent
• C l os e p acke d p l ane s sl i p i n cl os e pa cke d d i r ect i ons
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Dislo cat io n M o t io n
W as , p . 2 7 7
[ Fig. 7. 18 in p. 2 77 from Was, Gary S. Fundamentals of Radiation Materials Science , ISBN: 9783540494713 ] removed due to copyright restrictions.
G lissile vs. S essile S ect io n s
A lle n , “ K in e tic s o f Ma t e ria ls , ” p . 1 2 4
T w o edg e di sl o c a t i o ns m o v i ng t o w a r ds ea c h o t her f o r m a se ssile j og
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D i s l oc a ti on Loops
• Lo o p s h av e m i x ed ed g e/ s cr ew ch ar act er
• May b e ci r cular plane s of at om s b et w een t w o p l ane s
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D i s l oc a ti on Loop S our c e s
• C om e from se ss i l e s e c t i ons o f di sl oc a t i ons
O ld s t r a in d ir e c t io n
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Dislo cat io n V id eo s!
h t t p : / / w w w . n u m o d is . f r / t r id is / T E M / m e c h an is m s / m u lt ip lic a t io n . h t m l
D islo c a t io n so u r c e s in M o - 5N b
A video is played in class to demonstrate the concept.
Dislo cat io n V id eo s!
h t t p : / / w w w . n u m o d is . f r / t r id is / T E M / m e c h an is m s / m u lt ip lic a t io n . h t m l
A Fr a n k - R e a d S o u r c e in S ilic o n
A video is played in class to demonstrate the concept.
Dislo cat io n V id eo s!
h t t p : / / w w w . n u m o d is . f r / t r id is / T E M / m e c h an is m s / m u lt ip lic a t io n . h t m l
D islo c a t io n so u r c e in Ge a t hi g h t e m pe r a t u r e A video is played in class to demonstrate the concept.
Dislo cat io n V id eo s!
h t t p : / / w w w . n u m o d is . f r / t r id is / T E M / m e c h an is m s / m u lt ip lic a t io n . h t m l
D islo c a t io n so u r c e s a n d p ile u p in Ge A video is played in class to demonstrate the concept.
Dislo cat io n V id eo s!
h t t p : / / w w w . n u m o d is . f r / t r id is / T E M / m e c h an is m s / m u lt ip lic a t io n . h t m l
D islo c a t io n so u r c e s in S i A video is played in class to demonstrate the concept.
F o r ces Bet w een E d g e Dislo cat io n s
W a s , p . 289 - 290
• X & Y forc e s , no Z - forc e Pe a c h - K o hl e r E qua t i o n B ur g er s v ec t o r o f d is lo c a tio n ( 2 )
t r a nspo sed
L i ne v ec t o r o f
d is lo c a tio n ( 2 ) t r a nspo sed
F or c e v e c t or on d is lo c a tio n ( 2 )
S t r ess t enso r i nduc ed b y d is lo c a tio n ( 1 )
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All T o g et h er : L o o p s, M o vem en t , P ileu p
D isl o c a t io n s m o v in g & p il in g up i n I nc o ne l 617 (N i - ba s e d a l l o y) unde r in - si tu s t r a i ni ng i n t h e TE M
h t tp: / / y o utu.be / r - g e D w E8 Z5 Y
A video is played in class to demonstrate the concept.
G r ain Bo u n d ar ies ( 2D)
htt p : / / w w w - h r em. ms m. c a m. a c . u k / g a l l er y /
• R e gi ons of di f fe re nt o r ie n ta tio n
• May al so b e d i f f er en t c ry s ta l s tru c tu re
T E M i mag e o f a g r ai n b o u n d ar y i n p u r e Al
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G Bs can b e L in es o f Dislo cat io n s
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T i l t g r ai n b o u n d ar y i n Al
h t tp: / / w w w . tf .uni - k i e l .de / m a tw i s / a m a t / de f _ e n/ k a p_ 7/ ba c k bo ne / r 7_ 2_ 1.h t m l
This image is in the public domain. h t tp: / / m o i s e s pi ne da c a f .bl o g s po t.c o m /
T w in n in g
• A lte r n a te p la s tic d e f o r m a tio n m e c h a n ism
h t tp: / / m o i s e s pi ne da c a f .bl o g s po t.c o m / h t tp: / / dc g .m a t e r i a l s .dr e x e l .e du/ ? pa g e _ i d= 14# nuc l e a r
T w i n n i n g o b s e r v e d i n i r r ad i a t e d r ea c t o r pr essur e v essel s t eel
Courtesy of Dynamic Characterization Group, property of Drexel University. Used with permission.
h t tp: / / dc g .m a t e r i a l s .dr e x e l .e du/ ? pa g e _ i d= 14# nuc l e a r
T wi nni ng
Dif f e r e n tly o rie n t e d d is lo c a tio n s i nsi de/ o ut si de t w i n bo unda r y !
Courtesy of Dynamic Characterization Group, property of Drexel University. Used with permission.
In clu sio n s ( 3D)
• O t he r pha s e s t ra ppe d w ith in b a s e m a te r ia l
• Ex am p l es :
• S econda r y p ar t i cl e preci pit at es i n Z irc a loys
• C ar bide s i n s t eel s
• Y 2 O 3 pa r t i cl es i n O xide D i s pe r s i on S t r e ngt he ne d
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(O D S ) s te e ls S i ngl e c r y s ta l o f Mn S , spa c e gr o up Fm 3 � m , F C C c r y s t a l s tru c tu r e
em bedded i n A l ca t o r r ot or s t e e l
Co h er en t vs. In co h er en t
• W hi c h do y ou t hi nk w oul d be bet t e r a t s i nki ng defe c t s ? S t oppi ng di s l oc a t i ons ?
In c o h e r e n t i n c l u s i o n C o h e r e n t i n cl u s i o n
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S w it ch in g G ear s: S t r u ct u r al M at er ial P r o p er t ies
• G o a ls:
• U n d er st an d t r u e v s. en g i n eer i n g st r ess & st r ai n
• Q ua nt i f y a nd di f f e r e nt i a t e be t w e e n ha r dne s s , t oughne s s , s t r e ngt h, duc t i l i t y , s t i f f ne s s
• K now how t o m e a s ur e t he s e pr ope r t i e s
• R eso l v e st r esses o n t o sl i p sy st em s
• P r ed i ct t h e d i f f er en ces i n m ech an i cal r esp o n se b et w een s i ngl e , dua l , a nd pol yc r ys t a l l i ne m a t e r i a l s
Imag e s f r o m n o w o n ar e f r o m T . H . C o u r t n e y , M e c hani c al B e h a v i o r o f M a t e ri a l s unl ess o t her w i se no t ed
f e e l?
Reso lved Sh ear S t r ess
H o w m u c h sh e a r d o e s t h e slip s y s t e
• C onsi de r a s i ngl e c ryst a l ba r of FC C m a t e ri a l , t e ns i one d i n t he [ 001] di re c t i on:
m f e e l?
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Reso lved Sh ear S t r ess
h t tp : / / w w w . d o itp o m s . a c . u k/ tlp lib / s lip / p rin t a ll. p h p
• P r o ject f o r ce o n to t h e tilted p lan e c o n tain in g th e s lip sy stem ,
to g et
th e
str ess
𝐹
𝜎 𝑠𝑙 𝑖𝑝 = 𝐴
𝐹
= 𝐴 0 = 𝜎 c os 𝜃𝜃
𝑠 𝑙 𝑖𝑝
c os 𝜃𝜃
• A lso p ro j e c t s h ear d ir ectio n o f s lip
m o v em en t i n
𝜏 =
𝜎 c os 𝜆
Courtesy of University of Cambridge. Used with permission.
Reso lved Sh ear S t r ess
• T h e to ta l s h e a r s tr e s s b e c o m e s :
𝜎
𝜏 =
𝜎 cos 𝜆
cos 𝜃𝜃 =
𝑚
𝑚 =
1
cos 𝜆 cos 𝜃𝜃
Sc h mi d fa c t o r
• E f f e c tiv e ly r e d u c e s a p p lie s str e s s f e lt o n a s lip p la n e
Reso lved Sh ear S t r ess
• C onsi de r a s i ngl e c ryst a l ba r of FC C m a t e ri a l , t e ns i one d i n t he [ 001] di re c t i on:
H o w m uc h s he a r do e s t he s l i p s y s t e m f e e l ?
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E xam p les o f S h ear & S lip
• A l cat o r C - M od rot or s t e e l i n uni a xi a l t e ns i on:
Axis o f t e n sio n
Axis o f t e n sio n
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E vid en ce o f S lip S yst em s
h t tp : / / w w w . d o itp o m s . a c . u k/ tlp lib / s lip / p rin t a ll. p h p
Courtesy of University of Cambridge. Used with permission.
E vid en ce o f S lip S yst em s
h t t p : //w w w .d o i t p o ms .ac .u k /t l p l i b /mi l l e r _ i n d i c e s /p r i n t al l .p h p
Courtesy of University of Cambridge. Used with permission.
A s c an n i n g e l e c t r o n mi c r o g r ap h o f a s i n g l e c r y s t al o f c ad mi u m d e f o r mi n g b y d i s l o c a t i o n s l i p o n 1 0 0 p l an e s , f o r mi n g s t e p s o n t h e s u r f ac e
E vid en ce o f S lip S yst em s
N. Fr i e d man e t al . P h y s . R e v . L e tt . 109, 095507 ( 2012)
• N a nopi l l a r c om pr e s s i on t e s t s us i ng a di a m ond f l a t punc h
• C l ear 4 5 d eg r ee an g l es obs e r ve d
• S l i p sy st em s a c t i va t e d by s he ar
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E vid en ce o f S lip S yst em s
S. B r i n c k man n e t al . P h y s . R e v . L e tt . 100, 155502 ( 2008)
• N a nopi l l a r c om pr e s s i on t e s t s us i ng a di a m ond f l a t punc h
• C l ear 4 5 d eg r ee an g l es obs e r ve d
• S l i p sy st em s a c t i va t e d by s he ar
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Reso lved Sh ear S t r ess
• C onsi de r a s i ngl e c ryst a l ba r of SC m a t e ri a l , t e ns i one d i n t he [ 001] di re c t i on:
H o w m uc h s he a r do e s t he s l i p s y s t e m f e e l ?
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Reso lved Sh ear S t r ess
• C onsi de r a s i ngl e c ryst a l ba r of SC m a t e ri a l , t e ns i one d i n t he [ 001] di re c t i on:
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Reso lved Sh ear S t r ess
• C onsi de r a s i ngl e c ryst a l ba r of SC m a t e ri a l , t e ns i one d i n t he [ 0 1 1] di re c t i on:
m f e e l?
H o w m u c h sh e a r d o e s t h e slip s y s t e f e e l?
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W ill It S lip o r Br eak?
• Bal an ce b et w een t w o m ech an i s m s :
𝝉 𝑐 𝑟 𝑖𝑡 𝑖 𝑐 𝑎 𝑙 > 𝝈 𝑐𝑜 𝑠 𝝀𝝀 𝑐𝑜 𝑠 𝜽𝜽
v s.
𝝈 > 𝝈 𝑈 𝑇 𝑆
B o n d b r e ak i n g
Cr it ical Reso lved Sh ear S t r ess ( τ CRS S )
• S h e a r s tr e ss th a t is e n o u g h to g e t d is lo c a tio n s m ovi ng (pl a s t i c de form a t i on)
• Rel at ed t o th e y ie ld s t r e ss ( σ y ) , th e str e s s w h e r e p la s tic d e f o r m a tio n s ta r ts :
𝜎 𝑦
= 𝑚 𝜏 𝐶 𝑅 𝑆 𝑆
• NOT E : σ y ha s c rys t a l l ogra phi c
de pe nde nc e i n s i ngl e
c rys t a l s! W ha t a bout pol yc rys t a l s ?
τ CRS S
vs. T em p er at u r e
T he r m a l e ne r g y so lo w , t h a t sm a ll ba r r i e r s be c o m e in su r m o u n t a b le
C o mmo n l y c i t e d ma t e r i a l pr o pe r t y r e g i o n
D if f u sio n - e nha nc e d r e g i o n ( e a s i e r t o m ov e d islo c a t i o n s )
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Wha t H a ppe ns Whe n Dislo cat io n s G et S t u ck?
• C r o s s slip : sw itc h in g to o th e r slip p la n e s
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• R e s ol ve d s he a r st re ss m us t be hi gh e nough!
S t r ess vs. S t r ain
• St re ss: Forc e ove r a re a
• E ngi ne e ri n g st re ss : Forc e di vi de d by ori gi nal ar ea
• T r u e str e ss : Forc e di vi de d by ac t ual ar ea as i t
c hange s
𝜎 =
𝐹
𝐴 0
𝜎 𝑡
𝐹
=
𝐴 ( 𝑡 )
𝐹
=
𝐴 0
𝐴 0
𝐴 ( 𝑡 )
= 𝜎 𝐴 0
𝐴 ( 𝑡 )
• C onse rve
vol um e duri ng
s t re t c hi ng:
V 0 = V ( t )
S t r ess vs. S t r ain
𝐹
𝜎 =
𝐴 0
𝜎 𝑡
𝐹 𝐹
= =
𝐴 ( 𝑡 ) 𝐴 0
𝐴 0
𝐴 ( 𝑡 )
= 𝜎
𝐴 0
𝐴 ( 𝑡 )
𝑡
𝑡
• C onse rve
vol um e duri ng
s t re t c hi ng: V 0
= V ( t )
𝑉 = 𝐴 𝐿
= 𝑉
= 𝐴
𝐿
𝐴 ( 𝑡 )
𝑡
; =
𝐿 0
0 0 0
𝐴 0
𝐿 ( 𝑡 )
𝜎 𝑡
= 𝜎 𝐴 0
𝐴 ( 𝑡 )
= 𝜎
𝐿 ( 𝑇 )
𝐿 0
= 𝜎
𝐿 0
+ 𝛿𝛿 𝐿
= 𝜎
𝛿𝛿 𝐿
1 +
𝐿 0
𝐿 0
E ng i ne e r i n g s t r a i n ( ε )
T r u e vs. E n g in eer in g S t r ain
• E ngi ne e ri ng st ra i n ( ε ): 𝛿𝛿𝐿
𝐿 0
(from ori gi nal l e ngt h)
• T ru e st ra i n ( ε T ):
Inst a nt a ne ous
i nc re a s e
i n l e ngt h:
𝜀𝜀 𝑇
𝐿 ( 𝑡 )
= �
𝐿 0
𝑑 𝐿
𝐿 0 + 𝛿𝛿 𝐿
𝐿 0
𝐿
= ln 𝐿 ( 𝑡 )
− ln 𝐿 0
𝐿 𝑡
𝐿 0
= ln
𝜀𝜀 𝑇
= ln
= ln 1 + 𝜀𝜀
S t r ess- S t r ain Cu r ves
h t t p : / / k e y t o m e t a l s .c o m / p a g e .a s p x ?ID =C h e c k A r t i c l e & s i t e =k t s & N M=4 2
Courtesy of 2015 Key to Metals AG. Used with permission.
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S in g le, Du al, an d P o lycr yst als
D i s l oc a t i on pi l e up, pi nni ng
s l i p sy s te m
Pr im ar y
s l i p sy s te m
P r i m a r y s l i p s y s t e m
S e c o nda r y s l i p s y s t e m
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M easu r in g S t r ess -S tr a i n
J . M . Ger e, “M ec ha ni c s o f M a t er i a l s , ” pp. 1 2 , 1 4
U n ia x ial t e n s ile t e s t e r , w it h U n ia x ial c o m p r e s s io n t e s t e r , w it h e x t e n so me t e r f o r me a su r i n g s tr a i n e x t e n so me t e r a n d d i a me t e r me a su r e me n t
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Dislo cat io n s an d Def ect s
E . B it z ek a nd P. G u m bs ch , Dy na m i c a s pec t s of d i s l oc a t i on m ot i on : a t om i s t i c s i m ul a t i o ns , M a t er i a l s S ci ence a nd E ng i neer i ng A , 4 0 0 - 401 ( 2005) , pp. 4 0 - 44
• D e fe c t s c a n sl ow dow n (pi n) di sl oc a t i on s
A video is played in class to demonstrate the concept.
Review in g M at er ial P r o p er t ies
• Fi nd t he fol l ow i ng on a st re s s - stra i n di a gra m :
• T oughne s s
• St re ngt h
• D u c tility
• S tif f n e ss
• Pe rha ps de fi ne t he m fi rs t …
Y oung's M odul us (S ti ffne s s , E )
Measu r es el ast i c de f or m a t i on vs . s t r e s s
So u r ce: W ik im ed i a C o m m o n s
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T oughne s s ( G c )
● M eas u r es t h e en er g y i t t ak es t o s ep ar at e a m at er i al
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So u r ce: in v en to r . g r an tad es ig n . co m excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .
M at er ial P r o p er t ies o n S t r ess- S t r ain Diag r am
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Courtesy of Ben Best .Used with permission.
Courtesy of Ben Best . Used with permission.
h t t p : / / w w w .b e n b e s t .c o m / c r y o n i c s / l e s s o n s .h t m l
M at er ials Select io n Ch ar t s
© source unknown . All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .
h ttp ://w w w - g .e ng .c a m . a c .uk/ 125/ now / m f s / t ut o r i a l / non_ I E / c ha r t s .ht m l
F ailu r e Cr it er ia – Cr ack P r opa ga ti on
R esi st an ce t o cr ack pr opa ga t i on
-Y 1 , Y 2 ar e g eom et r i c f act ors ne ar 1
-σ * , F * ar e cr i t i ca l st r ess and f orce, r espe ct i ve l y
So u r ce: in v en to r . g r an tad es ig n . co m © source unknown . All rights reserved. This content is
excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .
F r act u r e T o u g h n ess – Real D a ta fr om A l c a tor C -M od
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E n g in e e r in g M a t e r ia ls Sc ie n c e , Mi l t on O hri ng , Ch . 10
F ailu r e Cr it er ia – F at ig u e
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Rep eat ed ap p l i cat i o n of str e s s c a n cau s e c ra c ks t o grow
Induc e d by vi bra t i ons, m ech an i cal l o ad i n g
T e llta le “ f a tig u e str ia tio n s ”
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair- use/ . W he r e do the s e
S our c e : w w w .s v .vt .e du/ c l a s s e s / M S E 2094_N ot e B ook/ 97C l a s s P r oj / a na l / ke l l y / f a t i g u e .ht m l c om e fr om ?
F ailu r e Cr it er ia – F at ig u e
St re ss (S) vs . num be r of c yc l e s ( N)
L o w e r lim it o f s tr e s s (w he re N is i nfi ni t e ) i s t h e “ s af e zo n e ”
W hy do the se
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S our c e : w w w .nd e - e d.or g / E duc a t i onR e s our c e s / C om m uni t y C ol l e ge / M a t e r i a l s / M e c h a ni c a l / S - N F at i g u e. h t m
F at ig u e St r iat io n s in Alcat o r C- M o d Ro t o r
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F ailu r e M ech an ism s in T en sio n
1. 1.
2. 2.
3. 3.
4.
4.
1 1. B r i t tl e f r a c tu r e
2 2 . . S in g le c r y s t a l slip b a n d s
3 3 . . I de a l duc t i l e f r a c t ur e ( f ul l
4 e l o ng a t i o n)
4. R e a lis t ic c u p - a n d - c o n e
f r a c tu r e
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S t a g e s o f c u p - a n d - c o n e f r a c tu r e f o r ma ti o n i n d u c t ile m a t e r ia ls
D ef ect s , S l i de 81
22. 14 : N uc l e a r M a t e ri a l s E n g in e e r in g M a t e r ia ls Sc ie n c e , Mi lt on O hri ng , Ch . 10
E xam p les o f Cu p - an d- Co n e F r act u r e in Alcat o r C- M o d
Br it t le & Du ct ile F r act u r e, S id e b y S id e
Mn S Pr e c ip it a t e
D u c t ile
B r i t tl e
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)
Cr eep – P last ic Def o r m at io n Belo w Y ield S t r ess
• I m a g in e s tr e tc h in g a b a r o f m e ta l w ith in th e e la stic re gi on
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h t t p : / / w w w .n a t i o n a l b o a r d .o r g / In d e x .a s p x ? p a g e ID =1 8 1
Cr eep – S t r ess vs. T im e
J . M . Ger e, “M ec ha ni c s o f M a t er i a l s , ” pp. 2 2
• St re ss inc re a se d e la stic a lly to σ 0
• H e l d for l ong t i m e
• S tr e s s a t c o n sta n t s t r ai n d ecr eas es d u e to cr eep
© CL Engineering. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .
Cr eep M ech an ism s
This image is in the public domain.
So u r ce: W ik im ed i a C o m m o n s
Pl a s t i c fl ow unde r c o n s ta n t s tr e ss
T e ns i on, gra vi t y . . .
H a ppe ns w e l l be l ow y ie ld str e s s
M u ltip le m o d e s (C obl e , N a ba rro - He r r i n g ...)
Cr eep M ech an ism s
• D islo c a tio n c lim b
• F ol l ow s pow e r l a w
• N a ba rro - H e rri ng (dif fusi ona l )
• V acanc y m ove m ent
• C obl e
• G r a i n bounda r y m ove m e nt
© Elsevier, Inc . All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .
E n g in e e r in g M a t e r ia ls Sc ie n c e , Mi l t on O hri ng , Ch . 10
F ailu r e Cr it er io n – Cr eep Li fe ti me
C re e p rupture lif e tim e c a n lim it use ful ne s s of pa rt
E x a m p le : A llo y s H T 9, T 91 i n hi gh t em p er at u r e s er v i ce c ondi t i ons
Courtesy of Elsevier, Inc., http://www.sciencedirect.com . Used with permission. Source: Klueh, R. L., and A. T. Nelson. " Ferritic / Martensitic Steels for Next-generation Reactors ." Journal of Nuclear Materials 371, no. 1-3 (2007): 37-52.
S our c e : R .L . K l ue h, A .T . N e l s on. J . N uc l . M at e r . , 371( 1- 3) : 37- 52 ( 2007) .
Cr eep F ailu r e b y T im e at T em p er at u r e an d Pr essu r e
© Terry Craig Totemeier. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .
Cr eep f a i l ur e o f a l l o y T9 1 due t o i m pr o per hea t t r ea t m e n t , hea t e d a bo v e A1 t em per a t ur e . I n T . T o t enm e i e r , “E x per i ence w i t h G r a de 9 1 S t eel i n t he F o s s i l
Po w e r I ndus t r y . ” P r es en t a t i o n, AL S T O M , F eb. 2 0 0 9 .
MIT OpenCourseWare http://ocw.mit.edu
22.14 Materials in Nuclear Engineering
Spring 2015
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