An analysis is presented of elastic stress and buckling behavior due to thermal stresses in silicon ribbon. Thermal profiles for reducing stresses and improving flatness in wide ribbon are discussed

Dillon, O. W., Jr.

English

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STRESS AND BUCKLING ANALYSIS 
UNIVERSITY OF KENTUCKY 
0. Dillon 
TECHNOLOOY 
. 
STRESS AilD BUCKLIIIG ANALYSIS 
APPROACH 
MODEL PATERIAL BEHAVIOR 
FMDEL BUCKLIIIG DUE TO THEMIAL STRESSES 
CONTRACTOR 
UMIVERS IT$ OF XEFITUCKY 
GOALS 
PROVIDE GUIilCiilCE BASED Oil ANALYSIS 
FOR THERi4AL PROFILES FOR REDUCING 
STRESSES AilD IllPROVING FLATAESS I N  
WIDE RIBBON 
HAVE RESULTS BE APPLICABLE TO ALL 
SHEET GRO\ITH SYSTEIIS , 
REPORT DATE 
STATUS 
E L A S i l C  STRESS A;.ID BUCKLlllG ANALYSIS 
COilPLETED FOR COilSTAI4T !lATERIAL PRO- 
PERT I ES . 
CRITICAL SHEET TIjICKIIESS VS. SHEET 
WIDE COMPARED FOR FOUR THENIAL PRO- 
F I I.ES . 
RESULTS ARE REASONABLY COI6 I STEIIT 
WITH EXPEPIIIENT. 
SURVEY OF TIIE ;iECHAIIICAL PROPERTIES 
i F  S lL lCOl l  
PRE-BGCXLCI) ,STCESStS l il PLASTIC RAIlGE 
https://ntrs.nasa.gov/search.jsp?R=19850024126 2020-03-22T19:48:32+00:00Z
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-iPt 
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Calculated Buckled Web Shape 
I 
I 
: . I  SILICON SHEET 
Sumino 
Stress vs Strain for Si (Tc;.nperature i l l  O C )  
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Stress vs Strain for Si (Strain Rate 1 Isec) 
O R I M A L  PA& ' :% 
OF POOR QUALITY 

. . 
. . 
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APPENDIX A 
The equat ions governing t he  s t m s  i n  a  r ibbon cons i s t  o f  those h i c h  
r e f l e c t  t h a t  t he  f m t e r i a l  f s  i n  e q u i l i b r i w .  t h a t  the &*onnations a r t  co:- 
p a t ~ b l e  and t h a t  there  i s  a  n a t e r i a l  c o n s t i t u t ~ v e  r e l a t i o n  h s u n ~ n ;  tha. 
! a )  one can neg lec t  the three stresses :lz. (b) 11at the mater ia l  IS  e la:- ,  - d
and t l ia t  Y~un:'s IWddlu5 and Poissons r ~ t i o  are constant:Zhe q o v e r r i ~ :  CO.;:.;. I -I 
Cons t i t u t i ve  r e l a t i o n s  
. , IIXx - v 
=xx E € ayy + aT 
Equations (A-1) combine t o  y i e l d  
I : h i l e  Eqs. (A-2)  t'Ir0llgh ( A - 4 )  y i e l d  
2  a o 2 a a,, a2a 2 2 
-u= ---+-+- &LJ
a A * ax  ;y ay axZ  
Pre-Buckled Stresses 
E l a s t i c  
-
, J . w  r,r 7 .  I:. 
.I--" "- 
, .!,b ! !. , .-.-- . - --z-..: 1. -.-. .- , . . 
kcond order central differences equivr lmts o f  these rpurtlmS a m :  
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Ua r s s u w  t h  S u l n o  ndel of  v l r c o p l r s t l c  k h r v l o r .  1 . r .  
.'JZ > OJN, 
DISLOCATION LKNSITY CHANCiS!! 
NEW: - SOME B U I S  FOR A 'SHAPE" FACTOR 
I- VS. 
K1 
K~ + m 
'0 1 M T E R I A L  "CONSTANTS" 
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The c o m p a t i b i l i t y  equat ion  i s  
Eqs ( 2 )  and ( 3 ) .  t o  y i e l d  
PULL RATE 
:. SOLVE VIA INTERATICN!! !! 
"0" = ELASTIC 
0 
I 
OUTPUT STRESSES (x ,y )  
STRAIN RATES (x,y)  
VERY NEW -5 ODISLOCATIOI( DENSITY (any) 
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le' x x  = . 1 1 4 7 x 1 0 ~ p a s c a 1 s  
nldx T y p i c a l  
oPC = . I 0 8 6  x 10' p a s c a l s  
XX,"ax 
2 Nfinal = 12/cm a t  o u t e r  edge 
2 6/cm a t  c e n t e r  
EVERY PROBLEM DIFFERENT 
; : sec" 
;PL : 10-9 , sec-l 
- 1 
- sec once i n  a w h i l e  
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1 . I ( I i 1 1 ' 1 ; ,  I X i [ , ~ ~ i  ..... L..!.. I .:..-I 

SILICON SI-JEET 
NOTE 1 : ELASTIC REGlON HO PROflLtW 
NOTE 2: WES NOT CMVERQ 
MIINS ipL s l o 3  SK-' 
50 2 Nm - I 0  Icn 
L 0.5 + 10. CONVERGES WITH I .r ;  TEW PROFlLr 
FOR STRESSES S L  ELASTIC 
F I X  RESIDUAL STRESSES 
PLASTICIT: I S  M L L  W T  I S  JUST AS BAD AS A LOT. 
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Problems and Concerns 
1. No a t  WELT ILTERFACE (PO) 
2. VALIDITY OF CONSTRANTS FOR SUHldO flODEL FOR RIFBON 
3. SHOULD WE THINK "TWIHS"? 
4. SHOULD UE UORK OTHER PROFILES? 
5. ROLE OF LHANGING "1" 


Stress and buckling analysis

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