Strengthening and fracture mechanisms in composite material

Tetelman, A. S.

English

NASA Technical Reports Server

MECHANISMS OF STRENGTHENING AND 
FRACTURE I N  COMPOSITE MATERIALS 
F i f t h  Progress  Report  t o  NASA 
June  1, 1966 t o  November 30, 1966 
C o n t r a c t  No. NSG-622 
II 
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A s s o c i a t e  P r o f e s s o r  
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Department o f  Materials S c i e n c e  
S tanford  U n i v e r s i t y  
S t a n f o r d ,  C a l i f o r n i a  
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A . .  
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I 
I 
INTRODUCTION 
This r e p o r t  d e s c r i b e s  r e sea rch  a c t i v i t i e s  t h a t  were performed 
dur ing  the  f i f t h  phase o f  a program designed t o  i n v e s t i g a t e  t h e  mechanisms 
o f  s t r zng then ing  and f r a c t u r e  of  composite materiais.  A s  mentioned i n  
t h e  previous progress  r e p o r t s ,  (subsequent ly  r e f e r r e d  t o  by PR number), 
f i v e  d i f f e r e n t  programs a r e  being c a r r i e d  o u t .  These are d iscussed  
s e p a r a t e l y  i n  t h e  fol lowing paragraphs.  
I .  The E f f e c t  o f  D r i l l e d  Holes on t h e  Notch Toughness 
of  I ron  Base Alloys.  (With C. A.. Rau, Graduate S tuden t ) .  
Two 0.0292" diameter  h o l e s ,  d r i l l e d  appropr i a t e ly ,  have been 
shown t o  inc rease  the  notch  toughness o f  s e v e r a l  i r o n  base  a l l o y s .  
Increased  load c a r r y  capac i ty  and reduced d u c t i l e  t o  b r i t t l e  t r a n s i t i o n  
temperatures  have be.en observed (PR 4 and t e c h n i c a l  r e p o r t  No. 1") i n  
slow-bend, t ens ion ,  and instrumented Charpy tes ts .  Although t h e  e l a s t i c  
s t ress  concen t r a t ion  f a c t o r  of the  notch is  reduced only  s l i g h t l y ,  ho les  
cause  a l o c a l  r e d i s t r i b u t i o n  of  p l a s t i c  s t r a i n  and corresponding 
r educ t ion  i n  p l a s t i c  s t r e s s  i n t e n s i f i c a t i o n .  Although a genera l  geometric 
e f f e c t ,  t he  magnitude o f  improvement from h o l e  d r i l l i n g  v a r i e s  wi th  
m i c r o s t r u c t u r e  (PR 4 ) .  
During t h e  p a s t  s i x  months, w e  have: (1) employed t h e  instrumented 
Charpy t e s t  t o  s tudy  t h e  e f f e c t  of more complex geometries on t h e  improvement 
o f  no tch  toughness.  It has been shown t h a t  i n  mild s tee l  (a)  saw c u t s  
between each hole  
t r a n s i t i o n  curve but  cause a s l i g h t l y  lower u l t i m a t e  load and a markedly 
lower genera l  y i e l d  load compared wi th  t h e  usua l  d r i l l e d  sample .  
and t h e  riotch s i d e  have no e f f e c t  on t h e  Charpy energy 
-1 - 
(b) Two l a r g e r  ho les  (0.0465", 0.0595" d iameter ,  8 = 75") 
reduce  t h e  Charpy t r a n s i t i o n  temperature T 15 percent  more than t h e  two 
0.0292" ho le s .  The load car ry ing  capac i ty  i s  increased only  s l i g h t l y  
a t  temperatures  below T and is  markedly decreased above T The gene ra l  
y i e l d  load also decreases  w i t h  inc reas ing  h o l e  s i z e .  
D 
D D' 
(c) Four 0.0292" holes  loca t ed  a s  shown i n  F igure  1 produce 
mixed e f f e c t s .  The load car ry ing  capac i ty  o f  t h e  ba r  i s  increased  a t  
low temperatures  bu t  reduced a t  high temperatures .  The genera l  y i e l d  
load is lower than  t h a t  o f  t he  two h o l e  samples whi le  t he - impac t  energy 
is modified as shown i n  F igure  1. 
(d) "S t r e s s - r e l i ev ing"  t h e  Charpy notch by machining an 
a d d i t i o n a l  Charpy notch  on each s i d e  o f  it improves t h e  notch  toughness.  
However, only 80 percent  o f  the r educ t ion  i n  T obtained w i t h  two ho le s  
i s  obtained wi th  t h e  notches,  and t h e  genera l  y i e l d  load i s  much lower 
i n  t h e  three-notch  specimen. 
D 
(e) Two 0,0292" holes  improve t h e  notch toughness of  sha rp ly  
notched samples (V-notch, p = 0.001"). The t r a n s i t i o n  temperature  i s  
cons ide rab ly  lowered, and a d e f i n i t e  bimodal behavior  i s  observed a f t e r  
gene ra l  y i e l d i n g .  I n  c o n t r a s t  to  t h e  Charpy notch ,  ho le s  have no 
measurable e f f e c t  on load car ry ing  c a p a c i t y  when f a i l u r e  occurs  p r i o r  
t o  50 percent  o f  gene ra l  y i e l d .  Above t h i s  l oad ,  d r i l l e d  samples  are as  
much as 100 percent  s t r o n g e r .  
( 2 ) .  Employed d i s l o c a t i o n  e t c h - p i t t i n g  t o  observe t h e  r e d i s -  
t r i b u t i o n  o f  l q c a l  s t r a i n  caused by four  holes  ( f i g u r e  1) i n  Charpy 
specimens loaded t o  var ious  f r a c t i o n s  of  genera l  y i e l d .  Comparison wi th  
prev ious  r e su l t s  f o r  two holes  is c o n s i s t e n t  w i th  t h e  observed r e l a t i v e  
-2 - 
. .  
TEST TEMPERATURE ("C 1 
Figure  1 The e f f e c t  of t w o  and fou r  ho le s  on t h e  Charpy impact t r a n s i t i o n  
p r o p e r t i e s  of m i l d  s t e e l .  
. 
. .  
improvements i n  f r a c t u r e  p r o p e r t i e s  a 
( 3 ) .  Determined t h e  e f f e c t  o f  specimen th ickness  (p lane  s t r a i n  
t o  p lane  stress) on t h e  improved notch-toughness of  d r i l l e d  Charpy samples. 
Instrumented Charpy t r a n s i t i o n  curves have been obta ined  f o r  Fe-3% S i  
samples a t  0.1", 0.2", and s tandard th i ckness  ( 0 . 3 9 4 " ) .  The shape of  
the t r a n s i t i o n  curve as w e l l  as the  t r a n s i t i o n  temperature  o f  s tandard  
specimens vary  cons iderably  with th i ckness  , but  f o r  each th i ckness  t h e  
same c h a r a c t e r i s t i c  improvements observed i n  t h e  s tandard  samples were 
no ted . 
( 4 ) .  Determined t h a t  t he  d r i l l i n g  s t r a i n s  produced by 
in t roduc ing  t h e  holes  a r e  not an important  f a c t o r  i n  ob ta in ing  the  
observed improvement. 
11. F r a c t u r e  Mechanisms i n  Quenched and Tempered S t e e l s .  
(with Dare1 Hodgson, Graduate Student)  
The use of  sphero id ized ,  hypo-eutectoid s t e e l s  i n  t h e  s tudy  
o f  d i s p e r s i o n  s t r eng then ing  is  d e s i r a b l e  f o r  s e v e r a l  reasons .  The 
cemen t i t e  (Fe C) p a r t i c l e s  formed by quenching and tempering p l a i n  
carbon s teels  a r e  nea r ly  i d e a l  i n  shape and d i s t r i b u t i o n .  The amount 
o f  t h i s  hard ,  d i spe r sed  phase and t h e  s i z e  of  t h e  p a r t i c l e s  may be 
changed e a s i l y  by using a l l o y s  of va r ious  carbon con ten t s  and by vary ing  
t h e  anneal ing temperature  a Yield deformation and f r a c t u r e  p r o p e r t i e s  o f  
t h e  i r o n  matrix a r e  w e l l  known, and t h e  d u c t i l e - b r i t t l e  t r a n s i t i o n  
al lows t e s t i n g  of  t h e  d i spe r s ions  when t h e  matrix a c t s  i n  e i t h e r  a d u c t i l e  
o r  b r i t t l e  manner. 
3 
Slow-bend Charpy specimens have been machined from seven a l l o y s  
o f  var ious  carbon con ten t s .  Curves of  y i e l d  load ,  f r a c t u r e  load and 
-3 - 
. 
. .  
p l a s t i c  bend angle  as a func t ion  o f  temperature  are being obtained f o r  
each a l l o y .  This i s  done f o r  both t h e  l a r g e s t  and t h e  smallest p a r t i c l e  
s i z e  o b t a i n a b l e  wi th  each a l l o y .  The major p o r t i o n  of t h i s  t e s t i n g  i s  
completed.  It was found i n  one o f  t h e  a l l o y s  t h a t  dec reas ing  t h e  p a r t i c l e  
s i z e  r a i s e d  t h e  y i e l d  stress from 53,000 p s i  t o  122,000 p s i  whi le  lowering 
t h e  n i l .  d u c t i l i t y  t r a n s i t i o n  by 100OC. 
T e n s i l e  specimens o f  each a l l o y  are a l s o  being t e s t e d .  These 
specimens have p a r t i c l e  s i z e s  corresponding t o  the  slow-bend specimens. 
T e n s i l e  y i e l d  s t r e n g t h ,  work hardening p r o p e r t i e s  and t e n s i l e  f r a c t u r e  
s t r e n g t h  are thus obtained as a func t ion  o f  temperature  f o r  each d i s p e r s i o n  
i n v e s t i g a t e d  . 
Upon completion of the mechanical t e s t i n g ,  r e p l i c a  e l e c t r o n  
microscopy w i l l  be  used t o  measure  average dimple s i z e  and dimple depth  
when t h e  a l l o y s  f r a c t u r e  i n  a f ibrous  manner. Techniques f o r  t h i s  have 
a l r e a d y  been s t u d i e d ,  
f u n c t i o n  of s t ress  and s t r a i n  for each d i s p e r s i o n  w i l l  a l s o  b e  s t u d i e d .  
The number of  cracked ca rb ide  p a r t i c l e s  as a 
It i s  hoped t h a t  time w i l l  al low a s tudy  o f  t h e  d i s p e r s i o n s  
us ing  t ransmiss ion  e l e c t r o n  microscopy. This w i l l  determine t h e  types  
o f  d i s l o c a t i o n  a r r ays  (p i le -ups ,  e t c  .) formed a t  each t e s t  temperature  
and w i l l  a l low comparison wi th  the  c a l c u l a t i o n s  mentioned elsewhere i n  
t h i s  r e p o r t .  
111. S t reng th  and Frac ture  o f  Tic-Mi-Mo Cermets. 
(with F. Darwish, Graduate Student)  
The purpose o f  t h i s  work i s  t o  e v a l u a t e  t h e  e l a s t i c  p r o p e r t i e s ,  
s t r e n g t h  l e v e l s ,  and f r a c t u r e  mechanisms i n  Tic-Ni-Mo cermets .  During 
t h e  l a s t  per iod t h e  fol lowing progress  has been made. Transverse  r u p t u r e  
-4 - 
. -  
f 
s t r e n g t h s  o f  two a l l o y s ,  whose volume f r a c t i o n s  (of hard phase) are 0.5 
and 0.73,  have been determined.  
ob ta ined  f o r  t h e  l a r g e  volume f r a c t i o n  a l l o y ;  i t  appears  t h a t  t h e  
c o n t i g u i t y  of  t h e  hard pahse i s  t h e  important  f a c t o r  i n  c o n t r o l l i n g  t h e  
s t r e n g t h  o f  t h e  composite. 
A s t r e n g t h  l e v e l  o f  300,000 p s i  was 
T e n s i l e  specimens a r e  being prepared by g r ind ing  t h e  s i n t e r e d  
compacts t o  requi red  shape and dimensions.  For t h i s  purpose a set  o f  
diamond t e n s i l e  g r i p s  ( f o r  holding t h e  t e n s i l e  specimens i n  t h e  I n s t r o n )  
have been made i n  a way t o  in su re  good alignment.  
specimen wi th  t h e  p u l l  rods would lead  t o  premature f a i l u r e  a t  s t ress  
l e v e l s  much l e s s  than  t h e  ac tua l  s t r e n g t h  o f  t h e  specimen. Cur ren t ly ,  
t h e  s t r e n g t h  i n  t ens ion  o f  composites w i t h  d i f f e r e n t  composition and 
p a r t i c l e  s i z e  i s  be ing  determined. Mic ros t r a in  measurements on the  
t e n s i l e  specimens t o  eva lua te  t h e i r  e l a s t i c  p r o p e r t i e s  ( E ,  p ropor t iona l  
l i m i t ,  . . . etc) t o  determine t h e  microcrack d e n s i t y  as func t ion  o f  
t h e  m i c r o s t r a i n ,  and t o  determine t h e  f r a c t u r e  mechanism w i l l  be done 
s h o r t l y .  
Misalignment o f  t h e  
I V .  Continuously Di s t r ibu ted  Dis loca t ions  i n  Two Phase Systems. 
(with D .  Ba rne t t ,  Graduate Student)  
Four problems involving stress concen t r a t ions  i n  two phase 
composite m a t e r i a l s  have been completely inves t iga t edus ing  t h e  method 
o f  cont inuously d i s t r i b u t e d  d i s l o c a t i o n s .  Closed form express ions  have 
been obtained f o r  t h e  stress f i e l d s  a s soc ia t ed  wi th :  
(1) a screw d i s l o c a t i o n  p i l e u p  a t  a r i g i d  c i r c u l a r  i n c l u s i o n .  
(2) a screw d i s l o c a t i o n  p i l e u p  a t  a ha l f -p l ane  o f  f i n i t e  
r i g i d i t y  
-5- 
. 
, .  
3 .  A screw d i s l o c a t i o n  p i l e u p  a t  a c i r c u l a r  i n c l u s i o n  o f  
f i n i t e  r i g i d i t y .  
4 .  An i n f i n i t e  sequence o f  screw p i l eups  on p a r a l l e l  s l i p  
planes a g a i n s t  a ha l f -p l ane  o f  f i n i t e  r i g i d i t y  (a model f o r  
work-hardening e f f e c t s ) .  
The e f f e c t  o f  t h e  f i n i t e  s i z e  and r i g i d i t y  o f  a hard second 
phase ahead o f  a p i l e u p  is t o  lower t h e  l o c a l  stresses by a f a c t o r  o f  
3 t o  6 from t h e  s t r e s s e s  pred ic ted  by homogeneous e l a s t i c i t y  theo ry .  A 
s imple  a n a l y s i s  i s  then appl ied  t o  p r e d i c t  t h e  p r o b a b i l i t y  o f  r e l i e v i n g  
t h e  l o c a l  stresses by d i s l o c a t i o n  c r o s s - s l i p  around t h e  i n c l u s i o n  as a 
func t ion  of  i n c l u s i o n  s i z e  and r i g i d i t y .  A more complete r e l a x a t i o n  
a n a l y s i s  r e q u i r e s  : 
(1) experimental  d a t a  on t h e  func t iona l  dependence o f  s l i p  
l i n e  l eng th  upon t h e  d i s t r i b u t i o n  o f  second phases p r e s e n t ,  
and 
(2) a s t a t i s t i c a l  study of  t h e  d i s t r i b u t i o n  of second phases 
p re sen t .  
V. E l a s t i c - P l a s t i c  Cracks in Two Phase Systems. 
(wi th  T .  Chou, Graduate Student)  
A t h e o r e t i c a l  approach has been used t o  i n v e s t i g a t e  t h e  behavior  
o f  t h e  e l a s t i c - p l a s t i c  c r ack  i n  a two phase system. The s i g n i f i c a n c e  
of t h i s  problem l ies  i n  determining c r i t e r i a  f o r  c rack  propagat ion  i n  
f i b e r  composites.  
A model o f  a shear  crack i n  a homogeneous mater ia l ,  o r i g i n a l l y  
suggested by B i lby ,  C o t t r e l l  and Swiden, i s  adopted i n  t h e  i n v e s t i g a t i o n .  
The spread o f  t h e  p l a s t i c  region has been c a l c u l a t e d  f o r  d i f f e r e n t  c r ack  
-6 - 
p o s i t i o n s  and arrangements o f  t h e  mate . r ia ls  . 
To d a t e  w e  have solved t h e  cases  o f  an e l a s t i c  c r ack  a t  a 
c e r t a i n  d i s t a n c e  from a two phase boundary and an e l a s t i c - p l a s t i c  c r ack  
w i t h  t h e  p l a s t i c  reg ion  o r  crack t i p  connected t o  t h e  two phase boundary. 
Owing t o  t h e  l imi t ed  method of s o l u t i o n s  i n  t h e  f i e l d  o f  s i n g u l a r  
i n t e g r a l  .equations and the  varying boundary condi t ions  t h a t  we have 
encountered i n  these  problems, an approach l ead ing  t o  a genera l  s o l u t i o n  
needs f u r t h e r  cons ide ra t ions .  
We b e l i e v e  t h a t  a general  s o l u t i o n  f o r  t h i s  problem may be 
obta ined  by employing t h e  numerical s o l u t i o n  of  s i n g u l a r  i n t e g r a l  
equa t ions .  Meanwhile, a t tempts  w i l l  a l s o  be made t o  o b t a i n  t h e  c losed  
form s o l u t i o n s  by cons ider ing  t h e  minimum energy a s soc ia t ed  wi th  t h e  
c racks  , namely, us ing  t h e  v a r i a t i o n  p r i n c i p l e  approach. 
- 7 -  


Mechanisms of Strengthening and Fracture in Composite Materials Fifth Progress Report, Jun. 1 - Nov. 30, 1966

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