17 The Influence of Vacuole Formation and Growth on the
Durability of Macromolecular Materials Downloaded from pubs.acs.org by YORK UNIV on 12/12/18. For personal use only.
Mechanical Behavior of Polymers R. J. FARRIS, R. FALABELLA, and Y. D. TSAI Polymer Science and Engineering Department, University of Massachusetts, Amherst, MA 01003 The mechanical behavior o f phase separated polymer blends and composites i s complicated by many factors of which the formation of crazes and vacuoles appears to be the dominant factor governing the stress-strain response (1-10). Crazes and vacuoles are the result o f strong local variations i n stress and strain a t the microstructural l e v e l . When the material i s subjected to high loads, vacuoles or crazes form i n the high stress regions of the microstructure and upon doing so greatly relieve the local multiaxial state of stress. In systems where these crazes cannot readily propagate, crazing will occur throughout the microstructure. Generally speaking the onset of microstructural crazing causes a volume dilatation, a loss i n modulus reinforcement, and an i r r e v e r s i b l e degradation o f the microstructure due to mechanical loads (1,2,6,7). It has been generally concluded that the mechanisms o f craze formation and growth are the mechanisms which distinguish the energy absorption c a p a b i l i t i e s of phase separated polymeric systems. Since most very high impact polymers are o f the crazing variety, there must be some truth to these arguments. I t is important to note however that over a decade ago the same reasoning was being put forth with regard to the mechanical behavior o f very highly filled elastomers. I t was erroneously concluded that because o f the large amounts o f near rigid particulate filler that these systems contained, vacuole formation and growth was to be expected and was i n fact the mechanism that permitted these systems to exhibit high elongations. Years l a t e r , when experiments were conducted under high superimposed pressure (1,2), it was found that pressure greatly suppressed vacuole formation and growth and generally resulted i n a marked improvement i n all mechanical prope r t i e s , especially the stress and energy absorption characteristics. Interestingly, i n the range o f s t r a i n before vacuole format i o n , pressure had no influence on the mechanical properties. The main purpose o f this paper is to demonstrate the s t r i k i n g s i m i l a r i t y between the behavior o f particulate filled polymers and phase separated polymers. The changes i n mechanical proper0-8412-0485-3/79/47-095-233$05.00/0 © 1979 American Chemical Society
234
DURABILITY OF MACROMOLECULAR MATERIALS
t i e s o f these m a t e r i a l s with deformation i s almost t o t a l l y dependent upon the vacuole formation process and the f a c t o r s cont r o l l i n g t h i s process a r e not t h a t well understood. The i n t e r e s t ing c o n c l u s i o n one can draw from the experiences o f r e s e a r c h e r s who work with h i g h l y f i l l e d polymers i s t h a t i f c r a z e formation c o u l d be suppressed, then the mechanical p r o p e r t i e s o f high impact polymers c o u l d be improved. T h i s o b s e r v a t i o n i s c o n t r a r y to the thoughts o f many i n the polymer community who b e l i e v e t h a t c r a z e formation and growth i s one o f the main mechanisms l e a d i n g to very high impact c h a r a c t e r i s t i c s . Another i n t e r e s t i n g o b s e r v a t i o n i s t h a t many thermal p l a s t i c s t h a t have been t e s t e d i n a u n i a x i a l t e n s i o n mode i n our l a b o r a t o r i e s e x h i b i t negative volume changes i n the s t r a i n r e g i o n bef o r e y i e l d . Others before have observed the same o r e q u a l l y conf u s i n g r e s u l t s and many r e s e a r c h e r s d i s m i s s such o b s e r v a t i o n s as experimental e r r o r s . I t i s demonstrated t h a t such o b s e r v a t i o n s can be r e a l and a r e p o s s i b l e w i t h i n the framework o f l i n e a r e l a s t i c theory. Experimental
A l l o f t h e data d i s c u s s e d i n t h i s paper was obtained using a gas d i l a t o m e t e r (9) i n c o n j u n c t i o n with a standard t e n s i l e t e s t e r . These d i l a t o m e t e r s y i e l d simultaneous and continuous measurements of s t r e s s , s t r a i n and volume d i l a t a t i o n over a wide range o f t e s t c o n d i t i o n s i n c l u d i n g s t r a i n r a t e , temperature and superimposed hyd r o s t a t i c p r e s s u r e . S t r e s s and s t r a i n a r e measured i n the usual manner w i t h i n the d i l a t o m e t e r which i s equipped with i n t e r n a l f o r c e t r a n s d u c e r s . Volume d i l a t a t i o n i s assessed by measuring the change i n pressure o f the gas surrounding the u n i a x i a l t e s t specimen as i t i s deformed i n a constant volume chamber. The i n strument i s q u i t e a c c u r a t e and o n l y responds t o changes i n sample volume. Under normal o p e r a t i n g c o n d i t i o n s the instrument can det e c t changes i n volume o f ±.02 percent and g r e a t e r accuracy can be achieved i f measures a r e taken to c o n t r o l temperature and minimize the f r e e a i r volume w i t h i n the t e s t c a v i t y . F i l l e d Elastomers
The s t r e s s - s t r a i n d i l a t a t i o n a l response o f f i l l e d polymers i s very s e n s i t i v e to m a t e r i a l f a c t o r s such as p a r t i c l e s i z e , f i l l e r c o n c e n t r a t i o n , c o u p l i n g agents t o enhance adhesion and mat r i x modulus and s t r e n g t h ( 6 ) . I t i s a l s o s e n s i t i v e t o t e s t cond i t i o n s such as s t r a i n r a t e , temperature, and s t r e s s f i e l d . Gene r a l l y speaking any m o d i f i c a t i o n s to the m a t e r i a l t h a t w i l l reduce vacuole d i l a t a t i o n such as reducing the p a r t i c l e s i z e , g r e a t l y improves the p r o p e r t i e s o f these m a t e r i a l s ( 6 ) . F i g u r e 1 i l l u s t r a t e s the behavior o f three h i g h l y f i l l e d elastomers. From t h i s data i t i s c l e a r t h a t y i e l d i n g o r s t r e s s s o f t e n i n g i s a d i r e c t r e s u l t o f volume d i l a t a t i o n caused by the formation and growth o f vacuoles. The e f f e c t o f superimposed pressure on t h e s t r e s s s t r a i n volume d i l a t a t i o n p r o p e r t i e s a r e shown i n f i g u r e 2 and 3 f o r
17.
FARMS ET AL.
Figure 1.
Mechanical
Behavior
of
Polymers
The stress-strain dilatational behavior of three highly filled elastomers
235
236
DURABILITY
OF
MACROMOLECULAR
MATERIALS
Strain
Figure 3. The stress-strain dilatational behavior of a 63.5 vol %filledelastomer at a series of hydrostatic pressures at a high strain rate
17.
FARMS
E T A L .
Mechanical
Behavior
of
237
Polymers
another h i g h l y f i l l e d rubber based s o l i d p r o p e l ! a n t f o r two d i f f erent s t r a i n r a t e s . These data c l e a r l y demonstrate that reduct i o n i n vacuole formation and growth v i a high pressure g r e a t l y improves t h e i r mechanical p r o p e r t i e s , e s p e c i a l l y strength and s t r a i n energy to r u p t u r e . With these low modulus composites high pressure acts l i k e a super bonding agent and does not allow f o r much vacuole formation. Vacuole d i l a t a t i o n information i t s e l f i s not simply i n t e r preted. The data instead are best understood through models o f m i c r o s t r u c t u r a l f a i l u r e ( 1 ) . Assuming a s i n g l e s i z e o f s p h e r i c a l f i l l e r p a r t i c l e s encompassed by e l l i p t i c a l l y shaped voids that form a r b i t r a r i l y i n s t r a i n , and once formed grow a t a constant rate with f u r t h e r deformation, then one can r e a d i l y separate vacuole growth from vacuole formation. Models such as the one desc r i b e d above have been substantiated by microscopic s t u d i e s . The s o l u t i o n of such models (1) i n d i c a t e s t h a t the f i r s t d e r i v a t i v e o f vacuole d i l a t a t i o n with respect to s t r a i n e , i s d i r e c t l y p r o p o r t i o n a l to the cumulative number o f vacuoles per u n i t volume,n, that e x i s t a t any s t r a i n . The second d e r i v a t i v e i s then d i r e c t l y proportional to the instantaneous frequency d i s t r i b u t i o n o f vacuo l e formation. These two r e s u l t s can be expressed mathematically as
n dn
-
cd(AVZM .
c d (AV/Vo)
{ 1 )
2
m
Figure 4 i l l u s t r a t e s the t y p i c a l volume d i l a t a t i o n - s t r a i n behavior along with i t s ' f i r s t and second d e r i v a t i v e s . Clearly these measures are r e a l i s t i c i n that the d e r i v a t i v e s do take on the c h a r a c t e r o f cumulative and instantaneous frequency d i s t r i b u tions. S i m i l a r models can be constructed to r e l a t e the l o s s i n s t i f f n e s s to the number o f vacuoles that have formed r e s u l t i n g i n very simple but accurate s t r e s s - s t r a i n r e l a t i o n s ( 1 ) . Phase Separated and F i l l e d Thermal P l a s t i c s Data s i m i l a r to that obtained on h i g h l y f i l l e d elastomers was r e c e n t l y taken on a v a r i e t y o f thermal p l a s t i c s . These data are i l l u s t r a t e d i n f i g u r e 5 f o r a p a r t i c u l a t e f i l l e d polyethylene with and without a bonding agent. Figure 6 and 7 i l l u s t r a t e s i m i l a r data f o r an ABS polymer with and without chopped glass f i b e r r e i n forcement. A d d i t i o n a l data on nylon and polypropylene, f i g u r e s 8 and 9, has been obtained and several other polymeric systems a l s o show s i m i l a r r e s u l t s i n t h a t y i e l d i n g i s caused by c a v i t a t i o n o f the m i c r o s t r u c t u r e . These data were a l l obtained using i n j e c t i o n molded samples provided by the polymer manufacturer. In every s i t u a t i o n using these samples negative volume changes have been observed p r i o r to y i e l d i n g followed by a sudden increase i n v o l ume r a t e a t y i e l d . The instrument was checked several times and i t demonstrated no s e n s i t i v i t y to load or s t r o k e . After deter-
238
DURABILITY
O F MACROMOLECULAR MATERIALS
AV/Vpy/
/ \
^ d
2
J
AV
Vo d €
2
/
\
/
/ /
Y
d AV
Vo d€
Strain.6 Figure 4.
Schematic of the dilatation-strain relationship and its first and second derivatives
Strain Figure 5.
The stress-strain dilatational behavior of a filled high-density polyethylene with and without a coupling agent
17.
FARRIS
E T A L .
\L 0
Mechanical
I
I
.02
.04
Figure 6.
Behavior
I
of
239
Polymers
I
.06 .08 Strain
1
.10
1—'
.12
The stress-strain dilatational behavior of ABS
Strain Figure 7.
The stress-strain dilatational behavior of filled ABS
DURABILITY
0
.02
.04
.06
O F
.08
MACROMOLECULAR
.10
.12
Strain Figure 9.
The stress-strain dilatational behavior of polypropylene
MATERIALS
17.
FARRIS
Mechanical
E T A L .
Behavior
of
241
Polymers
mining t h a t these negative volume changes were r e a l i t was thought that the e f f e c t could be induced by the method o f g r i p p i n g the samples. However, c o n s i d e r a b l e v a r i a t i o n s i n g r i p p i n g methods showed no s i g n i f i c a n t change i n the o b s e r v a t i o n s . Consequently, the e f f e c t i s considered r e a l and a l o g i c a l explanation must exist. The only p o s s i b l e explanation considered that i s c o n s i s t e n t with a l l o f our observations i s that o f a n i s o t r o p i c behavior. The reason most people dismiss such observations to "poor experiment a l technique" i s t h a t they r e s t r i c t t h e i r t h i n k i n g to i s o t r o p i c l i n e a r e l a s t i c i t y wherein such observations are impossible and a c o n t r a d i c t i o n to theory. With t h a t i n t e r p r e t a t i o n these data would y i e l d a value f o r P o i s s o n ' s r a t i o g r e a t e r than 0 . 5 which i s o f course impossible f o r an i s o t r o p i c l i n e a r s o l i d . The r e s t r i c t i o n s on P o i s s o n ' s r a t i o i n e l a s t i c i t y theory come about by imposing a p o s i t i v e d e f i n i t e s t r a i n energy requirement, t h a t i s i f the body i s i n a deformed s t a t e i t must possess a f i n i t e p o s i t i v e s t r a i n energy d e n s i t y . For a l i n e a r e l a s t i c i s o t r o p i c s o l i d the c o n s t i t u t i v e equation can always be expressed as 1 -v
^1
•v
where
-v
1
-v
•v - v
1
(3)
e. = principal strains a . = principal stresses E = Young's modulus v = Poisson's r a t i o
For the energy to be p o s i t i v e d e f i n i t e the compliance matrix must s a t i s f y c e r t a i n c o n d i t i o n s which can be summarized as f o l l o w s (a) every diagonal element must be g r e a t e r than zero (b) the determinant o f each submatrix remaining when the row and columns c o n t a i n i n g a diagonal element are deleted must be p o s i t i v e (c) the determinant o f the compliance matrix must be p o s i t i v e . For an i s o t r o p i c l i n e a r e l a s t i c s o l i d the f i r s t c o n d i t i o n i s a u t o m a t i c a l l y s a t i s f i e d since each diagonal element i s u n i t y . The second c o n d i t i o n r e s u l t s i n three i d e n t i c a l equations 1
The f i n a l
> 0
or
-1 < v < 1
c o n d i t i o n y i e l d s a stronger
1 - 3v
2
- 2v
In a u n i a x i a l
3
> 0
or
(4)
constraint
-1 < v < 1/2
(5)
t e n s i l e t e s t the volume d i l a t a t i o n simply be-
comes AV/Vo
=
| (1 - 2 v ) ,
(6)
which demands t h a t the s t r e s s and d i l a t a t i o n have the same sign i f v i s to be no l a r g e r than 0 . 5 .
242
DURABILITY
OF
MACROMOLECULAR
MATERIALS
Using i d e n t i c a l methods one can w r i t e the s t r e s s - s t r a i n equat i o n f o r an o r t h o t r o p i c l i n e a r e l a s t i c s o l i d i n terms o f the p r i n c i p a l values o f s t r e s s and s t r a i n as °i °2
(7)
J-3J L I _ W - 3j where the compliance matrix must be" symmetric i f the s t a t e o f s t r a i n energy i s to be unique and only a f u n c t i o n of the f i n a l s t a t e of s t r e s s and s t r a i n . In order to have a p o s i t i v e d e f i n i t e s t r a i n energy d e n s i t y the c o n d i t i o n s c i t e d above demand that 3
(a) C (b)
C
n
,
C
U
C
2
2
,
2 2
3
C
- C
2
3 3
1 2
- C
1 3
(d) c
2 2
c
- c
2 3
(e) C
1 1
C
3
C
3 3
2 2
C
3 3
11 23 C
>
(8)
> 0
2
+
2
> 0 > 0
2
(c) C C 3 n
> 0
3 3
> 0
2
20^023^ 3 - C ^ C ^
2
-
2 2
_
0
The volume change i n a u n i a x i a l t r o p i c case simply becomes
t e n s i l e t e s t f o r the o r t h o -
W < 11 12 13> * W In order to have negative volume changes in a t e n s i l e one must r e q u i r e that =
C
ll
+
C
12
C
+
c
13
+
