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The effects of gaseous environments on polymers
Materials Science and Engineering, 25 ( 1 9 7 6 ) 87 - 91
87
© Elsevier S e q u o i a S.A., L a u s a n n e - - P r i n t e d in the N e t h e r l a n d s
T h e Effects of Gaseous E n v i r o n m e n t s
o n Polymers
N O R M A N BROWN
Department of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, Pa. 19174 (U.S.A.)
1. I N T R O D U C T I O N
Environmental effects on polymers may be divided into two groups, those that involve chemical changes by breaking the primary or covalent bonds, and those t h a t disrupt the secondary or van der Waals- and hydrogen bonds. The former group includes chain sission, cross-linking, the covalent bonding of new species of atoms, and the rearrangement of existing atoms on the polymer chain. Grassie [1] has chosen to call all of the above effects " d e g r a d a t i o n " rather than restricting degradation to chain scission. In some cases, all forms of degradation may occur simultaneously. The c o m m o n causes of degradation are heat, light, and atmospheric oxygen. Mechanical stress may also be listed as a cause of degradation. Grassie [ 1 ] has written a review of degradation by light, heat, and oxygen. High-energy radiation, such as gamma rays and X-rays, also causes " d e g r a d a t i o n " which is more general and less selective than t h a t caused by light. Charlesby has reviewed high energy radiation effects [2]. This paper will not be concerned with degradation effects, but will consider effects which involve van der Waals- and hydrogen bonding. The important factors which attack the secondary bonds are heat, organic liquids, and gases such as nitrogen, oxygen, argon, and CO2. A very large fraction of the field of polymer science and technology is devoted to the effects of heat, but it will n o t be a major part of this paper. The effects of organic liquids include swelling and crazing. Swelling by organic liquids is an extensive subject which also has a long history of investigation and is well understood. Kambour [3] has reviewed the considerable work on crazing by organic liquids. The present paper will be concerned primarily with the fairly recent discovery [4] that a supposedly inert gas such as Ar can m o d i f y the mechanical behavior of polymers.
Subsequently, investigations [ 5, 6 ] have shown that N2, Ar, 02, and usually CO2, can affect the mechanical behavior of a polymer if it is tested at a sufficiently low temperature. Both [7 - 12] amorphous and crystalline and crosslinked [12] polymers are affected. The effect is general in that every polymer which has been tested in one or more of these gaseous environments at a sufficiently low temperature has had its mechanical behavior modified relative to its behavior in an inert environment such as under vacuum or in helium. Usually these gases cause c~azing and decrease the ultimate strength of the polymer, but there are also cases where they have increased the brittle fracture stress of polymers. The strengthening effect is one t h a t we know least about. First, the crazing effects of the gaseous environments will be considered.
2. R E V I E W O F E F F E C T S O F G A S E O U S ENVIRONMENTS
Figure 1 shows the typical effect of N 2 gas on the stress-strain curve of a polymer at 78 K as compared with the behavior under vacuum. The stress-strain behavior in a He environment is the same as that under vacuum,
25
~
V~um
x
He
te
Io5 5~ 0gl
T=90"K t i i I i i i I I I i I I i
5
10
STRAIN
(%)
Fig. 1. T h e e f f e c t of N2, He, and v a c u u m o n stressstrain curves o f p o l y c a r b o n a t e at 90 K.
88 at least for temperatures above 78 K. Theories [11, 13] and experiments [5, 6, 8, 11, 14] indicate that a particular gas loses its effectiveness at a critical temperature above the boiling point. Therefore, it is not expected that He would be effective at, or above, 78 K. There has not been sufficient experimentation below 78 K to determine whether He can cause any polymer to craze. The existing data [8] show only brittle fracture in the vicinity of 4.2 K. Since N2, 02, Ar, and CO2 are the only gases that have been tested, we do not know if other noble gases such as Ne, Kr, Xe cause crazing. It would be most interesting to know whether H2, and the whole host of c o m m o n gases such as CH4, CO, H28 , and NH3, cause crazing. Presumably, these gases should create crazing agents such as acetone, alcohol, and benzene. However, there have not been any quantitative experiments to determine the ranges of temperature and vapor pressure where the vapors of organic liquids cause crazing. Experiments with gaseous N 2 at one atmosphere pressure, and at 78 K and with the polymer in contact with the liquid N2, produce the same quantitative effect on the stressstrain curve [4, 8]. Thus, it appears that there is no difference between the effects of the gas and the liquid p e r se at the boiling point of the liquid. However, above the boiling point, the effect of the gas on the stress-strain curve decreases with increasing temperature, as 200
I
I
I
I
]
shown in Fig. 2. Finally, there is a critical temperature for a given pressure, above which the gas is not effective. This critical temperature increases as the gas pressure increases [6, 14]. Little [8] is known about the temperature effect below the boiling point of the liquid gases except that the polymer usually becomes intrinsically stronger as its temperature is decreased and, therefore, the stress for crazing should also increase. Imai and Brown [6, 14] obtained the following empirical equation which related the craze yield strength to the temperature and pressure of the environmental gas
ac/Os =
[P exp ( Q / R T ) / P * ] - ' .
~c Is the craze yield point, os the strength of the polymer in an inert environment, P and T are the pressure and temperature, P* and Q are constants for a given gas and polymer system, and n depends on the polymer but n o t o n the gas. Q is very close to the value for the heat of vaporization of each gas. The values of n ranged from about 0.08 to 0.13 depending on the polymer. At the present time, there is n o theory or understanding concerning the factors which determine the value of n. The environmental effects of solidified N2 and CO2 have been investigated [6, 8]. The vapor in equilibrium with the solid causes crazing. The effect of COz on the tensile strength of PMMA is shown in Fig. 2. It was found that above its sublimation temperature,
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I 300
I 550
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400
TEMPERATURE (K)
Fig. 2. Brittle fracture stress or shear yield p o i n t o f PMMA as a f u n c t i o n o f temperature for I atm o f various environmental gases. GHJ in He; A B in N 2 or Ar; CD in 0 2 ; FH in CO 2 ; F E in CO 2 vapor in equilibrium with solid CO 2 ; IJ in water.
89
CO2 behaved like gaseous N2, 0 2 , and At. Hiltner, Kastelic, and Baer [8] showed that solid nitrogen lowered the strength o f polyethylene terephthalate at temperatures down to 45 K, which is 18 K below the freezing point of N 2. Little is known a b o u t the temperature effect of the vapor pressure of other solids on crazing. 3. R E V I E W O F M E C H A N I S M O F G A S E O U S CRAZING
Before discussing w h y a gas such as argon causes crazing, a general statement a b o u t what we do not know a b o u t crazing should be made. We do not know why, under a particular stress, environment, strain rate, and temperature, one polymer will craze and another will not. In other words, we do n o t know h o w the structure of the molecule or h o w molecular morphology is related to crazing. Even though we do not know all the details of h o w an argon molecule, for example, causes crazing, the following general aspects of the p h e n o m e n o n make it understandable. When an unoriented polymer is exposed to stress, it deforms mainly by the stress first overcoming the van der Waals bond. The strength of the van der Waals bond in a polymer is comparable to the strength of the van der Waals bond in gases such a s N 2 and Ar. The only reason for the polymer not being gaseous is because it contains very long molecules. Thus, the N2 or Ar can interact with the polymer molecule almost as strongly as it can interact with itself. When the N2 or Ar dissolves in the polymer, it acts as a plasticizer by weakening the van der Waals bonds between polymer molecules. It has also been shown that when gases such as N2 or Ar adsorb on a polymer, the surface energy may be reduced by 25 - 50% [15 - 1 7 ] . Since crazing involves the generation of porosity and fibrillation, any agent which reduces the surface energy and acts like a plasticizer should make crazing easier. While most workers believe that the plasticizing effect may be greater than the surface effect, we still do not k n o w the details of the process at the molecular level. We know very little a b o u t the nature of the polymer surface when it is in the process of converting from a free surface to a porous mass. In addition, little is known a b o u t the porous state when the pores are of the order of the size of the gas molecules.
In order for the gas molecule to act as a plasticizer it is necessary for the gas to diffuse into the polymer. An extrapolation of the diffusion coefficient, as measured from around room temperature down to 78 K, indicates [13] that the diffusion of these gases is extremely slow (D ~ 10 - s l cm/s2). It would take a considerable time, relative to the time scale of the experiments, for the gas, by bulk diffusion, to penetrate the polymer by one molecular diameter at 78 K. The key to this dilemma is that the stress assists the diffusion of the gas [11, 13, 18], and the gas need only diffuse into the most open spaces between the polymer molecules in order to form a craze [11]. However, there have been practically no direct experiments on the effect of stress on diffusion. We have no diffusion data of gases into polymers far below room temperature. Every polymer tested in liquid nitrogen has been affected by the liquid nitrogen in either of two ways. Usually, crazes are produced, and the strength of the polymer is less than that in He or under vacuum. There are cases, such as nylon [9] and polyvinylidiene chloride, and for PMMA [13] and polycarbonate at very high strain rates, where the strength in liquid nitrogen is greater than in He or under vacuum. In the above cases, the polymer fails in a brittle manner and crazing is n o t observed throughout the gage section. Evidence of crazing prior to fracture can be observed on the fractured surface. The explanation [ 13] for this effect is that the liquid nitrogen blunts the crack that is responsible for the brittle fracture. At high strain rates, the gas does not have time to penetrate the polymer, plasticize it, and thus cause crazing. Therefore, the polymer breaks in a brittle fashion before it crazes. The defect or crack is n o t modified in He or under vacuum; however, in nitrogen the crack is blunted and, thereby, the stress concentration of the defect is reduced. It is thought that nylon and polyvinylidiene chloride behave at low strain rates like PC and PMMA do at high strain rates because the diffusion of N 2 in nylon and polyvinylidiene chloride is very low by comparison. Experiments remain to be carried o u t to test this speculation. Thus far, the effects of molecular N2 and 02 have been investigated. Nothing is known of the effects of atomic nitrogen and oxygen.
90
In general, the effects of molecules with unsaturated bonds should be of interest. In summary, it is not yet clear how much of the effect of craze-producing gases should be attributed to a reduction in surface energy and how much to a localized reduction in flow stress via plasticization. It may be that one cannot make a clear distinction between the surface and a thin sub-surface layer which is undergoing the formation of voids as the first step in crazing. Very little is known about the very first stage of crazing when the voids are about 10 )~ in size. Even less is known about the interaction of the gas and the stress during the nucleation of a craze.
4. THE DYNAMICS OF CRAZE DEFORMATION
The strain rate, go, associated with crazing can be described by the following equation: ~c = p T b f l v .
(1)
p Is the craze density, the number per unit surface area, 7 depends on the shape and size of the specimen and is the ratio of surface area per unit volume; b is the craze displacement which is related to the craze thickness; f is the shape factor describing the shape of the lenticular craze, which is approximately semielliptic; I is a measure of the size of the craze or its length; and v is the velocity of the craze. The above equation can be used to calculate the constant strain rate stress-strain curve [19], the creep curve, and the stress relaxation curve. So far, the equation has been checked at constant temperature and pressure with a variable stress. Little is known of how the changes in the temperature, pressure, and type of environmental gas affect p, b, and v, which are the basic parameters for characterizing the crazes. When the temperature, pressure and stress dependence of p, b, and v are known for each polymer and environmental gas, then the macroscopic deformation of each polymer can be predicted for the various types of deformation tests such as stress-strain, stress relaxation, and creep. The effects of the environmental gases on the fatigue behavior are completely unknown. No one has carried out low temperature fatigue tests under conditions where the temperature and pressure of the environmental gas such as N2, O2, CO2, or Ar have been con-
trolled. Whereas past experiments in these gaseous environments have been concerned with the effects of the gases or craze propagation, no experiments have been performed to measure their effects on crack propagation.
5. SUMMARY
The effect of inert gases on the mechanical properties of polymers is very general. There are certain areas which have not been explored, such as fatigue and crack propagation. The pressure range above one atmosphere has not been observed. The effects of stress on the diffusion of these gases are not known. The question of how much is a surface effect and how much is subsurface plasticization is n o t clear. The effects of gases other than N2, At, 02, and CO2 have not been determined.
ACKNOWLEDGEMENT
The research was supported by the U.S. Army Research Office.
REFERENCES 1 N. Grassie, Degradation, in A. D. Jenkins (ed.), Polymer Science, Vol. 2, North-Holland Publ. Co., Amsterdam, and American Elsevier, New York, 1972, pp. 1444 - 1541. 2 A. Charlesby, Radiation effects in polymers, in A. D. Jenkins (ed.), Polymer Science, Vol. 2, North-Holland Publ. Co., Amsterdam, and American Elsevier, New York, 1972, pp. 1554 - 1559. 3 R.P. Kambour, Macromol. Rev., 7 (1973).1. 4 M. F. Parrish and N. Brown, Nature (London), Phys. Sci., 237 (1972) 122. 5 H. G. Olf and A. Peterlin, Polymer, 14 (1973) 78. 6 Y. Imai and N. Brown, J. Mater. Sci., 11 (1976) 417. 7 N. Brown and M. F. Parrish, J. Polym. Sci., Polym. Lett. Ed., 10 (1972) 777. 8 A. Hiltner, J. A. Kastelic and E. Baer, in K. D. Pae, D. R. Morrow and Yu Chen (eds.), Advances in Polymer Science and Engineering, Plenum Press, New York, 1972, p. 335. 9 N. Brown and M. F. Parrish, in A. Bishay (ed.), Recent Advances in Science and Technology of Materials, Vol. 2, Plenum Press, New York, 1974, p. 1. 10 S. Fischer and N. Brown, J. Appl. Phys., 44 (1973) 4322. 11 H. G. Olf and A. Peterlin, J. Polym. Sci., Part A-2, 12 (1974) 2209.
91 12 W. T. Mead and P. E. Reed, Bull. Am. Phys. Soc., March Meeting in Atlanta, 1976, paper CJ11. 13 N. Brown, J. Polym. Sci., Part A-2, 11 (1973) 2099. 14 N. Brown and Y. Imai, J. Appl. Phys., 46 (1975) 10, 4130. 15 D. Graham, J. Phys. Chem., 66 (1962) 1815.
16 D. Graham, J. Phys. Chem., 68 (1964) 2188. 17 D.C. Braught, D. D. Bruning and J. J. Scholz, J. Colloid. Interface Sci., 31 (1969) 263. 18 N. Brown and S. Fischer, J. Polym. Sci., 13 (1975) 1315. 19 N. Brown, Philos. Mag., 32 (1975) 1041.
87
© Elsevier S e q u o i a S.A., L a u s a n n e - - P r i n t e d in the N e t h e r l a n d s
T h e Effects of Gaseous E n v i r o n m e n t s
o n Polymers
N O R M A N BROWN
Department of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, Pa. 19174 (U.S.A.)
1. I N T R O D U C T I O N
Environmental effects on polymers may be divided into two groups, those that involve chemical changes by breaking the primary or covalent bonds, and those t h a t disrupt the secondary or van der Waals- and hydrogen bonds. The former group includes chain sission, cross-linking, the covalent bonding of new species of atoms, and the rearrangement of existing atoms on the polymer chain. Grassie [1] has chosen to call all of the above effects " d e g r a d a t i o n " rather than restricting degradation to chain scission. In some cases, all forms of degradation may occur simultaneously. The c o m m o n causes of degradation are heat, light, and atmospheric oxygen. Mechanical stress may also be listed as a cause of degradation. Grassie [ 1 ] has written a review of degradation by light, heat, and oxygen. High-energy radiation, such as gamma rays and X-rays, also causes " d e g r a d a t i o n " which is more general and less selective than t h a t caused by light. Charlesby has reviewed high energy radiation effects [2]. This paper will not be concerned with degradation effects, but will consider effects which involve van der Waals- and hydrogen bonding. The important factors which attack the secondary bonds are heat, organic liquids, and gases such as nitrogen, oxygen, argon, and CO2. A very large fraction of the field of polymer science and technology is devoted to the effects of heat, but it will n o t be a major part of this paper. The effects of organic liquids include swelling and crazing. Swelling by organic liquids is an extensive subject which also has a long history of investigation and is well understood. Kambour [3] has reviewed the considerable work on crazing by organic liquids. The present paper will be concerned primarily with the fairly recent discovery [4] that a supposedly inert gas such as Ar can m o d i f y the mechanical behavior of polymers.
Subsequently, investigations [ 5, 6 ] have shown that N2, Ar, 02, and usually CO2, can affect the mechanical behavior of a polymer if it is tested at a sufficiently low temperature. Both [7 - 12] amorphous and crystalline and crosslinked [12] polymers are affected. The effect is general in that every polymer which has been tested in one or more of these gaseous environments at a sufficiently low temperature has had its mechanical behavior modified relative to its behavior in an inert environment such as under vacuum or in helium. Usually these gases cause c~azing and decrease the ultimate strength of the polymer, but there are also cases where they have increased the brittle fracture stress of polymers. The strengthening effect is one t h a t we know least about. First, the crazing effects of the gaseous environments will be considered.
2. R E V I E W O F E F F E C T S O F G A S E O U S ENVIRONMENTS
Figure 1 shows the typical effect of N 2 gas on the stress-strain curve of a polymer at 78 K as compared with the behavior under vacuum. The stress-strain behavior in a He environment is the same as that under vacuum,
25
~
V~um
x
He
te
Io5 5~ 0gl
T=90"K t i i I i i i I I I i I I i
5
10
STRAIN
(%)
Fig. 1. T h e e f f e c t of N2, He, and v a c u u m o n stressstrain curves o f p o l y c a r b o n a t e at 90 K.
88 at least for temperatures above 78 K. Theories [11, 13] and experiments [5, 6, 8, 11, 14] indicate that a particular gas loses its effectiveness at a critical temperature above the boiling point. Therefore, it is not expected that He would be effective at, or above, 78 K. There has not been sufficient experimentation below 78 K to determine whether He can cause any polymer to craze. The existing data [8] show only brittle fracture in the vicinity of 4.2 K. Since N2, 02, Ar, and CO2 are the only gases that have been tested, we do not know if other noble gases such as Ne, Kr, Xe cause crazing. It would be most interesting to know whether H2, and the whole host of c o m m o n gases such as CH4, CO, H28 , and NH3, cause crazing. Presumably, these gases should create crazing agents such as acetone, alcohol, and benzene. However, there have not been any quantitative experiments to determine the ranges of temperature and vapor pressure where the vapors of organic liquids cause crazing. Experiments with gaseous N 2 at one atmosphere pressure, and at 78 K and with the polymer in contact with the liquid N2, produce the same quantitative effect on the stressstrain curve [4, 8]. Thus, it appears that there is no difference between the effects of the gas and the liquid p e r se at the boiling point of the liquid. However, above the boiling point, the effect of the gas on the stress-strain curve decreases with increasing temperature, as 200
I
I
I
I
]
shown in Fig. 2. Finally, there is a critical temperature for a given pressure, above which the gas is not effective. This critical temperature increases as the gas pressure increases [6, 14]. Little [8] is known about the temperature effect below the boiling point of the liquid gases except that the polymer usually becomes intrinsically stronger as its temperature is decreased and, therefore, the stress for crazing should also increase. Imai and Brown [6, 14] obtained the following empirical equation which related the craze yield strength to the temperature and pressure of the environmental gas
ac/Os =
[P exp ( Q / R T ) / P * ] - ' .
~c Is the craze yield point, os the strength of the polymer in an inert environment, P and T are the pressure and temperature, P* and Q are constants for a given gas and polymer system, and n depends on the polymer but n o t o n the gas. Q is very close to the value for the heat of vaporization of each gas. The values of n ranged from about 0.08 to 0.13 depending on the polymer. At the present time, there is n o theory or understanding concerning the factors which determine the value of n. The environmental effects of solidified N2 and CO2 have been investigated [6, 8]. The vapor in equilibrium with the solid causes crazing. The effect of COz on the tensile strength of PMMA is shown in Fig. 2. It was found that above its sublimation temperature,
I
I
!
E
H I-
P erie
M
M
A
~ I ~
ON,
50
e
0
+
• A © 02
F
0
e~im
"e~_
cOz
I 50
~\ \",,
I I00
I 150
I ZOO
I 250
I 300
I 550
T'
400
TEMPERATURE (K)
Fig. 2. Brittle fracture stress or shear yield p o i n t o f PMMA as a f u n c t i o n o f temperature for I atm o f various environmental gases. GHJ in He; A B in N 2 or Ar; CD in 0 2 ; FH in CO 2 ; F E in CO 2 vapor in equilibrium with solid CO 2 ; IJ in water.
89
CO2 behaved like gaseous N2, 0 2 , and At. Hiltner, Kastelic, and Baer [8] showed that solid nitrogen lowered the strength o f polyethylene terephthalate at temperatures down to 45 K, which is 18 K below the freezing point of N 2. Little is known a b o u t the temperature effect of the vapor pressure of other solids on crazing. 3. R E V I E W O F M E C H A N I S M O F G A S E O U S CRAZING
Before discussing w h y a gas such as argon causes crazing, a general statement a b o u t what we do not know a b o u t crazing should be made. We do not know why, under a particular stress, environment, strain rate, and temperature, one polymer will craze and another will not. In other words, we do n o t know h o w the structure of the molecule or h o w molecular morphology is related to crazing. Even though we do not know all the details of h o w an argon molecule, for example, causes crazing, the following general aspects of the p h e n o m e n o n make it understandable. When an unoriented polymer is exposed to stress, it deforms mainly by the stress first overcoming the van der Waals bond. The strength of the van der Waals bond in a polymer is comparable to the strength of the van der Waals bond in gases such a s N 2 and Ar. The only reason for the polymer not being gaseous is because it contains very long molecules. Thus, the N2 or Ar can interact with the polymer molecule almost as strongly as it can interact with itself. When the N2 or Ar dissolves in the polymer, it acts as a plasticizer by weakening the van der Waals bonds between polymer molecules. It has also been shown that when gases such as N2 or Ar adsorb on a polymer, the surface energy may be reduced by 25 - 50% [15 - 1 7 ] . Since crazing involves the generation of porosity and fibrillation, any agent which reduces the surface energy and acts like a plasticizer should make crazing easier. While most workers believe that the plasticizing effect may be greater than the surface effect, we still do not k n o w the details of the process at the molecular level. We know very little a b o u t the nature of the polymer surface when it is in the process of converting from a free surface to a porous mass. In addition, little is known a b o u t the porous state when the pores are of the order of the size of the gas molecules.
In order for the gas molecule to act as a plasticizer it is necessary for the gas to diffuse into the polymer. An extrapolation of the diffusion coefficient, as measured from around room temperature down to 78 K, indicates [13] that the diffusion of these gases is extremely slow (D ~ 10 - s l cm/s2). It would take a considerable time, relative to the time scale of the experiments, for the gas, by bulk diffusion, to penetrate the polymer by one molecular diameter at 78 K. The key to this dilemma is that the stress assists the diffusion of the gas [11, 13, 18], and the gas need only diffuse into the most open spaces between the polymer molecules in order to form a craze [11]. However, there have been practically no direct experiments on the effect of stress on diffusion. We have no diffusion data of gases into polymers far below room temperature. Every polymer tested in liquid nitrogen has been affected by the liquid nitrogen in either of two ways. Usually, crazes are produced, and the strength of the polymer is less than that in He or under vacuum. There are cases, such as nylon [9] and polyvinylidiene chloride, and for PMMA [13] and polycarbonate at very high strain rates, where the strength in liquid nitrogen is greater than in He or under vacuum. In the above cases, the polymer fails in a brittle manner and crazing is n o t observed throughout the gage section. Evidence of crazing prior to fracture can be observed on the fractured surface. The explanation [ 13] for this effect is that the liquid nitrogen blunts the crack that is responsible for the brittle fracture. At high strain rates, the gas does not have time to penetrate the polymer, plasticize it, and thus cause crazing. Therefore, the polymer breaks in a brittle fashion before it crazes. The defect or crack is n o t modified in He or under vacuum; however, in nitrogen the crack is blunted and, thereby, the stress concentration of the defect is reduced. It is thought that nylon and polyvinylidiene chloride behave at low strain rates like PC and PMMA do at high strain rates because the diffusion of N 2 in nylon and polyvinylidiene chloride is very low by comparison. Experiments remain to be carried o u t to test this speculation. Thus far, the effects of molecular N2 and 02 have been investigated. Nothing is known of the effects of atomic nitrogen and oxygen.
90
In general, the effects of molecules with unsaturated bonds should be of interest. In summary, it is not yet clear how much of the effect of craze-producing gases should be attributed to a reduction in surface energy and how much to a localized reduction in flow stress via plasticization. It may be that one cannot make a clear distinction between the surface and a thin sub-surface layer which is undergoing the formation of voids as the first step in crazing. Very little is known about the very first stage of crazing when the voids are about 10 )~ in size. Even less is known about the interaction of the gas and the stress during the nucleation of a craze.
4. THE DYNAMICS OF CRAZE DEFORMATION
The strain rate, go, associated with crazing can be described by the following equation: ~c = p T b f l v .
(1)
p Is the craze density, the number per unit surface area, 7 depends on the shape and size of the specimen and is the ratio of surface area per unit volume; b is the craze displacement which is related to the craze thickness; f is the shape factor describing the shape of the lenticular craze, which is approximately semielliptic; I is a measure of the size of the craze or its length; and v is the velocity of the craze. The above equation can be used to calculate the constant strain rate stress-strain curve [19], the creep curve, and the stress relaxation curve. So far, the equation has been checked at constant temperature and pressure with a variable stress. Little is known of how the changes in the temperature, pressure, and type of environmental gas affect p, b, and v, which are the basic parameters for characterizing the crazes. When the temperature, pressure and stress dependence of p, b, and v are known for each polymer and environmental gas, then the macroscopic deformation of each polymer can be predicted for the various types of deformation tests such as stress-strain, stress relaxation, and creep. The effects of the environmental gases on the fatigue behavior are completely unknown. No one has carried out low temperature fatigue tests under conditions where the temperature and pressure of the environmental gas such as N2, O2, CO2, or Ar have been con-
trolled. Whereas past experiments in these gaseous environments have been concerned with the effects of the gases or craze propagation, no experiments have been performed to measure their effects on crack propagation.
5. SUMMARY
The effect of inert gases on the mechanical properties of polymers is very general. There are certain areas which have not been explored, such as fatigue and crack propagation. The pressure range above one atmosphere has not been observed. The effects of stress on the diffusion of these gases are not known. The question of how much is a surface effect and how much is subsurface plasticization is n o t clear. The effects of gases other than N2, At, 02, and CO2 have not been determined.
ACKNOWLEDGEMENT
The research was supported by the U.S. Army Research Office.
REFERENCES 1 N. Grassie, Degradation, in A. D. Jenkins (ed.), Polymer Science, Vol. 2, North-Holland Publ. Co., Amsterdam, and American Elsevier, New York, 1972, pp. 1444 - 1541. 2 A. Charlesby, Radiation effects in polymers, in A. D. Jenkins (ed.), Polymer Science, Vol. 2, North-Holland Publ. Co., Amsterdam, and American Elsevier, New York, 1972, pp. 1554 - 1559. 3 R.P. Kambour, Macromol. Rev., 7 (1973).1. 4 M. F. Parrish and N. Brown, Nature (London), Phys. Sci., 237 (1972) 122. 5 H. G. Olf and A. Peterlin, Polymer, 14 (1973) 78. 6 Y. Imai and N. Brown, J. Mater. Sci., 11 (1976) 417. 7 N. Brown and M. F. Parrish, J. Polym. Sci., Polym. Lett. Ed., 10 (1972) 777. 8 A. Hiltner, J. A. Kastelic and E. Baer, in K. D. Pae, D. R. Morrow and Yu Chen (eds.), Advances in Polymer Science and Engineering, Plenum Press, New York, 1972, p. 335. 9 N. Brown and M. F. Parrish, in A. Bishay (ed.), Recent Advances in Science and Technology of Materials, Vol. 2, Plenum Press, New York, 1974, p. 1. 10 S. Fischer and N. Brown, J. Appl. Phys., 44 (1973) 4322. 11 H. G. Olf and A. Peterlin, J. Polym. Sci., Part A-2, 12 (1974) 2209.
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