The Dependence of Craze Velocity on the Pressure and Temperature of the Environmental Gas

NORMAN BROWN and BRUCE D. METZGER,* Department of Materials Science and Engineering and the Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Synopsis

The craze velocity was determined for poly(chlorotrifluoroethy1ene) (PCTFE) in CH4 and for PCTFE, polystyrene, and poly(methy1 methacrylate) in Nz. It was found that for temperatures near the boiling point the velocity and number of crazes depended on the relative pressure given by P exp[-(Q,/R)(TB-' - T I ) ] , where P is the pressure, Qu is the heat of vaporization, and TA is the boiling point. The craze velocity was related to the coverage of the adsorbed gas. For coverages corresponding to a few monolayers the logarithm of the velocity was proportional to the relative pressure. As the temperature increases from TB, the creep rate decreases because gas desorbs with increasing temperature; the creep rate attains a minimum value at a temperature where the general process of thermally activated deformation becomes dominant.

INTRODUCTION

Environmental gases such as NZ, Oz, Ar, COz, etc., make polymers craze at low temperatures. Previous work1-12 showed how these gases affect the stress-strain behavior of polymers as compared to their behavior in an inert environment. It was determined that the tensile strength decreased as the parameter, P exp(Q/ R T ) , increased. Here P is the pressure, T is the temperature, and Q is a constant that depends on the polymer-gas system and is nearly equal to the heat of va- porization.

The tensile strength is a complex property that depends on both the number of crazes per unit area of surface p and their velocity u . This investigation was undertaken in order to separate the effects of P and T on u and p . Other in- vestigations on the effect of environment on craze velocity have been concerned with liquids. This is the first investigation to show how the velocity and number of crazes depend on the pressure and temperature of environmental gases.

The velocity of the crazes was measured during a constant stress experiment, i.e., during creep. I t can be determined in two equivalent ways as shown by Brown, Metzger, and Imai.13 In the direct method the velocity is obtained from measurements of craze length and time. In the other method the velocity is calculated from the creep rate and creep strain. The theory of Brown et al.,13 which was confirmed by experiments, shows that the creep equation for polymers that craze at low temperatures and in environmental gases is given by

(1) E = pyolh&& + vt)3

* Present address: Homer Research Laboratory, Bethlehem Steel Company, Bethlehem, P A 18016.

Journal of Polymer Science: Polymer Physics Edition, Vol. 18,1979-1992 (1980) 0 1980 John Wiley & Sons, Inc. 0098-1273/80/0018-1979$01.40

1980 BROWN AND METZGER

O 2 O s

I atrn

N, ENVIRONMENT

78 K

c T = 117MPa

I atrn 1 N, ENVIRONMENT

78 K

c T = 117MPa

0 . 2 5 a t m 0 I

0 5 10 15 20 25 TIME ( m i n )

Fig. 1. Creep curves of PCTFE a t various partial pressures of Nj? a t 78 K; u = 117 MPa.

where y is the ratio of surface to volume of the specimen, CY is related to the shape of the craze and is very close to 1.0, h 1 is the ratio of thickness to length of the craze, k2 is the ratio of width to the length of craze, lo is the initial length of the craze after the load is applied, and t is time. Equation (1) leads to the following equation which is used to determine the craze velocity:

u = At/e2/3 (2)

where A is a constant that contains p and the other parameters that describe the shape of the craze, and i is the creep rate. Equation (2) is useful for determining the dependence of u on P and T when using a single specimen with a constant A .

It was found that the combined effects of P, T were contained in the parameter, P exp(QIRT), as was found for the tensile strength. However, the functional dependences of p and u on the above parameter were different. A t low values of u , lnu was a linear function of the parameter but at higher values of u the slope of the function constantly decreased. The observed relationship between u and P exp(Q1RT) provides a basis for discussing the molecular mechanism through which the environmental gas controls the velocity of the craze.

EXPERIMENTAL METHODS

All the materials, poly(chlorotrifluoroethy1ene) (PCTFE), poly(methy1 methacrylate) (PMMA), and polystyrene (PS) have been used in previous in- vestigations and were found to have very reproducible mechanical behaviors as exhibited by their creep and stress-strain curves. The PCTFE was made from

CRAZE VELOCITY

0.20

0. I5

5 0.10 LL I- u)

0.05

0.01 ,

7 8 K

0

N, ENVIRONMENT

I ATMOSPHERE 0- = 117 MPa

L, !A 88 K 1 f

I I I I

I

1981

3M resin Kel-F-81; the sheets were compression molded and quenched from 3OOOC by the 3M Company. The PMMA was Plexiglas-G from Rohm and Haas and the PS from Westlake Plastic. The important and general results of this investigation do not hinge on the type of plastic nor on variations that may exist in a generic type. The specimens were a dumbbell shape about 1 mm thick, 1 5 mm wide, and 12.7 mm uniform gauge length.

The creep machine was a lever type with a 5:l load ratio. Creep rates over the range of 10-1 to min-l could be measured.

The specimen was enclosed in a copper environmental chamber which was cooled by liquid nitrogen. The temperature of the specimens was controlled within fO.l"C and the partial pressure of the active gas varied about fl% during an experiment. A given partial pressure was obtained by mixing the active gas with helium and controlling the flow rate of each gas by precision manometer- controlled flow meters.

The number of crazes per unit area was determined by counting the crazes on a photomicrograph. The average velocity of the crazes was determined by measuring the length of many crazes and dividing the average length by the time the specimen was under stress. Previous experiments by Brown and Fischerll showed that the velocity was constant under a constant stress.

There were two types of experiments: single specimen and multiple specimen experiments. In multiple specimen experiments a different specimen was used for each combination of P and T. The velocity of the crazes was determined directly by measuring the average length of the crazes and the time. Both the multiple specimen and single specimen experiments gave the same dependence of u on P and T and the same value of Q.

1982 BROWN AND METZGER

TABLE I Creep Tests of PCTFE in N2

P (atm) p(crazes/mm2) t (min) 1 (mm) V = l / t (mm/min)

1.00 0.79 0.75

1.00 0.75 0.50 0.25

1.00 0.75 0.50 0.35

0.85 0.75 0.50

1.00

1.00 0.75 0.50 0.25

1.00 0.75 0.50 0.25

0.50 0.25 0.15 0.10

0.25 0.15 0.05

85 66 62

185 113 85 19

151 132 85 21

34 28 15

77

272 219 139 64

360 250 132 66

398 378 303 96

886 648 227

u = 103 MPa; T = 78 K 20

100 510

u = 117 MPa; T = 78 K 4.2 6.8

18 817

u = 117 MPa; T = 80 K 5.2

12 48

322

55 111 540

105

CJ = 117 MPa; T = 85 K

u = 117 MPa; T = 88 K

u = 120.6 MPa; 7' = 78 K 2.7 6.8

14 445

u = 124 MPa; T = 78 K 1.5 4.1 5.4

u = 138MPa; T = 78K 1.6 3.6 9.3

u = 151.6 MPa; T = 78 K 1.4 2.8 8.4

49

38

0.90 0.87 0.95

0.50 0.49 0.47 0.72

0.43 0.45 0.53 0.58

0.56 0.40 0.84

1.3

0.36 0.46 0.40 0.39

0.40 0.41 0.51 0.40

0.31 0.19 0.31 0.43

0.19 0.18 0.19

4.5 x 10-2 8.7 x 10-3 1.9 x 10-3

1.2 x 10-1 7.2 x 2.6 x 8.8 X

8.3 X 3.8 X 1.1 x 10-2 1.8 x 10-3

3.6 x 10-3 1.0 x 10-2

1.6 x

1.2 x 10-2

1.3 X 10-1 6.8 x 2.9 X 8.8 X

2.7 X lo-' 1.0 x 10-1 9.4 x 10-2 8.2 x 10-3

1.9 x 10-1 5.3 x 10-2 3.3 x 10-2 1.1 x 10-2

1.4 X 10-1 6.4 x 2.3 x

In the single specimen experiment, the same specimen could be used for many combinations of P and T without removing the specimen from the creep machine. Equation (2) provided the basis for determining the relative velocity in a given specimen as long as the number of crazes did not change when P and T were varied. Since the number of crazes for a given stress was a maximum for the highest pressure and lowest temperature to which the specimen was exposed, the specimen was first exposed to the highest pressure and lowest temperature during the initial run; thereafter the number of crazes was constant for other combinations of P and T.

The procedure for the single specimen experiment was as follows: (i) The

CRAZE VELOCITY

I I I I 1 1 =I

1983

0 7 8 K

A 8 0 K 0 85 K 0 88 K

117 MPa 0

A

0

A

0

0

A O n

0

A

0

0 10-41 I I I I

0 0 2 0.4 0.6 0.8 1.0

PRESSURE ( A t m Fig. 3. Average creep rate of PCTFE vs. pressure of Nz for different temperatures (K): (0 ) 78,

(A) 80, (0 ) 85, (0) 88; u = 117 MPa.

specimen was loaded to a constant stress in an environment with the highest pressure and lowest temperature that would be used in the subsequent series of runs. (ii) The creep rate was measured for a short time and the strain incre- ment was measured. (iii) The specimen was partially unloaded so that the creep rate was zero. (v) The specimen was reloaded. (vi) The pressure and the creep rate was measured for a short time and the additional increment of creep strain was measured. (vii) The procedure was continued until the specimen fractured. The relative velocity of the crazes a t each value of P and T was equal to i/i2f3 in accordance with eq. (2). Depending on the fracture strain, six to about twenty different combinations of P and T could be examined on a single specimen. Most importantly, the values of the relative velocity were independent of the order in which the P pressures and temperatures were chosen as long as the factor A in eq. (2) was kept constant by not changing the number of crazes. As will be demonstrated by the experimental results the parameter that determines the craze density and the craze velocity is P exp(Q/RT) and the stress.

(iv) The pressure and temperature were changed.

1984 BROWN AND METZGER

lo-’ I I I I I 1

0 7 8 K

A 8 O K

0 8 5 K 0 8 8 K

117 M P a

.lp A I O

i I

1 I I I I I I

0 0.2 0.4 0.6 00 1.0 I

R E L A T I V E PRESSURE (PIP,)

Fig. 4. Creep rates of Figure 3 plotted against the relative pressure. Symbols as in Figure 3.

RESULTS

Creep Tests on Many Specimens The effects of P and T on the creep curves of PCTFE in N2 environments are

shown in Figures 1 and 2, respectively. The creep curves are all cubic in accor- dance with eq. (1). In general, increasing P increases the creep rate. However, increasing T decreases the creep rate which is contrary to expectation. As we shall see later, the usual behavior of increasing creep rate with increasing tem- perature occurs at temperatures further above the boiling point of the environ- mental gas. In order to understand the fundamental basis for the effects of P and T on creep, it is necessary to determine how the individual parameters in eq. (1) depend on P and T . Using a different specimen for many different combinations of P, T, and the stress c7 the parameters p7 u, k l , and k2 were measured. The results are shown in Table I. The geometric parameters k l and k2 were not sensitive to P, T, or c, but the primary effect of these variables was on p and u.

From the data in Table I it was found that the effects of P and T on the average creep rate could be combined into a single variable which we will call the relative pressure. The relative pressure is given by PIP,, where P, is the vapor pressure of the gas that would be in equilibrium with the liquid at that temperature. Thus

CRAZE VELOCITY 1985

$25$ 2 N 0 A 8 5 K 8 0 K

0 8 8 K p 20 117 MPa

a (L V

0

0.1 0.2

RELATIVE PRESSURE ( P I P v )

Fig. 5. Number of crazes vs. relative pressure for PCTFE in N2 at a stress of 117 MPa. Symbols as in Figure 3.

- = e x p [ - ? ( k - + ) ] P P" (3)

where Q, is the heat of vaporization and TB is the boiling point. In Figure 3 the average creep rate i is plotted against P for various T. In Figure 4, i is plotted against the relative pressure where for Nz, TB is 77.8 K, and Q, is 1335 cal/mole. It is seen that the relative pressure combines the effects of P and T .

In Figures 5 and 6, p and u are plotted against the relative pressures. It is seen that p is approximately a linear function of the relative pressure, whereas lnu is a linear function at low u. The relative pressure is also the important variable that controls the physical adsorption of gases on solid surfaces.

Creep tests on the other polymers, PMMA and PS, and in other gaseous en- vironments showed that at low temperatures near the boiling point, the effects of P and T on creep rate, p and u , could be combined in terms of the relative pressure. These experiments suggested that the effects of P and T on u were reversible and single valued.

Multiple Creep Tests on a Single Specimen

To test the idea that u was a single-valued and reversible function of P and T , a single specimen with a constant density of crazes was used. The same specimen was allowed to creep for a short period of time at a given combination of P and T. Using eq. (2) with A being constant because p was kept constant, the relative velocity was determined for the various combinations of P and T . The results for PCTFE in CH4, PCTFE in Nz, PS in Nz, and PMMA in Nz are shown in Figures 7,8,9, and 10, respectively. For CH4, TB is 111.7 K and QU is 1950 cal/mole. These experiments showed that the craze velocity was (a) in-

1986 BROWN AND METZGER

I € , , 1 l I I I

0 7 8 K A 8 O K 0 8 5 K 0 8 8 K

117 M P a

0 01 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 10

RELATIVE PRESSURE ( P/P,)

Fig. 6. Velocity of crazes vs. relative pressure for PCTFE in Nz a t a stress of 117 MPa. Symbols as in Figure 3.

dependent of the sequence of the t,ests and (b) depended on the relative pressure. The curve on the extreme left of each of the Figures 7-10 combines all data showing lnu as a function of the relative pressure.

Experiments with hydrogen environments at one atmosphere and at 78 K did not produce crazes. This result is expected because under these conditions the relative pressure is practically zero.

DISCUSSION

The results show that both the craze velocity and the density of crazes are monotonic function of the relative pressure given by the parameter

Also, the velocity is a reversible function of the effective pressure. The adsorption of gases on polymers as measured by the coverage is also reversible and governed by the above parameter. A detailed analysis of the adsorption isotherms shows that heat of adsorption is not exactly equal to Qo and also varies with the cov- erage. A similar calculation for the heat of adsorption can be made using the

CRAZE VELOCITY 1987

w

f 4 w !x

I I I I I PCTFE -CH, c = 121 MPa

0 01 0 0.2 04 06 0 8 10

PRESSURE (aim) OR RELATIVE PRESSURE

Fig. 7. Relative velocity of crazes in PCTFE in CH4 vs. pressure and a t various temperatures. Curve on extreme left is relative velocity vs. relative pressure and was obtained by combining all the curves. Temperatures (K): ( 0 ) 119.0, (0) 123.0, (A) 127.0, (0) 131.0, (V) 135.0; u = 121 MPa.

velocity isotherms in Figures 7-10 by assuming that the velocity is uniquely re- lated to the coverage. The heats of adsorption, so obtained, are nearly equal to Qo and vary somewhat with velocity.

It is of interest to quantitatively correlate the degree of coverage of the ad- sorbed gas to the craze velocity. It has been observed that for many polymers1"16 and graphite a t a relative pressure of about 0.2, the coverage is equivalent to a monolayer for inert gases such as N2. Figure 11 shows the data of Pierce17 on the coverage of N2 or graphite as a function of the relative pressure. The ad- sorption isotherms for polymers have the same general shape as for graphite which roughly follows the BET theory. Thus, by combining Figures 11 and 6, Figure 12 was produced showing how u probably varies with the number of layers of adsorbed N2. Figure 12 does not mean that the adsorbed layers are uniformly distributed on the surface.

Figures 6 and 12 show that if the velocity is extrapolated to zero coverage, the value is about cm/min. This is an important point because it says that crazes can grow at P = 0 although a t a rate which may be too slow to observe. Thus, it is best to take the viewpoint that there is no sharp boundary between the value of the velocity in vacuum and that in an N2 environment.

As N2 is added, the velocity increases exponentially with the coverage and then appears to reach a limiting value a t a coverage beyond about four layers. A possible explanation for this behavior is as follows. In order to enhance crazing, the gas must diffuse below the surface of the polymer in order to plasticize it.

1988 BROWN AND METZGER

10

$- c -2 > k V 0 1 _I w > l!d > 3 w

01

I I I I I

PCTFE- N2 u = 124 MPo

RELATIVE PRESSURE

- /* '*OK

' I

0.01 0 02 0.4 0.6 0.8 1.0

PRESSURE (atm) OR RELATIVE PRESSURE

Fig. 8. Same as Figure 7 except for PCTFE in Nz; rn = 124 MPa.

At low velocities the amount of gas that is effective is controlled by the concen- tration a t the surface. As the craze moves faster, the rate of diffusion into the polymer becomes more important until the rate of diffusion ultimately limits the velocity of the craze.

It is of interest to compare the velocity of a craze in gaseous environment with that in a liquid. Williams and co-workers18-20 and Kramer and Bubeck21 showed that for a craze growing from a crack a t high K I , the length increases as ~ ' 7 if the sides of the craze are protected from the liquid. The velocity is limited by hy- drodynamic transport of the liquid through the porous craze structure. As first suggested by Kambour22 the driving force is most likely the capillary pressure rather than atmospheric. For a gas the rate of permeation through the porous craze structure is extremely rapid because the gas has a much smaller viscosity than a liquid. Therefore, the internal surfaces of the craze should have the same coverage as the external surface of the specimen. Under these conditions the velocity of the craze is expected to be constant in a gaseous environment. Kramer and Burbeck21 also suggested the possibility that craze growth may be limited by diffusion ahead of the craze tip rather than by fluid transport through the craze as we have proposed above.

The results show that both the craze velocity and density of crazes decrease as the temperature increases above the boiling point. Thus, contrary to the usual creep behavior of materials we have a temperature range where the creep rate decreases with increasing temperature. In this temperature range the desorption of gas with increasing temperature dominates the creep behavior. Ultimately when the temperature is sufficiently high, the normal process of thermally ac- tivated deformation asserts itself so that the creep begins to increase with in-

CRAZE VELOCITY

I 0

1989

.I I i -

0 0 . 2 0 4 0 6 0.8 1.0

I l l 1 1 I

PS-N, u = 52.0 MPa

RELATIVE PRESSURE 7780K

/" 79.9'K

- 1 I I 1

PRESSURE (atrn) OR RELATIVE PRESSURE

0.5 06 07 08 09 10

Fig. 9. Same as Figure 7 except for PS in Nz; u = 52.0 MPa.

creasing temperature. Figure 13 shows how the creep rate of PCTFE in Nz goes through a minimum a t 120 K where the coverage becomes small so that the mechanism of thermally activated deformation can begin to dominate at higher temperatures.

I / I

1990 BROWN AND METZGER

I I I I I I I I I 8 -

I - I FROM C.J PIERCE J PHYS CHEM =,149(1953) t - FROM C J PIERCE J PHYS CHEM =,149(1953)

0 01 0 2 0 3 04 0 5 06 07 08 0 9 10 I I I I I I I I

0 01 0 2 0 3 04 0 5 06 07 08 0.9 10

RELATIVE PRESSURE (P/P,)

Fig. 11. Number of layers of Nz on graphite vs. the relative pressure (ref. 17).

An equation can now be written which describes the craze velocity in the region of low velocity, where lnu is a linear function of the relative pressure. Brown and Fischerll have previously shown that a t low velocities, the velocity varies exponentially with stress and is constant under a given stress. At low P

I I I I I

I I I I I 2 4 6 8 1 0

No. OF LAYERS OF N, 2

Fig. 12. Craze velocity in PCTFE vs. layers of adsorbed N2.

CRAZE VELOCITY 1991

P PCTFE

I I I I I

TEMPERATURE (OK)

Fig. 13. Creep rate of PCTFE vs. temperature in (1.0 atm) N:! environment. Below 120 K ad- Above 120 K thermally activated deformation processes sorption effects of the gas dominate.

dominate; u = 138 MPa.

where U is the activation energy for the deformation to produce crazing in the absence of N2, B1 is the slope of the curves in Figures 7-10, B2 is an activation volume, a is the stress, and uo is a constant. This equation shows that the ad- sorbed gas has the effect of reducing U just as does the work term B2a. This equation also predicts a minimum in the creep rate as shown in Figure 13. An- other important point about the above equation is that it shows that the rate- determining process is one of plastic deformation in which the adsorbed gas plays the role of reducing the activation energy. Probably the adsorbed gas reduces the activation energy by diffusing into a surface layer and thereby locally plas- ticizes the polymer.

CONCLUSIONS

(i) The velocity and number of crazes are functions of the relative pressure of the environmental gas.

(ii) A t low velocities, lnu is a linear function of P , but increases very slowly with P when the relative pressure produces a coverage of adsorbed gas which is more than about four monolayers.

(iii) At low coverage, lnu is nearly a linear function of the coverage of adsorbed gas, but a t higher coverage the velocity may be limited by the rate of diffusion of the gas into the polymer.

(iv) The velocity is determined by the rate of a microdeformation process whose activation energy is reduced by the plasticizing effect associated with the adsorbed gas.

The work was supported by the Army Research Office and by the NSF-MRL Program under Grant No. DMR-76-80994-A02.

1992 BROWN AND METZGER

References

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D. Pae, R. D. Morrow, and Yu Chen, Eds., Plenum, New York, 1972, p. 335. 4. S. Fischer and N. Brown, J . Appl. Phys., 44,4322 (1973). 5. M. F. Parrish and N. Brown, J. Macromol. Sci. Phys., B8,665 (1973). 6. H. G. Olf and A. Peterlin, Polymer, 14,78 (1973). 7. N. Brown and M. F. Parrish, in Recent Advances in Science and Technology of Materials,

8. H. G. Olf and A. Peterlin, J . Polym. Sci. Polym. Phys. Ed., 12,2209 (1974). 9. N. Brown and Y. Imai, J . Appl. Phys., 46,4130 (1975).

A. Bishay, Ed., Plenum, New York, 1974, Vol. 2, p. 1.

10. Y. Imai and N. Brown, J . Mater. Sci., 11,417 (1976). 11. N. Brown and S. Fischer, J . Polym. Sci. Polym. Phys. Ed., 13,1315 (1975). 12. Y. Imai and N. Brown, Polymer, 18,303 (1977). 13. N. Brown, B. D. Metzger, and Y. Imai, J . Polym. Sci. Polym. Phys. Ed., 16,1085 (1978). 14. D. Graham, J . Phys. Chem., 66,1815 (1962). 15. D. Graham, J . Phys. Chem., 68,2188 (1964). 16. D. C . Brought, D. D. Bruning, and J. J. Scholz, J. Colloid Interface Sci., 31,263 (1969). 17. C. J. Pierce, J. Phys. Chem., 57,149 (1953). 18. G . P. Marshall, L. E. Culver, and J. G. Williams, Proc. R. SOC. London Ser. A, 319, 165

19. J. G. Williams and G. P. Marshall, Proc. R. SOC. London Ser. A, 342,55 (1975). 20. I. D. Graham, J. G. Williams, and E. L. Zicky, Polymer, 17,439 (1976). 21. E. J. Kramer and R. A. B. Bubeck, J . Polym. Sci. Polym. Phys. Ed., 16,1195 (1978). 22. R. P. Kambour, J . Polym. Sci. Macromol. Reu., 7,1(1973).

(1970).

Received January 4,1980 Accepted April 16,1980