The craze initiation response of a polystyrene and a styrene-acrylonitrile copolymer during physical aging.
The failure of amorphous polymers in the glassy state is often preceded by a dilatational deformation process referred to as crazing (1). Additionally, polymers are often subjected to thermal treatments in which the temperature is rapidly changed from the melt (above the glass transition [T.sub.g]) to below [T.sub.g]. In this case the non-equilibrium glass undergoes spontaneous structural (volume or enthalpy) recovery towards equilibrium (2). Associated with the structural recovery are changes in such mechanical properties as modulus, yield strength and creep rupture lifetime which we refer to here as physical aging (2, 3) responses. While the theories (1, 4-10) of craze initiation indicate that the stress or strain at craze initiation depends upon such macroscopic properties as the yield stress and the shear modulus, which change during physical aging, there have been few studies of the effects of structural recovery on the craze response (or the craze response during physical aging).
Recently, Arnold (11) investigated the failure of polystyrene at two aging times, one day and 60 days, and demonstrated a higher strain at failure and a longer polymer lifetime for the sample aged one day. He noted that craze formation initiated earlier for the sample aged one day but that the crazes were more stable than those formed in the sample aged 60 days. Lifetime differences were attributed to the effects of aging on craze initiation, growth, and breakdown (11). Similarly, Ishikawa et al. (12) and Kambour et al. (13) found that crazing occurred at a lower strain for annealed or slowly cooled samples than for freshly quenched samples. [The slow cooling is equivalent to physical aging (2).] In contrast, Plummer and Donald (14) found that the strain to craze is independent of aging time. Crissman and McKenna (15, 16) also noted an essentially constant strain at failure in creep rupture experiments for poly(methylmethacrylate) aged for different times. Here it was only noted that the strain at craze initiation seemed to increase as the applied stress increased, indicating that the stress dependence of the craze initiation may not be the same as that for failure.
In the following we describe results from an investigation of the response of amorphous polystyrene (PS) and a styrene-acrylonitrile copolymer (SAN) during physical aging. First we summarize the models of craze initiation and then present results of craze initiation studies of PS and SAN using both equibiaxial stress and uniaxial strain test conditions.
THEORIES OF CRAZING
While there are several criteria proposed for the formation of crazes (1, 4-10), here we consider three widely used ones: the stress bias criterion of Sternstein and co-workers (6, 7); the porosity based model of Argon (8); the critical strain correlations of Kambour (1, 10).
According to Sternstein and Ongchin (6, 7) crazing should occur when the stress bias [[Sigma].sub.b] reaches a critical value of the magnitude of the difference between the first and second principal stresses [absolute value of [[Sigma].sub.1] - [[Sigma].sub.2]]:
[[Sigma].sub.b] = [absolute value of [[Sigma].sub.1] - [[Sigma].sub.2]] = A(T) + [B(T) / [I.sub.1] (1)
where A and B are material parameters that depend on temperature, T is temperature and [I.sub.1] is the first stress invariant (([I.sub.1] = [[Sigma].sub.1] + [[Sigma].sub.2] + [[Sigma].sub.3]). According to this model, crazing occurs as the result of a stress bias superimposed upon the dilatationally induced mobility caused by the hydrostatic component of the stress ([I.sub.1]/3). Hence, crazing doesn't occur in a pure hydrostatic tension and not in shear or compressive states of stress. Importantly, the model hypothesizes that the criterion for crazing is met when [I.sub.1] has a critical value [I.sub.1] [greater than] 0.
Since this study is concerned with the effects of structural recovery or physical aging and temperature on the craze initiation, the meaning of Equation 1 is not completely clear. However, it is known that A [less than] 0 and B [greater than] 0 and that the stress at crazing decreases with increasing temperature in constant rate of stress conditions. Further, to the extent that [Mathematical Expression Omitted] represents a dilatational or cavitational stress required to nucleate the craze process, we can deduce the expected effects of structural recovery on the material response. Our expectations are presented in Table 1.
Argon and co-workers proposed a craze initiation criterion that depends on attaining a critical porosity, [Beta], and a particular local stress state, when plastic expansion of the holes or micro-cracks leads to the formation of craze nuclei. The holes, or micro-cracks, are formed first by a thermally activated process. To a first approximation, the following is the local (at a flaw or heterogeneity) criterion for craze initiation:
[Sigma] = 2 [square root of 3[Tau]] / 3 ln(1 / [Beta]) and [[Beta].sub.i] [less than] 1 / 1 + 2[Mu]/[square root of 3[Tau]] (2)
where [Sigma] is the critical stress for craze initiation, [Beta] is the porosity, [[Beta].sub.i] is the initial porosity, [Mu] is the shear modulus, and [Tau] is the shear yield stress. Since both [Tau] and [Mu] increase with aging (3, 17), this model implies that the stress at crazing should increase as physical aging progresses. Furthermore, it might be expected that the initial porosity [[Beta].sub.i] decreases as aging time increases (densification occurs) and that [Beta] might decrease for a given applied stress owing to a stiffening of the material. These events would also suggest that the critical stress at crazing would increase as aging times get longer. Table 1 summarizes the expectations of the impact of structural recovery on crazing based on the Argon model.
As an aside, we note that Argon and Salama (9) proposed that craze propagation resulted from a "meniscus instability," or interface convolution, where the instability of the polymer "fluid" at the craze tip, which is under a suction gradient, results in "tufts" of polymer breaking off from the interface, and advancing the craze. The craze growth rate is proportional to a number of molecular and material parameters including the shear modulus, and indirectly, n, the exponent of the phenomenological constitutive equation [Mathematical Expression Omitted], where [[Sigma].sub.e] and [[Epsilon].sub.e], represent stress and strain, respectively, and A and n are functions of the polymeric material (9). Craze growth is not a part of this study.
In a semi-empirical approach, Kambour (10) investigated the critical strain for crazing, and determined the following correlations between the critical strain and material properties:
[[Epsilon].sub.c] [varies] CED x [Delta]T / [[Sigma].sub.y] and [[Epsilon].sub.c] [varies] CED x [Delta]T / E (3)
where CED is the Cohesive Energy Density (defined as the solubility parameter squared), [Delta]T is the difference between the glass transition temperature ([T.sub.g]) and the test temperature ([T.sub.Test]), [[Sigma].sub.y] is the tensile yield stress, and E is the Young's modulus. According to the correlations of Kambour, if the yield stress increases with aging time as expected, the critical strain should also decrease. Also, if one defines [Delta]T as the difference between the test temperature and the fictive temperature [T.sub.F]. (the extrapolation of the glassy volume or enthalpy to the liquid line along the glassy coefficient of expansion or enthalpy (2), one would anticipate [[Epsilon].sub.c] to decrease with aging (volume or enthalpy reduction during structural recovery). The expectations we have for the impact of structural recovery on the craze response from Eqs 3 are summarized in Table 1.
From the above we can anticipate what the impact of structural recovery should be on parameters such as the stress or strain to craze or the time to craze at a constant stress or strain as a function of aging time. The experimental results are compared, as far as possible, with the expectations given in Table 1.
Two materials were used as plaques: an injection molded commercial polystyrene and an injection molded commercial grade styrene-acrylonitrile copolymer (SAN), both from Dow Chemical Company (18). Before use in crazing experiments the samples were washed with Woolite (18) hypoallergenic laundry detergent, and then pressed at 150 [degrees] C to the appropriate thickness. Samples were wrapped in tissue and stored in plastic bags until annealing. To erase the injection molding induced thermal and mechanical histories, the samples were annealed in an oven at 117 [degrees] C (this annealing oven was measured to have a stability of [+ or -]3 [degrees] C during any given experiment). For aging at room temperature samples were wrapped in a tissue and stored in plastic bags until use. For higher temperatures, samples were wrapped in plastic Reynolds (18) oven bags, put in a double Reynolds (18) oven bag, and then placed in a silicone oil bath at either 40 [degrees] C or 60 [degrees] C (measurement of the bath temperatures indicated over the long aging times that the temperature fluctuated over a range of [+ or -]1 [degrees] C).
The first type of experiment was a biaxial test performed using the inflation of a circular film of 254 [[micro]meter] to 381 [[micro]meter] in thickness [apparatus of McKenna and Penn (19)]. The equibiaxial membrane stress at the pole of the inflated membrane is given by (20):
[Sigma] P[r.sub.c]/2t (4)
where [Sigma] is the membrane stress, P is the pressure, [r.sub.c] is the radius of curvature, and t is the thickness. The radius of curvature was determined using a spherometer. The criterion for craze initiation was the first visual observation of a craze using the naked eye with the aid of a flashlight. For samples tested at temperatures other than room temperature, the apparatus was preheated in an oven at either 40 [degrees] C or 60 [degrees] C ([+ or -]1 [degrees] C). Samples were inflated 30 min after annealing or removing from the silicone oil bath. For samples tested at 40 [degrees] C or 60 [degrees] C this allowed [approximately]15 min for the samples to reach thermal equilibrium in the test oven prior to inflation of the sheet for craze testing.
Uniaxial experiments were used to determine the critical strain at which crazing occurs by bending strips of material over a known varying curvature using a Bergen strain jig (21). In the critical strain experiments, samples were pressed to [approximately]508 [[micro]meter] thickness. For experiments carried out above room temperature, the jigs were pre-heated in an oven at either 40 [degrees] C or 60 [degrees] C ([+ or -]3 [degrees] C). At various times after loading, samples were removed from the oven for approximately two minutes to determine the position of the last craze. For these experiments, freshly quenched samples are defined as samples that were tested 15 to 20 min after annealing in order for thermal equilibration of the test jig to occur.
The results and their comparison with the expectations for each model are summarized in Table 2, Detailed results are presented in the following sections.
Equibiaxial Stress Tests
The effect of the aging time on the time for craze initiation at 60 [degrees] C for samples under equal biaxial stresses in the inflation apparatus is shown in Fig. 1. Several points are to be made from examination of this Figure. First, each data point represents a single measurement and the lines are placed as an aid to the eye. While there is considerable variability in the data (not unusual for failure related processes), there appear to be two regimes of behavior. At low stresses ([less than or equal to]11 MPa) the time to craze appears to follow a very strong dependence on the applied stress while at higher stresses ([greater than or equal to]11 MPa) the data seem to follow a lower stress dependence of the time to craze. The data at 22 [degrees] C seem to behave similarly, but the low to high stress demarcation has shifted to 15 to 16 MPa [ILLUSTRATION FOR FIGURE 2 OMITTED]. The 40 [degrees] C data (not shown) do not cover a [TABULAR DATA FOR TABLE 2 OMITTED] sufficient range of stresses to be conclusive. Interestingly, the the effect of aging is not obviously systematic.
Briefly summarizing, at 22 [degrees] C [ILLUSTRATION FOR FIGURE 2 OMITTED] there appears to be a slight increase in the time to craze as aging time increases in the low stress regime; however, the results are concentrated in the "crossover" from high to low slope and are not conclusive. Insufficient data were obtained at the high stresses to comment on these data. However, at 60 [degrees] C [ILLUSTRATION FOR FIGURE 1 OMITTED], it appears that at high stresses the time to craze decreases with aging time while at low stresses there is a single behavior. This combination of results would not be consistent with Eq 1. Because of the large variability in the data, firm conclusions are difficult to make, but the results for the polystyrene indicate that the impact of aging on the craze initiation behavior is complex and there may be two regimes of response. Importantly, the large variability in the polystyrene data is probably not due to the measurement method itself. This remark is substantiated by the results on the SAN in which the experimental scatter is significantly less than for the polystyrene, as discussed below.
While there are fewer results for the SAN copolymer, there is significantly less scatter in the data in Fig. 3 where the 22 [degrees] C aging response is shown for the SAN in biaxial tests. Here the results indicate that the time to craze increases with increasing aging time (from 20 h to 5 weeks), but that as the stress gets lower, the behaviors converge (or cross). This stress dependent impact of structural recovery on crazing seen in both the PS and SAN experiments is not currently readily explained. In fact, in the SAN, the higher the stress, the bigger the impact of aging on the time to craze - a result that is the opposite of the observation in viscoelastic measurements that the impact of aging is reduced as stress is increased (3).
Uniaxial Strain Tests
The uniaxial strain tests provide different information about crazing than do the biaxial stress tests. Besides the difference in deformation geometry, the test is designed to provide information about the time dependence of the appearance of a craze at different values of strain. In Fig. 4 the PS data are depicted as Critical Strain for crazing vs. time (after loading) at 22 [degrees] C for different aging times. As can be seen, the critical strain decreases as time increases and as aging time increases. The same data are cross-plotted in Fig. 5 as Critical Strain vs. aging time for different values of time (after loading). It can be readily seen that the strain at crazing decreases with loading time and with aging time. Interestingly, there is no evidence in these data of two regimes of behavior, as evidenced in the biaxial stress data. Similar data for the SAN at 22 [degrees] C are plotted as Critical Strain vs. (loading) time in Fig. 6. Again the critical strain decreases both with increasing (loading) time and aging time. The uniaxial strain testing is consistent with the concepts contained in Kambour's work, as described above. That is, aging should decrease the critical strain at craze initiation. The time dependence, on the other hand, suggests a more complicated picture than that expected from Eqs 3. It is known, for example, that the yield stress decreases with decreasing strain rate, which is equivalent, in some sense, to long relaxation times. Modulus similarly decreases. From Eqs 3, one would expect that the critical craze strain would increase because of the declining modulus and yield stress. This does not appear to be the case, as crazes continue to appear at ever smaller strains as loading time in the strain jig increases. On the other hand, if one considers that long (loading) times are equivalent to higher temperatures, then the effective [Delta]T in Eq 2 becomes less as loading time becomes greater and one might expect that the critical craze strain would also decrease as observed here.
For uniaxial testing, Eqs 3 anticipate that the temperature should have a significant effect on the time to craze. Figure 7 shows the impact of temperature on the time to craze in the uniaxial (relaxation) tests for the PS. As T increases ([Delta]T decreases) we observe that the critical strain to craze at a given loading time decreases and the loading time required for a given critical strain to craze decreases dramatically. Furthermore, we can compare the aging time effect on craze initiation with the temperature effect, anticipating that they might show similar influences if time-temperature and time-aging time correspondence principles of viscoelasticity (3) influence the craze initiation similarly. A plot of the logarithm of the time to attain a critical strain for crazing vs. 1/T, depicted in Fig. 8, shows that the impact of aging on the time to craze may be as great as the effect of temperature. This is particularly obvious in looking at the estimate of crazing time for the freshly quenched samples, which is long compared with the samples aged for two and five weeks.
On the other hand, a comparison of Figs. 1 and 2 shows that the impact of temperature on the craze response appears to be much greater for the constant biaxial stress tests than is aging. This is particularly obvious in the low stress regime. Why the craze response in constant stress tests and that in constant strain tests appear to be different is unclear at this time. The range of stresses studied in both cases is approximately the same. However, the biaxial stress tests have a (nearly) constant stress, while the Bergen jig tests are performed at a constant strain and the stress would be relaxing throughout the test. Future work should address this problem. An important point to be made here is that much of the data on crazing in the literature, besides that of Kambour, is taken under constant rate of deformation or stress conditions rather than in creep or relaxation as here. This might also be important to consider.
The impact of aging time, stress magnitude, and temperature on the crazing response of polystyrene and a styrene-acrylonitrile copolymer subjected to equibiaxial stress conditions has been studied. The same polymers were studied in uniaxial strain conditions and the critical strain to initiate a craze was measured as a function of loading time, temperature, and aging time. The general results are consistent with the expectation that the physical aging decreases the strain at crazing and increases the time to craze. However, there is some evidence that in the equibiaxial stress tests there are two regimes of response and that crazing under constant stress conditions may be different from that under constant strain conditions. At low stresses, aging has little effect on the time to craze and the stress dependence of the craze time is very strong. At higher stresses, the stress dependence becomes much less, but aging seems to decrease the time to craze in PS, yet increase it in the SAN. Consistent with expectations from Kambour's work (1, 10, 13), in constant strain experiments, increasing temperature and aging time both decrease the strain for craze initiation. The behavior and the expectations from three literature models are summarized in Table 2. Finally, further investigations are under way to more fully explore these phenomena.
Table 1. Expected Effects of Structural Recovery (Physical Aging) and Temperature on Craze Initiation.
Sternstein and Argon Models:
A. As aging time increases:
[[Sigma].sub.c], the stress at craze initiation, should increase because both the modulus G and the yield stress [[Sigma].sub.y] increase as aging time increases. This also implies that the time to craze at constant stress should increase.
B. As temperature increases:
[[Sigma].sub.c] should decrease because both G and [[Sigma].sub.y] decrease with increasing temperature.
C. As a caveat, the Argon model has a porosity term, which may change with aging and temperature but which is treated as a constant here.
A. As aging time increases:
[[Epsilon].sub.c], the strain for craze initiation at a given time after loading, should decrease because the reciprocal of the modulus 1/E and that of the yield stress 1/[[Sigma].sub.y] both decrease with increasing aging time. This allows the time to craze to vary with aging conditions because [[Epsilon].sub.c] depends on both time after load and aging time.
B. As temperature increases:
[[Epsilon].sub.c] should decrease because ([T.sub.g] - T) decreases.
C. A caveat here is that beyond the complexities of the time dependence of crazing, aging also affects the ([T.sub.g] - T) value. In normal cooling-type experiments, the structural recovery during aging causes the [T.sub.g] to decrease. If one heats the sample, however, it is often reported that the [T.sub.g] increases with aging. In either interpretation, the ([T.sub.g] - T) term in Kambour's relationships changes during aging.
Dr. G. Gusler would like to acknowledge support as an NRC Postdoctoral Research Associateship at NIST during her stay as a post-doctoral fellow in the NIST Polymers Division. We would also like to thank Dr. R. Bubeck and Dr. B. Landes of the Dow Chemical Company in Midland, Mich., for supplying the polystyrene and the styrene-acrylonitrile copolymer.
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18. Certain commercial materials and equipment are identified in this paper to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply necessarily that the product is the best available for the purpose.
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|Author:||Gusler, Gloria M.; McKenna, Gregory B.|
|Publication:||Polymer Engineering and Science|
|Date:||Sep 1, 1997|
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