# Measurement of the residual mechanical properties of crazed polycarbonate. I: Qualitative analysis.

Stephen B. Clay (*)

A new technique to quantify the bulk craze density of transparent plates was used to characterize the craze growth behavior of polycarbonate at various stress levels. The craze growth rates were found to exponentially increase with an increase in stress, obeying the Eyring equation for thermally activated processes In the presence of an applied stress. The residual mechanical properties of crazed polycarbonate were then correlated to the crazing stress, relative craze density and strain rate. The results show that increasing the bulk craze density does not affect the yield stress but decreases both the failure stress and ductility of polycarbonate. Also, a crazing stress of 40 MPa was found to cause a much larger degree of degradation of failure properties than a crazing stress of 45 MPa. Correlating the crazing stress to the craze microstructure revealed that fewer, larger crazes form at the lower crazing stress. Therefore, flaw size has a greater effect on the failure properties of polycarbonate than flaw q uantity.

INTRODUCTION

Crazes, which are crack-like defects in polymers less than 1 [micro]m wide consisting of a web of highly strained microfibrils, have been a subject of investigation for the past 30 years (1-4). One reason for such widespread interest Is the fact that these defects are likely sites for crack initiation and often cause brittle failure of an otherwise ductile polymer. Crazing is even more prominent as polymers find their way into applications where they are replacing metals. Many of these new service environments contain craze accelerating agents such as solvents, high stress, high temperature, and high humidity.

Many papers have been published in an attempt to explain the initiation of crazes (5, 6), but there is still no universally accepted model for this mechanism. It is believed that the first step is one of main chain motion and the formation of nanovoids that are precursors to crazes (7). These voids are of the order of 30 nm and often form at stress concentrations like surface flaws or contaminant particles, although this is not always the case (5). The process of these voids developing into the planar bands called crazes is not well understood. It has been postulated that the stress distribution in the region of one void causes the formation of more voids nearby, perpendicular to the maximum principal stress direction (6).

Craze growth can be broken up into two components: craze tip advancement and craze thickening or widening (8). Craze tip advancement probably occurs through the formation of more voids from the stress concentration at the tip. Craze thickening involves the drawing of craze fibrils from bulk polymer (9).

Crazing has been categorized as a viscoelastic deformation process like creep and stress relaxation involving multiple localized deformation sites instead of bulk deformation. A theory has been developed in an attempt to describe creep and stress relaxation properties as thermally activated rate processes (10). This theory may also apply to craze growth since similar changes in the polymer must occur in both crazing and creep, only to a smaller degree. The theory begins with the Arrhenius equation, as shown In Eq 1, which generally describes how the temperature affects the frequency of thermally activated processes, such as chemical reactions.

[v] = [v.sub.o] exp (- [DELTA]H/RT) (1)

where v is the frequency of the chemical reactions. [v.sub.o] is a constant, [DELTA]H is the activation energy required to overcome the potential energy barrier for a given process, R is the gas constant, and T is the absolute temperature. For crazing, the energy barrier comes from the requirement of the polymer molecules to slide past one another (via reptation) and to undergo conformational changes.

Building on the Arrhenius equation, a model was developed to describe the effect of an applied stress on a thermally activated rate process (10). The applied stress is believed to produce changes in the potential energy barrier in a way that decreases the height of the barrier in the direction of flow, enhancing reptation and conformational changes necessary for crazing.

The Eyring equation describes the strain rate in the direction of the applied stress in a thermally activated deformation process. The Eyring equation that applies when the term v[sigma]/RT is large is

e [approximately equal to] [e.sub.o]/2 exp(- [DELTA]H - v[sigma]/RT) (2)

where e is the strain rate, [e.sub.o] is a constant, v is an activation volume, [DELTA]H, R, and T are defined as above, and [sigma] is the applied stress. This equation mathematically models the changes in the energy barrier due to an applied stress. If craze growth is a thermally activated rate process, then the growth equation will be of the same form as Eq 2.

The most common deformation mechanism for polycarbonate is shear yielding. Shear yielding is a ductile process involving large scale molecular motion during which the bulk polymer necks down to a significantly smaller cross sectional area (10). During this process, polycarbonate elongates to as much as 110% of its original length before fracture. In contrast to shear yielding, polycarbonate also crazes, which involves only very localized plastic deformation zones as described above. A craze-dominated failure will exhibit more brittleness than the typical yielding behavior. It has been found that crazing and shear yielding are competing mechanisms in polycarbonate and govern whether the failure mechanism is ductile or brittle (10-12).

The crazing literature concentrates on the initiation and growth of crazes, but is incomplete in the area of determining the effect of crazes on the mechanical properties of polymers. One obvious reason for this void is the absence of a universally accepted technique to measure the amount of crazing on a polymeric sample. Since this paper is devoted to measuring the residual mechanical properties of crazed polycarbonate, a technique to quantify the amount of crazing was developed as described in References 13 and 14. It should be noted that using a different setup and measurement procedure, especially for the optical craze measurement, will most assuredly result in different relative craze densities. Data obtained from a different setup can be compared to the results in this work if an appropriate correlation factor is determined and applied to the data.

One attempt to analytically predict the effect of crazing on the mechanical properties of polystyrene (PS) was presented by Tang and co-workers (15). They used the finite element method (FEM) to predict the elastic modulus in the craze fibril direction ([E.sub.1]), the elastic modulus perpendicular to the fibril direction ([E.sub.2]), the shear modulus ([G.sub.12]), and Poisson's ratio ([v.sub.12]) of crazed PS. In their model, they could consider only uniform, low density crazes because of software limitations. Their models were built around polymers with much more crazing than what was experimentally considered in this study. The authors found that crazed polymers have lower strength since crazes have a lower modulus and higher porosity than the undamaged bulk polymer. They found that [E.sub.1] decreased significantly, [v.sub.12] and [G.sub.12] decreased slightly, and [E.sub.2] was not affected. These results show that the properties perpendicular to the crazes are most affected, which could be expec ted. For this reason, all of the mechanical property measurements reported in this paper are in the direction perpendicular to the craze surfaces.

EXPERIMENTAL DETAILS

The material used in this study was a commercial grade 6-mm-thick polycarbonate sheet supplied by McMaster Cam. The number average molecular weight as measured by GPC was 19,450 g/mol with a polydispersity index of 2.2. The glass transition temperature determined from DSC was found to be 147[degrees]C. The as-received yield stress and elastic modulus were measured to be 65 MPa and 2.3 GPa, respectively.

The plates were cut into ASTM D638 Type III dumbbell specimens and sanded by hand in 2 stages. The samples were then mounted in the grip plates and equilibrated to the testing environment of 24[degrees]C and 85 [+ or -] 5% rh. Craze testing was performed in a sealed chamber in the presence of a distilled water reservoir under constant load at 24[degrees]C and 85 [+ or -] 5% rh, as described in detail in previous work (13, 14). The range of stress tested for this study was 40 to 50 MPa. While under stress, the relative craze density, craze area divided by standard gauge area, was measured with a reflective imaging system (13, 14) consisting of a CCD camera, backlight, and frame grabber. The craze growth charts were created using relative craze densities measured on the stored images with SigmaScan Pro(TM) image analysis software (16).

After being crazed to the desired level, each sample was equilibrated in a small dessicator to 11.3% rh in the presence of lithium chloride (17). The samples were then placed in airtight sample bags and transported to the Instron universal testing machine. The residual mechanical properties were measured immediately upon removal from the sample bags.

The mechanical performance of crazed polycarbonate was characterized by measuring the yield stress, elastic modulus, failure stress, and ductility for constant strain rate tensile tests. An Instron universal testing machine was used to perform the tensile tests at strain rates of 0.2 and 2 [min.sup.-1]. The yield stress was taken to be the maximum magnitude of stress before the constant drawing region of the stress-strain curve. The failure stress was measured as the maximum stress obtained by the polycarbonate just prior to fracture. The elastic modulus was calculated by measuring the slope of the initial linear portion of the curve where the strain was measured by a 1" MTS extensometer with 15% travel. The measure of ductility was taken to be the final length of the necked portion of the gauge section after fracture, normalized to the original gauge length of 50 mm.

RESULTS

Craze Growth Characterization

In an attempt to build a model to predict the residual mechanical properties of crazed polycarbonate, several samples were crazed to a relative craze density of 10% at 40, 45, and 50 MPa. The two metrics used to characterize the crazing behavior were crazing rate, R([sigma]), and time to reach 1% relative craze density, [t.sub.c1]([sigma]). These metrics are graphically identified for one test case in Fig. 1.

The stress dependent crazing rates were measured by calculating the slope of the linear part of the craze growth curve for stable growth. Figure 2 shows the craze growth rates as functions of stress. Two things apparent from the graph are that the craze growth rate increases exponentially with stress, and a competition between crazing and shear yielding exists at a crazing stress of 50 MPa.

The former observation shows that once the applied stress is high enough to produce crazing in a reasonable time frame, increasing the stress by only 5 MPa increases the crazing rate by an order of magnitude. It should be noted that craze growth is possible at stress levels lower than those investigated in this study. Also, the Eyring stress-rate theory presented previously shows that if crazing can be represented as a thermally activated rate process, then the effect of stress on the crazing rate would be of the general form shown in Eq 2 in which rate increases exponentially with applied stress. Figure 2 shows this relationship, indicating that changes in the growth rate of bulk craze density can be represented by the Eyring model of thermally activated processes in the presence of an externally applied stress.

The latter observation is a result of competitive mechanisms as described in the Introduction. When a high enough energy level exists, large scale macrodeformation occurs in the form of shear yielding. Over half of the polycarbonate samples tested at 50 MPa initially showed a lower than expected craze growth rate, and after one to four hours began to neck. An uncharacteristically low crazing rate exists because most of the energy is being absorbed by large scale motion rather than by the localized plastic deformation that occurs in crazing. The stress-strain curve for this material exhibits a yield stress around 65 MPa when tested at a strain rate of 0.2 [min.sup.-1] and shows a draw stress between 46 and 48 MPa. These results indicate that the draw stress acts as a lower bound below which delayed necking will not occur in a reasonable time frame since many of the 50 MPa tests yielded and none of the 45 MPa tests did.

The second metric for craze behavior characterization, time to reach 1% relative craze density ([t.sub.c1]([sigma]), was measured for each data set and plotted as a function of crazing stress in Fig. 3. These results show that the time to 1% relative craze density decreases exponentially with crazing stress. It should be noted that the samples that experienced delayed necking do not obey the relationship defined by the trend line in Fig. 3. This is because these samples are experiencing an entirely different deformation mechanism.

Mathematically, the relationship shown in Fig. 2, R([sigma]), represents the slope of a craze growth characterization curve while the relationship in Fig. 3, [t.sub.c1]([sigma]), is a point on the craze growth curve. Equation 3 incorporates these two expressions into a single equation that can be used to predict the craze growth chart for the test material as a function of stress between 40 and 50 MPa.

D([sigma], t) = R([sigma]) [t - [t.sub.c1]([sigma]) + 1 (3)

where D([sigma], t) is the relative craze density in %, R([sigma]) is the craze growth rate as a function of stress as shown in Fig. 2, t is the time under load in hrs, and [t.sub.c1]([sigma]) is the time to reach 1% relative craze density as a function of stress as shown in Fig. 3. Figure 4, displaying the goodness of fit, shows that Eq 3 is accurate, but large data scatter exists at the lower stress levels. This scatter is inherent in craze formation because of the nature of crazes forming at microscopic flaws that have wide distributions of size and quantity.

Residual Mechanical Properties

The data presented below have been organized in a way to try to decouple the effects of crazing stress, strain rate, and relative craze density on the failure stress and ductility. The yield stress and elastic modulus were also measured, but the detailed results are not reported since no correlation was found to crazing. A correlation between the crazing stress and craze microstructure was found and will be presented.

Table 1 shows the effect of crazing stress, relative craze density, and strain rate on the failure stress and ductility of polycarbonate. First, a correlation will be sought between crazing stress and failure stress. It can be seen that a crazing stress of 40 MPa results in a lower failure stress than a 45 MPa crazing stress. The reason for this is not obvious without the explanation provided below regarding a correlation between the crazing stress and craze microstructure. The table also shows that the failure stresses of samples crazed at 40 MPa were approximately 10% smaller than for uncrazed samples. This should be expected since failure initiates at flaws, and a surface with a higher craze density contains more and/or larger flaws.

Next, the effect of strain rate on failure stress will be considered. Table 1 shows that the failure stress is not significantly affected by increasing the strain rate from 0.2 to 2 [min.sup.-1]. Also, it is clear that at a crazing stress of 40 MPa, the failure stress is lower for 1% crazed samples than for uncrazed samples, but the failure stress is relatively constant when going from 1 to 10% relative craze density.

The effect of crazing stress on the ductility of poly-carbonate will now be considered. Table 1 shows that the ductility of polycarbonate crazed at 40 MPa is much lower than for polycarbonate crazed at 45 MPa. This agrees with the failure stress results. In that a lower crazing stress is more detrimental to the durability of polycarbonate. To further investigate this observation, the magnitude of crazing stress will be correlated to the microstructure of the crazes below.

A correlation will now be sought between strain rate and ductility of crazed polycarbonate. The results presented in Table i Indicate that an increase in strain rate causes a decrease in ductility for crazed polycarbonate. The decrease in ductility at the higher strain rate Is a result of the material in the vicinity of a flaw having insufficient time to relax, resulting in brittle failure. Another conclusion is that for a crazing stress of 40 MPa. the ductility of polycarbonate decreases significantly with as little as 1% relative craze density. but little change Is seen between 1% and 10% relative craze density. The crazes act as flaws, causing a much more brittle failure mode than seen In pristine material. It should also be noted that the data scatter is large compared to the magnitude of the ductility parameter. As mentioned before, failure properties are dependent on flaw distribution which inherently exhibits wide scatter.

A correlation between the craze microstructure and mechanical properties will now be investigated. Figure 5 compares the microstructure of a typical craze formed at 40 MPa to one formed at 45 MPa. Both images were taken at a relative craze density of 10%. The area of the craze formed at 40 MPa was more than 2.5 times the area of the craze formed at 45 MPa. Similar results have been found In the literature (1). Table 2 shows that the increased area is mostly the result of increased length. The craze formed at 40 MPa is more than twice as long as the other craze but is only about 25% wider.

One reason why the lower stress creates fewer, larger crazes could be that the crazes often form at microscopic flaws that produce stress concentrations. At the lower crazing stress, there are fewer flaws large enough to increase the local stress to the magnitude required for craze initiation. Fewer craze initiation sites means fewer crazes. This concept is illustrated in Fig. 6.

Figure 6 is a schematic representation of a microscopic region in the polycarbonate, with the filled circles representing a distribution of flaws with stress concentrations too low to initiate crazes at 40 MPa but high enough to initiate crazes at 45 MPa. The open circles represent a distribution of flaws with stress concentrations sufficient for craze initiation at 40 MPa. Figure 6a shows the region after 40 MPa has been held for 24 hours. By this time, the relative craze density has reached 2%, but the testing continues until 10% is obtained. Figure 6b shows the region under 40 MPa after 100 hrs. The filled circles still do not have local stresses high enough for craze initiation, so the crazes on the open circles are now very large, making up 10% relative craze density.

Figure 6c shows the region with a stress of 45 MPa held for 24 hrs. At this magnitude of stress, the filled circles had a high enough magnitude of local stress to initiate crazes. Now the total relative craze density consists of many more crazes, reaching 10% much faster. Since more crazes are involved, the crazes on the open circles were not grown as large as when the 40 MPa stress was applied. This model demonstrates that when polycarbonate is crazed to 10% with a stress of 40 MPa, the sample contains fewer, larger crazes than with a stress of 45 MPa.

Correlating the microstructure of crazes fanned at 40 and 45 MPa to the residual failure strength and ductility described above shows that the larger crazes formed at the lower stress level cause a much larger decrease in the failure strength and ductility of polycarbonate. In other words, flaw size has a greater effect on the failure properties of polycarbonate than flaw quantity.

CONCLUSIONS

The first step in determining the effect of crazing amount on the mechanical properties of polycarbonate was to measure the craze growth rate as a function of stress level. Testing showed that the craze growth rate increased exponentially with an increase in stress. This behavior has been shown to follow the Eyring stress-rate model describing the effect of an externally applied stress on thermally activated deformation processes. It has also been shown that the time to reach 1% relative craze density exponentially decreased with increasing stress level.

A competition between crazing and shear yielding was found to exist at a crazing stress of 50 MPa for the test material. Yielding and crazing behavior have certain potential energy barriers which must be overcome before deformation will occur. Locally, the energy barrier for crazing Is overcome at fairly low bulk stress levels due to localized stress concentrations such as pre-existing flaws. The energy barrier for yielding is eventually overcome as the magnitude of the bulk stress is increased to a high enough level. Since the draw stress has been shown to act as a lower bound below which delayed necking will not occur in a reasonable time frame, it is believed that the magnitude of the draw stress provides the energy needed to overcome the potential energy barrier for macrodeformation.

Crazing was found to affect the failure properties of polycarbonate much more than the elastic and yielding properties. This is because the yield stress and elastic modulus involve the coordinated motion of the polymer chains in the entire bulk region of the gage section, of which stress-induced crazing is a very small part. The failure properties are governed by the statistical distribution of flaws, which is much higher for a crazed sample than an uncrazed sample.

A crazing stress of 40 MPa decreased the failure stress and ductility much more than a crazing stress of 45 MPa.. In correlating these results to the craze microstructure, it was found that the crazes formed with the lower crazing stress were more than 2.5 times as large as the crazes formed at the higher crazing stress. It is concluded that flaw size has a greater effect on the failure properties of polycarbonate than flaw quantity.

Increasing the relative craze density from 0% to 1% significantly decreased both the failure stress and ductility, but an increase from 1% to 10% did not further affect the mechanical properties. The failure stress was not significantly affected by changing the strain rate, but the ductility of crazed samples decreased with an increase in strain rate.

FUTURE WORK

The data obtained in this study will be used to build a predictive model for the residual mechanical properties of crazed polycarbonate using the Design of Experiments approach. The results obtained in this paper combined with the Design of Experiments models could be used to develop failure criteria for crazed polycarbonate based on craze severity rather than just craze initiation. A fully developed model should include external factors such as stress, temperature, humidity, solvent exposure, and ultraviolet exposure and material properties such as molecular weight, molecular orientation, and chemical structure.

ACKNOWLEDGMENT

The authors would like to acknowledge the Polymer Durability Group at Virginia Tech for technical support and facilities usage. Thanks is also due to Robert McCarty and the AFRL Next Generation Transparency program for providing funding and technical support throughout the scope of this project.

NOMENCLATURE

[T.sub.g] = Glass transition temperature

FEM = Finite element method

GPO = Gel permeation chromatography

DSC = Differential scanning calorimetry

ASTM = American Society for Testing and Materials

Rh = Relative humidity

CCD = Charge coupled device

(*.)Corresponding author. Email: stephen.clay@wpafb.af.mil

REFERENCES

(1.) R. P. Kambour, Journal of Polymer Science: Macromolecular Reviews, 7, 1 (1973).

(2.) T. C. B. McLeish, C. J. G. Plummer, and A. M. Donald, Polymer. 30, 1651 (1989).

(3.) S. S. Sternstein and L. Ongchin, Polymer Preprints, American Chemical Society. Division of Polymer Chemistry, 10, n2, 1117 (1969).

(4.) H. Z. Y. Han, T. C. B. McLeish, R. A. Duckett, N. J. Ward, A. F. Johnson, A. M. Donald, and M. Butler, Macromolecules, 31, 1348 (1998).

(5.) J. C. Arnold, Trends in Polymer Science (UK), 4, nl2, 403 (1996).

(6.) M. Ishikawa and H. Takahashi, Journal of Materials Science, 26, 1295 (1991).

(7.) J. Liu and A. F. Yee, Macromolecules, 33, 1338 (2000).

(8.) A. L. Volynskii and N. F. Bakeev, Solvent Crazing of Polymers, Elsevier, New York (1995).

(9.) G. J. Salomons, M. A. Singh, T. Bardouille, W. A. Foran, and M. S. Capel, Macromolecules, 32, 1264 (1999).

(10.) I. M. Ward and D. W. Hadley, An Introduction to the Mechanical Properties of Solid Polymers, John Wiley & Sons, Inc., New York (1993).

(11.) L. H. Sperling. Introduction to Physical Polymer Science, 2nd Edition, John Wiley & Sons, Inc., New York (1992).

(12.) S. A. Xu and S. C. Tjong, European Polymer Journal (USA), 34, n8, 1143 (1998).

(13.) S. B. Clay and R. G. Kander, "A New Method to Quantify Crazing in Various Environments," Polymer Engineering and Science, In press.

(14.) S. B. Clay, PhD dissertation, Virginia Polytechnic Institute and State University (2000) http://scholar.lib.vt.edu/theses/available/etd-08142000-13410044/.

(15.) C. Y. Tang, L. C. Chan, M. Jie, and C. H. Yu, Key Engineering Materials (Switzerland), 145-149, nl, 249 (1998).

(16.) SigmaScan Pro User's Manual, Jandel Corporation, San Rafael. Calif. (1995).

(17.) L Greenspan, "Humidity Fixed Points of Binary Saturated Aqueous Solutions," Journal of Research of the National Bureau of Standards-A. Physics and Chemistry, 81A, nl, 89, (Jan-Feb 1977).

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[Figure 5 omitted]

[Figure 6 omitted]

A new technique to quantify the bulk craze density of transparent plates was used to characterize the craze growth behavior of polycarbonate at various stress levels. The craze growth rates were found to exponentially increase with an increase in stress, obeying the Eyring equation for thermally activated processes In the presence of an applied stress. The residual mechanical properties of crazed polycarbonate were then correlated to the crazing stress, relative craze density and strain rate. The results show that increasing the bulk craze density does not affect the yield stress but decreases both the failure stress and ductility of polycarbonate. Also, a crazing stress of 40 MPa was found to cause a much larger degree of degradation of failure properties than a crazing stress of 45 MPa. Correlating the crazing stress to the craze microstructure revealed that fewer, larger crazes form at the lower crazing stress. Therefore, flaw size has a greater effect on the failure properties of polycarbonate than flaw q uantity.

INTRODUCTION

Crazes, which are crack-like defects in polymers less than 1 [micro]m wide consisting of a web of highly strained microfibrils, have been a subject of investigation for the past 30 years (1-4). One reason for such widespread interest Is the fact that these defects are likely sites for crack initiation and often cause brittle failure of an otherwise ductile polymer. Crazing is even more prominent as polymers find their way into applications where they are replacing metals. Many of these new service environments contain craze accelerating agents such as solvents, high stress, high temperature, and high humidity.

Many papers have been published in an attempt to explain the initiation of crazes (5, 6), but there is still no universally accepted model for this mechanism. It is believed that the first step is one of main chain motion and the formation of nanovoids that are precursors to crazes (7). These voids are of the order of 30 nm and often form at stress concentrations like surface flaws or contaminant particles, although this is not always the case (5). The process of these voids developing into the planar bands called crazes is not well understood. It has been postulated that the stress distribution in the region of one void causes the formation of more voids nearby, perpendicular to the maximum principal stress direction (6).

Craze growth can be broken up into two components: craze tip advancement and craze thickening or widening (8). Craze tip advancement probably occurs through the formation of more voids from the stress concentration at the tip. Craze thickening involves the drawing of craze fibrils from bulk polymer (9).

Crazing has been categorized as a viscoelastic deformation process like creep and stress relaxation involving multiple localized deformation sites instead of bulk deformation. A theory has been developed in an attempt to describe creep and stress relaxation properties as thermally activated rate processes (10). This theory may also apply to craze growth since similar changes in the polymer must occur in both crazing and creep, only to a smaller degree. The theory begins with the Arrhenius equation, as shown In Eq 1, which generally describes how the temperature affects the frequency of thermally activated processes, such as chemical reactions.

[v] = [v.sub.o] exp (- [DELTA]H/RT) (1)

where v is the frequency of the chemical reactions. [v.sub.o] is a constant, [DELTA]H is the activation energy required to overcome the potential energy barrier for a given process, R is the gas constant, and T is the absolute temperature. For crazing, the energy barrier comes from the requirement of the polymer molecules to slide past one another (via reptation) and to undergo conformational changes.

Building on the Arrhenius equation, a model was developed to describe the effect of an applied stress on a thermally activated rate process (10). The applied stress is believed to produce changes in the potential energy barrier in a way that decreases the height of the barrier in the direction of flow, enhancing reptation and conformational changes necessary for crazing.

The Eyring equation describes the strain rate in the direction of the applied stress in a thermally activated deformation process. The Eyring equation that applies when the term v[sigma]/RT is large is

e [approximately equal to] [e.sub.o]/2 exp(- [DELTA]H - v[sigma]/RT) (2)

where e is the strain rate, [e.sub.o] is a constant, v is an activation volume, [DELTA]H, R, and T are defined as above, and [sigma] is the applied stress. This equation mathematically models the changes in the energy barrier due to an applied stress. If craze growth is a thermally activated rate process, then the growth equation will be of the same form as Eq 2.

The most common deformation mechanism for polycarbonate is shear yielding. Shear yielding is a ductile process involving large scale molecular motion during which the bulk polymer necks down to a significantly smaller cross sectional area (10). During this process, polycarbonate elongates to as much as 110% of its original length before fracture. In contrast to shear yielding, polycarbonate also crazes, which involves only very localized plastic deformation zones as described above. A craze-dominated failure will exhibit more brittleness than the typical yielding behavior. It has been found that crazing and shear yielding are competing mechanisms in polycarbonate and govern whether the failure mechanism is ductile or brittle (10-12).

The crazing literature concentrates on the initiation and growth of crazes, but is incomplete in the area of determining the effect of crazes on the mechanical properties of polymers. One obvious reason for this void is the absence of a universally accepted technique to measure the amount of crazing on a polymeric sample. Since this paper is devoted to measuring the residual mechanical properties of crazed polycarbonate, a technique to quantify the amount of crazing was developed as described in References 13 and 14. It should be noted that using a different setup and measurement procedure, especially for the optical craze measurement, will most assuredly result in different relative craze densities. Data obtained from a different setup can be compared to the results in this work if an appropriate correlation factor is determined and applied to the data.

One attempt to analytically predict the effect of crazing on the mechanical properties of polystyrene (PS) was presented by Tang and co-workers (15). They used the finite element method (FEM) to predict the elastic modulus in the craze fibril direction ([E.sub.1]), the elastic modulus perpendicular to the fibril direction ([E.sub.2]), the shear modulus ([G.sub.12]), and Poisson's ratio ([v.sub.12]) of crazed PS. In their model, they could consider only uniform, low density crazes because of software limitations. Their models were built around polymers with much more crazing than what was experimentally considered in this study. The authors found that crazed polymers have lower strength since crazes have a lower modulus and higher porosity than the undamaged bulk polymer. They found that [E.sub.1] decreased significantly, [v.sub.12] and [G.sub.12] decreased slightly, and [E.sub.2] was not affected. These results show that the properties perpendicular to the crazes are most affected, which could be expec ted. For this reason, all of the mechanical property measurements reported in this paper are in the direction perpendicular to the craze surfaces.

EXPERIMENTAL DETAILS

The material used in this study was a commercial grade 6-mm-thick polycarbonate sheet supplied by McMaster Cam. The number average molecular weight as measured by GPC was 19,450 g/mol with a polydispersity index of 2.2. The glass transition temperature determined from DSC was found to be 147[degrees]C. The as-received yield stress and elastic modulus were measured to be 65 MPa and 2.3 GPa, respectively.

The plates were cut into ASTM D638 Type III dumbbell specimens and sanded by hand in 2 stages. The samples were then mounted in the grip plates and equilibrated to the testing environment of 24[degrees]C and 85 [+ or -] 5% rh. Craze testing was performed in a sealed chamber in the presence of a distilled water reservoir under constant load at 24[degrees]C and 85 [+ or -] 5% rh, as described in detail in previous work (13, 14). The range of stress tested for this study was 40 to 50 MPa. While under stress, the relative craze density, craze area divided by standard gauge area, was measured with a reflective imaging system (13, 14) consisting of a CCD camera, backlight, and frame grabber. The craze growth charts were created using relative craze densities measured on the stored images with SigmaScan Pro(TM) image analysis software (16).

After being crazed to the desired level, each sample was equilibrated in a small dessicator to 11.3% rh in the presence of lithium chloride (17). The samples were then placed in airtight sample bags and transported to the Instron universal testing machine. The residual mechanical properties were measured immediately upon removal from the sample bags.

The mechanical performance of crazed polycarbonate was characterized by measuring the yield stress, elastic modulus, failure stress, and ductility for constant strain rate tensile tests. An Instron universal testing machine was used to perform the tensile tests at strain rates of 0.2 and 2 [min.sup.-1]. The yield stress was taken to be the maximum magnitude of stress before the constant drawing region of the stress-strain curve. The failure stress was measured as the maximum stress obtained by the polycarbonate just prior to fracture. The elastic modulus was calculated by measuring the slope of the initial linear portion of the curve where the strain was measured by a 1" MTS extensometer with 15% travel. The measure of ductility was taken to be the final length of the necked portion of the gauge section after fracture, normalized to the original gauge length of 50 mm.

RESULTS

Craze Growth Characterization

In an attempt to build a model to predict the residual mechanical properties of crazed polycarbonate, several samples were crazed to a relative craze density of 10% at 40, 45, and 50 MPa. The two metrics used to characterize the crazing behavior were crazing rate, R([sigma]), and time to reach 1% relative craze density, [t.sub.c1]([sigma]). These metrics are graphically identified for one test case in Fig. 1.

The stress dependent crazing rates were measured by calculating the slope of the linear part of the craze growth curve for stable growth. Figure 2 shows the craze growth rates as functions of stress. Two things apparent from the graph are that the craze growth rate increases exponentially with stress, and a competition between crazing and shear yielding exists at a crazing stress of 50 MPa.

The former observation shows that once the applied stress is high enough to produce crazing in a reasonable time frame, increasing the stress by only 5 MPa increases the crazing rate by an order of magnitude. It should be noted that craze growth is possible at stress levels lower than those investigated in this study. Also, the Eyring stress-rate theory presented previously shows that if crazing can be represented as a thermally activated rate process, then the effect of stress on the crazing rate would be of the general form shown in Eq 2 in which rate increases exponentially with applied stress. Figure 2 shows this relationship, indicating that changes in the growth rate of bulk craze density can be represented by the Eyring model of thermally activated processes in the presence of an externally applied stress.

The latter observation is a result of competitive mechanisms as described in the Introduction. When a high enough energy level exists, large scale macrodeformation occurs in the form of shear yielding. Over half of the polycarbonate samples tested at 50 MPa initially showed a lower than expected craze growth rate, and after one to four hours began to neck. An uncharacteristically low crazing rate exists because most of the energy is being absorbed by large scale motion rather than by the localized plastic deformation that occurs in crazing. The stress-strain curve for this material exhibits a yield stress around 65 MPa when tested at a strain rate of 0.2 [min.sup.-1] and shows a draw stress between 46 and 48 MPa. These results indicate that the draw stress acts as a lower bound below which delayed necking will not occur in a reasonable time frame since many of the 50 MPa tests yielded and none of the 45 MPa tests did.

The second metric for craze behavior characterization, time to reach 1% relative craze density ([t.sub.c1]([sigma]), was measured for each data set and plotted as a function of crazing stress in Fig. 3. These results show that the time to 1% relative craze density decreases exponentially with crazing stress. It should be noted that the samples that experienced delayed necking do not obey the relationship defined by the trend line in Fig. 3. This is because these samples are experiencing an entirely different deformation mechanism.

Mathematically, the relationship shown in Fig. 2, R([sigma]), represents the slope of a craze growth characterization curve while the relationship in Fig. 3, [t.sub.c1]([sigma]), is a point on the craze growth curve. Equation 3 incorporates these two expressions into a single equation that can be used to predict the craze growth chart for the test material as a function of stress between 40 and 50 MPa.

D([sigma], t) = R([sigma]) [t - [t.sub.c1]([sigma]) + 1 (3)

where D([sigma], t) is the relative craze density in %, R([sigma]) is the craze growth rate as a function of stress as shown in Fig. 2, t is the time under load in hrs, and [t.sub.c1]([sigma]) is the time to reach 1% relative craze density as a function of stress as shown in Fig. 3. Figure 4, displaying the goodness of fit, shows that Eq 3 is accurate, but large data scatter exists at the lower stress levels. This scatter is inherent in craze formation because of the nature of crazes forming at microscopic flaws that have wide distributions of size and quantity.

Residual Mechanical Properties

The data presented below have been organized in a way to try to decouple the effects of crazing stress, strain rate, and relative craze density on the failure stress and ductility. The yield stress and elastic modulus were also measured, but the detailed results are not reported since no correlation was found to crazing. A correlation between the crazing stress and craze microstructure was found and will be presented.

Table 1 shows the effect of crazing stress, relative craze density, and strain rate on the failure stress and ductility of polycarbonate. First, a correlation will be sought between crazing stress and failure stress. It can be seen that a crazing stress of 40 MPa results in a lower failure stress than a 45 MPa crazing stress. The reason for this is not obvious without the explanation provided below regarding a correlation between the crazing stress and craze microstructure. The table also shows that the failure stresses of samples crazed at 40 MPa were approximately 10% smaller than for uncrazed samples. This should be expected since failure initiates at flaws, and a surface with a higher craze density contains more and/or larger flaws.

Next, the effect of strain rate on failure stress will be considered. Table 1 shows that the failure stress is not significantly affected by increasing the strain rate from 0.2 to 2 [min.sup.-1]. Also, it is clear that at a crazing stress of 40 MPa, the failure stress is lower for 1% crazed samples than for uncrazed samples, but the failure stress is relatively constant when going from 1 to 10% relative craze density.

The effect of crazing stress on the ductility of poly-carbonate will now be considered. Table 1 shows that the ductility of polycarbonate crazed at 40 MPa is much lower than for polycarbonate crazed at 45 MPa. This agrees with the failure stress results. In that a lower crazing stress is more detrimental to the durability of polycarbonate. To further investigate this observation, the magnitude of crazing stress will be correlated to the microstructure of the crazes below.

A correlation will now be sought between strain rate and ductility of crazed polycarbonate. The results presented in Table i Indicate that an increase in strain rate causes a decrease in ductility for crazed polycarbonate. The decrease in ductility at the higher strain rate Is a result of the material in the vicinity of a flaw having insufficient time to relax, resulting in brittle failure. Another conclusion is that for a crazing stress of 40 MPa. the ductility of polycarbonate decreases significantly with as little as 1% relative craze density. but little change Is seen between 1% and 10% relative craze density. The crazes act as flaws, causing a much more brittle failure mode than seen In pristine material. It should also be noted that the data scatter is large compared to the magnitude of the ductility parameter. As mentioned before, failure properties are dependent on flaw distribution which inherently exhibits wide scatter.

A correlation between the craze microstructure and mechanical properties will now be investigated. Figure 5 compares the microstructure of a typical craze formed at 40 MPa to one formed at 45 MPa. Both images were taken at a relative craze density of 10%. The area of the craze formed at 40 MPa was more than 2.5 times the area of the craze formed at 45 MPa. Similar results have been found In the literature (1). Table 2 shows that the increased area is mostly the result of increased length. The craze formed at 40 MPa is more than twice as long as the other craze but is only about 25% wider.

One reason why the lower stress creates fewer, larger crazes could be that the crazes often form at microscopic flaws that produce stress concentrations. At the lower crazing stress, there are fewer flaws large enough to increase the local stress to the magnitude required for craze initiation. Fewer craze initiation sites means fewer crazes. This concept is illustrated in Fig. 6.

Figure 6 is a schematic representation of a microscopic region in the polycarbonate, with the filled circles representing a distribution of flaws with stress concentrations too low to initiate crazes at 40 MPa but high enough to initiate crazes at 45 MPa. The open circles represent a distribution of flaws with stress concentrations sufficient for craze initiation at 40 MPa. Figure 6a shows the region after 40 MPa has been held for 24 hours. By this time, the relative craze density has reached 2%, but the testing continues until 10% is obtained. Figure 6b shows the region under 40 MPa after 100 hrs. The filled circles still do not have local stresses high enough for craze initiation, so the crazes on the open circles are now very large, making up 10% relative craze density.

Figure 6c shows the region with a stress of 45 MPa held for 24 hrs. At this magnitude of stress, the filled circles had a high enough magnitude of local stress to initiate crazes. Now the total relative craze density consists of many more crazes, reaching 10% much faster. Since more crazes are involved, the crazes on the open circles were not grown as large as when the 40 MPa stress was applied. This model demonstrates that when polycarbonate is crazed to 10% with a stress of 40 MPa, the sample contains fewer, larger crazes than with a stress of 45 MPa.

Correlating the microstructure of crazes fanned at 40 and 45 MPa to the residual failure strength and ductility described above shows that the larger crazes formed at the lower stress level cause a much larger decrease in the failure strength and ductility of polycarbonate. In other words, flaw size has a greater effect on the failure properties of polycarbonate than flaw quantity.

CONCLUSIONS

The first step in determining the effect of crazing amount on the mechanical properties of polycarbonate was to measure the craze growth rate as a function of stress level. Testing showed that the craze growth rate increased exponentially with an increase in stress. This behavior has been shown to follow the Eyring stress-rate model describing the effect of an externally applied stress on thermally activated deformation processes. It has also been shown that the time to reach 1% relative craze density exponentially decreased with increasing stress level.

A competition between crazing and shear yielding was found to exist at a crazing stress of 50 MPa for the test material. Yielding and crazing behavior have certain potential energy barriers which must be overcome before deformation will occur. Locally, the energy barrier for crazing Is overcome at fairly low bulk stress levels due to localized stress concentrations such as pre-existing flaws. The energy barrier for yielding is eventually overcome as the magnitude of the bulk stress is increased to a high enough level. Since the draw stress has been shown to act as a lower bound below which delayed necking will not occur in a reasonable time frame, it is believed that the magnitude of the draw stress provides the energy needed to overcome the potential energy barrier for macrodeformation.

Crazing was found to affect the failure properties of polycarbonate much more than the elastic and yielding properties. This is because the yield stress and elastic modulus involve the coordinated motion of the polymer chains in the entire bulk region of the gage section, of which stress-induced crazing is a very small part. The failure properties are governed by the statistical distribution of flaws, which is much higher for a crazed sample than an uncrazed sample.

A crazing stress of 40 MPa decreased the failure stress and ductility much more than a crazing stress of 45 MPa.. In correlating these results to the craze microstructure, it was found that the crazes formed with the lower crazing stress were more than 2.5 times as large as the crazes formed at the higher crazing stress. It is concluded that flaw size has a greater effect on the failure properties of polycarbonate than flaw quantity.

Increasing the relative craze density from 0% to 1% significantly decreased both the failure stress and ductility, but an increase from 1% to 10% did not further affect the mechanical properties. The failure stress was not significantly affected by changing the strain rate, but the ductility of crazed samples decreased with an increase in strain rate.

FUTURE WORK

The data obtained in this study will be used to build a predictive model for the residual mechanical properties of crazed polycarbonate using the Design of Experiments approach. The results obtained in this paper combined with the Design of Experiments models could be used to develop failure criteria for crazed polycarbonate based on craze severity rather than just craze initiation. A fully developed model should include external factors such as stress, temperature, humidity, solvent exposure, and ultraviolet exposure and material properties such as molecular weight, molecular orientation, and chemical structure.

ACKNOWLEDGMENT

The authors would like to acknowledge the Polymer Durability Group at Virginia Tech for technical support and facilities usage. Thanks is also due to Robert McCarty and the AFRL Next Generation Transparency program for providing funding and technical support throughout the scope of this project.

NOMENCLATURE

[T.sub.g] = Glass transition temperature

FEM = Finite element method

GPO = Gel permeation chromatography

DSC = Differential scanning calorimetry

ASTM = American Society for Testing and Materials

Rh = Relative humidity

CCD = Charge coupled device

(*.)Corresponding author. Email: stephen.clay@wpafb.af.mil

REFERENCES

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Table 1 Effect of Crazing Stress, Relative Craze Density, and Strain Rate on the Mechanical Performance of Crazed Polycarbonate (Average and Standard Deviation of 3 Tests). Crazing Relative Strain Failure Ductility Stress Craze Rate Stress Parameter (MPa) Density (%) ([min.sup.-1]) (MPa) (mm/mm) 0 0 0.2 54.6 (5.12) 2.56 (0.54) 40 1 0.2 49.4 (2.81) 1.58 (0.78) 40 10 0.2 47.4 (1.92) 1.26 (0.58) 45 1 0.2 57.5 (5.75) 2.92 (0.56) 45 10 0.2 58.3 (4.77) 3.00 (0.42) 0 0 2 58.1 (4.01) 2.78 (0.44) 40 1 2 50.4 (0.70) 0.70 (0.06) 40 10 2 51.3 (2.94) 1.12 (1.08) 45 1 2 56.0 (2.11) 2.60 (0.20) 45 10 2 52.2 (1.93) 1.80 (0.72) Table 2 Dimensions of Crazes Formed at 40 and 45 MPa. Crazing Stress [right arrow] 40 MPa 45 MPa Area ([micro][m.sup.2]) 57 22 Length ([micro]m) 110 50 Width ([micro]m) 0.68 0.54 Aspect ratio (L/W) 162 93

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Author: | Clay, Stephen B.; Kander, Ronald G. |
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Publication: | Polymer Engineering and Science |

Geographic Code: | 1USA |

Date: | Jan 1, 2002 |

Words: | 4477 |

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