# Determination of fracture toughness in rubber modified glassy polymers under impact conditions.

INTRODUCTION

The use of polymers is expanding into new fields and ever greater performance is demanded, especially on exposure to high strain rate. The measurements and analysis of the impact properties of polymers are still a controversial subject. The amount of energy absorbed by the polymer during impact depends on many variables, such as sample geometry, test temperature, impact velocity, and striker shape; relatively minor changes in any of these factors may induce the material to undergo a brittle-ductile transition. (1-3)

Conventional Izod and Charpy impact tests involve the measurement of the energy to break a notched specimen, generally divided by the ligament area. It is well known that such an analysis is not satisfactory, particularly since the parameter has a strong geometry dependence and doesn't provide a measurement of a critical initiation parameter. Fracture mechanics theory provides the necessary theoretical framework to overcome these disadvantages. However, to employ this theory under impact conditions is not simple, because of dynamic effects, and because it requires sophisticated acquisition data instrumentation. That is one reason why industry does not usually incorporate fracture analysis as a routine test.

Several methods have been developed for the analysis of impact data depending on whether the material undergoes brittle, ductile (3), or some intermediate mode of fracture. In our view, in aiming to change industry habits, the most appealing approaches are those that put the fracture mechanics problems in terms of energy rather than in terms of the maximum load. These methods involve the measuring of the energy consumed in the impact fracture by a pendulum impact machine, and the use of Charpy or Izod type specimens with sharp notches to suit the requirements of fracture mechanics. Early test programs demonstrated the utility of the approach when applied to brittle fracture (4-10). Data from these programs of work showed that for brittle fracture behavior, a basically linear relationship exists between the impact fracture energy and the specimen dimension and compliance function BW[Phi] (11). The slope of this relationship defines the critical strain energy release rate [G.sub.c] for unstable fracture. This assumption cannot be made where similar tests are carried out on materials showing nonlinear-elastic behavior. As Hodgkinson proposed (11), the fracture energy measured by an impact pendulum is a combination of crack initiation and propagation energies, including any energy to deform the material.

ABS (acrylonitrile-butadiene-styrene) and HIPS (butadiene rubber-modified polystyrene) are well-known rubber-modified thermoplastics. The most important characteristics of these multiphase products are the molecular weight of the matrix; phase-volume ratio; type of particle, particle size, and size distribution; interfacial bonding; and rubber crosslink density. Different combinations of these properties will lead to materials exhibiting different behaviors. Under the testing conditions used in this paper, all materials displayed nonlinear ductile behavior, with the sole exception of one modified polystyrene that displayed semiductile behavior.

Different approaches have appeared in the literature to provide an answer to the problem of testing materials exhibiting nonlinear effects: the elastic corrected method and [J.sub.c] analysis (1). The applicability of these methods to polymers has been questioned, and new approaches have been proposed (2, 3) that will also be considered in this paper.

These investigations aim to analyze the applicability of simple indirect methods for determining the impact fracture toughness of ductile polymers on ABS and modified PS and to compare the equivalence between the different critical parameters calculated from those methods.

EXPERIMENTAL

Materials

Four commercial grade materials have been investigated: two injection grade ABS type resins, mainly differing in rubber content (Monsanto Lustran ABS 240 and Lustran ABS 740); and two rubber-modified polystyrenes (PS) (Monsanto Lustrex 2220, medium impact, and Lustrex 4300, high impact), which also mainly differ in the rubber content. (Materials were kindly provided by Unistar Argentina S.A.)

Pellets of ABS resins were dried at 85 [degrees] C for 2 h under vacuum and then compression molded at 190 [degrees] C into thick plates 5, 6, 11 and 16 mm thick. Pellets of modified PS resins were dried at 65 [degrees] C for 2 h under vacuum and then compression molded at 180 [degrees] C into thick plates 5 and 6 mm thick. To release the residual stresses generated during molding, all plaques were submitted to a post-molding thermal treatment in which the samples were kept for 1 h at 120 [degrees] C for ABS and at 110 [degrees] C for PS under a slight pressure, and then slowly cooled to room temperature within the oven.

Ultrathin sections of compression molded specimens stained by Os[O.sub.4] were examined by transmission electron microscopy (TEM), and the numerical average diameter of the rubber subinclusions was calculated from the micrographs by means of a processing image PC software. ABS displayed a unimodal rubber-particle distribution while HIPS displayed a bimodal submicron rubber-particle distribution.

Table 1 and Table 2 display the materials' molecular and morphological data and conventional mechanical properties, respectively.

Impact Fracture Measurements

Impact experiments were carried out using a conventional ASTM D 256 non-instrumented Charpy Pendulum Instrument at an impact velocity of 3.5 m/s at 23 [degrees] C and at 80 [degrees] C. In the experiments carried out at 80 [degrees] C, ABS specimens were simply preheated in an oven at the desired temperature for at least 20 min and then quickly placed in the pendulum grips and impacted immediately.

Bars for impact characterization were cut from the compression molded plaques and then machined to reach the final dimensions and improve edge surface finishing. Tests were performed on samples with two different span lengths: 57 and 95 mm.

Sharp notches were introduced by scalpel-sliding a razor blade having an on-edge tip radius of 13 [[micro]meter]. The notch depth (a/W) was varied from 0.1 to 0.9. The thickness-to-depth ratios (B/W) were 0.5 and 1. For Lustran ABS 240 and for Lx 2220 resins, "V" and "U" side-grooved specimens were also tested. The reduction of thickness was 20% and the angle of "V" side grooves was 45 [degrees].

The impact fracture energy was taken directly from the scale on the machine. The energy values reported here were corrected by kinetics effects using the following equation:

[Mathematical Expression Omitted]

where g is the acceleration due to gravity, h is the height of fall (12), U[prime] is the uncorrected energy displayed by the instrument, and [K.sup.e] is the kinetic energy of the falling mass.

RESULTS AND DISCUSSION

Fracture Propagation Modes

Rubber toughening is one of the most successful methods of modifying the properties of brittle polymers. [TABULAR DATA FOR TABLE 1 OMITTED] Toughening mechanisms include crazing and shear yielding, both of which involve localized deformation of the brittle matrix associated with stress concentrations initiated by the rubber inclusions. Dispersed rubber particles toughen the matrix mainly by promoting multiple crazing in PS and by inducing an extensive combined crazing and yielding in SAN.

The presence of ductile fracture may be determined by the naked eye from the appearance of the fracture surface. The surface exhibits a whitening effect or becomes bright, reflecting light, due to craze formation (13). Another behavior was reported by Vu-Khanh and De Charentenay (2), a complex mode of fracture combining stable and unstable crack propagation mode: fracture initiates in a stable manner and at some point becomes unstable. They called it "semi-ductile" behavior. In these cases the fracture surfaces have different zones: shiny zones interspersed with dull zones. Figures 1a and b show macrophotos of typical fracture surfaces of ABS 240 and HIPS samples, respectively. Consistent with other authors' findings (1), all the broken samples appeared completely stress whitened, suggesting stable propagation. The surfaces of the broken samples of medium impact polystyrene, shown in Fig. 1c, exhibited a typical combined stable and unstable crack propagation mode displaying shiny and dull zones.

Wu (14) stated that the brittle-ductile (craze-yield) behavior of polymers and blends depends on both extrinsic and intrinsic variables. Extrinsic variables include rate, temperature, stress state, notch, and specimen geometry. Intrinsic variables include phase morphology and chain structure. Under a given extrinsic condition, different polymers or blends behave differently, because they have different chain structures and phase morphologies. The maximum responsiveness of a brittle polymer to rubber toughening occurs at an entanglement density close to 0.1 mmol/[cm.sup.3] in the matrix (14). In this range of entanglement density (such as SAN) the matrix can undergo massive combined crazing and yielding, as induced by rubber particles. In contrast, rubber particles mainly promote multiple crazing in brittle polymers having entanglement density [much less than] 0.1 mmol/[cm.sup.3] (such as PS).

The two rubber-modified polystyrenes investigated here displayed submicron particle diameters, which has been reported to be inefficient in toughening (15). However, Keskkula (16) reviewed the role of submicron particles in toughening in PS, reporting excellent impact strength in HIPS with bimodal rubber particle distribution and with the majority of the particles below the minimum critical rubber particle-size diameter. He suggested that a high concentration of small particles (small interparticle distance) controls the growth and termination of crazes. The crazes are initiated at large particles, and the small particles control the ductile PS ligament thickness in the fracture zone by a cooperative mechanism.

In light of the above discussion, the semiductile-ductile transition, which modified polystyrene has undergone through these investigations, may be justified in terms of the presence of a critical interparticular distance mainly associated with the difference in rubber content between Lustrex 2220 and 4300.

Data Analysis

Data points were analyzed following the different procedures proposed in the literature depending on the type of fracture exhibited by the materials, ductile or semiductile.

Ductile fracture with a stable crack propagation occurs with a continuous supply of energy from the striker to the specimen. Ductile effects during fracture, as suggested by Hodgkinson (11), are stress whitening, surface distortion, or hinging. In such cases the fracture energy measured by an impact pendulum is a combination of crack initiation and propagation energies. The latter includes any energy to deform the material. Regarding "semiductile" behavior, Vu-Khanh and De Charentenay (2) proposed that in the first zones the propagation of the crack is stable, that is, it develops on the basis of a continuous supply of additional energy from the external forces. In the second zone type, the fracture is unstable and the crack speed is very high in relation to that of the hammer. Fracture occurs with the aid of the strain energy stored in the sample.

Plati and Williams, corrected elastic method (1):

In the case of completely elastic behavior, the critical strain energy release rate [G.sub.c] can be expressed as follows (1):

[G.sub.c] = U/C dC/dA (2)

where C is the compliance of the specimen, U is the energy absorbed by the specimen during fracture, and A is the ligament area: B.(W - a). The factor C/(dC/d(d(a/W))) = [Phi], which depends on the length of crack size of the sample, can be calculated from the following equation (17):

[Phi] = [integral of] [Y.sup.2](x) xdx/[Y.sup.2](x)x + 1/18W 1/[Y.sup.2](x) x (3)

Y is computed from the equation given by Williams (18):

Y = [summation of] An[(a/W).sup.n] where 0 to 4

When the effects of plastic yielding are not negligible, Plati and Williams (1) proposed that LEFM could be extended by using an effective crack length, [a.sub.f] = a + [r.sub.p], where a is the original crack length and [r.sub.p] is the plastic zone length; [r.sub.p] is obtained iteratively by varying its value to give the best linear fit to the U vs. BW[Phi] plot.

The polynomial coefficients for the span-to-width ratios (S/W) used here were interpolated from the corresponding ones for S/W equal to 8 and 4 tabulated in Williams (18).

Plati and Williams, J analysis method:

Plati and Williams (1) also made a parallel proposal that under fully yielding conditions, as the elastic analysis is not still valid, the concept of [J.sub.c] should be used. In bending, [J.sub.c] can be determined as the double of the slope of the plot of the energy absorbed in the fracture U vs. the cross-sectional area of the ligament behind the notch, B.(W - a).

[J.sub.c] = 2U/B(W - a) (5)

For this expression to be valid, the energy absorbed, U, is that appropriate to the onset of crack propagation, which is not necessarily that under the complete load-deflection curve since this may represent extensive crack propagation (19).

Method of Vu-Khanh and De Charentenay:

Vu-Khanh and De Charentenay (2) proposed a model for the combined mode of fracture, called "semiductile."

They assumed that the fracture process takes place as ff there was only one stable crack propagation zone ([A.sub.1]), afterward, the remaining fractures are entirely brittle. The energy balance is therefore:

U = [G.sub.st][A.sub.1] + [G.sub.inst]BW[[Phi].sub.1] (6)

where [[Phi].sub.1] is [Phi] evaluated at the instability and [G.sub.st] is the mean value of the energy absorbed during the stable stage of propagation, obtained under the assumption that the variation in [G.sub.c] during stable propagation is linear.

From a plot of (U/[A.sub.1]) vs. (BW[Phi]/[A.sub.1]), [G.sub.st] and [G.sub.inst] can be obtained from the intercept and the slope of this straight line, respectively.

Vu-Khanh's method:

Recently, Vu-Khanh (3) proposed a new model for ductile impact fracture, assuming that the fracture energy [G.sub.r] varies linearly with crack extension following the expression:

[G.sub.r] = [G.sub.i] + [T.sub.a]A (7)

where [G.sub.i] is the fracture energy at crack initiation and [T.sub.a] is a material constant equivalent to the material tearing modulus that describes stable crack propagation.

The fracture energy, [G.sub.i], can be obtained from the U/A vs. A plot at the intercept of the curve.

ABS at Room Temperature

Hodgkinson (11) applied the elastic corrected method to highly ductile materials, proposing that ductile effects stem from plane stress, finding a certain dependence upon thickness in the measurements that supported his hypothesis. Figure 2 shows ABS 240 energy data points, corrected by plastic radius, against BW[Phi] obtained for samples having different thicknesses, with and without sidegrooves and tested with two different spans.

Figure 3 shows ABS 240 and 740 energy data fitted against ligament area. The linear correlation was found to be good.

Table 3 shows [r.sub.p] that leads to the best linear fit, the corresponding [G.sub.c] value; [J.sub.c] value and the correlation coefficients obtained for each analysis.

For both fittings, the results appeared to be independent of the B/W ratio and the span used as shown in Figs. 2 and 3. The critical initiation values calculated from the elastic corrected method are larger than that obtained from J method.

Results seem to have no influence of thickness, suggesting a plane strain condition at the crack tip; as confirmed by the minimum dimension calculated from ASTM E813 plain strain thickness requirements:

B, W - a [greater than] = 25([J.sub.c]/[[Sigma].sub.y]) (8)

assuming that [[Sigma].sub.y] in impact is equal to 80 MPa (this value was calculated by extrapolation at 3.5 m/s of the Eyring equation from [[Sigma].sub.y] values measured at different crosshead displacements).

Consistent with Newman's findings, our results were independent of the span, suggesting no rate effects at the testing conditions used here (20).

As shown in Table 3, [J.sub.c] increases with rubber content, consistent with the idea that at these rubber contents no important overlapping effects of stress fields are present. Dynamic [J.sub.c] appeared extremely higher than the ones obtained in static conditions (21).

ABS 240 data points were also fitted following Vu-Khanh's recommendations (3), [ILLUSTRATION FOR FIGURE 4 OMITTED]. In a later paper (22), Mai criticized some aspects of Vu-Khanh's model, stating that his model is equivalent to the "essential work of fracture" method, first developed by Broberg (23). This theory (24) was originally designated for plane stress ductile fracture of metals. For ductile materials with appropriate ligament length, the ligament will undergo full necking before crack initiation. Under this assumption, [W.sub.f] is the total work to fracture the specimen, We is the work for crack to growth inside the end zone, and [W.sub.p] is the work for plastic deformation that is not necessary condition for crack growth. In such conditions, for a given thickness, only the intercept value at A = 0, [W.sub.e], results to be a real material property, while [Beta]. [W.sub.p] is dependent on geometry. Cotterell (25) stated that We is equal to [J.sub.c], and the state of plane stress may arise from the usual size requirements for plain strain (Eq 8).

In the extreme case in which the plastic contribution [W.sub.p] is negligible respect to the "crack growth" work, if [W.sub.e] exists, it would be expected that Vu-Khanh's plots or "essential work of fracture" lead to a constant U/A value with respect to ligament area.

However, as it emerges from the results shown in Fig. 4, there is a decreasing trend between specific fracture energy and ligament area. Under impact bending conditions, the velocity of the crack varies during its propagation and the fracture energy cannot remain constant. Consequently, the concept of "essential work of fracture" does not appear to be applicable for the impact fracture characterization of rate-dependent materials like polymers.

[TABULAR DATA FOR TABLE 3 OMITTED]

The larger scatter found for data points [ILLUSTRATION FOR FIGURE 4 OMITTED] corresponding to small areas can be justified ff one considers that the absolute error in area determination is constant. This fact gives rise to an increasing relative error for small areas, which negatively affects the calculated U/A values.

Rubber Modified Polystyrene at Room Temperature

Figure 5 shows energy data points corrected by plastic radius against BW[Phi], and Fig. 6 shows energy data points vs. ligament area for Lustrex 4300 and Lustrex 2220. Critical values and statistics are displayed in Table 3.

In the case of the J method, the goodness of the fitting was excellent, and in the case of HIPS led to the same value of [J.sub.c] first published by Plati and Williams (1) for a high impact polystyrene of similar characteristics. Again, [G.sub.c] values were larger than [J.sub.c] ones, and large [r.sub.p] were necessary to reach an acceptable linear fitting. As an example, in the case of Lustrex 2220, Table 4 illustrates how the fitting is improved with the [r.sub.p] up to a maximum where the fit quality diminishes again. Obviously [G.sub.c] increased with the increase in [r.sub.p].

Figure 7 shows Vu-Khanh's plots for Lustrex 4300. The same considerations made with ABS are valid in this case.

For Lustrex 2220, as fracture surface revealed a semiductile behavior, data points were also fitted, following rigorously the method of Vu-Khanh and De Charentenay (2) Fig. 8. An acceptable fitting was found. Instability values resulted very close to the apparent [J.sub.c] value obtained without considering semiductile behavior. The [G.sub.inst] value that resulted was larger than the [G.sub.st] value. A similar result was reported by Vu-Khanh for PA11 (2) and was explained in terms of crack tip blunting before unstable crack propagation.

Consistent with fracture surface observations denoting a transition in the propagation mode, independently of the method used to evaluate the initiation criterion chose, a clear increasing trend with the rubber content was verified.

ABS Data at 80 [degrees] C

In room temperature tests, the extent of the craze whitening zone outside the process zone was inappreciable, while in the tests at higher temperatures, with the same characteristics stated before (17) a larger plastic zone appeared.

We assayed Lustran ABS 240 and 740 at 80 [degrees] C; the plots of energy data points against ligament area are shown in Fig. 9. In contrast to the findings of Newman and Williams (20), no negative intercept was found, even if the plastic zone depth was of the same order of penetration reported by these authors. The J method still showed a good correlation coefficient.

CONCLUDING REMARKS

The applicability of simple indirect methods for determining the impact fracture toughness of ductile polymers was analyzed with several commercial rubber modified thermoplastics (two injection grade ABS type resins and two rubber modified polystyrenes).

ABS and high impact polystyrene samples exhibited a whitening effect due to craze formation through the whole fracture surface, indicating that stable crack propagation was occurring. Medium impact polystyrene, however, exhibited a combined stable and unstable crack propagation mode, displaying shiny and dull zones on the surfaces of the broken samples.

Linear fittings between energy and ligament area (J method) always displayed high correlation coefficients.

The elastic corrected method gave somewhat complicated results because of the iterative calculations necessary to find [r.sub.p]. Relatively large [r.sub.p] values were calculated, leading to high critical values ([G.sub.c]).

The J method provides more conservative critical values than the elastic corrected method, especially at high toughness levels. This latter statement has serious implications for safety engineering design. However, both methods predict the same qualitative trends against rubber content.

At room temperature, plain strain conditions were always met. Results were independent of thickness and span-to-depth ratio.

For materials displaying ductile fracture, the essential work of fracture was also tried. Results suggested a rate effect that impeded the application of the essential work of fracture under impact conditions in bending.

The "semiductile" model of Vu-Khanh and De Charentenay (2) fitted Lustrex 2220 data points reasonably well. Instability values resulted that were very close to the apparent [J.sub.c] (2) value obtained in a simpler manner, without considering semiductile behavior.

Regarding studies carried out at 80 [degrees] C, the d method still accurately fit data points; showing a trend toward an increase in critical initiation value with the increase in temperature. Even if under this last condition the materials showed a considerable plastic zone, data points did not exhibit a negative intercept in the energy vs. ligament area plots. Therefore, the Williams' method (26) was inapplicable.

Further work will be done to determine impact J-R curves and initiation values by measuring J vs [Delta] a. This will allow us to compare the actual critical values with the ones obtained by indirect methods.

REFERENCES

1. E. Plati and J. G. Williams, Polym. Eng. Sci., 15, 470 (1975).

2. T. Vu-Khanh and F. X. de Charentenay, Polym. Eng. Sci., 25, 841 (1985).

3. T. Vu-Khanh, Polymer, 29, 1979 (1988).

4. J. G. Williams in Fracture Mechanics of Polymers, p. 237, Ellis Horwood, London (1984).

5. G. P. Marshall, J. G. Williams, and C. E. Turner, J. Mater. Sci., 8, 949 (1973).

6. M. Bramuzzo, Polym. Eng. Sci., 29, 1077 (1989).

7. C. E. Turner, Mater. Sci. Eng., 11, 275 (1973).

8. Y. Nakamura, M. Yamaguchi, and M. Okubo, Polym. Eng. Sci., 33, 279 (1993).

9. R. Greco and G. Ragosta, J. Mater. Sci., 23, 4171 (1988).

10. S. W. Koh, J. K. Kim, and Y. W. Mai, Polymer, 34, 3446 (1993).

11. J. M. Hodgkinson, K. H. L. Chow and J. G. Williams, 8th Intern. Conf Deform. Yield Fracture Polymers, 43/1, Churchill College, Cambridge, U.K. (April 1991).

12. D. R. Ireland, Instrumented Impact Testing, ASTM-STP 563, p. 7 (1973).

13. C. B. Bucknall, Plast., November 1967, 118.

14. S. Wu, Polym Intern, 29, 229 (1992).

15. C. B. Bucknall in Toughened Plastics, Applied Science, London (1977).

16. H. Keskkula, "Optimum Rubber Particle Size in High-Impact Polystyrene: Further Considerations," in Rubber-Toughened Plastics, C. K. Riew, Am. Chem. Soc. Series 12, 290 (1989).

17. J. G. Williams, in Fracture Mechanics of Polymers, p. 69, Ellis Horwood Limited, London (1984).

18. J. G. Williams, in Fracture Mechanics of Polymers, p. 67, Ellis Horwood Limited, London (1984).

19. A. J. Kinloch and R. J. Young in Fracture Behavior of Polymers, p. 196, Applied Science Publishers Ltd., England (1983).

20. L. V. Newman and J. G. Williams, Polym. Eng. Sci., 18, 893 (1978).

21. C. R. Bernal and P. M. Frontini, Polym. Testing, 11, 271 (1992).

22. Y.-W. Mai, Polymer Commun., 36, 330 (1989).

23. K. B. Broberg, J. Mech. Phys. Solids, 23, 215 (1975).

24. Y.-W. Mai and B. Cotterell, Int. J Fracture, 32, 105 (1986).

25. B. Cotterell and J. K. Reddel, Int. J. Fracture, 13, 267 (1977).

26. J. G. Williams, in Fracture Mechanics of Polymers, p. 262, Ellis Horwood Limited, London (1984).

The use of polymers is expanding into new fields and ever greater performance is demanded, especially on exposure to high strain rate. The measurements and analysis of the impact properties of polymers are still a controversial subject. The amount of energy absorbed by the polymer during impact depends on many variables, such as sample geometry, test temperature, impact velocity, and striker shape; relatively minor changes in any of these factors may induce the material to undergo a brittle-ductile transition. (1-3)

Conventional Izod and Charpy impact tests involve the measurement of the energy to break a notched specimen, generally divided by the ligament area. It is well known that such an analysis is not satisfactory, particularly since the parameter has a strong geometry dependence and doesn't provide a measurement of a critical initiation parameter. Fracture mechanics theory provides the necessary theoretical framework to overcome these disadvantages. However, to employ this theory under impact conditions is not simple, because of dynamic effects, and because it requires sophisticated acquisition data instrumentation. That is one reason why industry does not usually incorporate fracture analysis as a routine test.

Several methods have been developed for the analysis of impact data depending on whether the material undergoes brittle, ductile (3), or some intermediate mode of fracture. In our view, in aiming to change industry habits, the most appealing approaches are those that put the fracture mechanics problems in terms of energy rather than in terms of the maximum load. These methods involve the measuring of the energy consumed in the impact fracture by a pendulum impact machine, and the use of Charpy or Izod type specimens with sharp notches to suit the requirements of fracture mechanics. Early test programs demonstrated the utility of the approach when applied to brittle fracture (4-10). Data from these programs of work showed that for brittle fracture behavior, a basically linear relationship exists between the impact fracture energy and the specimen dimension and compliance function BW[Phi] (11). The slope of this relationship defines the critical strain energy release rate [G.sub.c] for unstable fracture. This assumption cannot be made where similar tests are carried out on materials showing nonlinear-elastic behavior. As Hodgkinson proposed (11), the fracture energy measured by an impact pendulum is a combination of crack initiation and propagation energies, including any energy to deform the material.

ABS (acrylonitrile-butadiene-styrene) and HIPS (butadiene rubber-modified polystyrene) are well-known rubber-modified thermoplastics. The most important characteristics of these multiphase products are the molecular weight of the matrix; phase-volume ratio; type of particle, particle size, and size distribution; interfacial bonding; and rubber crosslink density. Different combinations of these properties will lead to materials exhibiting different behaviors. Under the testing conditions used in this paper, all materials displayed nonlinear ductile behavior, with the sole exception of one modified polystyrene that displayed semiductile behavior.

Different approaches have appeared in the literature to provide an answer to the problem of testing materials exhibiting nonlinear effects: the elastic corrected method and [J.sub.c] analysis (1). The applicability of these methods to polymers has been questioned, and new approaches have been proposed (2, 3) that will also be considered in this paper.

These investigations aim to analyze the applicability of simple indirect methods for determining the impact fracture toughness of ductile polymers on ABS and modified PS and to compare the equivalence between the different critical parameters calculated from those methods.

EXPERIMENTAL

Materials

Four commercial grade materials have been investigated: two injection grade ABS type resins, mainly differing in rubber content (Monsanto Lustran ABS 240 and Lustran ABS 740); and two rubber-modified polystyrenes (PS) (Monsanto Lustrex 2220, medium impact, and Lustrex 4300, high impact), which also mainly differ in the rubber content. (Materials were kindly provided by Unistar Argentina S.A.)

Pellets of ABS resins were dried at 85 [degrees] C for 2 h under vacuum and then compression molded at 190 [degrees] C into thick plates 5, 6, 11 and 16 mm thick. Pellets of modified PS resins were dried at 65 [degrees] C for 2 h under vacuum and then compression molded at 180 [degrees] C into thick plates 5 and 6 mm thick. To release the residual stresses generated during molding, all plaques were submitted to a post-molding thermal treatment in which the samples were kept for 1 h at 120 [degrees] C for ABS and at 110 [degrees] C for PS under a slight pressure, and then slowly cooled to room temperature within the oven.

Ultrathin sections of compression molded specimens stained by Os[O.sub.4] were examined by transmission electron microscopy (TEM), and the numerical average diameter of the rubber subinclusions was calculated from the micrographs by means of a processing image PC software. ABS displayed a unimodal rubber-particle distribution while HIPS displayed a bimodal submicron rubber-particle distribution.

Table 1 and Table 2 display the materials' molecular and morphological data and conventional mechanical properties, respectively.

Impact Fracture Measurements

Impact experiments were carried out using a conventional ASTM D 256 non-instrumented Charpy Pendulum Instrument at an impact velocity of 3.5 m/s at 23 [degrees] C and at 80 [degrees] C. In the experiments carried out at 80 [degrees] C, ABS specimens were simply preheated in an oven at the desired temperature for at least 20 min and then quickly placed in the pendulum grips and impacted immediately.

Bars for impact characterization were cut from the compression molded plaques and then machined to reach the final dimensions and improve edge surface finishing. Tests were performed on samples with two different span lengths: 57 and 95 mm.

Sharp notches were introduced by scalpel-sliding a razor blade having an on-edge tip radius of 13 [[micro]meter]. The notch depth (a/W) was varied from 0.1 to 0.9. The thickness-to-depth ratios (B/W) were 0.5 and 1. For Lustran ABS 240 and for Lx 2220 resins, "V" and "U" side-grooved specimens were also tested. The reduction of thickness was 20% and the angle of "V" side grooves was 45 [degrees].

The impact fracture energy was taken directly from the scale on the machine. The energy values reported here were corrected by kinetics effects using the following equation:

[Mathematical Expression Omitted]

where g is the acceleration due to gravity, h is the height of fall (12), U[prime] is the uncorrected energy displayed by the instrument, and [K.sup.e] is the kinetic energy of the falling mass.

RESULTS AND DISCUSSION

Fracture Propagation Modes

Rubber toughening is one of the most successful methods of modifying the properties of brittle polymers. [TABULAR DATA FOR TABLE 1 OMITTED] Toughening mechanisms include crazing and shear yielding, both of which involve localized deformation of the brittle matrix associated with stress concentrations initiated by the rubber inclusions. Dispersed rubber particles toughen the matrix mainly by promoting multiple crazing in PS and by inducing an extensive combined crazing and yielding in SAN.

Table 2. Materials Conventional Mechanical Properties.

Impact Strength [[Sigma].sub.y] E Material (KG/[m.sup.2]) (MPa) (MPa)

Lustran ABS 240 5.3 47.5 2859.5 Lustran ABS 740 20.7 27.1 1823.4 Lustrex 2200 4.9 21.9 2608.1 Lustrex 4300 8.2 20.6 1936.7

The presence of ductile fracture may be determined by the naked eye from the appearance of the fracture surface. The surface exhibits a whitening effect or becomes bright, reflecting light, due to craze formation (13). Another behavior was reported by Vu-Khanh and De Charentenay (2), a complex mode of fracture combining stable and unstable crack propagation mode: fracture initiates in a stable manner and at some point becomes unstable. They called it "semi-ductile" behavior. In these cases the fracture surfaces have different zones: shiny zones interspersed with dull zones. Figures 1a and b show macrophotos of typical fracture surfaces of ABS 240 and HIPS samples, respectively. Consistent with other authors' findings (1), all the broken samples appeared completely stress whitened, suggesting stable propagation. The surfaces of the broken samples of medium impact polystyrene, shown in Fig. 1c, exhibited a typical combined stable and unstable crack propagation mode displaying shiny and dull zones.

Wu (14) stated that the brittle-ductile (craze-yield) behavior of polymers and blends depends on both extrinsic and intrinsic variables. Extrinsic variables include rate, temperature, stress state, notch, and specimen geometry. Intrinsic variables include phase morphology and chain structure. Under a given extrinsic condition, different polymers or blends behave differently, because they have different chain structures and phase morphologies. The maximum responsiveness of a brittle polymer to rubber toughening occurs at an entanglement density close to 0.1 mmol/[cm.sup.3] in the matrix (14). In this range of entanglement density (such as SAN) the matrix can undergo massive combined crazing and yielding, as induced by rubber particles. In contrast, rubber particles mainly promote multiple crazing in brittle polymers having entanglement density [much less than] 0.1 mmol/[cm.sup.3] (such as PS).

The two rubber-modified polystyrenes investigated here displayed submicron particle diameters, which has been reported to be inefficient in toughening (15). However, Keskkula (16) reviewed the role of submicron particles in toughening in PS, reporting excellent impact strength in HIPS with bimodal rubber particle distribution and with the majority of the particles below the minimum critical rubber particle-size diameter. He suggested that a high concentration of small particles (small interparticle distance) controls the growth and termination of crazes. The crazes are initiated at large particles, and the small particles control the ductile PS ligament thickness in the fracture zone by a cooperative mechanism.

In light of the above discussion, the semiductile-ductile transition, which modified polystyrene has undergone through these investigations, may be justified in terms of the presence of a critical interparticular distance mainly associated with the difference in rubber content between Lustrex 2220 and 4300.

Data Analysis

Data points were analyzed following the different procedures proposed in the literature depending on the type of fracture exhibited by the materials, ductile or semiductile.

Ductile fracture with a stable crack propagation occurs with a continuous supply of energy from the striker to the specimen. Ductile effects during fracture, as suggested by Hodgkinson (11), are stress whitening, surface distortion, or hinging. In such cases the fracture energy measured by an impact pendulum is a combination of crack initiation and propagation energies. The latter includes any energy to deform the material. Regarding "semiductile" behavior, Vu-Khanh and De Charentenay (2) proposed that in the first zones the propagation of the crack is stable, that is, it develops on the basis of a continuous supply of additional energy from the external forces. In the second zone type, the fracture is unstable and the crack speed is very high in relation to that of the hammer. Fracture occurs with the aid of the strain energy stored in the sample.

Plati and Williams, corrected elastic method (1):

In the case of completely elastic behavior, the critical strain energy release rate [G.sub.c] can be expressed as follows (1):

[G.sub.c] = U/C dC/dA (2)

where C is the compliance of the specimen, U is the energy absorbed by the specimen during fracture, and A is the ligament area: B.(W - a). The factor C/(dC/d(d(a/W))) = [Phi], which depends on the length of crack size of the sample, can be calculated from the following equation (17):

[Phi] = [integral of] [Y.sup.2](x) xdx/[Y.sup.2](x)x + 1/18W 1/[Y.sup.2](x) x (3)

Y is computed from the equation given by Williams (18):

Y = [summation of] An[(a/W).sup.n] where 0 to 4

When the effects of plastic yielding are not negligible, Plati and Williams (1) proposed that LEFM could be extended by using an effective crack length, [a.sub.f] = a + [r.sub.p], where a is the original crack length and [r.sub.p] is the plastic zone length; [r.sub.p] is obtained iteratively by varying its value to give the best linear fit to the U vs. BW[Phi] plot.

The polynomial coefficients for the span-to-width ratios (S/W) used here were interpolated from the corresponding ones for S/W equal to 8 and 4 tabulated in Williams (18).

Plati and Williams, J analysis method:

Plati and Williams (1) also made a parallel proposal that under fully yielding conditions, as the elastic analysis is not still valid, the concept of [J.sub.c] should be used. In bending, [J.sub.c] can be determined as the double of the slope of the plot of the energy absorbed in the fracture U vs. the cross-sectional area of the ligament behind the notch, B.(W - a).

[J.sub.c] = 2U/B(W - a) (5)

For this expression to be valid, the energy absorbed, U, is that appropriate to the onset of crack propagation, which is not necessarily that under the complete load-deflection curve since this may represent extensive crack propagation (19).

Method of Vu-Khanh and De Charentenay:

Vu-Khanh and De Charentenay (2) proposed a model for the combined mode of fracture, called "semiductile."

They assumed that the fracture process takes place as ff there was only one stable crack propagation zone ([A.sub.1]), afterward, the remaining fractures are entirely brittle. The energy balance is therefore:

U = [G.sub.st][A.sub.1] + [G.sub.inst]BW[[Phi].sub.1] (6)

where [[Phi].sub.1] is [Phi] evaluated at the instability and [G.sub.st] is the mean value of the energy absorbed during the stable stage of propagation, obtained under the assumption that the variation in [G.sub.c] during stable propagation is linear.

From a plot of (U/[A.sub.1]) vs. (BW[Phi]/[A.sub.1]), [G.sub.st] and [G.sub.inst] can be obtained from the intercept and the slope of this straight line, respectively.

Vu-Khanh's method:

Recently, Vu-Khanh (3) proposed a new model for ductile impact fracture, assuming that the fracture energy [G.sub.r] varies linearly with crack extension following the expression:

[G.sub.r] = [G.sub.i] + [T.sub.a]A (7)

where [G.sub.i] is the fracture energy at crack initiation and [T.sub.a] is a material constant equivalent to the material tearing modulus that describes stable crack propagation.

The fracture energy, [G.sub.i], can be obtained from the U/A vs. A plot at the intercept of the curve.

ABS at Room Temperature

Hodgkinson (11) applied the elastic corrected method to highly ductile materials, proposing that ductile effects stem from plane stress, finding a certain dependence upon thickness in the measurements that supported his hypothesis. Figure 2 shows ABS 240 energy data points, corrected by plastic radius, against BW[Phi] obtained for samples having different thicknesses, with and without sidegrooves and tested with two different spans.

Figure 3 shows ABS 240 and 740 energy data fitted against ligament area. The linear correlation was found to be good.

Table 3 shows [r.sub.p] that leads to the best linear fit, the corresponding [G.sub.c] value; [J.sub.c] value and the correlation coefficients obtained for each analysis.

For both fittings, the results appeared to be independent of the B/W ratio and the span used as shown in Figs. 2 and 3. The critical initiation values calculated from the elastic corrected method are larger than that obtained from J method.

Results seem to have no influence of thickness, suggesting a plane strain condition at the crack tip; as confirmed by the minimum dimension calculated from ASTM E813 plain strain thickness requirements:

B, W - a [greater than] = 25([J.sub.c]/[[Sigma].sub.y]) (8)

assuming that [[Sigma].sub.y] in impact is equal to 80 MPa (this value was calculated by extrapolation at 3.5 m/s of the Eyring equation from [[Sigma].sub.y] values measured at different crosshead displacements).

Consistent with Newman's findings, our results were independent of the span, suggesting no rate effects at the testing conditions used here (20).

As shown in Table 3, [J.sub.c] increases with rubber content, consistent with the idea that at these rubber contents no important overlapping effects of stress fields are present. Dynamic [J.sub.c] appeared extremely higher than the ones obtained in static conditions (21).

ABS 240 data points were also fitted following Vu-Khanh's recommendations (3), [ILLUSTRATION FOR FIGURE 4 OMITTED]. In a later paper (22), Mai criticized some aspects of Vu-Khanh's model, stating that his model is equivalent to the "essential work of fracture" method, first developed by Broberg (23). This theory (24) was originally designated for plane stress ductile fracture of metals. For ductile materials with appropriate ligament length, the ligament will undergo full necking before crack initiation. Under this assumption, [W.sub.f] is the total work to fracture the specimen, We is the work for crack to growth inside the end zone, and [W.sub.p] is the work for plastic deformation that is not necessary condition for crack growth. In such conditions, for a given thickness, only the intercept value at A = 0, [W.sub.e], results to be a real material property, while [Beta]. [W.sub.p] is dependent on geometry. Cotterell (25) stated that We is equal to [J.sub.c], and the state of plane stress may arise from the usual size requirements for plain strain (Eq 8).

In the extreme case in which the plastic contribution [W.sub.p] is negligible respect to the "crack growth" work, if [W.sub.e] exists, it would be expected that Vu-Khanh's plots or "essential work of fracture" lead to a constant U/A value with respect to ligament area.

However, as it emerges from the results shown in Fig. 4, there is a decreasing trend between specific fracture energy and ligament area. Under impact bending conditions, the velocity of the crack varies during its propagation and the fracture energy cannot remain constant. Consequently, the concept of "essential work of fracture" does not appear to be applicable for the impact fracture characterization of rate-dependent materials like polymers.

[TABULAR DATA FOR TABLE 3 OMITTED]

The larger scatter found for data points [ILLUSTRATION FOR FIGURE 4 OMITTED] corresponding to small areas can be justified ff one considers that the absolute error in area determination is constant. This fact gives rise to an increasing relative error for small areas, which negatively affects the calculated U/A values.

Rubber Modified Polystyrene at Room Temperature

Figure 5 shows energy data points corrected by plastic radius against BW[Phi], and Fig. 6 shows energy data points vs. ligament area for Lustrex 4300 and Lustrex 2220. Critical values and statistics are displayed in Table 3.

In the case of the J method, the goodness of the fitting was excellent, and in the case of HIPS led to the same value of [J.sub.c] first published by Plati and Williams (1) for a high impact polystyrene of similar characteristics. Again, [G.sub.c] values were larger than [J.sub.c] ones, and large [r.sub.p] were necessary to reach an acceptable linear fitting. As an example, in the case of Lustrex 2220, Table 4 illustrates how the fitting is improved with the [r.sub.p] up to a maximum where the fit quality diminishes again. Obviously [G.sub.c] increased with the increase in [r.sub.p].

Figure 7 shows Vu-Khanh's plots for Lustrex 4300. The same considerations made with ABS are valid in this case.

For Lustrex 2220, as fracture surface revealed a semiductile behavior, data points were also fitted, following rigorously the method of Vu-Khanh and De Charentenay (2) Fig. 8. An acceptable fitting was found. Instability values resulted very close to the apparent [J.sub.c] value obtained without considering semiductile behavior. The [G.sub.inst] value that resulted was larger than the [G.sub.st] value. A similar result was reported by Vu-Khanh for PA11 (2) and was explained in terms of crack tip blunting before unstable crack propagation.

Consistent with fracture surface observations denoting a transition in the propagation mode, independently of the method used to evaluate the initiation criterion chose, a clear increasing trend with the rubber content was verified.

Table 4. [G.sub.c] as a Function of Plastic Radio for LX 2220.

[r.sub.p] [G.sub.c] mm mJ/[mm.sup.2] [r.sup.2]

0.0 6.2 0.8831 1.0 8.6 0.9762 2.0 10.3 0.9932 2.2 10.6 0.9943 2.3 10.8 0.9947 2.4 10.9 0.9950 2.5 11.1 0.9952 2.6 11.3 0.9953 2.7 11.4 0.9952 3.0 11.9 0.9947

ABS Data at 80 [degrees] C

In room temperature tests, the extent of the craze whitening zone outside the process zone was inappreciable, while in the tests at higher temperatures, with the same characteristics stated before (17) a larger plastic zone appeared.

We assayed Lustran ABS 240 and 740 at 80 [degrees] C; the plots of energy data points against ligament area are shown in Fig. 9. In contrast to the findings of Newman and Williams (20), no negative intercept was found, even if the plastic zone depth was of the same order of penetration reported by these authors. The J method still showed a good correlation coefficient.

CONCLUDING REMARKS

The applicability of simple indirect methods for determining the impact fracture toughness of ductile polymers was analyzed with several commercial rubber modified thermoplastics (two injection grade ABS type resins and two rubber modified polystyrenes).

ABS and high impact polystyrene samples exhibited a whitening effect due to craze formation through the whole fracture surface, indicating that stable crack propagation was occurring. Medium impact polystyrene, however, exhibited a combined stable and unstable crack propagation mode, displaying shiny and dull zones on the surfaces of the broken samples.

Linear fittings between energy and ligament area (J method) always displayed high correlation coefficients.

The elastic corrected method gave somewhat complicated results because of the iterative calculations necessary to find [r.sub.p]. Relatively large [r.sub.p] values were calculated, leading to high critical values ([G.sub.c]).

The J method provides more conservative critical values than the elastic corrected method, especially at high toughness levels. This latter statement has serious implications for safety engineering design. However, both methods predict the same qualitative trends against rubber content.

At room temperature, plain strain conditions were always met. Results were independent of thickness and span-to-depth ratio.

For materials displaying ductile fracture, the essential work of fracture was also tried. Results suggested a rate effect that impeded the application of the essential work of fracture under impact conditions in bending.

The "semiductile" model of Vu-Khanh and De Charentenay (2) fitted Lustrex 2220 data points reasonably well. Instability values resulted that were very close to the apparent [J.sub.c] (2) value obtained in a simpler manner, without considering semiductile behavior.

Regarding studies carried out at 80 [degrees] C, the d method still accurately fit data points; showing a trend toward an increase in critical initiation value with the increase in temperature. Even if under this last condition the materials showed a considerable plastic zone, data points did not exhibit a negative intercept in the energy vs. ligament area plots. Therefore, the Williams' method (26) was inapplicable.

Further work will be done to determine impact J-R curves and initiation values by measuring J vs [Delta] a. This will allow us to compare the actual critical values with the ones obtained by indirect methods.

REFERENCES

1. E. Plati and J. G. Williams, Polym. Eng. Sci., 15, 470 (1975).

2. T. Vu-Khanh and F. X. de Charentenay, Polym. Eng. Sci., 25, 841 (1985).

3. T. Vu-Khanh, Polymer, 29, 1979 (1988).

4. J. G. Williams in Fracture Mechanics of Polymers, p. 237, Ellis Horwood, London (1984).

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10. S. W. Koh, J. K. Kim, and Y. W. Mai, Polymer, 34, 3446 (1993).

11. J. M. Hodgkinson, K. H. L. Chow and J. G. Williams, 8th Intern. Conf Deform. Yield Fracture Polymers, 43/1, Churchill College, Cambridge, U.K. (April 1991).

12. D. R. Ireland, Instrumented Impact Testing, ASTM-STP 563, p. 7 (1973).

13. C. B. Bucknall, Plast., November 1967, 118.

14. S. Wu, Polym Intern, 29, 229 (1992).

15. C. B. Bucknall in Toughened Plastics, Applied Science, London (1977).

16. H. Keskkula, "Optimum Rubber Particle Size in High-Impact Polystyrene: Further Considerations," in Rubber-Toughened Plastics, C. K. Riew, Am. Chem. Soc. Series 12, 290 (1989).

17. J. G. Williams, in Fracture Mechanics of Polymers, p. 69, Ellis Horwood Limited, London (1984).

18. J. G. Williams, in Fracture Mechanics of Polymers, p. 67, Ellis Horwood Limited, London (1984).

19. A. J. Kinloch and R. J. Young in Fracture Behavior of Polymers, p. 196, Applied Science Publishers Ltd., England (1983).

20. L. V. Newman and J. G. Williams, Polym. Eng. Sci., 18, 893 (1978).

21. C. R. Bernal and P. M. Frontini, Polym. Testing, 11, 271 (1992).

22. Y.-W. Mai, Polymer Commun., 36, 330 (1989).

23. K. B. Broberg, J. Mech. Phys. Solids, 23, 215 (1975).

24. Y.-W. Mai and B. Cotterell, Int. J Fracture, 32, 105 (1986).

25. B. Cotterell and J. K. Reddel, Int. J. Fracture, 13, 267 (1977).

26. J. G. Williams, in Fracture Mechanics of Polymers, p. 262, Ellis Horwood Limited, London (1984).

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Author: | Bernal, Celina R.; Frontini, Patricia M. |
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Publication: | Polymer Engineering and Science |

Date: | Nov 15, 1995 |

Words: | 4277 |

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