Effects of ABS rubber particles on rheology, melt failure, and thermoforming.

INTRODUCTION

Understanding rheology and failure mechanisms of polymer melts during uniaxial and biaxial stretching is necessary for prediction of material performance in a variety of commercial applications such as thermoforming and blow molding. Many investigators (1-18) have studied the extensional rheology of polymer melts and the effects of elongational viscosity behavior on melt failure. Several investigators (10-18) used the Considere criterion (19, 20), which was originally developed in solid mechanics and extended to quantitatively predict the critical Hencky strain to failure of polymer melts and solutions. Also, there are a number of experimental and simulation efforts (21-35) devoted to investigating the effects of material variables such as melt strength and elongational viscosity on processibility to reduce different kinds of failures during thermoforming processes. Many studies (5, 10, 15-18, 30-35) agree that elongational viscosity and strain hardening are very important material variables for improving pol ymer performance during processing. Especially, several investigators (30-35) concluded from their thermoforming studies that polymers with more strain hardening behavior show better thickness distribution than those with strain softening behavior.

It was reported that rubber modified polymers can also exhibit interesting rheological behaviors such as deviations from linear viscoelasticity not only at high strains (such as strain hardening in uniaxial extension, shear stress overshoot and steady shear viscosity) but also at small strains as a result of a yield stress and/or formation of higher-order particle structures such as agglomerates, skeletons or networks (3, 4). These properties of rubber modified polymers can be used to optimize their processing characteristics and improve product quality. Despite these investigations, the effects of rubber deformability and content in ABS on its elongational viscosity and strain hardening are still not clearly understood. In addition, few works have been devoted to understanding the basic mechanisms of melt failure of heterogeneous polymeric systems like ABS polymer during uniaxial and biaxial stretching. Heterogeneous polymeric systems and specifically rubber modified polymeric materials such as acrylonitrile -butadiene-styrene copolymers (ABS) are of particular interest since they possess excellent properties for consumer goods (toughness, durability, chemical and heat resistance, to name a few) and can be produced over a wide range of processing temperatures, especially in the thermoforming process (36).

The primary objectives of the present study are: i) to investigate the effect of rubber deformability and content in ABS on the rheological behavior as a function of temperature, putting emphasis on the melt elasticity and strain hardening, ii) to establish relationships among rheological properties, melt failure, and thermoforming performance, and iii) to provide reliable indicators to predict thermoforming performance of ABS polymers.

Li and Masuda (4) have studied the effect of rubber particle content up to 20 wt% on the elongational flow behavior of ABS at 170[degrees]C with a Meissner-type uniaxial extensional rheometer. They reported that the effect of rubber content on the linear elongation viscosity was weak at short times but became stronger with increasing time. All of their materials exhibited a deviation of elongation viscosity from linear viscoelastic behavior and higher elongational viscosity at high strain rates, due to a volumetric resistance effect on rubber deformation of polymer melts. However, the strain hardening property of a series of ABS polymers used in their study was not much changed, even though the rubber content varied from 5 to 20 wt%. Contrary to Li and Masuda's study (4), Takahashi et al. (5) investigated the effect of rubber deformability and content on the strain hardening with ABS polymers containing soft and hard rubber of 20 and 40 wt% in uniaxial extension. They observed that as the rubber content incre ased, strain hardening became weaker and strain softening even occurred in ABS with non-deformable hard rubber at higher rubber content of 40 wt% and experimental temperature of 150[degrees]C. Earlier, Saito (6-8) investigated the elongational viscosity of ABS polymer with rubber contents up to 16.7 wt%. The elongational viscosity depended on the rubber particle size and the dispersion of rubber particle in the matrix. Also, he reported that the rubber size in ABS showed weak influence on strain hardening: however, if agglomeration of rubber particles occurred during uniaxial extension, the strain hardening became stronger. The difference of the degree of AS grafting, which is the ratio of the weight of grafted AS to that of rubber particles, affected the elongational viscosity value, but showed littie influence on strain hardening. However, most previous strain hardening studies have been done at relatively low temperatures of 150-160[degrees]C and the effects of the rubber particles on the strain hardening were reported differently.

Polymer melts can be stretched uniformly only to a certain limit after which they fail either by a ductile failure mechanism (i.e., nonuniform deformation or necking) followed by ductile rupture or by cohesive fracture. Consequently, the onset of ductile failure constitutes a critical point in processing beyond which phenomena like uncontrolled bubble burst (polymer sheet inflation in thermoforming) and extreme sheet thinning result in specific areas. In the ABS case inhomogeneities in the styrene-acrylonitrile (SAN) matrix, weight fraction, properties and size distribution of rubber particles and the resultant morphology may lead to a lower tensile strength and premature melt failure in extensional flows. However, after the onset of nonuniform deformation there is still a significant amount of strain the material can undergo. When the neck occurs and is not stabilized due to strain softening or insufficient strain hardening (for example at small extension rates), its growth leads to rupture of the sample. Th e conditions for melt rupture in extension are discussed by several investigators (37-40).

The Considere criterion (19, 20) was originally developed in solid mechanics and then extended to quantitatively predict the critical Hencky strain of nonuniform deformation. The construction suggested by Considere (19) leads to the following criterion of nonuniform deformation in the tensile test of a solid sample:

dF/d[epsilon] [greater than or equal to] 0 (1)

here F([epsilon]) is the tensile force, and [epsilon] is the Hencky strain: [epsilon] = [epsilon] t in the case of a constant elongation rate, and related to the draw ratio L/[L.sub.0] by [epsilon] = In (L/[L.sub.0]), for specimen of length L and original length [L.sub.0]. Rearrangement gives the Considere structure in stress-strain relation:

d[sigma]/d[epsilon] [greater than or equal to] [sigma] (2)

here [sigma] = [sigma]([epsilon]) is the true tensile stress. The equality in Eq 1 and Eq 2 can be interpreted as a criterion for the onset of nonuniform deformation. This criterion comes from the realization that uniform deformation cannot proceed beyond the strain at which the measured tensile force exhibits a maximum. The Considere criterion and its equivalent condition were successfully used for prediction of ductile failure of solid polymers (10-12), polymer melts (13, 14), polymer solutions (15-17), and branched polymer melt (18) for their failure studies. Recently, we have investigated the modes and criteria of ABS melt failure in extension and compared several methods for detection of the onset of nonuniform deformation (41). Our study showed that the Considere criterion in the tensile stress-strain curve represented the simplest and the most effective indicator of the onset of ductile failure over a wide range of elongation rates and temperatures.

EXPERIMENTAL

Material

We studied a series of commercial ABS copolymers with different butadiene rubber contents and properties from Bayer Corporation. This series represents materials widely used in thermoforming. The copolymer matrix (styrene-acrylonitrile (SAN) copolymer) of all ABS polymers used in this study consisted of 30 wt% acrylonitrile and 70 wt% styrene. A pair of ABS polymers with molecular weight of copolymer matrix, [M.sub.w] = 70,000, constituting about 14 wt% rubber in the total composition was used for study of the rubber deformability. Based on transmission electron micrographs. Fig. 1, of these materials after fiber spinning with the same stress and plunger speed at a Hencky strain of 0.432 at 200[degrees]C and 240[degrees]C we denoted ABS-S14 as soft (more deformable) and ABS-H14 as hard (less deformable). The different deformability of the rubber particles is due to different degrees of crosslinking, particle structure, and size. The grafted rubber phases in ABS-H14 mostly are non-occluded in structure, while ABS-S14 has a more occluded rubber structure. Rubber particle sizes in ABS-H14 and ABS-S14 are number average diameters of 0.2 and 0.5 [micro]m, respectively. For the rubber content study a pair of ABS polymers with copolymer matrix [M.sub.w] = 60,000 constituting 12 and 24 wt% of the less deformable rubble particle was used and termed as ABS-H12 and ABS-H24, respectively. The rubber contents used in this study were placed between the previous Saito's (16.7 wt%), Li and Masuda's (up to 20 wt%), and Takahashi et al.'s (20 and 40 wt%) studies in which different results were reported. The matrix copolymers showed similar glass transition temperature, [T.sub.g] = 125[degrees]C.

Rheological and Failure Measurements

Small strain oscillatory shear measurements were conducted on the Rheometric Mechanical Spectrometer (RMS-800EH) and used to determine linear viscoelastic spectra of the material in the frequency range from [10.sup.-2] to [10.sup.2] [s.sup.-1] and in the temperature range from 140[degrees]C to 200[degrees]C. The shear stress growth coefficient measurements for the start-up of steady shear were performed for the shear rates [gamma] = 0.00 1 - 10.0 [s.sup.-1] at 170[degrees]C. The samples were examined after the experiment to ensure their uniformity and the absence of the edge instability.

We measured tensile stress growth coefficients for uniaxial elongation on a Meissner-type extensional rheometer (Rheometrics RME) for melt temperatures from 140[degrees]C to 200[degrees]C at constant elongation rates [epsilon] = 0.1 and 1.0 [s.sup.-1], which are typical for processing operations. The basic operating principle and detailed description of Meissner's extensional rheometer can be found in (42) and Rheometrics literature. We used 56-mm-long, 1.1-6.7-mm-wide and 0.5-1.4-mm-thick samples cut from the extruded ABS sheet. The samples were equilibrated in the RME at a chosen temperature for 10 mm. Density-temperature corrections to the sample cross-sectional area were made. Each test was repeated 3-5 times and one representative test was selected for analysis and figures. Measured tensile stresses were reproducible within [+ or -]10% error at short times (up to Hencky strain of 0.35) and [+ or -]1% after that until an apparent ductile failure point. Uniformity of the sample during extension and an appa rent onset of necking were observed by videotaping and slow motion playback. Results for samples that exhibited nonuniformity of cross-sectional area after loading or immediately after the test started were not considered. Also, to observe sample uniformity during the experiment, small black marker beads were applied on the sample surface before the experiment, and their motion (if any) during relaxation was videotaped. Samples were considered to undergo nonuniform relaxation during stress relaxation after cessation of elongation if any relative particle movement was observed during the relaxation portion. A detailed description of experimental method can be found in our previous studies (31, 41, 43).

Viscoelastic Constitutive Model

In this study the Wagner model (44), which is a KBKZ type single integral nonlinear viscoelastic constitutive model, was fit to shear and elongational experimental data to obtain [alpha] and [beta] parameters. K-BKZ type single integral models have the following general form:

{T = - pI + T

T = [[integral].sup.t.sub.-[infinity]] M(t - t')

[[[phi].sub.1]([I.sub.1], [I.sub.2])[C.sup.-1.sub.t](t') + [[phi].sub.2]([I.sub.1], [I.sub.2])[C.sub.t] (t')] dt' (3)

where [C.sup.-1.sub.t](t') and [c.sub.t] (t') are the Finger strain tensor and Cauchy strain tensor respectively, M(t - t') is the memory function, [I.sub.1](t, t') and [I.sub.2](t, t') are the first two invariants of the Finger tensor (the third invariant [I.sub.3] [equivalent] 1 for incompressible fluids), and damping functions [[phi].sub.1]([I.sub.1], [I.sub.2]), [[phi].sub.2] ([I.sub.1], [I.sub.2]) are defined as follows:

Wagner model:

[[phi].sub.1] = exp(- [beta] [[[alpha][I.sub.1] + (1 - [alpha])[I.sub.2] - 3].sup.0.5]); [[phi].sub.2] = 0 (4)

Also, the first two invariants of the Finger tensor, [I.sub.1](t, t') and [I.sub.2](t, t') for uniaxial and biaxial elongational flow are as follows:

Uniaxial: {[I.sub.1] = [e.sup.2[epsilon]] + 2[e.sup.-[epsilon]] [I.sub.2] = 2[e.sup.[epsilon]] + [e.sup.-2[epsilon]],

Biaxial: {[I.sub.1] = [e.sup.-2[epsilon]] + 2[e.sup.[epsilon]] [I.sub.2] = 2[e.sup.-[epsilon]] + [e.sup.2[epsilon]] (5)

The usual Lodge network model (45) was used to describe the memory function:

M(t - t') = [summation over (N/i=1)] [[eta].sub.i]/[[lambda].sup.2.sub.i] exp(-(t - t')/[[lambda].sub.i]) (6)

The following Arrhenius relation was used to describe the temperature dependence of material rheological behavior during thermoforming simulation.

[[eta].sup.0] (T) = [[eta].sup.0.sub.0]([T.sub.0]) exp[- A(T- [T.sub.0])] (7)

where [[eta].sup.0.sub.0]([T.sub.0]) is the zero shear viscosity at reference temperature [T.sub.0], [[eta].sup.0](T) is the zero shear viscosity at temperature T, and A is a fitted constant.

Strain Hardening Index

The polymer melts showed a higher elongational viscosity under fast constant uniaxial or biaxial extension rate compared with polymer melts at slow constant uniaxial or biaxial extension rate. We represented the temperature dependence of strain hardening index of ABS polymers used in this study as follows:

[[lambda].sub.n](strain hardening index) =

[[eta].sup.+.sub.E](high strain rate)/[[eta].sup.+.sub.E](low strain rate) at the same time (8)

More detailed description of the strain hardening index can be found in Takahashi et al's study (5). For this study, [[lambda].sub.n] was calculated from the Wagner model fits to the experimental data at the high strain rate of [epsilon] = 1.0 [S.sup.-1] and the lower strain rate [epsilon] = 0.1 [S.sup.-1].

Thermoforming Simulations

The effect of rubber content and deformability on thermoforming performance in terms of thickness distribution was predicted using the commercial simulation program T-SIM[R] (version 3.4, T-SIM CZ Ltd.). The detailed features and descriptions of T-SIM[R] simulation software can be found in (46). Coulomb's law of friction was enforced at areas of contact between sheet and mold and based on the previous measurement (31), the friction coefficient (f) of 0.25 was used. The heat transfer was calculated after the time step and the temperature field in the elements was modified on this basis. The Wagner model was used to predict the temperature dependence of viscosity during thermoforming simulation. Simulations were run under standard conditions of [T.sub.sheet] = 170[degrees]C, [T.sub.mold] = 90[degrees]C, bubble height = 390 mm. and sheet thickness = 3.05 mm. A more detailed description of simulation method can be found in our recent study (31). However, the effects of material shrinkage, sagging of the sheet, an d temperature distribution over the sheet on the thickness distribution were not simulated. Recent studies of shrinkage, sagging, and temperature distribution effects can be found in (47), (48), and (49, 50), respectively.

In order to compare the thermoforming performance in terms of part thickness distribution quantitatively, we used the Coefficient of Variation (COV), which is the standard deviation normalized by average thickness (e.g., STDEV/average thickness (mm) * (100). A smaller COV indicates a more uniform and thus better quality part. Our previous simulation studies (31, 49) have demonstrated that the simulated thickness distributions are consistent with experimental results, in terms of average thickness and COV.

RESULTS AND DISCUSSION

The Effects of Rubber Particles on Temperature Dependence of Viscosity and Melt Elasticity

Figure 2 provides dynamic viscosities of ABS-H12 and ABS-H24 measured in the frequency range from [10.sup.-2] to [10.sup.2] [S.sup.-1] at temperature range from 140[degrees]C to 200[degrees]C. Both ABS polymers exhibit the shear thinning. Both ABS polymers show very similar viscosity at relatively low temperatures below 1 170[degrees]C, where rheological behavior is dominated by the copolymer matrix. However, as temperature increase, the viscosity of ABS-H 12 decreases faster than that of ABS-H24 because of the difference of rubber particle content. As a result, ABS-H12 exhibits lower viscosity at the higher temperature of 200[degrees]C. Similar shear viscosity behavior can be observed in ABS-S14 and ABS-H14 in which ABS-S14 with soft rubber particles shows lower viscosity at high temperature, while it exhibits higher viscosity at low temperature than ABS-H14. Different temperature dependence of viscosities of ABS-S14 and ABS-H14 occurs as a result of larger deformation of soft rubber particles at high temperatures.

In order to quantitatively investigate the temperature dependence of shear viscosities in terms of rubber content and deformability, Arrhenius constants are obtained using Eq 7. A smaller Arrhenius constant (A) indicates a less temperature dependence of viscosity. Table 1 summarizes Arrhenius constants of the four different ABS polymers investigated in this study. Note that viscosities at shear rate of [10.sup.-2] [s.sup.-1] are used as reference viscosities rather than the zero shear viscosities.

Next, we investigate the effect of rubber particles included in ABS polymers on the melt elasticity using the method advanced by Han (51, 52). Figure 3 gives plots of log G' versus log G" obtained at different temperatures, showing temperature independence. It is well known that homopolymers show a slope of 2 in the plot of log G' versus log G". However, it is shown in Fig. 3 that ABS polymers deviate from a slope of 2 depending on the rubber content and deformability. For example, as the hard rubber particles are increased, the storage modulus of G' becomes larger value at the same value of loss modulus of G", and thus, ABS-H24 shows more melt elasticity than ABSH12. Therefore, melt elasticities of ABS polymers also have a close relationship with deformation of polymer and are greatly affected by rubber particles included in polymers.

Elongational Viscosities and the Constitutive Model

The measured uniaxial elongational viscosities at [epsilon] = 1.0 [s.sup.-1] in the temperature range of 140[degrees]C to 200[degrees]C along with the best fit by Wagner model are provided in Fig. 4. The content and deformability of rubber particles show little influence on uniaxial elongational viscosities in the linear region. As a result, elongational viscosities of ABS polymers have similar values until near the maximum (i.e., nonlinear region). Considerable strain hardening (or higher elongational viscosity) is exhibited at lower temperatures, but at higher temperature strain hardening is reduced primarily because of increasing mobility of the copolymer matrix. The effect of hard rubber content on the uniaxial elongational viscosities is emphasized in Fig. 4A. ABS-H12 with fewer hard rubber particles shows a higher viscosity at 140[degrees]C than ABS polymer containing more rubber particles. However, the uniaxial elongational viscosities are similar at 170[degrees]C, while ABS-H12 has a lower viscosity a t 200.[degrees]C. If soft rubber particles are used in ABS polymer, similar behaviors of elongational viscosity can be observed, as shown in Fig. 4B.

Our experimental observations of uniaxial elongational viscosities are consistent with the previous Li and Masuda's study (4) in which the effect of rubber content on the linear elongation viscosity was weak at short times but became stronger with increasing time. As extension time is increased, the elongational viscosity begins to deviate from linear viscoelastic behavior mainly because of the influence of content and deformability of rubber particle. The temperature dependence of elongational viscosity behavior is very consistent with that observed in shear flow (see Fig. 2 and Table I). However, the time at maximum uniaxial elongational viscosity shows little temperature dependence. It should be noted that the experimental elongational viscosity curves have a maximum followed by a sudden drop associated with melt failure due to necking or other instability. Thus, the maximum is an artifact of nonuniform deformation and melt failure, which occur during the decreasing strain hardening growth phase (41). The apparent Hencky strain-to-neck (strain at visually observed neck) is roughly constant (2.8 [+ or -] 0.30) within experimental error and independent of temperature and elongation rate.

The Wagner model parameter values obtained by fitting experimental data of ABS polymers at different temperatures are given in Table 2. Note that the model parameter values vary substantially with temperature. The temperature-specific model parameter values rather than the averages were used. The Wagner model effectively simulates the experimentally observed maximum in elongational viscosity. However, it also predicts a steady-state elongational viscosity, which is not observed experimentally because of sample failure.

We also predicted the biaxial elongational viscosity at high strain rate of 1.0 [S.sup.-1] at different temperatures using the Wagner model parameters. Since the [alpha] and [beta] parameters were obtained by fitting of experimental data in startup of steady shear and uniaxial elongation, the accuracy of extrapolation to biaxial elongation is questionable. However, the simulation software uses these parameters for all types of deformation. The results are shown in Fig. 5. The predicted biaxial elongational viscosity behavior is different from that of uniaxial elongational viscosity. As in uniaxial extension, the content and deformability of rubber particles show little influence on the simulated biaxial elongatonal viscosities in the linear region. From comparison of Fig. 5 with Fig. 4 it is clear that the model predicts lower biaxial elongational viscosities and earlier times at maximum in the biaxial elongational viscosity than those in the uniaxial extension. Also, as the temperature increases, maximum bia xial elongational viscosities are predicted at earlier times in ABS-H12 containing fewer hard rubber particles and in ABS-S14 with soft rubber particles.

The Effect of Rubber Particles on the Strain Hardening

It is well known that the strain hardening plays an important role in determining melt failure and processing performance. The usual definition of strain hardening (53, 54) is the upturn of an elongational viscosity above the linear viscoelastic start-up viscosity, corresponding to higher elongational viscosity under faster extension rate than under lower extension rate (5, 55). The effects of rubber content and deformability on the strain hardening property obtained using Eq 8 are provided in Fig. 6. All ABS polymers used in this study show strain hardening in the temperature range from 140[degrees]C to 200[degrees]C, regardless of rubber content and deformability. Our results are different from those of Takahashi et al's study (5), in which no strain hardening or even strain softening was observed in ABS with non-deformable hard rubber particles of 40 wt% at 150[degrees]C. Also, from Fig. 6 it is clear that ABS polymers containing fewer hard rubber particles or soft rubber at relatively low temperature at 1 40[degrees]C or 155[degrees]C show more strain hardening properties than ABS polymers with more hard rubber particles. These results of strain hardening at low temperatures of 140[degrees]C and 155[degrees]C are consistent with the observation of Takahashi et al's (5) at 150[degrees]C. However, as the temperature increases to 200[degrees]C, strain hardening of ABS with more hard rubber particles becomes stronger than that of ABS with fewer hard rubber and soft rubber, which is reverse of that at lower temperature and is not consistent with Takahashi et al's study (5) at 150[degrees]C.

Based on Saito's investigations (7-9) that the dispersed rubber size and the difference of the degree of AS grafting showed little influence on strain hardening, strain hardening of ABS polymer is mainly attributable to rubber content and deformability. Also, we can observe from Fig. 6 that as temperature increases from 140[degrees]C to 170[degrees]C, strain hardening decreases significantly, while less reduction of strain hardening is observed with further increase of temperature to 200[degrees]C. This may occur because of the agglomeration of rubber particles, which makes the strain hardening Stronger, as Saito (7-9) reported. Therefore, it should be mentioned that the conclusion of Takahashi et al.'s study about the effect of rubber particles on strain hardening obtained at lower temperature of 150[degrees]C may not be extendable to the entire range of temperature because of the temperature dependence of strain hardening. Strain hardening at lower temperature in both our study and Takahashi et al.'s study may occur primarily because of the matrix. At high temperature, the rubber content and deformability determines the strain hardening in that more hard rubber shows stronger strain hardening primarily because of more volumetric resistance effect on polymer deformation and more steric hinderance of rubber chains during extension, as proposed by Li and Masuda (4) and Tervoort and Govaert (56), respectively. Also, soft rubber exhibits weak strain hardening because of less resistance to extensibility in the elongational direction caused by a smaller degree of crosslinking and a more occluded structure. This result may associate with a known fact that more chemically crosslinked networks would be considered as a more entangled network of long chain-branched polymers, and both structures have a limited extensibility, which makes strain hardening stronger (54-56).

Temperature dependence of the rheological properties has been demonstrated in previous studies (31, 41, 43, 49). Especially, the importance of experimental temperature for amorphous polymers such as PS and ABS polymers was pointed out by several investigators (57-61). From the polymer processing point of view, the [T.sub.g] of an amorphous polymer cannot be regarded as being equivalent to the [T.sub.m] of a crystalline polymer, because viscosities of amorphous polymers at just over the [T.sub.g] are still too high to flow. Boyer (57) proposed that a liquid-liquid transition existed above glass transition, [T.sub.g], in amorphous polymers such as polystyrene, followed by Maxwell (58). Maxwell concluded that this liquid-liquid transition temperature is a very important factor in processing operations such as thermoforming, blow molding, and film forming. Processing above or below this transition produces products with very different end-use properties. He showed that the liquid-liquid transition temperature of polystyrene with a [T.sub.g] of 100[degrees]C was within the temperature range of 190[degrees]C to 200[degrees]C depending on the strain rate and total strain. Subsequently, Han et al. (59) and Lee and Han (60, 61) introduced the concept of 'critical flow temperature', [T.sub.cf], for amorphous polymers, to define a 'liquid state of amorphous polymer' for polymer processing, especially, in compounding equipment. They showed that [T.sub.cf] of amorphous polymer was approximately 55[degrees]C above [T.sub.g] depending on the shear rate. By considering previous studies (57-61) and the typical ABS thermoforming temperatures operated between 160[degrees]C and 200[degrees]C, more accurate information about strain hardening of ABS polymers should be obtained from a wide temperature range. This study clearly shows the temperature dependence of strain hardening of ABS polymer in which stronger stain hardening at lower temperatures becomes weaker at higher temperatures depending on rubber content and deformability.

Considere Criterion as the Onset of Nonuniform Deformation

Figure 7 provides the tensile force behavior of ABSH14 measured at strain rates of 1.0 [s.sup.-1] and temperatures l40[degrees]C-200[degrees]C as a function of Hencky strain. The Considere criterion at the maximum force is marked with a reverse triangle symbol. The Considere criterion observed from the elongational stress-strain curve is a simple and reliable predictor for the onset of nonuniform deformation (i.e., ductile failure) under conditions where cohesive (or brittle) fracture did not occur (41). In the same study the Considere criterion was found to overestimate the Hencky strain at onset of nonuniform deformation at high strain rate of 1.0 [s.sup.-1] at low temperature of 140[degrees]C where cohesive fracture occurs. Note that the apparent Hencky strain-to-neck is observed near the maximum stress within experimental error and roughly constant and independent of temperature and elongation rate.

Figure 8 provides the temperature and strain rate dependence of the effects of rubber content and deformability on the onset of nonuniform deformation. It can be observed from Fig. 8 that as temperature increases and strain rates decrease, the Considere criterion as the onset of nonuniform deformation occurs at earlier Hencky strain in all ABS polymers used in this study. These temperature and strain rate effects are consistent with those obtained from the previous melt failure study (41). This occurs because of the lower elongational viscosity at higher temperature and lower strain rate, as investigated by Yao et al. (16, 17). Also, ABS-H24 and ABS-H14 with more hard rubber particles show little change or even increase of Hencky strain at Considere criterion at relatively high temperature above 170[degrees]C and lower strain rate, which may occur because of the agglomeration of rubber particles. It is clear that as more hard rubber particles (i.e., ABS-H24) are used in ABS. nonuniform deformations occur at l arger Hencky strain at the relatively higher temperature of 170[degrees]C because of more elasticity and stronger strain hardening of polymer, except at the lower temperature of 140[degrees]C. This temperature dependence of the Considere criterion is very consistent with those of shear and elongational viscosities and strain hardening. Hencky strains at the onset of nonuniform deformation of Fig. 8 provide important information related to the processing operation in that ABS melts can be stretched uniformly only to a certain limit, after which they deform nonuniformly, followed by necking, and next by melt fracture (41).

Effects of Rubber Content and Deformability on the Thermoforming Performance

In order to investigate the relationship among rheological properties, melt failure, and thermoforming performance, effects of rubber content and deformability on thickness distribution of thermoformed parts were simulated. Vacuum snap-back forming was used for the thermoforming simulation. Immediately after completion of the heating cycle, the sheet undergoes a pre-stretching, which is implemented by moving the top vacuum box down over the sheet and pulling a vacuum. Following pre-stretching is a delay time until the rising mold contacts the deformed sheet. Forming is completed by continued upward motion of the mold, and final application of vacuum to pull in the remaining non-contacting regions. It should be noted that the vacuum snap-back thermoforming process is a very complex processing method, and thus, there are several important processing variables that have close relationships to material variables such as rheological properties and play important roles in determining thermoforming performance (31, 49). For thermoforming simulation study, the uniform sheet temperature over the sheet and the same friction coefficients were used.

Figure 9 presents thermoforming performances of ABS polymers used in this study at a uniform sheet temperature of 170[degrees]C, in terms of the thickness distribution along the symmetric line of the mold, while the COV is summarized in Table 3. It is clear from Fig. 9 and Table 3 that as the content of hard rubber particles is increased, the thickness distribution becomes more uniform. The most significant differences in thickness distribution occur in the back and top areas. Also, the rubber deformability plays an important role and shows a similar influence in determining the thickness distribution as that of the rubber content. As a result, when easily deformable rubber particles are used, the thickness distribution becomes less uniform. The differences in thickness distribution occur in all three areas of mold. Results of thermoforming performances at 170[degrees]C shown in Fig. 9 are generally consistent with their melt elasticity of Fig. 3 and strain hardening of Fig. 6, in which more elastic and stron ger stain hardening ABS polymers show more uniform thickness distribution of the thermoformed part. Our results are consistent with a well-known fact that a good thermoforming material must have sufficient elastic character and stronger strain hardening to avoid excessive thinning, with enough viscous character to provide flow under the applied stress.

Our previous thermoforming studies (31, 49) showed that thickness distribution of thermoformed parts of Fig. 9 is critically dependent on the bubble shape and next, the uniaxial elongational viscosity after contacting the mold. Formation of the bubble depends primarily on the rheological properties of the polymer, especially on the biaxial viscosity. The influence of the rubber particles on the bubble shape at the final height of 390 mm is summarized in Fig. 10. Note that in each case the blowing pressure profile was adjusted to obtain similar bubble heights of approximately 390 mm, consistent with industrial practice for this particular part. As the content of hard rubber particles is decreased, the bubble shapes become narrower with a sharp pole. This may occur because of less elasticity, strain hardening, and earlier time at maximum biaxial elongational viscosity peak (31). A similar change in bubble shape is observed when soft rubber particles are used. The effect of rubber deformability is slightly less conspicuous than that of the rubber content. In the case of ABS-H12 and ABS-S14, the narrowness of the bubble at its base resulted in its touching the mold in the bubble blowing stage. Thus, better thermoforming performance of ABS-H24 occurs because of the larger volume of the bubble with a wider bubble shape and thus, more material distribution to some areas with high extension ratio such as the top area of the mold used in this study. From Figs. 5, 9, and 10, it is clear that the time at maximum biaxial elongational viscosity has a significant influence on the bubble shape, where later times at maximum of ABS-H24 and ABS-H14 produce wider bubble shapes and more uniform thickness distribution.

In order to qualitatively investigate the relationship between thermoforming and nonuniform deformation, the total strain of the thermoformed part along the centerline was estimated from change of initial thickness after thermoforming, by assuming that the polymer sheet was uniaxially deformed during thermoforming. Previous experimental works on this part with grids and simulations have shown that the top and back areas of mold are mainly deformed by biaxial extension but that uniaxial elongational flow plays an Important role in determining the thickness distribution of the bottom area. Therefore, the total strains at the bottom area are more appropriate for this comparison. Figure 11 provides the estimated total strain of ABS-H24 and ABS-H12 along the symmetric line of the mold. The maximum total strain of 3.9 in the bottom area is much larger than Hencky strain of 1.5 at the onset of nonunifom deformation observed in uniaxial extension. It is thus clear that some portions of the thermoforming process may p roceed beyond the onset point of nonuniform deformation as determined by the Considere criterion. The result indicates that larger content of hard rubber particles (i.e., ABS-H24) shows smaller total strain and less nonuniform deformation, and consequently, better thermoforming performance, as shown in Fig. 11. More important, this indicates the critical influence of material behavior as it approaches and exceeds the limit of uniform deformation. Despite the fact that the linear viscoelastic behaviors of these four materials are very similar (see Fig. 4), the nonlinear behavior yields dramatically different thickness distributions during thermoforming. The final strain distribution is determined by the rheological properties of polymers and their temperature dependence as indicated by Arrhenius constants. Melt elasticity would be considered as melt strength, and thus, higher melt elasticity (or strength) provides better thermoforming performance. which is consistent with the melt strength study of Lau et al. (22). Overall, deformation history and elastic character of material played predominant roles in determining more uniform thickness distribution over temperature dependence of viscous character.

CONCLUSIONS

The rheological properties of ABS such as melt elasticity, time to maximum elongational viscosity, strain hardening, and melt failure (as the onset of nonuniform deformation) were investigated as functions of the content and deformability of rubber particles and were discussed in relationship to thermoforming performance. As fewer hard rubber particles or softer rubber particles were included, the polymers exhibited less melt elasticity and more temperature dependence of viscosity. Linear uniaxial and biaxial elongational viscosities are independent of the deformability and content of rubber particles. However, these rubber particles have great influence on the melt elasticity, strain hardening and/or softening, the time at the maximum biaxial elongational viscosity peak, and the onset of nonuniform deformation, which are of great importance in determining thermoforming performance. The onset point of nonuniform deformation at the Considere criterion began at a much smaller Hencky strain than the maximum stra in encountered in the thermoforming operation. Thus, some thermoformed parts with high draw ratios proceed beyond the onset point of nonuniform deformation. Melt elasticity, strain hardening, and the Considere criterion are very reliable and simple methods to predict melt failure and subsequently, thermoforming performance in which more elasticity, stronger strain hardening, and later onset of nonuniform deformation show more uniform part thickness distribution. This mainly occurs because of sufficient elastic character to avoid excessive thinning and stronger strain hardening to stretch uniformly up to larger Hencky strain. Deformation history and elastic character of material play predominant roles in determining the thickness distribution.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 11 OMITTED]

Table 1

Arrhenius Constants of ABS-H12, ABS-H24, ABS-H14, and ABS-S14 for
Temperature Dependence of Material Rheological Properties.

Polymer  Arrhenius Constant (A)

ABS-H12          0.0301
ABS-H24          0.0192
ABS-H14          0.0266
ABS-S14          0.0298
Table 2

Temperature Dependence of Best Fit Wagner Model Parameters, [alpha] and
[beta], of ABS Polymers Calculated From Temperature Specific Relaxation
Spectra.

ABS-H12)

Temperature ([degrees]C)  [alpha]  [beta]

          140             0.0534   0.1242
          155             0.0734   0.2687
          170             0.0884   0.3208
          185             0.1394   0.3320
          200             0.1456   0.3353

        Average           0.0894   0.2762

ABS-H24)

Temperature ([degrees]C)  [alpha]  [beta]

          140             0.0155   0.1317
          155             0.1282   0.2032
          170             0.5270   0.1790
          185             0.5354   0.2125
          200             0.2684   0.2517

        Average           0.2950   0.1956

ABS-H14)

Temperature ([degrees]C)  [alpha]  [beta]

          140             0.3202   0.1036
          155             0.2678   0.2012
          170             0.2893   0.2500
          185             0.2542   0.2825
          200             0.2747   0.2757

        Average           0.2781   0.2234

ABS-S14)

Temperature ([degrees]C)  [alpha]  [beta]

          140             0.2560   0.0454
          155             0.1986   0.1530
          170             0.0070   0.4106
          185             0.0010   0.4672
          200             0.0020   0.4452

        Average           0.0929   0.3043
Table 3

Comparison of the Simulated Thermoforming Performance of ABS-H12,
ABS-H24, ABS-H14, and ABS-S14.

Polymer  Coefficient of Variation (COV)

ABS-H12               31.2
ABS-H24               20.8
ABS-H14               24.6
ABS-S14               30.5

ACKNOWLEDGMENT 

The authors are grateful to the Bayer Corporation for the support of this work. We also appreciate the work of Mr. Warren H. Farnham of Solutia for his TEM measurements.

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JE KYUN LEE (1)

TERRY L. VIRKLER (2)

CHRIS E. SCOTT (1) *

* To whom correspondence should be addressed.

(1.) Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139

(2.) Polymers Division of Bayer Corporation Springfield, MA 01151