Creep and physical aging of injection molded, fiber reinforced polypropylene.

INTRODUCTION

A number of empirical functions are currently being developed to accommodate the influence of physical aging on the creep rate of plastics (1, 2), where physical aging involves slow structural changes in both amorphous and semicrystalline polymers as a result of the material being quenched from the melt to form a solid that is not in structural equilibrium. This effect is seen as a progressive increase in density and a decrease in the rate of change of compliance with log time during creep tests of long duration.

The molecular origins of creep and physical aging are not fully understood, although it has been suggested that for semicrystalline polymers, such as polypropylene at room temperature, changes in the mechanical properties are attributable to changes in the conformation of the tie molecules coupled with the motion of chains through the crystal lamellae (3, 4). These molecular rearrangements manifest themselves in dynamic mechanical measurements as an [Alpha] retardation process that can be characterized by a limiting compliance level at short times ([D.sub.0]), a magnitude ([Delta][D.sub.[Alpha]]), a mean retardation time ([Tau]) and a parameter m, which serves to define the width of the retardation time spectrum. This [Alpha] retardation process is superimposed on a shorter-time [Beta] retardation associated with the glass-transition of the amorphous regions of the material.

Most previous studies of the effects of physical aging on creep have been concerned with unreinforced materials using specimens cut from extruded or compression molded sheets. These materials are typically of high molecular weight and compression molded materials are often essentially unoriented, or isotropic, owing to the small shear deformations produced in the melt during processing. By contrast, injection molded plastics can have quite high degrees of local molecular or fiber orientation because of the high shear rates involved in the processing. Thus the resulting properties, including the creep behavior, may exhibit a substantial anisotropy. Furthermore, the relatively low molecular weight grades of polymer employed in injection molding could influence the degree of crystallinity and hence the shape of the creep curves through changes in the relative compliance contributions from overlapping relaxation processes.

In this paper we present an analysis of the influence of physical aging on the short- and long-term tensile creep behavior of injection molded plates of glass-fiber reinforced polypropylene. The analysis includes a comparison of two commonly used functions for modeling physical aging effects and forms part of a study of the range of applicability of such models.

An analysis of short-term creep data for unreinforced injection molded polypropylene and for other injection molded plastics is described elsewhere (2).

BRIEF SURVEY OF ANALYSIS METHODS

Values for some of the parameters required by the empirical functions that are used to model the influence of physical aging on the creep behavior of plastics can be obtained from tensile creep tests of limited duration. In these short-term tests the period of testing is kept below 0.3[t.sub.e] where [t.sub.e] is the period of elapsed time between quenching a sample from some elevated temperature [T.sub.[Alpha]] (at which the structure is at equilibrium with respect to the [Alpha]-process) and the instant of load application. During such a test changes in the mean retardation time are negligible. i.e. the age of the test piece is effectively constant (5). A number of such tests can be performed on a given test piece providing that enough time is allowed between successive loadings for the material to recover. The parameters obtained from a short-term test series can be used to predict the creep behavior over the limited timescale of 0.3[t.sub.e] for elapsed times other than those for which data are available.

In long-term creep tests, loads are applied to test pieces for periods of time [greater than]0.3[t.sub.e] and hence the age of the sample progressively increases during the period of measurement. A consequence of this further aging is that some of the parameters used in the functions that describe short-term creep become dependent on creep time as well as the initial age of the material. Appropriate time dependencies of these parameters having been established, creep behavior can be predicted not only for material of different ages but also for creep times in excess of those for which data have been obtained.

Analysis of Short-Term Data

For several polymers the time dependent compliance D(t) can be described over a limited timescale by

D(t) = [D.sub.o] exp[(t/[Tau]).sup.m] (1)

where [D.sub.o] is a limiting compliance at short times and [Tau] is the mean retardation time of a spectrum of times characterized by the parameter m. The kernel of this function is consistent with the stress relaxation function exp - [(t/[Tau]).sup.m] proposed by Kohlrausch (6) and extensively used by Struik and others (5, 7).

An alternative function that has been successfully used to describe the creep of predominantly semicrystalline polymers (4) is based on the Williams-Watts model for describing charge decay in dielectrics (8) and is consistent with the creep recovery function exp - [(t/[Tau].sup.m]. This creep function is of the form

D(t) = [D.sub.o] + [Delta][D.sub.[Alpha]](1 - exp - [(t/[Tau]).sup.m) (2)

The parameters [D.sub.o], [Tau], and m have a similar significance as in the Struik function (Equation 1) although it should be noted that the values of the parameters required to describe a given creep curve will be different. The quantity [Alpha][D.sub.[Alpha]] represents the magnitude of the relaxation process. A value for this parameter can either be obtained by least-squares optimization of the function to a series of short-term creep curves or estimated from an analysis of dynamic mechanical data (9). In Equations 1 and 2 it is usually found that [D.sub.o] decreases slightly with increasing [t.sub.e], while [Alpha][D.sub.[Alpha]] and rn remain essentially constant and the predominant effect of aging is through an increase in [Tau] with [t.sub.e].

For many applications a simpler function can be derived from Equation 2 based on the first term of the series expansion of the exponential term. This is written as a power law of the form

D(t) = [D.sub.o] + [Kt.sup.m] (3)

where K = [Delta][D.sub.[Alpha]]/[[Tau].sup.m]. This representation of the power law is consistent with Findley's equation (10) although the effects of physical aging on the parameters in his original work were not explored.

Analysis of Long-Term Data

The equations described in the previous section are valid only if there is no significant change in the effective age of a specimen during the test. If further aging of the test piece does occur as in a long-term test then one or more of the parameters will become time dependent. In general the decrease in creep rate attributable to further aging during a long-term test can be modeled to a good approximation in terms of a progressive increase in [Tau]. This can be achieved by replacing [(t/[Tau]).sup.m] by the integral [Mathematical Expression Omitted] where u is a dummy time variable. It has been suggested (11) that [Tau](u) can be described by a hyperbolic function of the form

[Tau](u) = ([[Tau].sup.2] + [C.sup.2][u.sup.2[Mu]prime]).sup.0.5] (4)

where C and [Mu][prime] are adjustable parameters and [Tau] is the initial mean retardation time. Substitution of the long-term integral into Equations 1 and 3 gives, respectively,

D(t) = [D.sub.o] exp[[integral of] du/[([[Tau].sup.2] + [C.sup.2][u.sup.2][prime]).sup.0.5] between limits of o to t].sup.m] (5)

and

D(t) = [D.sub.o] + [Alpha][D.sub.[Alpha]][[[integral of] du/[([[Tau].sup.2] + [C.sup.2][u.sup.2[Mu][prime]]).sup.0.5]].sup.m] (6)

EXPERIMENTAL

An injection molding grade glass-fiber reinforced polypropylene (PC072/3NAT) containing 13.2 vol% fibers was obtained from Himont (UK) Ltd. This material was injected into a coathanger-gated mold to produce square plaques of dimensions 150 x 150 x 2.66 mm. Details of the mold and the conditions used have been described elsewhere (12, 13). Rectangular test pieces of nominal dimensions 150 x 10 mm x the thickness of the plaque were cut parallel and perpendicular to the flow direction at the positions close to the center of the sheet [ILLUSTRATION FOR FIGURE 1 OMITTED]. Previous work (2) has shown that the creep compliances of test pieces cut from different positions in the plaque, but perpendicular to the direction of flow, are essentially the same. However, for specimens cut in a direction parallel to the flow, the compliances decrease by about 20% in going from the center to near the edge of the plate.

The fibers were found from optical micrographs to have an average length/diameter ratio of [approximately]39, and their distribution within the plaques was investigated using both optical microscopy and injection molding simulation software (Moldflow). The results of these analyses showed the typical skin-core structure characteristic of injection moldings. Although the mean fiber orientation was parallel to the direction of flow, the alignment of the fibers varied from skin to core: fibers in the outer skins were aligned parallel with the flow direction and those in the core transverse to it (12, 13).

Prior to creep testing, the test pieces were heated to 100 [degrees] C for a period of 30 min to erase any effects of thermal history. At the end of the annealing period the test pieces were quenched into water at 23 [+ or -] 1 [degree] C and after a period of 3-5 min removed and dried. They were then mounted in tensile creep rigs, described elsewhere (4, 14), and stored at the test temperature (23 [+ or -] 0.2 [degrees] C) for various periods of time, [t.sub.e].

Tensile stresses of 9.3 MPa and 5.6 MPa were applied to specimens cut parallel and perpendicular to the flow direction, respectively. This resulted in measured strains spanning the range 0.15-0.28% and ensured that the creep behavior was essentially linear. Single specimens that remained mounted within the test rig were used to obtain short-term creep data at different [t.sub.e], ranging from 3 to 200 hours, to minimize any variability due to material variations or sample misalignment. The test pieces were not exposed to any stress during the recovery periods between short-term tests as the lever arms of the creep rigs are counterbalanced. The long-term tests were conducted wherever possible on these same test pieces after a period of heating to 100 [degrees] C to erase the influence of thermal history. The repeatability of the creep tests was typically within 2%.

RESULTS AND DISCUSSION

Figure 2 shows creep data obtained from series of short-term tests for two test pieces cut from different plaques in directions parallel and perpendicular to the flow, respectively. From this Figure it is evident that at comparable ages a test piece where the mean fiber orientation is perpendicular to the applied force creeps significantly more than one where the mean fiber orientation is aligned with it, despite its being subjected to a lower stress.

Analysis of Creep Data From Specimens Cut Parallel to the Flow Direction

As mentioned in the Introduction, creep in polypropylene for times in excess of 1s is thought to be due to an [Alpha] relaxation process, superimposed on the shorter-time, glass-rubber [Beta] process. Determinations of creep compliance over a very wide time range for unreinforced, compression molded polypropylene revealed a substantial merging of the [Beta] and [Alpha] processes (4). Modeling of the [Beta] process in terms of a symmetrical Cole-Cole function further indicated that the compliance contribution from the [Beta] process reached an asymptotic limit at short creep times ([approximately]100s) (4). However, based on experimental evidence for wholly amorphous polymers, Struik (15) suggested that the compliance contribution for the glass-rubber [Beta] process may continue to increase linearly with log t in the long time region and to effectively produce an inclined baseline to the [Alpha]-compliance contribution. This suggestion was consistent with the shape of the creep curves for compression molded polypropylene at temperatures above about 50 [degrees] C. For injection molded polypropylene there is evidence to suggest that this overlap effect could be significant at room temperature (see Ref. 16 and inclined baseline analysis below).

The analysis of data described below first assumes that the [Beta] relaxation is fully relaxed over the timescale of our creep measurements so that the [Beta]-compliance contribution ([D.sub.o]) is constant and the creep may be described by Equation 1 or 3 without modification. This is equivalent to assuming a horizontal baseline to the [Alpha]-compliance contribution. In view of possible overlap effects from the [Beta]-process, we then present an analysis based on modifications to Equations 1 and 3 that allow for a linear increase in the [Beta]-compliance contribution with log t (inclined baseline).

Analysis Assuming a Horizontal Baseline

The short-term creep data have been modeled in terms of Equations 1 and 3 using a least-squares optimization routine to derive values for the parameters. During the initial phase of fitting the functions to the data, all the parameters were allowed to vary. Figure 3 shows a comparison of the fits of the equations with short-term test data covering a range of elapsed times from 3 to 200 h. From this Figure it is apparent that both functions are able to accurately describe the data.

[TABULAR DATA FOR TABLE 1 OMITTED]

As both m and [D.sub.o] showed a tendency to decrease with increasing elapsed time, the data were analyzed using mathematical descriptions of the elapsed time dependence of these parameters (Case 1), although the potential for simplifying the modeling by ignoring this apparent dependence was also explored and is described in Case 2.

Case 1: elapsed time dependent DO and m

The elapsed time dependence of the shape parameter m can be described by

[Mathematical Expression Omitted] (7)

for both the Struik and power law functions (4), where [m.sub.o] is the value of m at an elapsed time of is and [Epsilon] represents the rate at which it decreases with elapsed time. This reduction in m represents a slight broadening of the distribution of retardation times with increasing age of the material. The parameters used to calculate m for each elapsed time are given in Table 1.

A plot of log [D.sub.o] versus log [t.sub.e] was found to be linear and of slope k following the relationship

[Mathematical Expression Omitted] (8)

where B is the value of [D.sub.o] at an elapsed time of 1s. Values for B and k are given in Table 1.

The elapsed time dependence of the mean retardation time, [Tau] in Equation I can be described by

[Mathematical Expression Omitted] (9)

where [Mu] is the rate of aging (d log [Tau]/d log [t.sub.e]) and A is the value of [Tau] at [t.sub.e] = 1s (Table 1). This equation can also be used to determine the aging rate from the parameter K in the power law, since according to Equation 3, K = [Delta][D.sub.[Alpha]]/[[Tau].sup.m], where m is given by Equation 7. Thus

[Mathematical Expression Omitted] (10)

where [Mathematical Expression Omitted]. A plot of -1/m log K versus log [t.sub.e] yields a slope of [Mu] and an intercept A[prime] (Table 1). The predicted short-term behavior based on Equations 1 or 3 incorporating both the elapsed time dependent Do and m are now written, respectively, as

[Mathematical Expression Omitted] (11)

and

[Mathematical Expression Omitted] (12)

and are compared with short-term data in Fig. 4. As with Fig. 3, both functions are able to describe the short-term data with reasonable accuracy, but values of [Mu] (Table 1), differ markedly from those usually obtained for other grades of polypropylene.

Figure 5 shows creep data obtained over a relatively long period of time ([approximately]3 weeks) where significant further aging of the material occurs during the test period. These data can be modeled using Equations 5 or 6, which can be written as

[Mathematical Expression Omitted] (13)

and

[Mathematical Expression Omitted] (14)

to include the elapsed time dependence of [Tau], m and [D.sub.o] (Equations 7, 8, and 9), noting that [Mathematical Expression Omitted]. For simplicity the short-term aging rate [Mu] was assumed to be equal to that ([Mu][prime]) in the long-term regions of the creep curves, thus leaving only C or C[prime] in the equations to be determined by least-squares optimization. The integrals were solved numerically during the optimization process using a commercial software package (17).

Figure 5 shows a comparison of the calculated creep curves with experimental data for both the Struik equation and the power law. From this Figure it is apparent that neither function is able to accurately describe the long-term creep of the material. Predicted curves based on the Struik equation tend to diverge at long times (low [Mu] value) whereas the experimental curves converge over the same timescale. In contrast, predicted curves based on a power law show pronounced downward curvature and crossover at longer times; overpredicting the influence of further aging during the test period arises from a very high apparent [Mu] value calculated from short-term data. Attempts to improve the quality of the fits (particularly those obtained with the power law function) by relaxing the assumption that [Mu] = [Mu][prime] were generally unsuccessful.

Case 2: Constant DO and m

Given the unsatisfactory long-term behavior of the functions containing elapsed time dependent parameters m and [D.sub.o], an alternative simpler approach was used to model the long-term data by assuming the parameters to be constant. The values of m chosen for each function, 0.10 for the Struik function and 0.15 for the power law, were based on average values obtained by fitting the equations to the short-term data. Plots of either log [Tau] or - 1/m log K versus log [t.sub.e] were found to be linear following Equations 9 and 10 respectively, yielding the values of [Mu] and A or A[prime] listed in Table 2.

Figure 6 shows a comparison of short-term data with predictions based on the two functions using constant values for m and [D.sub.o] and calculated values for K and [Tau]. Although both functions accurately describe the creep behavior for short elapsed times, there is a notable difference between the predictions and the data obtained at [t.sub.e] = 200 h. It should also be noted that m and [Mu] values for both functions are significantly lower than previously reported values for other grades of (unreinforced) polypropylene (2, 18).

Equations 5 and 6 with [Tau] or K given by Equations 9 or 10, respectively, can be used without modification to describe long-term data as shown in Fig. 7. While there is a significant improvement in the quality of the fits to the data when compared with those obtained with a variable m and [D.sub.o] [ILLUSTRATION FOR FIGURE 5 OMITTED] there is a tendency with both functions for the calculated curves to converge more rapidly than the experimental curves at very long times. It should be noted that unlike the predictions based on Case 1 there is little difference in the behavior of the two functions.

Analysis Assuming an Inclined Baseline

Struik and others have extensively used superposition of short-term creep curves (7, 15, 19) to derive values for the aging rate [Mu]. This involves a combination of vertical and horizontal shifts of curves obtained at different elapsed times on to a creep curve arbitrarily chosen as a reference. The procedure relies on the shape of the creep curves being constant and implies that m is independent of elapsed time. Figure 8 shows superposition of the short-term creep curves onto data obtained for an elapsed time of 24 h and the shift directions required for the superposition are seen to be consistent with an inclined baseline of positive slope [ILLUSTRATION FOR FIGURE 8 OMITTED].

Equations 1 and 3, which describe short-term creep, can be modified to accommodate an inclined baseline by substituting the constant [D.sub.o] by a function of the form r + s log(t) where s represents the slope and r is the limiting compliance at a creep time of 1s to give, respectively

D(t) = [(r + s log(t))exp(t/[Tau]).sup.m] (15)

and

D(t) = (r + s log(t)) + [Kt.sup.m] (16)

It should be noted that while the value of s is common to both functions, r is not. The parameter s was obtained by plotting the vertical component of the shift required to superimpose short-term data obtained for different elapsed times onto a reference creep curve ([t.sub.e] = 24 h) against log time and found to be 6 x [10.sup.-3], noting that this procedure assumes that r is constant. During the initial phase of fitting Equations 15 and 16 to the data all the parameters were allowed to vary despite the assumption being made in superimposing the creep curves that m is constant. The results of this analysis revealed a tendency for m to decrease with [t.sub.e] despite superposition; thus situations were explored where m was either allowed to depend on elapsed time (Case 1) or be a constant (Case 2).

In the analysis that follows we focus mainly on the application of the Struik function, noting that a similarity was again observed between the Struik and the power law functions in fitting the creep data, particularly in the short-term.

Case 1: elapsed time dependent r and m

Keeping s constant, initial values for the remaining variables in Equation 15 were obtained by using a least-squares optimization routine. A plot of log m versus log [t.sub.e] was found to be linear as was found previously (Equation 7) where a horizontal baseline was assumed. The elapsed time dependence of the limiting compliance at short times, r can be described

by

[Mathematical Expression Omitted] (17)

where values for the parameters [a.sub.o] and v were obtained from a plot of log r versus log [t.sub.e] (Table 3).

Very good fits to the short-term data were obtained using Equation 15 with m and r calculated according to Equations 7 and 17, respectively, although the value of [Mu] was significantly larger than has been previously found for polypropylene (2, 15) (Table 3). The long-term data was modeled using a revised form of Equation 13, where the term [Mathematical Expression Omitted] was replaced by [Mathematical Expression Omitted]. Assuming that [Mu] = [Mu][prime], the only variable in the modified form of Equation 11 is C, which can be estimated by fitting this equation to the data using a least-squares optimization routine. Figure 9 shows a comparison of the "best fit" with the data. From the Figure it is apparent that the function overestimates the influence of physical aging on the creep rate at creep times in excess of [10.sup.4.5] s. The resultant curvature in the predicted creep curve is due to the high value of [Mu] used in the calculation. Attempts were made to improve the quality of the fit by reducing the size of [Mu][prime], the parameter controlling the aging rate at long times, but these were unsuccessful.

Case 2: Constant r and m

Figure 10 shows a comparison of short-term creep data with predictions based on Equations 15 and 16 with [Tau] and K calculated according to Equations 9 and 10. From this Figure it is apparent that there is very little difference between the two functions over this limited timescale although it should be noted that the quality of the fits tends to decrease with increasing elapsed time. The values of [Mu] and m, although higher than those obtained for the level baseline, are now consistent with those typically found in the literature for other processing routes and grades of polypropylene (2, 15).

Figure 11 shows fits of both the Struik and power law functions to long-term data. These fits were obtained by solving Equations 13 and 14 for C and C[prime] [TABULAR DATA FOR TABLE 3 OMITTED] (Table 4), respectively, after substitution of (r + s log(t)) for the term [Mathematical Expression Omitted]. It is apparent from Fig. 11 that there is very little to choose between the two functions over the timescale of the calculation. Furthermore, the fit obtained for this set of conditions appears to be better than that shown in Fig. 7, where m and [D.sub.0] are independent of elapsed time and a level baseline is assumed.

Analysis of Creep Data From Specimens Cut Perpendicular to the Flow Direction

The creep data obtained from test pieces cut perpendicular to the flow direction were analyzed following the procedures described previously except that the analysis was confined to the Struik function because of the close similarities between it and the power law.

The parameters obtained for each of the conditions described in the analysis of data obtained from test pieces cut parallel to the flow direction are given in Tables 1-4 with the exception of the combination of an inclined baseline with an elapsed time dependent s and m, which was not investigated.

As with the data obtained from test pieces cut parallel to the flow direction, the most successful fit to long-term data was obtained assuming an inclined baseline with constant values of s and m (Equation 15) as shown in Fig. 12.

Thus the effects of overlap observed for unreinforced, compression molded polypropylene at temperatures above 50 [degrees] C are evident for the reinforced injection molded material at room temperature. Similar effects have been observed for an unreinforced injection molded polypropylene (2), which could be due to the lower molecular weight grades of polymer used in injection molding. This could enhance the crystallinity or crystal lamellar thickness and reduce the relative compliance contribution from the [Alpha]-process. In this context note that, in contrast to the results of Struik (16), the short-time compliance levels for the unreinforced injection molded material (2) were lower than those obtained for a compression molded grade (4).

CONCLUSIONS

* Creep data obtained for specimens of glass-fiber reinforced polypropylene cut from injection molded square plates exhibit a substantial anisotropy. The compliance values are smaller for loading parallel to the flow (along which fibers are, on average, preferentially oriented) than for loading in the perpendicular direction.

* The Struik stretched exponential function (Equation 1) and a power law function (Equation 3) each provide a good description of short-term (t [less than or equal to] 0.3[t.sub.e]) creep compliance curves in the [Alpha]-relaxation region. However, best fits to the data require values for the distribution parameter m that decrease with age [t.sub.e] and values for the aging rate [Mu] = d log [Tau]/d log [t.sub.e] that differ considerably from typical values reported for compression molded grades of polypropylene at room temperature. Also the derived [Mu] values do not provide acceptable fits to the long-term data.

* The best overall description of both short- and long-term data (giving parameters consistent with those obtained for other grades of polypropylene) is obtained by fixing the values of m and [D.sub.0], and using modified forms of the creep functions, which allow for a positive inclination of the baseline to the [Alpha]creep compliance curves. This is consistent with the directions of shift required to superpose the curves obtained for different [t.sub.e].

* The successful use of an inclined baseline is ascribed to the effects of overlap of the short-time, glass-rubber ([Beta]) relaxation. Such effects could be larger for injection molded grades of polymer owing to their relatively low molecular weights and consequent higher degrees of crystallinity, which would serve to reduce the relative compliance contribution from the [Alpha]-process.

[TABULAR DATA FOR TABLE 4 OMITTED]

ACKNOWLEDGMENTS

The research described in this report was carried out as part of the "Materials Measurement Programme," a program of underpinning research financed by the United Kingdom Department of Trade and Industry.

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