Orientation in polypropylene sheets produced by die-drawing and rolling.
Thermoplastic polymers can be oriented by solid-state forming processes such as hydrostatic extrusion, die-drawing, or rolling to give products with enhanced mechanical properties (1, 2). For two-dimensional forming by die-drawing through a slit die or by rolling, the actual reduction ratio [R.sub.A] = [H.sub.B]/[H.sub.A], where [H.sub.A] and [H.sub.B] are the thicknesses of product and billet, respectively. Draw temperature, haul-off speed, and initial billet size determine [R.sub.A] and the mechanical properties of die-drawn polypropylene (3). Likewise, [R.sub.A] of polypropylene oriented by roll-drawing is proportional to the stretch ratio, to [H.sub.B], and to the reciprocal of the work-roll gap (4); [R.sub.A] increases with increasing rolling temperature (5). The roll-drawn product becomes more fibrous at higher [R.sub.A], although crystallinity appears to be roughly constant (6).
In die-drawing through a slit die and in rolling, there is elongation in the machine direction ([X.sub.3]), flattening in the normal direction ([X.sub.2]), but little change in the transverse direction ([X.sub.1]). The changes in mechanical and structural properties might therefore be large along [X.sub.3], relatively small along [X.sub.2], and insignificant along [X.sub.1], unlike those for uniaxially drawn products for which [X.sub.2] and [X.sub.1] are indistinguishable. Small increases in compliance and strength along [X.sub.2] but decreases along [X.sub.1], in "rolltruded" (rolled and drawn) polypropylene have been reported (7). Wide-angle X-ray diffraction (WAXD) gave pole figures for rolled polypropylene that showed definite changes in anisotropy as [R.sub.A] was increased from 2 to 4.5 (8).
In this research, which continues earlier work (3), isotactic polypropylene is oriented by drawing and rolling, alone and in combination. The anisotropies of the products' properties and textures are characterized by several techniques to determine how they differ from uniaxial. Because failure often limits the usefulness of oriented polymers, impact strength and failure modes are also reported. The results show that these products are much closer to uniaxial than one would expect from the plane-strain geometry of their formation.
For the die-drawing experiments, three billets B were cut and machined to the sizes needed from a 75-mm diameter polypropylene cylinder. The central core of the cylinder, [approximately]15 mm in diameter, was riot used because it contained small voids. To represent the isotropic material, a piece was machined from the original cylinder, with similar dimensions to the drawn products. A sample of the shavings from machining was sent to RAPRA for molecular weight measurements by gel permeation chromatography; two specimens gave [M.sub.w] = 6.62 x [10.sup.5], [M.sub.n] = 4.27 x [10.sup.4], and [M.sub.w] = 6.77 x [10.sup.5], [M.sub.n] = 5.00 x [10.sup.4]. Each billet was machined to size, its thickness [H.sub.B] and width [W.sub.B] were recorded, and straight lines a distance [L.sub.B] = 100 mm apart were drawn across its thickness. After being heated to 145 [degrees] C, the billets were drawn, at a steady speed of 1.08 mm/s through a tapered slotted die at 148 [degrees] C, in the large-scale drawing machine developed in this laboratory (9). The die converged with semi-angle 15 [degrees] to a slot of width 70 mm and thickness H = 3.0 mm. Each drawn product D cooled at constant length under tension overnight, during which time the force relaxed by [approximately]30%. It was then removed from the machine and its thickness [H.sub.D] and width [W.sub.D] were determined, from which the draw ratios [R.sub.A] of the three drawn products were found to be 2.2, 5.1, and 7.6. The lines across the thickness had deformed to approximate parabolas; their separation [L.sub.D], and also the displacements of the vertex [Delta] with respect to the surfaces, were measured. From the drawn products, and from an undrawn isotropic billet of similar thickness, appropriate specimens were cut for each experimental method for characterization, as described below.
The polypropylene for rolling was sheet (Barkston Plastics, Leeds, United Kingdom) of a grade similar to what was die-drawn, of thicknesses [H.sub.B] = 4.4 mm and 2.05 mm. Rolling was done using a roll mill (Dinkel Esslingen) with a 0.33 hp reversible motor with speed control, and electrically heated rolls of diameter [d.sub.R] = 65 mm, width 130 mm; the gap [h.sub.g] was variable between 0 and 4 mm. By closing the rolls on rods of known diameter, an approximate calibration of the gap in terms of the position of the controlling handwheel was possible. The roll mill was placed between a 2 m long oven and a caterpillar puller on a draw range. Temperature regulation of the rolls was checked in trials using an external thermocouple. Before each experiment, the cold rolls were cleaned with acetone. At a distance [L.sub.B] apart, marks were made on the polypropylene billet, [approximately]2 m long, and its width [W.sub.B] and thickness [H.sub.B] were measured at the marks. Each billet was put into the hot oven for about an hour, and then rolled through the heated rolls. The gap was changed a few times during an experiment. For rolling only, the puller was disengaged; for drawing, the rolls were stopped and the puller operated, while for rolling and drawing, the rolls rotated with the puller operating. Output speeds [v.sub.out] of the products were recorded; they were always much smaller than the surface speed [v.sub.roll] of the rolls, which was 7 to 15 mm/s. After cooling, the drawn or rolled thickness HA of the product was measured, together with its width [W.sub.A] at the marks and the separation [L.sub.A] between them. Without pulling, the products made by rolling only were not fiat except along their edges; in the central region there were corrugations, the wavelength [l.sub.c] and amplitude [a.sub.c] of which were also recorded.
Differential scanning calorimetry was done with a Perkin-Elmer system including a Model DSC7 calorimeter, a Model TAC 7/DX thermal analysis controller and a Model AD-4 Autobalance. After calibration with indium, 4-5 mg specimens cut from pieces of the drawn polypropylene products, and from machining shavings of the isotropic material, were tested at a heating rate of 10 [degrees] C/min.
X-ray diffraction was measured with a Huber X-ray set including a Model 151 flat monochromator illuminated with Cu K [Alpha] radiation, a Model 511.4 four-circle Eulerian cradle goniometer, and a Bicron 1XM040 detector, coupled to a Hewlett-Packard computer with Hutex software. The automated diffractometer controlled the angular position of the 30 x 20 mm specimen in terms of radial and circle angles [Alpha] and [Beta], and the angle 20 between the incident and diffracted X-ray beams. Specimens, from die-drawing or undrawn (isotropic), were 1 mm thick, while those from rolling had the thickness of the rolled product; they were oscillated in their own plane to enlarge the scanned area. Scans of 2[Theta] were made from 10 [degrees] to 30 [degrees] in 0.04 [degrees] steps with [Alpha] = 90 [degrees], both in reflection and in transmission. Then the system's routine for pole figure data collection was used over the whole range of [Alpha] and [Beta], with 2[Theta] fixed at its exact value for the (110) diffraction found from the 2[Theta] scan, the geometries being reflection and transmission for 0 [less than or equal to] [Alpha] [less than or equal to] 65 [degrees] and 60 [degrees] [less than or equal to] [Alpha] [less than or equal to] 90 [degrees], respectively. These scans were all done again, with 2[Theta] for the (040) and (130) diffractions. After corrections for air scattering were made using counts observed with no specimen, the data were corrected for departures from ideality using the results obtained with the isotropic specimen, by a routine in the software; then the results from reflection and from transmission were merged into a single data set, using another routine, and plotted as pole figures.
Elastic moduli of the die-drawn polypropylenes were measured by the ultrasonic method with the locally built apparatus that has been described (10, 11). Travel times for sound of frequency 2.25 MHz passing through the 55-mm square specimen were observed as a function of angle of incidence. The sound passes through the thickness of the specimen, assumed orthotropic, in the [X.sub.2] direction. When the draw direction is horizontal or vertical, the sound propagates in the [X.sub.3][X.sub.2] plane or the [X.sub.1][X.sub.2] plane respectively, and the method yields elastic stiffness constants (12) [C.sub.33], [C.sub.22], [C.sub.44], [C.sub.23], or [C.sub.11], [C.sub.22], [C.sub.66], [C.sub.12], respectively. To get the remaining stiffness constants, the specimen is cut along the draw ([X.sub.3]) direction into eight strips which are stacked to give a rebuilt rectangular piece with its length, height and thickness in the [X.sub.3], [X.sub.2] and [X.sub.1] directions. Sound now propagates in the [X.sub.3][X.sub.1] plane and [C.sub.33], [C.sub.11], [C.sub.55], [C.sub.31] are obtainable. Cutting the specimen into strips with smooth surfaces is easier when the cuts are along the draw ([X.sub.3]) direction, although precision in [C.sub.33] would be better if the strips could be cut across it. A computer program is used to find stiffness constants that minimize the sum of squares of deviations in the sound velocities.
An Instron Model TT-CM tensile test machine was used with dog-bone specimens cut from the die-drawn products; these had their original thickness ([X.sub.2]), gauge length in the draw direction ([X.sub.3]) 90 mm, and width ([X.sub.1]) 10 mm, with 20 x 20 mm gripped end tabs. The cross section had a smaller than standard area, to avoid excessive forces caused by straining the stiff material. Routing was used to cut two specimens from product with R = 7.6; subsequently, for R = 5.1, four better specimens were made using an engraving machine with a versatile template. For each specimen, three tests at low strains using an extensometer were done at an extension rate of 5 [[micro]meter]/s, followed by a test to failure at 33 [[micro]meter]/s.
The impact strength of the die-drawn products was measured with a Rosand Instrumented Falling Weight Impact Tester type 5. Its 10-mm diameter blunt impactor dart, loaded with a 25 kilogram weight, struck the specimen at 4.0 m/s. After the Advanced Instrumented Impact Analysis System recorded the force F as a function of time, using a 10 ms sweep time, the system's software calculated the maximum force [F.sub.max] and the total energy absorbed. The samples tested were from the PP die-drawn to R of 2.2, 5.1, and 7.6, from the undrawn billet of the same material, and also from the sheets of PP used for rolling. They were all 50 to 65 mm wide, cut into 65 mm lengths, to make nearly square pieces that completely covered the circular opening, of diameter d = 43.2 mm, in the anvil of the tester. At least three specimens of each material were tested, both at 25 [degrees] C and at -40 [degrees] C.
The three drawn products, which were made by drawing billets of different thicknesses through the same die, are identified (Table 1) by their reduction ratios R = [H.sub.B]/[H.sub.D], defined in terms of the thickness ([X.sub.2]). The draw force F increased roughly proportionally to R. Along [X.sub.3], the length ratio [L.sub.D]/[L.sub.B] increased to more than R, while there was a small narrowing in the width ([X.sub.1]). No significant change in volume to [L.sub.D][W.sub.D][H.sub.D] from [L.sub.B][W.sub.B][H.sub.B] was detectable.
In the first rolling trial with the oven and rolls at 150 [degrees] C, the polypropylene melted on the rolls. Some billets with [H.sub.B] = 4.4 mm were rolled with oven and rolls at 120 [degrees] C; with [H.sub.B]/[h.sub.g] = 1.5, the final reduction [H.sub.B]/[H.sub.A] was only 1.1 because of springback. At larger [H.sub.B]/[h.sub.g], the billet slipped on the rolls and did not roll through. From conventional theory for cold rolling, which is based on plastic flow with the stress constant at the yield stress [[Sigma].sub.Y] (13), excluding elastic recovery, [TABULAR DATA FOR TABLE 1 OMITTED] one can predict a maximum reduction ratio [H.sub.B]/H. It depends on the coefficient of friction [Mu] between billet and rolls, the ratio [H.sub.B]/[d.sub.R] of billet thickness [H.sub.B] to roll diameter [d.sub.R], and the ratio of drawing stress [Sigma] to yield stress [[Sigma].sub.Y]. Trying to roll to a larger reduction ratio would cause the material to slip over the whole roll surface. For [H.sub.B]/[d.sub.R] = 0.068, one calculates (with [Sigma] = 0) for [Mu] = 0.05 and [Mu] = 0.10 maximum reductions [H.sub.B]/H = 1.08 and 1.55 respectively, but for [Mu] = 0.2 the friction is large enough to allow rolling down to zero thickness without slipping. Without pulling, the billet did roll through when [H.sub.B]/[h.sub.g] = 1.5, but it slipped with [H.sub.B]/[h.sub.g] = 2.2, so that [Mu] was probably a little larger than 0.1. To increase the reduction it was necessary to decrease [H.sub.B]/[h.sub.g] by using thinner billets with [H.sub.B] = 2.05 mm.
In the experiments with the 2.05 mm thick billets, the oven was at 140 [degrees] C for most of its length and at 110 [degrees] C next to the roll mill; the rolls were at 120 [degrees] C. On Figs. 1 and 2 the observations of the reduction [H.sub.B]/[H.sub.A] near the edge are plotted to show the dependence on the roll gap [h.sub.g] and output speed [v.sub.out]. Curves approximating the data are also shown; they are drawn using empirical equations based on dimensional analysis. When the product was drawn by the puller, [v.sub.out] was an independent variable equal to the puller speed. However, for rolling only, [v.sub.out] and [H.sub.A] become [v.sub.out,R] and [H.sub.A,R], determined by [h.sub.g] for fixed [H.sub.B], any possible weak dependence on the roll speed being ignored. The lower heavy curves on Figs. 1 and 2, which represent rolling only, are from the empirical equations [v.sub.out,R] = [v.sub.roll][([h.sub.g]/[H.sub.B]).sup.3], and
1 - [H.sub.A,R]/[H.sub.B] = [(1 - [h.sub.g]/[H.sub.B]).sup.2] (1)
Alternatively, when the puller was operated with the rolls stopped, reduction, to a thickness [H.sub.A,S], was due to drawing only. No consistent dependence of [H.sub.B]/[H.sub.A,S] on [v.sub.out] was observed at the low speeds used ([ILLUSTRATION FOR FIGURE 1 OMITTED], right), and the experimental data were fitted to the linear equation
[H.sub.A,S] = [H.sub.B] - [h.sub.g]/[R.sub.0] + [h.sub.g]/[R.sub.1] (2)
Here [R.sub.0] and [R.sub.1], the extrapolated reductions at [h.sub.g]/[H.sub.B] = 0 and 1, were found to be 15.6 and 1.65, respectively. The upper heavy curve on Fig. 2 was calculated from this equation. Finally, when rolling was accompanied by drawing by the puller at a speed [v.sub.out], the product thickness [H.sub.A], as shown by the thin curves on Figs. 1 and 2, was calculated from
[H.sub.A] = [([v.sub.out,R]/[v.sub.out]).sup.1/3] (H.sub.A,R] - [H.sub.A,S]) + [H.sub.A,S] (3)
Each product from rolling only, without use of the puller, was corrugated in its central region, presumably because there the initial elongation in the rolling direction was greater. Subsequent elastic recovery (springback) would then cause the central region to buckle to allow its overall length to match that of the edge region. The elongation ratios of these products, made by rolling without drawing, are plotted against the reduction [H.sub.B]/[H.sub.A] in Fig. 3. Near the edge the decrease in thickness [H.sub.A] was [approximately]4% smaller than in the central region. Elongations in length were found from measurement of [L.sub.A] at the edge, and by multiplying those [L.sub.A] values by the calculated ratio of arc to chord lengths of the corrugations, assumed sinusoidal, to get [L.sub.A] in the central region. The central and edge strains [L.sub.A]/[L.sub.B] - 1 are respectively 2% and 14% smaller than central [H.sub.B]/[H.sub.A] - 1. With the assumptions that volume is constant and that the central region is 90% of the total product width, the lower curve on Fig. 3 was calculated to approximate the data for the transverse elongation [W.sub.A]/[W.sub.B], although in reality the central region appeared to be a smaller fraction of the total width. The central corrugations in these rolled products had wavelength [l.sub.c] and amplitude [a.sub.c]; the dimensionless reciprocals [H.sub.B]/[l.sub.c] and [H.sub.B]/[a.sub.c] are plotted against reduction [H.sub.B]/[H.sub.A] in Fig. 4.
The results of DSC measurements on the die-drawn polypropylenes are given in Table 2 and Fig. 5. Drawing the polypropylene raised both the melting temperature [T.sub.m] and the enthalpy of melting [Delta]h, and eliminated a small endotherm at about 146 [degrees] C. Table 2 lists the temperatures of the onset of melting and the peak of the endotherm, and the specific enthalpy of melting [Delta]h, as determined by the system's software in a consistent way with respect to the same baseline. The values may be in doubt by as much as 1 [degree] C and 3 J/g respectively. A second run was done with the specimen of draw ratio 5.1 after its melt had solidified again; this time the endotherm was indistinguishable from that of the isotropic sample. The average of the peak temperatures, 166.5 [degrees] C, is 21 [degrees] lower than the literature value 187.5 [degrees] C for [T.sub.m] (14). Low fractions of crystallinity x are obtained when the specific enthalpy of melting [Delta]h is divided by the literature value for the crystalline enthalpy of fusion [Delta][h.sub.f] = 207.1 J/g (14).
Densities were estimated by weighing and measuring the specimens used for the elastic moduli by the ultrasonic method. Using 852 kg/[m.sup.3] for the density of amorphous PP (15) and 946 kg/[m.sup.3] for that of the crystalline unit cell (16), one finds the crystalline fractions x in the seventh row of Table 2. Errors in the three dimensions and the mass propagate to give low precision: thus if the thickness [H.sub.D] is high by 20 [[micro]meter], the density value is low by 7 kg/[m.sup.3] and the crystallinity is low by 7%. The results indicate that the drawing process increases the crystalline fraction.
The intensity of Cu K[Alpha] X-ray diffraction in reflection geometry is shown on Fig. 6 as a function of angle 2[Theta]. Peaks occur at 2[Theta] = 14.4 [degrees], 17.4 [degrees], 19.0 [degrees], 22.3 [degrees], 26.1 [degrees], 28.8 [degrees]; the respective calculated positions (17) are 14.1 [degrees], 17.1 [degrees], 18.6 [degrees], 22.0 [degrees], 25.7 [degrees], 28.5 [degrees] for diffraction planes having Miller indices (110), (040), (130), (041), (060), (220) in monoclinic alpha crystals of polypropylene, with parameters a = 666, b = 2078, c = 649.5 pm, [Beta] = 99.62 [degrees] (16). The isotropic sample also had peaks at 16.5 [degrees] and 21.5 [degrees]; 16.1 [degrees] and 21.1 [degrees] are the calculated angles 2[Theta] for the (100) and (101) planes of the unstable hexagonal beta crystals, for which a = 636, b = 949 pm (16) (but 16.2 [degrees] and 21.3 [degrees] are calculated for the (021) and (111) planes of the alpha form). At angles 2[Theta] away from these peaks, diffraction is due to the amorphous fraction; the amorphous intensity under the peaks has also been estimated by interpolation and is shown on Fig. 6 as the thin curve under the base of the peaks. The areas, under this curve, and above it under the peaks, should be proportional to the amorphous and crystalline fractions, respectively, in a randomly oriented specimen (eighth to tenth rows of Table 2). Although the estimates of the crystalline fraction x from the different methods do not agree, the results suggest that drawing, even to a small draw ratio, disrupts the original structure of the polypropylene and develops an altered structure with increased crystallinity. However, at higher draw ratios the crystallinity is not much larger.
Table 2. Enthalpy, Density, and Crystallinity. Reduction ratio, R Isotropic 2.2 5.1 7.6 Melting onset, [degrees] C 154.7 159.7 162.4 157.5 Melting peak, [degrees] C 163.3 165.8 171.4 165.4 Enthalpy [Delta]h, J/g 86.8 105.6 106.2 108.5 x%, from [Delta]h 42 51 51 52 Density [Rho], kg/[m.sup.3] 901 910 918 917 x%, from [Rho] 55 64 72 71 Amorphous area(*) 1.66 9.86 10.45 Crystalline area(*) 1.03 6.26 19.12 x%, from 2[Theta] 38 * On plot of X-ray counts against 2[Theta], in 1000 counts x degrees.
The orientation of a polypropylene crystallite (18) can be specified by three Euler angles. Alternatively, one can give multiple sets of angles [[Theta].sub.i] that a vector attached to the crystallite make with a reference direction [X.sub.t] (i = 1, 2, 3) fixed in space. At a fixed value of 2[Theta], the intensity of the X-ray diffraction depends on the orientation of the specimen specified by the angles [Alpha] and [Beta] or by the position of their stereographic projection on the [X.sub.1][X.sub.3] plane. Figure 7 shows some pole figures, isometric plots of the merged and corrected intensity data as a function of [X.sub.1] and [X.sub.3]. The averages <[cos.sup.2][[Theta].sub.i]>, with the (110), (040) or (130) normal as the vector attached to the crystallite, can now be found, by integrating over [Alpha] and [Beta] these intensity data multiplied by the function of [Alpha] and [Beta] appropriate to that i (18). Since the three averages satisfy <[cos.sup.2][[Theta]1]> + <[cos.sup.2][[Theta].sub.2]> + <[cos.sup.2][[Theta].sub.3]> = 1, the three values can be represented by one point on a triangular diagram [ILLUSTRATION FOR FIGURE 8 OMITTED]. The apex of the triangle labeled i represents perfect orientation of the vector with one of the directions [X.sub.i], while the centroid of the triangle (marked by +) represents a random distribution of directions of the vector. The crystallographic b axis (the monoclinic axis) coincides with the (040) normal. For the c axis (the chain axis) <[cos.sup.2][[Theta].sub.i]> must be found indirectly from two other <[cos.sup.2][[Theta].sub.i]> values for two noncoplanar vectors [(17), Eq 4-34]. The X-ray results [ILLUSTRATION FOR FIGURE 8 OMITTED] show that the crystallographic c axes are aligned close to the machine direction [X.sub.3] and the b axes tend towards being perpendicular to [X.sub.3]. These results are confirmed by the (110) and (040) pole figures as shown in Fig. 7. The extent of c axis orientation is proportional to the reduction ratio R, whether the orientation is by die-drawing, rolling, or a combined process.
The die-drawn product with R = 7.6 was also measured using a different scanning pattern, the data from which were corrected by a different computer routine; the values of <[cos.sup.2][[Theta].sub.i]> from the two methods agreed within 0.05. Two specimens (R = 7.6), one cut from the surface of the product and the other from the middle, were found to have <[cos.sup.2][[Theta].sub.i]> values agreeing within 0.03.
Elastic constants of the die-drawn products measured by the ultrasonic method are tabulated (Table 3), both as stiffness constants [C.sub.ij], and as tensile moduli [E.sub.i] and Poisson's ratios [v.sub.ij], which give the lateral contraction in direction [X.sub.i] due to stress in direction j. Because the specimen of undrawn polypropylene was believed to be isotropic, it was not cut into strips, so that its [C.sub.55] and [C.sub.31] were never measured. It proved to differ slightly from isotropy, appearing transversely isotropic with the stiff direction [X.sub.2]. The assumptions [C.sub.55] = [C.sub.66] (= [C.sub.44]) and [C.sub.31] = [C.sub.12] (= [C.sub.23]) were used to include [C.sub.55] and [C.sub.31] in Table 3; the values satisfy [C.sub.55] = 1/2([C.sub.11] - [C.sub.31]). Because of the choice of cutting direction, the values for the draw direction [X.sub.3] may be in error by as much as 10%, but the precision should be better for the transverse and normal values.
The plots of nominal stress [Sigma] against Hencky strain [Epsilon] from tensile tests were distinctly nonlinear [ILLUSTRATION FOR FIGURE 9 OMITTED]. A linearly viscoelastic material gives such a curved plot because of stress relaxation: for a Maxwell fluid with modulus E and relaxation time [Tau], strained at a rate [Mathematical Expression Omitted]
[Mathematical Expression Omitted] (4)
However, the values of [Tau] fitting the data for [Mathematical Expression Omitted] and 3.70 x [10.sup.-4] [s.sup.-1] were roughly inversely proportional to [Mathematical Expression Omitted]. Thus the data actually fitted the nonlinear equation
[Sigma] = (E/[Kappa])(1 - [e.sup.-[Kappa][Epsilon]]) [approximately equal to] E[Epsilon] (5)
for small [Epsilon], where [Kappa] is constant. Best fits to the [Sigma] - [Epsilon] curves from single tests gave 50 [less than] [Kappa] [less than] 90; the standard error of the fit was not altered much by varying [Kappa] in this range. With [Kappa] fixed at 70, four best-fitting values of E were found from the three extensometer tests, and from the failure test with the data for [Epsilon] [less than] 0.014. Because variances between tests for the same specimen were comparable to variances between specimens, E averaged over all tests for each drawn product is reported (Table 4). With increasing stress, the specimens strained apparently homogeneously, without yielding or necking. They failed suddenly at a definite [TABULAR DATA FOR TABLE 3 OMITTED] failure strength and elongation (Table 4) by delaminating into thin layers in the [X.sub.1][X.sub.3] plane, which broke rapidly with a loud cracking sound. The energy absorption, or work to failure per unit volume, was calculated as the area under the [Sigma] - [Epsilon] curve (Table 4).
From the impact test data of the dependence of force F on time, the displacement w from first contact was calculated using Newton's law. The results are expressed as nominal material properties (Table 5) with the theory for elastic deflection of a centrally loaded clamped circular plate of thickness h and diameter d (19). The nominal modulus is obtained from the initial slope dF/dw as
[E.sub.n] = 3(1 - [v.sup.2])[d.sup.2]/16[Pi][h.sup.3] dF/dw (6)
where we take Poisson's ratio v = 1/3. Approximations to the stress and elongation at failure are derived from [F.sub.max], and w at [F.sub.max], as [F.sub.max]/[h.sup.2], and 4wh/[d.sup.2]. respectively. The failure energy per unit volume e = 4 x energy/[Pi][d.sup.2]h; e and [F.sub.max] depended significantly on R only at -40 [degrees] C (Table 5).
Six modes of failure were observed in the impact tests. A, the impactor dart punctured the specimen, cutting out a single lens-shaped piece of its own 10-mm diameter, to leave a circular hole; the first deformation seemed ductile. B, failure was brittle: an irregular hole, 20 to 30 mm in diameter, formed with a few short radial cracks out from it, five or six wedge-shaped fragments having broken off. C, the specimen was pierced making a small hole without fragments, and there was a short crack in the draw direction, rarely sufficient to split the specimen into two. D, a larger hole was made but fragments usually did not break away completely, remaining attached at one end; some delamination in the specimen plane occurred, but no crack. E, a large area of the specimen delaminated, but the laminae bent enough to allow the opening where the impactor dart pierced the specimen largely to close up when it was pulled out; there was a crack in the draw direction usually extending to both edges of the specimen so as to split it into two distinct pieces. F, damage resembled mode E but was more severe, with two cracks in the draw direction and much splintering of the laminae. The more highly oriented products suffered more damage (Table 5).
[TABULAR DATA FOR TABLE 4 OMITTED]
The geometry of deformation in the die-drawing process can be studied using results from continuum mechanics. Two-dimensional flow through a converging die satisfying the no-slip boundary condition and the Newtonian viscous constitutive law (20) would give a large vertex displacement [Delta] in the die-drawn product, while [Delta] = 0 for potential (irrotational) flow with perfect slip at the die walls. To get approximate agreement with the observed [Delta] (7th row, Table 1), we supposed that 0.4% of the flow had no slip and 99.6% was slipping irrotational flow, obtaining the calculated [Delta] values (8th row, Table 1). However, the draw force F, calculated for irrotational flow, using for the viscosity 60 MPa [multiplied by] s (10th row, Table 1) so as to agree with the average of the observed F, showed an unrealistically small increase with reduction ratio R at larger R, The viscous constitutive law underestimates the contribution to the force from the upstream region of the die, where the strain rate is small. Recent work on experimental observations and modeling of the flow behavior of polymer melts through an abrupt contraction geometry (21) may allow more accurate calculation of F.
The irrotational character of the deformation implies that there is no significant shearing near the die walls, as would occur in a flow with no slip. The history of deformation of the die-drawn product is thus the same at the surface and in the middle. This is confirmed by the agreement between the <[cos.sup.2][[Theta].sub.i]> values found from X-ray diffraction of specimens cut from the surface and the middle of one product. In contrast, a structure for roll-drawn polypropylene consisting of a microfibrillar skin, a transition zone, and a spherulitic core has been proposed (22), in order to explain data from shear-wave birefringence.
In rolling, the boundary conditions on the velocity and stress at the walls differ from those in die-drawing. The compressive forces from the rolls might be expected to widen the product in the transverse direction, so that the deformation would no longer be plane strain, but it would tend towards being biaxial. For plane strain the elongation ratios satisfy [W.sub.A]/[W.sub.B] = 1, [H.sub.A]/[H.sub.B] = [([L.sub.A]/[L.sub.B]).sup.-1], while for biaxial deformation [W.sub.A]/[W.sub.B] = [L.sub.A]/[L.sub.B], [H.sub.A]/[H.sub.B] = [([L.sub.A]/[L.sub.B]).sup.-2]. In intermediate kinds of deformation [W.sub.A]/[W.sub.B] = [([L.sub.A]/[L.sup.B]).sup.n-1], [H.sub.A]/[H.sub.B] = [([L.sub.A]/[L.sub.B]).sup.-n], where the exponent n has the limits 1 and 2 for plane strain and biaxial deformation, respectively. From the slopes of the plots of [L.sub.A]/[L.sub.B] against [H.sub.B]/[H.sub.A] (middle lines, [ILLUSTRATION FOR FIGURE 3 OMITTED]) for the products made by rolling only, n = 1.01 in the central region and n = 1.1 near the edge, so that the geometry of deformation is nowhere close to biaxial in any of them. The corrugations in the rolled products appear because the central region becomes longer than the edge. If a stress [Sigma] due to springback develops in the central region, use of the theory for buckling of a beam suggests that the wave-length [l.sub.c] should satisfy
[Mathematical Expression Omitted] (7)
[TABULAR DATA FOR TABLE 5 OMITTED]
The plot of [H.sub.B]/[l.sub.c] against [H.sub.B]/[H.sub.A] has the expected form of a straight line through the origin [ILLUSTRATION FOR FIGURE 4 OMITTED]; from the slope of the regression [Sigma]/E = 0.004, implying that a springback stress develops amounting to about 0.4% of the modulus. In this polypropylene of high molar mass, presumably a network structure gives significant entropic elasticity.
The DSC results (Table 2) show an increased crystalline fraction x in the die-drawn products, indicated by the rather consistent [Delta]h values from the areas under the melting endotherms. Exothermic shrinkage prior to melting, which is influenced in an irregular way by how much the specimen sticks to the sample pan (23), may account for the differences in position and shape of the melting endotherms. The melting temperatures, [approximately]24 [degrees] C lower than the literature value for alpha PP crystals (14), are close to those observed in this laboratory (24) for a PP containing [less than]1% of ethylene copolymerized. A similar decrease was seen for 2.8% ethylene in PP (14). It appears that die-drawing disrupts the original crystalline structure, and that a new, oriented, crystalline structure develops. Apparently larger increases in crystallinity at higher reduction ratio R are Indicated by the density measurements (7th row, Table 2), but they may be exaggerated because in oriented materials the amorphous density rises (23), so that our calculation using a constant amorphous density will overestimate x.
The WAXD pole figures [ILLUSTRATION FOR FIGURE 7 OMITTED] indicate that, as in prior work (18), the chain axis c orients in the machine direction [X.sub.3], with only a small component in the transverse direction [X.sub.1] becoming evident at high reduction ratios R. The values of <[cos.sup.2][[Theta].sub.i]> are close for R = 5.1 and 7.6 [ILLUSTRATION FOR FIGURE 8 OMITTED]; this is consistent with the leveling-off of the second moment [<[P.sub.2]([cos.sup.2][Theta])>.sub.c] at high R previously reported (24). Our finding that the (110), (040), and (130) normals tend to orient towards the [X.sub.1][X.sub.2] plane differs from the observation (25) that these normals all populate the normal [X.sub.2] direction in ultrahigh molecular weight PP cold-rolled to R [less than or equal to] 4.5, suggesting that in our PP of conventional molar mass the orientation process is not so complex. The unit cell of PP has approximately uniaxial symmetry (16); the previously inferred elastic network may act as a continuum in the deformation process tending to align the unit cells like rods in the direction [X.sub.3] of the largest eigenvalue of the deformation matrix.
Nearly all the elastic constants from the ultrasonic measurements (Table 3) show systematic trends as R increases from 2.2 to 7.6, but commonly the isotropic value does not conform to the trend, suggesting that its structure does differ from those of the die-drawn products. Drawing causes little change in the cross components of stiffness [C.sub.ij] for i [not equal to] j, so that the Poisson ratios [v.sub.ij] reflect the stiffness in the [X.sub.j] direction. For example, the small [v.sub.13] and [v.sub.23] show that a stress in the stiff [X.sub.3] direction causes very little lateral contraction. The values in Table B would not change much if the indices 1 and 2 were interchanged, again indicating that the symmetry of the die-drawn products is close to uniaxial. To a crude approximation, the elastic constants in the [X.sub.1] and [X.sub.2] directions can be considered unchanged by die-drawing. In the Instron tests, the time scale for measuring the tensile modulus E in the draw direction [X.sub.3] was long, [approximately]10 s; the values of E were just one-half (Table 4) the engineering modulus [E.sub.3] from the ultrasonic measurements, for which the time scale is 1/(2.25 MHz) = 4 x [10.sup.-7] s. Presumably there is a secondary relaxation process between these times, possibly the beta relaxation which is not suppressed by drawing to these low draw ratios. The nominal moduli [E.sub.n] estimated from the impact tests were even smaller in spite of their shorter time scale, 1-3 ms; perhaps the apparently linear plots of force against deflection were due not only to elastic deformation but also to failure processes.
In both the tensile tests (Instron) and the impact tests, the die-drawn products failed by delaminating in the [X.sub.1][X.sub.3] plane owing to (040) planar orientation. The failure energy per unit volume was 4 to 5 times larger in the tensile tests than in the impact tests (Tables 4, 5), since in the latter tests the outer parts of the circular specimen were not stressed to failure. After delamination, the laminae near the surface resembled those in the middle, indicating that the product was uniform through its thickness, with no distinct skin and core regions.
Both rolling and drawing polypropylene to moderate reduction ratios produce deformations that are close to plane strain. Elastic springback significantly decreases the reductions that can be attained by rolling. Drawing increases the crystallinity from [approximately]50% to [approximately]65%; thus it disrupts the original PP structure, developing greater crystallinity. The X-ray pole figure analysis of these samples shows that the c axes orient along the machine direction and the b axes tend towards being perpendicular to the drawing plane [X.sub.1][X.sub.3]. The c axis orientation is proportional to R. These results indicate an approximate uniaxial symmetry in the products, which was confirmed for the die-drawn ones by ultrasonic measurements of the stiffness matrix. The modulus [E.sub.3] in the draw direction is also roughly proportional to R, attaining 14.3 GPa for R = 7.6, while [E.sub.1] & [E.sub.2] and the shear moduli remain close to the tensile and shear moduli of the undrawn PP, 3.8 and 1.4 GPa respectively. Slow (Instron) tensile testing in the draw direction gives [E.sub.3] of about one-half the ultrasonic value, presumably because there are short-time relaxations. Failure in both tensile and impact tests is sudden, by delamination in the [X.sub.1][X.sub.3] plane.
In spite of the differences in how stresses are applied to the material in die-drawing and in rolling, both these processes give similar, almost plane-strain, deformations. However, the anisotropy of the products at equilibrium, as evidenced by WAXD or by the stiffness matrix, is close to uniaxial. Even under a stress field lacking axial symmetry, essentially uniaxially aligned crystallites appear to re-form, perhaps influenced by the molecular network structure expected in these polypropylenes.
The Engineering and Physical Sciences Research Council, U.K., generously aided the work through the award of a Visiting Fellowship to support C.E.C. Valuable help was given by C. C. Morath and the technical staff (production, making samples, measurements), Dr. A. P. Unwin (ideas for the research, WAXD), Dr. P. J. Hine (ultrasonic modulus, impact tests), and Dr. E. L. V. Lewis (rolling, WAXD).
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|Title Annotation:||First Symposium on Oriented Polymers|
|Author:||Chaffey, Charles E.; Taraiya, Ajay K.; Ward, Ian M.|
|Publication:||Polymer Engineering and Science|
|Date:||Nov 1, 1997|
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