Page 126 - Academic Press Encyclopedia of Physical Science and Technology 3rd Polymer

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Encyclopedia of Physical Science and Technology EN012c-593 July 26, 2001 15:56

632 Polymer Processing

of fracture. When slip-stick fracture occurs, the pressure known as die swell or extrudate swell. The common view
in a capillary begins to oscillate and the magnitude does is that die swell is related to unconstrained elastic recovery
not rise with increasing throughput. However, for gross (S ∞ ) following shear flow. S ∞ is related to the ratio of
fracture (and sharkskin for that matter) there are no signs the primary normal stress difference to the shear stress
of pressure oscillations. through the equation:
To reduce the detrimental effect of melt fracture through
N 1
die design or polymer modification, it is important to know S ∞ = . (28)
the origin of melt fracture. The major sources for melt 2τ yx
fracture are the die entry region, the die land, and the die Tanner’s theory for die swell for flow through a capillary
exit. For a polymer such as LDPE, fracture originates at predicts
the die entry. Large vortices form in the contraction at the 1 2 1/6
D p /D o = 0.1 + [1 + / 2 (S ] . (29)
die entry. As the extrusion rate is increased, the vortices ∞
no longer grow in size or intensity. Instead the flow takes Extrudate swell is more complicated than indicated by Eq.
on a spiral motion in the die entry sending sections of the (29) because it depends on a number of factors such as die
nearly stagnant fluid into the die at regular intervals. This length, exit geometry, and length of recovery time. First it
leads to regions of various flow histories passing through depends on the measurement method. The highest values
the die and leaving the die exit. When this type of frac- are obtained for polymers that are extruded isothermally
ture occurs, there is no indication of the flow problems into an oil bath. The lowest values are for the extrudate,
in the pressure measured along the die. By streamlining which is extruded into ambient air. Annealing allows the
the die entry or increasing the length of the die land it sample to almost reach the values obtained under isother-
is possible to reduce the amplitude of the distortion, but mal conditions. It depends on the capillary L /D with the
the critical wall shear stress for fracture is unchanged. The greatest swell being for the shortest capillary. This behav-
critical wall shear stress for the onset of fracture for LDPE ior has been attributed to the large amount of elastic energy
5
is of the order of 10 Pa. stored during the extensional flow in the entry region. It
LLDPE typically exhibits no strain hardening and is also observed that die swell depends on time after the
the onset of shear thinning is pushed to higher shear extrudate leaves the die. It is observed that a large portion
rates than for LDPE. This is because there is usually of the swell occurs instantaneously, while the remainder
no long-chain branching and the polydispersity is fairly of the diameter increase can occur over a period of several
low (<5.0). When a critical wall shear stress is reached minutes. Finally, D p /D o (equilibrium swell) is a func-
5
(e.g., ∼1.8 × 10 Pa), the polymer begins to stick and slip tion of the wall shear stress, τ R . In summary, capillary
at the die exit leading to sharkskin. As the throughput is die swell, B = D p /D o , is a function of the following vari-
increased, the polymer begins to stick and slip in the die ables:
land leading to large pressure oscillations and an irreg-
B = f (L/D,τ R , EG, E, t, t p /λ), (30)
ular extrudate (the critical stress for slip-stick is of the
5
order of 3 × 10 Pa). There is a distinct flattening of the where EG is the entrance geometry, E is the exit geometry,
flow curve (i.e., shear stress versus shear rate) indicating t is the time after a fluid element leaves the die, t p is the
a region where multiple flow rates are possible for the time required for the melt to pass through the die, and λ is
same wall shear stress. Eventually the flow curve appears the longest relaxation time for the fluid. The last quantity,
to become normal again at high shear rates, but then the t p /λ, is referred to as the Deborah number. Certainly the
sample exhibits severe fracture. HDPE also exhibits very ideas of elastic recovery are involved, but stresses other
little strain hardening, but the onset of shear thinning oc- than those generated in shear flow (e.g., extensional flow
curs at low shear rates because of the high degree of poly- at the die exit) must be considered.
dispersity. Usually HDPE does not exhibit sharkskin but
slip-stick and then gross fracture. When slip-stick fracture D. Dies
occurs (which results in the ripple and then bamboo types 1. Flat Film and Sheet Dies
of fracture), increasing the die length just makes the de-
gree of distortion worse. Using short lands can eliminate The salient features of a film (or sheet) die are shown in
slip-stick, but enhance sharkskin. Fig. 25. A film die consists of four major parts: the man-
ifold, the choker bar, the land, and the lips. The purpose
of the manifold is to distribute the melt uniformly over
C. Extrudate Swell
the width of the die. The land tends to act as a resistance
The phenomenon associated with the increase of the dia- to flow and also promotes better flow uniformity. In the
meter of an extrudate as a polymer leaves a capillary is event that the manifold does not quite provide the required