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Flow and thermally induced birefringence in gas-assisted tubular injection moldings: simulation and experiment.

INTRODUCTION

The gas-assisted
injection molding

n.
A manufacturing process for forming objects, as of plastic or metal, by heating the molding material to a fluid state and injecting it into a mold.
 (
GMM

GMM Gaussian Mixture Model
GMM General Membership Meeting
GMM Good Mobile Messaging
GMM GPRS Mobility Management
GMM Global Marijuana March
GMM Genetically Modified Microorganisms
) is an important process to
produce
polymeric
 /poly·mer·ic/ () exhibiting the characteristics of a polymer.


adj.
1. Having the properties of a polymer.

2.
 parts with
hollow

 sections. This process consists of
the partial filling of the
mold
 name for certain multicellular organisms of the various classes of the kingdom Fungi, characteristically having bodies composed of a cottony mycelium. The colors of molds are caused by the spores, which are borne on the mycelium.
 
cavity
 /cav·i·ty/ ()
1. a hollow place or space, or a potential space, within the body or one of its organs.

2. in dentistry, the lesion produced by caries.
, followed by the injection of

pressurized
  
tr.v. pres·sur·ized, pres·sur·iz·ing, pres·sur·iz·es
1. To maintain normal air pressure in (an enclosure, as an aircraft or submarine).

2.
 gas. During the melt injection stage, the polymer near the
mold wall solidifies forming a frozen-in layer. When the gas is

injected

adj.
1. Of or relating to a substance introduced into the body.

2. Of or relating to a blood vessel that is visibly distended with blood.



injected

1. introduced by injection.

2. congested.
, it displaces the polymer located in those regions where the
temperature is still high forming hollow sections while the polymer

displaced

 fills out the rest of the cavity. This step is known as the
primary gas penetration that occurs under imposed gas pressure.

Afterward
   also af·ter·wards
adv.
At a later time; subsequently.

Adv. 1. afterward - happening at a time subsequent to a reference time; "he apologized subsequently"; "he's going to the store but he'll be back here
, during the cooling stage, further gas penetration is
typically observed due to the polymer
contraction
 in physics: see expansion.


contraction, in grammar
 in writing: see abbreviation.


contraction - reduction
. This step is known as
the secondary gas penetration. Finally, when the polymer has
solidified
  
v. so·lid·i·fied, so·lid·i·fy·ing, so·lid·i·fies

v.tr.
1. To make solid, compact, or hard.

2. To make strong or united.

v.intr.
,
the gas pressure is relieved and the part is ejected from the mold (1).

In the
GAIM

GAIM Global Analysis, Integration and Modeling
GAIM GNU AIM  
 process, the
shear
 see strength of materials.


A straining action wherein applied forces produce a sliding or skewing type of deformation.
 and normal stresses generated in the
melt during polymer flow tends to
orient

v.
1. To locate or place in a particular relation to the points of the compass.

2. To align or position with respect to a point or system of reference.

3.
 the polymer molecules toward
the flow direction. Depending on the cooling rate, the
oriented
  
n.
1. Orient The countries of Asia, especially of eastern Asia.

2.
a. The luster characteristic of a pearl of high quality.

b. A pearl having exceptional luster.

3.
 molecules might not have time to relax and they become frozen-in when
the polymer temperature decreases below the
glass transition
temperature

, [T.sub.g] (2). Additionally, due to the significant
increase of
relaxation time

n. Physics
The time required for an exponential variable to decrease to 1/e (0.368) of its initial value.

Noun 1.
 of the polymer during cooling, the

deformation
 /de·for·ma·tion/ ()
1. in dysmorphology, a type of structural defect characterized by the abnormal form or position of a body part, caused by a nondisruptive mechanical force.

2.
 caused by the thermal contraction also induces the molecular
orientation generating considerable levels of residual stresses and

birefringence

The splitting which a wavefront experiences when a wave disturbance is propagated in an anisotropic material; also called double refraction. In anisotropic substances the velocity of a wave is a function of displacement direction.
. The final state of molecular orientation and residual
stresses causes optical and mechanical anisotropies in polymeric
articles (3), (4) that exert a strong influence on the performance of
the final product (5), (6). Spencer and Gilmore (6) provided a

comprehensible
  
adj.
Readily comprehended or understood; intelligible.



[Latin compreh
 explanation of the origin of residual stresses generated
in conventional injection moldings during flow and cooling stages. Shyu
and Isayev (7) and Shyu et al. (8) measured and simulated birefringence
in freely
quenched
  
tr.v. quenched, quench·ing, quench·es
1. To put out (a fire, for example); extinguish.

2. To suppress; squelch:
 
rectangular
  
adj.
1. Having the shape of a rectangle.

2. Having one or more right angles.

3. Designating a geometric coordinate system with mutually perpendicular axes.
 
plaques

n.pl 1. brain lesions found within the vacant areas between nerve cells.
2. deposits of cholesterol in artery walls that characterize arteriosclerosis.
 using the volume
relaxation

n.
1. The act of relaxing or the state of being relaxed.

2. Refreshment of body or mind.

3. A loosening or slackening.

4. The lengthening of inactive muscle or muscle fibers.
 theory developed by Rush (90. Carrillo and Isayev (10) applied this
theory to freely quenched PC and PS tubes and rods. They measured the
distribution of the birefringence components [DELTA]n and [n.sub.rr] -
n[
theta

][theta] along the radius, and the average birefringence [Less
Than Sign][n,.sub.zz] - n[theta][theta][Greater Than Sign] through the
sample diameter. The transient and residual thermal stresses were
calculated using a linear
viscoelastic

 
constitutive equation

 and the
birefringence components were calculated from thermal stresses using a
photoviscoelastic theory.

Numerical

 simulations play an important role in process and part
design. In recent years, significant progress has been made towards the
simulation of the polymer/gas interface distribution in GAIM moldings.
Potente and
Hansen
 , Gerhard Henrik Armauer 1746-1845.

Norwegian physician and bacteriologist who discovered (1869) the leprosy bacillus.
 (11), Cheng et at. (12-16),
Barton

 and Tumg (17),
Tumg (18), Li and Isayev (19), Lin et at. (20) and Polynkin et al. (21)
have studied extensively the influence of processing variables on the
polymer/gas interface distribution for various polymers and mold
geometries. The literature in relation to the influence of the
processing variables on the polymer/gas interface distribution in GAIM
has been discussed earlier (19), (22), (23). It was found that

generalized

adj.
1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain.

2. Not specifically adapted to a particular environment or function; not specialized.

3.
 Newtonian fluid
constitutive
 /con·sti·tu·tive/ () produced constantly or in fixed amounts, regardless of environmental conditions or demand.
 equations were sufficient to
describe both the melt flow and gas penetration processes. However, to
predict the residual stresses and birefringence in the GAIM moldings it
is necessary to
compute

 the time-dependent stress
buildup
 also build-up  
n.
1. The act or process of amassing or increasing:

2.
 and relaxation
that occurs during the nonisothermal melt flow. This can only be
accomplished by using viscoelastic constitutive equations.

One of the pioneering works on residual stresses and birefringence
determination using viscoelastic numerical simulations was performed by
Isayev and Hieber (24). They performed theoretical calculations of
residual stresses and three components of birefringence, An, [DELTA]n,
[n,.sub.zz] - [n.sub.yy] and the average birefringence [Less Than
Sign][n.sub.xx] - [n.sub.zz][Greater Than Sign] in strip moldings. The
calculations were made considering an
idealized
  
v. i·de·al·ized, i·de·al·iz·ing, i·de·al·iz·es

v.tr.
1. To regard as ideal.

2. To make or envision as ideal.

v.intr.
1.
 problem in a
Poiseuille-type flow between parallel plates using a finite-difference
scheme. The authors used the viscoelastic constitutive equation proposed
by Leonov (25) with two relaxation modes coupled with the
governing
  
v. gov·erned, gov·ern·ing, gov·erns

v.tr.
1. To make and administer the public policy and affairs of; exercise sovereign authority in.

2.
 equations for nonisothermal flow in both injection and cooling stages.
The theoretical calculations were compared with injection molding
experimental data available in the literature by
Wales
 Welsh Cymru, western peninsula and political division (principality) of Great Britain (1991 pop. 2,798,200), 8,016 sq mi (20,761 sq km), west of England; politically united with England since 1536. The capital is Cardiff.
 (26), (27),
Janeschitz-Kriegl (28), and Kamal et al. (29), showing in many respects
a good correlation.

Carrillo and Isayev [23] studied the influence of processing
variables on the polymer/gas interface distribution in GAIM
tubular
 /tu·bu·lar/ ()
1. shaped like a tube.

2. of or pertaining to a tubule.



tubular

1. pertaining to renal tubules.

2. pertaining to fallopian tube.
 injection moldings and simulated the gas penetration and flow-induced
birefringence using a viscoelastic model [25]. The authors computed the
flow-induced stresses and calculated the corresponding flow-induced
birefringence components An, [DELTA]n, [n,.sub.rr] - n[theta][theta],
and average birefringence < [n,.sub.zz] - n[theta][theta]> during
the melt injection, gas penetration, and cooling stages of tubular GAIM
moldings. The simulated birefringence components agreed with
measurements near the mold wall but predicted
negligible

 values near the
polymer/gas interface where the measured birefringence was significant.
Then, Carrillo and Isayev [30] complemented the simulated flow-induced
birefringence, calculated using a viscoelastic constitutive equation, by
including the thermally-induced birefringence in PS tubular moldings
obtained via GAIM. The thermally
induced
 /in·duced/ ()
1. produced artificially.

2. produced by induction.



adj artificially caused to occur.


induced

induction.
 birefringence was calculated
using the approach developed in [10]. The preliminary study [30]
indicated that including the thermally induced birefringence to the
flow-induced birefringence the results showed a better description of
the total birefringence in GAIM moldings.

Custodio et al. [31] simulated the evolution of flow-induced
stresses in GAIM using a
compressible
  
adj.
That can be compressed:



com·press
 version of the Rolie-Poly model
[32]. They found that the flow-induced stresses did not evolve further
during the packing and holding stages. Simulations showed that the
magnitude of the flow-induced orientation and related stresses in GAIM
is much lower than that in the conventional injection molding and it is
set during the melt injection phase only. The authors also computed the
thermally- and pressure-induced residual stresses in GAIM rectangular
moldings using a thermo-viscoelastic model. The computed stresses for
GAIM during melt injection and holding phases exhibited slightly higher

tensile

adj having a degree of elasticity; having the ability to be extended or stretched.
 stresses at the surface (polymer/mold interface). However, the
most noticeable difference is the absence of a
compressive
  
adj.
Serving to or able to compress.



com·pressive·ly adv.
 region, which
is typically observed in conventional injection
molded
  
n.
1. A hollow form or matrix for shaping a fluid or plastic substance.

2. A frame or model around or on which something is formed or shaped.

3. Something that is made in or shaped on a mold.
 parts. This
effect was explained by the fact that the pressures for GAIM are much
lower than those of conventional injection molding during the packing
and holding phases.

In our previous work (23) the influence of processing variables on
the distribution of the polymer/gas interface and the evolution and
residual flow-induced birefringence in PS GAIM moldings were studied. It
was found that some processing variables exerted a strong influence on
the birefringence level while other variables did not.

In the present work, various components of birefringence in PS and
PC
spiral
 /spi·ral/ ()
1. helical; winding like the thread of a screw.

2. helix; a winding structure.
 tubular injection moldings obtained by GAIM were measured and
simulated in the primary gas penetration region of the
sprue
 chronic disorder of the small intestine caused by impaired absorption of fat and other nutrients. Two forms of the disease exist. Tropical sprue occurs in central and northern South America, Asia, Africa, and other specific locations.
 and in the
primary gas penetration and solid regions of the spiral. Simulations
took into consideration the contributions of both flow- and
thermally-induced stresses. The flow-induced birefringence components,
calculated from the flow stresses using the stress optical rule, were
added with their respective thermally induced birefringence components
calculated from the thermal stresses using a photo-viscoelastic model.
The birefringence in GAIM moldings were measured along the radius from
the outer wall (polymer/mold interface) to the inner wall (polymer/gas
interface) of the GAIM moldings or to the center of the molding in the
solid region where the gas did not penetrate. The total birefringence
results are shown by considering only for the most influential molding
parameters on the birefringence (23), such as the melt temperature,
injection speed, and gasdelay time. The mold temperature, gas pressure,
and shot size did not exert a significant influence on the birefringence
and were omitted in this article.

EXPERIMENTAL PROCEDURES

Tubular injection moldings made of PS 615
APR

 26W supplied by
Dow

 Chemical, and PC Lexan 123 from General Electric were obtained by GAIM
using a spiral shape mold. It is noted that PS and PC exhibit very
different stress-optical functions that are available from earlier study
(33). Also, PS changes the sign of the birefringence from positive to
negative when temperature increases and passes through [T.sub.g], while
the birefringence of PC is positive above and below [T.sub.g]. This was
the reason why PS and PC were chosen in the present study. The samples
were obtained on an
injection molding machine

 Van Dorn 55 HPS-2.8F
equipped with a shut-off
nozzle
 
, a nitrogen injection unit and a data
acquisition system (34). The processing conditions employed to obtain
the PS and PC moldings are reported in Tables 1 and 2, respectively. In
case of PC, as seen from Table 2, the gas delay time was not varied.
This is due to a
solidification
  
v. so·lid·i·fied, so·lid·i·fy·ing, so·lid·i·fies

v.tr.
1. To make solid, compact, or hard.

2. To make strong or united.

v.intr.
 of the sprue even at short gas delay
time. The physical properties of PS used in simulations are taken from
our previous work (23). The physical properties of PS, PC, and nitrogen
used in simulations are listed in Table 3 (35-37). The experimental and
fitted shear-rate-dependent viscosity curves at various temperatures for
PS were provided in (23). Similar curves for PC are shown in Fig. 1. The
three-relaxation mode constitutive equation was used in fitting the
viscosity data coupled with the
WLF

WLF Waist Level Finder
WLF Viva La Figa  
 equation by means of the
least
squares method

. The tubular spiral injection moldings consisted of a

tapered
  
n.
1. A small or very slender candle.

2. A long wax-coated wick used to light candles or gas lamps.

3. A source of feeble light.

4.
a.
 sprue with a length of 72.1 mm, an entrance diameter of 4.57 mm
and an end diameter of 7.4 mm. The spiral had a total length of 58 cm
with a diameter of 10.1 -[+ or -] 0.1 mm. Four different regions of the
sample were: (1) the sprue, (2) the primary gas penetration, (3) the
secondary gas penetration, and (4) the solid region where no gas
penetrated. The
cylindrical coordinate system

 (z, r, [theta]) was used
to identify the flow,
radial
 /ra·di·al/ ()
1. pertaining to the radius of the arm or to the radial (lateral) aspect of the arm as opposed to the ulnar (medial) aspect; pertaining to a radius.

2.
 and
angular
 /an·gu·lar/ () sharply bent; having corners or angles.
 directions, respectively. To
measure the birefringence distribution [DELTA]n and n[theta][theta] -
[n.sup.rr] at different distances in the flow direction, slices having a
thickness of 0.5 and 1 mm were obtained parallel to the planes z - r and
r - [theta], respectively. The birefringence components were measured in
the sprue, in the primary gas penetration of the spiral and in the solid
section. The
retardation
 see mental retardation.
 of light through the PS slices was measured
using a Leitz crosspolarized
optical microscope

See under microscope.
 with a
tilting
  
v. tilt·ed, tilt·ing, tilts

v.tr.
1. To cause to slope, as by raising one end; incline:

2.
 four-orders compensator. The retardation of light through the PC slices
was measured with a tilting thirty-orders compensator. In addition, the
average birefringence [Less Than Sign]n[theta][theta] -
[n.sub.zz][Greater Than Sign] was measured using an optical
polariscope
 see polarization of light.
 Gaertner model L305. This polariscope has a light source with a
wavelength of 5.65 X [10.sup.-7] m and a seven order Babinet compensator
model L-133-A. Details of mold used, sample cutting procedures and
birefringence measurements were given in Ref. 23.

TABLE 1. Processing conditions used in manufacturing
PS moldings.

Run     Melt temp  Injec. speed  Gas-delay
no.  ([degrees]C)           (cm   time (s)
           for PS   [s.sup.-1])

1             180          7.62          0

2             200          7.62          0

3             230          7.62          0

4             200          1.27          0

5             200         15.24          0

6             200          7.62          3

7             200          7.62          6

TABLE 2. Processing conditions used in manufacturing PC
GAIM moldings.

Run   Melt temp  Injec. speed  Gas-delay
no.  ([degrees]           (cm   time (s)
          C)for   [s.sup.-1])
          PS/PC

1           280          7.62          0

2           300          7.62          0

3           320          7.62          0

4           300          2.54          0

5           300         15.24          0

Shot size 86.8%, gas pressure 10.34 MPa, mold
temperature 30[degrees]C. The shot size of the
fully filled mold is 7.315 cm (2.87 in).

TABLE 3. Material constants and properties of the polystyrene
and polycarbonate.

Material constants                                PS           PC

WLF equation                                    [35]

C1                                             8.285         7.27

C2 (K)                                         131.9          164

[T.sub.r] (K)                                  473.5          533

Leonov model                                    [35]

[eta]1 (Pa [s.sup.-1])                          2230          464

[eta]2 (Pa [s.sup.-1])                           447       754.83

[eta]3 (Pa [s.sup.-1])                                      43.64

[[theta].sub.1] (s)                           0.1466         0.01

[[theta].sub.2] (s)                          0.00489      0.00102

[[theta].sub.3] (s)                                       0.00011

S                                             4.84 X          3 X
                                         [10.sup.-3]  [10.sup.-3]

Tail equation                                   [35]         [36]

[[rho].sub.g.sup.0]([T.sub.g.sup.0])(kg         1021         1160
[m.sup.-3]

[T.sub.g.sup.0] (K)                              376          416

[[varies] .sub.1]([m.sup.3] [kg.sup.-1]      5.788 X       5.71 X
[K.sup.-1])                              [10.sup.-7]  [10.sup.-4]

[[varies].sub.s]([m.sup.3] [kg.sup.-1]       2.429 X      2.160 X
[K.sup.-1])                              [10.sup.-7]  [10.sup.-7]

C                                             0.0894       0.0894

[b.sub.1, 1] (Pa)                            4.615 X      1.740 X
                                          [10.sup.8]   [10.sup.8]

[b.sub.2, 1] ([K.sup.-1])                    3.019 X       4.39 X
                                         [10.sup.-3]  [10.sup.-3]

[b.sub.1, s] (Pa)                        3.301 X 108       2.56 X
                                                       [10.sup.9]

[b.sub.2, s] ([K.sup.-1])                     1.38 X       2.99 X
                                         [10.sup.-3]  [10.sup.-3]

[b.sub.3] (K [Pa.sup.-1])                      3.2 X       3.77 X
                                         [10.sup.-7]  [10.sup.-7]

Thermal properties                              [37]         [37]

[C.sub.p] (J [kg.sup.-1] [K.sup.-1])            1420         2150

K(W [m.sup.-1] [s.sup.-1] [K.sup.-1])           0.17        0.234

[rho] (kg [m.sup.-3]) at 25[degrees]C           1040         1052

[rho] (kg [m.sup.-3]) at 180[degrees]C           948          950

Stress-optical coefficient:                    [35];         [35]

[C.sup.fl] ([Pa.sup.-1])                      -5.2 X        5.6 X
                                         [10.sup.-9]  [10.sup.-9]

Material constants                       Nitrogen

WLF equation

C1

C2(K)

[T.sub.r](K)

Leonov model

[eta]1 (Pa [s.sup.-1])

[eta]2 (Pa [s.sup.-1])

[eta]3 (Pa [s.sup.-1])

[[theta].sub.1] (s)

[[theta].sub.2] (s)

[[theta].sub.3] (s)

S

Tail equation

[[rho].sub.g.sup.0]([T.sub.g.sup.0])(kg
[m.sup.-3]

[T.sub.g.sup.0] (K)

[[varies] .sub.1]([m.sup.3] [kg.sup.-1]
[K.sup.-1])

[[varies].sub.s]([m.sup.3] [kg.sup.-1]
[K.sup.-1])

C

[b.sub.1, 1] (Pa)

[b.sub.2, 1] ([K.sup.-1])

[b.sub.1, s] (Pa)

[b.sub.2, s] ([K.sup.-1])

[b.sub.3] (K [Pa.sup.-1])

Thermal properties                           [37]

[C.sub.p] (J [kg.sup.-1] [K.sup.-1])         1040

K(W [m.sup.-1] [s.sup.-1] [K.sup.-1])      0.0242

[rho] (kg [m.sup.-3]) at 25[degrees]C       1.138

[rho] (kg [m.sup.-3]) at 180[degrees]C

Stress-optical coefficient:

[C.sup.fl] ([Pa.sup.-1])

[FIGURE 1 OMITTED]

Simulation

The theoretical analysis of the flow-induced stresses and
birefringence generated during the GAIM process was disclosed in (23).
The theoretical analysis for the thermally induced residual stresses and
birefringence in
cylindrical

adj.
Of, relating to, or having the shape of a cylinder, especially of a circular cylinder.
 tubes and rods was shown in (10). In the
present work, as a first
approximation
 /ap·prox·i·ma·tion/ ()
1. the act or process of bringing into proximity or apposition.

2. a numerical value of limited accuracy.
, the flow- and thermally induced
birefringence during each step of the GAIM molding process were computed
separately for each time step under the assumptions made in (10) and
(23). Then, the respective components of the flow- and thermally induced
birefringence were summed and its comparison with the measured residual
birefringence in GAIM moldings was made.

Birefringence in PS GAIM Moldings

Figure 2 shows the measured and simulated total birefringence An
along with the simulated individual components of the flow- and
thermally induced birefringence, [DELTA]n, for PS Run No. 1, at various
distances from the sprue entrance: in the primary gas penetration region
of the sprue at a location of 4 cm (a), in the primary gas penetration
region of the spiral at a location of 16 cm (b), and in the solid region
of the spiral at a location of 28 cm (c). In the sprue and primary gas
penetration region of the spiral (Fig. 2a and b) the measured
birefringence, [DELTA]n, showed a maximum near the outer wall, it
decreased steeply toward the inner wall, and then showed a plateau in
the inner wall area. The simulated flow-induced [DELTA]n showed a
maximum near the outer wall, it decreased steeply towards the inner wall
where it relaxed almost completely. Simulated thermally induced [DELTA]n
showed a positive maximum near the outer wall, it decreased passing
through zero to a negative maximum near the inner wall. In the case of
PS moldings, simulations showed that, near the outer wall, the thermally
induced [DELTA]n was one
order of magnitude

 lower than the flow-induced
[DELTA]n. In this region, the flow-induced [DELTA]n was negative while
the thermally induced [DELTA]t was positive. As mentioned above, near
the inner wall, simulated flow-induced [DELTA]n was almost negligible.
This is because, when the flow stopped at the end of the gas penetration
stage, the flow-induced birefringence relaxed near the inner wall of the
GAIM molding, due to the high temperature of this region. However,
simulations showed that the thermal contraction that occurred during
cooling provided means for buildup of the birefringence [DELTA]n near
the inner wall, which showed a negative magnitude. In the solid section
of the spiral (Fig. 2c), the measured An showed a maximum near the outer
wall, it decreased toward the center, and showed an extensive plateau in
the core region. The simulated flow-induced [DELTA]n showed a maximum
near the outer wall and relaxed almost completely in the core region,
where the temperature was still high. However, simulations showed that
the thermal stresses generated during the cooling cause the
birefringence buildup in the core region.

[FIGURE 2 OMITTED]

When the thermally induced birefringence [DELTA]n was added to the
corresponding flow-induced birefringence [DELTA]n, the simulated total
birefringence provided a better description of the measured
birefringence in PS GAIM moldings. Simulations showed that, for the case
of PS moldings, [DELTA]n near the outer wall was caused mainly by
flow-induced stresses, since the magnitude of the thermally-induced
birefringence [DELTA]n at this location was significantly lower than
that of the flow-induced birefringence [DELTA]n. On the contrary, the
birefringence near the inner wall was mostly caused by thermal stresses
generated during cooling, since the flow-induced birefringence relaxed
almost completely in this region when the polymer stopped flowing. In
the solid region, the measured [DELTA]n in the core was significantly
lower than that near the outer wall. Simulated total [DELTA]n showed
that the birefringence in the core region of the solid section of the
molding was caused mainly by thermal stresses. Simulations also showed
that, for PS GAIM moldings at all locations
analyzed
  
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.

2. Chemistry To make a chemical analysis of.

3.
, the magnitude of
the thermally-induced birefringence [DELTA]n near the outer wall was
very low, compared to the corresponding flow-induced birefringence
[DELTA]n. Therefore, the magnitude of the simulated flow-induced
birefringence [DELTA]n, near the outer wall was not significantly
modified when the simulated thermally induced birefringence [DELTA]n was
added to it. However, the measured birefringence [DELTA]n near the inner
wall and that in the core region of the solid section, was only possible
to describe taking into consideration the contribution of the simulated
thermally induced birefringence [DELTA]n, since the flow induced
birefringence An relaxed almost completely.

Figure 3 shows the measured and total simulated birefringence
[n.sub.rr] - [n.sub.[theta][theta]] along with the individual components
of the simulated flow- and thermally induced birefringence, [n.sub.rr] -
[n.sub.[theta][theta]], for PS Run No. 1, at various distances from the
sprue entrance: in the primary gas penetration region of the sprue at a
location of 4 cm (a), in the primary gas penetration region or the
spiral at a location of 16 cm (b), and in the solid region of the spiral
at a location of 28 cm (c). In the sprue and primary gas penetration
region of the spiral (Fig. 3a and b), the measured birefringence
[n.sub.rr] - [n.sub.[theta][theta]] showed a maximum near the outer
wall, then decreased showing a minimum, and then increased showing a
maximum at the inner wall. The simulated flow-induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]] showed a maximum near the outer
wall, then, it decreased and relaxed almost completely near the inner
wall, since the high temperature of this region allowed the stresses to
relax when the polymer stopped flowing. The simulated thermally induced
birefringence [n.sub.rr] - [n.sub.[theta][theta]] showed a negative
value near the outer wall, then it increased passing through zero to a
positive value and showed a maximum near the inner wall. Simulations
showed that the flow-and thermally induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]] near the outer wall had a similar magnitude but
opposite sign. In the solid region (Fig. 3c) the measured birefringence
[n.sub.rr] - [n.sub.[theta][theta]] showed a maximum near the outer wall
and decreased showing an extensive plateau in the core region. The
flow-induced birefringence [n.sub.rr] - [n.sub.[theta][theta]] showed a
maximum near the inner wall, then it decreased and relaxed almost
completely in the core region. The thermally induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]] showed a
maximum magnitude

 near the
outer wall, it decreased passing through zero and showed a plateau in
the core region. The magnitudes of both thermally and flow-induced
birefringence [n.sub.rr] - [n.sub.[theta][theta]] are of the same order
near the outer wall and they have opposite sign. In the core region, the
flow-induced birefringence [n.sub.rr] - [n.sub.[theta][theta]] relaxed
almost completely while the thermally induced birefringence showed a
plateau. When the total birefringence [n.sub.rr] -
[n.sub.[theta][theta]] was computed, it showed a maximum near the outer
wall and decreased showing a plateau in the core region. In general, the
simulated flow-induced birefringence [n.sub.rr] - [n.sub.[theta][theta]]
near the outer wall was significantly lower than the simulated
flow-induced birefringence [DELTA]n. On the other hand, the simulated
thermally induced birefringence [n.sub.rr] - [n.sub.[theta][theta]] was
of the same order of magnitude as the flow-induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]]. Simulations suggested that the
contribution of the thermally induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]] in the plane r - [theta] was significant. It is
important to note that, in the solid region at 28 cm from the sprue
entrance (Fig. 3c), the total simulated birefringence, [n.sub.rr] -
[n.sub.[theta][theta]], showed a zero magnitude at the center of the

cylinder
 in mathematics, surface generated by a line moving parallel to a given fixed line and continually intersecting a given fixed curve called the directrix; each line of the family of lines forming the cylinder is called a ruling, or generator.
 while the measured birefringence showed a
nonzero
  
adj.
Not equal to zero.



  

Not equal to zero.
 value. This
is because, as discussed in (10), the plane strain approximation,
employed in the present simulations, yields the following relation
between the radial and
circumferential
 /cir·cum·fer·en·tial/ () pertaining to a circumference; encircling; peripheral.
 strains ([[epsilon].sub.rr] and
[[epsilon].sub.[theta][theta]]) at the center of the cylinder (r = 0)
[[epsilon].sub.[theta][theta]] =
1/r[[integral].sub.o.sup.r][[epsilon].sub.rr]dr. Using the
L'Hospital rule, this equation leads to
[[epsilon].sub.[theta][theta]] = [[epsilon].sub.rr] at r = 0. To avoid
this problem, the strains should be calculated using a three-dimensional
approach where the strain [[epsilon].sub.zz] would not be constant along
the radius as assumed in the plane strain approximation.

[FIGURE 3 OMITTED]

The following sections present the influence of the processing
conditions on the simulated total birefringence components, [DELTA]n and
[n.sub.rr] - [n.sub.[theta][theta]], and their comparison with the
measured birefringence for PS GAIM moldings.

The Effect of Melt Temperature

Figures 4 and 5 show the measured and simulated total
birefringence, [DELTA]n, for PS Runs No. 2 and 3, respectively,
corresponding to different melt temperatures at various distances from
the sprue entrance: in the primary gas penetration region of the sprue
at a location of 4 cm (a), in the primary gas penetration region of the
spiral at a location of 16 cm (b), and in the solid region at a location
of 28 cm (c). Measurements and simulations showed that the maximum of
[DELTA]n near the outer wall decreased when the melt temperature
increased. This is attributed to the reduction of the polymer viscosity
that generated lower shear and normal stresses during the melt injection
stage. Also, high melt temperature leads to short relaxation times
allowing the stresses to relax faster. Furthermore, the residual wall
thickness decreased when the melt temperature increased (23). The
reduction of the wall thickness leads to a lower thermally induced
birefringence at the inner wall, as shown in (10). Simulations showed
that by increasing the melt temperature the thermally induced
birefringence increased. However, at temperatures well above [T.sub.g]
the stresses and birefringence relax very fast (38). Consequently, it
was found that, by increasing the melt temperatures above 180[degrees]C,
the increase of thermally induced birefringence was negligible since the
majority of thermal stresses are generated when the polymer temperature
approaches to [T.sub.g].

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Comparing the total birefringence for Runs No. 1, 2, and 3 (Figs.
2, 4, and 5), it becomes apparent that the measured birefringence An
near the outer wall decreased when the melt temperature increased.
Furthermore, the thickness of the frozen-in birefringence decreased when
the melt temperature increased. Simulations qualitatively agreed with
measurements. The total birefringence An decreased when the melt
temperature increased mainly because the flow-induced birefringence
decreased when the temperature increased. However, the predicted
birefringence was higher than the simulated one. There are two possible
reasons for this
discrepancy

. First, it is impossible to measure
birefringence in the moldings close to their surface. Second, in heat
transfer calculations during cavity filling instant freezing assumption
was made such that as soon as the melt touches the mold surface it
assumed mold temperature (23). In fact, there is available literature
indicating the polymer does not necessarily attain the mold temperature
instantly (38).

Figures 6 and 7 show the measured and simulated total
birefringence, [n.sub.rr] - [n.sub.[theta][theta]], for PS Runs No. 2
and 3, respectively corresponding to different melt temperatures at
various distances from the sprue entrance: in the primary gas
penetration region of the sprue at a location of 4 cm (a), in the
primary gas penetration region of the spiral at a location of 16 cm (b),
and in the solid region of the spiral at a location of 28 cm (c). The
magnitude of the measured birefringence [n.sub.rr] -
[n.sub.[theta][theta]] was similar and no significant differences were
observed among the melt temperatures employed. The effect of the melt
temperature on the birefringence [n.sub.rr] - [n.sub.[theta][theta]] in
injection moldings was found to be minimal. Simulations indicated that
the total birefringence, [n.sub.rr] - [n.sub.[theta][theta]], at the
outer wall decreased slightly when the temperature increased. This is
primarily due to the decrease of the flow-induced birefringence when the
melt temperature increased. Furthermore, it is important to mention that
the birefringence [n.sub.rr] - [n.sub.[theta][theta]] at the center in
the solid section of the spiral (Figs. 6c and 7c) showed a zero
magnitude. This was because of the plane strain approximation employed
to calculate the thermally induced stresses, as explained earlier.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

The Effect of Injection Speed

Figures 4, 8, and 9 show the measured and simulated total
birefringence, [DELTA]n, for PS Runs No. 4, 2, and 5, respectively,
corresponding to different injection speeds at various distances from
the sprue entrance: in the primary gas penetration region of the sprue
at a location of 4 cm (a), in the primary gas penetration region of the
spiral at a location of 16 cm (b), and in the solid region of the spiral
(c). Simulations and experiments showed that the maximum of the
birefringence [DELTA]n near the outer wall increased with the injection
speed. This is because, by increasing the injection speed, the shear and
normal stresses increased during the melt injection stage. As a
consequence, the flow-induced birefringence increased. Furthermore, the
thickness of the frozen-in layer of [DELTA]n near the outer wall
decreased significantly when the injection speed increased, since high
injection speed yields short filling times, increases the melt
temperature by
viscous
 /vis·cous/ () sticky or gummy; having a high degree of viscosity.


adj.
1. Having relatively high resistance to flow.

2. Viscid.
 
dissipation

See also Debauchery.

Breitmann, Hans

lax indulger. [Am. Lit.: Hans Breitmann’s Ballads]

Burley, John

wasteful ne’er-do-well. [Br. Lit.
, and causes less heat being removed
by the end of the injection stage. The simulated thermally induced
birefringence [DELTA]n increased slightly when the injection speed
decreased. This is mainly due to the increase of the wall thickness when
the injection speed decreased as discussed in (10).

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

In the solid region of the spiral (Figs. 2c, 8c, and 9c), the
measured birefringence [DELTA]n showed a maximum near the outer wall, it
decreased and showed a plateau in the core region. Simulations showed
that these plateaus were caused by thermal stresses generated during
cooling. It was observed that measured and simulated birefringence
[DELTA]n at these plateaus did not increase as much as its value near
the outer wall when the injection speed was increased. This further
supports the theory that the birefringence near the outer wall of the PS
molding was caused mainly by the flow-induced stresses generated during
the melt injection stage, and the birefringence near the inner wall and
in the core region was caused mainly by the thermally induced stresses
generated during cooling.

Simulated results qualitatively described the effect of the
injection speed on the birefringence, An. However, near the outer wall,
the simulated An was higher than the measured one for the three
injection speeds employed. Near the inner wall, simulated birefringence
An for the injection speed of 1.27 [cm.sup.-1] was slightly higher than
that of injection speeds of 7.62 and 15.25 [cm.sup.-1] This is because
the wall thickness increased when the injection speed decreased. The
increase of the wall thickness caused the thermally induced stresses
increased which in turn increased the magnitude of [DELTA]n.

Figures 6, 10, and 11 show the measured and simulated total
birefringence, [n.sub.rr] - [n.sub.[theta][theta]], for PS Runs No. 4,
2, and 5, respectively, corresponding to different injection speeds at
various distances from the sprue entrance: in the primary gas
penetration region of the sprue at a location of 4 cm (a), in the
primary gas penetration region of the spiral at a location of 16 cm (b),
and in the solid region of the spiral (c). The measured and simulated
birefringence [n.sub.rr] - [n.sub.[theta][theta]] showed that its
maximum at the outer wall increased slightly with injection speed. This
is due to the increase of the flow-induced shear and normal stresses
with injection speed. Furthermore, the maximum of simulated
birefringence [n.sub.rr] - [n.sub.[theta][theta]] observed at the lowest
injection speed at about r/R = 0.8 increased and shifted towards the
outer wall when the injection speed increased. This is because the
flow-induced birefringence increased with the injection speed and the
frozen layer was thinner at the higher injection speed. Simulations
showed that the increase of thermally induced residual stresses due to
the increase of temperature due to viscous dissipation was negligible.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

The Effect of Gas-Delay Time

Figures 4, 12, and 13 show the measured and simulated total
birefringence, [DELTA]n, for PS Runs No. 2, 6, and 7, respectively,
corresponding to different gas delay times at various distances from the
sprue entrance: in the primary gas penetration region of the sprue at a
location of 4 cm (a), in the primary gas penetration region of the
spiral at a location of 11 cm (b), and in the solid section (c). When no
gas-delay time was employed to make the samples (Fig. 4), the measured
birefringence [DELTA]n showed maximum value at the outer wall, then, it
decreased showing a plateau towards the inner wall. However, when
gas-delay time was employed (Figs. 12 and 13), measured birefringence
[DELTA]n showed an increase further away from the outer wall indicating
the second maximum at about r/R = 0.75. This maximum was more evident in
the primary gas penetration region of the sprue (Figs. 12a and 13a) than
in the primary gas penetration region of the spiral (Figs. 12b and 13b),
since the diameter of the sprue was smaller than that of the spiral. The
magnitude of increase of this birefringence [DELTA]n becomes more
pronounced with its position shifted toward the inner wall when the
gas-delay time increased, as observed by comparing Figs. 12a and 13a.
Simulations showed that this shift was because of the solid layer
increased due to cooling during the delay time.

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

It is important to note that the increase of the simulated
birefringence [DELTA]n away from the outer wall at a gas-delay time of 6
s in the primary and solid regions of the spiral (Fig. 13b and c) was
lower than that at gas-delay of 3 s at the same locations (Fig. 12b and
c). This is due to the lower gas penetration speed at gas-delay time of
6 s, due to the high viscosity of the polymer caused by the temperature
decrease during the delay time.

The simulated total birefringence An agreed qualitatively with
measurements. Simulations demonstrated that the increase of [DELTA]n
further away from the outer wall was developed during the gas
penetration stage. Near the inner wall, the maximum of [DELTA]n
increased with the gas-delay time. This is because the wall thickness
increased with gas-delay time. Therefore, the thermally induced stresses
and birefringence increased. Furthermore, the flow-induced birefringence
during the gas penetration increased with gas-delay time.

Figures 6, 14, and 15 show the measured and simulated total
birefringence, [n.sub.rr] - [n.sub.[theta][theta]], for PS Runs No. 2,
6, and 7, respectively, corresponding to different gas delay times at
various distances from the sprue entrance: in the sprue region at a
distance of 4 cm from the sprue entrance (a), in the primary gas
penetration region of the spiral (b), and in the solid region (c). For
the gas-delay time of 0 s, measured and simulated total birefringence
[n.sub.rr] - [n.sub.[theta][theta]] showed a maximum close to the outer
wall, it decreased showing a minimum and then increased showing a
maximum near the inner wall. The maximum of birefringence [n.sub.rr] -
[n.sub.[theta][theta]] near the outer wall was formed during the melt
injection stage while the maximum near the inner wall was mainly induced
by the thermally induced stresses generated during cooling. For the
gas-delay times of 3 and 6 s (Figs. 14 and 15), the simulated maximum of
the total birefringence [n.sub.rr] - [n.sub.[theta][theta]] located at
about r/R = 0.75 for the gas delay time of 3 s increased and shifted
toward the inner wall when the gas-delay time increased to 6 s. When the
contribution of the thermally induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]] was taken into account, the total simulated
birefringence showed a higher value close to the inner wall when the
gas-delay time increased. This is because, the wall thickness increased
with the gas-delay time, as discussed in (10). As a consequence, the
thermally induced birefringence increased yielding a higher maximum of
birefringence [n.sub.rr] - [n.sub.[theta][theta]] near the inner wall.

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

Birefringence in PC GAIM Moldings

Figure 16 shows the measured birefringence An and the simulated
total, flow- and thermally induced birefringence. [DELTA]n, for PC Run
No. 1 at various distances from the sprue entrance: in the primary gas
penetration region of the sprue at a location of 4 cm (a), in the
primary gas penetration region of the spiral at a location of 16 cm (b),
and in the solid region of the spiral at a location of 48 cm (c). The
measured birefringence An showed a maximum near the outer wall and
decreased steeply showing a low value near the inner wall. The simulated
flow-induced birefringence [DELTA]n at the location of 4 and 16 cm
(Figs. 16a and b), showed a maximum near the outer wall. It decreased
steeply toward the inner wall, where it relaxed almost completely. In
the solid region (Fig. 16c), the flow-induced birefringence An also
showed a maximum near the outer wall. It decreased toward the center,
where it relaxed almost completely. At 4 and 16 cm, the simulated
thermally-induced birefringence [DELTA]n showed a high negative value
near the outer wall, it decreased towards the inner wall passing through
zero to a high positive value at the inner wall. In the solid region,
the thermally induced birefringence An showed a high negative value near
the outer wall, it increased passing through zero to a positive value in
the core region. It is important to note that, near the outer wall at
the locations of 4 and 16 cm, the flow-induced birefringence [DELTA]n
was higher than the thermally induced birefringence and they had
opposite sign. After combining the thermally and flow-induced
birefringence [DELTA]n, the total birefringence showed that the
contribution of the thermally induced birefringence for PC GAIM moldings
was significant. At 4 cm, the simulated total birefringence [DELTA]n
showed a positive maximum near the outer wall, it decreased to a minimum
and then increased towards the inner wall, showing a parabolic-like
distribution. At 16 cm, the simulated total birefringence [DELTA]n
showed a maximum near the outer wall, it decreased passing through zero
to a negative minimum, then, it increased towards the inner wall,
passing once more through zero to a positive maximum at the inner wall.
In the solid region. the total simulated birefringence [DELTA]n also
showed a maximum near the outer wall, it decreased toward the inner wall
passing through zero to a negative minimum. After that, it increased
passing once more through zero to a positive value in the extensive core
region. For the PC GAIM moldings, it was found that the magnitude of the
simulated flow-induced birefringence [DELTA]n was significantly modified
when the thermally induced birefringence An was included to calculate
the total birefringence. This is because the magnitude of the simulated
thermally induced birefringence [DELTA]n was of the same order as the
flow-induced birefringence [DELTA]n.

[FIGURE 16 OMITTED]

Figure 17 shows the measured birefringence [n.sub.rr] -
[n.sub.[theta][theta]] and the simulated total, flow- and thermally
induced birefringence [n.sub.rr] - [n.sub.[theta][theta]] for PC Run No.
1 at various distances from the sprue entrance: in the sprue region at 4
cm (a), in the primary gas penetration region of the spiral at 16 cm
(b), and in the solid region at 48 cm (c). At 4 cm from the sprue
entrance, the absolute value of the simulated flow-induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]] near the outer wall was similar to
that of the simulated thermally induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]]. However, at 16 cm from the sprue entrance, the
absolute value of the simulated flow-induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]] near the outer wall was smaller than the
corresponding thermally induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]]. It is important to note that the flow- and
thermally induced birefringence had opposite sign. For these two
locations, near the inner wall, the flow-induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]] relaxed almost completely and the
thermally induced birefringence [n.sub.rr] - [n.sub.[theta][theta]]
showed a highest positive value. In the solid region, the simulated
thermally induced birefringence [n.sub.rr] - [n.sub.[theta][theta]] near
the wall was significantly higher than the flow-induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]].

[FIGURE 17 OMITTED]

When the thermally induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]] was added to the flow-induced birefringence
[n.sub.rr] - [n.sub.[theta][theta]] the simulated total birefringence
showed large discrepancies with respect to measurements. At 4 cm from
the sprue entrance (Fig. 17a), birefringence [n.sub.rr] -
[n.sub.[theta][theta]] showed a positive maximum near the outer wall, it
decreased passing through zero to a negative minimum and increased
passing once more through zero to a positive value at the inner wall. At
the location of 16 cm, the simulated total birefringence showed a
negative minimum near the outer wall while the measured birefringence
[n.sub.rr] - [n.sub.[theta][theta]] showed a positive maximum. In the
solid region, the simulated total birefringence [n.sub.rr] -
[n.sub.[theta][theta]] showed a negative minimum near the outer wall, it
increased passing through zero to a positive value in the core.

The large magnitude of the simulated thermally induced
birefringence on the PC GAIM moldings and the low contribution of the
simulated flow-induced birefringence in the plane [n.sub.rr] -
[n.sub.[theta][theta]] led to large discrepancies between the total
simulated and measured birefringence [n.sub.rr] -
[n.sub.[theta][theta]]. Because of the large contribution of the
calculated thermally induced birefringence for PC samples, based on the
free
quenching

 assumption, its addition to the calculated flow-induced
birefringence led to significant a discrepancy between the measured and
calculated total birefringence. Clearly, future calculations need to
take into account the effect of
constrained
  
tr.v. con·strained, con·strain·ing, con·strains
1. To compel by physical, moral, or circumstantial force; oblige:  See Synonyms at force.

2.
 boundary conditions.

Effect of Melt Temperature

Figures 18 and 19 show the measured and simulated total
birefringence, [DELTA]n, for PC Runs No. 2 and 3, respectively,
corresponding to different melt temperatures at various distances from
the sprue entrance: in the sprue region at a location of 4 cm (a), in
the primary gas penetration region of the spiral at a location of 16 cm
(b). and in the solid region (c). At each location, the measured
birefringence [DELTA]n showed a slight decrease of its magnitude near
the outer wall when the temperature was increased (Figs. 16, 18, and
19). However, the simulated total birefringence [DELTA]n
appreciably
  
adj.
Possible to estimate, measure, or perceive:  See Synonyms at perceptible.
 decreased when the melt temperature was increased, due to a reduction of
the flow-induced birefringence that takes place at higher temperature.

[FIGURE 18 OMITTED]

[FIGURE 19 OMITTED]

Figures 20 and 21 show the measured and simulated total
birefringence, [n.sub.rr] - [n.sub.[theta][theta]], for PC Runs No. 2
and 3, respectively, corresponding to different melt temperatures at
various distances from the sprue entrance: in the sprue region at a
location of 4 cm (a), in the primary gas penetration region of the
spiral at a location of 16 cm (b), and in the solid region (c). The
measured birefringence [n.sub.rr] - [n.sub.[theta][theta]] showed no
significant differences for the three melt temperatures employed (Figs.
17, 20, and 21). The simulated total birefringence [n.sub.rr] -
[n.sub.[theta][theta]] at lower melt temperature showed a lower
magnitude near the outer wall. This is due to the decrease of the
flow-induced birefringence when the temperature increased, thus causing
the thermally induced birefringence to be dominant near the outer wall.
Near the inner wall and in the core region, the magnitude of the
birefringence [n.sub.rr] - [n.sub.[theta][theta]] was comparable for
three melt temperatures employed, since the birefringence in this region
was mainly caused by thermally induced residual stresses.

[FIGURE 20 OMITTED]

[FIGURE 21 OMITTED]

Effect of Injection Speed

Figures 18, 22, and 23 show the measured and simulated total
birefringence, [DELTA]n, for PC Runs No. 4, 2, and 5, respectively,
corresponding to different injection speeds at various distances from
the sprue entrance: in the sprue region at a location of 4 cm (a), in
the primary gas penetration region of the spiral at a location of 16 cm
(b), and in the solid region (c). The measured birefringence An showed a
decrease of the frozen-in thickness layer near the outer wall when the
injection speed was increased. Comparing Figs. 18a, 22a, and 23a, it
appears that the birefringence [DELTA]n is the highest at the lowest
injection speed in the sprue region which contradicts the observations
in the PS samples.

[FIGURE 22 OMITTED]

[FIGURE 23 OMITTED]

However, it should be noted that an increase of the injection speed
led to a reduction of the thickness of the frozen-in layer such that it
becomes so thin that birefringence measurements near the inner wall were
impossible to perform. The simulated total birefringence [DELTA]n showed
that the magnitude and the thickness of the frozen-in layer decreased
when the injection speed increased. In the solid region, the simulated
total birefringence showed a negative minimum. This minimum became lower
when the injection speed increased. This is because at high injection
speed, the thickness of the frozen-in layer of the flow-induced
birefringence decreased and the negative portion of the
thermally-induced birefringence near the outer wall became dominant. The
maximum of the simulated total birefringence [DELTA]n near the outer
wall increased with the injection speed. This is because, when the
injection speed increased, the simulated flow-induced birefringence
[DELTA]n increased. Meanwhile the magnitude of the thermally induced
birefringence remained in the same range. When the thermally and
flow-induced birefringence components were added, they rendered a higher
maximum of [DELTA]n.

Figures 20, 24, and 25 show the measured and simulated total
birefringence, [n.sub.rr] - [n.sub.[theta][theta]], for PC Runs No. 4,
2, and 5, respectively, corresponding to different injection speeds at
various distances from the sprue entrance: in the sprue region at a
location of 4 cm (a), in the primary gas penetration region of the
spiral at a location of 16 cm (b), and in the solid region (c). The
measured birefringence [n.sub.rr] - [n.sub.[theta][theta]] in the sprue
region (Figs. 20a, 24a, and 25a) seems to decrease as the injection
speed increased. However, this effect was caused by the reduction of the
frozen-in layer that made measurements near the outer wall difficult. In
the primary gas penetration region of the spiral and in the solid
section, the birefringence [n.sub.rr] - [n.sub.[theta][theta]] did not
show significant differences. Simulations showed that by increasing the
injection speed, the flow-induced birefringence [n.sub.rr] -
[n.sub.[theta][theta]] near the outer wall increased. Accordingly, the
simulated total birefringence [n.sub.rr] - [n.sub.[theta][theta]]
increased with an increase of the injection speed.

[FIGURE 24 OMITTED]

[FIGURE 25 OMITTED]

Total Average Birefringence in PS GAIM Moldings

This section contrasts the measured and simulated total average
birefringence < [n.sub.zz] - [n.sub.[theta][theta]] > in PS GAIM
moldings. The simulated thermally induced birefringence < [n.sub.zz]
- [n.sub.[theta][theta]] > was added to the simulated flow-induced
birefringence < [n.sub.zz] - [n.sub.[theta][theta]] > to obtain
the total simulated average birefringence. Figure 26 shows the measured
and simulated average birefringence < [n.sub.zz] -
[n.sub.[theta][theta]] > along the sprue and spiral length for PS
Runs No. 1, 2, and 3 corresponding to different melt temperatures. At
the three melt tem- peratures, the measured birefringence <
[n.sub.zz] - [n.sub.[theta][theta]] > decreases along the sprue
length and along the primary and secondary gas penetration regions of
the spiral. A short plateau in the primary gas penetration region of the
spiral is evident. At the end of this plateau the birefringence reduced
and then remained almost constant in the solid region. Clearly, the
overall magnitude of the average birefringence < [n.sub.zz] -
[n.sub.[theta][theta]] > decreased along the whole length of the
molding when the melt temperature increased. This behavior was caused by
a decrease in the relaxation time when the melt temperature increased.

[FIGURE 26 OMITTED]

Simulations showed qualitatively the effect of melt temperature on
the average birefringence < [n.sub.zz] - [n.sub.[theta][theta]]
>.Similar to the measured birefringence, the simulated average
birefringence < [n.sub.zz] - [n.sub.[theta][theta]] > showed that
it decreased along the sprue, showed a plateau along the primary gas
penetration region of the spiral and decreased to almost a constant
value in the solid region. Furthermore, the overall magnitude of the
simulated birefringence < [n.sub.zz] - [n.sub.[theta][theta]] >
decreased along the spiral when the melt temperature increased. In
general, at all melt temperatures the simulated birefringence <
[n.sub.zz] - [n.sub.[theta][theta]] > showed a higher magnitude than
the corresponding measured one. The deviation between the measurements
and simulations of birefringence < [n.sub.zz] -
[n.sub.[theta][theta]] > can be attributed to over-prediction of the
flow-induced birefringence.

Figure 27 shows the measured and simulated average birefringence,
[Less Than Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign],
with respect to the distance from the sprue entrance for PS Runs No. 4,
2, and 5 corresponding to different injection speeds. The measured
average birefringence at injection speeds of 1.27 and 7.62 cm [s.sup.-1]
in the primary gas penetration region had practically the same
magnitude. When the injection speed was increased to 15.24 cm
[s.sup.-1], the average birefringence was increased. However, in the
solid region, the measured birefringence [Less Than Sing][n.sub.zz] -
[n.sub.[theta][theta]][Greater Than Sign] for injection speed of 1.27 cm
[s.sup.-1] was higher than that for 7.62 and 15.24 cm [s.sup.-1]. The
latter two speeds showed similar values of birefringence. The measured
average birefringence for an injection speed of 1.27 cm [s.sup.-1]
showed a longer plateau in the primary gas penetration region because of
the increase of the gas penetration length with a decrease of the
injection speed.

[FIGURE 27 OMITTED]

Simulations showed that along the sprue the birefringence [Less
Than Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign]
increased when the injection speed decreased. However, the birefringence
in the primary gas penetration region of the spiral showed almost a
constant plateau at the three injection speeds. In agreement with the
measured value the calculated length of the plateau was increased at an
injection speed of 1.27 cm [s.sup.-1]. This was due to the increase in
the gas penetration length at a low injection speed. In the solid
region, the simulated average birefringence increased when the injection
speed decreased.

It is important to observe that the average birefringence in the
sprue, was the highest for the injection speed of 1.27 cm [s.sup.-1]
(Run No. 4). This is because, at low injection speed, the birefringence
developed near the wall gets frozen-in by the temperature drop near the
mold wall. Low injection speed created a thick frozen-in birefringence
layer. This effect was more evident in the sprue region where the
flow-induced birefringence was higher since the diameter of the sprue is
considerably lower than that of the spiral region.

Figure 28 shows the measured and simulated average birefringence
[Less Than Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign]
with respect to the distance from the sprue entrance for PS Runs No. 2,
6, and 7 corresponding to different gas delay times. In absence of
gas-delay time, the measured average birefringence was higher in the
sprue as well as in the spiral in the gas penetration region than that
at gas-delay times of 3 and 6 s. At gas-delay time of 6 s the measured
average birefringence was the lowest in the sprue and primary gas
penetration region of the spiral, even though at this delay time the
mold was not completely filled. In the solid region, the magnitude of
the measured average birefringence was similar at the three gas-delay
times. The decrease of the average birefringence when the gas-delay time
increased was attributed to the increase of the residual wall thickness
with gas-delay time. This is because when the retardation of light was
averaged along the wall thickness the magnitude of the average
birefringence was lower. Simulations qualitatively described the effect
of the gas-delay time on the average birefringence [[Less Than
Sing]][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign]. The
overall magnitude of the simulated birefringence [Less Than
Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign] decreased
along the length of the molding when the gas-delay time increased. This
was attributed to both the birefringence relaxation in the core region
during the delay time and the increase of the wall thickness with
gas-delay time. Thicker wall thickness renders a lower averaged value of
birefringence.

[FIGURE 28 OMITTED]

Simulations showed that the thermally induced average birefringence
[Less Than Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign]
in PS GAIM moldings was much lower than the flow-induced average
birefringence. Therefore, for the PS GAIM moldings the flow-induced
birefringence was the main factor causing residual birefringence.
Simulations also showed that the total simulated [Less Than
Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign] was not
significantly different from the flow-induced [Less Than Sing][n.sub.zz]
- [n.sub.[theta][theta]][Greater Than Sign], since the contribution of
the thermally induced [Less Than Sing][n.sub.zz] -
[n.sub.[theta][theta]][Greater Than Sign] was minimal for PS moldings.

Total Average Birefringence in PC GAIM Moldings

Figure 29 shows the measured and simulated total average
birefringence in PC GAIM moldings for PC Runs No. 4, 2, and 5 made at
various injection speeds. The simulated total birefringence [Less Than
Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign] showed that
the contribution of the thermally induced birefringence was significant
for PC moldings. This was especially evident in the solid region, where
the thermally induced birefringence was dominant over the flow-induced
birefringence. The simulated flow-induced average birefringence in PS
moldings was higher than that in PC moldings. This was because faster
relaxation of birefringence in extended region of the inner wall in PC
moldings leading to a lower thickness of the frozen-in layer, compared
to that in the PS moldings. Therefore, when the birefringence was
averaged over the wall thickness, the magnitude of the flow-induced
birefringence [Less Than Sing][n.sub.zz] -
[n.sub.[theta][theta]][Greater Than Sign] became low. However,
simulations and free quenching experiments demonstrated that the
magnitude of the thermally-induced birefringence in PC samples was
significant (10). Therefore, it is observed in Fig. 29 that the
birefringence in the solid region was higher than the birefringence in
the primary gas penetration region of the spiral. This behavior was
totally opposite to that observed in PS GAIM moldings in Figs. 26-28,
where the total average birefringence [Less Than Sing][n.sub.zz] -
[n.sub.[theta][theta]][Greater Than Sign] of the solid region was lower
than that of the primary gas penetration region. The difference in the
observed behavior of the frozen flow induced birefringence and the
thermally induced birefringence in PS and PC moldings is due the
difference in the viscoelastic and photoviscoelastic behavior of these
polymers and the thermal history experienced by these polymers during
molding process as explained in our earlier studies (10), (23).

[FIGURE 29 OMITTED]

CONCLUSIONS

Measurements of the residual birefringence components [DETA]n,
[n.sub.rr] - [n.sub.[theta][theta]] and [Less Than Sing][n.sub.zz] -
[n.sub.00] and simulations of the flow- and thermally induced
birefringence components [DETA]n, [n.sub.rr] - [n.sub.[theta][theta]]
and [Less Than Sing][n.sub.zz] - [n.sub.[theta][theta]] for PS GAIM
moldings were carried out. The obtained results showed that the
birefringence components near the outer wall were mainly caused by flow
during the melt injection stage. Simulations of the thermally induced
birefringence showed that the birefringence near the inner wall and in
the core region of the PS GAIM moldings was mainly caused by thermal
stresses generated during cooling. Simulations demonstrated that the
thermal birefringence, An, in PS GAIM moldings was one order of
magnitude lower than the flow-induced birefringence. However, the flow-
and thermally induced birefringence, had the same order of magnitude.
Combining the flow- and thermally induced birefringence calculated for
GAIM molding of PS, showed a better description of the measured
birefringence than the flow-induced birefringence alone. Simulations
showed that the average birefringence [Less Than Sing][n.sub.zz] -
[n.sub.[theta][theta]][Greater Than Sign] in PS GAIM moldings was
generated mainly by flow-induced stresses. The birefringence components
[DETA]n, [n.sub.rr] - [n.sub.[theta][theta]] and [Less Than
Sing][n.sub.zz] - [n.sub.[theta][theta]][Greater Than Sign] in PS GAIM
moldings was greatly influenced by processing conditions. For the case
of PC moldings, the contribution of the thermally induced birefringence
to the total birefringence was significant throughout the wall
thickness. In the sprue region, the flow-induced birefringence was
higher than the thermally induced birefringence. However, in the spiral
region, the magnitude of the flow- and thermally induced birefringence
near the outer wall was almost of the same order of magnitude. This
caused a discrepancy between the measured and simulated total
birefringence. The latter was evidently due to the free quenching
assumption made in calculations of the thermal birefringence.

Correspondence to: A.I. Isayev; e-mail: aisayevquakron.edu

DOI

 10.1002/pen.23298

Published online in Wiley Online Library (wileyonlinelibrary.com).

[c] 2012 Society of Plastics Engineers

REFERENCES

(1.) J.
Avery
 , Oswald 1877-1955.

American bacteriologist noted for establishing (1944) that DNA is responsible for the transmission of heritable characteristics.
, Ed., Gas-Assist Injection Molding, Hanser, Munich
(2001).

(2.) K. Oda, J.L. White, and E.S. Clark, Polym. Eng. Sci., 18, 25
(1978).

(3.) H. Janeschitz-Kriegl, Polymer Melt Rheology and
Flow
Birefringence

,
Springer

, Berlin, Chapter 1 (1983).

(4.) A.I. Isayev, Polym. Eng. Sci., 23, 271 (1983).

(5.) J.L. White and W. Dietz, PoLyn,. Eng. Sci., 19, 1081 (1979).

(6.) R.S. Spencer and G.D. Gilmore, Mod. Plast., 28, 97 (1950).

(7.) G.D. Shyu and A.I. Isayev,
SPE

 ANTEC Tech. Pap., 39, 1673
(1993).

(8.) G.D. Shyu, A.1. Isayev, and C.T. Li, I. Polym. Sci. B Polym.
Phys., 41, 1850 (2003).

(9.) K.C. Rush, J. Macromol. Sci. Phys. B, 2, 179 (1968).

(10.) A.J. Carrillo and A.1. lsayev, Polym. Eng. Sci., 51, 179
(2011).

(11.) H. Potente and M. Hansen, Int. Polym. Process., 8, 345
(1993).

(12.) S.C. Chen, N.T. Cheng, and S.Y. Hu, J. Appl. Polym. Scl., 67,
1553 (1998).

(13.) S.C. Chen, K.F. Hsu, and K.S. Hsu, J Appl. Polym. Scl., 58,
793 (1985).

(14.) S.C. Chen, KF. Hsu, and K.S. Hsu, Int J. Heat Mass Transfer,
39, 2957 (1996).

(15.) S.C. Chen, N.T. Cheng, and S.M Chao, Int. Polytn. Process.,
16, 90 (1999).

(16.) S.C. Chen, K.S. Hsu, and M.C. Jeng, SPE ANTEC Tech. Pap., 40,
417 (1994).

(17.) K.S. Barton and L.S. Turng, SPE ANTEC Tech. Pap., 42, 421
(1994).

(18.) L.S. Turng, SPE ANTEC Tech. Pap., 41, 74 (1993).

(19.) C.T. Li and A.I. Isayev, Polym. Eng. Sci., 44, 983 (2004).

(20.) C.T. Li, J.W.
Shin
 () the prominent anterior edge of the tibia or the leg.



saber shin  marked anterior convexity of the tibia, seen in congenital syphilis and in yaws.
, H.S. Lee, and A.1. Isayev, Polym Eng.
Sci. 44, 992 (2004).

(21.) A. Polynkin. J.F.T. Pittman, and J. Sienz, Polym. Eng. Sci.,
45, 1049 (2005).

(22.) A. Polynkin, J.F.T. Pittman, and J. Sienz, Polym. Eng. Sci.,
47, 713 (2007).

(23.) A.J. Carrillo and A.I. Isayev, Polym. Eng. Scl., 49, 2350
(2009).

(24.) A.1. Isayev and C.A. Hieber, Rheol. Acta, 19, 168 (1980).

(25.) A.I. Leonov, Rheol. Acta, 15, 85 (1976).

(26.) J.L.S. Wales, Polynt. Eng. Sci., 12, 358 (1972).

(27.) J.L.S. Wales, The Application of Flow Birefringence to

Rheological
  
n.
The study of the deformation and flow of matter.



rheo·log
 Studies of Polymer Melts, DeIf University Press, Netherlands
(1976).

(28.) H. Janeschitz-Kriegl, Rheol. Acta, 16, 327 (1977).

(29.) M.R. Kamal and V.
Tan

See tax anticipation note (TAN).
, SPE ANTEC Tech. Pap., 24, 121 (1978).

(30.) A.J. Carrillo and A.I. Isayev, SPE ANTEC Tech. Pap., 55, 654
(2009).

(31.) F.J.M.F. Custedio, P.D.
Anderson
 river, c.465 mi (750 km) long, rising in several lakes in N central Northwest Territories, Canada. It meanders north and west before receiving the Carnwath River and flowing north to Liverpool Bay, an arm of the Arctic
, G.W.M. Peters, A.M. Cunha,
and H.E.H. Meijer, Rheol Acta, 49, 23 (2010).

(32.) A.E. Likhtman and R.S. Graham, J Non-Newtonian Fluid Mech.,
114, 1 (2003).

(33.) G.D. Shyu, A.I. Isayev, and C.T. Li, J. Polym. Sci. B Polym.
Phys., 39, 2252 (2001).

(34.) J.W. Shin and A.I. Isayev, J.
Inject

v.
1. To introduce a substance, such as a drug or vaccine, into a body part.

2. To treat by means of injection.
. Mold. Technol., 4, 314
(2002).

(35.) G.D. Shyu, Birefringence and Residual Stresses in Molded
Articles of
Amorphous

 Polymers, PhD.
Dissertation
  
n.
A lengthy, formal treatise, especially one written by a candidate for the doctoral degree at a university; a thesis.



Noun

1.
, The
University of
Akron

,
Akron, Ohio

 (1993).

(36.) Moldflow Plastics Insight 6.1 Library, Software.

(37.) C.T. Li, Two-Component Injection and Transfer Molding:
Simulation and Experiment, Ph.D. Dissertation, The University of Akron,
Akron, Ohio (2003).

(38.) M.R. Kamal, A.E. Varela, and W.I. Patterson, Polym. Eng.
Sci., 39, 940 (1999).

Antonio J. Carrillo, AL Isayev

Department of Polymer Engineering, The University of Akron, Akron,
Ohio 44325-0301