Bartus 2003_Thesis

i
LONG-FIBER-REINFORCED THERMOPLASTIC: PROCESS MODELING AND
RESISTANCE TO BLUNT OBJECT IMPACT
by
SHANE D. BARTUS
A THESIS
Submitted to the graduate faculty of the University of Alabama at Birmingham,
in partial fulfillment of the requirements for the degree of
Master of Science
BIRMINGHAM, ALABAMA
2003

ii
ABSTRACT OF THESIS
GRADUATE SCHOOL, UNIVERSITY OF ALABAMA AT BIRMINGHAM
Degree: M.S.Mt.E Program Materials Engineering
Name of Candidate Shane D. Bartus
Committee Chair Uday K. Vaidya
Title Long-Fiber-Reinforced Thermoplastic: Process Modeling and Resistance to Blunt
Object Impact
The use of thermoplastic composites has steadily gained favor over such
traditional materials as steel in structural and semi-structural applications due to their
prominent physical and mechanical behavior, such as specific strength, damping,
corrosion resistance, and impact properties. Moreover, closed-molded discontinuous
long-fiber-reinforced thermoplastic composites (LFTs) share the attractive features of
greater strength, stiffness, and impact properties (in contrast to short-fiber-reinforced
thermoplastics), in addition to high volume processability, ability to fill complex
geometries, intrinsic recyclability, and the capacity for part integration. In this work,
three broad aspects in regard to the production and performance of LFTs were studied: I.
The effect of processing conditions and material properties on the extrusion/compression-
molding process used in the manufacture of LFTs through a simulation matrix performed
in Cadpress-TP, II. Damage tolerance of LFTs subjected to transverse blunt object impact
(BOI), treated from an experimental standpoint, in order to characterize energy
dissipation and damage modes and III. Fiber orientation of LFT, predicted from process
simulation, and its relationship to the failure mode under BOI. Through the simulation
matrix, it was determined for the flat plaque geometry investigated, that the mold
temperature, charge location, and melt viscosity had the greatest effect in the study on the

iii
component processing and final material properties, thereby making those parameters of
greatest importance to accurately model the phenomenon. LFT subjected to BOI
exhibited high impact energy dissipation, which increased linearly with increasing areal
density. The average impact energy dissipation at the critical velocity was 167 J and 121
J for a 4.61 g cm-2
specimen impacted by flat and conically shaped projectiles,
respectively. The fiber orientation also played a large role in energy dissipation; failure
appeared to occur along planes of preferential fiber orientation. The fracture paths
correlated well with the predicted fiber orientation in a Cadpress simulation. Impact
mass did not exhibit any appreciable effects on energy dissipation. This overall work
advances the state-of-the-art in LFTs with an automotive focus.

iv
ACKNOWLEDGEMENTS
It is difficult to overstate my eternal gratitude to my advisor, Dr. Uday K. Vaidya,
who encouraged my research while I worked for him as an undergraduate at my alma
mater and then granted me the opportunity to continue working under him as a graduate
student. He has gone far beyond what is required of an advisor and been a friend, as
well. Dr. Vaidya’s ardent interest in the advancement of composite materials motivates
our entire group. His patience and advice have been unfaltering since I first began work
with him almost four years ago.
This work reflects the contributions of many individuals. I thank my esteemed
committee members, Drs. Gregg M. Janowski, Krishan Chawla, and Klaus Gleich, for
their valuable time and effort. Their input and guidance provided invaluable
contributions to the quality research. In addition, I thank the individuals of our research
group, Abhay Raj Singh Guatam, Selvum Pillay, Juan Camilo Serrano, Chad Ulven,
Haibin Ning, Francis Samalot, Rajan Sriram, and Tujuana Shaw. I also thank Saulius
Drukteinis, David Downs, Joseph Puckett, Andrea Rossillon, Sean Boyle, and Paulo
Coelho for their friendship and support over the last two years.
Finally, I thank my family and friends for their encouragement and support during
this time. Their understanding and acceptance allowed me the freedom to pursue this
research, which would not have been possible without them.

v
TABLE OF CONTENTS
Page
ABSTRACT....................................................................................................................... iii
ACKNOWLEDGEMENTS............................................................................................... iv
LIST OF TABLES........................................................................................................... viii
LIST OF FIGURES ........................................................................................................... ix
INTRODUCTION ...............................................................................................................1
Thermoplastic Composites.......................................................................................1
OBJECTIVE ........................................................................................................................4
LITERATURE REVIEW ....................................................................................................5
Discontinuous Long-Fiber Reinforcement ..............................................................5
Material Property Models .......................................................................................7
Material Properties......................................................................................8
Modeling of tensile strength ........................................................................9
Modeling of tensile modulus .....................................................................11
Cottrell impact model ................................................................................14
CADPRESS-TP BACKGROUND....................................................................................20
EXPERIMENTAL PROCEDURE: PROCESS MODELING ..........................................28
Simulation Matrix..................................................................................................28
Process Variables...................................................................................................29
Mold temperature, Simulations 1-3 ...........................................................31
Charge location, Simulations 4-8...............................................................31
Boundary conditions..................................................................................33
Material Parameters ...................................................................................33
Fiber interaction coefficient, Simulations 9 and 10...................................35
Melt viscosity, Simulations 11-17 .............................................................35
PvT parameters, Simulations 18 and 19 ....................................................36
Simulation verification, Simulation 20......................................................37

vi
TABLE OF CONTENTS (Continued)
Page
RESULTS AND DISCUSSION: PROCESS MODELING ..............................................38
Process Parameter Results, Simulations 1-8..........................................................38
Mold temperature effects, Simulation 1-3 .................................................38
Effect of charge location, Simulations 4-8 ................................................39
Fiber interaction coefficient, Simulations 9 and 10...................................40
Material Processing Effects, Simulations 9 – 20. ..................................................40
Effect of melt viscosity, Simulations 11-17...............................................41
PvT parameters effects, Simulations 18 and 19.........................................43
Control run, Simulation 20 ........................................................................44
SUMMARY AND CONCLUSIONS: PROCESS MODELING ......................................62
LITERATURE REVIEW: BLUNT OBJECT IMPACT...................................................65
Categorization of impact........................................................................................65
Impactor mass and geometry .....................................................................66
Impact Energy........................................................................................................67
EXPERIMENTAL PROCEDURE: BLUNT OBJECT IMPACT.....................................69
Impact Test Apparatus...........................................................................................69
Firing valve and pressure vessel ................................................................70
Firing mechanism.......................................................................................72
Gas gun carriage and barrel .......................................................................72
Pressure data acquisition............................................................................73
Velocity data acquisition............................................................................74
Calibration curves......................................................................................75
Capture chamber........................................................................................76
Sample holder and boundary conditions....................................................79
Sample preparation ....................................................................................79
Blunt object impact test matrix..................................................................81
MATERIAL PROCESSING .............................................................................................82
Celstran®PP-GF40-03 Processing and Material Properties..................................82
Numeric Results and Analysis of the Impact Data................................................87
Damage Characterization.......................................................................................87
Effect of projectile geometry .....................................................................89
Areal density effects ..................................................................................91
Fiber orientation effects.............................................................................91
Micrograph Analysis..............................................................................................92
Correlation Between Predicted Fiber Orientation and Impact Failure Mode........94

vii
TABLE OF CONTENTS (Continued)
Page
CONCLUSION: BLUNT OBJECT IMPACT.................................................................133
LIST OF REFERENCES.................................................................................................135

viii
LIST OF TABLES
Table Page
1 Properties for 40 wt. % E-glass/polypropylene used in the material models.....8
2 Processing parameters ......................................................................................28
3 Fiber material parameters.................................................................................32
4 Composite material parameters ........................................................................33
5 Matrix material parameters...............................................................................33
6 Fiber interaction coefficient parameters investigated.......................................40
7 Fiber interaction coefficient study results ........................................................40
8 Melt viscosity parameters investigated ............................................................41
9 Melt viscosity parameter study results .............................................................41
10 PvT parameters investigated.............................................................................43
11 PvT parameter study results .............................................................................43
12 Blunt object impact projectile types.................................................................69
13 Blunt object impact test matrix.........................................................................80
14 Material properties of Celstran® PP-GF40-03 adopted from the Ticona
website .............................................................................................................83
15 Numerical results and analysis for the impact data on the top specimen.........86
16 Numerical results and analysis for the impact data on the center specimen ....86
17 Numerical results and analysis for the impact data on the bottom specimen...86
18 Numeric results and analysis of the velocity data for the top specimen ..........96
19 Numeric results and analysis of the velocity data for the center specimen......97
20 Numeric results and analysis of the velocity data for the bottom specimen ....98

ix
LIST OF FIGURES
Figure Page
1 Illustration of tensile and shear stress in a single fiber above, below and at the
critical fiber length, adapted from Chawla [9] ............................................................6
2 Normalized property models; Cox shear-lag modulus, Cottrell impact
strength, and Kelly-Tyson strength versus fiber length for 40 wt. % E-glass
fiber (14 μm diameter) in a polypropylene matrix......................................................7
3 Kelly-Tyson tensile strength model showing tensile strength versus log fiber
length for discrete aligned E-glass fibers (40 wt. %) and randomly oriented E-
glass fibers (40 wt. %) in a polypropylene matrix.....................................................10
4 Cox and Cox-Krenchel models for tensile modulus versus log fiber length of
uniaxially aligned fibers (Cox) and randomly oriented fibers (Cox-Krenchel)
for 40 wt. % E-Glass fibers in a polypropylene ......................................................13
5 Cottrell impact model for notched impact energy versus log fiber length of
uniaxially aligned E-Glass fibers (40 wt. %) in a polypropylene matrix .................16
6 Cottrell impact models (with and without consideration of fiber strain energy)
for notched impact energy versus log fiber length of uniaxially aligned E-
Glass fibers (40 wt. %) in a polypropylene matrix...................................................18
7 Charge locations. Charge location (a) was used in Simulations 1-3, (b) in
Simulation 4, (c) in 5, (d) in 7, (e) in 6, (f) in 8........................................................32
8 Charge location for the simulation verification study and for Simulations 9 –
20..............................................................................................................................37
9 Typical flow front at 50% filling for Simulations 1 – 3...........................................45
10 Flow fronts at 50% filling for Simulation 4 .............................................................45
13 Flow fronts for 80% filling showing the formation of knit lines in Simulation
7................................................................................................................................46

x
LIST OF FIGURES (Continued)
Figure Page
14 Flow fronts for 95% filling showing the formation of knit lines for two
charges placed in Simulation 8 ..................................................................................46
15 Typical flow front for Simulations 9 - 20 showing 50% filling................................47
16 Typical flow front for Simulations 9 – 20 showing 90% filling ...............................47
17 Force versus time for the control simulation, fiber interaction coeff. = 0.140..........48
18 Force versus time plot for the fiber interaction coefficient high (0.175)
simulation ..................................................................................................................48
19 Force versus time plot for the fiber interaction coefficient low (0.105)
simulation...................................................................................................................48
20 Force versus time for the control simulation, null viscosity = 4149 Pa s..................49
21 Force versus time for the low null viscosity (3112 Pa s) simulation.........................49
22 Force versus time for the high null viscosity (5186 Pa s) simulation........................49
23 Force versus time for the control simulation, infinite shear viscosity = 1.0 s ...........50
24 Force versus time for the low infinite shear viscosity (0.90 s) simulation ................50
25 Force versus time for the high infinite shear viscosity (1.10 s) simulation...............50
26 Force versus time for the control simulation, power law index = 0.599...................51
27 Force versus time for the low power law index (0.539) simulation..........................51
28 Force versus time for the high power law index (0.569) simulation.........................51
29 Force versus time plots for low and high PvT coefficient simulations
respectively ................................................................................................................52
30 Graphical representation of the fiber orientation in the (a) control run
(0.14), (b) low fiber interaction coefficient (0.105) simulation and (c) the
high fiber interaction coefficient (0.175) simulation.................................................53
31 Illustration of the selected element locations for the fiber orientation
distribution function comparison: (a) element 39, (b) element 29, and (c)
element 937................................................................................................................54

xi
Figure Page
32 Fiber distribution function of element 39 in the control simulation, fiber
interaction coeff. = 0.140...................................................................................... 55
33 Fiber distribution function of element 39 in the low fiber interaction
coefficient (0.105) simulation .............................................................................. 55
34 Fiber distribution function of element 39 in the high fiber interaction
orientation coeff. = 0.140 ..................................................................................... 56
36 Fiber distribution function of element 29 in the low fiber interaction
37 Fiber distribution function of element 29 in the high fiber interaction
orientation 0.140................................................................................................... 57
39 Fiber distribution function of element 937 in low fiber interaction coefficient
(0.105) simulation................................................................................................. 57
40 Fiber distribution function of element 937 in high fiber interaction coefficient
(0.175) simulation................................................................................................. 57
41 Maximum nodal pressure (Pa) for the control simulation, where the
maximum nodal pressure is 12.29 MPa, null viscosity = 4149 Pa s .................... 58
42 Maximum nodal pressure (Pa) for the low null viscosity (3112 Pa s)
simulation, where the maximum nodal pressure is 12.37 MPa............................ 58
43 Maximum nodal pressure (Pa) for the high null viscosity (5186 Pa s)
simulation, where the maximum nodal pressure is 12.26 MPa............................ 58
44 Graphical representation of the fiber orientation in the (a) control run (null
viscosity = 4149 Pa s), (b) low zero shear viscosity (3112 Pa s) simulation,
and (c) the high zero shear viscosity (5186 Pa s) simulation ............................... 59
45 Graphical representation of the fiber orientation in the (a) control run
(infinite shear viscosity = 1.0 s), (b) low infinite shear viscosity (0.90 s)
simulation, and (c) the high infinite shear viscosity (1.10 s) simulation.............. 60

xii
Figure Page
46 Graphical representation of the fiber orientation in the (a) control run (power
law index = 0.599), (b) low power law index (0.539) simulation, and (c) the
high power law index (0.659) simulation..............................................................61
47 Disassembled poppet valve: (a) two halves of the valve body, (b) valve
center carrier, (c) valve, (d) barrel union, and (e) front valve face .......................71
48 Gas gun assembly on the carriage showing the pressure vessel, pressure
transducer, firing valve, and firing mechanism....................................................73
49 Typical calibration curves for pressure versus velocity for the incident (1)
and residual (2) velocity chronographs shown for a 100 g sabot.........................75
50 Pro/E drawing of the capture chamber with the access door removed..................77
51 Image of the capture chamber showing the (a) light bank, (b) barrel, (c)
access door, (d) toggle clamps, (e) polycarbonate data acquisition
windows and the (f) incident, and (g) residual velocity chronographs ................77
52 Pro/E drawing of the kinetic deflector showing the path of the projectile............78
53 (a) Schematic of the top and side views of the tab plaque (not shown to
scale) and the representative sections that were cut from it and (b) Pro/E
isoperimetric drawing of the tab plaque...............................................................79
54 Critical velocity versus projectile mass for the top specimen, showing the
velocity as an exponentially decreasing function of projectile mass ...................96
55 Critical velocity versus projectile mass for the center specimen, showing
the velocity as an exponentially decreasing function of projectile mass .............97
56 Critical velocity versus projectile mass for the bottom specimen, showing
the velocity as an exponentially decreasing function of projectile mass...............98
57 Effect of projectile mass, energy versus projectile mass for the top
specimen ................................................................................................................99
58 Effect of projectile mass, energy versus projectile mass, for the center
specimen ................................................................................................................100
59 Effect of projectile mass, energy versus projectile mass, for the bottom
specimen ................................................................................................................101

xiii
Figure Page
60 Energy (J) versus projectile mass (g) for the bottom, center, and top
specimens with a linear regression analysis, fitted though the mean of each
data set, indicative of the independent relationship between projectile mass
(impact velocity) and the energy dissipation upon impact.................................... 102
61 Energy (J) versus areal density (g cm-2
), plotted as a linear regression fit
though the mean of the data for the 25 g, 50 g, 100 g, and 160 g flat
projectiles illustrating that no significant relationship exits between the
projectile mass and energy dissipation in the mass range examined..................... 103
62 Energy (J) versus areal density (g cm-2
), plotted as a linear regression fit
through the mean of the data for the 25 g, and 50 g conical projectiles
illustrating that no significant relationship exits between the projectile mass
and energy dissipation in the mass range examined.............................................. 104
63 High-speed image taken at 14,000 frames s-1
showing a 100 g flat tipped
projectile exemplifying projectile tilting just after impacting the sample............. 105
64 High-speed images of a BOI illustrating the onset of damage, K.E. 142.3J......... 106
65 High-speed images taken at 14,000 frames s-1
showing a 100 g flat projectile
after the initial impact and while rebounding, K.E. 142.3 J.................................. 106
66 Impactor impressions left on the target for a projectile tilted (a) and normal
(b) .......................................................................................................................... 107
67 Energy versus areal density for flat and conically tipped impactors showing a
linearly increasing trend via linear regression fit through the mean of all the
impact data............................................................................................................. 108
68 Impacted samples showing the location of sections taken for SEM analysis ....... 109
69 SEM of sample 34B, taken normal to the fracture surface, showing the path
of fracture following the main fiber orientation angle .......................................... 110
70 SEM image of sample 34B showing fiber pull-out and fiber breakage ................ 111
71 SEM image of sample 39C showing fiber pull-out............................................... 112
72 SEM of sample 1C showing fiber pull-out (fiber sliding) and fiber matrix
pull away ............................................................................................................... 113
73 Micrograph of sample 1C showing fiber pull-out lengths in excess of
approximately 3 mm.............................................................................................. 114

xiv
Figure Page
74 SEM image of sample 1C showing fiber pull-out................................................. 115
75 SEM of sample 34T showing a high degree of orientation and ductile pulling
of fibrils ................................................................................................................. 116
76 Micrograph of sample 34T illustrating a brittle-matrix fracture with ductile
pulling of fibrils.....................................................................................................117
77 SEM image of sample 38T normal to the fracture surface showing fiber pull-
out and breakage ...................................................................................................118
78 SEM of sample 39C showing variations in fiber orientation through the
thickness of the section, taken normal to the fracture plane..................................119
79 Illustration of a possible failure mechanism of the samples tested showing a
transverse view of a test plaque with the fracture path following a preferential
plane of fiber orientation .......................................................................................120
80 (a) Bottom specimen (020920-1-12B), impacted with a 50 g flat projectile,
exhibiting a typical fracture pattern, (b) graphical representation of fiber
orientation predicted in Cadpress showing the representative area of
specimen (B) with the fracture pattern superimposed over the results .................121
81 (a) Bottom specimen (020920-1-63B), impacted with a 25 g flat projectile,
specimen (B) with the fracture pattern superimposed over the results .................122
82 (a) Center specimen (020920-1-16C), impacted with a 25 g flat projectile,
specimen (C) with the fracture pattern superimposed over the results .................123
specimen (C) with the fracture pattern superimposed over the results .................124
specimen (C) with the fracture pattern superimposed over the results ................. 125

xv
Figure Page
85 Top specimen (020919-1-35T), impacted with a 50 g flat projectile,
specimen (T) with the fracture pattern superimposed over the results..................126
86 (a) Top specimen (020919-1-107T), impacted with a 160 g flat projectile,
specimen (T) with the fracture pattern superimposed over the results.................. 127
87 (a) Bottom specimen (020920-1-27B), impacted with a 50 g conical
projectile, exhibiting a typical fracture pattern, (b) graphical representation of
fiber orientation predicted in Cadpress showing the representative area of
specimen (B) with the fracture pattern superimposed over the results ................. 128
88 (a) Bottom specimen (020920-1-22B), impacted with a 50 g conical
specimen (B) with the fracture pattern superimposed over the results ................. 129
specimen (C) with the fracture pattern superimposed over the results ................. 130
90 (a) Bottom specimen (020920-1-87T), impacted with a 50 g conical
specimen (T) with the fracture pattern superimposed over the results.................. 131
91 (a) Superimposed view of the fracture patterns over the entire tab plaque for
the flat projectiles from Figures 75(a), 79(a) and 80(a). (b) Superimposed
view of the fracture patterns over the entire tab plaque, for the conical
projectiles from Figures 83(a), 84(a) and 85(a) ................................................... 132

1
INTRODUCTION
Thermoplastic Composites
The current U.S. market for such materials is in excess of 4.54 X 108
kg per
annum, half of which is consumed by the automotive industry [1]. Long-fiber-reinforced
thermoplastic (LFT) composites have one of the highest growth rates in the polymer
material areas, sustaining a projected 30% growth from 2000 to 2004 [2]. Thermoplastic
composites typically comprise a cost-effective commodity matrix, such as polypropylene
(PP), polyethylene (PE), or nylon, reinforced with glass, carbon, or aramid fibers. E-glass
is the most common reinforcement since the automotive market niche is driven more by
cost/performance ratio than weight/performance ratio as demanded by the aerospace
industry.
Thermoplastic composites used in these applications can be short-fiber-reinforced
Thermoplastic (SFRT), glass mat thermoplastic (GMT), or LFT. Injection-molded SFRT
composites (starting fiber lengths less than 4 mm) are currently the most prevalent of the
aforementioned composites. However, the full advantage of the reinforcing fiber is not
realized, due to the low fiber aspect ratio. Injection-molded LFTs also suffer from
excessive fiber length degradation in the plastification and injection stages. In addition,
difficulties arise in processing components with high fiber content and starting fiber
lengths in excess of 13 mm, due to the high melt viscosity.
GMTs consist of a chopped or continuous fiber mat reinforcement in a
thermoplastic matrix. Preparation is done by melt impregnation of non-woven glass mat

2
(dry route) or by mixing chopped fiber with polymer powder in a fluid medium (wet
route), both of which are heated in a GMT oven prior to compression-molding [3].
The large fiber aspect ratio of the reinforcement takes full advantage of the fiber
for strengthening, in contrast to its short fiber counterpart. Injection, injection-
compression, and extrusion-compression-molding techniques are employed for LFT
processing. LFT fiber lengths are typically greater than 13 mm and depend on the
desired properties, fiber concentration, and processing technique. LFTs offer several
advantages in contrast to GMTs, such as the possibility to work without semi-finished
mats (e.g. inline extrusion) making it less labor intensive, and lower compression forces
due to a decrease in melt viscosity, which results in capital cost savings in tooling and
machinery. Moreover, LFTs offer higher surface quality; less part rejection, due to an
increase in the ability to fill complex features; and integrated recycleablity. Another
advantage is greater freedom in choosing fiber and matrix materials.
In compression-molding, fibers develop in plane orientations during flow, which
can plague the consolidated component. Preferential orientation during compression-
molding can reduce strength and stiffness in a critical area and will induce warping
through anisotropic contraction upon cooling [4]. A considerable amount of work has
been done with injection and compression-molding short-fiber-reinforced thermoplastics
and thermosets, examining the state of fiber orientation and flow fronts. Very little work
has been on done modeling long-fiber reinforcement and the analytical effect of the
processing conditions and material properties. Work in this area will be beneficial in
component design, material selection, and process variables. In addition, reasonable
goals can be set in obtaining material properties required for process modeling.

3
As the use of LFTs grows in automotive and other industries, the need to
determine the impact properties of these materials increases, in order to ensure the safety
and stability of designed structures [5]. LFT was recently employed for the underside
“belly pan” of Daimler Chrysler’s PT Cruiser [3]. Sheet molding compound (SMC) was
first employed for this application. However, it proved too brittle, since that component
needed to be flexible and withstand impact from stones and other objects [3]. Few
authors have attempted to characterize the impact performance of discontinuous,
randomly oriented LFT thermoplastics.
The fiber architectures inherent in LFTs make an accurate characterization of the
failure mechanisms complex. Most efforts in understanding the impact performance and
failure mechanisms of LFTs have primarily focused on Charpy and Izod impact testing,
and to an even lesser degree, low velocity drop-tower impact testing [6]. Very little work
has looked into the effect of intermediate velocity blunt object impact (BOI) on LFTs.
Intermediate velocities are greater than low velocity drop tower impacts or pendulum
type impacts (10m s-1
), yet slower than high velocity ballistic type impacts. The velocity
range for this purpose simulates the effect of blunt objects, such as rocks and debris,
traveling at highway speeds for automotive applications, as well as impact induced by
debris from hurricanes and tornadoes for storm shelter and military housing applications.
This work can also be extended to transverse-loaded energy dissipation under high
loading rate for automobile crash mitigation purposes.

4
OBJECTIVE
The objective of this work can be divided into three categories:
I. Obtain a quantitative understanding of the processing conditions/material
property relationship in the manufacture of compression-molded LFTs.
II. Provide an understanding of the impact behavior of LFTs under various
intermediate velocity BOIs to assist engineers and scientists in obtaining reliable data
relevant to practical applications.
III. Deduce a qualitative relationship between the fiber orientations predicted in a
process simulation and the respective failure modes seen under BOI.

5
LITERATURE REVIEW
Discontinuous Long-Fiber Reinforcement
Traditional processing of LFT begins by hot melt impregnating a tow of
reinforcing fibers with a thermoplastic matrix and subsequently chopping the continuous
tow into pellets of a set length. Hot-melt impregnation is done by wirecoating, cross-
head extrusion, or thermoplastic pultrusion techniques [3]. The LFT pellets are then fed
into a single-screw plasticator where they are fed down the barrel by the screw, heated
above the melting point of the matrix, and extruded as a charge (shot). The shot is then
placed on a tool and compression molded.
Extrusion/compression molding of LFT has been rapidly gaining favor over
traditional injection molding (especially with in-line compounding) and GMT
compression molding, due to superior mechanical properties at a comparable cost [7].
The fiber aspect ratio, defined as the length to diameter ratio, differentiates short fiber
from long-fiber reinforcement. The aspect ratio of a long-fiber is typically an order of
magnitude greater than that of a short fiber [8]. While short-fiber-reinforced
thermoplastics realize substantial gains in mechanical properties over that of the neat
material, the full potential of the reinforcement is not obtained, because the fiber is below
a critical length.
The critical fiber length is given in equation (1):
τ
σ r
Lc
max
= (1)

6
where Lc is the critical fiber length, r is the fiber radius, σmax is the tensile stress acting on
the fiber, and τ is the interfacial shear strength, equation (2) [9].
This equation is based on several simplifying assumptions, the first of which is
that the strain to failure for the fiber is less than that of the matrix. This is a reasonable
assumption in the case of thermoplastic matrices. A shortcoming of this equation is that
it assumes the interfacial shear stress in constant over the fiber length. It has been shown
that fibers produce higher stresses at the fiber tips, resulting in a lower elongation to
failure [10]. This is illustrated in Figure 1, adapted from Chawla [9].
l
r
2
σ
τ = (2)
Cd
l
d
l
⎟
⎠
⎞
⎜
⎝
⎛
<
Cd
l
d
l
⎟
⎠
⎞
⎜
⎝
⎛
=
Cd
l
d
l
⎟
⎠
⎞
⎜
⎝
⎛
>
σf
τ
Figure 1 Illustration of tensile and shear stress in a single fiber above,
below, and at the critical fiber length, adapted from Chawla [9].

7
Assuming that, below the critical fiber length, the force required for debonding
increases linearly with fiber length, the interfacial shear strength can be determined from
the slope of the load required for pull-out versus fiber length. Above the critical fiber
length, sufficient interfacial shear stress exists for fiber breakage to occur. This is the
basis for the subsequent material models.
Material Property Models
Several models have been developed in order to predict the modulus, tensile
strength, and impact strength for discontinuous fiber-reinforced composites. For the
normalized Kelly and Tyson theoretical model shown in Figure 2, the composite strength
approaches 90% that of a continuous fiber-reinforced composite, as the fiber length
approaches 14 mm [11]. For the Cox modulus model, Figure 2, 90% of the composite
Figure 2 Normalized property models; Cox shear-lag modulus, Cottrell impact
strength, and Kelly-Tyson strength versus fiber length for 40 wt. % E-glass fiber (14
μm diameter) in a polypropylene matrix.

8
stiffness is realized at a fiber length of 0.8 mm [12]. The Cottrell impact model shown in
Figure 2 illustrates that the theoretical impact resistance of discontinuous fiber-reinforced
composites is optimum at the critical fiber length, 3.35 mm [13]. These property models
are interrelated and will be discussed in detail below. The material properties used in the
models are given in the next section.
Material Properties. The material properties in Table 1 were chosen to reflect
those of commercial polypropylene and E-glass and were obtained from the literature [3,
6, 14, 15, 27, 33].
Table 1 Properties for 40 wt. % E-glass/polypropylene used in the material models
Nomenclature Value Unit Property
D 14 μm Fiber diameter
Ef 75 GPa Fiber modulus
Lc 3.35 mm Critical fiber length from equation (1)
σfj 1.82 GPa Fiber tensile strength
Gm 6.56 MPa Matrix shear modulus from equation (8)
Em 1.60 GPa Matrix Modulus
τ 3.80 MPa Interfacial shear strength from equation (2)
σm 38.80 MPa Matrix strength
Um 1000 J m-2
Matrix fracture energy
Ud 500 J m-2
Interface fracture energy
τfs 0.910 MPa Static frictional interfacial shear strength
τfd 0.455 MPa Dynamic frictional interfacial shear strength
αm 96 μm m-1 o
C-1
Coefficient of thermal expansion (matrix)
αf 5 μm m-1 o
C-1
Coefficient of thermal expansion (fiber)
Ts 120 o
C Solidification temperature

9
Modeling of tensile strength. The model for the prediction of a polymer composite
strength with discrete aligned fibers, originally developed by Kelly and Tyson [13]
(1965), is well known. The original work was based on copper/tungsten and
copper/molybdenum metal matrix composites but has since found applications in
polymer matrix composites [11]. The theory of strengthening for fiber-reinforced
composites is based on the idea that interfacial shear stresses at the fiber-matrix interface
are limited by the flow stress of the matrix or by the shear strength of the interface [11].
Table 1 (Continued)
Nomenclature Value Unit Property
Tt 20 o
C Test temperature
σr 9.10 MPa
Radial stresses due to thermal shrinkage from
equation (17)
Xi 4 Geometric parameter for square packing of fibers
ηo 1 Orientation factor (discrete aligned fibers)
ηo 0.375
Orientation factor (random fiber orientation)
from equation (13)
ηl 0.277 Fiber length efficiency factor from equation (6)
β 22301 Shear-lag parameter from equation (7)
Wf 0.40 Fiber weight fraction
Vi 0.187 Volume faction of subcritical length fibers
Vj 0.187 Volume faction of supercritical length fibers
Vf 0.187 Fiber volume fraction
νf 0.20 Poisson's ratio (fiber)
νm 0.25 Poisson's ratio (matrix)
ρs 0.10
Coefficient of static friction at fiber-matrix
interface
ρd 0.05
Coefficient of dynamic friction at fiber-matrix
interface
L 0.01-100 Fiber length in millimeters

10
In order for embedded fibers to fracture upon loading, the fiber length must be greater
than the critical length defined in equation (1). If the fibers are below critical length,
pull-out will result. The Kelly-Tyson model is given in equation (3), and the variables
are given in Table 1.
The summation terms in equation (3) arise from the contribution of subcritical and
supercritical fiber lengths. If only fibers of uniform length are considered, the summation
terms cancel, which is the case in the material models shown in Figures 2 and 3.
( ) umf
j
c
jfj
ii
uc V
L
L
V
D
VL
σσ
τ
σ −+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−Σ+⎥
⎦
⎤
⎢
⎣
⎡
Σ= 1
2
1 (3)
Figure 3 Kelly-Tyson tensile strength model showing tensile strength versus log
fiber length for discrete aligned E-glass fibers (40 wt. %) and randomly oriented E-
glass fibers (40 wt. %) in a polypropylene matrix. The dashed line indicates the
critical fiber length, 3.35 mm from equation (1). The fiber diameter was taken as 14
μm.

11
Equation (3) cannot be integrated to take randomly oriented fibers into account,
which gives rise to the need for a fiber efficiency factor. Chou published an equation to
calculate the fiber efficiency factor, ηo, for random, planar laminates containing fibers of
uniform length, equation (4) [15]. The variables in equation (4) are given in Table 1.
Thomason and Vlug investigated the applicability of equation (4) in reference to the
Kelly-Tyson material model. The theoretical prediction of 0.20-0.25 from equation (4)
showed a good correlation to experimental results in which a linear regression gave a
fiber orientation factor of 0.20 for oriented E-glass fibers (10–40 wt. %) in a
polypropylene matrix [14].
A random orientation factor of ηo = 0.375 was used in the Kelly-Tyson tensile
strength model shown in Figure 3 [16]. A dramatic decrease in tensile strength is seen in
the case of randomly oriented fibers, signifying a strong off-axis effect; this is well
known for unidirectional laminates. This indicates that laminate strength is most likely
governed by fibers oriented parallel to the loading direction, thus making knowledge of
the fiber orientation state a primary concern.
Modeling of tensile modulus. The Cox shear-lag model was developed in 1952 to
predict composite stiffness for aligned discontinuous elastic fibers in an elastic matrix
[12]. Krenchel improved the model by incorporating an orientation parameter, ηo, to
account for variations in planar fiber orientations. The Cox-Krenchel model is given in
equation (5), where ηl is the fiber-length efficiency factor described in equation (6) and
( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−
−+
−×−+= −
2
2
122
3
11
11
log
2
1
cos12
3
8
β
β
ββββ
π
ηo (4)

12
β is the shear-lag parameter from equation (7). The shear modulus of the matrix, Gm, can
be calculated from equation (8). The r/R factor in equation (7) is related to fiber volume
fraction by equation (9).
The term Xi in equation (9) is dependent on the geometric packing arrangement of the
fibers. A value of Xi = 4 was used in the calculation, which is appropriate for square
packing of fibers [17]. The Krenchel orientation factor can be calculated from equation
(10):
where
For example, four fiber layers with 0o
, 90o
, 45o
, and -45o
planar orientations can be
described by equation (12):
nn
n
o a θη 4
cosΣ= (10)
1=Σ n
n
a (11)
( ) ( )fiVRr Χ= πlnln (9)
( ) mfffloc EVEVE −+= 1ηη (5)
( )
⎥
⎦
⎤
⎢
⎣
⎡
−=
2
2tan
1
L
L
l
β
β
η (6)
( )
2
1
/ln
22
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=
RrE
G
D f
m
β (7)
( )υ+
=
12
m
m
E
G (8)

13
Solving equation (10) with the parameters given in equation (12) results in a Krenchel
orientation parameter of 0.375, equation (13):
An orientation factor 0.375 is considered random and can be verified upon integration of
(10) from -900
< θ < 900
, with the exact solution given in equation (14):
which is approximately equal to 0.358 [17]. The remaining variables are described in
Table 1. Figure 4 shows the Cox and Cox-Krenchel tensile modulus models as a
4
4
2
0
41
4
3
2
1
4321
πθ
πθ
πθ
θ
−=
=
=
=
====
and
aaaa (12)
( ) 8/3414101410 =+++=η (13)
π
θθ
π
π
π 8
9
cos
1
0
2
2
4
== ∫−
d (14)
Figure 4 Cox and Cox-Krenchel models for tensile modulus versus log fiber length
of uniaxially aligned fibers (Cox) and randomly oriented fibers (Cox-Krenchel) for
40 wt. % E-Glass fibers in a polypropylene matrix.

14
function of fiber length.
As with tensile strength, fiber orientation plays a pivotal role on the tensile
modulus, which is illustrated in Figures 3 and 4. The effect of fiber orientation is much
more predominant than the effect of fiber aspect ratio, since 90% of the tensile modulus
is realized at sub-millimeter fiber lengths. Less than half of the tensile modulus (~43%)
is seen in the randomly oriented model at 90% of the theoretical tensile modulus, in
contrast to the uniaxially aligned fiber model.
Cottrell impact model. In 1964, Cottrell developed a model to predict the notched
impact strength of discontinuous uniaxially aligned fiber composites [13]. It is important
to identify the failure mechanisms present during impact that account for energy
absorption. Deformation and fracture of the matrix takes place in front of the crack tip.
Concurrently, the matrix transfers load to the fibers by shear. If the applied load exceeds
the fiber-matrix interfacial shear strength, debonding may occur.
Transfer of load may still occur to a debonded fiber via frictional forces along the
interface. Fibers may fracture if the stress level exceeds the fiber strength, or fracture
may occur prematurely from local flaws present along the fiber length, and inherent in
the fiber itself. Fibers that have debonded will still dissipate energy as they are pulled out
from the matrix. All of these mechanisms are incorporated into the Cottrell impact model
[13]. Like the Kelly-Tyson model, the Cottrell model incorporates equations for
subcritical and supercritical fiber lengths, as defined by equation (1). When L>Lc, the
predicted impact energy dissipation is given in equation (15):
(15)( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+⎥
⎦
⎤
⎢
⎣
⎡
+−=
D
LV
D
LUV
UVU
ffdf
mfc
6
1
2
τ

15
where the three terms encompass matrix fracture, fiber/matrix debonding, and fiber pull-
out energies. When L>Lc, the predicted impact energy dissipation is calculated from
equation (16):
where the four terms account for matrix fracture, fiber fracture and debonding, and pull-
out limited to the critical fiber length. The energy dissipated by the matrix is small,
because the presence of fibers inhibits large deformations [6].
The interfacial shear friction, τf, will not normally equal the interfacial shear
strength, τ. The calculated interfacial friction (τf = 0.910 MPa) is an order of magnitude
lower than the interfacial shear strength (τ = 3.8 MPa) reported by Thomason and Vlug
for polypropylene and E-glass [6]. The coefficient of friction between the fiber and
interface, τf = μdσr, can be determined from the radial stresses, due to thermal mismatch
between the fiber and matrix at processing temperature and test temperature from
equation (17). The variables are described in Table 1.
The interfacial friction tends to be significant in thermoplastic composites, with a
high degree of thermal mismatch between the fiber/matrix and a large temperature
change due to elevated processing temperatures. The interfacial friction plays an
important role in the fiber pull-out energy and is thought to be the predominate
mechanism of energy dissipation [6].
( ) ( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+⎥
⎦
⎤
⎢
⎣
⎡ −
+−=
DL
LV
DL
ULV
L
ULLV
UVU
fcfdcffcf
mfc
6
1
32
τ
(16)
( )( )
( ) ( ) mmfff
mftsfm
R
EEV
EETT
υυ
αα
σ
++++
−−
=
121
(17)

16
The Cottrell model for notched impact energy dissipation versus log fiber length
is shown in Figure 5. Due to the brittle fracture of glass fibers, the contribution of energy
dissipation in considered negligible (e.g. Uf = 0). The large peak in the predicted impact
strength is associated with the critical fiber length. When L < Lc, the failure mode is
predominately fiber pull-out, whereas fiber failure dominates for L > Lc. There is very
little experimental support for the peak at the critical fiber length in the Cottrell model.
Cooper [18] reported some evidence of this phenomenon for ductile fibers in a brittle
matrix (copper/epoxy), but Thomason and Vlug found no indication of a decrease in
impact strength for fibers above critical length for PP/E-glass composites [6]. Wald and
Figure 5 Cottrell impact model for notched impact energy versus log fiber length of
uniaxially aligned E-Glass fibers (40 wt. %) in a polypropylene matrix. The peak
corresponds to the critical fiber length, Lc = 3.35 mm.

17
Schriever [19] also found evidence of high impact strength in GMTs, which typically
contain fiber lengths of 25-50 mm.
The experimental data from Thomason and Vlug on PP/E-glass suggested that
fiber strain energy might play an important role in the energy absorption process,
accounting for the discrepancy in long-fiber-reinforced composite impact strength [6].
The total energy involved in fracture of a single fiber is given by equation (18)
where L is the gauge length of the test specimen and the remaining variables are given in
Table 1. The strain energy stored in a fiber is dissipated in the form of heat and acoustic
energy upon fracture [6]. In the case of fibers below the critical length, the strain energy
is released in a similar manner as they debond from the matrix. This also contributes to
the explanation of an increase in impact strength of PP/E-glass composites with a
decrease in temperature [6]. As the test temperature decreases, the interfacial friction
increases from equation (17), increasing the impact strength. In addition, an increase in
strength of glass fibers has been reported with decreasing temperature, σf/dT ~5 MPa0
C-1
,
which would contribute to the fiber strain-energy absorption in equation (18) [6].
If fiber strain energy contributes to impact energy absorption, equation (18) can
be incorporated into equation (16) to yield the impact strength. The Cottrell impact
strength versus log fiber length is plotted with the original and modified models in Figure
6.
f
f
f
E
L
U
2
2
σ
= (18)

18
A comprehensive experimental database on the effect of aspect ratio on composite
strength, stiffness, and impact properties is not currently available [3]. Moreover, the
work done on characterizing the effect of aspect ratio on the aforementioned is typically
done with fiber-friendly processing methods when, in actuality, a significant amount of
fiber length degradation and bending occur during processing [21]. Thomason and Vlug
have shown that a direct relationship exists between Charpy impact energy dissipation
and tensile strength, which indicates that the parameters governing laminate strength also
govern resistance to impact [6]. Assuming a uniform or, more accurately, an average
fiber length and fiber concentration for a given discontinuous fiber-reinforced material,
the composite strength is dictated by only the fiber orientation. If one accepts that impact
Figure 6 Cottrell impact models (with and without consideration of fiber strain
energy) for notched impact energy versus log fiber length of uniaxially aligned E-
Glass fibers (40 wt. %) in a polypropylene matrix. The fiber diameter is 14 μm.

19
strength is dictated by the fiber orientation, the composite failure will occur along planes
parallel to areas of high preferential fiber orientation. Therefore, knowledge of the
orientation state should allow one to qualitatively predict areas that may be susceptible to
damage under impact.

20
CADPRESS-TP BACKGROUND
Cadpress-Thermoplastic (or Express) was developed jointly by M-Base
Engineering and Software, in conjunction with their academic partner, the Institut fur
Kunststoffverarbeitung (IKV) in Aachen, Germany, and The Madison Group with their
academic partner, the Processing Research Center at the University of Wisconsin,
Madison [22]. Currently, CADPRESS-TP is probably the only commercial software
suitable for simulating compression-molding of discrete long-fiber-reinforced
thermoplastics. The fundamental background of Cadpress-TP (Cadpress) and its
relationship to other work on process modeling of thermoplastic composites are given in
this chapter.
Cadpress performs two discrete, albeit dependent, simulations that reproduce the
process-induced material properties, shrinkage, and warpage of complex discontinuous
fiber-reinforced thermoplastic matrices when compression molded using finite element
methods [22]. The first part of the program simulates the flow behavior of the melt
during the filling stage of compression molding. It is during the filling stage that flow-
induced fiber orientation develops, upon which the final mechanical and
thermomechanical properties are highly dependent [22].
The user has the option of an isothermal or non-isothermal flow calculation, but
the non-isothermal simulation is inherently more accurate, due to the non-Newtonian
nature of polymer solutions, which undergo shear thinning. The temperature dependent
melt viscosity does not share a linear relationship with shear rate. In the case of shear

21
thinning, the apparent viscosity decreases with increasing shear rate [23]. Background
will not be given for the isothermal flow calculation for brevity. The flow simulation
follows the control volume approach based on a static, finite element mesh. The flow
front progression is defined by a fill factor assigned to each element for three stages of
filling: fi = 1, for fully filled; 0 < fj < 1, for partial filling; and fk = 0, for no filling.
In the case of thermoplastic melts, the material cools rapidly as it encounters the
mold walls, increasing the viscosity locally until the melt no longer flows. The non-
isothermal calculation takes into account the local variations in viscosity with equations
19 and 20.
The shear rate, γ& , in equation 19 corresponds to the velocity gradient through the
flow channel height, accounting for the shear rate dependency of the viscosity. The three
parameters in equation 19 e.g., P1, P2 and P3, are the zero shear or null viscosity, the
infinite shear viscosity, and the power law index, respectively. The temperature
dependency of the viscosity is addressed by the temperature shift coefficient, aT, equation
20 [22].
The flow simulation can be described using the generalized Hele-Shaw flow
model for incompressible, inelastic, non-Newtonian fluid under non-isothermal
conditions [22, 24-32]. The temperature and shear-rate dependent viscosity are then used
to determine the non-isothermal, non-Newtonian flow conductivity, which is given in
( ) 3
2
1
1
p
T
T
Pa
aP
γ
η
&+
=
( ) ( )
( )
( )
( )S
o
S
SB
o
SB
T
TTC
TT
TTC
TT
a
−+
−
−
−+
−
=
6.101
86.8
6.101
86.8
log
(19)
(20)

22
equation 21. The flow conductivity, equation 21, is a function of the flow channel height,
h.
Due to the highly temperature-dependent nature of compression molding,
calculation of the temperature distribution is imperative. Energy transport is considered
in equations 22, 23, and 24, which are the convection, conduction, and diffusion terms,
respectively. The energy transport equations are solved in conjunction with the
governing flow equations. After filling, the diffusion and convection terms drop out of
the energy equation, leaving only the conduction term. The solution to the differential
equation is solved using a one-dimensional implicit finite difference form of the equation
(22).
Upon ejection, a second energy balance must be applied to account for heat
transfer to the surroundings as the part cools to ambient temperature, in which case the
diffusion and convection terms must be reintroduced. The warpage phenomenon,
common in compression and injection molding, requires modifying the boundary
conditions for the energy equations. The coefficient of thermal diffusion, λ, must then be
modified to reflect the heat transfer from the part to the surroundings [22].
η12
3
h
S = (21)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
+
∂
∂
−
y
T
x
T
c yxp ννρ (22)
zz
y
yz
x
xz
∂
∂
−
∂
∂
−
ν
τ
ν
τ (23)
2
2
z
T
t
T
c p
∂
∂
=
∂
∂
λρ (24)
= 0
= 0

23
The most critical calculation in the simulation is the prediction of fiber
orientation, from which the thermomechanical and final mechanical properties of the
component are determined. The fiber orientation calculation starts at the very beginning
of the simulation and is continued until the mold cavity is filled. Jeffery provided the
first model to attempt to predict fiber orientation [23]. The Jeffery model does not
consider fiber-fiber interactions and can only be applied in the dilute fiber volume
regime, φf <<(d/l) 2
, in which the fiber-fiber interactions are infrequent and purely
hydrodynamic [24].
The Jeffery model for predicting fiber orientation was modified by Folgar and
Tucker to account for fiber interaction with a damping term, known as the fiber
interaction coefficient, C1. The rotary diffusivity can than be expressed as Dr = C1γ&
[25]. The same model has been used by several other authors for the prediction of fiber
orientation in injection, injection/compression, and compression-molded short-fiber-
reinforced thermoplastics [22, 24-32].
The fiber interaction coefficient can be expressed in terms of the root-mean-
square angle change caused by the fiber-fiber interactions or can be determined
empirically in the absence of any knowledge of the fiber angle change caused by
mechanical contact [24]. The fiber interaction coefficient depends on the number of fiber
contacts, N, built up in the flow fields, so it not only accounts for the fiber volume
content but also the fiber aspect ratio [8]. Fibers have a tendency to resist alignment in
the flow where they are in contact with one another. It is, however, inherently unstable,
requiring the help of an additional numerical procedure.

24
Several simplifying assumptions must also be made to efficiently conduct the
rather intensive calculations [22]. The first of which is that the fibers are considered rigid
bodies with uniform length and diameter. Also, the fiber-matrix melt is considered
incompressible, and the viscosity of the matrix is so high that inertial and buoyancy
effects are negligible. Another assumption is that there are no externally applied forces
or moments on the fibers. In addition, the interaction between two fibers is assumed to
take place when the fibers’ centers of gravity move past one another within a distance
that is smaller than the length of the fibers. Long fibers may deviate from the rigid body
behavior by bending. This is handled by treating the filament as a series of single, linked,
inflexible filaments [22].
Since it is computationally inefficient to consider each fiber interaction
separately, the Folgar-Tucker model uses a statistical approximation of the entire domain.
The Gaussian probability distribution, ψ, of the fiber orientation must satisfy the
continuity equation, which accounts for all of the fibers rotating in and out of an arbitrary
control volume, equation (25). Equation (26) gives the rotational speed of a single fiber
with the addition of a damping term. The variable, γ& , is the scalar magnitude of the
strain rate tensor, describing the frequency of fiber-fiber interaction. Equation (27) is
used in equation (28) to calculate the fluid velocity for variable layers, based on the shear
velocity present at a given layer.

25
The differential equation for the calculation of fiber rotation is not solvable by
analytical methods, requiring a numeric solution. The governing equations are first
discretized and rewritten in implicit form [22]. The fiber angles are then discretized into
25 angle classes, from 0° to 180°, with respect to the local coordinate system and are
displayed as a fiber orientation distribution, fiber frequency versus angle class [22]. This
is done for each of the five discrete layers from the midplane, assuming symmetry about
the midplane. Dividing the geometry into layers allows for the consideration in the
different velocity profiles with respect to the flow channel height. This is necessary since
the flow channel height is transient, because of mold closing and the cooling and eventual
freezing of the material. The systems of equations are solved using a Gaussian-based
matrix-solving algorithm [22].
In the flow front, the fibers rotate while being transported across element
boundaries, implying that a different fiber orientation as well as volumetric content may
be present at a given time step. An average flow rate for each element is calculated in
order to satisfy the continuity requirements. The anisotropic elastic material properties
(25)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
+−−
∂
∂
−
∂
∂
=
∂
∂
),,
2
,
2
,
2
2
cossincos
sincossin(
yyxy
yxxx
IC
t φνφφν
φνφνφψ
φφ
ψ
γ
ψ
&
yyxyyxxxIC
t
,,
2
,
2
, cossincossincossin
1
φνφφνφνφνφ
φ
ψ
ψ
γ
φ
++−−
∂
∂
−=
∂
∂
& (26)
1++= μνμ νγν Sh& (28)
yyxyyxxx ,
22
,,,
2
2)(2 ννννγ +++=&
(27)

26
are calculated by first applying the micromechanical Halpin-Tsai empirical expressions,
given as equations 29-34. The expressions account for the aspect ratio of discontinuous
fiber reinforcement. The variables for equations 29–34 are described in Table 1.
However, the Halpin-Tsai expressions can only be used in the unidirectional case.
Therefore, the 25 different fiber orientation angles are thought of as 25 discrete layers
and treated using classical laminate theory. The laminates are combined using the
principle of superposition, also known as Continuum Theory, derived by Puck and
Halpin, to give the composite anisotropic elastic material properties for each element
[22].
Physical and mechanical material property data are very limited in the relatively
new realm of LFT composites. The material behavior, both in processing and in the final
product, differs significantly from its SFRT analogy. Significant improvements in tensile
strength and stiffness, as well as impact resistance, have been documented with
whereGG M ,
5.01
5.01
12
Φ−
Φ+
=
ξ
1=ξ (34)
1
2
2112
E
E
νν = (33)
2=ξwhereEE M ,
1
1
2
Φ−
Φ+
=
κ
ξκ
(30)
whereEE M ,
1
1
1
Φ−
Φ+
=
κ
ξκ
F
F
d
l
2=ξ (29)
ξ
κ
+
−
=
M
F
M
F
E
E
E
E
1
(31)
)1(21 Φ−+Φ= ννν F
(32)

27
increasing aspect ratio [2, 5, 6, 10-12, 14-16, 19, 33]. However, a major drawback is
seen in the processing of such materials. The high melt viscosity of LFTs with large fiber
aspect ratios and high volumetric fiber content require extrusion/compression molding,
whereas injection molding can still be used for shorter reinforcements with low fiber
loading.
Compression molding can be modeled effectively using Cadpress-TP
compression-molding software, which simulates the processes from the time the charge is
placed in the mold to the time when the part has cooled to the user-determined limiting
temperature outside the mold. From this important processing information, mechanical
property data, and shrinkage and warpage data are calculated. This offers the immense
advantage of decreased development time. Furthermore, the part design, processing
conditions, and mechanical performance can be optimized without having to produce an
actual component. Moreover, the manufacturing process can be controlled/optimized to
generate favorable processing conditions and fiber orientation states to obtain the best
possible components from such a process [27,28].
Difficulties, however, arise in obtaining accurate material data for the
compression-molding simulations. A vast array of data is required, much of which is
costly and/or difficult to obtain. The software can be utilized to determine the sensitivity
to changes in processing conditions and material parameters, and to resolve which of the
parameters are most likely to effect processing and component performance through a
simulation matrix.

28
EXPERIMENTAL PROCEDURE: PROCESS MODELING
Simulation Matrix
The properties of a material are related to its structure, and processing controls
the structure. This has a particular relevance to the compression-molding process, in
which the material is made while producing the component [29]. The goal in the
experimental Cadpress-TP simulation matrix is to determine the effect of material
properties and processing parameters on the manufacturing and properties of compression
molded long-fiber thermoplastics. There are three required inputs for Cadpress-TP, the
discretized model, the material properties, and the processing parameters. The processing
parameters, along with their default values, are given in Table 2.
Table 2 Processing parameters
Parameter Default value Units
Mold closing velocity 10 mm s-1
Mold temperature (top) 60 o
C
Mold temperature (bottom) 60 o
C
Idle time (to place charge) 0 s
Ambient temperature 20 o
C
Cooling time 40 s
Heat transfer coefficient (air) 5.00E-06 W mm-2
K-1
Heat transfer coefficient (mold) 0.002 W mm-2
K-1
Maximum press force 1000 kN
Boundary conditions Geometry dependent
Charge location Geometry dependent
Charge preorientation 0.318, all 25 layers

29
The component chosen for the study is a tab plaque flow tool with a flat insert
located at Southern Research Institute Composites Manufacturing Center, Birmingham,
AL. In order to create the finite element mesh, a solid model was first constructed in
Pro/ENGINEER (Pro/E). The model was simplified by removing small radii and drafts.
Next, the flow tool model was discretized using both HyperMesh 5.1 and ANSYS 5.7
with several different mesh densities and was imported into Cadpress-TP. Altair
HyperMesh is a powerful finite element pre- and post-processor that enables generation
of finite element and finite difference models for engineering simulation and analysis.
The Cadpress software requires an elastic triangular three-node element with six
degrees of freedom and midplane nodes (ANSYS: SHELL 63). Optimizing the mesh
density is essential because CADPRESS-TP is computationally intensive. In the final
discretized model, a mesh density of 0.0356 elements mm-2
(5446 elements with an area
of 1.53 X 105
mm2
) was used.
Process Variables
Mold temperature, Simulations 1–3. A simulation matrix was constructed in
order to investigate the effect of various processing conditions and material properties.
The selected parameters were looked at independently, holding all other variables
constant. The required processing parameter inputs are shown in Table 2. The default
values are approximately those of GMT, PP/40 wt. % E-glass. The process parameters
selected for study, namely mold temperature and charge location, can be readily
controlled in practice.

30
A temperature gradient between the male and female mold halves is often
maintained in order to control the shear edge through thermal expansion. For the
material parameter simulations, the mold temperatures were set at 70o
C and 60o
C for the
male and female mold halves, respectively. In the mold temperature effect simulations,
the temperatures of the top and bottom molds were made equal. Intuitively, increasing
the mold temperature will aid in mold filling but may actually increase the cycle time
through an increase in cooling time. Quantitative analysis of this type is difficult to
ascertain without the aid of modeling. Simulation 2 was the control run, with a default
mold temperature of 60°C, while in Simulations 1 and 3, the mold temperatures were
30°C and 90°C, respectively. The effect of mold temperature on flow fronts, the time
and pressure required for consolidation, and shrinkage and warpage in the consolidated
part were considered.
Charge location, Simulations 4-8. The charge location is the area in which the
fiber/matrix melt is placed on the compression-molding tool just prior to closing the
mold. The charge location can be easily modified, both in simulation and in practice, and
can have a significant effect on the mechanical and thermomechanical properties. In
addition, knowledge of the flow progression can aid in the prediction of knit lines (weld
lines), which have adverse affects on mechanical properties. The flow progression also
allows for prediction of areas for air entrapment. The different charge locations
examined are shown in Figure 7.

31
Figure 7 Charge locations. Charge location (a) was used in
Simulations 1-3, (b) in Simulation 4, (c) in 5, (d) in 7, (e) in 6, (f)
in 8.
(a) (c)(b)
(f)(e)(d)

32
The preorientation of the fibers in the charge, conversely, are dependent on the
plastication process. Typically, a single screw extruder is utilized; the charge
preorientation is mainly dependent on the type of plasticator. Therefore, a random
preorientation will be assumed for all 25 layers of the charge.
Boundary conditions. The boundary conditions are required to prevent free body
rotation in the shrinkage and warpage calculation. Default values of the remaining
variables are believed to have little influence on the process or are difficult to control in
practice; for example, the thermal conductivity of the mold is dependent on the mold
material.
Material Parameters. Tables 3, 4, and 5 provide the material property inputs and
their default values for the fiber, matrix, and the composite melt, as required for the
simulations.
Table 3 Fiber material parameters
Fiber aspect ratio 2000
Elastic modulus 7.30E+04 N mm-2
Coefficient of linear expansion 3.00E-06 o
K-1
Poisson’s ratio 0.22
Thermal conductivity 8.50E-04 W mm-1 o
K-1
Specific heat capacity 0.84 J g-1 o
C-1
Density 2.52 g cm-3

33
Table 4 Composite material parameters
Parameter Default value Unit
No-flow temperature 150 o
C
Volumetric fiber content 0.16
Thermal diffusivity 0.08 mm2
s-1
Thermal conductivity 0.17 W m-1 o
K-1
Carreau-Parameter 1
(Null viscosity)
4149 Pa s
Carreau-Parameter 2
(Infinite shear viscosity)
1 s
Carreau-Parameter 3
(Power law index)
0.599
Fiber interaction coefficient 0.14
Table 5 Matrix material parameters
Poisson’s ratio 0.35
1.89E-03 o
K-1
-1.54E-06 o
K-2
-3.05E-08 o
K-3
Elastic modulus 1.68E+03 N mm-2
-2.21E+01 N mm-2 o
C-1
7.98E-02 N mm-2 o
C-2
-4.15E-05 N mm-2 o
C-3
Coefficient of linear expansion 3.41E+04 cm3
bar g-1
5.48E+04 cm3
bar g-1 o
K-1
2.38E+08 bar
3.07E+04 bar
1.17E-07 cm3
g-1
0.11 o
K-1
2.98E-03 bar-1
PvT data 3.37E+04 cm3
bar g-1
1.12 cm3
bar g-1 o
K-1
1.38E+03 bar
2.91E+04 bar
Crystallization temperature 1.34E+02 o
C
0.02 o
C bar-1

34
Many of the parameters used in the flow simulation and fiber orientation
calculations are not solvable by analytical methods or are based on other calculations or
are solvable only by numeric methods [4].
Quantitative analysis is beneficial in understanding which properties are the most
critical in obtaining accurate results, as properties vary greatly depending on the material
purveyor. Other properties, such as fiber aspect ratio, can be chosen in the production of
the LFT pellets. Knowledge of material property effects could save a considerable
amount of time and money while optimizing the performance from a given material and
aid in obtaining accurate modeling results.
The material parameters chosen for the study are those thought to suit this
criterion and are as follows: the fiber interaction coefficient, melt viscosity, and the PvT
coefficients. These parameters were expected to have the greatest effect in material
parameter simulations.
Fiber interaction coefficient, Simulations 9 and 10. The fiber interaction
coefficient has not been determined accurately via analytical methods and is usually
determined empirically [24]. The effect of the interaction coefficient was evaluated by
varying it + 25% from the default value of 0.140. The effect on the degree of fiber
orientation was evaluated graphically as well as quantitatively for selected elements.
Melt viscosity, Simulations 11–17. The melt viscosity is particularly difficult to
determine experimentally. This is due not only to its non-Newtonian, non-isothermal
nature, but also because standard methods of measuring it produce in situ fiber length

35
degradation, thereby decreasing the viscosity [8]. Equation 19 gives the viscosity as a
function of temperature and shear rate. Noting only the shear-rate dependency of the
viscosity, it becomes a function of three parameters: the zero shear or null viscosity, the
infinite shear viscosity, and the power law index. The null viscosity was varied + 25% of
the default value given in Table 5. The infinite shear viscosity and power law index were
varied + 10% of the default values given in Table 5. The time and pressure for
consolidation and flow front effects were investigated in the study of melt viscosity.
PvT parameters, Simulations 18 and 19. Due to the complicated nature of
thermoplastic composites in the filling stage of compression-molding, one must consider
the influence of the temperature and pressure of a material during flow and in the
calculation of shrinkage and warpage in order to determine if the material is frozen. This
requires knowledge of the glass transition and crystallization temperatures with respect to
their pressure dependency. The coefficient of thermal expansion is also dependent on
transient temperature and pressure. This information is obtained from a PvT diagram.
Unfortunately, PvT data is very limited and rather difficult to obtain, particularly when
considering the wide number of matrix materials available. This made the influence of
the PvT coefficients on processing of special interest.
All four PvT coefficients were varied + 25% of their default values given in Table
4. The results were examined in terms of flow front effects, pressure, and the time
required to consolidate, as well as nodal pressure.

36
Simulation verification, Simulation 20. A qualitative relationship between
fracture paths of impacted specimens and the predicted fiber orientation was used to
verify a simulation, representing the tab plaque component produced, which is discussed
in material processing. The results are discussed in detail in the BOI results and
discussion. In the process simulation, all the default variables were used, with the
exception of mold temperature (60o
C and 70o
C for the male and female mold halves,
respectively); charge shape and location, which is shown in Figure 8; and the melt
temperature (230o
C).
Figure 8 Charge location for the simulation verification study and for simulations
9-20. The charge shape and location were chosen as best to represent the
processing conditions outlined in material processing.
Charge location

38
RESULTS AND DISCUSSION: PROCESS MODELING
A parametric study of processing and material property effects was conducted
based on Cadpress-TP compression-molding simulations of LFT in order to determine
the sensitivity of said parameters using the flow tool geometry, which was shown in
Figure 8. The graphic representations of selected results are given in Figures 8-46 at the
end of the chapter.
Process Parameter Results, Simulations 1-8
Mold temperature effects, Simulations 1-3. In the study of mold temperature
effects, Simulation 2 was the control run, with a default mold temperature of 60°C; in
Simulations 1 and 3, the mold temperatures were 30°C and 90°C, respectively. All other
variables given in Tables 3, 4, and 5 were held constant. The charge location shown in
Figure 8(a) was used in all three runs.
In Simulation 1, the force required for consolidation increased by approximately
100 kN (4% increase) in contrast to the control run, while in Simulation 3, the force
decreased by 200 kN (8% decrease). The greater decrease in force for an equivalent
increase in temperature (30o
C increase) is attributed to the non-isothermal temperature
shift coefficient used in the calculation of the melt viscosity. The time required to fill the
mold cavity remained roughly the same. The mold temperature effected the deformation
after ejection from the mold. The least amount of deformation occurred in the 60°C mold
temperature (1.653 mm), and the greatest deformation in the low temperature (30°C)

39
simulation (3.317 mm). Only a slight increase in deformation was noted in the high mold
temperature simulation (1.824 mm). No significant effects were seen in the flow fronts
or fiber orientations. For the geometry used in Simulations 1-3, a 30o
C increase in
temperature yielded the greatest effect on processing (two-fold decrease in consolidation
force), in contrast to an equivalent decrease in temperature from the control run. The
component warpage was minimized at the control run mold temperature of 60o
C.
Effect of charge location, Simulations 4-8. Five different charge locations were
investigated in order to determine their effect on the force and time required to
consolidate, and to determine locations for knit lines. The different charge locations
investigated are shown in Figure 8(b)-(f). The maximum force required for consolidation
remained approximately the same, with slight variations in the force versus time profiles.
These small variations are not likely to have a drastic influence in processing. However,
significant differences in flow fronts were noted. The formation of knit lines can be seen
in Figures 13 and 14 for charge locations (d) and (f). The extent of knit lines in Figure
13 was unexpected, as opposed to multiple charge configurations in which knit lines are
inevitable. Knit lines are undesirable, since they have been shown to exhibit adverse
affects on the mechanical properties and aesthetics of the final component.
Material Processing Effects, Simulations 9 – 20.
The flow progression in Simulations 9-20 was essentially the same in all cases.
Typical flow fronts at 50% and 90% filling for the respective simulations are shown in
Figures 15-16.

40
Fiber interaction coefficient, Simulations 9 and 10. The fiber interaction
coefficient is difficult to ascertain, making its influence on the flow simulation important.
For the geometry and material properties used in the study, very little effect from the
fiber interaction coefficient was noted. The numeric values used in the study was given
in Table 6, along with the maximum nodal pressure in Table 7. The software is unlikely
to be able to resolve minute differences in the nodal pressure. More intriguing, however,
was the lack of an effect on the fiber orientation, shown graphically in Figures 30(a)-(c)
and quantitatively in Figures 32-40. The elements selected are shown in Figure 31.
Virtually no distinction can be made between the simulations. One would expect a
decrease in fiber orientation with increasing fiber interaction coefficient, which inhibits
the ability of a fiber to rotate within the melt. The lack of difference may be due to the
rather simple geometry investigated and the large ratio of the charge area to the mold area
(roughly 26%).
Table 6 Fiber interaction coefficient parameters investigated
Simulation Fiber interaction coefficient
Control 0.140
Interaction low 0.105
Interaction high 0.175
Table 7 Fiber interaction coefficient study results
Simulation Maximum nodal pressure (MPa)
Control 12.29
Interaction low 12.29
Interaction high 12.28

41
Effect of melt viscosity, Simulations 11 – 17. Three parameters are required to
model the non-Newtonian nature of polymers in the flow simulation: the zero shear or
null viscosity, the infinite shear viscosity, and the power law index. Each was
investigated independently using the values given in Table 8. The values obtained in
Table 9 are from the force versus time plots in Figures 17-28. The results for each
simulation are shown in Table 9 along with Figures 41-46, which are given at the end of
the chapter.
In all the simulations, the consolidation force, estimated from the force versus
time plots in Figures 20-28, remained a constant 1.17 MN. The maximum nodal pressure
Table 8 Melt viscosity parameters investigated
Simulation Zero shear viscosity (Pa s) Infinite shear viscosity (s)
Power law
index
Control 4149 1.00 0.599
Zero shear low 3112 1.00 0.599
Zero shear high 5186 1.00 0.599
Infinite shear low 4149 0.90 0.599
Infinite shear high 4149 1.10 0.599
Power index low 4149 1.00 0.539
Power index high 4149 1.00 0.659
Table 9 Melt viscosity parameter study results
Simulation
Maximum nodal
pressure (MPa)
Consolidation force
(MN)
Consolidation time (s)
Control 12.29 1.17 1.49
Zero shear low 12.37 1.17 1.19
Zero shear high 12.26 1.17 2.10
Infinite shear low 12.26 1.17 1.67
Infinite shear high 12.31 1.17 1.35
Power index low 12.17 1.17 2.35
Power index high 12.80 1.17 1.15

42
varied slightly, from 12.17–12.80 Mpa; however, the time for the melt to consolidate
varied considerably. The most significant effect was seen in the melt viscosity study
based on the power law index variations. The time to consolidate increased with a
decreasing power law index as shown in Table 9, in which the two extremities varied by
1.2 s. This may seem insignificant at first, but in a 500,000-part run, typical of an
original equipment manufacture (OEM), it would result in an increased manufacturing
time of approximately 167 h. Figures 26, 27, and 28 showing the force versus time
consolidation plots, indicate that the force required for consolidation increases faster as
the power law index decreases, which is expected from the non-Newtonian viscosity
equation (19).
The infinite shear viscosity effect seemed the least significant in the study. This
could be due to the relatively low shear rate used, based on a linear mold closing velocity
of 10 mm s-1
, which would also indicate why the zero shear or null viscosity had a
slightly greater significance. In the zero shear viscosity study, the slope of the force
versus time consolidation plot decreased with increasing zero shear viscosity, shown in
Figures 20, 21, and 22. In the high zero shear simulation (5186 Pa s), the slope of the
force versus time plot is almost vertical as shown in Figure 22.
The fiber orientation was relatively unaffected in the zero shear viscosity study.
A slightly higher degree of orientation can be seen in the low zero shear study, Figure 44.
This may be due to an increase in mobility for the fibers to orient themselves in the flow
resulting from a decrease in melt viscosity. There was virtually no difference in the
graphical fiber orientations seen in the infinite shear viscosity study in Figure 45, again
most likely attributed to the low shear rate used in the simulations. The power law index

43
inquiry exhibited some variation in the graphical fiber orientation shown in Figure 46.
The highest degree of relative fiber orientation was seen in the high power law index
simulation, followed by the control run and then the low power law index simulation. In
all cases, as the melt viscosity increased, the fiber orientation decreased.
PvT parameter effects, Simulations 18 and 19. The PvT parameters had the least
significant effect in the material parameter study. The parameters investigated are given
in Table 10, with the respective results in Table 11. The results indicate no prominent
effects in the processing or nodal pressure. No effect from the PvT parameters study was
seen in the fiber orientation either. This may be because the PvT parameters are used
primarily in the warpage calculation, which was not investigated in this case. The PvT
parameters can be used to determine whether a given layer is frozen. However, the
Table 10 PvT parameters investigated
Simulation
Coeff. 1
(cm3
bar g-1
)
Coeff. 2
(cm3
bar g-1 o
K-1
)
Coeff. 3 (bar) Coeff. 4 (bar)
Control 33709 1.12 1379 29122
PvT low 25282 0.84 1035 21842
PvT high 42136 1.40 1724 36402
Table 11 PvT parameter study results
Simulation
Maximum nodal
pressure (MPa)
Consolidation
force (MN)
Consolidation
time (s)
Control 12.29 1.18 1.5
PvT low 12.29 1.18 1.5
PvT high 12.29 1.18 1.5

44
crystallization temperature can be used by itself without taking into consideration its
pressure dependency. The Cadpress Theory manual does not discuss this in detail.
Control run, Simulation 20. The results from the control run were used as a base
line for all of the material parameter simulations. The process and material parameters
used are given in Tables 2-5, and results are given in Figures 15-17, 20, 23, 26, 30(a), 32,
35, 38, 41, 44(a), 45(a), and 46(a). The fiber orientation results were then used to verify
the control run simulation in results and discussion: blunt object impact, through a
qualitative comparison between the predicted fiber orientation and the failure modes of
LFT subjected to BOI.

45
Figure 10 Flow fronts at 50%
filling for Simulation 4.
Figure 9 Typical flow front at 50%
filling for Simulations 1–3.

46
Figure 13 Flow fronts for 80% filling showing the
formation of knit lines in Simulation 7.
Figure 14 Flow fronts for 95% filling showing the formation
of knit lines for two charges placed in Simulation 8

47
Figure 15 Typical flow front for Simulations 9-20 showing 50% filling.
Figure 16 Typical flow front for Simulations 9–20 showing 90% filling.

48
Figure 17 Force versus time for the control
simulation, fiber interaction coeff. = 0.140.
Figure 19 Force versus time diagram for the fiber
interaction coefficient low (0.105) simulation.
Figure 18 Force versus time diagram for the
fiber interaction coefficient high (0.175)
simulation.

49
Figure 22 Force versus time for the high null
viscosity (5186 Pa s) simulation.
Figure 21 Force versus time for the low null
viscosity (3112 Pa s) simulation.
simulation, null viscosity = 4149 Pa s.

50
Figure 25 Force versus time for the high infinite
shear viscosity (1.10 s) simulation.
Figure 24 Force versus time for the low infinite
shear viscosity (0.90 s) simulation.
simulation, infinite shear viscosity = 1.0 s.

51
Figure 28 Force versus time for the high power
law index (0.569) simulation.
Figure 27 Force versus time for the low power
simulation, power law index = 0.599.

52
b
a
Figure 29(a) and (b) Force versus time plots for low and
high PvT parameter simulations, respectively.

53
Figure 30 Graphical representation of the fiber orientation in the (a) control run
(0.14), (b) low fiber interaction coefficient (0.105) simulation, and (c) the high
fiber interaction coefficient (0.175) simulation.
b
a
c
Graphical representation of
an element indicating a close
to random fiber orientation
an element in which the
main fiber orientation is
indicated by the arrow

54
Figure 31 Illustration of selected element locations for the fiber orientation
distribution function comparison: (a) element 39, (b) element 29, and (c) element 937.
The locations were chosen as intermediate locations of interest.
a cb

55
Figure 32 Fiber distribution function of element 39 in the
control simulation, fiber interaction coeff. = 0.140.
Figure 33 Fiber distribution function of element 39
in the low fiber interaction coefficient (0.105)
simulation.
Figure 34 Fiber distribution function of element 39
in the high fiber interaction coefficient (0.175)
simulation.

56
Figure 35 Fiber distribution function of element 29 in the
control simulation, fiber orientation coeff. = 0.140.
Figure 36 Fiber distribution function of element 29 in
the low fiber interaction coefficient (0.105) simulation.
Figure 37 Fiber distribution function of element 29 in the high
fiber interaction coefficient (0.175) simulation.

57
Figure 38 Fiber distribution function of element 937 in
the control simulation, fiber orientation 0.140.
Figure 39 Fiber distribution function of element 937 in low fiber
interaction coefficient (0.105) simulation.
Figure 40 Fiber distribution function of element 937 in high fiber
interaction coefficient (0.175) simulation.

58
Figure 41 Maximum nodal pressure (Pa) for the control simulation,
where the maximum nodal pressure is 12.29 MPa, null viscosity = 4149
Pa s.
Figure 43 Maximum nodal pressure (Pa) for the high null viscosity
(5186 Pa s) simulation, where the maximum nodal pressure is 12.26
MPa.
Figure 42 Maximum nodal pressure (Pa) for the low null viscosity
(3112 Pa s) simulation, where the maximum nodal pressure is 12.37
MPa.

59
a
b
c
(null viscosity = 4149 Pa s), (b) low zero shear viscosity (3112 Pa s) simulation, and
(c) the high zero shear viscosity (5186 Pa s) simulation.

60
c
(infinite shear viscosity = 1.0 s), (b) low infinite shear viscosity (0.90 s) simulation,
and (c) the high infinite shear viscosity (1.10 s) simulation.
b
a

61
a
b
c
Figure 46 Graphical representation of the fiber orientation in the (a) control run (power
law index = 0.599), (b) low power law index (0.539) simulation, and (c) the high power

62
SUMMARY AND CONCLUSIONS: PROCESS MODELING
Eight simulations were used to investigate the effect of mold temperature (three)
and charge location (five) in the processing of LFT composites for the tab-plaque flow
tool geometry.
Mold temperature had a significant affect on processing. A 30o
C increase in mold
temperature (mold temperature = 90o
C) decreased the force required for consolidation by
8%, whereas a 30o
C decrease in mold temperature (mold temperature = 30o
C) increased
the force required for consolidation by only 4%. This is attributed to the non-isothermal
dependency of the viscosity, which is accounted for by the temperature shift coefficient.
A 60o
C mold temperature simulation yielded the least warpage in the consolidated
component, followed closely by the 90o
C mold temperature simulation (~10% increase).
In the 30o
C mold temperature simulation, warpage increased by approximately 90%. The
warpage increase with decreasing mold temperature is thought to arise from an increase
in the high thermal gradient between the polymer melt and the mold.
The charge location study indicated that flow progression could be modeled and
optimized in order to avoid weld (knit) lines. The weld lines in this simple geometry
could be avoided by using a slight variation in charge placement.
Eleven simulations were conducted to understand material property effects on the
process simulations of the tab-plaque flow tool geometry. Three simulations were
conducted to determine the effect of the four parameter PvT coefficients, three

63
simulations investigated the fiber interaction coefficient, and six simulations were used to
determine the effects of the non-Newtonian, non-isothermal viscosity equation.
Negligible effects were seen in varying the fiber interaction coefficient and the
PvT parameters studies. The PvT parameters are thought to play a more significant role
in the warpage calculation, which was not studied in detail. The low dependency on the
fiber interaction coefficient may be attributed to the relatively small distance required for
flow progression. This decreases the time for the fibers to reorient in the flow. Also, a
random pre-orientation of the charge was assumed. This could influence the tendency for
fibers to orient depending on the direction of the fiber pre-orientation relative to the flow
progression
Melt viscosity played a substantial role on the processing effects and, to a lesser
degree, the fiber orientation. The power law index had the most significant effect in the
melt viscosity study. Therefore, it is the most important value to determine
experimentally. As the power law index decreased (increasing the viscosity), the time for
the melt to consolidate increased and fiber orientation decreased. This may be due to an
increase in the melt viscosity. The zero shear viscosity also had a significant effect on
processing, and to a lesser degree, the fiber orientation. The same dependency on melt
viscosity seen in the power law index study was observed in the zero shear viscosity
study. As melt viscosity increases, the time required for consolidation increases and fiber
orientation decreases. The infinite shear viscosity study resulted in the least significant
effects. This may be attributed to the low shear imposed on the melt in the simulation.
The shear rate is dependent on the mold-closing velocity. The mold-closing velocity

64
used in all simulations was 10 mm s-1
. Forty to fifty mm s-1
may have been a more
appropriate choice for the mold-closing velocity.
The simulation matrix illustrated how a process might be optimized before a
component is ever produced. Practical goals in obtaining material parameters were
established for the geometry studied. It is important to note that geometries of increasing
complexity may have different dependencies on the material properties that were
investigated. In addition, the synergistic effects between properties were not taken into
account, since only one parameter was varied in a given simulation.
For the simulation matrix in this study, varying the PvT parameters + 25% from
their default value had very little effect on the results. The same was noted in the case of
the fiber interaction coefficient, which was varied + 10%. For the material and
processing parameters used with the geometry considered, the simulations were relatively
insensitive to the PvT parameters and the fiber interaction coefficient. However, the
three-parameter melt viscosity (null viscosity + 25%, infinite shear viscosity + 10%, and
power law index + 10%) had a considerable effect on the processing results and also an
effect on the mechanical properties in the consolidated component, making an accurate
characterization of the melt viscosity of greatest importance in the material parameter
study. In all cases in the melt viscosity parameter study, the most significant effect was
seen in the fiber orientation and the time for the component to consolidate. As the
parameters were varied in such a way that the viscosity would increase, the degree of
fiber orientation decreased and the time for the component to consolidate increased.

Bartus 2003_Thesis

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (14)

Similar to Bartus 2003_Thesis

Similar to Bartus 2003_Thesis (20)

Bartus 2003_Thesis