bartus 2003_thesis
TRANSCRIPT
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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
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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
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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.
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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.
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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
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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
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TABLE OF CONTENTS (Continued)
Page
CONCLUSION: BLUNT OBJECT IMPACT.................................................................133
LIST OF REFERENCES.................................................................................................135
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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
11 Flow fronts at 50% filling for Simulation 5 .............................................................45
12 Flow fronts at 50% filling for Simulation 6 .............................................................45
13 Flow fronts for 80% filling showing the formation of knit lines in Simulation 7 ................................................................................................................................46
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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
LIST OF FIGURES (Continued)
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 coefficient (0.175) simulation .............................................................................. 55
35 Fiber distribution function of element 29 in the control simulation, fiber orientation coeff. = 0.140 ..................................................................................... 56
36 Fiber distribution function of element 29 in the low fiber interaction coefficient (0.105) simulation .............................................................................. 56
37 Fiber distribution function of element 29 in the high fiber interaction coefficient (0.175) simulation .............................................................................. 56
38 Fiber distribution function of element 937 in the control simulation, fiber 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
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LIST OF FIGURES (Continued)
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
LIST OF FIGURES (Continued)
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
LIST OF FIGURES (Continued)
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, 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 .................122
82 (a) Center specimen (020920-1-16C), impacted with a 25 g flat projectile, exhibiting a typical fracture pattern, (b) graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results .................123
83 (a) Center specimen (020919-1-35C), impacted with a 160 g flat projectile, exhibiting a typical fracture pattern, (b) graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results .................124
84 (a) Center specimen (020919-1-32C), impacted with a 160 g flat projectile, exhibiting a typical fracture pattern, (b) graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results ................. 125
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LIST OF FIGURES (Continued)
Figure Page
85 Top specimen (020919-1-35T), 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 (T) with the fracture pattern superimposed over the results..................126
86 (a) Top specimen (020919-1-107T), impacted with a 160 g flat projectile, exhibiting a typical fracture pattern, (b) graphical representation of fiber orientation predicted in Cadpress showing the representative area of 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 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 ................. 129
89 (a) Center specimen (020919-1-61C), impacted with a 25 g flat projectile, exhibiting a typical fracture pattern, (b) graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results ................. 130
90 (a) Bottom specimen (020920-1-87T), 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 (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):
τσ rLc
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].
lr
2στ = (2)
Cdl
dl
⎟⎠⎞
⎜⎝⎛<
Cdl
dl
⎟⎠⎞
⎜⎝⎛=
Cdl
dl
⎟⎠⎞
⎜⎝⎛>
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 oC-1 Coefficient of thermal expansion (matrix)
αf 5 μm m-1 oC-1 Coefficient of thermal expansion (fiber)
Ts 120 oC 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 oC 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.
( ) umfj
cjfj
iiuc V
LLV
DVL σστσ −+
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−Σ+⎥⎦
⎤⎢⎣⎡Σ= 1
21 (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
2122
3 11
11log
21cos12
38
β
βββββ
πηo (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):
nnno a θη 4cosΣ= (10)
1=Σ nna (11)
( ) ( )fiVRr Χ= πlnln (9)
( ) mfffloc EVEVE −+= 1ηη (5)
( )⎥⎦
⎤⎢⎣
⎡−=
22tan1
LL
l ββη (6)
( )21
/ln22
⎥⎥⎦
⎤
⎢⎢⎣
⎡=
RrEG
D f
mβ (7)
( )υ+=
12m
mEG (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
442
0
41
4
3
2
1
4321
πθπθπθ
θ
−====
====and
aaaa (12)
( ) 8/3414101410 =+++=η (13)
πθθ
ππ
π 89cos10
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) ( )⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡+−=
DLV
DLUV
UVU ffdfmfc 6
12τ
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].
( ) ( )⎥⎥⎦
⎤
⎢⎢⎣
⎡+
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡ −+−=
DLLV
DLULV
LULLV
UVU fcfdcffcfmfc 6
132 τ
(16)
( )( )( ) ( ) mmfff
mftsfmR EEV
EETTυυ
αασ
++++
−−=
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 MPa0C-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
ff E
LU
2
2σ= (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 pT
T
PaaP
γη
&+=
( ) ( )( )
( )( )S
oS
SBo
SBT TTC
TTTTC
TTa−+
−−
−+−
=6.10186.8
6.10186.8log
(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
3hS = (21)
⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
+∂∂
−yT
xTc yxp ννρ (22)
zzy
yzx
xz ∂
∂−
∂∂
−ν
τντ (23)
2
2
zT
tTc 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
yxxxIC
t φνφφν
φνφνφψ
φφψγψ
&
yyxyyxxxICt ,,
2,
2, cossincossincossin1 φνφφνφνφνφ
φψ
ψγφ
++−−∂∂
−=∂∂
& (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 ,5.015.01
12 Φ−Φ+
=ξ
1=ξ (34)
1
22112 E
Eνν = (33)
2=ξwhereEE M ,1
12 Φ−
Φ+=
κξκ (30)
whereEE M ,1
11 Φ−
Φ+=
κξκ
F
F
dl2=ξ (29)
ξκ
+
−=
M
F
M
F
EEEE 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 oC Mold temperature (bottom) 60 oC Idle time (to place charge) 0 s Ambient temperature 20 oC 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 70oC and 60oC 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 Parameter Default value Units Fiber aspect ratio 2000 Elastic modulus 7.30E+04 N mm-2 Coefficient of linear expansion 3.00E-06 oK-1 Poisson’s ratio 0.22 Thermal conductivity 8.50E-04 W mm-1 oK-1 Specific heat capacity 0.84 J g-1 oC-1 Density 2.52 g cm-3
33
Table 4 Composite material parameters Parameter Default value Unit No-flow temperature 150 oC Volumetric fiber content 0.16 Thermal diffusivity 0.08 mm2 s-1 Thermal conductivity 0.17 W m-1 oK-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 Parameter Default value Units Poisson’s ratio 0.35 1.89E-03 oK-1 -1.54E-06 oK-2 -3.05E-08 oK-3 Elastic modulus 1.68E+03 N mm-2 -2.21E+01 N mm-2 oC-1 7.98E-02 N mm-2 oC-2 -4.15E-05 N mm-2 oC-3 Coefficient of linear expansion 3.41E+04 cm3 bar g-1 5.48E+04 cm3 bar g-1 oK-1 2.38E+08 bar 3.07E+04 bar 1.17E-07 cm3 g-1 0.11 oK-1 2.98E-03 bar-1 PvT data 3.37E+04 cm3 bar g-1 1.12 cm3 bar g-1 oK-1 1.38E+03 bar 2.91E+04 bar Crystallization temperature 1.34E+02 oC 0.02 oC 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 (60oC and 70oC for the male and female mold halves,
respectively); charge shape and location, which is shown in Figure 8; and the melt
temperature (230oC).
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 (30oC 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 30oC 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 60oC.
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 oK-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 12 Flow fronts at 50% filling for Simulation 6.
Figure 11 Flow fronts at 50% filling for Simulation 5.
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.
Figure 20 Force versus time for the control 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.
Figure 23 Force versus time for the control 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 law index (0.539) simulation.
Figure 26 Force versus time for the control 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
Graphical representation of 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 c b
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
Figure 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.
Graphical representation of an element indicating a close to random fiber orientation
Graphical representation of an element in which the main fiber orientation is indicated by the arrow
60
c
Figure 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.
b
a
Graphical representation of an element indicating a close to random fiber orientation
Graphical representation of an element in which the main fiber orientation is indicated by the arrow
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 law index (0.659) simulation.
Graphical representation of an element indicating a close to random fiber orientation
Graphical representation of an element in which the main fiber orientation is indicated by the arrow
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 30oC increase in mold
temperature (mold temperature = 90oC) decreased the force required for consolidation by
8%, whereas a 30oC decrease in mold temperature (mold temperature = 30oC) 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 60oC mold temperature simulation yielded the least warpage in the consolidated
component, followed closely by the 90oC mold temperature simulation (~10% increase).
In the 30oC 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.
65
LITERATURE REVIEW: BLUNT OBJECT IMPACT
Categorization of impact
A considerable amount of work has gone into studying transverse impact on
composite structures [34-41]. The authors of this work [34-41] have focused primarily
on continuous fiber composites with thermoset matrices. The work done in thermoplastic
matrices has been mainly been limited to PEEK, an aerospace material. Most of the
literature available pertains either to Charpy and Izod tests or low or high velocity
impact.
Charpy and Izod, which are pendulum-type test configurations, are constrained in
terms of specimen size, impact direction, and boundary conditions [5]. Moreover,
Charpy and Izod testing, especially in the notched configuration, force the specimen to
fail at a predetermined area rather than along the weakest plane. This could skew results
because of the highly anisotropic nature of LFTs. The velocity range, impactor
geometry, and impactor mass should reflect the type of threats a component may
encounter in service. In this case, a more representative test would be in the intermediate
velocity range with a blunt object impactor. This would simulate the effect of stones and
other debris a vehicle might encounter at highway speeds. In addition, the importance of
this test methodology lies not only in the characterization of debris hits, but also energy
dissipation and failure mechanisms under high loading rate.
It is important to define low, intermediate, and high velocities, as the use of these
terms tend to vary among authors [34]. Some authors contend that high velocity refers to
66
conditions resulting in complete perforation of the target. However, this phenomenon
can be readily observed in drop tower testing in which the maximum obtainable velocity
is typically less than 10 m s-1. For the remainder of this thesis, the term low velocity will
be reserved for velocities less than 10 m s-1 with large mass impactors and large target
deformations. The definition of high velocity impact will follow that of Abrate, in which
the ratio between the impactor velocity and the transverse compressive wave velocity is
greater than the maximum strain to failure in that direction [34]. Damage induced by
high velocity impact is typically introduced by the first few compression waves though
the thickness when the global plate motion has not been established [34].
Intermediate velocity will be considered to fall between the low and high velocity
regimes. The main difference is that, depending on the projectile mass, large deformation
may occur in the intermediate velocity range, particularly in the case of massive
projectiles, but may differ from low velocity impacts with regard to loading rate and
momentum effects.
Impactor mass and geometry. The impactor size, shape, mass, material, and angle
of incidence all have a strong influence on the response of the specimen [34]. A blunt
object will be defined as a large diameter projectile that will emulate the effects of debris
to characterize energy absorption upon impact. Jenq et al. [40] found that the momentum
transfer to graphite/epoxy targets by flat impactors was about four times greater than that
of a sharp or conically tipped impactor when the penetrator was fired at high velocity.
Cantwell and Morton [41] studied the effect of projectile mass on energy absorption in
composites while maintaining the impactor size and shape. It was found that varying the
67
projectile mass had a significant effect on the resulting damage. Cantwell and Morton
[41] suggest that lighter projectiles are more damaging to the overall load-bearing
capacity of the composite because the incident energy is dissipated over a very small area
immediately adjacent to the point of impact. This may or may not be the case with
intermediate velocity impact, depending on the target material, boundary conditions,
projectile shape, and projectile mass.
Impact Energy
The energy absorbed in the system, Eabsorbed, can be described as having two
components: the energy absorbed in creating damage in the specimen, Edamage, and the
energy absorbed by the system through vibration, heat, elastic response of the specimen,
and elastic behavior of the projectile or supports, ESL, equation (37):
where the Edamage term includes the energies associated with the specimen indentation,
matrix damage, fiber breakage, fiber debonding, and fiber pull-out. The energy absorbed
in the system can be equated to the energy put into the system, e.g. the kinetic energy
(KE) of the impactor shown in equation (38):
where m is the projectile mass, and Vo and Vf are the initial and residual projectile
velocities. The energy spent in the elastic response of the projectile and supports has
been shown to be small and will not be considered, simplifying the equation (38) to yield
equation (39) [35].
Eabsorbed = KE = ½ m Vo 2 - ½ m Vf 2 +ESL (38)
Eabsorbed = Edamage + ESL (37)
68
The highest impact energy is absorbed at the ballistic limit of the material in
which the projectile imbeds itself in the specimen. However, embedding a projectile in
thin specimens is unlikely, due to an inadequate area between the target and projectile for
fictional forces to act upon. Since the residual velocity of a non-penetrating projectile is
small, it will not be included in the energy balance. Therefore, the Vf term is not part of
the energy balance unless the projectile perforates the specimen and has a detectible exit
velocity. Otherwise, the initial velocity is assumed equal to the critical velocity, Vo = Vc.
This is similar to the V50 ballistic limit, which is defined as the projectile having a 50%
probability of completely penetrating the specimen at the critical velocity with a
deviation in velocity less than 40 m s-1 [34]. Given the low critical velocity of blunt
object impact, a more conservative deviation is appropriate. Since a standard test method
does not exist for blunt object impact, the critical velocity will be considered on the basis
of a standard deviation in velocity no greater than 10 m s-1, in which 50% of the
projectiles do not perforate the specimen.
Eabsorbed = KE = ½ m Vo 2 - ½ m Vf 2 (39)
69
EXPERIMENTAL PROCEDURE: BLUNT OBJECT IMPACT
Impact Test Apparatus
An understanding of LFT behavior while it undergoes high energy, high strain
rate impact is essential in promoting its use in automotive and other markets. A gas gun
was used to propel a variety of projectiles as shown in Table 12, with a velocity range of
approximately 45 m s-1 to 140 m s-1 to simulate the effects of blunt object impacts. The
wide range of projectile mass helped in determining velocity effects, while the blunt
projectile shape aided in characterization of perforation mechanisms.
Since an impact apparatus was unavailable, the design and construction had to be
undertaken before testing could proceed. The objective in the design phase was to
encompass velocities from approximately 10 m s-1 to 400 m s-1 for projectile masses
ranging from 2 g up to 500 g with a maximum projectile diameter of 38 mm. The test
Table 12 Blunt object impact projectile types Projectile Weight (g) Shape Material Dimensions (mm) Sabot 160 Flat Aluminum 37.71 (φ) x 50 Sabot 100 Flat Aluminum 37.71 (φ) x 50** Sabot 50 Flat UHMWPE 37.71 (φ) x 48 Sabot 50 Conical UHMWPE 37.71 (φ) x 55, 60° shoulder Sabot 25 Flat UHMWPE 37.71 (φ) x 37** Sabot 25 Conical UHMWPE 37.71 (φ) x 41, 60° shoulder** ** Denotes sabots in which material was removed from the center to reduce mass
70
apparatus required a high degree of flexibility so that a wide range of tests can be
performed.
Pneumatic propulsion or gas guns have been successfully implemented for such
tests in the past and are more prevalent than propellant propulsion guns firing standard
cartridges [34, 37, 38]. A driving force for this trend is the flexibility in directly varying
the projectile velocity by working fluid pressure, as opposed to propellant propulsion, or
center fire guns, where the powder charge is metered to alter the projectile velocity. In
addition, propellant guns fire projectiles that should be classified as high velocity.
Another drawback with chemical propulsion is that projectile types are limited in terms
of size, shape, mass, and materials. The largest round available in standard center fire
cartages is the 0.50 caliber Browning machine gun (BMG), which would not accurately
emulate the effect of blunt object impacts. Clearly, the logical choice for a test apparatus
is a gas gun, consisting of a high-pressure fluid source, regulator, pressure transducer,
pressure vessel, valve, barrel, velocity sensors, capture chamber, specimen fixture, and
projectile arrest.
Firing valve and pressure vessel. The firing valve is a critical component in the
test apparatus since it controls the working fluid flow. The crucial criteria in the valve
design are fast actuation, ability to operate at working pressures in excess of 1.70 MPa,
high flow rate, safe operation, and repeatability. Several candidates are commercially
available in the form of pneumatic or solenoid-actuated ball and butterfly valves.
However, a poppet valve similar to the type used in air rifles meets the aforesaid criteria
and can be manufactured in-house cost effectively. The disassembled poppet valve is
71
shown in Figure 47. The valve outside diameter is 45 mm and is sealed to the valve
guide by two rubber O-rings. The valve operates at a pressure range of 27.5 kPa and 1.72
MPa. The valve is guided by the center carrier and is held in place by a sear pin. The
valve body and center carrier guide the sear pin.
The pressure vessel limits the upper pressure range to approximately 1.70 MPa.
The pressure vessel was welded at North Dakota State University, Fargo, ND, and was
non-destructively tested with X-ray radiography at Midwest Industrial X-ray Inc., Fargo,
ND. Using a conservative yield strength for mild steel of 210 MPa, the factor of safety is
a
a
b
c
d
e
Figure 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.
72
five, based on an operating pressure of 1.70 MPa and the assumption of a thin-walled
pressure vessel, using equation (40) given by Shigley and Michke:
where σt,max is the maximum principle tangential stress, Pmax is the maximum working
pressure, di is the inside diameter of the pressure vessel, and t is the wall thickness [42].
Firing mechanism. Pulling the sear pin, which retains the valve and guide, opens
the valve. A four-bar linkage is used to gain mechanical advantage and is actuated by a
solenoid. Nitrogen, the working fluid in the pressure vessel, forces the valve open. The
solenoid is operated via remote control containing an ‘arm/safe’ two position toggle
switch and a ‘fire’ push button switch for safety. A mechanical safety is located on the
four-bar linkage, preventing the sear pin from being pulled prematurely. The firing
sequence requires that the mechanical safety be removed, and then, once the operator is
in a safe location, the ‘arm’ switch is thrown. A red LED indicates that the remote
trigger is hot. Finally, the fire switch is depressed, actuating the solenoid and opening the
valve.
Gas gun carriage and barrel. The valve, pressure vessel, and firing mechanism
are mounted on a carriage, allowing them to translate such that the barrel can be loaded
from the breach. The valve is coupled to the barrel with a union. The barrel is mild steel
seamless tubing, 4.57 m long with a 37.49 mm inside diameter and 51.31 mm outside
ttdP i
t 2)(max
max,+
=σ (40)
73
diameter with 50.8 μm true indicated roundness (TIR). A muzzle brake with sixteen
15.875-mm diameter holes + 15 μm was implemented 61 cm from the barrel end to
exhaust the working fluid before it enters the capture chamber and to reduce recoil. The
gas assembly and carriage are shown in Figure 48.
Pressure data acquisition. Since the velocity is particularly sensitive at lower
pressures, accurate and repeatable pressure readings are critical. A Rosemont® 2088
Smart pressure transducer was used for this task. The operating pressure range is from 0
- 1.034 x 106 Pa gauge (0 - 150 psig) with a resolution of 0.690 Pa gauge (1 x 10-4 psig).
Figure 48 Gas gun assembly on the carriage showing the pressure vessel, pressure transducer, firing valve, and firing mechanism.
74
The transducer can be readily interfaced with a personal computer serial port using the
VIATOR® RS 232 Interface. The transducer also has a digital readout for taking manual
measurements, thereby negating the need for a PC. It was calibrated for a pressure range
of 0 - 1034 kPa (0 - 150 psig) in accordance with the user manual.
Velocity data acquisition. Projectile velocity is a critical measurement in impact
testing. The energy of an impact is a function of the velocity squared, so precise
measurement is imperative. The most common way to measure projectile velocity is via
chronographs, which consist of two photoelectric sensors separated by a known distance
with a timer (chronograph) to record the event. When the first photoelectric sensor
detects an object, the timer is tripped and stopped when the second photoelectric sensor
detects an object. Knowing the time for a projectile to travel a given distance allows for
the calculation of velocity.
Two CED Millennium chronographs were used for velocity acquisition. An
independent German test lab reported that the CED Millennium chronographs were
within 0.2% (99.8%) of the true laboratory recordings [43]. The first chronograph was
placed just in front of the sample holder to measure the incident velocity and the other
chronograph just behind the sample holder to measure residual velocity. Both are
mounted on the outside of the capture chamber to prevent damage from the projectile or
impact debris. A light source is placed on the other side of the chamber with 25.7 mm (1
in) polycarbonate windows separating them as shown in Figure 51. Light diffusers were
placed in front of the windows between the light sources and chronographs to alleviate
variations in lighting. Four 150-W flood lamps were used for the light source.
75
Calibration Curves. Plotting the working fluid pressure versus the velocity for a
given projectile and fitting a curve to the plot establishes a calibration curve. A typical
calibration curve is shown in Figure 49 for a 100 g sabot. A curve, in this case a second
order polynomial, is fitted to the data, allowing calculation of the required pressure to
obtain a given velocity. The calibration curves have also shown that, if a consistent
projectile diameter is maintained, the velocity will become a function of only the
projectile mass and pressure. Hence, the velocity of a new projectile can then be
predicted based on previous testing.
Velocity2 = -0.004*(P)2 + 1.3*(P) - 3.2
R2 = 0.9986
Velocity1 = -0.005*(P)2 + 1.5*(P) - 9.0
R2 = 0.9989
30
40
50
60
70
80
90
100
110
30 50 70 90 110 130Pressure (kPa)
Vel
ocity
(m s-1
)
Chronograph 2 Chronograph 1
Figure 49 Typical calibration curves for pressure versus velocity for the incident (1) and residual (2) velocity chronographs shown for a 100 g sabot. A second-order polynomial was fitted to the data with an R2 value approaching one where y is the velocity (m s-1) and x is the pressure (kPa). The y error bars indicate a 5% deviation
76
Capture chamber. A capture chamber is a control volume with a large access
door, which provides for velocity data acquisition, the sample holder, and the projectile
arrest. The components were designed and assembled using Pro-E. The overall
dimensions are 33 cm by 33 cm by 183 cm. The Pro-E assembly is shown in Figure 50,
and the finished capture chamber is shown in Figure 51.
An important requirement of the chamber is to safely arrest the projectile after
impacting the specimen. All of the structural materials used in the capture chamber
constructions of 6.35 mm (1/4 in.) thick mild steel with the exception of a 12.7 (1/2 in.)
kinetic deflector, which serves as a bullet trap. LSDYNA 3-D was used to verify whether
the chamber wall could safely contain a projectile. A flat 12.7 mm (1/2 in.), 16 g,
fragment-simulating projectile was used to impact of the center of a fully clamped 30.48
mm by 30.48 cm (12 in. by 12 in.), 6.35 mm (1/4 in.) thick mild steel plate. The impact
was assumed normal to the plate to determine the minimum impact velocity required for
perforation of the chamber walls in a worst-case scenario. No plastic deformation was
assumed in the projectile. The first velocity examined was 400 m s-1, and penetration
occurred. The velocity was decreased until the ballistic limit was determined at
approximately 330 m s-1. Since a normal impact on the walls is not possible, the capture
chamber provides adequate protection as impact resistance increases substantially as the
impact angle of incidence increases. This concept was used in the design of the kinetic
deflector, which was used as the projectile arrest as shown in Figure 50. The design
insured that, regardless of where a projectile made contact with the arrest, it would be
safely contained. Thick, 12.7 mm cold-rolled 1018 steel was used for the kinetic defector
and was welded as shown in the schematic in Figure 52.
77
Figure 50 Pro/E drawing of the capture chamber with the access door removed. The windows are backlit for the photoelectric sensors in the chronographs
Kinetic Deflector Barrel Sample Holder Mounts
Figure 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.
a
b
cf
d
e
g
78
A heavy-duty, 1.52 m long hinge allows full access to the capture chamber door.
Six 1780 N (400 lbf) toggle clamps, placed on three sides of the chamber, secure the door
before firing as shown in Figures 51(c) and 51(d).
Sample holder and boundary conditions. The boundary condition for testing was
simply supported on four sides, with the supports 160 mm apart. The simply supported
boundary condition allowed for rotation and was chosen to emulate the support
conditions LFT would see in service. The supports allowed 25.4 mm of deflection.
Sample preparation. A minimum of five samples were tested for each
configuration in an attempt to accurately determine the critical velocity. Three equal size
Projectile Path
Figure 52 Pro/E drawing of the kinetic deflector showing the path of the projectile.
79
samples (470.4 cm2) were cut from each of the LFT plaques produced for blunt object
impact testing, and the tabs were removed. The samples are shown schematically (with
the tabs still in place) in Figure 53.
The average weight and standard deviation for the three samples was 206.32 g
(S.D.= 1.358 g), 219.8 g (S.D.= 1.822 g), and 225.27 g (S.D.= 1.056 g) for the bottom,
center, and top samples, respectively. This yielded an average areal density of 4.39 g cm-
2, 4.67 g cm-2, and 4.79 g cm-2 for the bottom, center, and top samples. The areal density
is of interest because impact energy absorption is often described in terms of it. The
Figure 53(a) and (b) (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.
600 mm
Top
Center
Bottom
240 mm
a b
80
variations in areal density are due to a thickness disparity caused by the lack of automatic
leveling on the compression molder.
Blunt object impact test matrix. A minimum of five samples was examined for
each of the 18 configurations in the test matrix outlined in Table 13.
The goal in the impact-testing phase was to establish whether a relationship
existed between the critical energy dissipation and impact mass, e.g. effect of projectile
velocity, the projectile geometry, and areal density.
The residual velocity due to rebound was measured using a Vision Research, Inc.
high-speed camera (Model: Phantom V5.0), at 14,000 frames second-1 with 40 μs
Table 13 Blunt object impact test matrix Projectile mass (g) Projectile geometry Areal density of specimen (g cm-2) 25 Flat 4.39 25 Flat 4.67 25 Flat 4.79 50 Flat 4.39 50 Flat 4.67 50 Flat 4.79 100 Flat 4.39 100 Flat 4.67 100 Flat 4.79 160 Flat 4.39 160 Flat 4.67 160 Flat 4.79 25 Conical 4.39 25 Conical 4.67 25 Conical 4.79 50 Conical 4.39 50 Conical 4.67 50 Conical 4.79
81
exposures. The maximum rebound velocity of a 100 g non-perforating sabot was
calculated to be approximately 8.4 m s-1. Since the residual velocity from a rebounding
projectile was small, it will not be included in the energy balance.
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MATERIAL PROCESSING
Celstran®PP-GF40-03 Processing and Material Properties
Test plaques, with the geometry shown in Figure 53 were fabricated at Southern
Research Institute, Birmingham, Alabama, using Celstran® PP-GF40-03, 40 wt. % long
glass fiber-reinforced, chemically coupled, heat stabilized polypropylene manufactured
by Ticona. The color number is AF 3001 (natural), stock number GL0175, and lot
number W7650. The starting fiber length was 25.4 mm. The plasticator and 3.56 MN
(400(US)-ton) compression molder used were manufactured by C.A. Lawton Co. The
idle time was 5 seconds with a 30 second cooling time. This gave a cycle time of
approximately 60 seconds. The system pressure in the plasticator was 1.25 MPa, the
backpressure 2.07 MPa, the screw speed 9-10 rpm, and the melt temperature at the knife
was 232°C.
The mold temperatures, checked every 40 cycles, remained constant at 54°C and
76°C for the top and bottom mold halves respectively. The plaque temperature at the
time of ejection varied from 87.5°C to 90.0°C and from 45°C to 51°C five minutes after
ejection for an ambient temperature of 31-32°C. Twenty-four trial plaques formed before
making a 160 plaque run to ensure the system was at steady state. The plaque ID is as
follows: (year, month, date, lot number, plaque number) e.g. (020919-1-#). The first lot
of plaques was manufactured on September 19, 2002. The mechanical properties are
given in Table 14 from the Ticona website [44].
83
Table 14 Material properties of Celstran® PP-GF40-03 adopted from the Ticona website [44]. Property Method Value Units Density ISO 1183 1,210 kg m-3
Tensile modulus (1mm/min) ISO 527-2/1A 7,900 MPa Tensile stress at break ISO 527-2/1A 100 MPa Tensile strain at break ISO 527-2/1A 2.0 % Flexural modulus ISO 178 8,000 MPa Flexural strength ISO 178 175 MPa Charpy notched impact strength at 23°C ISO 179/1eA 20 kJ m-2
84
RESULTS AND DISCUSSION: BLUNT OBJECT IMPACT
Blunt Object Impact Results
LFT panels (PP/40% E-glass) were impacted in the intermediate velocity range of
42.8 m s-1–140.4 m s-1, with projectile masses varying between 23.7 g–160.7 g, and with
both conical and flat configurations. This range in projectile velocity and geometry will
simulate the effect of blunt objects, such as rocks and debris, traveling at highway speeds
and greater. This work also provides insight into high-strain-rate energy dissipation and
failure mechanisms, such as a structural composite may undergo in the event on an
automobile accident.
A minimum of five samples were tested for each eighteen configurations in an
attempt to determine the critical impact velocity (or ballistic limit). Three test specimens
of LFT PP/40 wt. % E-glass, shown in Figure 53(a), were considered, representing fiber
orientation effects, in addition to unintentional variations in areal density. The results
will be discussed in terms of projectile mass, projectile geometry, and areal density,
respectively.
Effect of projectile mass. In the first phase of testing, the effect of projectile mass
was examined by determining the critical impact velocity for three test specimens, top
(areal density = 4.789 g cm-2), center (areal density = 4.674 g cm-2), and bottom (areal
density = 4.386 g cm-2). The goal in this phase of testing was to establish if impact
velocity had an effect on energy dissipation and failure modes. Impact mass variation is
85
an established technique in varying strain rate and often used in instrumented low
velocity drop-weight testing [44]. The critical impact velocity versus projectile mass
results are given in Figures 54, 55, and 56 for the top, center, and bottom specimens, and
the statistical significance is shown in Tables 23, 24, and 25.
Impact velocity alone does not describe the impact properties of a material, but it
can affect the energy dissipated in an impact. It is shown only to illustrate the variations
in impact velocity with projectile mass. In all cases examined, the critical velocity
decreased exponentially as a function of projectile mass. Material failure requires
energy, and the remaining results will be represented as such.
The impact energy versus projectile mass is given in the subsequent Figures 57,
58, and 59 for same samples, calculated from the data shown in Figures 54, 55, and 56.
For the range investigated, no clear relationships were observed between impact energy
and projectile mass. This is shown in Figure 60, where a linear regression was fit to the
mean of all the impact energy versus projectile mass data. The mean critical energy
dissipation data and the numeric results and analysis for the top, center, and bottom are
given in Tables 15, 16, and 17 as a function of projectile mass and shape. Variations in
energy dissipated for the three different samples are attributed to deviations in areal
density and fiber orientation effects. The effect of orientation will be discussed in detail
at the end of the chapter.
86
Table 15 Numerical results and analysis for the impact data on the top specimen Projectile Mean (J) S.D. (J) 95% C.I. (J)25 g Flat 190.2 6.5 5.7 25 g Conical 127.7 5.9 5.2 50 g Flat 178.4 21.1 18.5 50 g Conical 134.3 12.9 11.3 100 g Flat 153.8 12.5 11.0 160 g Flat 177.0 15.9 11.8 Flat projectiles 175.0 19.0 11.8 Conical projectiles 131.0 10.1 4.2
Table 16 Numerical results and analysis for the impact data on the center specimen Projectile Mean (J) S.D. (J) 95% C.I. (J)25 g Flat 201.9 30.5 26.8 25 g Conical 118.6 15.5 15.2 50 g Flat 174.9 26.4 19.6 50 g Conical 126.1 16.4 14.4 100 g Flat 141.6 5.7 5.0 160 g Flat 179.9 4.5 3.6 Flat projectiles 174.9 28.2 18.4 Conical projectiles 122.8 15.5 6.3
Table 17 Numerical results and analysis for the impact data on the bottom specimen Projectile Mean (J) S.D. (J) 95% C.I. (J)25 g Flat 157.0 14.0 12.3 25 g Conical 114.0 11.1 10.9 50 g Flat 146.4 20.5 13.4 50 g Conical 110.5 13.4 11.7 100 g Flat 143.0 7.9 6.9 160 g Flat 160.5 7.9 7.0 Flat projectiles 151.3 15.8 6.1 Conical projectiles 112.0 7.7 7.7
87
Numeric Results and Analysis of the Impact Data
Numeric analysis was conducted on the velocity data. Since the energy
dissipation is a function of the velocity squared, the standard deviation is greater for the
energy data as opposed to the statistic significance of the experimental velocity data, as
shown in Tables 15, 16, 17, 23, 24, and 25. The largest standard deviation in the velocity
data was 9.8 m s-1, which corresponds to a standard deviation in the energy data of 30.5 J
for the center specimen impacted with the 25 g flat projectile. This standard deviation is
actually greater than that of all the flat and conical projectiles for a given sample, e.g. the
deviation of the flat projectiles on the center specimen was 28.2 J (Table 16). Moreover,
the deviation for the flat projectiles on the center specimen was approximately 33%
greater than the next highest deviation, corresponding to the average deviation for the flat
projectiles on the top specimen, as shown in Table 15. Figure 61 illustrates the average
impact energy versus areal density for the flat impactors. Overall, the 25 g projectile
exhibited the highest energy dissipated upon impact, followed by the 160 g, 50 g, and 100
g projectiles, respectively. In a similar plot, Figure 62, for the conical projectiles,
virtually no influence of mass is observed.
Damage Characterization
The primary theory behind the deviation stems from observations of three series
of high-speed images capturing the impact event of a 100 g, flat-tipped projectile. Upon
closer examination of the impact event, a slight tilting of the projectile was noticed. This
is illustrated in Figure 63, which captures the projectile tilting just after impact. The
damage progression is also shown at the end of the chapter via high-speed imagery in
88
Figures 64 and 65. Another point of interest noted from the high-speed images is that the
impact phenomenon exhibited characteristics of both low and high velocity.
The first impact event captured was below the critical velocity, resulting in no
visible damage. In the other two image series, where the impact occurred at close to the
critical velocity for the 100 g flat projectile, incipient damage was observed before global
plate motion was established. This is a characteristic of high velocity impact. Then, as
momentum effects took over, a large global displacement was observed (approximately
25 mm), an attribute of low velocity impact. The specimen actually met the back of the
sample support because it was only simply supported on two sides in order to allow for
observation of the event.
Damage began at the first point of contact on the target, which resulted in a shear
plug or punch-though failure. This is thought to be a result of an increase in contact
stresses at the point of impact due to a decrease in the contact area of the projectile. All
samples impacted with the 100 g projectile were impacted under the exact test
configuration, and all data show a marked decrease in energy dissipation. The gas gun
was realigned before further testing was carried out, and the impression left by
subsequent impactors did not indicate projectile tilting. A typical impactor impression
for an oblique impact is shown in Figure 66(a), and a normal impact impression is shown
in Figure 66(b).
A marked increase in contact stresses is also thought to be responsible for a
decrease in energy dissipation for the conical projectiles, discussed in the next section. In
cases where the projectile impacted normal to the specimen, damage is thought to initiate
at weak planes parallel to areas of high fiber orientation or in areas where fiber clumping
89
occurs. Other factors that may have contributed to data deviation are impactor material
properties and inconsistencies in the impact response of test specimen. Abrate noted that
the elastic material properties of the impactor could affect the perforation energy, e.g. that
higher modulus materials result in higher contact stresses due to a decrease in elastic
deformation during the onset of damage [34]. This is, of course, assuming that there is
no plastic deformation of the impactor. Since two different materials were used in the
mass affect study, UHMWPE and aluminum, a decrease in energy dissipation would be
expected in the case of the higher modulus aluminum projectile. The standard deviation
is too large to make any conclusions as to whether the impactor material type played a
significant role in energy dissipation.
Variations in data were most likely caused by irregularities in the impact response
of test specimens. Although great care was taken in consistently impacting the same area
of all the specimens, sample shifting is impossible to control in the case of a simply
supported sample. In addition, with the current sample holder, there is no way to
accurately insure even clamping pressure, especially with variations in sample thickness
and process-induced warping. Both factors may have led to variations in the impact
response of the target. After impacting a specimen, the line of support at the four support
areas leaves an imprint. Variations in the imprint were noted, although attempts to
minimize this were unsuccessful and may have influenced the energy dissipation.
Effect of projectile geometry. In the preliminary testing of the flat impactors, it
was surmised that inadvertent projectile tilting affected the energy dissipation of the
sample. It is thought that this marked decrease in energy stems from an increase in
90
contact stresses at the point of impact. As one would expect, a sharp or conically tipped
projectile would also result in a substantial decrease in perforation energy, in contrast to a
normally impacting flat projectile. Projectile mass seemed to play even less of a role in
the study of conically shaped projectiles, whose results exhibited a greater statistical
significance than the flat-shaped projectile study. If contact stress plays a dominant role
in sample perforation, it would follow that less deviation would occur in conically shaped
projectiles in which projectile tilting would not adversely affect the contact area.
Both projectile geometries inflicted planar cracking of the specimens upon
impact. Damage from flat projectiles initiated along the periphery of the impact area and
propagated radially along two or three planes, away from the area of initial damage.
However, specimens impacted with conical projectiles exhibited a higher degree of crack
branching. Damage from conical projectiles began at the point of initial contact,
subjecting the specimen to high local contact stresses. It is possible that crack branching
results from the increased fiber strain energy at the point of contact for samples subjected
to impact with conical projectiles. When the fibers fracture, the release of strain energy
is greater than the energy required to create a single crack plane. The crack must
bifurcate in order to dissipate excess energy.
Neglecting projectile mass affects and plotting projectile geometry as a function
of energy dissipation and areal density, an increasingly linear trend develops. Figure 63
illustrates this proclivity in which a linear regression was fit through the mean of the data
for the flat and conical projectile geometries, resulting in R-squared values of 0.93 and
0.97 respectively. The mean numeric data is reported next to the respective data set,
Figure 67. On average, a decrease in critical energy dissipation for the bottom, center,
91
and top specimens was approximately 26% (areal density = 4.39 g cm-2), 30% (areal
density = 4.67 g cm-2), and 25% (areal density = 4.79 g cm-2), respectively, when
subjected to impact by conically tipped projectiles.
Areal density effects. It is common practice to report impact data as a function of
areal density, or weight area-1, for continuous fiber-reinforced composites. This was also
done in the case of the LFT specimens, shown in Figures 61, 62, and 67. Variations in
the energy dissipation of each of the samples were first attributed to the variations in
areal density, especially considering the expected linear increase in energy dissipation.
However, in the post mortem examination of the impacted specimens, similarities
between the fracture patterns of the three different samples were qualitatively established,
suggesting that a common failure mechanism might be at play.
Fiber orientation effects. Thomason and Vlug [6] surmised that a linear
relationship exists between tensile and impact strength. As the ultimate tensile strength
increases, the impact strength increases. Since tensile strength is a strong function of
fiber orientation, as shown in Figure 4, impact strength would be expected to follow
similar trends. No known models of impact strength as a function of discontinuous fiber
orientation exist, and current models for uniaxially aligned fibers, Figures 5 and 6, have
not been well documented [6]. Intuitively, fracture seems most likely to follow the
weakest plane, e.g. the plane perpendicular to the main fiber orientation. This type of
failure was seen in sections taken from the specimens representing typical failure modes,
shown in Figure 68 using scanning electron microscopy (SEM). The SEM images were
92
taken normal to the fracture surface, as in Figures 69-78. A simplified illustration of
what may be occurring is shown in Figure 79, which shows a theoretical transverse view
of fiber orientation and fracture path. The impact occurs at the top of the illustration and
follows the plane with a higher degree of fiber orientation. As the crack propagates,
energy is dissipated though fiber debonding, fiber pull-out, fiber breakage, and matrix
fracture. The crack will continue to propagate until the energy for fracture is spent or the
crack is blunted by fibers oriented perpendicular to the fracture path.
Micrograph analysis
SEM analysis of the impacted LFT sample fracture surface revealed that the
predominant modes of failure where fiber debonding/pull-out, fiber fracture, fiber-matrix
pull away and matrix fracture, as in Figures 69-78. It is difficult to discern the
difference between fiber fracture and fiber pull-out in discontinuous fiber composites.
Upon close examination, part of the fiber/matrix interfacial surface can be seen where the
fiber fractured and pulled out, as in Figure 71. This type of fracture also appears in
Figures 70-72, 74, and 76-78. Fiber pull-out is evident in every micrograph.
Fiber pull-out occurs when the interfacial stresses at the fiber-matrix interface
exceed the interfacial strength, causing the fiber to debond from the matrix. The impact
load is carried by the interfacial friction force imposed on the fiber from the matrix and
through matrix cracking. The magnitude of the interfacial friction is a function of the
debonded fiber surface roughness, the fiber length, and the radial stresses on the fiber
imposed by thermal contraction. The thermal contract results from thermal mismatch
between the fiber and matrix at processing temperature and test temperature.
93
As the test temperature decreases, e.g. increasing the thermal gradient, the radial
stresses increase. The surface roughness of the fiber is mainly dependent on chemical
coupling and fiber wetting at the fiber-matrix interface. Fibers sized for the matrix
exhibit increased chemical coupling though an increase in fiber wetability. The
debonded surface of a properly sized fiber is typically rough in appearance when viewed
at sufficient magnification.
If the fiber is above critical length, fiber breakage must occur for the fiber to pull-
out. This phenomenon, known as fiber fragmentation, occurs when the interfacial
stresses exceed the fiber strength. This is likely to have occurred in the impacted LFT
samples. However, it is not easy to characterize the phenomenon without low fiber
loading in a transparent matrix, clearly not the case with the samples examined.
Three possible modes of failure appear in the matrix: brittle fracture, crazing-
tearing (stress whitening), and separation of fibrils, as in Figures 71, 72, and 74-76. A
smooth fracture surface indicates brittle fracture, as in Figures 71 and 72. This was the
most common failure mode seen in the SEM micrograph analysis. The matrix fails in a
brittle manner because the fiber reinforcement inhibits large matrix deformations.
Crazing-tearing, indicated by the white areas in the micrographs shown in Figures 70, 71,
and 73, is also common in thermoplastic matrices subjected to strain. The ductile pulling
of fibrils, as in Figures 76 and 77, also indicates a brittle failure. No attempt was made to
quantify the matrix failure modes. The contribution of energy dissipation from matrix is
typically small in contrast to the reinforcement.
94
Correlation Between Predicted Fiber Orientation and Impact Failure Mode
The failure mode of discontinuous fiber-reinforced composites subjected to
impact differs from the failure mode of laminated composites, both in appearance and
damage mechanisms. Laminated composites subjected to transverse impact usually
exhibit damage variation though the thickness, e.g. delamination. The delamination
usually grows in area through the thickness (Christmas tree pattern or conical pattern),
toward the tensile face of the impact specimen [34]. This damage mechanism contributes
a significant amount of impact energy dissipation. Conversely, discontinuous fiber-
reinforced composites do not have a laminated architecture and dissipate energy through
planar cracking, as in Figures 66, 68, and 80-90. As shown before, the planar cracking
appears to advance along areas with preferential fiber orientation. Since it is not practical
to quantify the fiber orientation along the entire fracture surface of the specimens, an
attempt was made to correlate the fracture path with the fiber orientation predicted in the
Cadpress control run simulation.
The control run simulation used material and process parameters closest to those
used to produce the LFT tab plaque specimens. The parameters are outlined in Tables 2-
5. One noteworthy assumption was a random pre-orientation of the charge. Matrix burn
off revealed some preferential orientation in the charge roughly parallel to the extrusion
axis. However, a quantitative analysis of the fiber pre-orientation in the charge is
difficult, so it was assumed to be random.
Assuming that the control run simulation provided a reasonably accurate
representation of the fiber orientation, one would expect to see a correlation between
fiber orientation and the fracture path. Macro photos were taken of representative
95
specimens exemplifying typical fracture patterns. The fracture path was traced using
free-form sketch and grouped to a frame around periphery of the specimen. The aspect
ratio of the trace was maintained and superimposed over the respective area from the
fiber orientation predication. This is shown in Figures 80-91 for both flat and conical
impactors. The graphical representation of fiber orientation is described in Figures 30,
and 44-46.
The fracture pattern correlates well with the planes of high or preferential fiber
orientation predicted in the control run simulation. In addition, it appears that cracks may
have a tendency to advance along areas where an abrupt change in local fiber orientation
occurs. This is shown in Figures 80-91; however, it was not confirmed experimentally.
The abrupt changes in local fiber orientation may also be a mechanism for crack blunting.
Understanding the correlation between LFT failure mechanisms and the predicted
fiber orientation can aid engineers in component and process design. Because of the
strong off-axis effect from fiber orientation, tensile strength and modulus are optimized
(in one direction) when the fibers are uniaxially aligned. If this was the case, the
component may actually be susceptible to impact damage along the uniaxially aligned
fibers. A random orientation would likely provide the highest impact strength by creating
a torturous path for crack propagation. More over, LFTs with a random fiber orientation
would also exhibit greater damage tolerance because of crack blunting.
96
Table 18 Numeric results and analysis of the velocity data for the top specimen Projectile Mean (m s-1) S.D. (m s-1) 95% C.I. (m s-1) 25 g Flat 124.4 2.5 2.4 25 g Conical 103.5 2.4 2.1 50 g Flat 84.2 4.5 4.0 50 g Conical 76.4 3.9 3.4 100 g Flat 56.0 2.3 2.0 160 g Flat 46.9 2.1 1.6
0
30
60
90
120
150
0 20 40 60 80 100 120 140 160 180Projectile Mass (g)
Vel
coci
ty (m
s-1)
25 g flat projectile 25 g conical projectile
50 g flat projectile 50 g conical projectile
100 g flat projectile 160 g flat projectile
Figure 54 Critical velocity versus projectile mass for the top specimen (areal density = 4.79 g cm-2) , showing the velocity as an exponentially decreasing function of projectile mass.
97
Table 19 Numeric results and analysis of the velocity data for the center specimen Projectile Mean (m s-1) S.D. (m s-1) 95% C.I. (m s-1) 25 g Flat 127.2 9.8 8.6 25 g Conical 97.8 6.6 7.5 50 g Flat 83.3 6.3 4.7 50 g Conical 72.9 4.9 4.3 100 g Flat 53.8 1.1 0.9 160 g Flat 47.3 0.6 0.5
0
30
60
90
120
150
0 20 40 60 80 100 120 140 160 180Projectile Mass (g)
Vel
coci
ty (m
s-1)
25 g flat projectile 25 g conical projectile
50 g flat projectile 50 g conical projectile
100 g flat projectile 160 g flat projectile
Figure 55 Critical velocity versus projectile mass for the center specimen (areal density = 4.67 g cm-2), showing the velocity as an exponentially decreasing function of projectile mass.
98
Table 20 Numeric results and analysis of the velocity data for the bottom specimen Projectile Mean (m s-1) S.D. (m s-1) 95% C.I. (m s-1) 25 g Flat 111.1 6.2 5.4 25 g Conical 97.9 4.9 4.8 50 g Flat 76.8 5.3 3.6 50 g Conical 68.2 4.1 3.6 100 g Flat 54.0 1.5 1.3 160 g Flat 44.7 1.1 1.0
0
30
60
90
120
150
0 50 100 150 200Projectile Mass (g)
Vel
ocity
(m s-1
)25 g Flat 25 g Conical
50 g Flat 50 g Conical
100 g Flat 160 g Flat
Figure 56 Critical velocity versus projectile mass for the bottom specimen (areal density = 4.39 g cm-2), showing the velocity as an exponentially decreasing function of projectile mass.
99
25
50
75
100
125
150
175
200
225
250
0 20 40 60 80 100 120 140 160 180Projectile Mass (g)
Ene
rgy
(J)
Figure 57 Effect of projectile mass, critical energy versus projectile mass for the top specimen.
Flat projectiles
Conical projectiles
100
Figure 58 Effect of projectile mass, critical energy versus projectile mass, for the center specimen.
25
50
75
100
125
150
175
200
225
250
0 20 40 60 80 100 120 140 160 180Projectile Mass (g)
Ene
rgy
(J)
Flat projectiles
Conical projectiles
101
25
50
75
100
125
150
175
200
225
250
0 20 40 60 80 100 120 140 160 180Projectile Mass (g)
Ene
rgy
(J)
Figure 59 Effect of projectile mass, critical energy versus projectile mass, for the bottom specimen.
Flat projectiles
Conical projectiles
102
25
50
75
100
125
150
175
200
225
250
0 20 40 60 80 100 120 140 160 180Projectile Mass (g)
Ene
rgy
(J)
bottom, flat impactor (average)bottom, conical impactor (average)center, flat impactor (average)center, conical impactor (aveage)top, flat impactor (average)top, conical impactor (average)
Figure 60 Energy (J) versus projectile mass (g) for the bottom, center, and top specimens with a linear regression analysis, fitted through the mean of each data set, indicative of the independent relationship between projectile mass (impact velocity) and the energy dissipation upon impact. The trend in decreasing energy dissipation in the flat and conical data sets is most likely due to a decrease in areal density and fiber orientation effects.
areal density
areal density
103
25
50
75
100
125
150
175
200
225
250
4.3 4.4 4.5 4.6 4.7 4.8 4.9Areal Density (g cm-2)
Ene
rgy
(J)
50 g flat tip projectile
25 g flat tip projetile
100 g flat tip projectile
160 g flat tip projectile
Figure 61 Energy (J) versus areal density (g cm-2), plotted as a linear regression fit through 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.
104
25
50
75
100
125
150
175
200
225
250
4.3 4.4 4.5 4.6 4.7 4.8 4.9Areal Density (g cm-2)
Ene
rgy
(J)
50 g conical tip projectile
25 g conical tip projectile
Figure 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.
105
Figure 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.
Punch through
50 mm
106
Figure 64 High-speed images of a BOI illustrating the onset of damage, K.E. 142.3J. High-speed image taken at 14,000 frames s-1 showing a 100 g flat-tipped projectile just prior to impact, exemplifying projectile tilting.
a
)
b
)
Figure 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. 142.3J.
107
Figure 66 Impactor impressions left on the target for a projectile tilted (a) and normal (b).
(a)
(b)
108
Figure 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. The results of 106 impacted samples are shown, which represent increasing areal density for the bottom, center, and top specimens, respectively, which illustrate the influence of impactor geometry. The linear regression for the flat and conically tipped projectiles is given in the top right of the graph with the respective R2 values.
175.0 J174.9 J
151.3 J
131.0 J
122.8 J112.0 J
Energy (Flat) = 63.2*(Areal Density) - 124.6R2 = 0.93
Energy (Conical) = 45.2*(Areal Density) - 86.5R2 = 0.97
25
50
75
100
125
150
175
200
225
250
4.3 4.4 4.5 4.6 4.7 4.8 4.9Areal Density (g cm-2)
Ene
rgy
(J)
bottom, flat impactor center, flat impactor
top, flat impactor bottom, conical impactor
center, concial impactor top, conical impactor
Conical impactors
Flat impactors
109
a
e
c d
b
f
Figure 68 Impacted samples showing the location of sections taken for SEM analysis. The respective samples are (a) 34T, (b) 38T, (c) 34B, (d) 39B(1) and 39B(2), (e) 33C, and (f) 1C. At least two representative samples from the impacted LFT panels were sectioned from each of the three locations- top, center, and bottom. The locations analyzed are indicated by the rectangular box.
110
Figure 69 SEM of sample 34B, taken normal to the fracture surface, showing the path of fracture following the main fiber orientation angle. The dominant failure modes are fiber pull-out, fiber breakage, and matrix fracture.
Impact direction
111
Figure 70 SEM image of sample 34B showing fiber pull-out and fiber breakage. The rough fiber surface indicates strong interfacial fiber-matrix bonding. A mixture of crazing-tearing and brittle fracture is evident in the matrix.
Fiber pull-out
Fiber breakage
112
Figure 71 SEM image of sample 39C showing fiber pull-out. Matrix failure appears to have a combination of crazing-tearing (stress whitening) and brittle fracture (smooth appearance).
Crazing-tearing
Brittle fracture
113
Figure 72 SEM of sample 1C showing fiber pull-out (fiber sliding) and fiber matrix pull away.
Impact direction
Fiber pull-out
Fiber-matrix pull away
114
Figure 73 Micrograph of sample 1C showing fiber pull-out lengths in excess of approximately 3 mm. Also, note again, a high degree of fiber orientation
Impact direction
115
Figure 74 SEM image of sample 1C showing fiber pull-out.
116
Figure 75 SEM of sample 34T showing a high degree of orientation and ductile pulling of fibrils. Fiber clumping also appears to be present.
Fibrils
117
Figure 76 Micrograph of sample 34T illustrating a brittle-matrix fracture with ductile pulling of fibrils.
118
Figure 77 SEM image of sample 38T normal to the fracture surface showing fiber pull-out and breakage.
119
Figure 78 SEM of sample 39C showing variations in fiber orientation through the thickness of the section, taken normal to the fracture plane.
120
Figure 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.
Fracture path
Fibers blunting crack propagation
Impact area
121
(a)
(b)
Figure 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.
122
Figure 81 (a) Bottom specimen (020920-1-63B), impacted with a 25 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.
(b)
(a)
123
Figure 82 (a) Center specimen (020920-1-16C), impacted with a 25 g flat projectile, exhibiting a typical fracture pattern, (b) Graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results.
(a)
(b)
124
Figure 83 (a) Center specimen (020919-1-35C), impacted with a 160 g flat projectile, exhibiting a typical fracture pattern, (b) Graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results.
(b)
(a)
125
Figure 84 (a) Center specimen (020919-1-32C), impacted with a 160 g flat projectile, exhibiting a typical fracture pattern, (b) Graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results.
126
Figure 85 (a) Top specimen (020919-1-35T), 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 the specimen (b) with the fracture pattern superimposed over the results.
(a)
(b)
127
Figure 86 (a) Top specimen (020919-1-107T), impacted with a 160 g flat projectile, exhibiting a typical fracture pattern, (b) Graphical representation of fiber orientation predicted in Cadpress showing the representative area of the specimen (b) with the fracture pattern superimposed over the results.
(b)
(a)
128
Figure 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.
(b)
(a)
129
Figure 88 (a) Bottom specimen (020920-1-22B), 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.
(a)
(b)
130
Figure 89 (a) Center specimen (020919-1-61C), impacted with a 25 g flat projectile, exhibiting a typical fracture pattern, (b) Graphical representation of fiber orientation predicted in Cadpress showing the representative area of specimen (C) with the fracture pattern superimposed over the results.
(b)
(a)
131
Figure 90 (a) Bottom specimen (020920-1-87T), 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 (T) with the fracture pattern superimposed over the results.
(b)
(a)
132
Figure 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).
(a)
(b)
Increasingly random fiber orientation
Higher degree of orientation
133
CONCLUSION: BLUNT OBJECT IMPACT
The effects of LFTs subjected to BOI were investigated as a function of projectile
mass and geometry. The average critical energy dissipated for PP/40 wt. % E-glass
(average areal density = 4.61 g cm-2) was 167 J and 121 J for the flat and conical
projectiles, respectively. The predominant energy dissipation mechanisms are fiber
fracture, fiber debonding, fiber pull-out, and matrix fracture.
For panels impacted by the flat-tipped projectile with normal incidence, e.g. full
contact of the projectile face with the sample, the limiting damage occurred by punch-
through (shear plug). The damage initiated around the periphery of the impactor as a
result of high transverse shear stresses. Assuming a uniform shear stress distribution,
failure occurred in areas with preferential fiber orientation tangent to the impact area.
Away from the impactor, the dominant failure mode occurred by simultaneous tearing
(planar cracking) across planes of preferential fiber orientation.
In the 100 g flat impactor study, the edge of the projectile made the first contact
resulting from a slight tilting upon or prior to contact. This consequently resulted in an
initial notch arising from increased contact stresses, followed by punch-through and
subsequent tearing. The increase in contact stresses decreased the critical energy
required for perforation. This is also thought to be the mechanism for a decrease in
energy dissipation for the conically tipped projectiles.
Energy dissipation (critical energy) for samples subjected to conical projectile
impact was approximately 27% less than for samples impacted by flat projectiles.
134
However, samples impacted by conical projectiles exhibited a higher degree of damage,
e.g. more fracture surface as a result of increased crack branching. This may be a result
of increased fiber-strain energy at the point of impact for samples impacted with the
conical projectiles. When the fibers fracture, the release of strain energy is greater than
the energy required to create a single crack plane, resulting in crack bifurcation in order
to dissipate the excess energy.
Impactor velocity did not result in any appreciable effects on the critical energy
dissipation in the specimens. This indicates that the material was not sensitive to the
loading rate in the range investigated. Neglecting projectile mass effects, and plotting
projectile geometry as a function of critical energy dissipation and specimen areal
density, a linearly increasing trend develops. In addition to areal density effects, fiber
orientation may also play a critical role in energy dissipation. The energy dissipation of
impacted LFTs appears to decrease as areal density decreases and as fiber orientation
increases. The degree to which this occurs was analyzed qualitatively in the control run
simulation.
The fracture pattern correlated well with the planes of high or preferential fiber
orientation predicted in the Cadpress control run simulation. The cracks have a tendency
to advance along areas where an abrupt change in local fiber orientation occurs. Abrupt
changes in local fiber orientation may also be a mechanism for crack blunting. This
indicates that components exhibiting a high degree of anisotropy, or abrupt changes in
fiber orientation, will be susceptible to impact damage. A random orientation would
likely provide the maximum impact strength by creating a torturous path for crack
propagation. More over, LFTs with a random fiber orientation would also exhibit greater
damage tolerance, due to crack blunting.
135
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