Fiber Jamming and Fiber Matrix Separation during Compression

Transcription

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© 2006 Carl Hanser Verlag, München
Wissenschaftlicher
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UniversitätsProfessoren der
Kunststofftechnik
Zeitschrift Kunststofftechnik
Journal of Plastics Technology
archivierte, rezensierte Internetzeitschrift des Wissenschaftlichen Arbeitskreises Kunststofftechnik (WAK)
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www.kunststofftech.com; www.plasticseng.com
eingereicht/handed in: 29.05.2006
angenommen/accepted: 19.06.2006
Alejandro Londoño-Hurtado, Prof. Tim Osswald
Department of Mechanical Engineering, University of Wisconsin, Madison
Fiber Jamming and Fiber Matrix Separation
during Compression Molding
Fiber jamming is perhaps the least understood defect in molding of polymer composites. This paper
presents a description of the problem, introduces a mechanistic model and a dimensional analysis
developed to predict fiber distribution in ribbed sections.
Autor/author
Alejandro Londoño-Hurtado, Prof. Tim Osswald
Department of Mechanical Engineering,
University of Wisconsin-Madison
1513 University Avenue
Madison, WI 53706
E-Mail-Adresse: osswald@engr.wisc.edu
londonohurta@wisc.edu
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Carl Hanser Verlag
Zeitschrift Kunststofftechnik/Journal of Plastics Technology 2 (2006) 4
FIBER JAMMING AND FIBER MATRIX SEPARATION DURING
COMPRESSION MOLDING
Alejandro Londoño-Hurtado, Prof. Tim Osswald . University of Wisconsin,
Madison.
Fiber jamming is perhaps the least understood defect in molding of polymer
composites. This paper presents a description of the problem, introduces a
mechanistic model and a dimensional analysis developed to predict fiber
distribution in ribbed sections.
In diesem artikel wird ein mechanitisches Model der Faser/Matrix-Entmischung
entwickelt und eine Ähnlichkeitsanalyse fur geripte SMC und GMT Bauteilen
presentiert. Faser/Matrix-Entmischung ist vielleicht einer der am wenigsten
verstandenem phenomenen in der Faserverbuntwerkstoffe-Verarbeitung.
1
Alejandro Londoño-Hurtado, Tim Osswald
Fiber Jamming
Compression molding of sheet molding compounds (SMC) and glass mat
reinforced thermoplastics (GMT) are common processes used to produce
lightweight inexpensive fiber reinforced parts, especially for the automotive
industry. During the manufacturing process, the material is squeezed and
forced to flow until the charge covers the whole mold cavity. This causes
material to flow around sharp corners and into areas that are difficult to access
by the molding compound, such as ribs and bosses. As the material is forced to
flow, the resin matrix is often squeezed out of the bed of fibers. This leads to
fiber density distributions throughout a part; Figure 1. depicts this behavior.
These variations affect the mechanical properties of the finished part as well as
their surface finish. Variations in fiber density within a part will lead to surface
waviness and defects in the finished product. Fiber-matrix separation is perhaps
the least understood and understudied effect in fiber reinforced materials
molding processes.
Figure 1:
Uneven fiber distribution in a compression molded part
Mechanistic mathematical models that simulate fiber flow have been used for
more than four decades. The work of Batchelor [1] and his slender body theory
can be highlighted as one of the precursors in the study of suspended particles
in fluids. Jeffery [2,3] and Tucker [4,5] provided the foundations for many of the
current models . In recent years, Brady et. al. [6-8] have also made important
contributions in this area, having significant influence in later works. Phan-Thien
et. al. [9] incorporated long range hydrodynamic interactions into Jeffery's
model. Schmidt et. al. [10] have done work for flexible fibers at low
concentrations. Simulations at high fiber concentrations are a matter of interest
for polymer processing. The work presented in this paper is part of an effort to
characterize the processing of fiber reinforced composites.
1 CHARACTERIZATION OF FIBER SUSPENSIONS
Fiber suspensions are classified according to the amount of concentration of
fibers in the matrix. A fiber suspension is said to be dilute if less than one fiber
on average is found in a spherical volume of diameter equal to the fiber length,
nL3 ≤ 1 , where n is the number of fibers per unit volume. A semi-dilute regime is
2
Alejandro Londoño Hurtado, Tim Osswald
Fiber Jamming
characterized by 1 < nL3 < r p and nL2 << 1 . Here L is the fiber length and r p is
the aspect ratio of a fiber of diameter D.
rp =
L
D
(1)
In the semi-concentrated regime, fibers are significantly disturbed by other
fibers during rotation and they can no longer rotate smoothly without crossing
through the excluded volume of another fiber [11].
A suspension is said to be concentrated when nL3 > r p . In this case, fibers are
assumed to be interacting with each other and the effect of mechanical contacts
becomes dominant. The presence of mechanical contacts can significantly
increase the stress in a suspension by changing fiber orientation as well as by
transmitting stress through contacting fibers.
For small aspect ratios, mechanical contacts are the main mechanism causing
orientational dispersion. Far field hydrodynamics starts playing a decisive role
for higher aspect ratios. As the fiber concentration is increased, it is likely that
contact and hydrodynamic forces will have a joint effect. At very high
concentrations, a state where each fiber has several mechanical contacts,
mechanical contacts will prevail over far field hydrodynamic interactions [12,13].
The number of fibers, any given fiber may interact with as it rotates, is called the
crowding factor N crowd [14]
N crowd =
2φcrit r p
2
3
(2)
Where φcrit is known as the critical concentration and is defined as one fiber, on
average, in the spherical volume with a diameter equal to the fiber length.
Above this concentration, fibers are not able to rotate without contacting other
fibers. The formation of fiber networks is determined by the combination of
processing parameters and material properties, which will be covered in the
next section.
2 FIBER NETWORK FORMATION
When a fiber suspension is driven by a flow, the fibers are subjected to viscous
and dynamic forces that cause them to bend. When the flow comes to rest, the
fibers try to regain their original unstrained shape. Depending on the
concentration, a fraction of the fibers will come in contact with other fibers and
they will come to rest in strained positions where forces will be transmitted from
fiber to fiber.
When a fiber is locked into a network in a strained configuration, it must
possess at least three contact points with other fibers [15]. These contact points
must be located on alternate sides of the fiber. At low concentrations, there will
3
Fiber Jamming
be some fibers that do not become entangled in this manner. Fiber network
formation and fiber jamming is governed by processing and physical
parameters. For a specific process, the effect of a certain parameter may vary
in magnitude or not have any effect at all, as is the case of magnetic effects in
compression molding. The following parameters have been identified to play a
role in fiber network formation [16]:
Colloidal forces: These forces are caused by the chemical characteristics of
the fibers and the suspending fluid; they are usually not taken into account
when modeling fiber motion in glass fiber composites.
Surface tension effects: These are due to entrained gas within a fiber
suspension. Bubbles of gas may appear in fiber suspensions due to mixing or
other processing factors. Bubbles stay in particle interstices and create an
effective attractive force between particles due to free surface effects.
Mechanical surface linkages: Its origin is in contacts involving irregularly
shaped fibers with surface protrusions. Also, small fibrous entities (fibrils) of the
fiber may extend out from the fiber surface. In this case, the fibrils of contacting
fiber surfaces may become mechanically entangled.
Elastic fiber interlocking: This is found when fibers form an elastic network.
Flowing fiber suspensions may experience sufficient viscous forces to cause
fibers to elastically deform from an equilibrium configuration. As the fibers
attempt to relax, they can become locked in elastically strained configurations
due to contacts with other fibers. The fiber surfaces experience friction forces
that are proportional to the normal force between fibers, and the normal force is
a function of the fiber flexibility
Flocculation: Occurs when a dispersion of fibers is dilute enough and fibers
tend to aggregate in groups or flocs. This process is known as flocculation and
only occurs if fibers interact.
Experimental studies [14] have shown that although N crowd is directly related to
flocculation, a high value of N crowd doesn't necessarily imply that flocculation
will take place [12]. Other parameters like r p and the viscosity of the matrix, are
also involved. For example, when the fluid's viscosity is increased, the value of
the crowding factor at which flocculation occurs is also increased.
3 MECHANISTIC ANALYSIS OF FIBER SUSPENSIONS
In order to study the fiber interactions occurring in the compression molding
process, a mechanistic mathematical model was used to predict the
configuration. These kind of models use the classical equations of motion,
combined with the momentum equations for fluid flow, to study the movement of
4
Fiber Jamming
the fibers in a suspension at any time from the start of the flow until it has
ceased. The following section describes the methodology used to model fiber
suspensions subject to a shearing flow.
3.1 SIMULATION METHOD
The simulation used in this work, models fiber suspensions as linked cylinders
with hemispherical end caps, connected by ball and socket joints as shown in
Fig 2. In the case of polymer processing, some assumptions and simplifications
are made without altering the accuracy of the results. As a first simplification,
fiber extensibility is neglected, since fiber length remains virtually unchanged in
polymer processing processes. Far field hydrodynamic interactions can be
neglected for high fiber concentrations since frictional forces dominate the flow.
Finally, the fibers are assumed as neutrally buoyant with no other external fields
applied.
The equations of motion for a fiber include the reaction forces between the
hinges and contact forces between fibers:
Nc i
Fi hyd + X i +1 − X i + ∑ FIKcon = 0
(3)
k
Where Fi hyd are the hydrodynamic drag forces, X i are the joint forces in the
hinges and FIKcon are the contact forces. The equation of momentum is,
Nc i
Ti hyd + Yi +1 − Yi + Lp i × [X i +1 + X i ] + ∑ Gik × Fikcon = 0
(4)
k
Figure 2:
Schematic diagram of a model fiber.
5
Fiber Jamming
Where Ti hyd is the hydrodynamic torque, Yi the joint torque and the third and
fourth terms are the torques exerted by the joint forces and the contact forces,
respectively. The term Gik is the distance from the segment center to the point
of application of the contact force.
The hydrodynamic drag force, Fi hyd , and torque, Ti hyd , are approximated with
the expressions for an isolated prolate spheroid with an equivalent ratio re ,
.
Fi hyd = 6πη o LAi .(U i∞ − r i )
(5)
Ti hyd = 8πηo L3 (Ci .(Ω ∞ − ωi ) + H i : E ∞ )
(6)
Where η o is the viscosity of the fluid, L is the length of the fiber, U ∞ is the fluid
.
velocity and r is the velocity of the center of mass of the segment. The terms
Ω ∞ and ω i are the ambient and segment angular velocities, respectively. The
vorticity of the fluid is E ∞ . Tensors Ai , C i and, H i are the resistance drag
tensors.
The restoring torques Yi are used to model different fiber flexibilities. Fibers can
bend and twist since they are composed by spheroids connected by hinges. If
these torques were not included in the equations of momentum, the fibers
would immediately bend at the joints with the start of the flow. Different
magnitudes of fiber flexibility can be modeled by changing the amount of these
torques. The expression for the bending and twisting torque is given by,
(
Yi = −k b (θ i − θ ieq )eib + 0.67(γ i − γ ieq )eit
)
(7)
Where θ ieq and γ ieq are the bending and twisting equilibrium angles. When a
fiber is not deformed, θ ieq = θ i and γ ieq = γ i , and the resulting torque is zero. The
constant k b is the bending constant of the fiber. A high k b means the fiber is
rigid while a low k b means the fiber is flexible.
For a known initial position of the fibers, it is possible to integrate in time to a
new particle configuration at a time t+dt and the system can be updated. Figure
3. shows simulation results for an initially randomly oriented fiber network
subjected to shear flow. The unit cell used, employed a periodicity condition,
where the fiber leaving one side of the wall enters through the opposite side.
The sequence of graphs in the figure demonstrates that the fibers tend to align
along the plane of shear.
This model works perfectly with dilute and semi-dilute fiber suspensions.
However, when the fiber concentration is augmented ,i.e., the suspension is
concentrated, it becomes harder to track fiber to fiber contacts and the fibers
are so packed that the simulation model can no longer correctly describe the
flow. Furthermore, there exists the possibility of the fibers overlapping if the time
step is too big. The simulation is then limited to very small time steps.
6
Fiber Jamming
Simulations where the fiber concentration by volume is more than 1 % become
impractical.
The neglection of the hydrodynamic effects in concentrated suspensions is
based in the idea that the fluid between fibers does not cause a hydrodynamic
effect [17,18]. The hydrodynamic force is based on the ideal situation where a
fiber of a given geometry is immersed in a free flowing fluid. This might be true
for dilute and semi dilute suspensions, where the fiber interactions are
minimum. However, in the case of a concentrated suspension, this is not the
case since fibers are constantly in contact with each other, and the interaction
with the flow is far from the ideal case. It has been suggested that for the case
of concentrated suspensions, the force of friction, the normal force and a
lubrication force are orders of magnitude greater than the hydrodynamic force.
The lubrication force replaces the hydrodynamic force since, in reality, there is
only a thin film of fluid that lubricates the movement between fibers [19,20]. The
following section presents a dimensional analysis created to evaluate the
relevance of each of the competing forces in the processing of fiber reinforced
composites.
Figure 3:
Fiber matrix simulation for a fiber concentration of 1%.
4 DIMENSIONAL ANALYSIS FOR COMPRESSION MOLDING
OF A RIBBED SECTION
Fundamental dimensional analysis was conducted on mechanistic models of
fiber suspensions to study the influence of processing variables on the final
quality of the part. Figure 4. shows a schematic of the compression molding of a
ribbed part. An upper platen is lowered with a force F which exerts a pressure p
7
Fiber Jamming
.
on the charge. The charge is squeezed at a closing speed h until the mold is
completely filled with a final flange thickness h.
Figure 4:
Schematic of compression molding of a ribbed part.
The fibers have a length L, area moment of inertia I, Young's modulus E and
diameter D.
The fiber bed has a permeability K which is expressed in terms of D'Arcy's Law.
Bakharev and Tucker [21] used this law to describe flow through a porous
medium. The flow of the resin through the fiber bed is modeled as one
dimensional flow of a Non-Newtonian fluid through a porous material,
⎛ K ⎞⎛ − dp ⎞
⎟⎟
V = ⎜⎜ ⎟⎟⎜⎜
⎝ η ⎠⎝ dy ⎠
(8)
K = 0.00025D 2φ −2.4
(9)
where V is the velocity of the resin, η the viscosity of the resin, D the fiber
diameter and φ the volume fraction of fibers. With a mold cover charge of
.
about 50% , the velocity V can be assumed to be equal to the closing speed h
of the compression molding machine.
The relevant parameters for the dimensional analysis are summarized as
follows:
.
Process variables: closing speed h , pressure p, mold closing force F,
average fiber distance δ o .
Geometric variables: fiber length L, fiber diameter D, flange thickness h, fiber's
area moment of inertia I.
8
Fiber Jamming
Physical or material properties: matrix viscosity η , permeability K and
Young's modulus of the fiber E.
It should be noted that the volume fraction, φ , is already a dimensionless
number. From the dimensional analysis, the following Π -groups are obtained:
Π1 =
Π2 =
Π3 =
L
I
(10)
1/ 4
D
(11)
I 1/ 4
h
I
(12)
1/ 4
.
Π4 =
Π5 =
ηh
(13)
EI 1 / 4
K
(14)
I 1/ 2
Π6 =
F
EI 1 / 2
(15)
Π7 =
p
E
(16)
The Π -groups can be rearranged to obtain the following dimensionless
numbers:
.
Π 4 Π1 Π 3
η h h 3L2
ℵ1 =
=
Π5
KEI
2
3
(17)
.
ℵ2 = Π 4 Π 3 =
3
η h h3
EI
Π1
L2
ℵ3 =
=
Π5
K
(18)
2
ℵ4 =
L4D 2
3
4δ o h 3
(19)
(20)
Each of these numbers have a physical significance. They can be expressed in
terms of D'Arcy's forces FD hydrodynamic forces FH and fiber bending forces
FB .
9
Fiber Jamming
The dimensionless number ℵ1 is the ratio between D'Arcy's and fiber bending
forces,
ℵ1 =
D' Arcy ' s Forces
Fiber Bending Forces
(21)
A value of ℵ1 less than one, is an indicator of fiber bending forces being greater
than D'Arcy's forces, leading to significant fiber matrix separation or fiber
jamming. When ℵ1 > 1 , the force needed to bend the fibers is lower than the
force needed to make the matrix flow through the fiber bed. In this case, fibers
will also be dragged into the rib, diminishing the effects of fiber matrix
separation. The higher the values of ℵ1 , the less the chance of fiber matrix
separation. Figure 5. shows the behavior of ℵ1 for different fiber concentrations
and different fiber diameters. The graph shows that for a given fiber
concentration, lower fiber diameters have higher ℵ1 . In other words, fibers with
lower diameter require less bending force to flow into the rib and decrease the
chance of fiber matrix separation.
Figure 5:
ℵ1 Vs. φ for different fiber diameters.
10
Fiber Jamming
Figure 6. shows the variation of ℵ1 with fiber concentrations for different resin
matrix viscosities. The higher the viscosity of a charge, the more difficult it is for
the charge to flow through the fiber bed. This explains why, for a given fiber
concentration, higher viscosities have higher values of ℵ1 . Figure 7. shows the
influence of the closing speed in the final part distribution on fiber matrix
separation. A higher closing speed increases the D'Arcy forces, dragging the
fibers into the ribbed section, and therefore reducing fiber matrix separation
effects.
The dimensionless number ℵ2 is the ratio between hydrodynamic forces and
fiber bending forces. The dimensionless number ℵ3 is the ratio between
D'Arcy's forces and hydrodynamic forces,
ℵ2 =
ℵ3 =
Hydrodynamic Forces
Fiber Bending Forces
D' Arcy ' s Forces
Hydrodynamic Forces
(22)
(23)
A high value of
ℵ2 is indicative of hydrodynamic forces prevailing over
bending forces. This is usually not the case in compression molding, since the
fiber bending forces are orders of magnitude higher than the hydrodynamic
forces. Figure 8. shows the the behavior of ℵ 3 versus fiber concentration for
different fiber diameters. It can be observed that D'Arcy's forces are orders of
magnitude higher than hydrodynamic forces. Only for very low fiber
concentrations, hydrodynamic forces play an important role. For a given fiber
concentration, a smaller radius means a lower hydrodynamic force and
therefore higher ℵ 3 .
The dimensionless number ℵ4 is the ratio between lubrication forces and
hydrodynamic forces.
ℵ4 =
Lubrication Forces
Hydrodynamic Forces
(24)
Figure 9. shows the dimensionless number for different average fiber
separations. At low fiber concentrations, the hydrodynamic forces dominate the
lubrication forces. As the fiber concentration increases, the lubrication forces
start playing the dominant role, to the point that hydrodynamic forces can be
neglected. These results are in accordance with the observations made in
experimental results [18,19] and raise the possibility of simplifying the
simulation algorithm.
The suspension inter-fiber friction can be expressed in terms of known forces.
Typical Coulombic friction is given by
Ff = µFN
(25)
11
Figure 6:
ℵ1 Vs. φ for different resin viscosities.
Figure 7:
ℵ1 Vs. φ for different mold closing velocities.
Fiber Jamming
12
Fiber Jamming
Where Ff and µ are the force and the coefficient of friction, respectively. The
force FN is the normal force between contacting fibers. This normal force can
be assumed equal to the isotropic pressure applied to the charge times the
projected surface area of the fiber Af .
FN = PAf
(26)
Where
Af = DL
(27)
Expressing the pressure in terms of D'Arcy's forces and finding the ratio with
respect to hydrodynamic forces, a final dimensionless number is obtained.
Friction Forces
L2
ℵ5 =
=µ
= µℵ3
Hydrodynamic Forces
K
(28)
This result suggests that D'Arcy's and lubrication forces have the same
behavior when compared to hydrodynamic forces. In other words, Figure 8. is
equivalent to plotting ℵ5 versus fiber diameter without the dampening
introduced by the coefficient of friction µ . It is then concluded that friction forces
dominate over hydrodynamic forces at high fiber concentrations.
Figure 8:
ℵ3 Vs. φ for different fiber diameters.
13
Figure 9:
Fiber Jamming
ℵ4 Vs. φ for different fiber separations.
5 CONCLUSIONS
The dimensional analysis presented in this paper is aimed at verifying that
hydrodynamic forces may be neglected and at maintaining the physical
connection of an industrial process with a complex mathematical simulation.
With the help of dimensional analysis it is possible to refine the computer
simulations and optimize computational time otherwise spent in unrealistic
processes. Dimensional analysis supports and validates simulation results that
otherwise might lose touch with reality.
By conducting a simple dimensional analysis, it was found that at high fiber
concentrations, the effect of the hydrodynamic forces can be neglected and
replaced by a lubrication effect. This result is in accordance with the behavior
found in experiments. The importance of this result should not be overlooked
since for concentrated fiber suspensions, most of the problems encountered in
the simulations are caused by increasing fiber to fiber contact and tracking the
hydrodynamics of the flow. The lubrication simplification could lead to
successful simulations of highly concentrated fiber suspensions.
14
Fiber Jamming
6 REFERENCES
[1]
G. K Batchelor.
Slender-body theory for particles of
arbitrary cross-section in stokes flow.
Journal of Fluid Mechanics, 44 part
3:419.440, 1970.
[2]
G.B. Jeffery.
Proc. Roy. Soc., 111:110, 1926.
[3]
G.B. Jeffery.
The motion of ellipsoidal particles
immersed in a viscous fluid. Proc. Roy.
Soc., A102:161, 1922.
[4]
F.P. Folgar and C.
L. Tucker.
Orientation behavior of fibers in
concentrated suspensions. Reinf. Plast.
Comp., 3:98, 1984.
[5]
T.A. Osswald and
C. L. Tucker.
Compression mold filling simulation for
nonplanar parts. International Polymer
Processing, 5(2):79.87, 1990.
[6]
G. Bossis and J.F.
Brady.
Dynamic
simulation
of
sheared
suspensions. l. general method. Journal
of Chemical Physics, 80:5141.5154,
1984.
[7]
Ivan L Claeys and
John F. Brady.
Suspensions of prolate spheroids in
stokes flow. part 2. statistically
homogeneus dispersions. J. Fluid Mech.,
251:443.477, 1992.
[8]
Ivan L Claeys and
John F. Brady.
Suspensions of prolate spheroids in
stokes flow. part 3. hydrodynamic
transport properties of crystalline
dispersions. J. Fluid Mech., 251:479.500,
1992.
[9]
X.J. Fan, N. PhanThien, and R.
Zheng.
A direct simulation of fibre suspensions.
J.
Non-Newtonian
Fluid
Mech.,
74:113.135, 1998.
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Fiber Jamming
[10]
Christian F.
Schmidt, L.H.
Switzer, and D.J.
Klingenberg.
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of fiber properties and interfiber friction.
J. Rheology,44:781.809, 2000.
[11]
B. Herzhaft and E.
Guazzelli.
Experimental study of the sedimentation
for dilute and semi-dilute suspensions of
fibres.
Journal
of
Fluid
Mechanics,384:133.158, 1999.
[12]
L. Switzer.
Simulating Systems of Flexible Fibers.
Ph.D. thesis, University of WisconsinMadison, 2002.
[13]
R.R.
Sundararajakumar
and D.L Koch.
Structure and properties of sheared fiber
suspensions with mechanical contacts.
Journal of Non-Newtonian Fluid
Mechanics, 73:205.239, 1997.
[14]
R.J. Kerekes and
C.J. Schell.
Characterization of fibre flocculation
regimes by a crowding factor. Journal of
Pulp and Paper Science, 18:32.38, 1992.
[15]
D. Wahren.
Fiber network structures in papermaking
operations. In Paper Science and
technology ,the Cutting edge, 1979.
[16]
R.J. Kerekes, R. M.
Soszynski, and P. a.
Tam Doo.
The flocculation of pulp fibres. In
Transactions of the eighth fundamental
research symposium held at Oxford,
1985.
[17]
A. Moghaddam and
Staffan Toll.
Fibre suspension rheology: effect of
concentration, aspect ratio and fibre size.
Rheologica Acta, 45:315.320, 2006.
[18]
J. E. Manson K. A.
Ericsson, S. Toll.
The two-way interaction between
anisotropic flow and fiber orientation in
squeeze flow. J. Rheol., 41(3):491. 511,
1997.
[19]
Colin Servais,
Andre Luciani, Jan
Fiber-fiber interaction in concentrated
suspensions: Dispersed fiber bundles. J.
16
Fiber Jamming
Anders, and J. E.
Manson.
Rheol,43(4):991.1003, 1999.
[20]
Colin Servais,
Andre Luciani, JanAnders, and J.E.
Manson
Squeeze flow of concentrated long fibre
suspensions: experiments and model. J.
Non-Newtonian Fluid Mech., 104:165184, 2002.
[21]
A.S. Bakharev and
C. L. Tucker.
Predicting the effect if preforming on rtm
mold filling. In Society of Plastic
Engineers Inc., Technical Papers Volume
XLII,1996.
Keywords: Fiber jamming , fiber matrix separation, computer simulations,
dimensional analysis.
Contact:
Prof. Tim Osswald (osswald@engr.wisc.edu)
Alejandro Londoño-Hurtado (londonohurta@wisc.edu)
Department of Mechanical Engineering, University of Wisconsin, Madison.
1513 University Avenue, 317 Mechanical Engineering Building.
17

Fiber Jamming and Fiber Matrix Separation during Compression

Transcription

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