1. University of Miami
Master’s Project (MAE 751) – Micromechanical
Analysis of Hybrid Composites
Dr. Karkainnen
Omar Kashkash
12/14/2015

2. Abstract
A micromechanical analysis has been done for a hybrid composite model with
carbon and dyneema SK-60 fibers for military applications. The finite element
analysis was done using ABAQUS software to obtain stiffness and strength
properties. Different fiber combinations were studied for comparison.
Introduction
Hybrid composites have increased in popularity due to their unique features
that can be used to meet various design requirements in a more economical way
than conventional composites. For example, expensive fibers such as graphite and
boron can partially be replaced by less expensive fibers such as glass and Kevlar.
Hybrid composites can contain several different fiber types in a single matrix,
however, it has been found that a combination of only two types of fibers would
be most beneficial. Some of the specific advantages of hybrid composites over
conventional composites include balanced strength and stiffness, balanced
bending and membrane mechanical properties, balanced thermal distortion
stability, reduced weight and/or cost, improved fatigue resistance, reduced notch
sensitivity, improved fracture toughness and/or crack arresting properties, and
improved impact resistance.
A computational model is created using ABAQUS software that can easily be
modified to model hybrid composites of different volume fractions of
constituents. This saves the designer valuable time and resource as opposed to
experimental techniques that require fabrication of various composites with
various fibers, their volume fractions and matrix properties in hybrid composites
which are time consuming and cost prohibitive.
In this paper, a computational model is presented in which finite element based
micromechanics is used to obtain results of strength and stiffness properties.
Direct Micromechanics Method (DMM) is used for predicting strength, which is
based on first element failure method; although conservative, it provides a good
estimate for failure initiation [1 & 2].

3. Carbon Dyneema Hybrid Composites
Dyneema fibers are made from ultrahigh molecular weight polyethylene
(UHMWPE). In the process called gel spinning the very long molecules are
dissolved in a volatile solvent and spun through a spinnerette. In the solution the
molecules get disentangled and remain so after cooling in gel-like filaments (See
Figure 1). As the fiber is drawn, a very high level of macromolecular orientation is
attained and a high fiber with a very high tenacity and modulus is obtained (See
Figure 2). This fiber is now available as Dyneema SK60. It is characterised by a
parallel orientation greater than 95% and a high level of crystallinity (up to 85%).
This gives Dyneema SK60 its specific properties. A comparison with other fibers is
given below (See Table 1). On a weight-for-weight basis Dyneema is the strongest
fiber on the market. Its tensile strength is 2.7 GPa, which combined with a density
less than 1, gives a tenacity, or specific strength, of 30 g/den. Modulus is also very
high: 87 GPa and on a specific basis 1.000 g/den. Even higher values may be
expected in the future as research continues. A comparison of Dyneema with
other high performance fibrers is given below (See Figures 3 & 4). Figure 3 gives
specific strength versus specific modulus while Figure 4 is the stress/strain
diagram. Dyneema SK60 is advantageous in composites where weight saving is
important. Dyneema composites can be strong and stiff in tension and that light
weight composites can be made using this fiber. However, compression and shear
modulus will often be limiting when using only Dyneema fibers in a composite. So,
in general, hybrids will be used in which the strong points of the Dyneema fiber in
the construction will lower the weight and give high stiffness and high tensile
strength with a good dimensional stability. Composites made from carbon fibers
are extremely strong, stiff and lightweight structural materials. Therefore, such
composites are very suitable for application as aircraft skin material. However,
sheets from carbon composite skins are somewhat sensitive to the out of plane
loads caused by impact. Hybridizing with gel-spun polyethylene fibers is a well-
known way to improve the resistance against impact [3, 4, and 5]

4. Figure.1 Dyneema Gel Spinning Process
Figure.2 Macromolecular orientation of Dyneema SK60

6. The low compressive strength of Dyneema SK60 makes it unsuitable for structural
aerospace composites as a sole fiber ingredient. Compression resistant fibers like
glass or carbon are needed for such applications. However, Dyneema® fibers are
excellent for armor applications [6]. This is due to the combination of high tensile
strength, low density and intrinsic fiber toughness. This fiber toughness is
illustrated below (See Figures 5 & 6). Figure 5 shows a knotted filament. The
curvatures in the knot and the transverse deformation are impossible for other
high strength fiber types like glass, carbon or aramid fibers. Figure 6 shows
filaments that are tensioned over the edge of a sharp razor blade. Again, a sharp
curvature and extensive transverse deformation occur, allowing pressure re-
distribution over a larger distance along the blade edge. Thus the excellent cutting
resistance is explained. Both pictures illustrate the damage tolerance of
Dyneema® on micro-scale. Hybridization with a carbon fiber composite may add
damage tolerance to the composite on macro scale.

7. Results from [7] show that hybridizing the carbon composite with Dyneema®
fibers improves the resistance to impact considerably. The impact resistance
increases with increasing amount of Dyneema® fibers. Figure 7 shows a Scanning
Electron Microscope (SEM) picture indicating deformed, but unbroken Dyneema®
fibers together with broken carbon fibers, thus illustrating the contribution of the
damage tolerant Dyneema® fibers to the impact resistance of the hybrid
composite

8. Methodology
After a plain weave hybrid composite model has been created (See Figures 8 and
9), the following steps were done to run 6 unit strain cases in ABAQUS software
[8]:
Figure 8. Location and definition in RVE

9. Figure 9. Warp and Weft yarns
- In property module, define material properties of fiber, matrix, and
interface (See Table 2). Also, define local material coordinates to easily
interpret longitudinal stresses for both Carbon (Warp) and Dyneema (Weft)
fibers by setting the primary axis 1 along the direction of fibers (See Figure
10).
Table.2 Mechanical Properties of UD laminates (approx. 55% fiber in epoxy
laminates)
Engineering constants Carbon IM7 fiber Dyneema SK60 fiber
E1 (GPa) 136 46.6
E2 (GPa) 11.5 3.6
E3 (GPa) 11.5 3.6
V12 0.31 0.32
V13 0.31 0.32
V23 0.35 0.35
G12 (GPa) 5.19 1.1
G13 (GPa) 5.19 1.1
G23 (GPa) 4.26 1.374045802
Density of fibers 0.002 0.002
Matrix data

10. Young’s modulus (GPa) 3.5
Poisson’s ratio 0.35
Density 0.00125
Interface data
Density 0.00125
Young’s modulus (GPa) 3.5
Poisons ratio 0.35
Figure.10 Local Material Coordinates of fibers
- In mesh module, 3-D continuum elements can be hexahedral (bricks),
wedges, or tetrahedral. Whenever possible, hexahedral elements or
second- order tetrahedral elements should be used in ABAQUS (See Figures
11, 12, and 13). First-order tetrahedral (C3D4) have a simple, constant-
strain formulation, and very fine meshes are required for an accurate
solution.

11. Figure.11 Meshed yarns
Figure.12 Meshed Interface
Figure.13 Meshed Representative Volume Element (RVE)
- In load module, boundary conditions are defined for each unit strain case
with unit normal strain cases having four boundary conditions and unit

12. shear strain cases having three boundary conditions (See Figures 14 & 15,
Table 3, and Appendices).
Figure.14 Definition of each side in RVE
Figure.15 Degrees of freedom

13. Table.3 Boundary conditions for both unit normal strain and unit shear
strain cases
Unit normal
strain cases
front back right left top bottom
Case1 U*1=6 U1=0 U3=0 U3=0 U2=0 U2=0
Case2 U1=0 U1=0 U3=0 U3=0 U2=1.38 U2=0
Case3 U1=0 U1=0 U3=0 U3=6 U2=0 U2=0
Unit shear strain
cases
Case1 U1=0 ;
U2=1.38
U1=0 ;
U2=0
U3=0 U3=0
Case2 U1=0 U1=0 U3=0 ;
U2=0
U3=0 ;
U2=1.38
Case3 U1=0 ;
U3=6
U1=0 ;
U3=0
U2=0 U2=0
*Boundary conditions are in units of mm and only displacement degrees of
freedom were used in the simulation
- In job module, a job is made for each unit strain case.
- In visualization module, a representative volume element (RVE) analysis is
done to obtain forces at every node on a surface. The summation of these
forces divided by the area of the surface outputs stress on that surface. This
analysis is put into an EXCEL file to invert stiffness [C] matrix into
compliance [S] matrix from which elastic constants(stiffness properties) can
be found [9, 10, 11, 12, & 13].
Results
A comparison of stress strain graphs highlighting the first fiber to fail
longitudinally in each unit strain case while highlighting matrix failure if it occurs
before it. For both RVE’s, all the elements experience failure due to the full unit
strain case applied except for a very few that will be noted below. The five modes
of failure are fiber (longitudinal, transverse, and shear) and matrix (normal and
shear). Highlighting the first longitudinal failure for the fiber in either warp (x dir.)
or weft (z dir.) doesn’t represent composite failure because the other fiber have

14. not failed longitudinally yet. This method is called the first element failure
method which is conservative and important as a first step. Note in the graphs
that a single asterisk is for matrix failure and a double asterisk is for first
longitudinal fiber failure.
0.00749255, 107.8706198
CF, x dir. Longitudinal
Failure **
0.001659329,
23.88945026
Epoxy Normal Failure*
0.006382979,
91.89606593
Epoxy Shear
Failure*
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Hybrid Unit Strain Case 1:ϵx=1
0.007398066,
118.5163775
CF, x dir. Longitudinal
Failure**
0.00163606,
26.20953984
Epoxy Normal Failure*
0.006435986,
103.1039359
Epoxy Shear Failure*
-1000
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Unit Strain Case 1:ϵx=1

15. 0.281060364,
1326.310722
CF, x dir. Longitudinal
0.003257979,
15.37424933
Epoxy Normal Failure*
0.022169249,
104.6156504
Epoxy Shear
-400
-200
0
200
400
600
800
1000
1200
1400
1600
1800
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
HybridUnit Strain Case 2:ϵy=1
0.000325745, 1.887087512
CF, x dir. Longitudinal failure with
CF, x&z dir. Shear failure occuring before it
-500
0
500
1000
1500
2000
2500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Unit Strain Case 2:ϵy=1
0.016589003,
146.1145424
DF, z dir. Longitudinal
Failure**
0.00251411,
22.14406781
Epoxy Normal Failure*
0.010334482,
91.02524542
Epoxy Shear Failure*
-500
0
500
1000
1500
2000
-0.05 0 0.05 0.1 0.15 0.2 0.25
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Hybrid Unit Strain Case 3:ϵz=1

16. 0.007398066,
118.5163775
CF, x dir. Longitudinal
Failure**
0.00163606,
26.20953984
Epoxy Normal Failure*
0.006435986,
103.1039359
Epoxy Shear Failure*
-1000
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Unit Strain Case 3:ϵz=1
0.215422277,
14.62795312
CF, x dir. Longitudinal
Failure**
0.044343891,
3.011110897
Epoxy Normal Failure*
0.209176788,
14.20386182
Epoxy Shear Failure*
0
2
4
6
8
10
12
14
16
0 0.05 0.1 0.15 0.2 0.25
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Hybrid Unit Strain Case 4:γxy=1
0.209498869,
1153.121065
CF, x dir. Longitudinal
Failure**
and CF, z dir.
Longitudinal doesn't
fail
0.043324492,
238.4661268
Epoxy Normal Failure*
0.203323131,
1119.128643
Epoxy Shear Failure*
-200
0
200
400
600
800
1000
1200
1400
-0.05 0 0.05 0.1 0.15 0.2 0.25
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Unit Strain Case 4:γxy=1

17. 0.579489962,
31.95328161
DF, z dir. Longitudinal
Failure**
0.050107373,
2.762938279
Epoxy Normal Failure*
0.289629399,
15.97026757
Epoxy Shear Failure*
-5
0
5
10
15
20
25
30
35
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Hybrid Unit Strain Case 5:γyz=1
0.209498869, 1153.121065
CF, x dir. Longitudinal
Failure**
and CF, z dir. Longitudinal
doesn't fail
0.043324492,
238.4661268
Epoxy Normal Failure*
0.203323131,
1119.128643
Epoxy Shear Failure*
-200
0
200
400
600
800
1000
1200
1400
-0.05 0 0.05 0.1 0.15 0.2 0.25
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Unit Strain Case 5:γyz=1

18. Table.4 Allowable Composite and Matrix Strength Properties
Fibers -> Dyneema SK60 Carbon IM7
Longitudinal Stress 1068 1760
Transverse Stress 7.2 81.3
Shear Stress 15.9 0.48
Matrix -> Epoxy
Longitudinal Stress 49
Shear Stress 93
*units are in MPa
This table is used for comparing the stress values obtained from Abaqus as
a result of each of the unit strain cases with those from the literature and
0.031333452,
41.67619244
CF, x dir. Longitudinal
Failure
0.006344685,
8.438977635
Epoxy Normal Failure*
0.023111332,
30.74006399
Epoxy Shear Failure*
-100
0
100
200
300
400
500
600
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Hybrid Unit Strain Case 6:γzx=1
0.027056111,
1.965828857
CF, x dir. Longitudinal
Failure**
0.005675237 ,
0.412348458
Epoxy Normal Failure*
0.017247774,
1.253179853
Epoxy Shear Failure*
-5
0
5
10
15
20
25
30
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Stress(σfcellandτfcell(Mpa))
Failure Strain in the Material (ϵf and γf)
Unit Strain Case 6:γzx=1

19. plotting the stress strain graphs.
The uniaxial failure points for the warp(x dir.) and weft (z dir.) are defined
as the longitudinal far field stress that causes fiber failure in the warp from
unit strain case 1 and weft from unit strain case 3 for both RVE’s [14 & 15].
Table.5 Stiffness properties for both RVE’s
Engineering Constants C,C C,Dyneema
Ex (GPa) 16.01991262 14.39705033
Ey (GPa) 5.793144219 4.718953262
Ez (GPa) 16.02313277 8.807915952
Vxy 0.455247679 0.455636536
Vyx 0.455247709 0.149344901
0, 146.1145424
Hybrid
-107.8706198, 0
Hybrid
0, 118.5163775
Non-hybrid
118.5163775, 0
Non-hybrid
-200
-150
-100
-50
0
50
100
150
200
-150 -100 -50 0 50 100 150
WarpMPa
Weft MPa
Uniaxial Failure Points
Hybrid
Non-hybrid

20. Vyz 0.164650914 0.235034449
Vzy 0.164650774 0.438690752
Vzx 0.109435236 0.100312805
Vxz 0.109413166 0.163966889
Gxy (GPa) 5.504187539 0.067903623
Gyz (GPa) 0.072619677 0.055140354
Gxz (GPa) 0.072657481 1.33008621
Discussion
From table.5 and the stress strain graphs the first unit strain
comparison between RVE’s has values of Ex= 16 and 14.4 GPa’s, for the
non-hybrid and hybrid, respectively. The hybrid experiences first
longitudinal fiber failure perhaps because the dyneema allows the
carbon fibers to strain faster and thus fail faster due to the RVE plain
weave geometry.
Conclusion
In general, the amount of Dyneema® fibers will not be higher than 50%, usually
even lower. Very high amounts of Dyneema® fibers are reserved for composites
with armor functionality only. Such composites utilize the tensile strength and
damage resistance of Dyneema® fibers to a full extent, but exhibit hardly the
balance of properties of structural materials. Combination with carbon fibers
provides more balanced structural properties.
Composites allow trading of property directions by choosing relative amounts of
fibers in different orientations. The amounts of choices are increased, considering
that replacing carbon fibers by Dyneema® fibers allow trading of compression
strength and ILSS against impact resistance. Hybrid composites with carbon fibers
and Dyneema® fibers show considerably improved impact resistance over
composites with carbon fibers only .

21. Moreover, application of carbon Dyneema® hybrid composites can be considered
as an improvement option over pure carbon composites if the situations below
apply:
1. The structure is critical on impact resistance
2. The structure is mainly designed for tension load, and/or
3. The structure is a thin skin
Consequently, it is concluded that Carbon Dyneema® hybrid composites may be
attractive for structures where impact resistance is the limiting load case and
flexural resistance is important as well [16, 17, & 18].
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Appendices
Unit Normal Strain cases
Case 1:𝜀 𝑥 = 1

24. Case 2: 𝜀 𝑦 = 1

26. Case 3: 𝜀 𝑧 = 1

28. Unit Shear strain cases
Case 1: 𝜀 𝑥𝑦 = 1

30. Case 2: 𝜀 𝑦𝑧 = 1

32. Case 3: 𝜀 𝑥𝑧 = 1

34. Representative Volume Element (RVE)
Warp and Weft Yarns

35. Matrix
Matrix with Interface

36. Interface
Assemblage of yarns, interface, and matrix

37. Meshed yarns
Meshed Interface
Meshed RVE

38. Local Material Coordinates in Yarns
Skin material version of RVE