NASA/TM— 2006-214096
Composite Erosion by Computational Simulation
Christos C. Chamis
Glenn Research Center, Cleveland, Ohio
February 2006
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NASA/TM— 2006-2 1 4096
Composite Erosion by Computational Simulation
Christos C. Chamis
Glenn Research Center, Cleveland, Ohio
Prepared for the
SAMPE 2006
sponsored by the Society for the Advancement of Material and Process Engineering
Long Beach, CaHfomia, April 30-May 4, 2006
National Aeronautics and
Space Administration
Glenn Research Center
Cleveland, Ohio 44135
February 2006
Level of Review: This material has been technically reviewed by technical management.
Available from
NASA Center for Aerospace Information
7121 Standard Drive
Hanover, MD 21076-1320
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Available electronically at http://gltrs.grc.nasa.gov
Composite Erosion by Computational Simulation
Christos C. Chamis
National Aeronautics and Space Administration
Glenn Research Center
Cleveland, Ohio 44135
Abstract
Composite degradation is evaluated by computational simulation when the erosion degradation occurs
on a ply-by-ply basis and the degrading medium (device) is normal to the ply. The computational
simulation is performed by a multi factor interaction model and by a multi scale and multi physics
available computer code. The erosion process degrades both the fiber and the matrix simultaneously in the
same slice (ply). Both the fiber volume ratio and the matrix volume ratio approach zero while the void
volume ratio increases as the ply degrades. The multi factor interaction model simulates the erosion
degradation, provided that the exponents and factor ratios are selected judiciously. Results obtained by the
computational composite mechanics show that most composite characterization properties degrade
monotonically and approach "zero" as the ply degrades completely.
1. Introduction
Composites erosion is an important design requirement when composite structures are subjected to
erosion environments. A significant amount of research has been and continues to be conducted on that
subject. Some of that research is summarized in references 1 and 2. Reference 1 covers research up to 1986.
This is a multi author publication by specialists in all aspects of erosion. Reference 2 is another multi author
publication that covers tribology research up to 1993. This publication also covers various aspects of
tribology research that has been performed through August of 1992. These two publications provide a very
good orientation for beginners in composites erosion and some of the concepts described in the present
article. Specific aspects of erosion in injection moulded thermoplastic composites are described in
reference 3. The main feature in this reference is that erosion occurs on a composite slice (ply) at the time.
Friction and wear of several polymer composites are investigated experimentally in reference 4. The main
finding in that investigation is that the friction coefficient remains constant and does depend on which
surface the eroding device is acting. They found that for the various laminates that they tested the coefficient
of friction was about the same. They also found that the prodding mass depends on the pressure exerted by
the eroding device on the eroding surface. Barkoula and Karger-Kocsis performed solid particle tests (ref 5)
on composites with different fiber/matrix adhesion. They found that improvements in the interface bond
reduce substantially the eroded mass for the same testing conditions. The only simulation that was found is
that for thermal analysis by finite element for the heat transfer in sliding friction (ref 6). They found that the
finite element can be used in that sliding situation. An ASME publication (ref 7) describes micro and nano
tribology. This publication deals mainly with chemistry at the nano scale. The articles that were reviewed do
not deal with the composite mechanics simulation of the composite erosion and the composite properties as
the erosion proceeds. It became obvious to the author that an investigation that utilizes simulation of the
composite erosion was needed. Therefore, the objective of the present investigation is to use computational
composite mechanics in order to evaluate composite erosion and the respective composite degradation in
terms of its degraded properties. Specifically, the application of available computational methods ICAN
(ref 8) to evaluate composite degradation due to erosion. The other computational simulation method used
was the Multi Factor Interaction Model (MFIM) which can be used to simulate composite erosion when the
exponents of each factor and their respective ratios are chosen judiciously. The erosion considered is that as
the erosion progresses as the fiber volume ratio the matrix volume ratio and the fiber diameter decrease
simultaneously. The properties predicted then will be as each slice in a ply degrades due to the changes in
those variables.
NASA/TM— 2006-214096
/\ Longitudinal
(parallel)
Transverse
(anti-parallel)
o o o o o,
,00000/
10 00 00/
^ o o o 0/
0000/
0000/
,^„„„„„^„JOOO,'
/^o^o^o^o^oo 00 00 00 '
/^o^°^o O O O O O O O O O,'
''o n n o o 00 n o n o o '
^\ Shear
(normal)
Figure 1. — Three modes of erosion.
2. Fundamentals of Erosion
In this section we consider the fundamental modes of erosion which are illustrated in figure 1. As can
be seen in that figure, there are three modes of erosion which are taken to be consistent with those of
mechanical stress. The reason for this is that subsequent transformation of erosion will follow that of the
stress tensor. It is assumed that the longitudinal (erosion parallel to the fibers) will be the most resistant to
the eroding stress because the stiffness of the fibers is the greatest in that direction (fig. 1(a)). The second
mode of erosion is transverse to the fiber direction (fig. 1(b)). In this case, the fiber stiffness is about an
order of magnitude lower than the longitudinal and, therefore, the erosion will be about an order of
magnitude higher than the longitudinal (fig. 1(b)). The third mode of erosion is that due to shear stress as
depicted in figure 1(c). The resistance to erosion in this mode will be about proportional to the shear
stiffness of the laminate which is approaching two orders of magnitude lower than the longitudinal
stiffness. In this case, the erosion resistance will be about two orders of magnitude higher than the
longitudinal. The magnitude of the eroding stress depends on the applied normal force to that plane and
the plane's respective coefficient of friction. Data shows that the coefficient of friction is the same for all
three modes (1). Therefore, the eroding stress will depend on the force that is acting on that surface and
the stress developed there from.
3. Coefficient of Friction
It would be meaningful to have a coefficient of friction which is a function of the constituents in the
composite. Considering the fact (1) that the coefficient of friction is not direction dependent and it does
depend on the fiber volume ratio. Then a coefficient of friction can be determined by assuming that the
eroding force will strain and, therefore, erode fibers and the matrix in the same amount and create voids
as well. The coefficient of friction (|x) is generally defined as:
F„
M = -
(1)
where F„ represents the force normal to the surface and A is the area on which the force acts. The area
includes both the fiber and the matrix and any voids that may be present or created as a result of the erosion
process. Now, assuming an area of unit thickness (i) we have the volume is equal
NASA/TM— 2006-214096
V = At = Aft + A„jt + Ayt
where the subscripts/, m, and v denote fiber, matrix and voids respectively.
Dividing through by t we obtain
(2)
Divide through by A
j^ — -^ f ' ^fn ' -^v
AAA
Let Aj/A = kfi AJA = k^, and AJA = k^^ we obtain the following result:
Since the strain is constant due to eroding device, then the local stresses are proportional to the local
stiffness.
1
kf k
/ ^
This equation is the same as that in reference 1. Rearranging equation (8) yields:
1 _ \^mkf +\ifk^
Mc =
Hf n„j
(3)
(4)
(5)
(6)
fJ/ll =AfEfne; a^i = A^Eyne; Uy = AyE^e =o;{Ey = o)
The force on the eroding surface is
F^Afafn+A^a^n=Fnlic^N^^ (7)
Noting that the friction coefficient has the same units as the modules, and making the equivalent
substitution and neglecting the void term, we obtain the equation for the friction coefficient:
(8)
Mm kf + [If k„
Upon dividing by |X/
^f
-kf+k^ k +k
f \
(9)
(10)
(11)
y^f J
Equation (1 1) shows that for constant k^ and (|x,„/|Xy-), |Xc will decrease as i/- increases which is an
interesting result.
NASA/TM— 2006-214096
4. Composite Wear Due To Erosion
Composites will erode if there is an erosive device which degrades the composites. Experimental data
shows that the wear volume in an eroded composite is a function of several quantities as shown below (1):
Q^f{v,ii,,E,S
ins
Nzzkf)
(12)
Where Q is the eroded volume, Fis the eroding device velocity, |Xe is the composite friction
coefficient, Sfi2s is the composite shear strength, N^^ is the normal load, E = E^is the composite modulus
normal to the eroding plane, and kf is the fiber volume fraction in the composite. That volume of the
erosion includes (1) wear or fiber thinning, (2) matrix thinning or gauging that will cause fiber breaks or
fiber peeling. Two methods of solution will be pursued. (1) is the multi factor interaction model, and (2) a
heuristic method based on the physics of the problem.
5. Erosion Simulation by the MFIM
We can now express the degraded volume by applying the multi factor interaction module in
expanded form.
Qc_
Qi
1-
v_
\ei
/
M<
1--
eif
1-
^.
eif
^zzF
,_E.
Eel
£4
1--
en
'nis J
esf
1--
'.fF
ee
(13)
One disadvantage of MFIM is the selection of the exponents, e\ through e(,. A sample example of the
difficulty is illustrated in figure 2 where the non-eroded composite thickness is plotted versus a constant
value of mean ratio or a constant value of the exponents. In the first case the exponents are varying from
0.1 to 0.9 and in the second case the ratios vary from 0.1 to 0.9. The important observation in figure 2 is
that the remaining thickness erodes a lot faster at the early part of the erosion process. The MFIM results
0.7
If)
c
o
a:
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Constant exponent = 0.5
Variable ratio = 0.1 to 1.0
Constant
ratio - 0.5
Variable
exponent = 0.1 to 1.0
\ \ \
0.6 0.5 0.4 0.3 0.2 0.1
Variable mean or variable exponent
0.0
Figure 2. — Remaining ply thickness decreases rapidly with increases in
mean ratio or exponent.
NASA/TM— 2006-214096
for assuming a constant value of all the exponents of 0.5 and/or variable mean ratio are summarized in
table 1. It is seen in this table that the remaining thickness is QJQi = 0.0085, which is very low. The
sensitivities with respect to the remaining thickness are summarized in the last column of this table.
Another example is one with varying exponents and ratios simultaneously. The results are summarized in
table 2. It can be seen that the ratio value QJQi = 0.0026. Apparently a multitude of eroded values are
obtainable by using the MFIM. Another example of the inclusiveness of MFIM is summarized in table 3.
As can be seen, the ratio value QJQi = 0.9906. The corresponding sensitivities are listed in the last
column of that table. Experimental values range from to 0.005 |xm for normal erosion versus time
(ref. 1). Using this as an anchoring point, the value obtained in table 3 of 0.996 is compared to 0.024. The
0.024 value can be readily obtained with some manipulation of the exponents and the ratios in the MFIM.
The interesting point to be made is that the MFIM has many degrees of freedom which permit simulation
of any measured data irrespective of how the data was obtained.
TABLE 1
Term
Exponent
Factor Ratio
Relative to Q,
1
0.5
0.8
-0.0212
2
0.5
0.9
-0.0424
3
0.5
0.5
-0.0085
4
0.5
0.8
-0.0212
5
0.5
0.9
-0.0424
6
0.5
0.6
-0.0106
7
0.5
0.1
-0.0047
Note: QJQi = 0.0085
TABLE 2
Term
Exponent
Factor Ratio
Relative to Q,
1
0.6
0.8
-0.0212
2
0.8
0.9
-0.0424
3
0.5
0.5
-0.0085
4
0.4
0.8
-0.0212
5
0.7
0.9
-0.0424
6
0.5
0.6
-0.0106
7
0.9
0.1
-0.0047
Note: QJQi = 0.0026
TABLE 3
Term
Exponent
Factor Ratio
Relative to Q,
1
-0.6
0.8
2.9719
2
0.8
0.9
-7.9251
3
-0.5
0.5
0.9906
4
0.4
0.8
-1.9813
5
-0.7
0.9
6.9345
6
0.5
0.6
-1.2383
7
-0.1
0.1
0.1101
Note: QJQi= Q.996
6. Simulation by Computational Composite Mechanics
The simulation of the composite erosion by using computational composite mechanics is based on the
following assumption: "The eroded composite will occur on a ply-per-ply basis where the eroding device
degrades equal thickness of fiber and matrix." What is needed then is to simulate the erosion degradation
in the exposed ply first. Once this is done the erosion in subsequent places in the laminate can be
accomplished by following the same procedure that was for simulating the erosion degradation in the
exposed ply. The procedure to be described below is based on having available a computational
composite mechanics code whose micromechanics are based on constituent materials and fiber diameter.
NASA/TM— 2006-214096
fiber, matrix, and void volume ratios. The constituent properties for the simulation are listed in table 4 for
fiber and in table 5 for matrix. The results described below are for all the composite properties of a
uniaxial ply as it erodes from its pristine conditions to its end. The erosion is assumed to progress as the
eroding device erodes the fibers and the matrix in the plan as was described previously.
TABLE 4. AS-4 GRAPHITE FIBER PROPERTIES
TABLE 5. INTERMEDIATE MODULU
AND STRENGTH EPOXY MATRIX
Number of fibers
per end
Nf
10000
number
Filament equivalent
diameter
df
0.300E-03
inches
Weight density
Rhof
0.630E-01
lb/in**3
Normal moduli (11)
Efll
0.329E+08
psi
Normal moduli (22)
Ef22
0.199E+07
psi
Poisson's ratio (12)
Nufl2
0.200E+00
non-dim
Poisson's ratio (23)
Nuf23
0.250E+00
non-dim
Shear moduli (12)
Gfl2
0.200E+07
psi
Shear moduli (23)
Gf23
O.lOOE+07
psi
Thermal expansion
coef (11)
Alfaf 1 1
-0.550E-06
in/in/F
Thermal expansion
coef (22)
Alfaf22
0.560E-05
in/in/F
Heat conductivity
(ll)in/hr/in**2/F
Kfll
0.403E+01
BTU-
Heat conductivity
(22) in/hr/in**2/F
Kf22
0.403E+00
BTU-
Heat capacity
Cf
0.170E+00
BTU/lb/F
Fiber tensile
strength
SfT
0.430E+06
psi
Fiber compressive
strength
SfC
0.430E+06
psi
Weight density
Rhom
0.440E-01
lb/in* *3
Normal modulus
Em
0.530E+06
psi
Poisson's ratio
Num
0.350E+00
non-dim
Thermal expansion
coef
Alfa m
0.360E-04
in/in/F
Matrix heat conductivity
in/hr/in**2/F
Km
8.681E-03
BTU
Heat capacity
Cm
0.250E+00
BTU/lb/F
Matrix tensile strength
SmT
0.155E+05
psi
Matrix compressive
strength
SmC
0.350E+05
psi
Matrix shear
strength
SmS
0.130E+05
psi
Allowable tensile
strain
eps mX
0.200E-01
in/in
Allowable compressive
strain
eps mC
0.500E-01
in/in
Allowable shear strain
eps mS
0.350E-01
in/in
Allowable torsional
strain
eps
mTOR
0.350E-01
in/in
Void heat conductivity
in/hr/in**2/F
kv
0.225E+00
BTU
Glass transition
temperature
Tgdr
0.420E+03
F
(Scales: in = 25 mm; lb/in' = 6.41E-6 kg/m'; E+6 psi = 6.8 GPa;
J-in/hr/in^/°C; BTU/lb/°F = 4.19E3J/kg/°C; ksi = 6.89 MPa; °F -
E-6(in/in)/°F = 0.51E-6(cm/cm)/°C BTU-in/hr/in7°F = 0.07
1.82 °C)
7. Erosion Effects on ply Configuration
The ply configuration geometric affects are summarized in figure 3. The ply thickness is defined as
t i . The inter fiber distance is defined as 5 ^ . The ply fiber volume ratio is defined as kf, the matrix as k„
and the void as K. These geometric properties are coded in the computer code ICAN (ref 8). The erosion
affects on the ply thickness is illustrated in figure 4. The ordinate in this figure shows the remaining ply
thickness as the fiber volume ration decreases. It is observed in figure 4 that the thickness degrades
hnearly as the fiber volume ratio decreases. In figure 5 the remaining fiber diameter also decreases
hnearly as the fiber volume ratio decreases. The matrix volume ratio decreases nonlinearly as the fiber
volume ratio decreases as shown in figure 6. The void volume ratio increases nonlinearly as the fiber
volume ratio decreases, as shown in figure 7. It is interesting to note that the void volume ratio reaches
about 1.0, indicating that both the volume fraction of the fiber and of the matrix have completely
degraded. The inter fiber distance increases nonlinearly as the fiber volume ratio decreases as shown in
figure 8. It is interesting to note in figure 8 that the inter fiber distance increases about five times as the
ply approaches total degradation.
NASA/TM— 2006-214096
-Vo\6(kv)
Partial volumes:
Ply density:
Resin volume ratio:
Fiber volume ratio:
Weight ratios:
Ply thickness (S.A.):
Interply thickness:
Inter fiber spacing (S.A.):
Contiguous fibers (S.A.):
kf +k„j +ky =1
Pi =^fPf +km9m
km^i}-- K )/[l + (pm/p/ )(lAm " O]
kf^{\-k,)l[\ + (pflp„,)(\lXf-\)]
^/ +^m -1
t(, =l/27Vy df^n/kf
Ply^
■ '" ■ ■' ''••(•
Matrix (m)
bji =1/2 jT^/kf -2 df
kf =7i/4~ 0.785
Figure 3. — Micromechanics, geometric relationships.
i
Nf
T
H 8. h
■ Fiber (kf)
5^
5.0x10-2
0.5 0.4 0.3 0.2 0.1
Erosion decreases fiber volume ratio
Figure 4. — Erosion effects on ply thickness ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength matrix).
0.0
NASA/TM— 2006-214096
3.0x10^
E
CD
T3
i_
O)
c
'c
'nj
E
1.5
0.0
±
±
0.6
0.5 0.4 0.3 0.2
Erosion decreases fiber volume ratio
0.1
0.0
Figure 5. — Erosion effects on fiber diameter ([0/±45/902/±45/0]
as-grapfiite-fiber/intermediate modulus and strength matrix),
(in. = 25 mm).
0.5 0.4 0.3 0.2 0.1
Fiber volume ratio decreases with erosion
Figure 6. — Erosion effects on matrix volume ratio ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength matrix).
0.0
NASA/TM— 2006-214096
0.4 0.3 0.2
Erosion decreases fiber volume ratio
0.0
Figure 7. — Erosion effects on void volume ratio ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength matrix).
2.5x10-4
0)
o
c
B
T3
2.0
1.5
1.0
0.5
0.0
±
±
0.6 0.5 0.4 0.3 0.2
Erosion decreases fiber volume ratio
0.1
0.0
Figure 8. — Erosion effects on inter-fiber spacing ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength matrix),
(in. = 25 mm).
8. Thermal Properties Degradation
The micro mechanics equations that control thermal properties erosion degradation are summarized in
figure 9. These equations are coded in the ICAN computer code. The £ subscript denotes ply property
while the number subscripts denote directions. The ply longitudinal heat conductivity decreases hnearly
as the fiber volume ratio decreases as shown in figure 10. It is interesting to note in figure 10 that the
longitudinal heat conductivity approaches "0" as the fiber volume ratio approaches zero. The ply
transverse heat conductivity decreases initially nonlinearly, then levels off and remains insensitive to a
decreasing fiber volume ratio as shown in figure 1 1 . The thermal heat capacity remains relatively
insensitive as the fiber volume ratio degrades as can be seen in figure 12. The erosion degraded thermal
longitudinal expansion coefficient degrades nonlinearly with degraded fiber volume ratio as shown in
NASA/TM— 2006-214096
Heat capacity:
Longitudinal conductivity:
Q = — [kf pfCf + k^ p^ Cm j
Kai -kf^fn +f^mKm
/'-^ — ' — \ —
^ \ \ ^lVlatrix(m)
\ ^ Fiber (f)
^ Ply (i)
Transverse conductivity:
For voids:
Km (l - ^J^f JKm + -
KmJkf
1-Jkj(l-K^/Kf22y
K
K„
(i-V^)^„
J^myl^v
\-^{\-K^lK,)
m
Longitudinal thermal
expansion coefficient:
Transverse thermal
expansion coefficient:
o-m
kf afiiEfii + i„ a^ E„j
-III
a/22 = a/22 ^jkf + (l - 7^j(l + kf^in E f\ \ JE(x ip-m^'^m
Figure 9. — Composite micromechanics, thermal properties.
0.4 0.3 0.2 0.1
Erosion decreases fiber volume ratio
Figure 10. — Erosion effects on the longitudinal heat conductivity
([0/±45/902/±45/0] as-graphite-fiber/intermediate modulus and
strength matrix). (Btu-in./hr/in.2/T = 0.07 J-m/hr/m2rC).
0.0
NASA/TM— 2006-214096
10
0.25
0.20
o
o Q: 0.15
W o
In S
0.05 _
0.00
±
±
±
0.6 0.5 0.4 0.3 0.2
Erosion decreases fiber volume ratio
0.1
0.0
Figure 1 1 . — Erosion effects on transverse lieat conductivity
([0/±45/902/±45/0] as-graphite-fiber/intermediate modulus
and strength matrix). (Btu-in./hr/in.2/T = 0.07 J-m/hr/m2/°C).
0.3 r-
CD
o
to
Q.
CO
O
"cD
0.2
in
O
Q.
E
o
O
0.1
±
±
±
0.6 0.5 0.4 0.3 0.2
Erosion decreases fiber volume ratio
0.1
0.0
Figure 12. — Erosion effects on the composite thermal heat capacity
([0/±45/902/±45/0] as-graphite-fiber/intermediate modulus and
strength matrix). (Btu/lb/T = 4.19-3 j/kg/°C).
NASA/TM— 2006-214096
11
figure 13. Note that it approaches zero as the fiber volume ratio degrades to zero as it should since both
constituents have degraded. The corresponding transverse thermal expansion coefficient is also nonlinear
as shown in figure 14. However, this coefficient increases with degraded fiber volume ratio as is observed
in figure 14.
0.0x10-5
0.4 0.3 0.2
Erosion decreases fiber volume ratio
Figure 13. — Erosion degrades longitudinal thermal expansion coefficient
([0/±45/902/±45/0] as-graphite-fiber/intermediate modulus and
strength matrix). (10-6(in./in.)°F = 0.51(cm/cm)10-6/°C).
0.0
4.0x10-5
0.4 0.3 0.2
Erosion decreases fiber volume ratio
Figure 14. — Erosion effect on transverse thermal expansion coefficient
([0/±45/902/±45/0] as-graphite-fiber/intermediate modulus and
strength matrix). (10-6(in./in.)°F = 0.51(cm/cm)10-6rC).
0.0
NASA/TM— 2006-214096
12
9. Erosion Degradation on Mechanical Properties
(Moduli and Poisson's Ratios)
The equations from which these properties are evaluated are summarized in figure 15. These
equations have been coded in ICAN (ref 8). As noted in figure 15, there are six of these equations: two
for normal moduli, two for shear moduli and two for Poisson's ratios. It is important to note that the void
volume ratio is included as noted in the geometric properties in figure 3. The erosion effects on the ply
longitudinal modulus degrades rapidly as the voids degradation increases and approaches zero as the
voids approach 0.7 as can be seen in figure 16. This behavior is expected since the fiber volume ratio in
that ply has completely degraded. The corresponding transverse modulus degrades rapidly nonlinearly
and it too approaches zero as the voids increase to about 0.7 as is seen in figure 17. This behavior is
expected also since the matrix erodes as well and the voids increase. The in-plane shear modulus erodes
rapidly nonlinearly and this modulus approaches zero as the void degradation approaches 0.7 as can be
observed in figure 18. The through-the-thickness shear modulus degrades equally as well as can be
observed in figure 19. Note that this modulus has a lower value at the non-degraded state. The in-plane
Poisson's ratio remains about unaffected of the erosion degradation as can be seen in figure 20. The
through-the-thickness Poisson's ratio decreases rapidly after the void volume ratio increases beyond the
0.04 as can be seen in figure 21. This behavior is not obvious from the equation in figure 15. Note that
these properties can be used to guide experimental programs in composites erosion.
Longitudinal modulus:
Efii =kf Efii +k^E^
Transverse modulus:
Shear modulus:
Shear modulus:
Poisson's ratio:
^122 - "
rn ^^
l-^(l-E^/Ef22} =
'B3
/^ ^m _ /^
«3
G(23 - '
G„
-^k^[l-G„,/Gf23}
''»"''''
r-^ — I — i —
^ \ \ ^ Matrix (m)
Vfl2 = V ^/12 + *m V„ = V ^3
■ Fiber {f)
■PiyW
Poisson's ratio:
m,
^/22
■1
2G^23
Figure 15. — Composite micromechanics, mechanical properties.
NASA/TM— 2006-214096
13
2.50x106
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 16. — Erosion effect on ply longitudinal modulus (106 psi = 6.89 GPa).
2.50x106
2.00
to
■=" 1.50
(O
13
T3
O
1.00
0.50
0.00
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 17. — Erosion effect on ply transverse modulus (106 psi = 6.89 GPa).
NASA/TM— 2006-214096
14
2.25x106
1.00
CO
^0.75
(O
T3
O
0.50
0.25
0.00
±
I
I
±
I
I
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 18. — Erosion effect on ply sliear modulus (106 psi = 6.89 GPa).
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
Figure 19. — Erosion effect on through-thickness shear modulus
(106 psi = 6.89 GPa).
0.70
NASA/TM— 2006-214096
15
0.5
>
6
+-'
cc
tn
"c
o
en
<2
o
D.
(D
c
TO
Q.
C
_><
D.
0.4
0.3
0.2
0.1
0.0
0.6
±
±
±
±
0.10 0.20 0.30 0.40 0.50 0.60
0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
Figure 20. — Erosion effect on Poisson's ratio, v^-|2-
0.70
0.10 0.20 0.30 0.40 0.50 0.60 0.70
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
Figure 21. — Erosion effect on Poisson's ratio, v^3.
10. Uniaxial Strength Erosion Degradation
The equations for predicting uniaxial ply strengths with no erosion present are summarized in
figure 22. These equations are coded in the ICAN composite mechanics computer code. The erosion
degradation affects these strengths from the degradation in the fibers, in the matrix and the increase in the
void volume ratios as described previously and is shown in figure 3. There are five of these strengths:
longitudinal tension, longitudinal compression, transverse tension, transverse compression and in-plane
shear. How the erosion affects these ply uniaxial strength is described below. The tensile strength
degrades nonhnearly with increases in the void volume ratio and decreases in the fiber volume ratio as is
shown in figure 23. The longitudinal compressive strength degrades very rapidly with increase in void
volume ratio and comparable decreases in the fiber volume ratio as is shown in figure 24. The transverse
tensile strength decreases nonhnearly very rapidly as the void degradation increases and the fiber volume
ratio decreases as is shown in figure 25. The longitudinal transverse compressive strength decreases
nonhnearly as the void volume ratio increases and the fiber volume ratio decreases as shown in figure 26.
The intralaminar shear strength decreases nonhnearly as the void volume ratio in creases and the fiber
NASA/TM— 2006-214096
16
volume ratio decreases as shown in figure 27. The significance of these results is that any or all of these
strengths can be used to evaluate the amount of erosion experimentally.
1. Longitudinal tension:
2. Longitudinal compression:
Fiber compression:
Delamination/shear:
Microbuckling:
3. Transverse tension:
4. Transverse compression:
5. Intralaminar shear:
6. For voids:
Siiij- -kj-Sjf
^nic ~^f^fc
Saic ~105'«25' +2.5 SmT
nic
l-k
1 ^
V
G
/12
2
1
y
an
\-[f}-kf){^-E^lEf22)^
'mT
2
1
Snic ~\- [JkJ - kf ) (l - E^JEf 22 )_
Sfiis ~ [l - [yjkf -kf j (l - Gm/G/i2)J S„
J,
S^«[\-[Ak,li^-kf)nf\s,
o
o
o
o
o
u
u
o
Void
Figure 22. — Composite micromechanics, uniaxial strengths, in-plane.
0.5
D) <f>
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 23. — Uniaxial ply strength degradation from erosion, (ksi = 6.89 MPa).
NASA/TM— 2006-214096
17
250
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 24. — Uniaxial ply compressive strength degradation from erosion.
(I<si = 6.89 MPa).
25.0
20.0 -
OJ ^
>
15.0
2 10.0
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 25. — Uniaxial ply transverse tensile strength degradation from erosion,
(ksi = 6.89 GPa).
25.0
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 26. — Uniaxial ply transverse compressive strength degradation from
erosion, (ksi = 6.89 GPa).
NASA/TM— 2006-214096
18
25.0
C
i_
^ _
CO ^
(D .
^ C
U) O
CO "cS
c -o
1 E
CD "O
20.0
15.0
10.0
5.0
0.0
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 27. — Uniaxial ply intra-laminar shear strength degradation from erosion,
(ksi = 6.89 GPa).
11. Erosion Effects on Laminate Strengths
The laminate strengths coded in the ICAN computer code are based on two principles, (1) when the
first ply fails the laminate failed and (2) when the fibers fail in every ply in the laminate then the laminate
failed. For purposes of this evaluation, only the first ply failure is appropriate because that is the only ply
that will erode first. Also, these results are important because they can be used to direct experimental
programs when multi angle laminates are exposed to ply erosion degradation. There are five different
strengths for laminate degradation. These are axial tension, axial compression, transverse tension, transverse
compression and laminate in-plane shear.
The predicted axial tensile strength of an eroded laminate is plotted versus increasing void volume
ratio and decreasing fiber volume ratio in figure 28. It is observed that this strength decreases rapidly
initially and near the end; it remains relatively level in the middle. The predicted laminate compressive
strength is plotted in figure 29 versus increasing void volume ratio and decreasing fiber volume ratio. It is
observed in figure 29 that this laminate strength degrades rapidly and nonlinearly in a continuous fashion
until the void volume ratio becomes very large and the fiber volume ratio approaches zero. The laminate
transverse tensile strength is plotted in figure 30 versus void volume ratio increase and fiber volume ratio
decrease. This strength decreases rapidly initially and near the end but remains relatively insensitive in the
middle. It exhibits the same behavior as the axial tensile strength. The laminate transverse compressive
strength is plotted in figure 31 versus increasing void volume ratio and decreasing fiber volume ratio. It
can be observed in figure 3 1 that this strength is insensitive to erosion through most of the range and
decreases rapidly and nonlinearly near the end. The laminate in-plane shear strength is plotted in figure 32
versus increasing void volume ratio and decreasing fiber volume ratio. It is observed in figure 32 that this
strength has unique characteristics in that it is bi-modal having both concave and convex parts. It is
nonlinear throughout the region and decreases rapidly near the end. This strength will be appropriate for
guiding experimental effort if the erosion is caused by shear stress predominately. This corresponds to the
results in figures 2 to 4 (ref 9) where the wear is plotted versus fiber volume ratio.
It is important to emphasize that inclusion of the eroded laminate strengths are simulated by using
laminate theory combined with ply stress influence equations in addition to the equations summarized
previously. These also are coded in the ICAN computer code which is truly an integrated computer code
from micro mechanics to laminate theory; it also includes thermal and moisture effects. That computer
code really represents a virtual composite mechanics laboratory.
NASA/TM— 2006-214096
19
100 r-
c
en .
aj .
TO "
c
i» CO
TO
'55
c
CD
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 28. — Erosion effects on laminate tensile strength ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength epoxy). (ksi = 6.89 GPa).
100
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 29. — Erosion effects on laminate compressive strength ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength epoxy). (ksi = 6.89 GPa).
100
±
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 30. — Erosion effects on laminate tensile strength ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength epoxy). (ksi = 6.89 GPa).
NASA/TM— 2006-214096
20
(U
U)
1_
CD
>
CO
c _
to </>
i= ^
(U
>
100
80
^ ?; 60
CO
O c
O 0)
to
c
40 -
20 -
±
±
±
±
±
±
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 31 . — Erosion effects on laminate compressive strength ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength epoxy). (ksi = 6.89 GPa).
100
(/} X
to
c
80 -
60
40
20 -
J_
J_
J_
±
0.10 0.20 0.30 0.40 0.50 0.60
0.6 0.5 0.4 0.3 0.2 0.1 0.0
Void erosion increase/fiber volume ratio decrease
0.70
Figure 32. — Erosion effects on laminate shear strength ([0/±45/902/±45/0]
as-graphite-fiber/intermediate modulus and strength epoxy). (ksi = 6.89 GPa).
12. Concluding Remarks
The composite erosion degradation is evaluated by two methods — the Multi Factor Interaction Model
(MFIM) and by a computational simulation composites code ICAN (Integrated Composite Analyzer).
Results obtained from these two methods show that:
1 . The MFIM can be used to evaluate composite erosion. However, care is required to selecting the
exponents and each factor ratios.
2. The ICAN evaluation is consistent with the physics of the multi scale models that are included in
ICAN and can predict degradation in all the ply properties: geometric characterization, physical
properties, thermal properties and mechanical properties (moduli and strengths).
3. Some of these degraded properties can be used to identify composite erosion effects and also can be
used to guide experimental investigations.
4. As would be expected, the majority of the properties go to zero as the fiber and the matrix approach
complete degradation.
NASA/TM— 2006-214096
21
5. The void volume ratio increases with composite degradation, as both fiber volume ratio and matrix
volume ratio approach "zero" as is used in the composite erosion.
6. Computational composite mechanics is applicable when erosion occurs on a ply-per-ply basis and the
eroding medium is normal to the ply.
7. The eroding medium degrades both the fiber and the matrix in the same slice through the composite
thickness.
8. The friction factor is not dependent on the eroding direction but depends on the pressure exerted by
the eroding medium.
9. Practically all composite properties degrade monotonically except the laminate shear strength which
degrades in a bimodal fashion.
13. References
1. Klaus Friedrich, ed.: Friction and Wear of Polvmer Composites , Composite Materials Series 1,
Elsevier, Amsterdam, 1986.
2. Klaus Friedrich, ed.: Advances in Composite Tribology , Composite Materials Series 8 Elsevier,
Amsterdam, 1993.
3. R. Reinicke, F. Haupert, and K. Friedrich, Tribologv Behavior of Selected, Injection Moulded
Thermoplastic Composites , Part A 29, p. 763, 1988.
4. Klaus Friedrich and Petra Reinicke, Friction and Wear of Polymer Based Composites, Mechanics of
Composite Materials , Vol. 34, No. 8, p. 503, 1998.
5. M.M. Barkoula and J. Karger-Kocsis, Journal of Reinforced Plastics and Composites ,
Vol. 21, No. 15, p. 1377,2002.
6. K. Friedrich, et al.. Numerical and Finite Element Contact and Thermal Analvsis of Real Composite-
Steel Surfaces in Sliding Contact , Elsevier, p. 368, 1999.
7. N. Ohmae, J.M. Martin, and S. Mori, Micro and Nano Tribology, ASME 2005 .
8. P.L.N. Murthy, C.A. Ginty, and J.G. Sanfehz, "ICAN (Integrated Composite Analyzer)" NASA TP
3290, 1993.
9. M. Fahim, J. Indumathi, and J. Buwe, Statistical Data Analysis of Abrasive Wear Performance of
Polyetherimide and Composites, Journal of Reinforced Plastics and Composites , Vol. 20, No. 12, p.
1013,2001.
NASA/TM— 2006-214096 22
REPORT DOCUMENTATION PAGE
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1 . AGENCY USE ONLY (Leave blank)
2. REPORT DATE
February 2006
3. REPORT TYPE AND DATES COVERED
Technical Memorandum
4. TITLE AND SUBTITLE
Composite Erosion by Computational Simulation
5. FUNDING NUMBERS
WBS-984754.02.07.03
6. AUTHOR(S)
Christos C. Chamis
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
John H. Glenn Research Center at Lewis Field
Cleveland, Ohio 44135-3191
8. PERFORMING ORGANIZATION
REPORT NUMBER
E- 15300-1
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, DC 20546-0001
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
NASA TM- 2006-2 14096
11. SUPPLEMENTARY NOTES
Prepared for the SAMPE 2006 sponsored by the Society for the Advancement of Material and Process Engineering,
Long Beach, California, April 30-May 4, 2006. Responsible person, Christos C. Chamis, organization code R,
216-433-3252.
12a. DISTRIBUTION/AVAILABILITY STATEMENT
Unclassified -Unlimited
Subject Categories; 24 and 39
Available electronicallv at http://sltrs.grc.nasa.gov
This publication is available from the NASA Center for AeroSpace Information, 301-621-0390.
12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
Composite degradation is evaluated by computational simulation when the erosion degradation occurs on a ply-by-ply basis
and the degrading medium (device) is nonnal to the ply. The computational simulation is perfonned by a multi factor
interaction model and by a inulti scale and multi physics available computer code. The erosion process degrades both the
fiber and the matrix simultaneously in the same slice (ply). Both the fiber volume ratio and the matrix volume ratio approach
zero while the void volume ratio increases as the ply degrades. The multi factor interaction model simulates the erosion
degradation, provided that the exponents and factor ratios are selected judiciously. Results obtained by the computational
composite mechanics show that most composite characterization properties degrade monotonically and approach "zero" as
the ply degrades completely.
14. SUBJECT TERMS
Properties degradation; Friction coefficient; Ply-by-ply removal; Nanotonic deterioration
15. NUMBER OF PAGES
28
16. PRICE CODE
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