Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Composite Erosion by Computational Simulation

NASA/TM—2006-214096

February 2006
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Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Composite Erosion by Computational Simulation

NASA/TM—2006-214096

February 2006

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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
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Level of Review: This material has been technically reviewed by technical management.
NASA/TM—2006-214096 1

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 2

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 (μ) is generally defined as: 

A

Fn μ = (1) 

where Fn 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 (t) we have the volume is equal 
NASA/TM—2006-214096 3

V At A t A t A t = = f + m + v (2) 

where the subscripts f, m, and ν denote fiber, matrix and voids respectively. 

Dividing through by t we obtain 

A = Af + Am + Av (3) 

Divide through by A

A

A

A

A

A

Af m v 1 = + + (4) 

Let Af/A = kf; Am/A = km, and Aν/A = kv, we obtain the following result: 

1 = kt + km + kv (5) 

Since the strain is constant due to eroding device, then the local stresses are proportional to the local 

stiffness. 

A E e A E e A E e o (E o) σ f 11 = f f 11 ; σm1 = m m ; σv = v v = ; v = (6) 

The force on the eroding surface is 

F = Af σ f 11 + Am σm11 = Fn μc = Nzz (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: 

m

m

f

f

c

k k

μ

+

μ = μ

1 (8) 

This equation is the same as that in reference 1. Rearranging equation (8) yields: 

f m

m f f m

c

k k

μ μ

μ + μ = μ

1 (9) 

m f f m

f m

c μ k + μ k

μ μ

μ = (10) 

Upon dividing by μf

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

μ

μ +

μ =

+

μ

μ

μ μ =

f

m m f

m

f m

f

m

m c

k k k k

 (11) 

Equation (11) shows that for constant km and (μm/μf), μc will decrease as kf increases which is an 

interesting result. 
NASA/TM—2006-214096 4

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,μc , E, Sl12S,N zz,k f ) (12) 

Where Q is the eroded volume, V is the eroding device velocity, μc is the composite friction 

coefficient, Sl12S is the composite shear strength, Nzz is the normal load, E = Ec 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. 

6 1 2 3 4 5 3

12

12 1 1 1 1 1 1

e

fF

f e

S

e

c

c

e

zzF

zz

e

c

c

e

i i

c

k

k

S

S

E

E

N

N

V

V

Q

Q

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

μ

μ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − l

l

l l

(13) 

One disadvantage of MFIM is the selection of the exponents, e1 through e6. 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 
NASA/TM—2006-214096 5

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 Qc/Qi = 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 Qc/Qi = 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 Qc/Qi = 0.9906. The corresponding sensitivities are listed in the last 

column of that table. Experimental values range from 0 to 0.005 μm 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 Qc

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: Qc/Qi = 0.0085 

TABLE 2 

Term Exponent Factor Ratio Relative to Qc

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: Qc/Qi = 0.0026 

TABLE 3 

Term Exponent Factor Ratio Relative to Qc

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: Qc/Qi = 0.996 

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 6

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

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) Ef11 0.329E+08 psi 

Normal moduli (22) Ef22 0.199E+07 psi 

Poisson’s ratio (12) Nuf12 0.200E+00 non-dim 

Poisson’s ratio (23) Nuf23 0.250E+00 non-dim 

Shear moduli (12) Gf12 0.200E+07 psi 

Shear moduli (23) Gf23 0.100E+07 psi 

Thermal expansion 

coef. (11) 

Alfaf11 –0.550E-06 in/in/F 

Thermal expansion 

coef. (22) 

Alfaf22 0.560E-05 in/in/F 

Heat conductivity 

(11) in/hr/in**2/F 

Kf11 0.403E+01 BTUHeat conductivity 

(22) in/hr/in**2/F 

Kf22 0.403E+00 BTUHeat capacity Cf 0.170E+00 BTU/lb/F 

Fiber tensile 

strength 

SfT 0.430E+06 psi 

Fiber compressive 

strength 

SfC 0.430E+06 psi 

(Scales: in = 25 mm; lb/in3 = 6.41E-6 kg/m3; E+6 psi = 6.8 GPa; E-6(in/in)/°F = 0.51E-6(cm/cm)/°C BTU-in/hr/in2/°F = 0.07 

J-in/hr/in2

/°C; BTU/lb/°F = 4.19E3J/kg/°C; ksi = 6.89 MPa; °F = 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 l . The inter fiber distance is defined as δ l . The ply fiber volume ratio is defined as kf, the matrix as km

and the void as kν. 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 

linearly as the fiber volume ratio decreases. In figure 5 the remaining fiber diameter also decreases 

linearly 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. 

TABLE 5. INTERMEDIATE MODULU 

AND STRENGTH EPOXY MATRIX 

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 mT 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 
NASA/TM—2006-214096 7

Partial volumes: k f + km + kv = 1

Ply density: ρl = k f ρ f + kmρm

Resin volume ratio: km = ( ) 1− kv [1+ (ρm ρ f )(1 λm −1)]

Fiber volume ratio: k f = ( ) 1− kv [1+ (ρ f ρm )(1 λ f −1)]

Weight ratios: λ f + λm =1

Ply thickness (S.A.): N f d f k f tl =1 2 π

Interply thickness: δl = 1 2[ π k f − 2] d f

Inter fiber spacing (S.A.): δs = δl 

Contiguous fibers (S.A.): k f = π 4 ~ 0.785

Figure 3.—Micromechanics, geometric relationships. 
NASA/TM—2006-214096 8
NASA/TM—2006-214096 9

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 l subscript denotes ply property 

while the number subscripts denote directions. The ply longitudinal heat conductivity decreases linearly 

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 11. 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 10

Heat capacity: C ( ) k f ρ f C f + km ρm Cm ρ = l

l

1

Longitudinal conductivity: 

Kl11 = k f K f 11 + km Km

Transverse conductivity: ( ) ( ) 33

22

22

1 1

l 1 Kl

k K K

K k

K k K

f m f

m f

f m = − − − +

For voids: ( ) ( ) v m v

m v m v m k K K

K k

K k K − − = − +

1 1

1

Longitudinal thermal 

expansion coefficient: 11

11 11

11

l

l E

k f α f E f + km αm Em α =

Transverse thermal 

expansion coefficient: αl22 = α f 22 k f + (1− k f )(1+ k f νm E f 11 El11)αm = αl33

Figure 9.—Composite micromechanics, thermal properties. 
NASA/TM—2006-214096 11
NASA/TM—2006-214096 12

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. 
NASA/TM—2006-214096 13

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: El11 = k f E f 11 + km Em

Transverse modulus: ( ) 33

22

22 1 1 l El k E E

E E

f m f

m

− − = =

Shear modulus: ( ) 13

12

12 1 1 l Gl k G G

G G

f m f

m = − − =

Shear modulus: ( ) 23

23 1 1 f m f

m

k G G

G G − − l =

Poisson’s ratio: νl12 = k f ν f 12 + km νm = νl13

Poisson’s ratio: 1

2 23

22 ν 23 = −

l

l

l G

E

Figure 15.—Composite micromechanics, mechanical properties. 
NASA/TM—2006-214096 14
NASA/TM—2006-214096 15
NASA/TM—2006-214096 16

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 nonlinearly 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 nonlinearly 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 

nonlinearly as the void volume ratio increases and the fiber volume ratio decreases as shown in figure 26. 

The intralaminar shear strength decreases nonlinearly as the void volume ratio in creases and the fiber 
NASA/TM—2006-214096 17

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: T f fT S ≈ k S l11

2. Longitudinal compression: 

 Fiber compression: Sl11C ≈ k f S fC

 Delamination/shear: Sl11C ≈ 10Sl12S + 2.5 SmT

 Microbuckling: ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − −

≈

12

11

1 1

f

m f

m C

G

G k

G Sl

3. Transverse tension: Sl22T ≈ [ ] 1− ( k f − k f ) (1− Em E f 22 ) SmT

4. Transverse compression: Sl22C ≈ [ ] 1− ( k f − k f ) (1− Em E f 22 ) SmC

5. Intralaminar shear: Sl12S ≈ [ ] 1− ( k f − k f ) (1− Gm Gf 12 ) SmS

6. For voids: Sm { [ kv ( k f ) ] }Sm

1 2

≈ 1− 4 1− π

Figure 22.—Composite micromechanics, uniaxial strengths, in-plane. 
NASA/TM—2006-214096 18
NASA/TM—2006-214096 19

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 31 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 20
NASA/TM—2006-214096 21

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 22

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 Polymer 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, Tribology 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 Analysis of Real CompositeSteel 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. Sanfeliz, “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. 
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28

Composite Erosion by Computational Simulation

Christos C. Chamis

Properties degradation; Friction coefficient; Ply-by-ply removal; Nanotonic deterioration

Unclassified -Unlimited

Subject Categories: 24 and 39

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.

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.