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NASA/TM— 2006-214096 Composite Erosion by Computational Simulation Christos C. Chamis Glenn Research Center, Cleveland, Ohio February 2006 NASA STI Program ... in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Infonnation (STI) program plays a key part in helping NASA maintain this important role. The NASA STI Program operates under the auspices of the Agency Chief Information Officer. It collects, organizes, provides for archiving, and disseminates NASA's STI. The NASA STI program provides access to the NASA Aeronautics and Space Database and its public interface, the NASA Technical Reports Server, thus providing one of the largest collections of aeronautical and space science STI in the world. Results are published in both non-NASA channels and by NASA in the NASA STI Report Series, which includes the following report types: • TECHNICAL PUBLICATION. 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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 Form Approved 0MB No. 0704-0188 Public reporting burden for this coiiection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 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 17. SECURITY CLASSIFICATION OF REPORT Unclassified 18. SECURITY CLASSIFICATION OF THIS PAGE Unclassified 19. SECURITY CLASSIFICATION OF ABSTRACT Unclassified 20. LIMITATION OF ABSTRACT NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102