Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Galib H. Abumeri

QSS Group, Inc., Cleveland, Ohio

Simulated Data for High Temperature

Composite Design

NASA/TM—2006-214111

February 2006
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Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Galib H. Abumeri

QSS Group, Inc., Cleveland, Ohio

Simulated Data for High Temperature

Composite Design

NASA/TM—2006-214111

February 2006

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NASA/TM—2006-214111 1

Simulated Data for High Temperature Composite Design 

Christos C. Chamis 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Galib H. Abumeri 

QSS Group, Inc. 

Cleveland, Ohio 44135 

Abstract 

The paper describes an effective formal method that can be used to simulate design properties for 

composites that is inclusive of all the effects that influence those properties. This effective simulation 

method is integrated computer codes that include composite micromechanics, composite macromechanics, 

laminate theory, structural analysis, and multi-factor interaction model. Demonstration of the method 

includes sample examples for static, thermal, and fracture reliability for a unidirectional metal matrix 

composite as well as rupture strength and fatigue strength for a high temperature super alloy. Typical results 

obtained for a unidirectional composite show that the thermal properties are more sensitive to internal local 

damage, the longitudinal properties degrade slowly with temperature, the transverse and shear properties 

degrade rapidly with temperature as do rupture strength and fatigue strength for super alloys. 

Introduction 

As candidate materials for advanced high temperature aerospace structures, metal matrix composites 

(MMCs) have been the subject of considerable interest and extensive research. With concurrent advances 

in processing, fabrication, and experimental mechanics, MMCs will increasingly be used as structural 

materials for advanced propulsion systems. The extreme temperatures and stresses of these propulsion 

systems create a hostile environment for the composite to withstand. Therefore, the analysis and design of 

these materials are critically important and require the use of mathematical models to predict thermal and 

mechanical behavior. One such model is the computer code METCAN (METal matrix Composite 

ANalyzer, reference 1) developed at NASA Glenn Research Center. 

This paper presents the mechanical and thermal properties of a unidirectional composite from silicon 

carbide (SiC)/titanium (Ti6) MMC as computationally simulated by METCAN from constituents properties 

as described subsequently. It provides results for one fiber volume ratio at a range of temperatures in 

graphical form. These plots include stress-strain, elastic and shear moduli, Poisson’s ratio, thermal 

expansion, and thermal conductivity. Similar information can be readily generated for: 1) other loading 

condition, 2) other composites, and 3) other service conditions. A list of symbols used is included in the 

appendix where a short table of conversion factors from customary units to SI units is also included. 

Background 

METCAN has the capability to predict many aspects of high temperature MMCs by using room 

temperature constituent properties. METCAN’s integrated approach is illustrated in figure 1 as a cyclic 

arrangement that defines the computational methodology for each load increment. As can be seen from 

the figure, this predictive capability consists of several computational modules encompassing the material 

nonlinear behavior (bottom), composite mechanics (sides), and the finite element analysis of structural 

components (top). Material nonlinearity is treated at the constituent level, where the current material 

model, namely the Multi-Factor Interaction Model (MFIM), figure 2, describes a time-temperature-stress 
NASA/TM—2006-214111 2
NASA/TM—2006-214111 3

dependence of a constituent’s mechanical and thermal properties at any point in its material history 

(ref. 2). Characteristic properties of the composite are calculated from the instantaneous constituent 

properties using composite mechanics. This synthesis results in a point description of equivalent pseudohomogeneous properties for the composite. 

Naturally, some assumptions have been made in the development of this code. The MFIM utilizes a 

large number of exponents that, ideally, have been calculated from experimental data. When reliable 

experimental data is unavailable, default values are used. These values were established from studies 

conducted on other MMCs (ref. 3). The exponents used in this study are summarized in table 1. Secondly, 

the Ti6 matrix melting temperature in METCAN was given a value close to the consolidation 

temperature. Since the matrix has no remaining strength at the consolidation temperature and METCAN 

must simulate this behavior, the actual melting temperature was replaced with one that was slightly higher 

than the consolidation temperature. The room temperature constituent properties used are listed in table 2. 

Verification of METCAN (comparisons with experimental data) is described in reference 4. 

Additionally, a modification was made in METCAN for this particular task. Since progressive failure 

of the composite was not a consideration, the method of stopping the program after failure was altered 

slightly. Normally, when failure occurs in one region, the load is channeled into the remaining regions 

until the composite suffers a complete fracture. For this study, once failure takes place in a critical region, 

the simulation is stopped and the material properties for that strain are set at zero. Under a longitudinal 

load, this critical region is defined as the fiber. For transverse and shear loads, the determining sector is 

the micro-region A of the matrix (fig. 2). 

TABLE 1.—METCAN EXPONENTS 

 Values 

Exp Array 

Location 

Property Determining

Property 

SiC Ti6 

A 2 Modulus σ 0.25 0.50 

m 3 Modulus σ 0.25 0.50 

n 4 Modulus T 0.25 0.587 

A 5 Strength σ 0.25 0.50 

m 6 Strength σ 0.0 0.0 

n 7 Strength T 0.25 0.902 

A 8 Poisson’s Ratio σ 0.25 0.50 

m 9 Poisson’s Ratio σ 0.25 0.50 

n 10 Poisson’s Ratio T 0.25 0.50 

A 14 Heat 

Conductivity σ 0.25 0.50 

m 15 Heat 

Conductivity σ 0.0 0.50 

n 16 Heat 

Conductivity T 0.25 0.50 

A 17 CTE σ 0.25 0.50 

m 18 CTE σ 0.0 0.50 

n 19 CTE T 0.25 0.037 
NASA/TM—2006-214111 4

TABLE 2.—INPUT CONSTITUENT PROPERTIES AT ROOM TEMPERATURE 

Fiber: Silicon Carbide on 

Aluminum 

Matrix: Titanium 

Property 

(units) 

Property 

(units) 

Ti6 

Nf 1 Kν 0.019 

Df 0.0102 ρm (lb/in∗∗3) 0.170 

ρf (lb/in∗∗3) 0.110 TMm(F) 1740 

TMf 4870 Em (Mpsi) 16.5 

Ef11 (Mpsi) 62.0 νm 0.300 

Ef22 (Mpsi) 62.0 αm (Hin/in/F) 5.24 

Gf12 (Mpsi) 26.1 Km (BTU/hr/F/in) 0.390 

Gf23 (Mpsi) 26.1 Cm (BTU/lb) 0.120 

νf12 0.190 SmT (ksi) 74.0 

νf23 0.190 Smc (ksi) 74.0 

αf11 (Hin/in/F) 2.72 Sms (ksi) 74.0 

αf22 (Hin/in/F) 2.72 εmT (in/in) 44.4 

Kf11 (BTU/hr/F/in) 0.750 εmc (in/in) 0.350 

Kf22 (BTU/hr/F/in) 0.750 εmS (in/in) 0.350 

Cf (BTU/lb) 0.290 εmTOR (in/in) 0.350 

Sf1T (ksi) 500 Processing Temperature 1200 °F 

Sf1C (ksi) 500 

Sf2T (ksi) 500 

Sf2C (ksi) 500 

Sf12s (ksi) 300 

Sf23s (ksi) 300 

Results and Significances

For this evaluation, a perfect bond was assumed to exist between the fiber and the matrix. This is 

reflected by the plots which depict the upper boundaries of the material properties. Fiber volume ratio 

(FVR) of 0.30 provided a good test for this material. Longitudinal loads were imposed on a unidirectional 

Silicon Carbide fiber Titanium Matrix (SiC/Ti6) composite system at three different temperatures (70, 

500, and 1000 °F) to obtain an extensive profile of the thermal and mechanical properties. 

In order to properly model a composite, the residual stresses generated by processing is included. To 

accomplish this, the cool-down history from consolidation temperature to room temperature (70 °F) was 

simulated before the mechanical load was applied. For the high temperature cases (500 and 1000 °F), the 

load was applied after the heat-up from room temperature to service temperature. Due to the mismatch in 

the coefficient of thermal expansion (CTE), the stresses developed in the fiber were compressive while 

those developed in the matrix were tensile. 

Table 3 presents the anticipated tangent properties of each composite. As predicted by METCAN, 

each composite’s thermal and mechanical properties were evaluated at the test temperature after a small 

increment of load was applied. Material properties resulting from a compressive load will vary, but not 

significantly, from those listed in table 3. 
NASA/TM—2006-214111 5

TABLE 3.—ANTICIPATED INITIAL THERMAL AND MECHANICAL 

PROPERTIES OF A UNIDIRECTIONAL COMPOSITE (0.30 FVR SiC/Ti6) 

Temperature in °F 

Property Units 70 500 1000

α111 ppm/F 4.577 4.389 4.205 

α122 ppm/F 5.571 5.245 5.003 

α133 ppm/F 5.571 5.245 5.003 

C1 BTU/lb 0.157 0.157 0.157 

K111 BTU/F-hr*in 0.585 0.619 0.706 

K122 BTU/F-hr*in 0.572 0.606 0.701 

K133 BTU/F-hr*in 0.572 0.606 0.701 

E111 Mpsi 26.676 25.606 23.618 

E122 Mpsi 17.884 16.410 13.293 

K133 Mpsi 17.884 16.410 13.293 

G112 Mpsi 8.373 7.052 5.378 

G123 Mpsi 7.227 6.750 5.586 

G113 Mpsi 8.373 7.052 5.378 

S111T Ksi 195.00 180.00 160.00 

S111C Ksi 193.05 178.20 158.40 

S122T Ksi 64.75 50.75 35.00 

S122C Ksi 101.75 74.25 45.00 

S112 Ksi 43.75 36.25 23.75 

S123 Ksi 43.75 36.25 23.75 

S113 Ksi 43.75 36.25 23.75 

ν112 in/in 0.255 0.222 0.183 

ν1123 in in 0.237 0.215 0.190 

ν131 in/in 0.171 0.143 0.103 

ρ1 lb/in**3 0.152 0.152 0.152 

Note: Properties obtained under initial tensile load. 

Strengths obtained from respective stress/strain curves. 

The plots presented in figures 3 to 10 demonstrate METCAN’s ability to capture the behavior of a 

metal matrix composite at varying temperatures for one fiber volume ratio. By using these plots as an 

initial guideline, it becomes clear that the behavior at various fiber volume ratios for different composites 

can be similarly simulated. It should also become clear that obtaining all this information by test will be 

time and cost prohibitive. 

All the properties in figures 3 to 10 are plotted against longitudinal strain for commonality. The stress 

strain curve is plotted in figure 3. Note the mild nonlinearity for almost the entire range. Note also the 

decrease with temperature. The longitudinal modulus is plotted in figure 4. The discontinuities indicate 

local region (sector A in fig. 2) fractures. It is important to note these discontinuities are imperceptible in 

the stress-strain plots in figure 3. As can be seen, the modulus decreases continuously and exhibits an 

abrupt drop near composite fracture which occurs as a result of fiber fractures. 
NASA/TM—2006-214111 6

A comparable plot for the transverse modulus is shown in figure 5. Note the insensitivity of the 

transverse modulus with respect to longitudinal strain. The interpretation for this is that transverse local 

damage (cracks) has negligible effect on the transverse modulus when a unidirectional composite is 

loaded along the longitudinal (fiber) direction. Similarly for the in-plane shear modulus, Gl12 plotted 

versus longitudinal strain εl11 in figure 6. However, this is not the case when the composite is loaded in 

the transverse or in-plane shear. 
NASA/TM—2006-214111 7

The in-plane major Poisson’s ratio νl12 is plotted versus εl11 in figure 7. As can be observed, νl12 is not 

sensitive to εl11 which is comparable to El22 and Gl12 and for the same reasons that were mentioned. A 

different situation arises when the through-the-thickness νl32 is plotted versus εl11. The results are 

displayed in figure 8. Note that the magnitude increases continuously with discontinuous “jumps” in the 

region 0.3≤εl11≤0.5. These discontinuous jumps coincide with those in the longitudinal modulus in 

figure 4. Note also the rapid increase near the fracture region and almost instantaneous drop at fracture. 
NASA/TM—2006-214111 8

The reasons for this behavior are the same as previously mentioned. The conclusion from this discussion 

is that local directional damage may be present that may be detected by some properties and may be 

insensitive to others. The graphical results described thus far demonstrate that generalizations should be 

avoided when interpreting test results from these complex composites tested at high temperatures. 
NASA/TM—2006-214111 9

The longitudinal thermal expansion coefficient αl11 is plotted versus longitudinal strain in figure 9. 

The curves increase nonlinearly up to the local longitudinal damage exhibited by the instantaneous 

discontinuity drop. Thereafter remain insensitive till fracture. The important point to be made from the 

results in figure 9 is that longitudinal thermal expansion monitoring during loading may be a sensitive test 

to identify local damage in these types of composites. Comparable results for longitudinal thermal 

conductivity Kl11 are shown in figure 10. The behavior for Kl11 is more pronounced than that for αl11. 

However, the interpretation and point to be made are similar to those made for αl11. 

Time dependent (rupture strength) behavior can be simulated by activating the time factor in the 

MFIM, which is the last term in the MFIM in figure 2. The combined thermal time effects can be 

simulated by activating the temperature and time factors (first and last terms, figure 2) simultaneously. 

The combined results obtained for a monolithic super alloy are shown in figure 11. Also, two 

experimental available points are plotted for comparison. The important point to be noted is that 

information for preliminary designs or early assessments can be generated for emerging or projected 

materials for specific applications. Comparable information can be generated for fatigue endurance. This 

is obtained by activating the mechanical fatigue factor (sixth term) in the equation in figure 2. These 

results are plotted in figure 12. Note the relatively rapid drop at small cyclic ratios and the leveling as the 

cyclic ratio increases. Fatigue resistance for composites has been also evaluated as reported in 

references 5 and 6. Probabilistic fatigue in composites is described in references 7 and 8. 
NASA/TM—2006-214111 10
NASA/TM—2006-214111 11

The major observations from the above discussion are that: (1) The highest laminate strength is along 

the fiber direction; (2) The room temperature laminate transverse and shear strengths decrease 

substantially with temperature. The decreases are about 18 percent for the longitudinal tensile strength 

and about 55 percent for the transverse and shear strengths. Of lesser significance are the observations 

that: (1) The thermal expansion coefficient and the thermal conductivity indicate abrupt changes in 

regions where one or both constituents failed. These sharp drops correspond to a somewhat imperceptible 

change in the slope of the stress-strain plot in figure 3. 

Concluding Remarks 

The evaluation presents simulated (METCAN generated) results at temperatures of 70, 500, and 

1000 °F for SiC/Ti6 at a fiber volume ratio of 0.30. It includes the following: (1) Table of Anticipated 

Thermal and Mechanical Properties, (2) Stress-Strain Curves, (3) Thermal Conductivities, (4) Thermal 

Expansions, (5) Elastic and Shear Moduli, and (6) Poisson’s Ratios. It also includes simulated results for 

stress rupture and fatigue resistance of a high temperature super alloy. It is noted that the method is 

general and applicable to all types of composites, loading conditions, and service environments. 

Some general trends are: 

• The highest ultimate tensile strength (UTS) is along the fiber. The room temperature transverse and 

shear strengths are roughly one third and one fourth, respectively, of the longitudinal UTS. 

Temperature causes these two strengths to degrade by approximately 55 percent while the 

longitudinal strength degrades by only 18 percent. 

• Some of the curves for the coefficient of thermal expansion (CTE α) and thermal conductivity (K) 

indicate abrupt changes in regions where one or both of the constituents failed. These sharp drops 
NASA/TM—2006-214111 12

correspond to a sometimes imperceptible change in the slope of the stress-strain plot. When a failure 

of this type occurs, the mechanism for heat transfer is disrupted. 

• The elastic (E) and shear (G) moduli experience a moderate degradation due to increasing 

temperature. The highest modulus is along the fiber (26 Mpsi). The transverse moduli are somewhat 

less (18 Mpsi) while the shear moduli are much smaller (8 Mpsi). 

• The major Poisson’s ratio remains about constant as temperature and longitudinal strain increase. The 

through-the-thickness Poisson’s ratio increases nonlinearly with increasing strain and temperature, 

which is reflected in the behavior of the corresponding decreases in the longitudinal modulus. 

• The rupture strength of a high temperature super alloy decreases rapidly with exposure time and with 

exposure temperature. The major decrease is from 1500 to 2000 °F because 2000 °F is approaching 

the melting temperature of the matrix. 

• The fatigue strength of the super alloy decreases rapidly at low cyclic ratios and decreases somewhat 

slower as the cyclic ratio increases. 

• The collective results demonstrate the versatility and effectiveness of multi level computational 

simulation coupled with a multi factor interaction model. 

References

1. Hopkins, D.A. and Murthy, P.L.N.: METCAN—The Metal Matrix Composite Analyzer. 

NASA CP 3003, vol. 2, 1988. 

2. Chamis, C.C. and Minnetyan, L.: A Multi-Factor Interaction Model (MFIM) for Damage Initiation 

and Progressions. Presented in the Session on Damage Initiation and Prediction in Composites at the 

2001 ASME International Mechanical Engineering Congress and Exposition (IMECE), New York, 

NY, November 11–16, 2001. 

3. Hopkins, D.A.: Nonlinear Analysis of High Temperature Multilayered Fiber Composite Structures. 

NASA TM 83754, 1984. 

4. Lee, H.J., Murthy, P.L.N., and Chamis, C.C.: METCAN Updates for High Temperature Composite 

Behavior: Simulation/Verification. NASA TM 103682, 1991. 

5. Chamis, C.C., Murthy, P.L.N., and Hopkins, D.A.: Computational simulation of High Temperature 

Metal Matrix Composites Cyclic Behavior. NASA TM 102115, 1988. 

6. Minnetyan, L., Abdi, F., and Chamis, C.C.: Cyclic Fatigue Damage Evolution in Airfoil Structures, 

46th International SAMPE Symposium, vol. 46, Book 1 of 2, pp. 1037–1048, May 5–10, 2001. 

7. Minnetyan, L., Chamis, C.C., Abdi, F., and Huang. D.: Probabilistic Cyclic Fatigue of Composite 

Structures, 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials 

Conference, Seattle, WA, No. AIAA–2001–1375, pp. 1–7, April 16–19, 2001. 

8. Minnetyan, L., Huang, D., and Chamis, C.C.: Probabilistic Fatigue Life Evaluation of Composite 

Structures, 46th International SAMPE Symposium, vol. 46, Book 1 of 2, pp. 985–994, May 6–10, 

2001. 
NASA/TM—2006-214111 13

Appendix—Symbols List 

C = Heat Capacity (BTU/Ib) 

E = Normal Modulus (Mpsi) 

G = Shear Modulus (Mpsi) 

K = Thermal Conductivity (BTU/°F*hr*in) 

S = Strength (Ksi) 

α = Coefficient of Thermal Expansion (ppm/°F) 

ε = Strain (in/in %) 

ν = Poisson’s Ratio (in/in) 

ρ = Density (lb/in3

) 

Subscripts 

A = L Ply Related Quantity 

T, C = Tension, Compression 

1,2,3 = Material Coordinate System Axes 

CONVERSION FACTORS 

Property English Units Multiply By SI Units 

Modulus, 

(G&E) 

Mpsi 6.89 GPa 

Strength, 

(S) 

Ksi 6.89 MPa 

Thermal Conductivity,

(K) 

BTU/°F*hr*in 6.94 W/m-°K 

Heat Capacity, 

(C) 

BTU/Ib 2.326 kJ/Kg 

CTE, 

(α) 

ppm/°F 1.8×10–6 mm/mm K 

Density, 

(ρ) 

lb/in3

 27.7 g/cm3
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WBS 984754.02.07.03

19

Simulated Data for High Temperature Composite Design

Christos C. Chamis and Galib H. Abumeri

Composites; High temperature; Design properties; Mechanical; Thermal; Static;

Rupture; Fatigue

Unclassified -Unlimited

Subject Category: 24

Christos C. Chamis, NASA Glenn Research Center; and Galib H. Abumeri, QSS Group, Inc., 21000 Brookpark

Road, Cleveland, Ohio 44135. Responsible person, Christos C. Chamis, organization code R, 216–433–3252.

The paper describes an effective formal method that can be used to simulate design properties for composites that is

inclusive of all the effects that influence those properties. This effective simulation method is integrated computer

codes that include composite micromechanics, composite macromechanics, laminate theory, structural analysis, and

multi-factor interaction model. Demonstration of the method includes sample examples for static, thermal, and fracture

reliability for a unidirectional metal matrix composite as well as rupture strength and fatigue strength for a high

temperature super alloy. Typical results obtained for a unidirectional composite show that the thermal properties are

more sensitive to internal local damage, the longitudinal properties degrade slowly with temperature, the transverse and

shear properties degrade rapidly with temperature as do rupture strength and fatigue strength for super alloys.