Roy M. Sullivan

Glenn Research Center, Cleveland, Ohio

Eric H. Stokes

Southern Research Institute, Birmingham, Alabama

Eric H. Baker

Connecticut Reserve Technologies, Cleveland, Ohio

Effect of Water on the Thermo-Mechanical Behavior

of Carbon Cloth Phenolic

NASA/TM—2011-216981

February 2011
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (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 Offi cer. 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. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

 443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
Roy M. Sullivan

Glenn Research Center, Cleveland, Ohio

Eric H. Stokes

Southern Research Institute, Birmingham, Alabama

Eric H. Baker

Connecticut Reserve Technologies, Cleveland, Ohio

Effect of Water on the Thermo-Mechanical Behavior

of Carbon Cloth Phenolic

NASA/TM—2011-216981

February 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

40th SMBS, 36th PEDCS, 27th RNTS, and 25th SEPS

sponsored by the JANNAF Interagency Propulsion Committee

Orlando, Florida, December 6–10, 2010
Acknowledgments

Roy M. Sullivan and Eric H. Baker are grateful for funding from the RSRM V Project under NASA’s Constellation Program. 

Roy M. Sullivan is also grateful for funding from the Hypersonics Project under NASA’s Fundamental Aeronautics Program.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

This report is a formal draft or working 

paper, intended to solicit comments and 

ideas from a technical peer group.
NASA/TM—2011-216981 1 

Effect of Water on the Thermo-Mechanical Behavior 

of Carbon Cloth Phenolic 

Roy M. Sullivan 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Eric H. Stokes 

Southern Research Institute 

Birmingham, Alabama 35211 

Eric H. Baker 

Connecticut Reserve Technologies 

Cleveland, Ohio 44135 

Abstract 

The results of thermo-mechanical experiments, which were conducted previously by one of the 

authors, are reviewed. The strain in the direction normal to the fabric plane was measured as a function of 

temperature for a variety of initial moisture contents and heating rates. In this paper, the general features 

of the thermo-mechanical response are discussed and the effect of heating rate and initial moisture content 

are highlighted. The mechanical interaction between the phenolic polymer and water trapped within its 

free volumes as the polymer is heated to high temperatures is discussed. An equation for the internal 

stresses which are generated within the polymer due to trapped water is obtained from the total stress 

expression for a binary mixture of polymer and water. Numerical solutions for moisture diffusion in the 

thermo-mechanical experiments were performed and the results of these solutions are presented. The 

results of the moisture diffusion solutions help to explain the effects of heating rate and moisture content 

on the strain behavior normal to the fabric plane. 

Introduction 

Carbon cloth phenolic (CCP) is a laminated, carbon fabric-reinforced phenolic matrix composite used as 

the thermal insulation in solid rocket motor nozzles. The CCP insulation protects the metallic structural 

components of the nozzle assembly from the high temperature exhaust gases during motor operation. In this 

application, CCP composites are exposed to very high surface heat fluxes. Flame surface temperatures are in 

the vicinity of 5000 F and thermal gradients in excess of several thousand degrees per inch can develop 

within the CCP insulation. The high temperatures and severe thermal gradients sometimes result in localized 

material failures. The most common failure is delamination. 

Delamination failures are the result of excessive interlaminar stresses within the CCP insulation. For a 

long time, the solid rocket motor community has sought an analysis tool which is capable of accurately 

calculating the interlaminar stresses in CCP insulation that are caused by the surface heat fluxes during 

motor operation. The magnitudes of the interlaminar stresses are dictated by several factors. Of particular 

significance is the thermo-mechanical behavior of the material in the direction normal to the fabric plane, 

the material direction which we shall referred to as the ply-normal direction. 

The thermo-mechanical behavior of CCP is measured with the thermo-mechanical analysis (TMA) 

experiments. The TMA experiments are laboratory experiments, where specimens are heated at a constant 

heating rate and the dimensional changes are measured as a function of temperature. The strains which are 

measured in the TMA experiment are the result of the various chemical and physical processes which occur 

within the material as it is heated to high temperatures, such as thermal expansion, glass transition, moisture 
NASA/TM—2011-216981 2 

desorption and thermal decomposition. In this paper, the term thermal expansion refers only to the volume 

increase which is associated with the thermally-induced increase in the amplitude of vibration of the polymer 

molecules about their equilibrium position. Thermal expansion is only one of the possible sources of strain 

which is measured in the TMA tests. 

The thermo-mechanical behavior of the CCP in the direction normal to the fabric plane is significantly 

affected by the presence of moisture in the material. Moisture has two primary influences on the TMA 

response. First, water which is present in the material will lower the glass transition temperature. This effect 

has been reported by many previous authors (Refs. 1 to 5). The change from a hard, brittle behavior to rubbery 

behavior at glass transition is due to an increase in the mobility and the flexibility of the polymer segments. 

The intra-molecular bonds are primarily covalent bonds, while the intermolecular attractions are due to 

secondary bonding forces, which range from the weak van der Waals forces to the much stronger hydrogen 

bonds. The glass transition temperature is the temperature at which there is sufficient thermal energy to 

overcome the secondary forces between the polymer molecules and permit large-scale cooperative motion of 

the chain segments (Ref. 6). The absorption of moisture increases the distance between polymer molecules. 

This reduces the intermolecular forces between polymer molecules and reduces the thermal energy required 

for glass transition. Thus, the glass transition temperature is reduced. 

The second effect of water on the TMA response is related to the hygrothermal stresses which are 

generated within the polymer upon heating. Water which is trapped inside the CCP material as it is heated to 

high temperatures can exert significant pressures. Pressurized water within the material will induce tensile 

stresses in the polymer network and a resulting increase in the strain response. These stress-induced strains can 

be a significant portion of the total strain which is measured in the TMA tests. Furthermore, these tensile 

stresses in the polymer may contribute significantly to delamination failures. As a result, it is necessary to 

determine the magnitude of these tensile stresses for any combination of moisture content and heating rate 

which may be experienced. 

The objective of this paper is to discuss the role of moisture and moisture diffusion on the thermomechanical behavior as the CCP is heated to high temperatures. In the next section, we will review the results 

of previously-conducted TMA experiments that measured the effect of moisture content and heating rate on 

the strain response normal to the fabric plane. In the following section, we discuss the mechanical interaction 

between the phenolic polymer and water trapped within its free volumes as the polymer is heated to high 

temperatures. An equation for the internal stress which is generated within the polymer due to trapped water is 

obtained from the total stress expression for a binary mixture of polymer and water. Next, the results of a series 

of numerical solutions for moisture diffusion in the TMA experiments are presented. The diffusion solutions 

are performed for various initial moisture contents and heating rates. By comparing the predicted moisture 

content results with the measured strain results, we obtain a more thorough understanding of the interaction of 

water with the phenolic polymer and the effect of this interaction on the observed thermo-mechanical behavior. 

In this manner, we can start to formulate the essential ingredients of an analysis tool for calculating the 

interlaminar stresses in CCP insulation during motor operation. 

Review of Ply-Normal Thermo-Mechanical Analysis Experiments 

Stokes (Ref. 7) measured the effect of moisture content and heating rate on the ply-normal thermomechanical behavior of FM5055 carbon phenolic, a particular carbon phenolic made using 91LD phenolic 

resin. The carbon fabric was derived from rayon yarn supplied by Avtex Rayon. The tests were conducted on 

cylindrical specimens with a diameter of 0.25 in. and a length of 1.0 in. The specimens were fabricated so that 

the ply-normal direction is coincident with the specimen axial direction. The specimens were pre-conditioned 

to moisture contents of 2, 4.5, 6.1, 8.5, and 8.9 percent. Stokes (Ref. 7) measured the strain as a function of 

temperature as the specimens were heated at a constant rate of 2 and 10 F/sec. The average strain response for 

each of the five initial moisture contents is shown in Figure 1. The results for a 2 F/sec heating rate are shown 

in Figure 1(a) and the results for a 10 F/sec heating rate are shown in Figure 1(b). 
NASA/TM—2011-216981 3 

a) 2 F/sec b) 10 F/sec

Figure 1.—TMA strain response normal to fabric plane versus temperature for specimens preconditioned to five initial moisture contents and heated at 2 and 10 F/sec (from Stokes (Ref. 7)). 

a) 2 F/sec, b) 10 F/sec. 

a) 2 percent initial moisture b) 4.5 percent initial moisture

 c) 6.1 percent initial moisture d) 8.5 percent initial moisture

Figure 2.—TMA strain response normal to fabric plane versus temperature for specimens pre-conditioned to four 

initial moisture contents and heated at 2 and 10 F/sec (from Stokes (Ref. 7)). a) 2 percent initial moisture, 

b) 4.5 percent initial moisture, c) 6.1 percent initial moisture, d) 8.5 percent initial moisture. 

These same results are redisplayed in Figure 2 to illustrate the effect of heating rate. In each of the plots in 

Figure 2, the 2 and 10 F/sec heating rate results are displayed for a specific initial moisture content. The 

results for 2, 4.5, 6.1, and 8.5 percent moisture are shown in Figures 2(a) to (d), respectively. 
NASA/TM—2011-216981 4 

In addition to highlighting the influence of heating rate and initial moisture content on the thermomechanical behavior, the results shown in Figures 1 and 2 also serve to demonstrate the typical features of 

the thermo-mechanical behavior of carbon cloth phenolic normal to the fabric plane. At low temperatures, 

the strain curves are linear and the slopes of the curves are small. At these low temperatures, the polymer 

is in the glassy state and the strain is due solely to the thermal expansion of the glassy polymer. The 

coefficient of thermal expansion of the glassy polymer αg is estimated from Figures 1 and 2 to be 

approximately 9×10–6 F–1. 

The transition from glassy to rubbery behavior in the phenolic polymer occurs over a range of 

temperatures. The glass transition temperature Tg lies roughly at the center of this temperature range. As 

the glass transition temperature is approached, the strain curve begins to deviate from the initial linear 

portion of the curve. There is a sudden increase in the slope of the curve and a corresponding increase in 

the strain magnitude. The magnitude of the strain increase which follows glass transition is proportional 

to the initial moisture content and to the heating rate. Also, the temperature at which the glass transition 

begins to occur is dependent upon the initial moisture content; an increase in the moisture content causes 

the glass transition to begin at a lower temperature. However, the temperature at which glass transition 

begins does not seem to be dependent upon the heating rate, as this temperature is the same for the 2 and 

10 °F/sec results for all four initial moisture conditions shown in Figure 2. 

Notice that the TMA strain response for 4.5 and 6.1 percent moisture in Figure 1 appear to exhibit the 

same glass transition initiation temperature. The same is true for the 8.5 and 8.9 percent curves. A 

reasonable estimate of the glass transition initiation temperature for 2, 4.5, and 8.5 percent moisture is 

400, 300, and 260 F, respectively. Using these values, the glass transition initiation temperature is 

plotted versus initial moisture content in Figure 3. 

Most of the strain curves exhibit a double peak response. The first peak follows the glass transition 

and the second peak occurs at the onset of decomposition, within the range 800 to 1000 °F. The 

temperature at which decomposition occurs appears to be dependent upon the heating rate. The 

decomposition temperature is shifted to higher values with an increase in the heating rate. This is to be 

expected since the decomposition process is a kinetic process and this behavior is characteristic of kinetic, 

temperature dependent processes. 

There is a dramatic decrease in the strain following the decomposition peak. This decrease in strain is 

due to the volumetric shrinkage associated with the mass loss which occurs during polymer decomposition. 

The shrinkage strain remains fairly consistent for all initial moisture content conditions and both heating 

rates. This shrinkage strain has a value of 55 to 60 mils/in. 

Figure 3.—Glass transition initiation temperature plotted 

versus initial moisture content, estimated from the TMA 

strain plots in Figure 1. 
NASA/TM—2011-216981 5 

Figure 4.—TMA strain response normal to the fabric plane 

versus temperature for three heating rates (from Stokes 

(Ref. 8)). 

There appears to be a permanent offset between the 2 and 10 F/sec TMA response (Fig. 2). The 

strain curves for the higher heating rates are offset from the strain curves for the lower heating rates, with 

the higher heating rate curves having larger strain magnitudes. The strain offset appears to originate 

during the strain increase that occurs during glass transition. This indicates that there is considerable 

irreversible strain occurring within this temperature region. The value of the strain offset remains fairly 

constant even as the material is heated through polymer decomposition and charring. There is also a strain 

offset associated with two moisture content values (Fig. 1), but this offset is not as pronounced as the 

offset between the two heating rates. 

The results shown in Figure 4 are taken from Stokes (Ref. 8) and further demonstrate the effect of 

heating rate on the thermo-mechanical response. These results were obtained using a cylindrical test 

specimen with a diameter of 0.25 in. and heating rates of 10 F/min, 1 F/sec, and 10 F/sec. The initial 

moisture content in the test specimens was not reported. However, these specimens were tested in the asreceived condition, which typically contains 3.5 to 4.5 percent moisture. By comparing the strain response 

in Figure 4 to the results shown in Figures 1 and 2, it appears that the initial moisture contents are in this 

same range of moisture contents. 

The TMA response for the 10 F/min heating rate does not seem to exhibit a glass transition behavior. 

The curve is linear from room temperature until the onset of polymer decomposition at approximately 

800 °F. The slope of the curve below 800 °F is equal to the glass coefficient of expansion (9×10–6 F–1). 

Notice that there is only one distinguishable peak in the 1 F/sec TMA response. Like all the other 

strain curves, the strain is linear at low temperatures, with a slope equal to the glass coefficient of thermal 

expansion, and, at glass transition, there is a sudden increase in the slope and a corresponding increase in 

the strain magnitude. However, shortly after the glass transition, the slope becomes constant, with a value 

that appears to be approximately equal to the glass coefficient of expansion. The slope remains constant 

until the onset of decomposition. The strain curves shown in Figure 2 for a 2 percent initial moisture 

content exhibit a very similar strain behavior. 

Mechanical Interaction of Polymer and Water in TMA Experiments 

Many authors (Refs. 9 to 17) have speculated that absorbed water will exist within the polymer in two 

states: bound water and free water. Bound water molecules are immobilized and are attached to the 

polymer molecule by forming secondary bonds with hydrophilic groups such as hydroxyl groups in the 

phenolic polymer. Free water resides in the free volume, which are the unoccupied or “free” spaces 

between the polymer molecules. Free water is relatively free to travel throughout the free volume. 
NASA/TM—2011-216981 6 

Denoting the free volume by Vf and the volume occupied by polymer molecules by Vp, the free volume 

fraction and polymer volume fraction is by definition f = Vf /V and p = Vp /V, respectively, where V is the 

total volume given by V = Vp+Vf. 

Some authors (Refs. 10, 12, 13, and 17) have suggested that the bound water disrupts the hydrogen 

bonds between the polymer molecules, causing swelling and increasing the mobility of the polymer 

segments. As a result, it is the bound water that is usually assumed to be responsible for the moisture 

swelling and the lowering of the glass transition temperature. The results of moisture swelling studies 

conducted by Stokes (Ref. 17) on carbon cloth phenolic composite specimens reveal a very low swelling 

efficiency, indicating that the majority of the absorbed water resides in the free volumes. Although we 

acknowledge the effect of bound water on the glass transition temperature, for the present study, we will 

assume that the water within the carbon phenolic specimens is primarily free water. The volume fraction 

of water is defined as w = Vw /V, where Vw is that portion of the free volume that is occupied by water 

molecules. 

If moisture absorption in the phenolic polymer is an exothermic process, then by van ’t Hoff’s 

equation the equilibrium moisture content will decrease with an increase in temperature and water will be 

released as the material is heated (Refs. 18 and 19). Through various moisture conditioning and drying 

studies conducted on CCP, it appears that the equilibrium moisture content will be very small at 

temperatures not much higher than the boiling point of water. If the specimen is heated faster than the 

water can diffuse to an exterior surface and become liberated from the specimen, then the moisture 

content within the polymer will be in excess of the equilibrium moisture content. Under this nonequilibrium condition, the excess water, which is momentarily trapped within the polymer, exerts a 

pressure on the network of polymer molecules. 

The driving force for the strain increase at glass transition is pressurized water within the free 

volumes of the polymer. The viscosity and Young’s modulus of the polymer is significantly reduced at 

the glass transition due to an increase in the mobility of the polymer segments. The response to a large 

polymer network stress and a sudden drop in the Young’s modulus and viscosity is the rather dramatic 

increase in strain which is observed as the glass transition temperature is approached. 

In addition, it should be noted that, according to the free volume theory, the increase in the strain rate 

which occurs at glass transition is due to an increase in the free volume fraction (Refs. 3, 20, and 21). This 

can be written as αr = αg+df /dT, where αr is the slope of the strain curve in the rubbery state above glass 

transition. Thus, it may be stated more specifically that the increase in the slope of the strain response at 

glass transition is due to a volumetric straining of the free volume which is caused by pressurized water. 

Furthermore, since the strain increase at glass transition appears to be largely an irreversible strain, we 

must conclude that the increase in the free volumes is also largely irreversible. 

In order to analyze the effect of water on the thermo-mechanical behavior, we will treat the polymer 

containing water as a condensed mixture of polymer and water, similar to the approach taken in Sullivan 

(Ref. 22). The total stress on the polymer/water mixture may be written as the sum of the contributions 

from the individual constituents, weighted according to the amount of volume that each constituent 

occupies. The total stress tensor may be written p

p ij w ij  wij    , where wij and p ij are the partial 

stress of water and polymer, respectively. The partial stress of water is written ij w wij   P , where Pw is 

the partial pressure of water and ij is the Kronecker delta function. The negative sign appears in the 

previous expression, since a positive increase in the water partial pressure will result in a negative 

increase (compression increase) in the total stress. Using contracted notation and denoting the direction 

normal to the fabric plane with the subscript n, the total stress in this direction is written 

p n  wPw  pn (1)
NASA/TM—2011-216981 7 

The volume fractions of water and polymer may also be expressed as the product of the partial 

volume and partial density, w  wvw and p p p    v . The partial density of water in the polymer/water 

mixture w is the mass of water per unit total volume of mixture (w  mw /V ) and the partial volume of 

water in the mixture vw is the volume occupied by each gram of water ( vw  Vw / mw ). 

Just as the pressure on a homogenous substance is dependent upon the temperature and its specific 

volume, the partial pressure of water in the mixture Pw is a function of the temperature and the partial 

volume vw. The partial pressure is an increasing function of the temperature and it is inversely 

proportional to the partial volume. The variation of the partial volume vw with temperature will be 

governed by the free volume of the polymer. That is, the volume that each water molecule occupies 

depends upon the amount of volume made available by the polymer network. 

Since there are no mechanical restraints placed upon the specimen during the TMA test, the 

composite level stresses in the specimen are zero. In addition, the carbon fibers will not act to impart a 

restraining stress to the polymer/water mixture in the ply-normal direction. We can therefore set 

Equation (1) equal to zero and obtain  w p  w p n   /  P . Given that w  wvw , we therefore have 

w w w p n   v P . Thus, the stress imparted to the polymer network in the ply-normal direction during the 

TMA tests is proportional to the amount of moisture in the specimen (w ) and dependent upon the 

thermodynamic state of the water which defines the values of vw and Pw at each temperature. 

In the TMA specimen, it is expected that the partial volume of water will increase with temperature 

since water resides in the free volume and the free volume increases with the increase in strain above the 

glass transition temperature. The exact path of thermodynamic states that is traveled will depend upon the 

modulus and viscosity of the polymer network since these properties will determine how the free volume 

changes with temperature. This in turn will affect how the partial volume of water changes with 

temperature. At this point however, the partial volume of water and its variation with temperature cannot 

be quantified, since the relationship between the volume fraction of water w and the free volume 

fraction  f is not known. We have only that w   f , based on our assumption that the majority of the 

water resides within the free volume. 

The thermodynamic state of water in the TMA specimen is expected to be somewhat different from 

its thermodynamic state in the restrained thermal growth (RTG) experiment. Sullivan (Ref. 22) showed 

that, in the RTG experiment, water in the polymer free volumes is in a compressed liquid state and the 

thermodynamic state of the water traces a nearly constant volume path on a P-V-T diagram as the 

temperature is increased. Sullivan (Ref. 22) attributed this to the mechanical constraint placed on the 

specimens during the RTG experiment. 

Moisture Diffusion in TMA Experiments 

To help analyze the effect of water on the thermo-mechanical behavior shown in Figures 1, 2, and 4, 

numerical solutions for the moisture diffusion in the 0.25 in. diameter TMA specimens were performed. It 

was assumed that the diffusion of moisture in the TMA specimen could be simulated using Fick’s first 

law with temperature-dependent moisture diffusivity. Fick’s first law is written Jw   cw

 D  , where 

Jw

 is the water mass flux vector, D

 is a second-order tensor of moisture diffusivity coefficients and cw

is the moisture content, which may be written in terms of the partial densities as   w w w p c   /    . 

Combining Fick’s first law with the mass continuity equation cw / t   Jw  0   results in a transient 

moisture diffusion equation with cw as the solution variable. The two-dimensional, axisymmetric form of 

the transient moisture diffusion equation was solved using ABAQUS (Ref. 23) (Dassault Systèmes 
NASA/TM—2011-216981 8 

Simulia Corp.) and the DCAX4 mass diffusion elements. The boundary condition cw  0 was imposed on 

all external surfaces of the specimen. 

During the TMA tests, moisture diffusion occurs in the plane of the carbon fabric and in the direction 

normal to the fabric plane. Previous moisture diffusivity measurements on carbon phenolic specimens 

indicate that the ratio of the moisture diffusivity in the in-plane and ply-normal directions can vary 

considerably (Ref. 24). In some cases, the moisture diffusivity in the ply-normal direction Dn was 

approximately equal to the value in the in-plane direction, while in other cases, the in-plane diffusivity Df

was several orders of magnitude greater than the ply-normal diffusivity. In order to address the potential 

effect of two-dimensional diffusion, we performed the numerical simulations using the following two 

extreme cases: 1) ply-normal diffusivity was set equal to zero (Dn = 0) and 2) the ply-normal moisture 

diffusivity was set equal to the in-plane diffusivity (Dn = Df). The results indicate that moisture diffusion 

in the ply-normal direction had a negligible effect on the average moisture content in the TMA 

specimens. This is not surprising, since the cylindrical TMA specimen has a large length to diameter ratio 

(1.0/0.25). The amount of moisture that flows across the end surfaces will be a small fraction of the total 

moisture mass flow. All of the moisture diffusion results which will be presented in the following 

paragraphs were obtained from numerical solutions with Dn = 0. 

It’s common practice to express the variation of the moisture diffusivity with temperature using an 

exponential function of the form 





 



   RT

E D D a o exp (2)

where Do is the pre-exponential coefficient, Ea is the activation energy, R is the universal gas constant and 

T is the absolute temperature. It follows from this equation that a plot of the natural log of the diffusivity 

versus the inverse of the absolute temperature is a straight line with a slope of –Ea/R and a y-intercept of 

lnDo. 

In an attempt to determine the best approach for moisture conditioning carbon phenolic specimens, 

Stokes (Ref. 25) conditioned FM5055 carbon phenolic specimens in various relative humidity 

environments and at a handful of different temperatures and measured the moisture uptake or weight loss 

versus time profiles for each conditioning environment. Sullivan, et al. (Ref. 26) deduced the value of the 

in-plane diffusivity at each test temperature by performing numerical solutions for the moisture diffusion 

and comparing the numerical solution results with the weight loss/gain versus time histories measured by 

Stokes (Ref. 25). The values of the in-plane diffusivity at each test temperature which were obtained in 

Sullivan, et al. (Ref. 26) are shown as the individual data points in Figure 5. Note that the results are 

plotted as the natural log of diffusivity versus the inverse of the absolute temperature. A fairly good fit to 

the data (R2

 = 0.960) is obtained with the linear function using the values Do = 1.77×106 in.2/hr and 

Ea = 16.64 kcal/mole. This is shown as the solid line in Figure 5. The value of 16.64 kcal/mole for the 

activation energy compares well with the value obtained by previous authors for epoxy and epoxy 

composites (Refs. 2, 12, and 16). 

In order to simulate the moisture diffusion in the constant heating rate TMA tests, the diffusivity must 

be continuously updated as the temperature is increased. At the end of each time step, the temperature 

was increased according to the time step increment and the heating rate. The moisture diffusivity was then 

updated using Equation (2) and the new temperature and the solution was performed for the next time 

step. This process was repeated until the conclusion of the simulation. 

We performed a series of moisture diffusion solutions for a uniform initial moisture content of 2, 4.5, 

6.1, and 8.5 percent and a heating rate of 2 and 10 °F/sec. The time incremental numerical solution yields 

the spatial distribution of the moisture content at each time step, and thus at each temperature. The 

moisture content distributions were used to calculate the volume average moisture content in the 

specimen at each time and temperature. The results of these numerical solutions are shown in Figure 6, 

where the average moisture content is plotted versus temperature. The 10 °F/sec results are plotted with 
NASA/TM—2011-216981 9 

Figure 5.—Plot of natural log of diffusivity versus the 

inverse of the absolute temperature (from Sullivan, 

et al. (Ref. 26)). 

Figure 6.—Average moisture content versus temperature from 

numerical solutions of moisture diffusion in TMA specimens. 

Solid lines are 10 F/sec results and dashed lines are 2 F/sec 

results. Also plotted is moisture content versus the estimated 

glass transition initiation temperature from Figure 3. 

solid lines and the 2 °F/sec results are plotted with dashed lines. We have also included the estimated 

glass transition initiation temperature versus initial moisture content (dashed black line) which was shown 

previously in Figure 3. In Figure 6, this is plotted with temperature as the abscissa. 

The results in Figure 6 show that, for both 2 and 10 °F/sec heating rates, there is not a significant 

amount of moisture diffusion prior to reaching the glass transition initiation temperature and thus the 

moisture content for the 2 °F/sec specimen is roughly the same as for the 10 °F/sec specimen. These 

results are consistent with the thermo-mechanical behavior shown in Figure 2, where it was observed that 

the glass transition temperature was not affected by the heating rate. Recalling that the glass transition 

temperature is dependent upon the moisture content, we would not expect the glass transition temperature 

to be dependent upon the heating rate, since, prior to the glass transition temperature, the moisture content 

is not dependent upon the heating rate. 
NASA/TM—2011-216981 10 

There are significant differences between the 2 °F/sec results and the 10 °F/sec results after the glass 

transition. In comparing two specimens that start with the same initial moisture content, the specimen 

which is heated at the higher rate will contain more moisture than the specimen heated at the slower rate 

at temperatures above the glass transition initiation temperature. 

The relationship between moisture content and the TMA strain response is illustrated by the 

composite plots in Figure 7. The predicted moisture content and the measured strain are plotted versus 

temperature for 2, 4.5, and 8.5 percent initial moisture content and heating rates of 2 and 10 °F/sec. 

Again, the plot of glass transition initiation temperature versus moisture content from Figure 3 is 

included. The temperature at which the average moisture content curve intersects the plot of moisture 

content versus the estimated glass transition initiation temperature should coincide with the temperature at 

which the TMA strain response begins to exhibit glass transition behavior. This appears to be 

approximately true for all cases shown in Figure 7. 

As the specimen is heated past the glass transition, the increase in strain occurs simultaneously with 

moisture diffusion. At this point, the 2 and 10 °F/sec predicted moisture content curves begin to diverge. 

As the difference between the two moisture content curves increases, the 2 and 10 °F/sec strain curves 

also begin to diverge. The higher heating rate results in a larger strain since there is more moisture present 

at any given temperature and since the polymer network stress is proportional to the amount of moisture 

in the specimen. Larger polymer network stresses lead to higher strain rates and higher cumulative strains. 

 a) 2 percent initial moisture b) 4.5 percent initial moisture

c) 8.5 percent initial moisture 

Figure 7.—Composite plots of predicted average moisture content (solid lines) and measured strain (dashed lines) 

versus temperature for heating rates of 2 and 10 F/sec. The plot of moisture content versus glass transition 

initiation temperature is also included. a) 2 percent initial moisture. b) 4.5 percent initial moisture. c) 8.5 percent 

initial moisture. 
NASA/TM—2011-216981 11 

For the strain curves with a double peak behavior, the temperature of the first peak is the temperature at 

which the polymer network stress p n becomes so small that it cannot produce any additional strain in the 

polymer network. The polymer network stress becomes small due to the effusion of moisture from the 

specimen. There is also a decrease in the partial pressure of water due to the increase in the free volumes 

which accompanies the strain increase. Although at this point, the relative magnitude of the latter effect is 

not certain. As the polymer stress becomes small, any elastic strain that was stored in the polymer 

network is recovered. Notice that for the 4.5 and 8.5 percent results, the temperature at the apex of the 

first peak in the thermo-mechanical response coincides with the temperature at which the predicted 

moisture content approaches zero. For the 2 percent results, the strain curve does not have a distinct first 

peak. In this case, the temperature at which the predicted moisture content approaches zero coincides with 

the temperature at which the slope of the strain curve decreases and returns to the glass coefficient of 

expansion αg. 

We also performed a series of moisture diffusion solutions for heating rates of 10 °F/min, 1 °F/sec 

and 10 °F/sec to help explain the thermo-mechanical behavior shown in Figure 4. In these simulations, 

the specimen heated at 10 and 1 °F/sec was assumed to have an initial moisture content of 3 and 

4 percent, respectively. These initial moisture contents were chosen based on the apparent glass transition 

initiation temperature which is evident from the strain curves in Figure 4. Since the 10 °F/min strain curve 

does not exhibit an obvious glass transition behavior, we were not able to deduce the glass transition 

initiation temperature and estimate the initial moisture content. For the 10 °F/min simulation, we assumed 

initial moisture contents of both 3 and 4 percent. 

The results of these numerical solutions are shown in Figure 8, where the predicted moisture content 

and strain response are plotted versus temperature. We have again included the estimated glass transition 

initiation temperature versus moisture content which was shown previously in Figure 3. For a heating rate 

of 10 °F/min, the predicted moisture content curve will not intersect the plot of glass transition initiation 

temperature versus the moisture content until temperatures above 500 °F, at which point there is no 

moisture left in the specimen. This is true whether the initial moisture content is 3 or 4 percent. This 

would explain the strain behavior for the 10 °F/min heating rate, which is linear from room temperature 

until the onset of decomposition with a slope equal to the glass coefficient of expansion αg. Since the 

moisture has left the specimen before the glass transition temperature is reached, there would be no 

appreciable increase in the free volume and we would not expect an increase in the strain rate above that 

of the glass coefficient of thermal expansion. 

 a) 10 °F/sec and 10 °F/min results b) 1 °F/sec and 10 °F/min results

Figure 8.—Composite plots of predicted average moisture content (solid lines) and measured strain (dashed lines) 

versus temperature for heating rates of 10 F/min, 1 F/sec, and 10 F/sec. The plot of moisture content versus 

glass transition initiation temperature is also included. a) 10 F/sec and 10 F/min results. b) 1 F/sec and 

10 F/min results. 
NASA/TM—2011-216981 12 

The moisture diffusion solution results also help to explain the thermo-mechanical behavior in the 

1 °F/sec heating rate results. In view of the predicted moisture content results shown in Figure 8, it 

appears that, for 1 °F/sec heating rate, glass transition would begin in the vicinity of 400 °F and that the 

moisture will have evaporated from the specimen at temperatures slightly above 500 °F. This is consistent 

with the measured thermo-mechanical behavior, where the glass transition begins at temperatures just 

under 400 °F and the slope of the strain curve becomes constant and equal to the glass expansion 

coefficient αg at approximately 500 °F. Although the material may experience a glass transition and 

become rubbery at 400 °F, if there is no water left in the specimen above 500 °F, there will be no partial 

pressure to cause an increase in the free volumes. We would therefore expect the strain response above 

500 °F to have a constant slope equal to the glass coefficient of expansion. 

Concluding Remarks 

The presence of water in carbon cloth phenolic composites plays a significant role in the thermomechanical behavior normal to the fabric plane. The amount of water determines the glass transition 

temperature, the temperature at which the mechanical behavior of the polymer transitions from glassy to 

rubbery. Water is also a major source of strain as the material is heated above the glass transition 

temperature. The amount of water which is in excess of the equilibrium moisture content will exert a 

stress on the polymer network and the magnitude of this stress is proportional to the amount of excess 

water. There are indications that the polymer network stress produces both elastic and inelastic strains. 

The response to a large polymer network stress and a sudden drop in the Young’s modulus and viscosity 

is the rather dramatic increase in the strain which is observed at glass transition. Thus, the amount of 

water within the polymer determines the temperature at which the rapid rise in strain is observed and the 

magnitude of this strain increase. 

In this paper, we proposed to use a moisture diffusion model which is based on Fick’s law with a 

temperature dependent diffusivity to simulate the moisture diffusion in the TMA experiments. The results 

of the moisture diffusion solutions help to illustrate the interaction of water and polymer and its effect on 

the various features of the thermo-mechanical response. For example, the analysis results reveal why the 

glass transition temperature is not a function of the heating rate. In addition, the results indicate that an 

increase in the strain rate will not occur at the glass transition temperature if there is no moisture 

remaining in the specimen when the glass transition temperature is reached. If there is no water left at 

glass transition, then the strain rate will be the same as the glass thermal expansion coefficient, even 

though the modulus and viscosity may have decreased dramatically at glass transition. 

References 

1. Couchman P.R. and Karasz F.E., 1978. A classical thermodynamic discussion of the effect of 

composition on glass-transition temperatures. Macromolecules 11(1), 117–119. 

2. DeIasi R. and Whiteside J.B., 1978. Effect of moisture on epoxy resins and composites, in: Vinson, 

J.R. (Ed.), Advanced Composite Materials-Environmental Effects. ASTM STP 658, pp. 2–20. 

3. McKague E.L., Reynolds J.D. and Halkias J.E., 1978. Swelling and glass transition relations for 

epoxy matrix material in humid environments. Journal of Applied Polymer Science 22, 1643–1654. 

4. Reimschuessel H.K., 1978. Relationships on the effect of water on glass transition temperature and 

Young’s modulus of Nylon 6. Journal of Polymer Science 16, 1229–1236. 

5. Ellis T.S. and Karasz F.E., 1984. Interaction of epoxy resins with water: the depression of glass 

transition temperature. Polymer 25, 664–669. 

6. Ebewele R.O., 2000. Polymer Science and Technology, CRC Press. 

7. Stokes E.H., 1990. Across-ply mechanical and thermal characteristics of FM5055 (Avtex preshutdown) as a function of the material’s moisture content. Southern Research Institute Report, 

SRI-MME-90-1109-6526-5. 
NASA/TM—2011-216981 13 

8. Stokes E.H., 1988. The physical, mechanical and thermal properties of the FM5055 404 aft inlet ring 

(vol. 4: thermal tests, gas permeability and thermal expansion). Southern Research Institute Report, 

SRI-EAS-88-201-6032-1. 

9. Carter H.G. and Kibler K.G., 1978. Langmuir-type model for anomalous moisture diffusion in 

composite resins. Journal of Composite Materials 12, 118–131. 

10. Adamson M.J., 1980. Thermal expansion and swelling of cured epoxy resin used in graphite/epoxy 

composite materials. Journal of Materials Science 15, 1736–1745. 

11. Lele A.K., Hirve M.M., Badiger M.V. and Mashelkar R.A., 1997. Predictions of bound water content 

in poly (N-isopropylacrylamide) gel. Macromolecules 30, 157–159. 

12. Zhou J. and Lucas J.P., 1999a. Hygrothermal effects of epoxy resin. Part I: the nature of water in 

epoxy. Polymer 40, 5505–5512. 

13. Zhou J. and Lucas J.P., 1999b. Hygrothermal effects of epoxy resin. Part II: variations of glass 

transition temperature. Polymer 40, 5513–5522. 

14. Suh D.W., Ku M.K., Nam J.D., Kim B.S. and Yoon, S.C., 2001. Equilibrium water uptake of 

epoxy/carbon fiber composites in hygrothermal environmental conditions. Journal of Composite 

Materials 35(3) 264–278. 

15. Liu W.G. and Yao K.D., 2001. What causes the unfrozen water in polymers: hydrogen bonds between 

water and polymer chains?. Polymer 42, 3943–3947. 

16. Popineau S., Rondeau-Mouro C., Sulpice-Gaillet C. and Shanahan M.E.R., 2005. Free/bound water 

absorption in an epoxy adhesive,” Polymer 46, 10733–10740. 

17. Stokes, E.H., 1993. Anomalous swelling behavior of FM5055 carbon phenolic composite. AIAA 

Journal 31(3), 584–589. 

18. El-Sa’ad L., Darby M.I. and Yates B., 1990. Moisture absorptioin by epoxy resins: the reverse 

thermal effect. Journal of Materials Science 25, 3577–3582. 

19. Bao L.R. and Yee A.F., 2002. Effect of temperature on moisture absorption in a bismaleimide resin 

and its carbon fiber composites. Polymer 43, 3987–3997. 

20. Williams M.L., Landel R.F. and Ferry J.D., 1955. J. Am. Chem. Soc. 77, 3701. 

21. Kelley F.N. and Bueche F., 1961. Viscosity and glass temperature relations for polymer-diluent 

systems. Journal of Polymer Science L, 549–556. 

22. Sullivan R.M., 1996. The effect of water on thermal stresses in polymer composites. ASME J. Appl. 

Mech. 63(1), 173–179. 

23. ABAQUS/CAE Version 6.8-1, Dassault Systèmes Simulia Corp., Providence, RI, © Dassault 

Systèmes, 2008. 

24. Stokes E.H., “Moisture related characteristics of phenolic resin based composites,” JANNAF 

Propulsion Meeting, Tampa, FL, 4–8 December 1995. 

25. Stokes E.H., 1987. The effect of moisture on the mechanical and thermal response of FM5055 carbon 

phenolic composites. Southern Research Institute Report, SRI-EAS-87-1244-6245-6. 

26. Sullivan R.M., Stokes E.H. and Baker E.H., 2010. Effect of time at temperature on the x-ply tensile 

modulus of carbon cloth phenolic composites. NASA/TM—2010-216921. 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection 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 Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-02-2011 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Effect of Water on the Thermo-Mechanical Behavior of Carbon Cloth Phenolic 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Sullivan, Roy, M.; Stokes, Eric, H.; Baker, Eric, H. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 136905.08.01.16.04 

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-17622 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2011-216981 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 18, 24, 27, and 39 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The results of thermo-mechanical experiments, which were conducted previously by one of the authors, are reviewed. The strain in the 

direction normal to the fabric plane was measured as a function of temperature for a variety of initial moisture contents and heating rates. In 

this paper, the general features of the thermo-mechanical response are discussed and the effect of heating rate and initial moisture content 

are highlighted. The mechanical interaction between the phenolic polymer and water trapped within its free volumes as the polymer is 

heated to high temperatures is discussed. An equation for the internal stresses which are generated within the polymer due to trapped water 

is obtained from the total stress expression for a binary mixture of polymer and water. Numerical solutions for moisture diffusion in the 

thermo-mechanical experiments were performed and the results of these solutions are presented. The results of the moisture diffusion 

solutions help to explain the effects of heating rate and moisture content on the strain behavior normal to the fabric plane.

15. SUBJECT TERMS

Thermal expansion; Moisture; Moisture content; Glass transition temperature; Heating; Diffusion; Diffusivity 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

19 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18