Characterization of Low Density Glass Filled Epoxies 

by Matthew J. Quesenberry, Phillip H. Madison, and Robert E. Jensen 

ARL-TR-2938 March 2003 

Approved for public release; distribution is unlimited. 
NOTICES 

Disclaimers 

The findings in this report are not to be construed as an official Department of the Army position unless 

so designated by other authorized documents. 

Citation of manufacturer’s or trade names does not constitute an official endorsement or approval of the 

use thereof. 

Destroy this report when it is no longer needed. Do not return it to the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-2938 March 2003 

Characterization of Low Density Glass Filled Epoxies 

Matthew J. Quesenberry 

University of Delaware 

Phillip H. Madison and Robert E. Jensen 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
i

Acknowledgments 

This research was supported in part by an appointment to the Research Participation Program at 

the U.S. Army Research Laboratory (ARL) administered by the Oak Ridge Institute for Science 

and Education through an interagency agreement between the U.S. Department of Energy and 

ARL. The authors also wish to acknowledge the ARL Composite Materials Research Materials 

Center of Excellence contract DAAD19-01-2-0001 to the University of Delaware Center for 

Composite Materials for partial funding of this project. Finally, the authors also would like to 

thank the late Professor Roy L. McCullough for his support and advice during the project. He 

will be missed. 
ii

Contents 

Acknowledgments i

List of Figures iii

List of Tables iii

1. Introduction 1

2. Theory 3

2.1 Density.............................................................................................................................3 

2.2 CTE .................................................................................................................................3 

2.3 Composite Modulus ........................................................................................................4 

2.3.1 Hollow Glass Filler .............................................................................................7 

2.3.2 Mixed Hollow and Solid Spheres........................................................................8 

3. Experimental 9

3.1 Materials..........................................................................................................................9 

3.2 Characterization.............................................................................................................12 

4. Results and Discussion 12

4.1 Solid vs. Hollow Glass Filler ........................................................................................12 

4.1.1 Density...............................................................................................................12 

4.1.2 CTE ...................................................................................................................13 

4.1.3 Young’s Modulus..............................................................................................14 

4.2 Combined Mixed Solid and Hollow Glass Filler ..........................................................15 

5. Conclusion 18

6. References 19

Report Documentation Page 21
iii

List of Figures 

Figure 1. A schematic of an encapsulating potting compound showing the coverage of a 

surface mounted device..............................................................................................................1 

Figure 2. Chemical structures of DGEBA epoxy, DICY curing agent, and 2-MI catalyst. ...........9 

Figure 3. Particle size distributions for the hollow (S) and solid (T) glass fillers.....................10 

Figure 4. SEM images of the (a) hollow and (b) solid glass fillers. .............................................11 

Figure 5. Plots of composite density vs. volume fraction of filler for composites filled with 

hollow glass spheres (S) and solid glass spheres (T). The ROM (equation 1) is used to 

predict the experimental densities. Density measurements were precise to ± 0.02 g/cm3

.......13 

Figure 6. Composite CTE vs. volume fraction of hollow glass filler (). Composite CTE at 

Vf = 0.45 solid glass filler (§) illustrated for comparative purposes. ROM and 

Schapery’s lower bound fit to hollow glass filled composite data. .........................................14 

Figure 7. Plot of experimental composite modulus vs. volume fraction of hollow glass filler 

along with theoretical predictions via the C-Combining Rule.................................................15 

Figure 8. Plot of experimental composite modulus vs. volume fraction of solid glass filler 

along with theoretical predictions via the S-Combining Rule, Voigt model, and Reuss 

model........................................................................................................................................16 

Figure 9. Density, elastic modulus, and CTE, are plotted for the ternary composite of solid 

and hollow glass filler in epoxy. Overall Vf = 0.45. ...............................................................16 

List of Tables 

Table 1. Summary of constitutive materials properties for the matrix epoxy, solid glass filler, 

and hollow glass filler..............................................................................................................11 

Table 2. Summary of experimental determinations of Vf, ρ, void content, CTE, and E..............17 
1

1. Introduction 

Electronic devices are often encapsulated with a highly filled polymeric material, known as a 

potting compound, that primarily serves to protect the sensitive and conductive components from 

outside environmental effects (Figure 1) [1, 2]. The matrix polymer is typically composed of a 

thermosetting epoxy resin, which exhibits flow prior to cure and allows for continuous 

encapsulation of the electronic component. However, the use of a pure epoxy resin as an 

encapsulant material, or potting compound, alone is insufficient due to a relatively high 

coefficient of thermal expansion (CTE) (CTE > 60 × 10!6

/°C) [3]. The high values of CTE for 

the epoxy resins are inconsistent with those of the metallic electronic components and result in 

excessive residual stress and mechanical fatiguing of the electronic device during the cyclic 

heating and cooling encountered during normal operation [4]. Inclusion of particulate fillers has 

been used extensively to reinforce thermosetting epoxy resins to reduce cost, degree of 

shrinkage, CTE, and to raise the thermal conductivity and glass transition temperature [5]. In 

addition, particulate fillers also tend to increase stiffness relative to the bulk epoxy. 

Potting compound

Device

Circuit board

Figure 1. A schematic of an encapsulating potting compound 

showing the coverage of a surface mounted device. 

Silica-based E-glass, which has a CTE of ~5 × 10!6/°C, has been widely utilized as a particulate 

filler in epoxy-based resins to reduce the overall CTE of the potting compound, making it more 

suitable for electronics applications [2, 6]. These types of encapsulating compounds are 

inexpensive and commonly used in a wide range of commercial electronics products, from 

personal computers to cell phones [3]. However, silica based E-glass filler has a relatively high 

density (ρf = 2.54 g/cm3

) in comparison to the epoxy matrix (ρm ~1.15 g/cm3) and results in a 

substantial weight increase when the potting compound is heavily loaded [7]. Consequently, 

lower density filler that can also effectively reduce the CTE of the encapsulant system is 

desirable for mass-critical applications, such as those found in aerospace and aviation 
2

electronics. Reduction in mass becomes an even more important issue for the high strain-rate 

applications of Army interest where there are critical momentum considerations. 

While historically solid glass filler has been utilized in electronic potting compounds, recent 

studies have shown that hollow glass microspheres may be used as a lightweight alternative 

[1–3]. Such hollow glass fillers are readily available at low cost and are termed microspheres, 

hollow glass beads, hollow glass spheres, or microballoons. These microspheres, through 

variations in glass wall thickness and particle diameter, have low densities in the range of 

0.1–1.0 g/cm3 [6]. Hollow glass microspheres have been widely employed as particulate filler in 

polymeric systems for over three decades [8]. Hollow glass microspheres have essentially the 

same CTE as their solid counterparts, but have a much lower density [6]. Hollow glass 

microspheres were originally designed to decrease evaporation of oil and petroleum in large 

containers and as a means to increase buoyancy in ships and submarines. Hollow glass 

microspheres have more recently been exploited in the aeronautical, aerospace, automotive, civil 

and industrial engineering, and electronics industries as syntactic foams [9–12]. Incorporation of 

hollow glass microspheres as filler in polymeric matrixes to produce syntactic foams results in 

unique composite properties including good shear stiffness and strength, fatigue and impact 

resistance, low density, and high strength to weight ratio, which have largely facilitated their 

widespread application [13]. To obtain the low CTE and ρc required, hollow glass filler may be 

substituted for the standard solid glass filler. However, one possible disadvantage of a hollow 

microsphere filled epoxy composite is a relatively low modulus and compressive strength when 

compared to traditional solid glass filler. 

While epoxy-based potting compounds incorporating either pure solid glass filler or pure hollow 

microsphere filler have been studied extensively in the literature, little research has been 

performed involving mixed hollow microsphere/solid glass filler combinations. Potential 

electronic potting compound applications of U.S. Army interest may not necessarily be driven by 

the need to minimize the CTE or density at the cost of substantial loss in modulus, but rather 

may require a specific mixture of hollow and solid fillers to achieve a balance of these properties 

for optimum performance. This report will discuss the application of composite micromechanics 

in the analysis of ρc, CTE, and Ec for a series of epoxy-based electronic potting compounds 

highly loaded with mixtures of hollow microspheres and solid glass filler. Knowledge of the 

fundamental thermal and mechanical properties of these systems will serve as a useful guide in 

the formulation of advanced electronic potting compounds suitable for the high strain-rate 

applications of U.S. Army interest. 
3

2. Theory 

2.1 Density 

The density of a composite material (ρc) can have dramatic effects on the global performance of 

the component during use. Addition of high-density filler will subsequently increase the overall 

composite density. Generally, aerospace applications require lightweight materials because they 

require less energy to propel. Typically, the overall density of a filled composite, regardless of 

whether the filler is hollow, solid, or a mixture of the two, can be accurately predicted by the 

Rule of Mixtures (ROM) in equation 1 [14]: 

ρc =Vf ρ f +Vm ρ m , (1) 

where 

ρf = filler density, 

ρm = matrix density, 

Vf = volume fraction of filler, and 

Vm = volume fraction of matrix. 

2.2 CTE 

The coefficient of thermal expansion (α) is defined as the ratio of the change in length of a 

material per degree Celsius. Thermal expansion is of critical importance in design 

considerations, as it can dictate important parameters such as the composite filler size and shape 

[13]. Utilizing the CTE of the pure component matrix (αm) and filler (αf), several mathematical 

models will be applied to predict the composite CTE (αc) of the three filled epoxy systems, 

including the standard ROM, Schapery’s upper and lower bounds, as well as the methodology of 

Dzenis and Maksimov [15, 16]. 

As a first order approximation to αc the standard ROM serves as an adequate model [1]. The 

ROM as applied to CTE is described in equation 2: 

α c =Vfα f +Vmα m . (2) 

Schapery derived an exact relationship between composite bulk modulus (kc) and αc, which is 

based upon thermoelastic energy principles and complementary energy functions [15]. Since 

exact measurements of Kc are difficult to obtain, Schapery incorporated upper and lower bounds 

solutions to αc as described by equations 3 and 4, respectively. 
4

(K K )

(K K )(α α )

K

K

α α

m f

f m

l

m c

l

c

f

m

u

c −

− − = + ; (3) 

, (K K )

(K K )(α α )

K

K

α α

m f

f m

u

m c

u

c

f

m

l

c −

− − = + (4) 

where u Kc and l Kc are calculated using Hashin’s and Shtrikman’s bounding solutions for bulk 

modulus as described by equations 5 and 6: 

(3K 4G )

3V

K K

1

V K K

f f

f

m f

m

f

u

c

+

+ −

= + ; (5) 

(3K 4G )

3V

K K

1

V K K

m m

m

f m

f

m

l

c

+

+ −

= + . (6) 

For predictive approaches in the determination of composite CTE the pure component CTE for a 

single hollow sphere (αh) must first be estimated. Dzenis and Maksimov derived the following 

expression to approximate αh [16]: 















 − −

− = + − −

h s

1

s

1

n

n s

h s K

1

K

1

K K

α α

α α , (7) 

where Kh is the bulk modulus of hollow sphere, and c, s, and n again refer to the composite, 

shell, and nucleus properties, respectively. Kh is determined via an analogous modulus analysis 

by Dzenis and Maksimov, which will be described in a later section. 

2.3 Composite Modulus 

The Voigt and Reuss models are the two most basic models used to describe the properties of a 

two-phase composite system consisting of a spherical filler inclusion embedded in a continuous 

matrix material. The Voigt model, which is described by equations 8 and 9, assumes that the 

particulate inclusions and matrix material are subjected to constant strain. This model typically 

acts as an upper bound to experimental data for composite samples where the filler compliance is 

stiff in comparison to the matrix. Young’s modulus is easily determined once ν, G, and K are 

known, as described by equations 10–12. For each of these equations, the subscript c refers to 

the composite property. 
5

Kc = VmK m + Vf Kf ; (8) 

Gc = VmG m + Vf Gf ; (9) 

( ) +ν = 2 1

E G ; (10) 

3( ) 1 2ν

E K − = ; (11) 

3K G

9KG E

+ = , (12) 

where 

K = bulk modulus, 

G = shear modulus, 

Vf = volume fraction of filler, 

Vm = volume fraction of matrix, and 

ν = Poisson’s ratio. 

The Reuss model (equation 13) assumes constant stress and typically acts as a lower bound for 

experimental data:

f

f

m

m

c E

V

E

V

E

1 = + . (13) 

The estimates of the effective composite moduli determined from the Voigt and Reuss models 

represent extremes in behavior. The Voigt model attributes more significance to the “rigid” 

phase, whereas the Reuss model emphasizes the “compliant” phase. If the properties of the 

constituent components differ by an order of magnitude, the results obtained from these models 

will differ by an order of magnitude [17]. 

The conditions of constant stress or strain across the filler-matrix boundaries are 

thermodynamically impossible; therefore, more rigorous models have been proposed in an effort 

to increase the predictive accuracy of the Voigt and the Reuss models using bounding 

relationships or self-consistent field theories [18]. The modulus properties of the glass filled 

composites to be studied for this research will be modeled using the S-Combining Rule 

(equations 14–16), which was developed by McGee and McCullough in an effort to enhance the 

high-volume fraction accuracy of the thermodynamically derived Hashin and Shtrikman rigorous 

upper bound [19]. 
6

) S

1

S

1

γV V ( S

V

S

V

S

1

l u

f m

u

f

l

m

c

= + + − ; (14) 





 





















+ −

− = +

S V (S S )(1- η )

V (S S ) S S 1

f f m f Sf

m m f

u f ;

 (15) 

































− −

− = − S v (S S )(1- η )V (S S ) S S 1

m m m f Sm

f m f

l m ,

 (16) 

where the parameters Sf and Sm (i.e., Kf, Km, Gf, and Gm) are defined by 

3(1 υ )

1 υ

η

j

j

Kj −

+ = ;

 (17) 

15(1 υ )

2(4 - 5υ )

η

j

j

Gj − = ,

 (18) 

where 

j = matrix (m) or the filler (f). 

The S-Combining Rule is derived from a series expansion of the compliance matrix, thus the 

parameter Sc refers to the composite bulk modulus (Kc) or composite shear modulus (Gc). 

Similar to the Voigt model, Ec is determined with appropriate substitution into equation 12. The 

upper and lower bounds, Su and Sl, respectively, are modified forms of the Hashin-Shtrikman 

upper and lower bounds for the bulk and shear modulus (i.e., Ku, Gu, Kl, and Gl). Hashin and 

Shtrikman developed their models based on the assumptions of macroscopic isotropy and quasihomogeneity of the composite, where the shape of the filler is not a limiting factor [19]. These 

conditions are generally applicable in the case of a spherical filler uniformly dispersed in a 

polymeric matrix [16]. The enhancement in the high volume fraction accuracy of the 

S-Combining Rule is the result of an added phase continuity parameter (γ), as defined by 

equation 19: 

c

c 2 1

γ φ

φ − = , (19) 

where 

γ = phase continuity parameter, and 

φc = critical volume fraction. 
7

Simply stated, these considerations imply that at some critical volume fraction of filler (φc = 2/3 

for the case of spherical filler) a transition in phase contiguity must occur so that in the 

neighborhood of Vf = φc, the composite system will become more homogeneous with filler [18]. 

If the filler modulus is stiffer in comparison to the matrix modulus, then the S-Combining Rule 

compensates by shifting the predicted solution to the upper bound at higher volume loadings. 

2.3.1 Hollow Glass Filler 

The C-Combining Rule, shown in equation 20, is based upon the series expansion of the elastic 

constant matrix for property predictions [18]. This rule is applicable for the case of a matrix 

filled with a more compliant filler, such as a matrix epoxy loaded with hollow glass spheres (i.e., 

Ef < Em). 

P V P V P λ V V (P P ) c = m u + f l + p f m u − l , (20) 

where 

λp = phase continuity parameter, and 

P = bulk modulus (K) or shear modulus (G). 

The upper and lower bounds, Pu and Pl, respectively, are determined using equations 21 and 22, 

where ηPf and ηPm are equivalent to equations 17 and 18 as shown previously. 





 





















− −

− = −

m m f Pm

f m f

u m P V (P P )η

V (P P ) P P 1

m

; (21) 





 





















− −

− = +

f f m f Pf

m m f

l f P V (P P )η

V (P P ) P P 1 . (22) 

Similar to the γ-term in the S-Combining Rule, the phase continuity parameter (λp) is utilized in 

the C-Combining Rule and calculated using equation 23 with a critical packing factor (φc) of 2/3. 

[ ] c c c Pm

c

p 1 2 (1 )η

2 1 λ

φ φ φ

φ

− −

− = .

 (23) 

All parameters used in the C-Combining Rule are well known and easily found in the literature, 

except for the pure component elastic modulus of the hollow glass filler (Ef) and the pure 

component Poisson’s ratio of the hollow glass filler (υf). Thus, an accurate method for 

determining these values is needed. 

Dzenis and Maksimov [16] postulated that the ratio between the hollow volume and the shell 

volume was equivalent to volume fraction (Vs), which is defined by equation 24: 
8

3

Vs 



 





− = R r

r , (24) 

where 

r = inside shell diameter, and 

R = outside shell diameter. 

Values of Vs are then substituted into equations 25 and 26, which results in the pure component 

bulk (Kh) and shear moduli (Gh) of the hollow glass filler. Simply stated, this technique is 

treating the hollow glass filler as a “composite material” in itself. Once the “composite” 

properties of the hollow glass filler are known, traditional micromechanics for the global 

properties of the particulate filled composite can then be determined. 

(3K 4G )

3(1- V )

K K

1

K K

s s

s

n s

h s

+

+ −

= +

ν ; (25) 

5G (3K 4G )

6(1- V )(K 2G )

G G

1 G G

s s s

s s s

n s

h s

+

+

+ −

= +

ν . (26) 

The subscripts s and n refer to the shell and nucleus properties, respectively. For the case of the 

hollow glass spheres, the bulk and shear moduli of the nucleus, Kn and Gn, are both 0.0 GPa. 

The pure component Young’s modulus (Ef) and Poisson’s Ratio (υf) for the hollow glass filler 

can now be calculated by substituting these predetermined values for the bulk and shear moduli 

into equations 11 and 12, respectively. 

2.3.2 Mixed Hollow and Solid Spheres 

A two-step algorithm, proposed by Jancar and DiBenedetto [20], was used to describe the elastic 

modulus of the ternary composite system, consisting of a mixture of solid and hollow glass 

spheres in an epoxy matrix. Assuming a completely homogeneous ternary mixture with perfect 

bonding, the modulus of the compliant hollow spherical glass filler in the epoxy matrix should 

first be determined. This is based on the similarity in modulus properties hollow glass spheres 

and the matrix epoxy. The resulting epoxy-hollow glass filler system will, in turn, assume the 

form of a new pseudo matrix and subsequently be filled with the more rigid solid glass filler 

inclusions. The C-Combining Rule, which is valid for a composite consisting of an epoxy matrix 

with hollow glass filler, will be used first, and then, the S-Combining Rule will be used to model 

the solid glass spheres within this system. 
9

3. Experimental 

3.1 Materials 

The composite samples used in this project consisted of an epoxy matrix loaded with varying 

amounts of solid and hollow glass filler. The epoxy utilized was based upon diglycidyl ether of 

bisphenol A (DGEBA).*

 The curing agent dicyanodiamide (DICY)† and the catalyst 2-methyl 

imidazole (2-MI) ‡ were also used in this epoxy resin system. The DICY and 2-MI were added 

to the DGEBA epoxy resin in concentrations of 6 and 1 parts per hundred (phr) resin by weight, 

respectively. Differential scanning calorimetry (DCS)§

 (heating rate = 10 °C/min) was 

performed on a neat sample of the cured matrix epoxy system, which yielded a glass transition 

temperature (Tg) of 118 °C, which was determined at the inflection point of the heat flow vs. 

temperature plot. Figure 2 depicts the chemical structures for the epoxy, curing agent, and 

catalyst used. 

Figure 2. Chemical structures of DGEBA epoxy, DICY curing agent, 

and 2-MI catalyst.

The solid glass spheres were obtained from Potters Industries Inc. under their registered trade 

name Spheriglass. The modulus, Poisson’s ratio, and CTE of these spheres are reported in 

literature to have values of 72 GPa, 0.23, and 0.5 × 10!6

/°C, respectively [6]. The hollow glass 

spheres** had a density of 0.37 g/cm3

, as reported by the manufacturer. The modulus and 

Poisson’s ratio for the hollow glass spheres were calculated to be 1.99 GPa and 0.21, 

respectively, via the theoretical procedures previously described by equations 24–26. Although 

gas is present within the cavity of the hollow glass spheres, for simplification purposes the center 

 *

 DER 332, Dow Chemical Co. 

†

 Dyhard 100S, SKW Chemicals. 

‡

 Avocado Research Chemicals, Ltd. 

§

 DSC 2980, TA Instruments. 

**K37 hollow microspheres, 3M Corp. 

CH3

CH3

O O

OH n

CH3

CH3 O

O

O

O

N N

CH3

H2N C N C N

H

NH

DGEBA

DICY 2-MI
10

volume was assumed to be a vacuum. The outer shell properties were assumed as those of 

standard E-glass, thus a CTE for the hollow microspheres of 3.25 × 10!6

/°C can then be 

calculated using equation 7. Figure 3 provides a representation of the difference in particle size 

between the two types of glass filler. The particle size distributions were obtained using a 

Horiba Instruments LA 900 light scattering particle size analyzer. Low concentrations of filler 

were dispersed in water with the aid of a high molecular weight block copolymer surfactant*

with the use of an ultrasonicator. The particle size distributions were measured immediately 

after dispersion to ensure that negligible settling or floating of the particles occurred due to 

mismatch in density when compared to the aqueous dispersing medium. Both the solid and 

hollow glass spheres displayed bimodal particle size distributions, with the solid spheres biased 

towards slightly smaller diameters than the hollow spheres. Scanning electron microscopy 

(SEM) was also used to examine the particle size and shape of the hollow and solid spheres, as 

seen in Figure 4. 

Figure 3. Particle size distributions for the hollow (S) and solid (T) 

glass fillers. 

Table 1 summarizes the pure component properties for each of the materials used in the analysis 

of composite properties, DGEBA-based matrix epoxy, solid glass spheres, and hollow glass 

spheres. 

Solid or hollow glass spheres were added in varying volume fractions to this initial epoxy 

mixture. For the solid/hollow filler blends, the solid and hollow glass fillers were added to the 

matrix epoxy at volume ratios of 0:100, 25:75, 50:50, 75:25, and 100:0, respectively, while 

 *

 Pluronic F-108, BASF Corp. 

0.1 1 10 100

0

2

4

6

8

10

12

Frequency

Diameter (μm)

 hollow glass spheres

 solid glass spheres
11

Figure 4. SEM images of the (a) hollow and (b) solid glass fillers. 

Table 1. Summary of constitutive materials properties for the matrix epoxy, solid 

glass filler, and hollow glass filler. 

Property Matrix Solid Glass Filler Hollow Glass Filler 

CTE (× 10!6/°C) 70.7a

 0.5b 3.25c

E (GPa) 2.45a 76b 1.99c

ν 0.33b

 0.23b 0.21c

G (GPa) 0.92c 30.9b 0.82c

K (GPa) 2.47c 46.9b 1.15c

ρ (g/cm3) 1.19a

 2.54b 0.37d

 a Experimental value as described in section 3.2. 

 b Literature value [6]. 

 c Calculated value [16]. 

 d As reported by manufacturer. 

maintaining an overall constant volume fraction of filler equal to 0.45. Additionally, 3 phr of 

treated fumed silica*

 was added to the epoxy system to prevent settling or floating of the

solid or hollow glass spheres during cure of the matrix system. All samples were mixed 

thoroughly using a Ross double planetary mixer and subsequently degassed at 50 °C under 

vacuum until no visible air bubbles could be observed. Tensile specimens [21] were cured in 

silicon molds between polytetrafluoroethylene sheets at 80 °C for 2 hr and further postcured at 

160 °C for 1 hr. The samples were allowed to slow cool in the powered-off oven to minimize 

residual stresses after completion of the cure cycle. The samples were carefully removed from 

the molds and polished to remove any rough edges and then stored in a desiccator at room 

temperature. 

 *

 TS-720, Cabot Corp. 

(a) (b)
12

3.2 Characterization 

The densities and void contents of all of the samples were determined using buoyancy techniques 

according to American Society for Testing and Materials (ASTM) standard test methods 

[22, 23]. Water was used as the submersion liquid for samples where ρc > 1. For the samples 

where ρc < 1, hexane was used as the immersion liquid. A minimum of five replicates were 

performed for each density and void content measurement. 

A Perkin Elmer thermal mechanical analyzer (TMA-7) was used to determine the CTE for each 

sample according to ASTM E831-00 [24]. The samples were tested using an expansion probe 

from room temperature to 250 °C at 10 °C/min. The CTE values were determined from the 

slope of the expansion vs. temperature curve. The CTE values reported were calculated by 

averaging the results from two samples at each particular filler volume fraction. 

An Instron 4505 equipped with a 1000-lb load cell was used to determine the Young’s modulus 

of the samples according to ASTM method D638-01 [21]. The samples were pulled at a strain 

rate of 0.05 in/min at room temperature until either a load of 100 lb was reached or the sample 

failed. Stress and strain data were collected, and E was calculated by determining the slope of 

the elastic region of the stress vs. strain curve. Five samples were run at each particular filler 

volume fraction to obtain the average reported E values. 

4. Results and Discussion 

4.1 Solid vs. Hollow Glass Filler

4.1.1 Density 

The first stage of composite analysis was the determination of the effect of volume fraction of 

filler to the density of the composite. The results of the density analysis, including both the 

experimental data and the ROM predictive model, are shown in Figure 5. The standard deviation 

associated with each data point at each particular volume fraction was negligible (<0.02 g/cm3

for all samples studied). As can be seen in Figure 5, the standard ROM for density provides an 

accurate prediction of composite density. As expected, the density of the composites containing 

solid glass increased with increasing volume fraction of filler, while the density of the 

composites containing hollow glass filler showed the opposite trend. This opposite trend in 

density becomes more critical at higher volume fractions. For example, it has been shown here 

that at Vf = 0.45, the hollow glass sphere filled resins had a considerably lower density 

(0.83 g/cm3

) when compared to the solid glass filled resins (1.79 g/cm3). This is significant as 

potting compounds are typically loaded with filler at concentrations greater than this point.
13

Figure 5. Plots of composite density vs. volume fraction of 

filler for composites filled with hollow glass spheres 

(S) and solid glass spheres (T). The ROM 

(equation 1) is used to predict the experimental 

densities. Density measurements were precise to 

± 0.02 g/cm3

. 

4.1.2 CTE 

The CTE of the composites was also examined as a function of the volume fraction of filler 

loaded into the system. Figure 6 displays a plot of CTE vs. volume fraction for composite 

samples filled with hollow glass microspheres, along with ROM (equation 2) and Schapery’s 

lower bound (equation 4) predictive models. The results for the hollow glass filler indicate that 

the composite CTE decreases in a similar manner in comparison to reported results for 

encapsulants loaded with solid glass fillers. Figure 6 shows a single data point for a composite 

loaded with solid glass filler at Vf = 0.45, which lies within experimental error of the CTE values 

measured for the hollow glass filler (37.3 × 10!6

/°C vs. 39.1 × 10!6/°C, respectively). These 

values correspond well with a value of ~35 × 10!6

/°C as reported in the literature [1]. 

The model predictions by the ROM and Schapery’s bounding relationships also proved 

interesting. The simple ROM provides a reasonable approximation of the experimental results. 

As a more thermodynamically correct rigorous approximation, Schapery’s bounding 

relationships failed to describe the composite CTE when hollow filler was incorporated into the 

matrix phase. Schapery’s lower bound predicts CTE values greater than the ROM expression. 

Additionally, the predicted CTE values calculated from both Schapery’s upper bound (not shown 

in Figure 6) and lower bound expressions for composites containing hollow glass overlay each

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

ρC (g / cm3

)

Vf Filler

 hollow glass filler

 solid glass filler
14

Figure 6. Composite CTE vs. volume fraction of hollow glass 

filler (). Composite CTE at Vf = 0.45 solid glass 

filler (§) illustrated for comparative purposes. ROM 

and Schapery’s lower bound fit to hollow glass filled 

composite data. 

other. The breakdown of Schapery’s bounding methods for CTE in the case of a hollow filler are 

not surprising considering that these relationships are dependent upon Gf and Kf, which in the 

case of the hollow glass filler are lower values than the matrix phase. As will be seen in section 

4.1.3, bounding methods for response prediction are more accurate when the properties of the 

phases differ by a large extent. Despite the difficulty in applying the bounding relationships to 

the experimental data, these results indicate that there is no significant difference in composite 

CTE when either hollow or solid glass filler is used. 

4.1.3 Young’s Modulus 

The experimental and predicted Young’s modulus values were determined for both solid and 

hollow glass filled composites. Figure 7 shows a plot of Ec vs. volume fraction of hollow glass 

filler and values calculated utilizing the C-Combining Rule. This plot clearly shows that the 

experimentally determined elastic modulus values do not correlate well with those calculated 

using the C-Combining Rule. The predictive model indicates that the composite elastic modulus 

should decrease with increasing volume fraction of hollow glass filler; however, the 

experimental data shows little to no change with increasing volume fraction of filler. The 

breakdown of the bounding relationship to accurately predict Ec arises from the negligible 

difference in magnitude between modulus of the epoxy matrix and hollow glass filler. 

0.0 0.2 0.4 0.6 0.8 1.0

0

10

20

30

40

50

60

70

CTE (x 10- 6 / °C)

Vf Filler

 hollow glass filler

 solid glass filler

 ROM (hollow)

 Shapery's lower bound (hollow)
15

Figure 7. Plot of experimental composite modulus vs. volume fraction 

of hollow glass filler along with theoretical predictions via the 

C-Combining Rule. 

Figure 8 shows the plot of experimentally determined elastic composite modulus vs. volume 

fraction of solid glass filler and calculated values determined using the S-Combining Rule, the 

Voigt model, and the Reuss model. This plot shows the superior accuracy of the S-Combining 

Rule in comparison to the Voigt and Reuss models when the high modulus solid glass filler is 

incorporated into the matrix epoxy phase. Unlike the hollow glass filler, the composite modulus 

is increased significantly for the case of solid glass filler. For example, at 0.45 volume fraction 

of filler, the modulus of the hollow glass sphere composite and the solid glass sphere composite 

were experimentally determined to be ~2.7 and 10.1 GPa, respectively. 

4.2 Combined Mixed Solid and Hollow Glass Filler 

Binary filler combinations of solid and hollow glass were added to the matrix epoxy to yield 

ternary composite systems. For these mixed filler systems, the volume fraction of filler was held 

constant at 0.45 and the ratio of solid to hollow glass filler was varied. As mentioned in section 

3, the solid and hollow glass fillers were added to the matrix epoxy at volume ratios of 0:100, 

25:75, 50:50, 75:25, and 100:0, respectively. Each of the three material properties previously 

discussed, ρc, CTE, and Ec, for the single filler systems were determined for the ternary 

composites and are shown in Figure 9 and summarized in Table 2. 

0.0 0.2 0.4 0.6 0.8 1.0

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Ec (GPa)

Vf Hollow Glass Filler

 hollow glass filler

 C-Combining rule
16

Figure 8. Plot of experimental composite modulus vs. volume fraction of 

solid glass filler along with theoretical predictions via the 

S-Combining Rule, Voigt model, and Reuss model. 

Figure 9. Density, elastic modulus, and CTE, are plotted for the ternary 

composite of solid and hollow glass filler in epoxy. Overall Vf

= 0.45. 

0.0 0.1 0.2 0.3 0.4 0.5

3

6

9

12

15

Ec (GPa)

Vf Solid Glass Filler

 solid glass filler

 Voigt model

 Reuss model

 S-Combining rule

1.0 0.8 0.6 0.4 0.2 0.0

2

3

4

5

6

7

8

9

10

11

0.9

1.2

1.5

1.8

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

Ec (GPa)

Vf Solid Glass Spheres

 Elastic Modulus

 S-Combining Rule

ρ ( g/cm3 )

 Density

 Rule of Mixtures

 CTE ( ppm / °C )

 CTE

Vf

 Hollow Glass Spheres
17

Table 2. Summary of experimental determinations of Vf, ρ, void content, CTE, and E. 

Filler Vf ρc 

(g/cm3) 

Void Content 

(%) 

CTE 

(× 10!6

/°C) 

Ec 

 (GPa) 

Neat — 1.19 0.002 70.7 2.45 

Hollow 0.15 1.08 1.02 57.2 2.70 

Hollow 0.25 1.01 2.43 48.6 3.07 

Hollow 0.35 0.94 3.65 42.2 2.61 

Hollow 0.45 0.83 1.18 39.1 2.67 

Hollow 0.55 0.75 1.13 34.7 2.80 

Solid 0.05 1.21 0.24 — 3.13 

Solid 0.15 1.34 1.16 — 3.90 

Solid 0.25 1.49 0.50 — 4.99 

Solid 0.29 1.55 0.14 — 5.70 

Solid 0.45 1.79 0.51 37.3 10.1 

Solid 0.50 1.84 1.12 — 12.9 

Hollow/solid (25:75) 0.46 1.62 0.76 36.9 7.97 

Hollow/solid (50:50) 0.43 1.31 0.49 37.1 4.83 

Hollow/solid (75:25) 0.46 1.01 1.17 39.0 3.66 

Note: Error values are not tabulated, but are illustrated in all relative plots.

The overall composite CTE for the ternary mixtures remained constant at ~38.3 × 10!6/°C across 

the entire range of filler combinations. This result is as expected as the CTE of the hollow and 

glass filler are nearly identical. Also as expected, ρc decreases significantly as the relative 

volume fraction of hollow glass within the binary filler mixtures increases. The experimental 

composite density at a solid to hollow filler ratio of 50:50 is 1.31 g/cm3

, which is 0.48 g/cm3

lower than the case of pure solid filler added to the matrix system at the identical volume 

fraction. The ROM (equation 1) was determined for the ternary mixtures and provided an 

excellent fit of ρc. 

Due to the breakdown of the C-Combining Rule to accurately model the composite modulus 

when hollow glass filler was incorporated into the matrix epoxy, the matrix epoxy and hollow 

glass filler were assumed to have the same modulus (2.45 GPa). Thus, in fitting the 

S-Combining Rule to the ternary composite system, the methodology proposed by Jancar and 

DiBenedetto [20] is simplified by adjusting the matrix volume fraction to reflect the combined 

volume of epoxy resin and hollow glass filler while the filler volume fraction is composed solely 

of solid glass. After the adjustments in volume fraction are made, the S-Combining Rule 

provided an excellent prediction of the ternary composite modulus. As expected, the modulus 

decreases as the relative volume fraction of hollow glass filler increases. 
18

5. Conclusion 

The purpose of this work was to predict and determine the thermal and mechanical properties of 

a glass-epoxy composite to be used for electronic potting compounds. Through material 

characterization, key mechanical and thermal properties were determined, including composite 

density, modulus, and coefficient of thermal expansion. 

The density of the composites containing hollow glass spheres decreased with increasing filler 

volume fraction, which is opposite for the case of solid glass filler. This characteristic is highly 

desirable for electronic potting compounds, because decreasing the mass of the system reduces 

the inertial forces exerted during high-stress applications. The overall weight of the electronic 

device will also be reduced, therefore reducing the energy needed to propel the device. At a 

volume fraction of filler of 0.45, the density of the composites incorporating hollow glass 

spheres was one-half that observed for the composites loaded with solid glass filler. 

Composite CTE was not compromised by incorporation of hollow glass filler when compared to 

solid glass filled counterparts. At a volume fraction of 0.45, the CTE was determined to be 

~38.3 × 10!6

/°C for both the composites filled with solid and hollow glass. 

Analysis of the mechanical properties of the systems indicated that the composites loaded with 

hollow glass spheres showed an elastic modulus that was approximately three times lower than 

those filled with the solid glass. The high strain-rate properties of the potting compounds were 

not determined at this time, and modulus may or may not be a critical factor to device 

survivability. However, as the study of the ternary composite indicated, there could possibly be 

a combination of hollow and solid glass filler that strikes a balance between decreased density 

and adequate modulus properties. 
19

6. References 

1. Wong, C. P., and R. S. Bollampally. “Thermal Conductivity, Elastic Modulus, and 

Coefficient of Thermal Expansion of Polymer Composites Filled With Ceramic Particles for 

Electronic Packaging.” Journal of Applied Polymer Science, vol. 74, pp. 3396–3403, 1999. 

2. Harper, C. A. (ed.) Electronic Packaging and Interconnection Handbook, 3rd Ed. New 

York: McGraw-Hill, 2000. 

3. Zweben, C. “Metal-Matrix Composites for Electronic Packaging.” Journal of Electronics 

Materials, vol. 44, pp. 15–23, 1992. 

4. Shen, Y. L., A. Needleman, and S. Suresh. “Coefficients of Thermal Expansion of MetalMatrix Composites for Electronic Packaging.” Metallurgical and Materials Transactions A, 

vol. 25A, pp. 839–849, 1994. 

5. Garg, A. C., and Y. W. Mai. “Failure Mechanisms in Toughened Epoxy Resins—A 

Review.” Composites Science and Technology, vol. 31, pp. 179–223, 1988. 

6. Smith, J. C. “Experimental Values for the Elastic Constants of a Particulate-Filled Glassy 

Polymer.” Journal of Applied Physics and Chemistry, vol. 80A, pp. 45–49, 1976. 

7. Kim, H. S., and M. A. Khamis. “Fracture and Impact Behaviours of the Hollow Microsphere/Epoxy Resin Composites.” Composites: Part A, vol. 32, pp. 1311–1317, 2001. 

8. Volk, M. C. “Syntactic Foams.” Encyclopedia of Polymer Science and Technology, New 

York: Reinhold, vol. 8, pp. 752–757, 1969. 

9. Hutov, F. A. “Syntactic Polymer Foams.” Advances in Polymer Science, vol. 73, 

pp. 63–123, 1986. 

10. DeRuntz, J. A., and O. Hoffman. “The Static Strength of Syntactic Foams.” Journal of 

Applied Mechanics, Transactions of the ASME, pp. 551–557, 1969. 

11. Rizzi, E., E. Papa, and A. Corigliano. “Mechanical Behavior of a Syntactic Foam: 

Experiments and Modeling.” International Journal of Solids and Structures, vol. 37, 

pp. 5773–5794, 2000. 

12. Lee, H., and K. Neville. “Epoxy-Resin Foams.” Plastic Foams, edited by K. C. Frisch and 

J. H. Saunders, New York: Marcel Dekker, pp. 701–733, 1973. 

13. Sternfield, A. “New Types of Sources of Micro-Spheres Can Help Widen RP Markets.” 

Modern Plastics International, vol. 12, pp. 43–45, 1982. 

14. Peters, S. T. (ed.) Handbook of Composites. New York: Chapman & Hall, 1998. 
20

15. Schapery, R. A. “Thermal Expansion Coefficients of Composite Materials Based on Energy 

Principles.” Journal of Composite Materials, vol. 2, pp. 380, 1968. 

16. Dzenis, Yu. A., and R. D. Maksimov. “Prediction of the Physical-Mechanical Properties of 

Hollow-Sphere Reinforced Plastics.” Mechanics of Composite Materials, vol. 27, pp. 263–

270, 1991. 

17. McGee, S., and R. L. McCullough. “Combining Rules for Predicting the Thermoelastic 

Properties of Particulate Filled Polymers, Polyblends, and Foams.” Polymer Composites, 

vol. 2, pp. 149–161, 1981. 

18. Hill, R. “Continuum Micro-Mechanics of Elastoplastic Polycrystals.” Journal of the 

Mechanics and Physics of Solids, vol. 13, pp. 89, 1965. 

19. Hashin, Z., and S. Shtrikman. “A Variational Approach to the Theory of the Elastic 

Behaviour of Multiphase Materials.” Journal of the Mechanics and Physics of Solid, 

vol. 11, pp. 127–140, 1963. 

20. Jancar, J., and A. T. DiBenedetto. “The Mechanical Properties of Ternary Composites of 

Polypropylene With Inorganic Fillers and Elastomer Inclusion.” Journal of Materials 

Science, vol. 29, pp. 4651–4658, 1994. 

21. American Society for Testing and Materials. “Standard Test Method for Tensile Properties 

of Plastics.” ASTM D638-01, West Conshohoken, PA, 2001. 

22. American Society for Testing and Materials. “Standard Test Methods for Density and 

Specific Gravity (Relative Density) of Plastics by Displacement.” ASTM D792-00, West 

Conshohoken, PA, 2001. 

23. American Society for Testing and Materials. “Standard Test Methods for Void Content of 

Reinforced Plastics.” ASTM D2734-94, West Conshohoken, PA, 1994. 

24. American Society for Testing and Materials. “Standard Test Method for Linear Thermal 

Expansion of Solid Materials by Thermomechanical Analysis.” ASTM E831-00, West 

Conshohoken, PA, 2001.
21

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4. TITLE AND SUBTITLE 

Characterization of Low Density Glass Filled Epoxies 

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AH42 

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6. AUTHOR(S) 

Matthew J. Quesenberry,* Phillip H. Madison, and Robert E. Jensen 

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U.S. Army Research Laboratory 

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Aberdeen Proving Ground, MD 21005-5069 

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*University of Delaware Center for Composite Materials, Newark, DE 19716. 

14. ABSTRACT 

This report discusses the experimental determination and modeling of several thermophysical and mechanical properties of glass 

filled epoxy composite systems for potential use as electronic potting compounds. Resin systems containing diglycidyl ether of

bisphenol A epoxy, dicyandiamide curing agent, and 2-methylimidazole catalyst were produced with three different 

combinations of fillers: (1) solid glass spheres, (2) hollow glass spheres, and (3) mixed solid-hollow glass spheres. The density 

(ρ), coefficient of thermal expansion, and Young’s modulus (E) of these different particulate filled composites were 

experimentally determined and modeled to elucidate the relationship between specific filler characteristics and resulting 

mechanical and thermophysical properties. 

The S-Combining Rule was found to correlate well with the experimental results for the solid glass sphere filled composites, but 

failed to accurately model ultimate composite properties when the hollow glass spherical filler was incorporated. The inaccuracy 

of micromechanical rules applied to the low-density composites was due to the minimal differences in modulus between the 

hollow spherical glass filler (Ef) and Em. However, reasonable micromechanical modulus approximations for the composites 

containing mixed hollow and solid spherical glass filler could be obtained. 

15. SUBJECT TERMS

micromechanics, potting compound, modulus, density, CTE 

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Robert E. Jensen 

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