**Table of Contents**

[**Executive Summary** ii](#__RefHeading___Toc97685940)

[**Towards A Methodology for the Characterization of Fire Resistive
Materials with Respect to Thermal Performance Models**
1](#__RefHeading___Toc97685941)

A methodology for characterizing fire resistive materials (FRMs) with
respect to thermal performance models is presented. Properties that must
be assessed include thermal conductivity, heat capacity, density, and
enthalpies of reactions and phase changes. Experimental and
computational techniques for quantifying each of these properties are
recommended.

[**Microstructure and Materials Science of Fire Resistive Materials**
13](#__RefHeading___Toc97685942)

The application of x-ray microtomography to characterizing the
three-dimensional microstructure of FRMs is presented. The 3-D
microstructures are analyzed to determine the overall \"coarse\"
porosity and the size of each individual pore. This information, along
with the microstructure image, can be used to compute estimates of the
thermal conductivity of these composite materials as a function of
temperature.

[**A Slug Calorimeter for Evaluating the Thermal Performance of Fire
Resistive Materials** 22](#__RefHeading___Toc97685943)

The design, development, and evaluation of a simple slug calorimeter for
evaluating the high temperature thermal conductivity of fire resistive
materials are presented. The presented test method provides effective
thermal conductivities in the temperature range from 30 ^o^C to about
700 ^o^C, and through the use of multiple heating/cooling cycles also
provides critical information on the influences of reactions and the
convective transport of reaction gases on the measured effective thermal
conductivity.

[**Critical and Subcritical Adhesion Measurements of a Model Epoxy
Coating Exposed to Moisture Using the Shaft-Loaded Blister Test**
36](#__RefHeading___Toc97685944)

A novel test method for adhesive coatings is presented. The shaft-loaded
blister test (SLBT) employs a fracture mechanics-based approach, rather
than a strength-based approach (pull-off and lap shear), to characterize
the adhesion of materials. A fracture mechanics-based approach is
advantageous because it explores adhesive failure mechanisms observed in
the actual application of the adhesive as well as providing engineering
parameters for the design of adhesive joints and coatings.

[**Influence of Experimental Set-up and Plastic Deformation on the
Shaft-loaded Blister Test** 51](#__RefHeading___Toc97685945)

The viability of using the SLBT as a test method for measuring the
adhesion and mechanical properties of thin films and coatings is
explored. Evidence is presented that the SLBT is relatively insensitive
to the effects of plastic deformation that often affect conventional
adhesion test methods such as the peel test.

[**Comparison of Subcritical Adhesion Test Methods: The Shaft-loaded
Blister Test vs. the Wedge Test** 70](#__RefHeading___Toc97685946)

This work is part of the ongoing effort to develop the shaft-loaded
blister test into an adhesion test method that engineers and scientists
can use for the design of adhesive joints and coatings. Here, we compare
the results from the SLBT with the more conventional double cantilever
beam wedge test.

[**Appendix A. Project Listing for BFRL Research and Development for the
Safety of Threatened Buildings Program**
77](#__RefHeading___Toc97685947)

**Executive Summary**[]{#__RefHeading___Toc97685940 .anchor}

As part of its Research and Development for the Safety of Threatened
Buildings Program (see Appendix A), the Building and Fire Research
Laboratory (BFRL) at the National Institute of Standards and Technology
(NIST) has initiated a research project on fire resistive materials
(FRMs) for structural steel. This report summarizes the research
performed in this program during 2004. The ongoing WTC investigation has
highlighted the criticality of the performance of FRMs during a fire or
multi-hazard exposure. Both the adhesion and the thermal performance of
the FRMs are paramount for successfully protecting the steel from
failure due to loss of its mechanical properties when its temperature
rises beyond some critical level (around 500 ^o^C). As with any
material, it is the underlying microstructure of the FRM that must be
engineered to control the thermal and adhesion properties of the final
product. With these considerations in mind, initial BFRL/NIST research
on these materials has focused on a three prong approach, characterizing
the **microstructure**, **adhesion**, and **thermal properties** of
these materials. As is illustrated by the papers included in this
report, both computational and experimental methodologies are under
development. The ultimate goal is to provide the industry with the
measurement and computational tools to make better decisions during
their materials' development and optimization processes, and ultimately
to produce better, safer, and more reliable fire resistive materials.

On July 14, 2005, a meeting with industry representatives will be held
at NIST to explore the possibility of creating a NIST/industry
consortium on Fire Resistive Materials to further advance the goals of
this research program. Interested parties may contact any of the three
project investigators: Dale Bentz (<dale.bentz@nist.gov>), Emmett
O'Brien (<emmett.obrien@nist.gov>), or Christopher White
(<christopher.white@nist.gov>).

Submitted to Fire and Materials (2004)

**Towards A Methodology for the Characterization of Fire Resistive
Materials with Respect to Thermal Performance
Models**[]{#__RefHeading___Toc97685941 .anchor}

Dale P. Bentz, Kuldeep R. Prasad, Jiann C. Yang

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8615

E-mail: <dale.bentz@nist.gov>

Phone : (301) 975-5865

Fax : (301) 990-6891

**Abstract**

A methodology is proposed for the characterization of fire resistive
materials with respect to thermal performance models. Typically in these
models, materials are characterized by their densities, heat capacities,
thermal conductivities, and any enthalpies (of reaction or phase
changes). For true performance modeling, these thermophysical properties
need to be determined as a function of temperature for a wide
temperature range from room temperature to over 1000 ^o^C. Here, a
combined experimental/theoretical/modeling approach is proposed for
providing these critical input parameters. Particularly, the
relationship between the three-dimensional microstructure of the fire
resistive materials and their thermal conductivities is highlighted.

***Introduction***

As progress is made in the integration of structural and fire
performance models for structural steel, one key component is a proper
and accurate characterization of the thermophysical properties of the
fire resistive materials (FRM). To predict the surface temperatures of
the steel and its subsequent mechanical performance, an understanding of
the energy transfer from the fire to the steel through the FRM is
paramount. The four major thermophysical properties needed to model the
thermal performance of the FRMs are: density, heat capacity, thermal
conductivity, and enthalpy (of reactions and phase changes).
Furthermore, these properties are needed as a function of temperature,
from room temperature to temperatures greater than 1000 ^o^C. In this
paper, various approaches for obtaining these data are reviewed and
critiqued. It appears that a combination of experimental measurements
and theoretical/modeling computations will provide the most robust and
accurate characterization for these materials. While the mechanical
integrity and adhesion properties of the FRMs as a function of
temperature are also critical to successful performance during a fire
exposure, they will not be considered in this initial study.

***Materials***

Representative samples of four spray-applied FRMs were obtained from two
of the largest manufacturers in the industry. Two of the materials are
mainly composed of mineral fibers with a portland cement-based binder.
The other two are gypsum-based with either vermiculite or expanded
polystyrene beads as lightweight extenders. In the sections that follow,
the materials will be identified only by their binder components,
portland cement and gypsum, respectively. Two of the materials (one
portland cement-based and one gypsum-based) are currently available in
the U.S. marketplace, while the other two were of interest for
historical reasons and are still in use in various existing structures.
In the latter case, the materials were supplied by the manufacturers in
a condition that matched the historical materials as closely as
possible. Samples of both of the portland cement-based and one of the
gypsum-based materials were sent to a commercial testing laboratory for
evaluation of thermal conductivity, heat capacity, and density (via mass
and thermal expansion measurements).^1^ In addition, the materials were
characterized by thermogravimetric, dimensional, differential scanning
calorimetry, and optical microscopy analysis in the NIST labs.

***Properties***

[Density:]{.underline}

The two contributions to the density of any material are its mass and
its volume. FRMs are complex in that both of these contributions are
changing during a fire exposure. As exemplified in Figures 1 and 2, most
FRMs will lose mass in a monotonic fashion during a high temperature or
fire exposure, due to some combination of dehydration, decarbonation,
and decomposition of organic compounds. Their volume, however, may
either increase or decrease. An increase in volume may be observed as
the solid network supporting the FRM expands with increasing temperature
or more dramatically when an intumescent coating foams during thermal
degradation. A decrease in volume may be observed as shrinkage
accompanies the mass loss from this solid network.

Figure 1: Example thermogravimetric results for a gypsum-based
spray-applied FRM with a nominal heating rate of 5 ^o^C/min. Results are
for two nominally identical ≈50 mg replicates. Maximum observed
coefficient of variation (COV) for mass loss between the two replicate
samples is 0.9 %.

![](media/image1.wmf){width="5.924305555555556in"
height="3.5701388888888888in"}

Mass loss can be quantified using thermogravimetric analysis (TGA), as
described in ASTM E1131.^2^ Of course, the results will vary with the
programmed heating rate, sample size, and sample environment. As shown
in Figure 1, spray-applied FRMs may lose as much as 25 % of their
initial mass during exposure to 800 ^o^C. This mass loss also provides
critical input for calculating the enthalpies of reaction for the
in-place FRM. Once a set of reactions is hypothesized, the standard
heats of reactions may be calculated and normalized by the measured mass
loss to calculate the enthalpy change for the in-place material, as will
be demonstrated later in this paper.

Volume changes (thermal expansion) can be measured using a dilatometer
(ASTM E228) or interferometry (ASTM E289).^2^ High temperature
measurements (e.g., \> 600 ^o^C) are often complicated by the large
dimensional changes that may be experienced in FRMs, along with their
generally fragile nature. In addition, spray-applied materials are
inherently anisotropic and may thus exhibit different coefficients of
thermal expansion in the in-plane and through-thickness dimensions.

Typically, the density at any given temperature is calculated as the
ratio of the measured mass at that temperature to the measured volume at
that temperature.

Figure 2: Example thermogravimetric results for a portland cement-based
spray-applied FRM with a heating rate of 5 ^o^C/min. Results are given
for two nominally identical ≈50 mg replicates. Maximum observed COV for
mass loss between the two replicate samples is 0.4 %.

![](media/image2.wmf){width="5.519444444444445in"
height="3.3222222222222224in"}

[Heat Capacity:]{.underline}

Two common approaches to estimating heat capacity are to 1) calculate
C~p~ from a measurement of thermal diffusivity and knowledge of the
density and thermal conductivity of the FRM, or 2) measure C~p~ directly
using a differential scanning calorimeter (DSC). The former is often
complicated by the dynamic nature of FRMs, as they typically lose
significant mass during the measurement time. An exciting recent
development for the latter method is the availability of commercial
simultaneous thermal analysis (STA) units. These units permit the
simultaneous monitoring of heat flow and mass during exposure to a
(high) temperature regime. With conventional DSC, only the heat flow is
measured and to obtain the specific heat per unit mass of material that
is the required input for thermal performance models, the results need
to be adjusted by mass measurements (TGA) made on a companion sample.
The advantages of making both measurements simultaneously on the same
material specimen are obvious. In addition, newer commercial STA units
may allow for larger sample volumes/masses (on the order of 1 g as
opposed to the 50 mg to 100 mg typical of most DSCs). This is especially
important for typical spray-applied FRMs that may exhibit a
microstructural heterogeneity on the scale of millimeters.

For FRMs whose mass composition is exactly known, an alternative
approach is to calculate the FRM heat capacity as a mass-weighted
average of the heat capacities of the component materials. Of course,
this requires that C~p~ data as a function of temperature are available
for each component.

To obtain quantitative C~p~ data (via ASTM E1269 for example^2^), the
typical procedure is to use a sapphire or other reference specimen to
obtain a correction factor (graciously named the "calorimetric
sensitivity" in the ASTM E1269 standard) under the same operating
conditions as those used for the test specimen. Due to typical mass
mismatch between the reference and sample pans, further corrections may
be needed based on the known tabulated heat capacities of aluminum or
gold (pans) as a function of temperature. A typical set of DSC curves
for a spray-applied FRM are provided in Figure 3. The presence of
several endothermic peaks is clearly indicated. The binder component of
this particular FRM is portland cement-based and the first two peaks
(around 100 ^o^C) correspond to the loss of bulk water and (loosely)
bound water from gel-like hydration products respectively, the third
peak (near 400 ^o^C) to the loss of chemically bound water from calcium
hydroxide, and the fourth peak (near 650 ^o^C) most likely to the loss
of carbon dioxide from carbonated reaction products. This material
exhibited about a 10 % mass loss during exposure up to 700 ^o^C. By
integrating the area under these peaks, the corresponding enthalpies of
reaction could be estimated. However, with the small sample size
employed in this experiment (\< 10 mg), a quantitative interpretation is
hindered by the previously mentioned heterogeneity of the material,
e.g., most likely a representative volume was not sampled in this
specific DSC measurement.

[Enthalpies of Reaction:]{.underline}

If the chemical composition of the FRM is known, the potential exists to
calculate the enthalpies of reaction from heats of formation and heat
capacity data.^3,4^ The standard procedure is to "cool" the reactants
down from the reaction temperature to a reference state (temperature) of
25 ^o^C, compute the heat of reaction at 25 ^o^C, and then heat the
products back up to the reaction temperature.^4^ Here, we will
illustrate this simple procedure for a gypsum-based FRM. Gypsum, which
contains two molecules of water for each molecule of calcium sulfate,
undergoes two dehydration reactions when exposed to elevated
temperatures, first converting to calcium sulfate hemihydrate and then
to the anhydrite form of calcium sulfate. The heat capacities and heats
of formation (H~f~) of the relevant compounds are provided in Table
1.^3,4^ Care must be taken to consider water in its gas phase form as
the reaction temperatures being considered are always above 100 ^o^C.
Using these properties and the known dehydration reaction
stoichiometries (e.g.,

Figure 3: Example DSC results (original and mass corrected) for a
portland cement-based spray-applied FRM using gold pans and a sapphire
reference.

![](media/image3.wmf){width="5.876388888888889in"
height="4.177083333333333in"}

CaSO~4~-2H~2~O  CaSO~4~-0.5H~2~O + 1.5 H~2~O and CaSO~4~-0.5H~2~O 
CaSO~4~ + 0.5 H~2~O), heats of reaction of 3.01 kJ/g water lost at 150
^o^C and 2.35 kJ/g water lost at 250 ^o^C are calculated for the
dehydrations to hemihydrate and anhydrite, respectively. These values
are in reasonable agreement with those recently summarized for gypsum
plasterboard by Thomas.^5^ These values could then be multiplied by the
corresponding measured mass loss in these temperature ranges (from
Figure 1 for example) to obtain the enthalpy changes due to reactions
for a particular FRM during fire exposure. Similar calculations can be
employed for portland cement-based and intumescent FRMs, as long as
their specific decomposition reactions and corresponding thermophysical
properties are known.^6,7^ It is worth noting that not all reactions in
commercially available FRMs are endothermic in nature, as organic
components may provide significant exotherms, further supplementing the
energy being provided by a fire.

^Table\ I.\ Thermophysical\ Properties\ for\ Gypsum-based\ Compounds\ at\ 25\ oC.3,4^

+------------------+-----------------+---------------+---------------+
| Compound         | Molar mass      | C~p~ (J/mol•  | H~f~ (kJ/mol) |
|                  | (g/mol)         | ^o^C)         |               |
+------------------+-----------------+---------------+---------------+
| Gypsum           | 172.17          | 186.15        | -2024.1       |
| (CaSO~4~-2H~2~O) |                 |               |               |
+------------------+-----------------+---------------+---------------+
| Hemihydrate      | 145.15          | 119.5         | -1577.9       |
|                  |                 |               |               |
| (C               |                 |               |               |
| aSO~4~-0.5H~2~O) |                 |               |               |
+------------------+-----------------+---------------+---------------+
| Anhydrite        | 136.14          | 99.73         | -1435.1       |
| (CaSO~4~)        |                 |               |               |
+------------------+-----------------+---------------+---------------+
| H~2~O (gas)      | 18.02           | 33.62         | -242.01       |
+------------------+-----------------+---------------+---------------+

[Thermal Conductivity:]{.underline}

A wide variety of experimental techniques exist for measuring the
thermal conductivity of materials at elevated temperatures: high
temperature guarded hot plate (ASTM C177), heat flow meter apparatus
(ASTM C518), laser flash diffusivity methods (ASTM E1461), and transient
line/hot wire (ASTM C1113) and plane source methods.^2,8-10^ Similar to
the discussion presented for concrete by Flynn,^8^ these measurements
are always complicated by the dynamic nature of the FRM which is
undergoing degradation even as its thermal conductivity is being
measured.

An alternative to measuring the thermal conductivities of FRMs at high
temperatures is to measure the value at room temperature (or perhaps up
to 100 ^o^C) and "predict" the higher temperature values based on some
theory for the conductivity of composite (porous) materials. Example
theories that are closer to reality than the simplest parallel and
series models include those of Russell,^11^ Frey,^12^ and Bruggeman.^13^
For example, the theory of Russell estimates the thermal conductivity of
the porous material, *k*, as^11^:

$k = k_{\text{solid}}\frac{\text{vp}^{\frac{2}{3}} + 1 - p^{\frac{2}{3}}}{v(p^{\frac{2}{3}} - p) + 1 - p^{\frac{2}{3}} + p}$
(1)

where *v* = *k*~gas~/*k*~solid~,

*k*~solid~= thermal conductivity of solid material,

*p* = porosity = (ρ~max~-ρ~matl~)/ρ~max~,

ρ~max~ = density of solid material in the porous system,

ρ~matl~ = density of the porous material, and

*k*~gas~ = thermal conductivity of gas = *k*~cond~ + *k*~rad~

For a spherical pore of radius *r*, the radiation contribution to the
overall thermal conductivity of the pore is^14^:

$k_{\text{rad}} = \frac{\text{16}}{3}r\sigma\text{ET}^{3}$ (2)

with *σ* = Stefan-Boltzmann constant (5.669x10^-8^ W/m^2^•K^4^),

*E* = emissivity of solid material (1.0 for black bodies), and

*T* = absolute temperature (K).

Knowing the densities of the FRM and the base solid components (by
grinding to a powder and measuring in an alcohol solution, for
instance), one can calculate the porosity of the FRM. This, along with
estimates of the solid's thermal conductivity and the material's typical
pore radius, and the tabulated thermal conductivity of air as a function
of temperature,^3,15^ permits the estimation of the thermal conductivity
of the FRM at elevated temperatures. As shown in Figures 4 and 5,
application of this theory to both portland cement-based and
gypsum-based spray-applied FRMs yields results in good agreement with
existing measurements. While the measured values of ρ~max~ and ρ~matl~
were used in the calculations, in each case, the pore radius was a
floating parameter that was adjusted to give a reasonable fit to the
experimental data. But, in each case, the adjusted value for the pore
radius is in agreement with visual optical microscopy observations of
the characteristic pore sizes in these materials (Figures 6 to 8). These
figures illustrate the potential of applying this approach in lieu of or
to minimize the number of complicated and costly high temperature
measurements for these materials. The approach also points out the
advantage of incorporating smaller pores into the FRM structure, as the
insulating performance of materials with larger ones will suffer
significantly due to radiation effects at higher temperatures.

Figure 4: Measured thermal conductivities^1^ and predictions based on
theory of Russell/Loeb^11,14^ for two similar portland cement-based
spray-applied FRMs.

![](media/image4.wmf){width="5.888194444444444in"
height="3.5541666666666667in"}

Figure 5: Measured thermal conductivities^1^ and predictions based on
theory of Russell/Loeb^11,14^ for a gypsum-based spray-applied FRM.

![](media/image5.wmf){width="5.995833333333334in"
height="3.6194444444444445in"}

Figure 6: Optical micrograph for portland cement-based spray-applied
FRM-A. Typical pore **diameter** as indicated by the labeled scale bars
in the middle of the two images is on the order of 1.0 mm corresponding
to a pore radius of 0.5 mm. The original image is on the left and a
contrast-enhanced version that better highlights the porosity is shown
on the right.

![](media/image6.jpeg){width="3.1743055555555557in"
height="2.3854166666666665in"}
![](media/image7.jpeg){width="2.5340277777777778in"
height="2.3854166666666665in"}

Figure 7: Optical micrograph for portland cement-based spray-applied
FRM-B. Typical pore **diameter** as indicated by the labeled scale bars
in the middle of the two images is on the order of 1.5 mm corresponding
to a pore radius of 0.75 mm. The original image is on the left and a
contrast-enhanced version that better highlights the porosity is shown
on the right.

![](media/image8.jpeg){width="3.1743055555555557in"
height="2.3854166666666665in"}
![](media/image9.jpeg){width="2.629861111111111in"
height="2.3854166666666665in"}

Successful application of this theory requires a detailed understanding
of the dynamic microstructure of the FRM. For example, one widely used
spray-applied FRM utilizes expanded polystyrene (EPS) beads as a
lightweight aggregate. When these highly porous beads burn out at
elevated temperatures, even though the total porosity will not change
significantly, a new larger size of characteristic pores will be created
within the microstructure, potentially leading to an increase in thermal
conductivity. Intumescents will also be a challenging application, as in
this case, the pore size and total porosity are both dynamic variables
that change dramatically during the fire exposure and charring of the
coating.

A more detailed microstructural analysis is possible via the utilization
of x-ray microtomography which can capture the three-dimensional
microstructure of materials with a voxel dimension on the order of
micrometers.^16^ Example two-dimensional images (slices) obtained for
both gypsum-based and portland cement-based FRMs using one of the X-ray
microtomography units available at the Center for Quantitative Imaging
at Pennsylvania State University are provided in Figure 9.[^1] These
digital image-based three-dimensional microstructures can be segmented
into solid and pore phases, and finite element and finite difference
techniques applied to compute their equivalent thermal conductivity.^17^
For example, a numerical temperature gradient could be placed across the
microstructure and the computed heat flow used to determine the thermal
conductivity of the composite 3-D microstructure. Thus, this approach is
similar to that used in conventional computational thermal analysis, but
it is being applied at the microstructure scale instead of the
conventional macro (structure) scale.

Figure 8: Optical micrograph for gypsum-based spray-applied FRM-C.
Typical pore **diameter** as indicated by the labeled scale bars in the
middle of the images is on the order of 0.4 mm corresponding to a pore
radius of 0.2 mm. The original image is on the left and a
contrast-enhanced version that better highlights the porosity is shown
on the right.

![](media/image10.jpeg){width="3.109722222222222in"
height="2.332638888888889in"} ![](media/image11.jpeg){width="2.41875in"
height="2.3229166666666665in"}

***Recommended Procedures***

A recommended approach for supplying the thermophysical properties
needed by thermal performance models is the following:

1\) density -- determine density via the concurrent measurement of mass
and dimensional changes using thermogravimetric and thermal expansion
measurements,

2\) heat capacity -- determine heat capacity as a function of
temperature using the largest readily available sample cell and a STA
unit, and following the ASTM E1269 protocols,^2^

3\) enthalpies of reaction -- compute enthalpies based on the mass loss
(TGA) measurement and the calculated enthalpies of reaction based on a
detailed knowledge of the FRM and its thermal decomposition (these
calculations can be critically examined by comparison with analysis of
the endotherms and exotherms in the STA results), and

4\) thermal conductivity -- supplement direct "low" temperature thermal
conductivity measurements with detailed characterization of the
microstructure of the FRM (porosity and pore size) and application of
the theory of Russell (or other equivalent) to provide high temperature
estimates.

Figure 9: Examples of two-dimensional images from three-dimensional
microtomography data sets for gypsum-based (left) and mineral
fiber/portland cement-based (right) FRMs. Materials were imaged in a
polypropylene tube with a nominal inner diameter (ID) of 27 mm.

![](media/image12.jpeg){width="3.1680555555555556in" height="3.125in"}
![](media/image13.jpeg){width="3.1118055555555557in" height="3.125in"}

***A Word of Caution about Aging Tests***

One of the action items that came out of the initial FEMA study^18^ of
the collapse of the World Trade Center was that the durability of FRMs
is a little-considered but critically important component of their long
term performance. In response to this, Underwriters Laboratories, along
with the FRM industry and end users, are developing a draft standard to
assess the durability of FRMs^19^, based on their existing evaluations
of intumescent coatings for outdoor use. The basic procedure is to
expose the FRM to some aging environment and then verify through thermal
exposure (fire) testing that the performance of the aged material is at
least equivalent to a specified percentage of that of the original
material. Performance is generally assessed in terms of the time that it
takes a steel (duct) pipe protected with the FRM to reach a specific
temperature (typically 538 ^o^C) when exposed to a standard temperature
rise curve "fire environment". In developing these durability exposures,
care must be taken that the exposure conditions are both reasonable and
applicable to the various classes of spray-applied FRMs. For example, as
shown in Figure 10, the current practice of exposing intumescents to a
temperature of 70 ^o^C for 270 days can result in considerable mass loss
for other types of spray-applied FRMs, even for much shorter exposures
of two to three months (particularly those based on gypsum binders).
Since the loss of water due to dehydration during a fire exposure is one
of the mechanisms by which these materials "insulate" the steel
substrate, it would be expected that these "aged" materials would
exhibit an inferior performance in comparison to their original
counterparts. But, is it the material performance or the aging
conditions that should be called into question? When moisture is added
to the aging exposures, the degradation may become even greater for
conventional fibrous insulating materials.^20^

Figure 10: Mass loss (fraction) upon long term (two month to three
month) oven exposure to different temperatures for gypsum-based (FRM-D)
and portland cement-based (FRM-E) FRMs (sample size of ≈3 g).

![](media/image14.wmf){width="6.497916666666667in" height="2.875in"}

***Acknowledgements***

The authors would like to thank Dr. Phillip M. Halleck and Dr. Abraham
S. Grader of the Center for Quantitative Imaging, Pennsylvania State
University, for supplying the microtomographic images shown in Figure 9.

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Graham J, Porterfield J, Quenard D, Vallee F, Sallee H, Boller E,
Baruchel J, *J. Res. NIST* 2002; **107**:137.

17\) Garboczi EJ. "Finite Element and Finite Difference Programs for
Computing the Linear Electric and Elastic Properties of Digital Images
of Random Materials," NISTIR **6269**, U.S. Department of Commerce,
December 1998.

18\) FEMA 403, "World Trade Center Building Performance Study: Data
Collection, Preliminary Observations, and Recommendations," Federal
Emergency Management Administration, Washington, DC, May 2002.

19\) Standard for Durability Tests for Fire Resistive Materials Applied
to Structural Steel, UL 2431, Draft 1.1, Underwriters Laboratories Inc.,
Northbrook, IL, 2003.

20\) Low NMP. "Material Degradation of Thermal Insulating Mineral
Fibers," Thermal Insulation: Materials and Systems, ASTM STP **922**,
F.J. Powell and S.L. Matthews, Eds., American Society for Testing and
Materials: Philadelphia, 1987; p. 477.

Presented at ASCE/SEI Structures Congress, New York, April 2005.

**Microstructure and Materials Science of Fire Resistive
Materials**[]{#__RefHeading___Toc97685942 .anchor}

Dale P. Bentz^1^, Phillip M. Halleck^2^, Michelle N. Clarke^1^, Edward
J. Garboczi^1^,

and Abraham S. Grader^2^

^1^Building and Fire Research Laboratory, National Institute of
Standards and Technology, 100 Bureau Drive Stop 8615, Gaithersburg, MD
20899-8615;

PH (301) 975-5865; FAX (301) 990-6891; e-mail: <dale.bentz@nist.gov>

^2^Center for Quantitative Imaging, The Pennsylvania State University,
University Park, PA 16802-5000; PH (814) 863-1701; FAX (814) 865-3248;

e-mail: <phil@pnge.psu.edu>

***Abstract***

Fire resistive materials (FRMs) are a critical component in the design
of safe buildings. Current performance testing is strongly based on the
ability of the FRM to adhere to and to control the temperature rise of
its substrate. A fundamental understanding of the microstructure and
performance properties of these materials is sorely needed to model
their performance in real world systems and scenarios. While room
temperature properties are more easily evaluated, it is the high
temperature properties of the materials that are critical to performance
during an actual fire. This paper will describe preliminary efforts in
an experimental/computer modeling program being conducted at NIST to
apply a materials science approach to characterizing the microstructure
and properties of these materials. Three-dimensional x-ray
microtomography is applied to obtain a representation of the
microstructure of the materials. These microstructures can then be
analyzed quantitatively to characterize critical parameters such as
porosity and pore sizes, and the effects of these parameters on
properties such as thermal conductivity. This analysis, along with
characterization of the density and heat capacity of the FRM as a
function of temperature, will provide the inputs needed for thermal
performance models.

***Introduction***

Fire resistive materials (FRMs) perform a critical function in building
safety by protecting steel components from high temperature conditions
during a fire or multi-hazard exposure. These materials generally delay
the transfer of energy from the ongoing fire to the steel via a
combination of a low thermal conductivity and a variety of endothermic
reactions, such as dehydration and decarbonation of cementitious and
gypsum-based binders. In addition to heat transfer through the FRM by
conduction, at higher temperatures, transfer by radiation also makes a
substantial contribution to material performance. Radiation transfer in
a porous material is influenced by both overall porosity and by the size
and shape of the individual "pores" (Russell, 1935; Loeb, 1954).

Currently, FRMs are evaluated and certified based mainly on their
ability to limit the temperature rise of the substrate steel when
exposed in a furnace to a standard temperature rise curve (ASTM E119;
ASTM, 2004). The FRMs are thus rated for a specific period of time for
protecting a specific member of the steel construction, e.g., a 2 h
rating for protecting beams or a 3 h rating for protecting columns. The
E119 test is strictly pass/fail and as such does not truly quantify
material performance. Furthermore, it is extremely difficult to
extrapolate E119 test results to real fire scenarios. Clearly, the
development of new FRMs and an increased understanding of the thermal
performance of existing ones would benefit greatly from a materials
science-based approach to characterizing these materials.

Recently (Bentz et al., 2004), it has been suggested that to
characterize FRMs with respect to thermal performance models,
measurements/calculations of the following thermophysical properties are
required: thermal conductivity, density, heat capacity, and any
enthalpies of reactions or phase changes occurring in the temperature
range of interest. This paper focuses on a computational approach to
estimating thermal conductivity based on a detailed analysis of the
three-dimensional microstructure of the FRMs. Such an approach may
provide a viable alternative to the expensive and often difficult
measurement of thermal conductivity at elevated temperatures for these
dynamic materials. Additionally, the approach should provide valuable
insights into the microstructural features that most influence thermal
performance, so that existing products may be optimized and new ones
formulated with minimal effort.

The basic approach is to capture the three-dimensional microstructure of
FRMs at sub-millimeter resolution using x-ray microtomography. Image
processing and finite difference computer programs are then utilized to
extract the key microstructural features (pores) and determine their
influence on the thermal conductivity as a function of material
temperature. Finally, the computational results are compared to
experimental measurements performed on the same materials to both
evaluate the accuracy of the computational approach and to identify
areas where improvements are needed.

***Experimental Procedures***

Sprayed parallelepiped samples of the following FRMs were obtained from
their manufacturers: one FRM with a gypsum binder and two FRMs
containing mineral fibers with a binder based on portland cement.
Samples of each material were sent to a private testing laboratory
(Anter Laboratories, 2004) for experimental measurement of their thermal
conductivities as a function of temperature using a standard hot wire
technique (ASTM, 2004). The testing laboratory reported their results
for thermal conductivity to be normally within ± 3 %. For each material,
nominal 25 mm (1") diameter cylindrical cores were carefully extracted
using a utility knife. The cores were then placed in 27 mm inner
diameter (ID) polypropylene tubes and mounted for viewing by the x-ray
microtomography system at the Center for Quantitative Imaging at the
Pennsylvania State University[^2].

Volumetric x-ray CT data were collected using the facility\'s microfocus
x-ray source at a voltage setting of 185 kV and a low tube current of 50
μA to minimize focal spot size and thus optimize spatial resolution. We
positioned the sample in the gantry to magnify the sample, and
calibrated the resulting voxel dimensions against a dimensional standard
for precision and to allow combining adjacent data sets without
overlapping or skipping portions of the sample volume.

Because of the different microstructures present in the two types of
FRMs examined in this study (e.g., characteristic feature dimensions),
the microtomography data sets were acquired with different voxel
dimensions. The microtomography data sets for the gypsum-based FRM were
acquired with voxel dimensions of dx =dy =0.0273 mm and dz =0.0361 mm.
Each data set consisted of a 1024 x 1024 x ≈750 array of 16-bit x-ray
absorption values on an arbitrary scale. For this sample we collected
approximately 750 slices covering a volume about 28 mm long by 28 mm in
diameter. For the fiber/cement-based FRMs, in order to cover a larger
representative sample volume, the magnification was reduced by
repositioning the sample between the source and the detector, resulting
in voxel dimensions of dx =dy =0.0586 mm and dz =0.0740 mm, for data
arrays 512 pixels by 512 pixels by 492. Thus, the data cover sample
volumes about 36 mm long by 30 mm in diameter. Each individual
two-dimensional slice was available as a 16-bit tiff-format image for
further processing as described below.

***Computational Procedures***

The three-dimensional FRM microstructure data sets were processed using
the following computational procedures:

1)  segmentation into binary images- utilizing the commercially
    available Image Pro software package, each two-dimensional FRM slice
    image was segmented into a binary image of "pores" and "solids" by
    manually choosing a greylevel threshold; the chosen threshold was
    held constant for all of the two-dimensional slices comprising each
    FRM material but varied between the three different materials, due
    to inherent contrast variations.

2)  extraction of a subvolume- a 200 by 200 by 200 voxel subvolume was
    extracted from each three-dimensional data set; in each case, the
    subvolume was chosen away from the sample edges and in an attempt to
    select as representative a volume of the overall material as
    possible.

3)  isolation of pores and quantification of pore volumes- each binary
    subvolume data set was further analyzed to identify individual pores
    and determine their volumes (by voxel counting); computer programs
    were written in the C programming language to perform pore
    separations utilizing such common image processing algorithms as
    erosion/dilation and watershed segmentation (Russ and Russ, 1988).

4)  prediction of thermal conductivity- the processed subvolumes were
    used as input into a finite difference program (Garboczi, 1998) to
    estimate the thermal conductivity of the composite FRMs based on an
    electrical analogy; a voltage (temperature) gradient was placed
    across the microstructure and the resulting currents (heat flows)
    were computed for each microstructure element (node).

To utilize the finite difference program, it is necessary to assign
thermal conductivities to the "pore" and "solid" components of the
underlying microstructure. Knowing the pore volume of each individual
pore, equivalent radii were calculated assuming a spherical pore
geometry. Then, the thermal conductivity of a pore of radius *r* at
material temperature *T* was given by:

> $k_{\text{pore}} = k_{\text{gas}} + k_{\text{rad}}$ (1)

where:

> *k*~gas~ = thermal conductivity of air at temperature *T,* and
> according to (Loeb, 1954),
>
> $k_{\text{rad}} = \frac{\text{16}}{3}r\sigma\text{ET}^{3}$ (2)

with *r* = pore radius (m),

*σ* = Stefan-Boltzmann constant (5.669x10^-8^ W/m^2^•K^4^),

*E* = emissivity of solid material (1.0 for black bodies), and

*T* = absolute temperature (K).

In this way, each different size pore in the three-dimensional
microstructure was assigned a different thermal conductivity value.

When considering the "correct" thermal conductivity to assign to the
"solids", several complications arise. First, while the microtomography
clearly indicates the coarser pores (50 μm to 100 μm and greater in
diameter) present in the microstructure, the remaining solid phases are
themselves porous. While it may have been possible to estimate the local
"micro-porosity" based on the greylevel intensity at each solid voxel in
the three-dimensional microstructure, instead, a single "fine" porosity
value within all solid voxels was estimated based on the measured
densities of the original FRMs, the measured densities obtained by
grinding them to a fine powder (hopefully removing all internal
porosity), and the microtomography-measured coarse porosity volume
fraction for each material. Then, the theory of (Russell, 1935) was used
to estimate the thermal conductivity of the porous solid component of
the microstructures, *k*~ps~, as:

$k_{\text{ps}} = k_{\text{solid}}\frac{\text{vp}^{\frac{2}{3}} + 1 - p^{\frac{2}{3}}}{v(p^{\frac{2}{3}} - p) + 1 - p^{\frac{2}{3}} + p}$
(3)

where *v* = *k*~pore~/*k*~solid~,

*p* = porosity of the "solid" voxels,

*k*~solid~= thermal conductivity of solid (powder) material, and

*k*~pore~ = thermal conductivity of pores in the "solid" voxels =
*k*~gas~ + *k*~rad~

For calculations of *k*~rad~ for equation (3), an upper bound pore
diameter equal to the smallest of the voxel dimensions was chosen for
each material (e.g., 0.0273 mm or 0.0586 mm). The thermal conductivities
of the solid powders, *k*~solid~, were chosen as 0.8 W/m•K for the
gypsum-based FRM and 0.4 W/m•K for the fiber/cement-based FRMs, to
provide predictions in agreement with the room temperature measured
values of thermal conductivity (Anter Laboratories, 2004). In applying
the theory of Russell, the density (porosity) of the porous material was
adjusted to account for its measured mass loss as a function of
temperature. The gypsum-based FRM loses about 25 % of its mass upon
heating to 1000 ^o^C, while the fiber/cement-based FRMs lose between 10
% and 15 % (Anter Laboratories, 2004).

For the gypsum-based FRM, a further complication is that the thermal
conductivity of anhydrite (dehydrated gypsum) is nearly four times that
of gypsum (Horai, 1971). Based on the measured mass loss of the
gypsum-based FRM and utilizing the Hashin-Shtrikman upper and lowers
bounds for thermal conductivity (Hashin and Shtrikman, 1962), it was
estimated that upon complete conversion of the gypsum to anhydrite, the
thermal conductivity of the solid FRM powder should increase to be on
the order of 1.66 W/m•K. Thus, for temperatures above the nominal
dehydration temperature for gypsum of about 300 ^o^C, the finite
difference computations were performed with *k*~ps~ values based on both
gypsum and anhydrite for comparison to experimental data.

***Results***

Figure 1 illustrates the microstructural features captured by the x-ray
microtomography for the two types of FRMs. For the gypsum-based material
on the left, one can easily observe plate-like vermiculite particles
surrounded by a porous gypsum binder. For the fiber/cement-based FRM on
the right, substantially larger pores are observed. The bright
"particles" observed in this image are most likely agglomerations of the
cement particles that are bonding together fibrous subregions of the
microstructure. As observed more clearly in the three-dimensional
representations of microstructure provided in Figures 2 and 3, while the
pores in the gypsum-based FRM definitely appear to be comprised of
closed roughly spherical shapes, those in the fiber/cement-based FRM may
be interconnected across large regions of the microstructure. These
differences in pore shape/connectivity would also be expected to
influence the thermal conductivities of these two materials,
particularly at elevated temperatures.

![](media/image15.jpeg){width="2.7555555555555555in"
height="2.7555555555555555in"}
![](media/image16.jpeg){width="2.747916666666667in"
height="2.747916666666667in"}

**Figure 1. Two-dimensional x-ray microtomography images from a
gypsum-based FRM (left: 28 mm by 28 mm) and a fiber/cement-based FRM**

**(right: 30 mm by 30 mm), illustrating some of the differences in
microstructural features.**

![](media/image17.jpeg){width="2.7493055555555554in"
height="1.9048611111111111in"}
![](media/image18.jpeg){width="2.872916666666667in"
height="1.9055555555555554in"}

**Figure 2. Renderings of the three-dimensional x-ray microtomography
original data sets (100 by 200 by 200 voxels with a 100 by 100 by 100
voxel volume removed for increased visual clarity) for a gypsum-based
FRM (left) and a fiber/cement-based FRM (right). Pores are dark and
"solid" regions are bright.**

![](media/image19.jpeg){width="2.722916666666667in"
height="2.8743055555555554in"}
![](media/image20.jpeg){width="2.970833333333333in" height="2.88125in"}

**Figure 3. False color renderings of the individual pores isolated
using the watershed segmentation algorithm in a gypsum-based FRM (left:
120 by 120 by 120 voxels) and a fiber/cement-based FRM (right: 200 by
200 by 200 voxels).**

The thermal conductivity predictions and measurements for the
gypsum-based FRM are provided in Figure 4. While good agreement between
the experimental results and the computational predictions is observed
for temperatures below 300 ^o^C, above this temperature the gypsum-based
predictions underestimate the measured values while the anhydrite-based
predictions generally overestimate the measured values, although
providing a reasonable fit for temperatures above 600 ^o^C. This could
indicate that (during the experimental measurement of its thermal
conductivity) in the intermediate temperature range of 300 ^o^C to 600
^o^C, the FRM possibly contained a mixture of gypsum (hemihydrate) and
anhydrite. These results highlight one of the inherent difficulties in
equitably measuring the thermal conductivity of FRMs at elevated
temperatures, the fact that their mass, their chemical composition, and
their microstructure may all be changing during the course of the
measurement.

The importance of pore size in controlling high temperature thermal
conductivity is indicated by the results shown for the first of the
fiber/cement-based FRMs in Figure 5. Here, because of the non-spherical
shape of many of the pores, the watershed segmentation algorithm
subdivided the largest porous "regions" into two or more individual
pores. In this case, better agreement with the experimental data was
observed for the three-dimensional microstructure where the pores were
identified by the simple application of a burning algorithm without any
application of erosions/dilations to the binary image subvolume. As
illustrated in Figure 6, similar results were observed for the second
fiber/cement-based FRM, where larger thermal conductivities are observed
at the highest measured temperatures due to both an increased porosity
and a generally larger pore size.

A large degree of anisotropy in the three-dimensional subvolumes was
observed for these FRMs, as indicated by the large difference between
the computed thermal conductivities for the (x and y) directions and the
z direction. In Figure 3, several large flat plate-like porous regions
oriented

![](media/image21.wmf){width="5.21875in" height="3.1666666666666665in"}

**Figure 4. Measured and predicted thermal conductivities for a
gypsum-based FRM as a function of temperature, for the case where
individual pores were identified using a watershed segmentation
algorithm (Russ and Russ, 1988).**

![](media/image22.wmf){width="5.113888888888889in"
height="3.279861111111111in"}

**Figure 5. Measured and predicted thermal conductivities for the first
fiber/cement-based FRM as a function of temperature.**

in the xy (spraying) plane are clearly observed to comprise a major
fraction of the subvolume. It should be noted that the three-dimensional
box in Figure 3 has been rotated to better view these pores and that the
z-direction moves from left to right in the labeled subvolume.
Furthermore, for these materials, it must also be noted that some of the
underestimation of the experimental results is likely due to energy
transfer through the FRMs by radiation transmission and scattering

![](media/image23.wmf){width="5.114583333333333in"
height="3.2916666666666665in"}

**Figure 6. Measured and predicted thermal conductivities for a second
fiber/cement-based FRM as a function of temperature.**

(Flynn and Gorthala, 1997), due to their overall fibrous nature and
likely percolated three-dimensional pore networks. The theory of Loeb
(Loeb, 1954) does not account for this mode of radiation transport
through the porous material, as it assumes a porous solid comprised of
isolated (not interconnected) pores.

***Conclusions***

The procedures and results presented indicate the viability of utilizing
microstructural characterization and computation to estimate the thermal
conductivity of FRMs at elevated temperatures. However, the
computational procedures can not be applied blindly, due to the many
complicating factors present in these materials. It is only with a
detailed understanding of the microstructural components of these
materials and their changing nature with increasing temperature that
truly adequate predictions can be envisioned. The influences of total
porosity (or equivalently density), pore size, and pore connectivity on
heat transfer were all highlighted in the current case studies.

***Acknowledgements***

The authors would like to thank Mr. John Winpigler of BFRL/NIST for
measuring the powder densities of the various FRMs.

***References***

Anter Laboratories, Inc. (2004). "Transmittal of Test Results." report
to NIST.

ASTM (2004), *ASTM Annual Book of Standards*, ASTM International, West
Conshohocken.

Bentz, D.P., Prasad, K.R., and Yang, J.C. (2004). "Towards a Methodology
for the Characterization of Fire Resistive Materials with Respect to
Thermal Performance Models." submitted to *Fire and Materials.*

Flynn, D.R., and Gorthala, R. (1997). "Radiation Scattering Versus
Radiation Absorption- Effects on Performance of Thermal Insulation Under
Non-Steady-State Conditions." *Insulation Materials: Testing and
Applications: Third Volume, ASTM STP 1320*, American Society for Testing
and Materials, West Conshohocken, PA, 366-380.

Garboczi, E.J. (1998). "Finite Element and Finite Difference Programs
for Computing the Linear Electric and Elastic Properties of Digital
Images of Random Materials." NISTIR 6269, U.S. Department of Commerce.

Hashin, Z., and Shtrikman, S. (1962). "A Variational Approach to the
Theory of the Effective Magnetic Permeability of Multiphase
Materials*."* *J. Appl. Phys*., 33, 3125-3131.

Horai, K. (1971). "Thermal Conductivity of Rock-Forming Minerals." *J.
Geophys. Res.*, 76(5), 1278-1308.

Loeb, A.L. (1954). "Thermal Conductivity: VIII, A Theory of Thermal
Conductivity of Porous Materials." *J. Am. Ceram. Soc.*, 37, 96-99.

Russ, J.C., and Russ, J.C. (1988). "Improved Implementation of a Convex
Segmentation Algorithm." *Acta Stereologica,* 7(1), 33-40.

Russell, H.W. (1935). "Principles of Heat Flow in Porous Insulators."
*J. Am. Ceram. Soc*., 18, 1-5.

Submitted to Fire and Materials (2004)

**A Slug Calorimeter for Evaluating the Thermal Performance of Fire
Resistive Materials**[]{#__RefHeading___Toc97685943 .anchor}

D.P. Bentz, D.R. Flynn[^3], J.H. Kim[^4], and R.R. Zarr

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8615

**Abstract**

The utilization of a slug calorimeter to evaluate the thermal
performance of fire resistive materials (FRMs) is presented. The basic
specimen configuration consists of a "sandwich", with a square central
stainless steel plate (slug) surrounded on two sides by the FRM. This
sandwich configuration provides an adiabatic boundary condition at the
central axis of the slug plate that greatly simplifies the analysis. The
other four (thin) sides of the steel plate (and FRM specimens) are
insulated using a low thermal conductivity fumed-silica board. Metal
plates manufactured from a high temperature alloy, with eight holes for
retaining screws, are placed on the exterior surfaces of the FRMs to
provide a frame for placing the entire sandwich specimen slightly in
compression. The entire configuration is **centrally** placed at the
bottom of an electrically-heated box furnace and the temperatures of the
metal slug and exterior FRM surfaces are monitored during multiple
heating and cooling cycles. Knowing the heat capacities and densities of
the steel slug and the FRM, an effective thermal conductivity for the
FRM can be estimated. The effective thermal conductivity of the FRM will
be influenced by its true thermal conductivity and by any endothermic or
exothermic reactions or phase changes occurring within the FRM.
Preliminary tests have been conducted on two commonly used FRMs and on a
non-reactive fumed-silica board to demonstrate the feasibility of
determining high temperature thermal conductivities using this method.
This small scale furnace test can potentially be related to a standard
ASTM E119 testing configuration by determining the time necessary for
the steel slug to reach a specific "failure" temperature (e.g., 538
^o^C).

**Introduction**

Fire resistive materials (FRMs) are currently generally evaluated using
the ASTM standard test method E119.^1^ This test provides a time
"rating" for which the FRM will adequately protect a specific element or
subsystem of a structure. Two of the major criteria determining the
performance of a FRM are the measured average and maximum temperatures
of a series of thermocouples placed on the (steel) substrate. While
useful as practical failure criteria, these data alone provide little
insight into the key thermal properties of the FRM that would allow a
better understanding of its performance. The thermal performance of the
FRM is controlled by its heat capacity, density, thermal conductivity,
and any heat released, absorbed, or transported due to chemical
reactions (dehydrations, etc.) and phase changes.^2^ The goal of this
paper is to present an experimental setup that maintains the "spirit" of
the ASTM E119 test setup while providing detailed data on the
fundamental thermophysical properties and thermal performance of the
FRM.

The key components extracted from the ASTM E119 testing are that a steel
substrate is protected by a specific thickness of FRM material and is
exposed to a controlled temperature-time environment in a furnace. The
test specimen size is reduced from the ASTM E119 testing to a square 152
mm by 152 mm specimen that is nominally 25 mm in thickness.
Thermocouples are placed in the steel substrate and also at the
"exposed" surfaces of the FRMs to monitor dynamically the temperature
gradient that exists across the sample. Additionally, by using a
"sandwich" specimen configuration and a central stainless steel plate of
known mass and thermal properties, the heat flow through the FRM
specimens can be easily estimated from a simple energy balance, taking
advantage of the adiabatic boundary condition that exists at the central
axis of the steel plate slug. Knowing the heat flow and the temperature
gradient, an "effective" thermal conductivity for the FRM as a function
of temperature can be determined. This effective thermal conductivity
will be influenced by the true thermal conductivity of the material, any
endothermic or exothermic reactions occurring in the FRM, and any
additional energy/mass transport due to vaporization of water (steam)
and other reaction products formed from dehydration, decarbonation, etc.
of the FRM material. The influence of these reactions can be
conveniently explored by exposing the sandwich specimen to multiple
heating/cooling cycles, as the reactions will likely be present only
during the first heating cycle. This approach is presented in more
detail in the sections that follow. A somewhat similar approach for
determining an effective thermal conductivity of intumescent coatings
using a cone calorimeter and numerical analysis has been presented
recently.^3^

**Experimental**

*Slug Design*

An AISI Type 304 stainless steel plate 152 mm by 152 mm was cut from a
sheet having a thickness of 12.7 mm. To monitor the temperature of the
steel slug, three vertical holes 3.5 mm in diameter were milled into the
plate along its central axis, extending 51 mm, 76 mm, and 102 mm into
the plate's depth. The holes were located at distances of 51 mm, 76 mm,
and 102 mm from the plate's edge as shown in Figure 1. The steel plate
mass was 2340 g. A density value of 8000 kg/m^3^ for 304 stainless steel
was taken from the literature^4^, along with heat capacity values as a
function of temperature^5^, as shown in Figure 2. Before testing any
specimens, the steel plate was heated to a temperature of 700 ^o^C
during two separate runs in the furnace. The plate can be optionally
fitted with two allen screws (one on each side) to enable the final
sandwich specimen to be suspended from an external balance on two wires.
Care must be taken to assure that the wire diameter is sufficient to
support the dead load during the temperature rise experienced during an
actual test run. For our purposes, 16 gauge Chromel[^5] wire has been
found to be sufficient, while 24 gauge wire resulted in two premature
failures during preliminary tests, with a total load on the order of
5000 g. Optionally, the final sandwich configuration can be set in the
bottom center of the (bottom loading) box furnace, as shown in Figure 3,
if only temperatures and not mass are to be monitored during the test.

Figure 1- Design of the steel plate slug calorimeter.

*Furnace Setup*

All experiments were conducted in an electrically-heated box furnace
with a working volume of 360 mm by 360 mm by 360 mm and a maximum
operating temperature of 1500 ^o^C. The bottom surface of the furnace is
located on hydraulic elements and can be moved up and down for loading
and unloading of specimens (Figure 3). A series of five Type N
thermocouples, insulated for high temperature applications, were
introduced into the furnace through an entry port in the top. The
thermocouples were connected to a constant temperature zone box, where
their differential voltages were monitored using a digital multimeter
and digital voltmeter. The thermocouples were monitored periodically and
recorded on a computer. Measurement in ice water yielded an average
standard deviation of 0.05 ^o^C among the five thermocouples.

Figure 2- Literature values^5^ and fitted curve for heat capacity of 304
stainless steel. Fitted curve is of the form *c*~p~ = A + BT + Cln(T)
with T in degrees K.

![](media/image24.wmf){width="6.113194444444445in"
height="2.9569444444444444in"}

Figure 3-- A completed sandwich specimen of the fumed-silica insulation
board mounted and ready for testing in the box furnace.

![](media/image25.jpeg){width="6.133333333333334in"
height="3.729861111111111in"}

*FRM and Insulation Materials*

Samples of two mineral fiber/portland cement-based FRMs were obtained
from a manufacturer. The samples were of nominal size 300 mm by 300 mm
by 25 mm. Heat capacities, densities, and thermal conductivities of
these materials had been previously determined by various
laboratories.^2,6,7^ Here, the two materials shall be designated as FRM
A and FRM B. The room temperature densities of FRM A and FRM B were
measured to be 314 kg/m^3^ and 237 kg/m^3^, respectively.^6^ The heat
capacity and mass loss measurements versus temperature for the two
materials are provided in Figures 4 and 5. The testing laboratory
reported their heat capacity values to be normally within ± 5 %.^6^ For
each test run in the furnace, two panels of dimensions 152 mm by 152 mm
by 25 mm were cut from the larger panels to use in the sandwich specimen
configuration. The initial mass of each specimen was measured and
recorded. The specimens of the FRMs were not preconditioned prior to
evaluation in the box furnace.

Figure 4- Measured values^6^ and fitted curves for heat capacities vs.
temperature of the two FRMs. Fitted curves are of the form *c*~p~ = A +
BT + Cln(T) with T in degrees K.

![](media/image26.wmf){width="5.7340277777777775in"
height="3.0118055555555556in"}

A fumed-silica insulation board with a low thermal conductivity (≈0.02
W/m•K) was used both as thermal insulation in the sandwich configuration
and as a non-reactive "reference" material for evaluating the
experimental setup. The board is available as NIST Standard Reference
Material 1449 (http://ts.nist.gov/) and its room temperature^8^ and high
temperature^9^ thermal conductivities have both been previously measured
by NIST. Specimens^8^ were obtained in panels having nominal dimensions
of 600 mm by 600 mm by 25 mm with a nominal bulk density of about 310
kg/m^3^. For the purposes of this study, smaller sections were carefully
cut as needed from one large panel using a hand saw. All samples were
pre-conditioned overnight in a 100 ^o^C oven prior to being used as
insulation or test specimens in the box furnace setup. The panels had
been previously heat treated at 650 ^o^C for 8 h by the manufacturer.^8^
The heat capacity of the fumed-silica board as a function of temperature
was measured using a differential scanning calorimeter (DSC) and the
ASTM E1269 standard technique^1^ and determined to be on the order of
(1000 ± 100) J/(kg•K), in good agreement with the limited data available
in the literature for similar materials currently in production.^10,11^

*Testing Procedure*

The specimens and slug plate were surrounded by a 63.5 mm (total
thickness), 25.4 mm wide guard of the fumed-silica insulation board and
mounted between two Inconel frame plates (see Figure 3). The entire
assembly was held together by a set of eight retaining screws (two on

Figure 5- Values^6^ measured according to ASTM E1131^1^ and fitted
curves for mass loss vs. temperature of the two FRMs. Fitted curves are
of the form M = A + BT + Cln(T) with T in degrees K.

![](media/image27.wmf){width="5.452083333333333in"
height="3.0034722222222223in"}

each of the four edges of the plates). The assembled sandwich was either
suspended from two wires or simply placed on the bottom center of the
box furnace and the thermocouples were mounted; three Type N
thermocouples were placed at the various depths in the center slug plate
and one each was placed on the two exterior surfaces of the specimens
being evaluated, between the specimens and the retaining Inconel plates.
In addition to these thermocouples, the temperatures of the zone box and
the furnace were also monitored and recorded. In most tests, the furnace
temperature was programmed to follow a curve similar to the standard
ASTM E119 temperature-time curve^1^, but with a less rapid initial
temperature rise, due to limitations on the heating rate of the furnace.
The actual temperature-time curve employed will be shown in the results
to follow. The tests were generally aborted by turning off the furnace
power when the central steel slug reached an average temperature of 550
^o^C. However, the thermocouples still monitored temperatures during
cooling. Thus, while the heating portion of the tests generally occurred
over a period of 1 h to 2 h, the cooling portion could take as long as
24 h to 48 h, when the furnace was not opened to accelerate the cooling.
Additional tests were conducted at slower heating rates to determine the
sensitivity of the computed thermal conductivities to this parameter.
Typically, the furnace temperature was linearly raised to 600 ^o^C
during the course of either 4 h or 16 h and then held there until the
center slug plate also attained nearly this temperature, at which point
the furnace was turned off and a cooling curve monitored.

**Analysis**

Assuming one-dimensional heat flow through the FRM components of the
specimen sandwich, a solution will be determined for the case where the
temperature of the surfaces of the exposed specimens is
increasing/decreasing at a constant rate. We consider a pair of FRM
specimens, each of thickness *l,* with the initial condition that the
temperature is constant through the thickness of the specimen and slug,
i.e., T(z,0)=0. By symmetry, the mid-plane of the steel slug plate will
be an adiabatic boundary, so that we need only consider one specimen and
one half of the steel slug plate. Assuming constant properties, the
temperature in the specimen must satisfy:

$\frac{\partial^{2}T}{\partial z^{2}} = \frac{1}{\alpha}\frac{\partial T}{\partial t}$
(1)

where α=*k/C* is the thermal diffusivity \[m^2^/s\], *k* is the thermal
conductivity \[W/(m•K)\], *C*=*ρc~p~* is the volumetric heat capacity
\[J/(m^3^•K)\], and ρ is density \[kg/m^3^\], all for the FRM specimen
material. The steel slug plate is assumed to have a sufficiently high
thermal conductivity that it can be considered to be isothermal at any
given time. The "thermal capacity" of the slug plate, per unit area, is
taken to be 2*H* = (areal density of the plate)x(heat capacity of the
plate), with the factor of 2 arising from the fact that we need only
consider one half of the steel slug plate. The thermal capacity, *H*,
has units \[J/(m^2^•K)\].

The boundary condition at the exposed surface of the specimen, *z*=0,
is:

$T(0,t) = \text{Ft}$ (2)

where *F* is the (constant) temperature increase rate having the units
\[K/s\]. The boundary condition at the specimen surface, *z=l*, which is
in contact with the steel slug plate is:

$k\frac{\partial T}{\partial z} + H\frac{\partial T}{\partial t} = 0$
(3)

which follows from the fact that the heat conducted out of this face of
the specimen must equal the heat absorbed by (one half of) the steel
slug plate.

Assuming that the transient (exponentially decaying) terms in the
solution, which depend on the thermal diffusivity of the FRM specimen
and time, can be neglected, we arrive at a solution of the form:

$T(z,t) = F\left\lbrack t - \frac{\left( H + \text{lC} \right)z}{k} + \frac{\text{Cz}^{2}}{2k} \right\rbrack$
(4)

The temperature difference across the specimen of the FRM, ∆*T*, is
thus:

$\Delta T = T(0,t) - T(l,t) = \frac{\text{Fl}}{k}\left\lbrack H + \frac{\text{lC}}{2} \right\rbrack$
(5)

Finally, the thermal conductivity of the specimen can be computed as:

$k = \frac{\text{Fl}\left( H + \frac{\text{lC}}{2} \right)}{\Delta T}$
(6)

If the masses of the slug (M~S~) and FRM specimen (M~FRM~) are known,
equation (6) can be rewritten as:

$k = \frac{\text{Fl}\left( M_{S}c_{p}^{S} + M_{\text{FRM}}c_{p}^{\text{FRM}} \right)}{2A\Delta T}$
(7)

where A is the cross-sectional area of the slug (or specimen, 0.152 m by
0.152 m = 0.0232 m^2^ in our experimental setup), and *c~p~^S^* and
*c~p~^FRM^* refer to the heat capacities of the steel plate and FRM
specimen in units of \[J/(kg•K)\], respectively. A similar analysis can
be performed for the cooling case (*F*\<0, *T(z*,0)=constant), and it
can be shown that equation (7) applies in this case as well.

Equation (7) was conveniently implemented in a spreadsheet program to
determine the effective thermal conductivity from the acquired
temperature-time data points. The measured temperature-versus-time
series for the slug and for the exterior FRM surfaces were used to
compute the instantaneous values of *F* (∂*T*/∂*t*) and ∆*T* for use in
equation (7). Measured heat capacities of the 304 stainless steel
(Figure 2) and FRMs (Figure 4) as a function of temperature and mass
losses versus temperature for the FRMs (Figure 5) were used to further
refine the parameters used in equation (7). The resulting values of *k*
will be graphed against the mean specimen temperature
(\[*T*(0,*t*)+*T*(*l,t*)\]/2) in the results that follow. While this
paper presents preliminary results to indicate the feasibility of
utilizing the slug calorimeter method to evaluate the thermal
performance and specifically the effective thermal conductivity of FRMs,
an expanded uncertainty analysis could be conducted based on equation
(7) and the law of propagation of uncertainty.^12^ Assuming that the
heat capacities of the steel slug and the FRM specimen are fairly well
known and that lengths and masses can be measured with less than 1%
uncertainty, the uncertainties in the thermocouple measurements at high
temperatures, which are used to calculate both *F* and ∆*T* in equation
(7), will be the most significant contributors to the overall
uncertainty. Thus, the uncertainty can be reduced simply by applying
equation (7) over a larger time interval. For example, assuming an
optimistic uncertainty of 1 ^o^C for the thermocouple readings at high
temperatures, changing the sampling frequency from 1 min to 5 min
reduces the estimated uncertainty in the effective thermal conductivity
from about 25 % to about 5 % for thermal conductivities computed in the
temperature range of 400 ^o^C to 700 ^o^C during heating. During
cooling, using a 25 min interval to calculate the effective thermal
conductivity reduces its uncertainty to about 8 % from a value of about
40 % for 5 min intervals.

**Results and Discussion**

*1) Fire Resistive Materials*

The individual thermocouple temperatures collected during a single
heating/cooling cycle of FRM A are provided in Figure 6. The ASTM E119
standard temperature-time curve^1^ is shown for comparison to the
heating curve achievable in the electric furnace. It is worth noting
that during a portion of the heating curve the exterior FRM surface
temperatures actually exceed the "ambient" temperature of the furnace,
most likely due to enhanced radiation transfer between the Inconel
retaining plates and the individual furnace elements. This reinforces
the need to center the sandwich specimen in the furnace, so that both
sides (specimens) are exposed to nominally the same thermal environment.
There is little variability among the three thermocouples mounted in the
steel slug, indicating that the assumption that it behaves as an
isothermal slug mass is a generally valid one. Since these three
thermocouples are also mounted at different depths in the steel plate, a
low variability among them also supports the validity of the assumption
of one-dimensional heat transfer through the FRM that is critical to the
quantitative analysis. In Figure 6, it is clearly observed that even
after the furnace is turned off (as indicated by the peak in the furnace
and outer FRM temperature curves near 100 min), the temperature in the
steel slug continues to rise due to the thermal inertia (lag) of the
system. When the interior temperature of the slug exceeds the exterior
temperature of the FRM, the direction of the specimen heat flow
reverses.

Figure 6- Temperature vs. time data for one heating/cooling cycle for
FRM A specimens.

![](media/image28.wmf){width="5.64375in" height="3.06875in"}

One performance criterion that could be conveniently extracted from the
data in Figure 6 is the time necessary for the steel slug to reach some
specific temperature, such as 538 ^o^C for example.^1^ For the initial
heating cycle of FRM A shown in Figure 6, approximately 105 min were
required for the steel slug to achieve this temperature. For two
subsequent heating cycles, these times were observed to be on the order
of 110 min. These results suggest that most of the performance of this
particular FRM is achieved via its "low" thermal conductivity and not
via the contribution of significant endothermic reactions, as will be
discussed in more detail when the computed thermal conductivity curves
are presented below.

Equation (7) was applied to the data shown in Figure 6 and the computed
thermal conductivity values for five different heating/cooling cycles
are provided in Figure 7 in comparison to the previously measured
values. One of the testing laboratories reported their results for
thermal conductivity to be normally within ± 3 %.^6^ The first three
heating cycles followed the furnace heating curve shown in Figure 6. For
the fourth and fifth heating cycles, as outlined above, the furnace
temperature was ramped to 600 ^o^C in 4 h and 16 h, respectively. The
cooling curves for the third and fourth cycles are incomplete due to
power outages that occurred during the course of these experimental
runs. The computed thermal conductivity values agree with the values
measured previously using either a hot wire^6^ (ASTM C1113^1^) or a
transient plane source (TPS) method^7,13^ to within 15 % for
temperatures up to 600 ^o^C. The computed values at temperatures above
600 ^o^C for the first three heating cycles are clearly higher than
those previously measured, which could be due to enhanced heat transfer
by radiation in these highly porous fibrous materials^14^ sandwiched
between the "radiating" exterior Inconel plates and the interior steel
slug. It is observed that, after the initial transients, the data for
the five different cooling curves are all quite similar, indicating that
an equilibrium had been reached within the FRM with respect to reactions
after the first heating cycle.

Figure 7-- Effective thermal conductivity results for FRM A in
comparison to measured data.^6,7^

![](media/image29.wmf){width="5.993055555555555in"
height="3.1958333333333333in"}

A comparison of the heating curves is even more informative. The
differences among the heating curves for the first and the two
subsequent runs should be indicative of the reactions, etc. occurring in
the FRM. In the data in Figure 7, two phenomena appear to be
contributing to these differences. First, there is an endothermic
contribution, most likely due to dehydration of the hydrated cement
component of the FRM. This is indicated by the downward "peaks" in the
first heating curve that fall below the nominal thermal conductivity
values. These endothermic reactions should reduce the heat flow through
the specimen and thus appear as a reduction in the "effective" thermal
conductivity. In Figure 7, they are clearly present for mean
temperatures between 300 ^o^C and 400 ^o^C. Interestingly, prior to and
beyond this range of temperatures, there appear to be several smaller
exothermic peaks relative to the baseline curves. There are at least two
possibilities for the cause of these apparent exotherms. One would be
the presence of true exothermic reactions within the FRM, such as those
that would be generally expected during the decomposition of any organic
components within the material. The second (more likely) possibility is
that this increase in effective thermal conductivity is due to the
convection of superheated steam and gases created during the endothermic
dehydration reactions. The particular FRMs evaluated in this preliminary
study have a high porosity and a fairly open pore structure so that the
steam produced during the dehydration reactions (and its accompanying
energy) could be easily driven inward towards the stainless steel plate
slug. This phenomenon would appear as an apparent increase in the
effective thermal conductivity of the FRM material, and would likely
only be present during the initial heating cycle. This same transport of
steam/gas, or more specifically the lack thereof, is responsible for the
often observed spalling of high-performance (low permeability) concrete
during fire exposure.^15^

In Figure 7, it can be observed that by combining the effective thermal
conductivity results produced during a complete heating/cooling cycle
such as cycle #2, a much larger temperature range can be covered than
that covered by an individual heating or cooling curve. This is due to
the transient effects present both during the initial part of the
heating curve and during the transition that occurs as the direction of
heat flow is reversed during the cooling cycle. Much of the transient
effect on heating was removed when the heating rate was slowed to either
≈150 ^o^C/h or ≈37.5 ^o^C/h, as illustrated by the results in Figure 7
for heating curves 4 and 5, respectively.

Based on these considerations, the following experimental procedure will
be adopted for all future testing of FRMs using this slug calorimeter.
The first two heating/cooling cycles will follow the heating curve shown
in Figure 6, with natural cooling. Finally, a third heating/cooling
cycle will consist of heating the furnace to 600 ^o^C slowly over the
course of 4 h, then holding this temperature until it is also nearly
achieved by the slug plate, followed once again by natural cooling.
These three sets of curves will be used to characterize the thermal
performance of the FRM as presented above.

The testing protocol outlined above was applied to the evaluation of FRM
B. For the first two heating curves, times of 104 min and 102 min,
respectively, were required for the inner steel slug to reach a
temperature of 538 ^o^C, slightly less than those observed for FRM A
above. The effective thermal conductivities computed from equation (7)
are provided in Figure 8. The results are quite similar to those in
Figure 7 with a few characteristic differences. In comparing the heating
curves for the 1^st^ and 2^nd^ cycles in Figure 8, it is observed that
the endotherms and exotherms are generally smaller in magnitude in
comparison to those observed in Figure 7. This is consistent with the
lower mass loss (less reaction) of FRM B relative to FRM A (Figure 5).
In addition, there is some indication of an additional high temperature
endothermic reaction present for FRM B, possibly due to decarbonation of
the carbonated portland cement component of the FRM. Secondly, there is
a larger observed difference between the slug calorimeter and the
previously measured thermal conductivities at higher temperatures (\>
400 ^o^C) than that observed in Figure 7. Because FRM B has a
significantly lower density and higher (open) porosity than FRM A, it
would be expected that any increased heat transfer due to radiation
between the Inconel plates and the stainless steel slug would be
enhanced in this material relative to FRM A. For temperatures below
about 400 ^o^C, where these radiation effects would expected to be much
less significant, the agreement between the slug calorimeter effective
thermal conductivity values and those previously measured is within 20
%.

*2) Fumed-Silica Insulation Board*

In addition to being used as a guard insulation material, the
fumed-silica board was also utilized as the specimens themselves in one
set of three heating/cooling cycles. The material is non- reactive, so
that the computed thermal conductivity results can be compared directly
to the previously measured values.^8,9^ However, an additional
complication arises in this case. When the fumed-silica board is used
only as guard insulation, it has a much lower thermal conductivity than
the typical FRM specimens and the assumption of one-dimensional heat
transfer through the

Figure 8-- Effective thermal conductivity results for FRM B in
comparison to measured data.^6,7^

![](media/image30.wmf){width="5.95in" height="3.279861111111111in"}

thickness of the guarded square FRM specimens appears to be valid, as
indicated by the results presented above. Conversely, when the
fumed-silica board is used for the specimens as well, the relative heat
transfer through the "guarded" areas of the sandwich configurations
becomes significant. While the temperature rise of the slug is still
indicative of the heat flow into the slug, the area (*A* in equation
(7)) for this flow is no longer simply 0.152 m by 0.152 m. For the
analysis presented below, it has been assumed that in this case, the
total area available for heat transfer is given by the total area of
specimen surrounded by the guard (0.203 m by 0.203 m) plus the area of
the thin sides of one half of the slug calorimeter (two times 0.203 m by
0.00635 m plus two times 0.152 m by 0.00635 m). In addition, the mass of
the "FRM" specimen was taken as the mass of the fumed-silica insulation
board specimen plus the masses of all of the guard materials comprising
one half of the sandwich specimen configuration.

Physically, these first order approximations seem reasonable and as
shown in Figure 9, they do produce thermal conductivities for the
cooling curves that are both reproducible and that agree with the
previously measured data to within about 5 %. The data in Figure 9
appear much noisier than those in Figures 7 and 8, but it must be kept
in mind that the scale on the y-axis in Figure 9 has been reduced by a
factor of eight relative to that employed in the other two figures. One
other point worth noting from Figure 9 is that once again, only the
heating results for the third run, where a more gradual heating curve
(extending only up to 500 ^o^C in this case) was employed, compare
favorably to the gradual cooling results for the three runs and the
previously measured data. In the first two runs that employed basically
the same heating rate as that shown in Figure 6, due to the low thermal
conductivity (and thermal diffusivity) of the fumed-silica board,
"steady-state" conditions were apparently only approached at the very
end of the heating curve (500 ^o^C and beyond). The reproducibility of
the heating and cooling curves for the first two runs in Figure 9 does
provide further support that the fumed-silica board is indeed behaving
as a non-reactive material over the temperature range employed in this
preliminary study. The results for run 3 with the slower heating rate
indicate once again the potential for piecing together the thermal
conductivity values determined from the heating and cooling curves to
provide a single thermal conductivity versus temperature curve that
covers a larger temperature range than either of its two component
curves. Radiation effects are seen to be of much less importance in this
material as the computed values of *k* agree well with those previously
measured over the entire temperature range investigated with the slug
calorimeter. Of course, the fumed-silica insulation board had been
formulated specifically to minimize radiation transfer at high
temperatures via the addition of an opacifier.^8^

Figure 9-- Computed effective thermal conductivity results for
fumed-silica insulation board in comparison to previously measured NIST
data (with error bars indicating ± 5 %).^8,9^ Note: NIST data have been
corrected to values for one standard atmosphere of pressure (sea level)
using the procedure provided in reference 9.

![](media/image31.wmf){width="6.045833333333333in"
height="3.595833333333333in"}

The first two heating tests with the fumed-silica insulation board were
terminated when the **exterior** of the specimens reached a temperature
of about 900 ^o^C, quite similar to the termination point used for the
testing of the two FRMs. However, in comparison to the FRMs, where the
slug had achieved a temperature of about 540 ^o^C at this point, for the
fumed-silica board, the interior slug temperature was still **well below
200** **^o^C** at this time. Naturally, this reinforces the critical
importance of using a low thermal conductivity material to protect steel
structures exposed to fire.

**Conclusions and Future Directions**

The use of a slug calorimeter for evaluating the thermal performance of
fire resistive materials has been successfully demonstrated. Key
components of the system include the use of a "sandwich" specimen to
provide an adiabatic boundary condition at its central axis and the
utilization of multiple heating/cooling cycles to provide information on
the influence of reactions and convective transport on the computed
effective thermal conductivity values. The results obtained in this
relatively simple small scale test can provide valuable insights into
the mechanisms through which the FRM protects the steel substrate in an
actual fire.

The current experimental setup is now being modified to include an
exhaust fume hood at the top of the furnace so that it may be applied to
a wider variety of FRMs that emit organics as well as water and CO~2~.
It is envisioned that further modifications to the experimental setup
may be required to evaluate intumescents and other FRMs that undergo
considerable changes in their dimensions during exposure to a fire.

**References:**

1\) *ASTM Annual Book of Standards*; ASTM International: West
Conshohocken, 2004.

2\) Bentz, D.P., Prasad, K.R., and Yang, J.C., "Towards a Methodology
for the Characterization of Fire Resistive Materials with Respect to
Thermal Performance Models," submitted to *Fire and Materials*, 2004.

3\) Bartholmai, M., Schriever, R., and Schartel, B., "Influence of
External Heat Flux and Coating Thickness on the Thermal Insulation
Properties of Two Different Intumescent Coatings Using Cone Calorimeter
and Numerical Analysis," *Fire and Materials*, **27**, 151-162, 2003.

4\) Metals Handbook, 10^th^ edition, ASM International, Materials Park,
OH, 1990.

5\) Bogaard, R.H., Desai, P.D., Li, H.H., and Ho, C.Y., "Thermophysical
Properties of Stainless Steels," *Thermochimica Acta*, **218**, 373-393,
1993.

6\) Anter Laboratories, Inc., Transmittal of Test Results, report to
NIST, 2004.

7\) Dinges, C. (Hot Disk Laboratories), Report on Measurements on
Samples Supplied by NIST, report to NIST, 2004.

8\) Zarr, R.R., Somers, T.A., and Ebberts, D.F., "Room-Temperature
Thermal Conductivity of Fumed-Silica Insulation for a Standard Reference
Material," NISTIR **88-3847**, U.S. Department of Commerce, October
1988.

9\) Smith, D.R., and Hust, J.G., "Microporous Fumed-Silica Insulation
Board as a Candidate Standard Reference Material of Thermal Resistance,"
NISTIR **88-3901**, U.S. Department of Commerce, October 1988.

10\) Culimeta Textilglas Technologie GmbH & Co., General Information:
Flexipor© Microporous Insulating Board,
[http://www.culimeta.de](http://www.culimeta.de/), accessed September
2004.

11\) Microtherm, Microtherm® Insulation -- Product and Performance Data,
[http://www.microtherm.uk.com](http://www.microtherm.uk.com/), accessed
October 2004.

12\) Taylor, B.N., and Kuyatt, C.E., "Guidelines for Evaluating and
Expressing the Uncertainty of NIST Measurement Results," NIST Technical
Note No. **1297**, U.S. Department of Commerce, Washington, D.C.,
September 1994.

13\) Gustafsson, S.E., "Transient Plane Source Techniques for Thermal
Conductivity and Thermal Diffusivity Measurements of Solid Materials,"
*Rev. of Sci. Instrum.*, **62** (3), 797-804, 1991.

14\) Flynn, D.R., and Gorthala, R., "Radiation Scattering Versus
Radiation Absorption- Effects on Performance of Thermal Insulation Under
Non-Steady-State Conditions," *Insulation Materials: Testing and
Applications: Third Volume, ASTM STP 1320*, American Society for Testing
and Materials, West Conshohocken, PA, 366-380, 1997.

15\) Bentz, D.P., \"Fibers, Percolation, and Spalling of High
Performance Concrete,\" *ACI Materials Journal*, **97** (3), 351-359,
2000.

*Journal of Adhesion*, Vol. 81, 1-18, 2005

**Critical and Subcritical Adhesion Measurements of a Model Epoxy
Coating Exposed to Moisture Using the Shaft-Loaded Blister
Test**[]{#__RefHeading___Toc97685944 .anchor}

E. P. O'Brien^◊^

Center for Adhesive and Sealant Science

Virginia Tech, Blacksburg, 24061

S. L. Case

Lord Corporation

Cary, North Carolina 27512

T. C. Ward\*

Department of Chemistry

Virginia Tech, Blacksburg, 24061

Virginia, USA

\*Address correspondence to Thomas C. Ward, Department of Chemistry,
2107 Hahn Hall (0344), Virginia Tech, Blacksburg, VA 24061, USA. E-mail:
<tward@vt.edu>

^◊^Current address: National Institute of Standards and Technology,
Buildings and Fire Research Laboratory, Gaithersburg, Maryland 20899

### Abstract

The shaft-loaded blister test (SLBT) was used to investigate the
adhesion between a model epoxy coating and a silicon oxide surface as a
function of relative humidity. Critical and sub-critical strain energy
release rates were measured using specimens that incorporate reinforcing
layers of Kapton® film. A simplified procedure that eliminates the need
for video imaging to measure the blister radius and fracture energy was
developed. A critical relative humidity level for adhesion loss was
observed, in agreement with previous measurements for polymeric systems.
The SLBT was confirmed to be particularly attractive for fracture energy
measurements on thin, strongly adhered coatings and films which
otherwise tend to be problematic.

**Key Words**: shaft-loaded blister test, water-assisted subcritical
crack growth, stress corrosion cracking, epoxies, moisture, durability,
microelectronics, critical relative humidity, wedge test, coatings, thin
films

### Introduction

Water is often regarded as the primary agent in the reduction of service
life and reliability of adhesive joints and composites. \[1\] This is
resultant from absorption of atmospheric moisture into the polymeric
adhesive, which typically accumulates at the interface and displaces the
polymer from the adherend surface. \[2, 3\] Epoxy adhesives are
particularly sensitive to moisture, resulting in a dramatic loss of
adhesion strength when exposed to moisture above a critical relative
humidity level. \[4-11\] The critical relative humidity level (RH) is
typically between (50 -- 70) %.

Sub-critical adhesion testing is of practical interest to engineers and
scientists because it explores adhesive debonding in a range of crack
velocities and applied strain energy release rates, *G*, which are
significantly less than required for catastrophic failure. Therefore
sub-critical adhesion testing simulates the failure occurring in the
real-life application or service life of the adhesive. Crack growth can
be driven by small applied loads generated by residual stresses,
thermomechanical cycling, and mechanical or vibrational loading during
service. \[12\] An additional advantage of sub-critical testing over
conventional adhesion tests is the reduced ambiguity associated with the
dependence on crack velocity of the measured adhesion energy, which is
associated with viscoelastic effects at the crack tip and in the bulk
adhesive.

The effects of an invasive environment on adhesive bonds can be examined
with subcritical adhesion measurements where tests during submersion in
heated hostile fluids are possible. The average crack velocity, *v*
(*da*/*dt*) and the applied strain energy release rate, *G*, are
measured, where *a* is the crack length. A schematic of a typical *v-G*
curve is shown in Figure 1. Three regions are usually observed, which
are related to the mechanism for crack advancement. \[12-14\] Region III
is associated with critical fracture events, which is independent of the
environment for bulk glass fracture. Region II is strongly environment
dependent, but only weakly dependent on the crack driving energy. This
is characteristic of fracture where diffusion of the penetrant or
environmental fluid to the crack tip is the rate limiting step for crack
advancement. In Region I low crack velocities and low applied crack
driving energies are found. The crack velocity is thought to be
controlled by a stress-activated chemical reaction of the penetrant with
the bonds at the crack tip. \[15\] At the lowest crack velocities, below
Region I, there exists a threshold value of crack driving energy,
*G*~Th~, below which no crack propagation is observed.

Figure 1. Schematic of a typical *v*-*G* curve illustrating the three
regions of crack growth and the threshold value of *G*.

![](media/image32.wmf){width="3.5in" height="2.9069444444444446in"}

Traditionally, subcritical fracture test specimens have been laminated
beams, where the adhesive is bonded between two parallel rectangular
rigid adherends. Examples of the laminated beam type experiments are the
double cantilever beam (DCB) wedge test \[16\], the asymmetric double
cantilever beam test \[15\], the double cleavage drilled compression
specimen \[17\], and the four-point flexure samples \[18\]. The
advantages of laminated beam type specimens are: 1) the adhesive is
loaded elastically away from the crack tip, 2) high strain energy
release rates are obtainable, 3) the fracture mechanics models for
analysis are well understood, and 4) the specimens can be self-loading.
The disadvantage of these type of tests is that they may require a
sophisticated experimental set-up to measure the crack length (video
camera, acoustic or electrical methods). Additionally for samples
exposed to a fluid environment, the equilibration time may be long due
to the two impermeable substrates causing diffusion into the adhesive
only from the edge. This leads to a heterogeneous distribution of
diffusant in the adhesive joint.

With respect to the laminated beam type specimens, there are advantages
to utilizing the shaft-loaded blister test. The time for environmental
saturation is relatively short, resulting from the exposed face and
short diffusion path. \[19, 20\] In addition, the specimen geometry is
axisymmetric, which reduces any misleading edge effects caused by
degradation of the interface away from the crack tip. Some disadvantages
of the shaft-loaded blister test are that its fracture mechanics models
have not been studied as extensively as the laminated beam specimens;
and, like most coatings tests, the maximum value of the strain energy
release rate before film rupture occurs is limited by the film's
mechanical strength and the intrinsic interfacial toughness. Plastic
yielding of the coating also complicates the analysis. Furthermore, the
strain energy release rate is a function of 1/*a*^4/3^ and therefore
will approach a threshold value of *G* more slowly than beam type
specimens. For the DCB wedge test, the strain energy release rate
decreases as a function of 1/*a*^4^. Therefore, a wide range of *G*
values can be obtained for a relatively small change in crack length and
the threshold energy can be rapidly approached.

In this work, the shaft-loaded blister test (SLBT) was used to
investigate the effects of relative humidity on an epoxy coating bonded
to glass and silicon wafers. A typical experiment utilizes the
controlled displacement of a spherically capped shaft, driven by a
universal testing machine (UTM) to create a growing blister, as an
alternative to applying fluid or gas media to generate the fracture
(Figure 2). \[21-27\] Although the SLBT has been used extensively to
study polymer and thin film adhesion, to date the technique has not been
adapted to the study of moisture assisted subcritical crack growth.
Specimens were tested by two methods: (1) the more common critical
method where adhesive failure is essentially catastrophic and (2) by
modifying the SLBT configuration and measuring adhesion over a long time
scale in subcritical crack growth experiment.

## Experimental

### *Materials*

The model epoxy adhesive was Epon 862 bisphenol-f resin (Shell Chemical
Corporation, Houston, TX) mixed with 10 parts per hundred resin (phr) of
1,4-butanediol (added to increase the solubility of the curing agent)
and cured with 3 phr of 4-methyl-2-phenylimidazole. \[28\] Details of
the physical properties of the model epoxy can be found elsewhere.
\[28\] Quartz and silicon wafers were utilized as substrates. The quartz
substrates were obtained from ChemGlass Inc. (Vineland, NJ) in a 15.24 x
15.24 x 0.9525 cm^3^ (6" x 6" x 3/8") sheet. The silicon wafer
substrates, supplied by Hewlett-Packard Co. (Corvallis, OR) were 152.4
mm (6" inch) diameter with a thermally grown silicon oxide 10 nm thick.

Figure 2. Schematic of the shaft-loaded blister test.

![](media/image33.wmf){width="3.4631944444444445in"
height="2.988888888888889in"}

### Blister Test Specimen Preparation

#### Critical Adhesion Measurements

Critical adhesion measurements were made on the model epoxy bonded to
quartz. Quartz is an appropriate substrate for our investigation since
it will support significant loads (due to its thickness) in convenient
SLBT geometries. It is also composed mostly of silicon oxide, having a
surface similar to silicon wafers used in the microelectronics industry.
A schematic of the critical shaft-loaded blister test specimens is shown
in Figure 3. Quartz sheets were cut into 3.6 x 3.6 cm^2^ (1.5 x 1.5
in.^2^) squares and a 0.8 cm (0.31") diameter hole was drilled in the
center. A pre-crack was fabricated by placing a 0.95 cm (3/8") diameter
piece of Kapton® pressure sensitive adhesive tape (PSAT) over the hole
in the center of the quartz substrate. The Kapton® PSAT consists of a 25
μm (1 mil) thick Kapton® backing and a 37.5 μm (1.5 mil) thick acrylic
pressure sensitive adhesive. The tape also provided additional
mechanical reinforcement to the thin epoxy film at the highly stressed
contact area between the coating and shaft-tip. To prepare the specimen,
the un-cured model epoxy was first coated on the quartz substrate. A 50
micron (2 mil) thick piece of Kapton® film (no PSA) was then placed on
top of the epoxy coating. The Kapton® film acts as a mechanical
reinforcing layer for the epoxy coating. The resulting adhesive coating
is therefore a composite of the model epoxy, Kapton® PSAT (located
solely in the center) and Kapton® film. A schematic of the test specimen
is shown in Figure 3. The sample was then cured in a convection oven for
one hour at 130 °C and placed in a dessicator to slowly cool
(approximately 30 minutes). The typical epoxy film thickness varied
between samples from (50 to 100) μm, with ± 5 μm uniformity in the
films. Samples were conditioned at constant relative humidity (8, 29,
42, 71, or 98 %) for 3 days at room temperature. This was sufficient
time for the adhesive to be saturated. The relative humidity was
regulated using saturated salt solutions. \[29-31\] After environmental
exposure, the samples were immediately tested at ambient temperature and
humidity (≈50%). Three samples were tested for each relative humidity
using an universal testing machine (UTM) and shaft terminated with a
ball bearing approximately 0.63 cm (1/4") in diameter. The UTM cross
head displacement rate was 0.1 mm/sec.

Figure 3. Schematic of critical shaft-loaded blister test specimen.

#### ![](media/image34.wmf){width="5.996527777777778in" height="1.8368055555555556in"}

#### Constant Load Subcritical SLBT Specimens

Subcritical adhesion measurements of the model epoxy were obtained using
the silicon wafer substrates. A hole approximately 12.5 mm in diameter
was produced in the center of the silicon wafer using a diamond coated
drill bit and a Dremel® tool. Care must be taken when drilling the
brittle wafers. The wafer was then rinsed with isopropyl alcohol and
dried under a stream of ultra-high purity nitrogen gas. The hole in the
wafer was then covered with a 0.95 cm (3/8") diameter piece of Kapton®
PSAT. The wafer was uniformly coated with epoxy adhesive using a
pneumatically driven doctor blade. A (152.4 x 152.4) mm^2^ (6" x 6")
square piece of Kapton® (50 μm thick) was carefully applied on the wafer
to avoid disrupting the adhesive and forming air bubbles. The coated
wafer (with Kapton®) was cured under identical conditions to the
"critical" specimens described previously.

To develop the sub-critical blister test specimen, a sample must be
self-loading, the integrity of the thin adhesive coating must be
maintained, and the sample must be exposed to the fluid. A schematic of
a scheme meeting these requirements is shown in Figure 4. To fabricate a
simple self-loading, yet constant load, SLBT specimen, a hole was
punched in the center of the coating that can accommodate a 2.54 mm (or
4/40") stainless steel machine screw. The machine screw acts as the
fastener from which to suspend a "dead load" via a flexible wire. A
non-corrosive and high density material such as lead is recommended as
the weight because of the corrosive nature of the saturated salt
solutions. The punched hole containing the screw was sealed with a room
temperature cure epoxy (Devcon 2-ton epoxy, Danvers, MA). The entire
SLBT specimen was placed in a large glass vessel and conditioned at
constant relative humidity (42, 71, or 98%) at room temperature. These
values span the critical relative humidity value for adhesion loss.

### Analysis

The strain energy release rate (crack driving energy), *G*, can be
calculated from the "load-based equation" (Equation 1) based on the
load, *P*, and blister radius, *a*. \[12\]

Equation 1
$G = \left( \frac{1}{\text{16}\pi^{4}\text{Eh}} \right)^{\frac{1}{3}}\left( \frac{P}{a} \right)^{\frac{4}{3}}$

Figure 4. Schematic of the sub-critical shaft-loaded blister test
specimen.

![](media/image35.wmf){width="5.813888888888889in"
height="3.4069444444444446in"}

where *E* is the Young's tensile modulus, and *h* is the thickness of
the adhesive coating. The modulus of the coating for the bi-layer film
(Kapton® and epoxy adhesive) is estimated from a simple rule of
mixtures:

Equation 2 *E*~composite~ = *v*~Kapton®~ *E*~Kapton®~ +*v*~Epoxy~
*E*~Epoxy~

where *E*~composite~ is the modulus of the composite, *v*~Kapton®~ and
*v*~Epoxy~ are the volume fractions of the Kapton® backing and epoxy,
respectively, and *E*~Kapton®~ and *E*~Epoxy~ are the moduli of the
Kapton® backing and epoxy, approximately 2.5 GPa \[28\] and 6 GPa
\[32\], respectively.

Equation 1 for the strain energy release rate is independent of the
amount of plastic deformation that might occur in the adhesive at the
contact zone between the shaft-tip and adhesive coating. \[27\] This is
located in the center of the blister and is also where the load is
suspended in the subcritical experiments. The expression for the crack
driving energy (Equation 1) is also relatively insensitive to the value
of (*Eh*) because the film's tensile rigidity (*Eh*) is raised to the
(-1/3) power. As a consequence, the SLBT is particularly advantageous
for environmental durability testing since *G* is not strongly dependent
on the values of the modulus and thickness, which are functions of the
moisture content, temperature, and exposure time. The contribution of
the Kapton® PSAT is negligible for the same reasons that *G* is
independent of plastic deformation in the center of the blister.

For the critical adhesion measurements, samples were tested using
loading and unloading cycles, which were repeated up to seven times, to
determine the crack length as a function of load. The load applied by
the UTM as a function of the resulting central shaft displacement
(*w*~0~) for successive cycles on a single sample is shown in Figure 5.
In this test procedure, the film was loaded and the crack was allowed to
propagate several mm. The load was removed, as was the sample from the
UTM, and two or three measurements were made to calculate the average
blister radius. This procedure is different from the typical blister
radius measurement where the crack is allowed to propagate continuously
and the diameter is observed simultaneously with a video camera. An
example of our typical load as a function of blister radius curve is
shown in Figure 6. Note that the fitted line passes through the origin
as Equation 1 suggests. Utilizing the successive loading and unloading
cycles, considerable effort involving measuring the blister radius with
a video camera has been eliminated. And unlike beam type specimens that
utilize opaque adherends, the crack length can be readily measured in
our configuration. Therefore, the SLBT requires only an UTM and
eliminates the need for sophisticated crack measuring equipment.

Figure 5. Successive load as a function of central shaft displacement
curves for 98% relative humidity. The filled in symbols are the loading
curves and the unfilled symbols are the unloading curves.

![](media/image36.wmf){width="6.002083333333333in"
height="3.536111111111111in"}

For the sub-critical experiments the average blister radius was measured
periodically. The average crack velocity, *v*, (*da*/*dt*) was
determined from the relationship between the average blister radius as a
function of time. Again, no optical equipment was necessary.

## Results and Discussion

### *Critical Strain Energy Release Rates*

The calculated strain energy release rates are shown in Figure 7 as a
function of the relative humidity. At (8, 29, and 42) % relative
humidity, the film always ruptured before debond growth occurred,
indicating very high interfacial toughness. However, the adhesive
interface of specimens conditioned at the high relative humidities
degrades sufficiently for debonding to occur. The resulting strain
energy release rates are (163 ± 27 and 111 ± 27) J/m^2^ for 71 % and 98
% relative humidity, respectively. A dramatic loss of adhesion occurs
above 70 % relative humidity, suggesting that there is a critical
relative humidity environmental conditioning level for adhesion loss. In
the case of film rupture, based on the initial hole size, *a*~0~, and
the maximum load at break, a lower bound of the strain energy release
rate can be estimated. The values of *G* calculated from the load at
rupture are not reported.

Figure 6. Load (*P*) as function of blister radius (*a*) at 98% relative
humidity.

![](media/image37.wmf){width="5.999305555555556in" height="3.56875in"}

Figure 7. Summary of strain energy release rates *G* (J/m^2^) as a
function of relative humidity for critical SLBT.

![](media/image38.wmf){width="6.002777777777778in"
height="3.4763888888888888in"}

While exhibiting beneficial attributes such as axisymmetric geometry and
the short saturation times, and the relatively simple sample preparation
and test procedures, the shaft-loaded blister test has some
shortcomings; namely, the adhesive film can rupture before debonding
occurs resulting in more qualitative observations. This may be assigned
to the large stresses generated within the film near the contact area
between the film and shaft tip. Significant, visible, plastic
deformation at the contact area may still arise, even if film rupture
does not occur and crack propagation takes place. However if plastic
deformation is confined solely to the center of the blister and not at
the crack tip, equation 1 remains valid. \[27\] One method to reduce
plastic deformation and maintain the mechanical integrity of the film is
to reduce the applied load, and therefore the stress on the film. This
strategy was employed in the subcritical fracture experiments.

### *Constant Load Sub-Critical Fracture*

The *v*-*G* curves obtained for the model epoxy as a function of
relative humidity (42, 71, and 98 %) are shown in Figure 8. For each
specimen, the initial value of the crack driving energy was
approximately 40 J/m^2^. As the crack advances, the value of the strain
energy release rate gradually decreases as the size of the blister
radius increases until the crack appears to arrest at the value of
*G*~Th~. The average along with one standard deviation of *G*~Th~ as a
function of relative humidity is listed is Table 1. The value of *G*~Th~
for 42 % relative humidity conditioning is significantly greater than
either 71 % or 98 % relative humidity cases. Moreover, *G*~Th~ is almost
identical for the 71 % and 98 % relative humidity exposures. In some
cases, *G*~Th~ has been found to be dependent on the concentration of
water molecules at the crack tip, and therefore the relative humidity.
\[15, 18, 33\] Other work has shown that above a critical relative
humidity value ranging between (50 to 70) %, the adhesive fracture
energy is constant and is independent of the vapor pressure. \[34, 35\]
Condensation at the crack tip due to capillary forces may negate any
differences in the effect of moisture level conditioning at high
humidity. This behavior is predicted from the classic Kelvin equation
for the meniscus radius. From that equation, at 70 % relative humidity
the meniscus radius is predicted to be approximately 1 nm, about the
size of a bond length or molecule.

Figure 8. SLBT debond velocity (m/s) as a function of crack driving
energy, *G*, (J/m^2^) and relative humidity (42, 71, and 98 %).

![](media/image39.png){width="5.708333333333333in"
height="3.7291666666666665in"}

Table 1. Threshold crack driving energy, *G*~Th~, as function of
relative humidity.

  --------------------- ---------------- ---------------- ----------------
                        42 % rh          71% rh           98% rh

  Average *G*~Th~       25.2             10.2             11.5
  (J/m^2^)                                                

  Standard Deviation    4.9              2.1              2.6
  --------------------- ---------------- ---------------- ----------------

Residual stress can also affect the adhesion measurement, if the *G*~Th~
is similar in magnitude to *G* attributable to residual stress. The
residual stresses in the coating originate from the contraction of the
epoxy during cure and the difference in the coefficient of thermal
expansion (CTE) between the substrate, epoxy, and Kapton® backing.
During the critical experiments, residual stress is not expected to be a
factor as the stress applied by the UTM is much greater than the
residual stress in the film.\[36\] Depending on if the residual stress
is tensile or compressive, the applied strain energy release rate will
be less than or greater than the zero residual stress condition. \[37,
38\]

The tensile residual stress in the model epoxy film bonded to glass was
estimated from two different methods. In the first method, residual
stress was estimated from the radius of curvature of a bimaterial strip
of epoxy to glass and found to be 5.5 MPa. \[39\] In the second method,
the residual stresses were estimated from Equation 3. \[40\]

Equation 3 $\sigma_{r} = - \frac{E}{(1 - \nu)}\Delta\alpha\Delta T$

where ∆*α* is the difference in the CTE between the substrate and
adhesive and ∆*T* is the difference between the temperature of the
sample and the stress free temperature. Utilizing values of the stress
free temperature and CTE \[39\], the residual stress was found to be as
high as 20.7 MPa. These values were for the dry coatings that have been
immediately removed from the oven such that the stresses have had little
time to relax.

To determine if residual stresses play a role in our subcritical
adhesion measurements, the value of *G*~Th~ was compared to the strain
energy release rate of a coating delaminating from residual stress (see
Equation 4). \[40, 41\]

Equation 4 $G = \frac{{h\sigma}_{r^{2}}(1 - \upsilon)}{2E}$

Where *σ~r~* is the residual stress and *υ* is the Poisson ratio. Using
the values of residual stress determined from the bimaterial specimen
and Equation 3, the strain energy release rate in the dry coating was
found to be 0.2 and 2.6 J/m^2^, respectively.

Below the critical relative humidity, at 42 %, the values of *G*~Th~
obtained by the SLBT are much greater than the *G* attributable to
residual stress. Therefore at 42 % relative humidity, residual stress is
not likely a significant factor. However, at high relative humilities,
both the *G* values from residual stress and the SLBT are similar in
magnitude which suggests that residual stress may play a role. However
at high relative humidities, there is evidence that the tensile residual
stresses in the dry state relax and decrease to zero or can even become
compressive. \[42, 43\] In the case where there is compressive residual
stress, the measured threshold value of *G*~Th~ will be greater than the
unstressed condition, leading to an overestimation of *G*~Th~,
suggesting the interface is more durable than it appears. It should be
noted that for this adhesive, after saturation, the bimaterial strips
did not exhibit any signs of compressive stresses. The evidence shows
that debond growth is not driven by tensile residual stresses, but by
the applied load and presence of moisture.

The adhesive fracture energy can also be affected by changes in the
mechanical properties of the epoxy and backing due to moisture
absorption. Although it is expected that the Kapton® will not be
drastically affected by the moisture, some epoxies have shown a decrease
in the modulus by as much as 80 % in high humidity. \[19\] The modulus
of the model epoxy used in this work was found to decrease modestly by
18 % relative to its dry condition. \[39\] The modulus change and
thickness change due to swelling has little effect on the measured
debond driving energy, as *G* \~ (1 / *Eh*)^1/3^. This insensitivity to
changes in modulus makes the SLBT particularly advantageous for
environmental durability studies. The strain energy release rate can
also be calculated as: *G* = *P w* / (4 *π* *a*^2^).\[44\] This
expression is independent of the mechanical properties and it requires
in addition to the load and blister radius, that the displacement, *w*,
to be measured. Mechanical properties of the film can also change due to
creep of the adhesive and backing. Creep in the subcritical SLBT may be
caused by the suspended loads and resulting stress, the plasticizing
effects of humidity, and the long duration of the experiment which in
this work was up to 4 months. Creep should not affect the strain energy
release rate because Equation 1 depends solely on the mechanical
properties of the film at the crack front. Therefore, as the crack
continually advances, the film located directly at the crack front is
loaded for only a brief period of time.

Experimental uncertainty in the calculation of the values of *G*, and
crack velocity, *v*, are introduced from the measurement of the blister
radius, *a*, as well as from any slight asymmetry of the blister. The
error associated with measuring the blister radius with the micrometer
is approximately ± 0.2 mm. Furthermore, the blister radius may not be
perfectly symmetric, although this difference is generally small (0.1 to
0.2 mm). In the most extreme cases, the difference between two
measurements of the same blister radius is as large as 0.5 mm. Asymmetry
can be caused by differences in thickness, residual stress in the epoxy,
in the Kapton® backing \[45\], and any heterogeneities in the intrinsic
interfacial adhesive toughness. The experimental uncertainty due to the
asymmetry of the blister is essentially unavoidable and difficult to
reduce below 0.1 mm. The error attributable to the blister radius
measurement depends on the magnitude of the value of *G* and crack
velocity. For values of *G* between (20 - 50) J/m^2^ the error is ± (1
-- 2) J/m^2^, whereas for values of *G* between (1 -- 20) J/m^2^ the
error is between ± (0.1 -- 0.5) J/m^2^. Crack velocities on the order of
10^-8^ and 10^-9^ m/s have errors on the order of ± 10 %, which is much
less than the inherent scatter. The error is significant for crack
velocities of 10^-10^ m/s or less. However at these crack velocities,
the experimental limit of the measurement has been reached and these
cracks appear to arrest.

The quartz substrate and the silicon wafer substrates were expected to
produce similar adhesion results given that both have surfaces composed
of silicon oxide. In the model epoxy-quartz experiments, a critical
level of relative humidity was observed where adhesion loss occurred.
That is, at a relative humidity of 42%, the reinforced epoxy film
ruptured and the adhesive fracture energy was relatively large.
Utilizing the constant load sub-critical SLBT, however, the adhesive
system could be characterized above and below the critical relative
humidity. Therefore by reducing the applied strain energy release rate,
and consequently the applied stresses in the adhesive coating, the
integrity of the epoxy coating was maintained and the adhesive could be
controllably debonded. In addition, from the sub-critical SLBT
experiments the evidence of a critical level of relative humidity for
adhesion loss was much more qualitative. These results show that the
constant-load sub-critical shaft-loaded blister test is a promising new
technique for studying the effects of the environmental degradation on
adhesive joints and coatings. Given the great difficulty in testing
thin, strongly adhered coatings and films, this technique is
particularly attractive. Furthermore, we have demonstrated the
sub-critical SLBT can be applied to the study of polymer adhesion to
brittle silicon wafers which are usually difficult to test given their
fragile nature.

The sub-critical SLBT specimen has clarified the mechanism for crack
growth in this adhesive system within the range of applied crack driving
energies studied. In this work, specimens are different than the
classical subcritical crack growth experiments in glasses. This is
because the entire adhesive bond is saturated and moisture is already
present at the crack tip and vicinity. Therefore, the rate limiting step
for crack growth, which produces Region II (the diffusion of moisture to
the crack tip), has been "turned off". This strongly suggests that the
mechanism for crack growth in these experiments is not dependent on
moisture diffusion, but rather also dependent on stress. Similar results
that showed diffusion was not the rate limiting step for subcritical
crack growth were obtained by Singh and Dillard who studied sub-critical
fracture of an epoxy bonded to glass in a fluid environment using the
DCB wedge test. \[46\] They tested two types of samples that controlled
the path of diffusion of liquid into the adhesive joint and therefore
the role of the fluid molecules on debond growth. One set of specimens
were saturated with fluid prior to applying the wedge and therefore the
mechanism for Region II crack propagation was turned off. The other set
of specimens were initially dry (0 % concentration of penetrant) and the
wedge was applied at the same time as the specimen was introduced to the
fluid environment. They observed identical *v*-*G* curves between the
two types of samples, which suggests that the diffusion of fluid to the
crack tip is not the rate limiting step for debond growth. This supports
the argument that the mechanism for crack growth in our work is a
stress-dependent phenomenon, and not diffusion controlled, indicating
that our present results fall in Region I of the *v-G* diagram.

This work has shown that the SLBT has a number of advantages over other
adhesive coating test methods (1) it is an open face coating that
reaches saturation rapidly, (2) axisymmetric, (3) simple sample
preparation, (4) easily measured debond growth, (5) self loading
samples, (6) insensitivity to plastic deformation and creep away from
the crack tip, and (7) measuring adhesion to thin brittle substrates is
possible. A few limitations to the SLBT exist which are common to other
peel type test geometries. The most prominently when the adhesive
interface is strong and the film is thin, the adhesive can experience
large stresses, leading to film rupture. Also, a concern is delamination
of the backing from the adhesive rather than delamination at the
adhesive-substrate interface. Much higher strain energy release rates
can be achieved with more conventional beam type specimens, but one may
encounter other problems such as sample preparation or crack measurement
issues. A possible method to increase the available strain energy
release rate in the SLBT is to use a thicker backing that will adhere
strongly to the adhesive even in a moist environment and be able to
support higher loads without creep. Under these conditions, the adhesive
may behave less like a stretching membrane and more like a bending plate
and a different expression for the strain energy release rate is
applicable. \[24\]

This work convincingly shows that the subcritical SLBT is an excellent
method for testing the durability of adhesive coatings. In addition to
studying the effect of water vapor, the effects of temperature, various
chemical and mechanical stresses (continuous and cyclic), corrosion, and
ultraviolet radiation exposure can be investigated with the SLBT. Any
changes in the mechanical properties of the adhesive and backing due to
exposure to aggressive conditions must be considered. However, changes
at the crack front and in the adhered coating must be accounted for
only. This is due to the same reason creep in the film is not
considered. Caution must be taken if the test temperature of the
adhesive is close to its glass transition or if the yield stress is
sufficiently low that plastic deformation and viscoelasticity at the
crack front is possible. In the case where the SLBT specimen is exposed
to moisture and chemicals, the adhesive may be significantly plasticized
or swollen such that there is no longer linear elastic behavior at the
crack front. Therefore many types of glassy adhesives can be tested
within the assumptions of the model. For soft materials like pressure
sensitive adhesives and rubbers, cavitation and finger-like
instabilities caused by confinement of the adhesive between the backing
and substrate can complicate the analysis.

### Conclusions

The SLBT was demonstrated to be a simple and informative method for
characterizing the degradation of adhesive bonds accelerated by
environmental moisture, without the need for sophisticated crack length
measurements. Notably, the SLBT was modified for sub-critical fracture
testing by applying a self-loading mechanism whereby a mass is suspended
from the center of the inverted blister. Our results illustrate the
benefits and shortcomings of the SLBT, suggesting that this test method
is advantageous for testing thin adhesive coatings which often rupture
under high stresses imposed by more conventional test methods.
Furthermore, the low applied stresses enables testing of adhesives
bonded to fragile, brittle silicon wafers. This study has also provided
an additional example of a critical relative humidity for adhesion loss
which has been previously observed in many epoxy systems.

## Acknowledgements

The authors would like to gratefully acknowledge the financial support
of the Center for Adhesive and Sealant Science at Virginia Tech, the
Adhesive and Sealant Council, and the Hewlett-Packard Company
(Corvallis, OR). The authors thank David A. Dillard and Kai-Tak Wan for
their valuable ideas and discussions. Donation of the epoxy resin by the
Shell Corporation (Houston, TX) is appreciated. The authors also
acknowledge Aaron Forster, Amanda Forster, and Bryan Vogt for their
input on this manuscript. Emmett O'Brien thanks Tom Seery, Christopher
White, and Jonathan Martin for funding during the preparation of this
manuscript. The authors thank the late Francis VanDamme for fabricating
the quartz substrates.

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Accepted for Publication in *The Journal of Adhesion*, 2005

**Influence of** **Experimental** **Set-up and** **Plastic**
**Deformation on the** **Shaft-loaded** **Blister**
**Test**[]{#__RefHeading___Toc97685945 .anchor}

Emmett P. O'Brien†‡\*, Stephanie Goldfarb⊥, Christopher C. White†

†National Institute of Standards and Technology

Buildings and Fire Research Laboratory

Gaithersburg, MD 20899

‡University of Connecticut

Institute of Materials Science

Storrs, CT 06269

⊥Cornell University

Department of Mechanical Engineering

Ithaca, NY 14850

\*author of correspondence, E-Mail: emmett.obrien@nist.gov

**Key words**: pressure sensitive adhesive tapes, coatings, fracture,
yielding, thin film, membrane, bending plate, bulge test, point load,
sphere, contact radius

**Abstract**

In the shaft-loaded blister test (SLBT), plastic deformation often
occurs at the contact area between the shaft-tip and adhesive layer,
leading to a larger displacement (blister height) than if the film was
loaded elastically. As a consequence, incorporating the displacement
variable into the analysis can result in misleading values of the
applied strain energy release rate, G. In this work, the influence of
plastic yielding at the contact area on G of a thin film was
investigated as a function of some common SLBT experimental variables,
namely, substrate hole diameter, film thickness, and shaft tip diameter.
Test specimens consisted of plies of pressure sensitive adhesive tape
adhered to a rigid glass substrate. G was calculated from the following
equations: (1) load-based, (2) hybrid, (3) displacement-based, and (4)
combination. Decreasing the film thickness, increasing the hole
diameter, or decreasing the shaft-tip diameter lead to more plastic
yielding at the contact area as well as to an increase in blister
height. The increased blister height due to plastic deformation lead to
disagreement among the values of G calculated from the different
equations when the displacement variable was included in the
calculation. However, the load-based equation, which does not include
the displacement, was determined to be independent of plastic yielding
and the "correct" equation for calculating G. In addition, the film
tensile rigidity (*Eh*) was calculated using an experimental compliance
calibration. The effects of film thickness on the mechanical behavior of
the film (bending plate vs. stretching membrane) as well as methods to
determine the displacement due to plastic deformation are also
discussed.

**Introduction**

Plastic deformation complicates testing adhesive joints and coatings by
invalidating the assumptions of linear elasticity, causing adhesive
rupture due to large applied forces and creating creep in long term
experiments. Coatings are particularly susceptible to plastic
deformation or yielding due to the large stresses generated in the film
during testing which is a consequence of the small cross-sectional area
(thinness) and strong adhesion \[1\]. Recently the shaft-loaded blister
test (SLBT) has been developed to measure the adhesion \[2-9\] as well
as the mechanical properties of thin films and coatings \[2, 6, 10-15\].
In this experiment, a spherically-capped shaft applies a central load to
a film which results in a deflection and delamination (Figure 1). These
blister test geometry experiments and analysis have also recently been
adopted for measuring the mechanical response of films using a flat
punch in a variety of applications \[13, 16-21\]. The strain energy
release rate, G, can be calculated from the following expressions that
were derived using linear elasticity \[6\]:

$G = \left( \frac{1}{\text{16}\pi^{4}\text{Eh}} \right)^{13}\left( \frac{P}{a} \right)^{43}$
load-based equation (1)

$G = \frac{1}{\pi^{2}\text{Eh}}\left( \frac{P}{w} \right)^{2}$ hybrid
equation (2)

$G = \frac{\text{Eh}}{\text{16}}\left( \frac{w}{a} \right)^{4}$
displacement-based equation (3)

Where *P* is the applied load, *a* is the debond radius, *w* is the
displacement or blister height, *E* is Young's modulus of the adhesive
film, and *h* is the film thickness. The value of G calculated from
equation 1 depends strongly on the load and the value of G calculated
from equation 3 depends strongly on the displacement. Equation 2 is a
combination of equation 1 and 3. Therefore equations 1, 2, and 3 are
referred to as the load-based, hybrid, and displacement-based equations,
respectively. Combining any two of equations 1, 2, or 3 reveals a fourth
equation, denoted as the combination equation, which is identical to
that derived by Williams \[22\] and Jensen \[23\] and does not
incorporate the stiffness (*Eh*) of the film:

$G = \frac{1}{4\pi}\frac{\text{Pw}}{a^{2}}$ combination equation (4)

The linear elastic equations for a stretching membrane predict the
following constitutive relation \[6, 10\]:

$\text{Pa}^{2} = \left( \frac{\pi\text{Eh}}{4} \right)w^{3}$ (5)

where collectively *Eh* is known as the film tensile rigidity, which
defines the film stiffness. The value of *Eh* of the adhesive layer can
be calculated from a compliance calibration where a graph of *Pa*^2^ as
a function of *w*^3^ yields a slope equal to (*πEh*) / 4.

Previous work on the SLBT has shown that significant plastic deformation
inevitably occurs at the contact area between the shaft-tip and the
adhesive film (Figure 2) \[2, 6, 9, 10\]. As

Figure 1. Schematic of the shaft-loaded blister test. *P* is the load,
*w* is the displacement or blister height, *a* is the blister radius,
*R* is the radius of the shaft-tip, and *θ* is the half angle subtended
from the shaft-tip.

![](media/image40.png){width="6.25in" height="3.5729166666666665in"}

a consequence, the blister height or displacement is overestimated
(relative to the elastic model), leading to disagreement among the
values of G if the displacement value is incorporated into the
calculation (equations 2, 3, and 4). Wan and Mai derived expressions to
calculate G that account for plastic deformation at the contact area
\[6\]. However, this increased complexity was found to be unnecessary if
G was calculated from the load-based equation, which does not
incorporate the displacement value and is believed to be independent of
plastic deformation at the contact area \[2\]. For clarity and
convenience we discuss why the load-based equation is believed to be
independent of plastic deformation. More details can be found in the
work by O'Brien *et. al.* \[2\]. In that work, G was measured for
stacked layers of PSAT adhered to aluminum. It was argued that if
plastic deformation is confined to the area of the shaft-tip, and linear
elasticity is valid at the crack front (i.e. the yield stress in the
peel arm was not exceeded), then it can be assumed that the load and
blister radius are in equilibrium. As a consequence, the assumption of
linear elasticity and the application of the load-based equation are
valid. Therefore the value of G calculated from load-based equation is
"correct" despite the presence of plastic deformation at the contact
area. The arguments are supported by consistency of the values of G
calculated from the load-based equation for the different stacked layers
of PSAT. The work presented in this paper further supports the argument.

As just mentioned, if the stress at the crack front is greater than the
yield stress of the film or if the size of the plastic zone at the crack
tip is greater than or equal to the film thickness, the linear elastic
expressions for G are inapplicable. Equation 6 can be used to calculate
the effective membrane stress (for a point load configuration) and can
therefore be used to determine if elasticity at the crack front is a
good assumption \[6\]:

Figure 2. Schematic of the area of plastic deformation at the contact
area between the shaft-tip and the film. The *δ* symbol is the
penetration of the sphere into the film or displacement due to plastic
deformation.

![](media/image41.wmf){width="3.9153543307086616in"
height="1.5133858267716536in"}

*N*~eff~ = (G *Eh*)^1/2^ \[(log *a*/*r*)^2^ + 3/4\]^1/2^ (6)

where *r* is the radial distance from the center of the blister. If the
stress exceeds the product of the yield stress, *σ*~y~, and the film
thickness, *h*, then yielding can occur (*N*~Max~ ≥ *σ*~y~ *h*).
Additional, but more complex, equations for the membrane stress can be
found in the work of Wan and Liao \[10\].

The shaft-tip diameter defines the contact area and thus the stress in
the film. Wan and Liao found that the maximum membrane stress, *N*~Max~,
can be expressed as \[10\]:

$N_{\text{Max}} = \frac{P}{2\pi R\text{sin}^{2}\theta}$ (7)

where *R* is the radius of the shaft-tip, and *θ* is the half angle that
extends from the contact area to the center of the shaft-tip (Figure 1).
As a result, a smaller shaft-tip diameter or a thinner film is expected
to result in more plastic deformation and to overestimate displacement.

In this work, the influence of plastic deformation at the contact area
on the SLBT is explored by varying the substrate hole diameter, film
thickness, and shaft tip diameter. The substrate hole diameter is a test
parameter chosen by the experimenter and deserves exploration, despite
the fact that for linear elastic conditions the size of the initial
debond should not matter. More specifically, the applied load, *P*,
debond radius, *a*, displacement or blister height, *w*, are measured
and used to calculate G using four equations: (1) load-based, (2)
hybrid, (3) displacement-based and (4) combination. With the sole
exception of the load-based equation, each equation incorporates the
displacement value and is sensitive to the treatment of plastic
deformation. In addition, the film tensile rigidity (*Eh*) was
calculated using an experimental compliance calibration. The effects of
film thickness on the mechanical behavior of the film (bending plate vs.
stretching membrane) as well as methods to determine the displacement
due to plastic deformation are also discussed. Test specimens consisted
of pressure sensitive adhesive tape (PSAT), up to 3 layers thick,
adhered to a rigid glass surface.

**Experimental**[^6]

The adhesive tested in this work was Kapton pressure sensitive adhesive
tape (PSAT), consisting of a silicon based thermosetting adhesive of
thickness 38.1 μm (1.5 mil) covered by a Kapton backing of thickness
25.4 μm (1 mil). The soda lime glass substrate was 9.6 mm thick and was
cleaned with acetone prior to each application of the tape. Three
different hole diameters were investigated: (6.7, 9.8, and 12.9) mm,
denoted as small, medium and large, respectively. To vary the thickness
of the film, *n* stacked plies of PSAT were used, up to *n* = 3. The
Young's modulus of the Kapton tape is roughly (3.1 ± 0.1) GPa. In the
calculation of the film stiffness, *Eh*, the stiffness of the backing
dominates and the soft adhesive layer was ignored. The bonded PSA
dimensions were (25.4 x 25.4) mm^2^.

Experiments were performed on a UTM, which measured displacement and
load, at a cross-head displacement rate of 0.1 mm/s. Steel ball-bearings
were used as the shaft-tip and were fastened to a steel shaft with a
2-part epoxy. The shaft was attached to a 100 kg load cell via a
modified drill chuck. Three different shaft-tip diameters were
investigated denoted as small, medium, and large: (3.2, 6.4, and 9.5)
mm, respectively. During the experiment the image of the propagating
blister debond was measured using a digital video camera. Note that a
fine powder (or other non-stick layer) can be placed between the film
and shaft-tip to reduce adhesion at the contact area.

Uncertainty in the calculated value of G is introduced by the value of
the blister radius which is calculated from half the average of the
blister diameter in the *x* and *y* directions of the video image. The
value of the blister radius is affected by any non-symmetry of the
blister shape and the measurement from the video image. Asymmetry
between the *x* and *y* direction was generally small (0.1 mm to 0.2 mm)
and was likely caused by residual stress \[24\] and anisotropy in the
Kapton backing \[25\], and any heterogeneities in the intrinsic
interfacial adhesive toughness. The uncertainty in the value of G
attributable to the blister radius measurement depends on the magnitude
of the value of G and the equation. For the load-based equation and
values of G observed in this work ranging between (20 to 50) J/m^2^, the
uncertainty is ± (1 to 2) J/m^2^. For the displacement-based equation
and G values between (80 to 130) J/m^2^, the uncertainty is ± (10 -- 12)
J/m^2^. For the combination equation and G values between (35 to 45)
J/m^2^, the uncertainty is ± (1 -- 2) J/m^2^. For all experiments the
standard deviation due to the sample to sample variation is equal to or
more than the uncertainty introduced by the blister radius.

**Results and Discussion**

*Effects of Varied Substrate Hole Diameter Size on* *G*

The values of G as a function of the initial substrate hole size were
calculated for a single ply and the medium size ball bearing (6.4 mm
diameter). The average values for the data sets gathered from these
measurements are shown in Figure 3 (a -- d) (for clarity error bars are
not shown). From the slopes of these plots (a -- d) the value of G can
be calculated from the load-based, hybrid, displacement-based, and
combination equations, respectively. The average values of G and single
standard deviation are listed in Table 1. The average and standard
deviation are calculated from the values of G obtained from 8 samples.

Figure 3. Adhesion results for varied initial hole size: (a) load as a
function of blister radius, (b) load as a function of displacement, (c)
displacement as a function of blister radius, and (d) load-displacement
as a function of blister radius squared. Symbols are: small diameter
(×), medium diameter (▲), and large diameter (○).

![](media/image42.wmf){width="6.0in" height="3.9493055555555556in"}

**Table 1.** Applied strain energy release rate, G, (J/m^2^) determined
from the load-based, hybrid, displacement-based, and combination
equation as a function of the blister hole size. The mean ± one standard
deviation about the mean is shown.

  -------------- -------------- -------------- ---------------- ---------------
                 *load*         *hybrid*       *displacement*   *combination*

  *small*        32.3 ± 2.2     22.4 ± 1.4     85.0 ± 6.6       40.2 ± 2.0

  *medium*       30.8 ± 0.7     18.5 ± 3.0     94.4 ± 31.3      39.6 ± 3.5

  *large*        29.8 ± 4.3     15.6 ± 1.6     127.0 ± 30.8     42.6 ± 2.3
  -------------- -------------- -------------- ---------------- ---------------

Table 1 shows that the calculated value of G depends on which equation
was utilized. This observation is consistent with most shaft-loaded
blister test experiments and results, probably due to the always present
plastic yielding at the contact area \[2, 6, 9, 10\]. As discussed in
the experimental section, previous work has shown that for a Kapton PSAT
bonded to aluminum, that the load-based equation is not only independent
of plastic deformation at the contact zone but also agrees well with the
value of G obtained from the pull-off test \[2\]. Note that the
assumption of linear elasticity at the debond front is valid because the
effective membrane stress *N*~eff~ (equation 5) is well below the yield
stress of the backing. This suggests that the load-based equation
(equation 1) is the most "correct" and preferred of equations 2, 3, and
4. Table 1 shows that the value of G calculated from the hybrid equation
is smaller, and the values calculated from the displacement-based and
combination equation are larger, than the "correct" value of G
determined from the load-based equation. Under ideal linear elastic
conditions the value of G should be the same for every equation, but the
dependence of the calculated G on displacement determines the
sensitivity to the "overestimated" displacement (relative to the elastic
case). For instance, in the displacement-based equation because the
value of displacement is in the numerator and is raised to the fourth
power (G \~ *w*^4^), the G is much greater than the load-based equation
where displacement is not used in the calculation.

Although Figure 3 reveals substrate hole size has no significant
influence on the measured parameters (*P*, *w*, *a*) over the size range
studied; Table 1 shows the hole size can influence the calculated value
of G when the displacement is incorporated into the equation. As the
hole size increases, the calculated G decreases and increases for the
hybrid and displacement-based equations, respectively. This suggests
that as the substrate hole size increases, the displacement or blister
height increases, presumably due to an increase in plastic deformation
at the contact zone. The calculated value of G was not affected by hole
size when using the load-based equation which is expected given that the
independence on yielding at the contact zone. Calculations based on the
combination equation were also independent of hole size*.*

*Effects of Varied Shaft-Tip Diameter Size and Film Thickness on* *G*

Figures 4, 5, and 6 show, for *n* = 1, the effects of shaft-tip diameter
on the measured load, displacement and blister radius. Graphs of the
data sets for *n* = 2 and 3 are not shown, because the same trends were
observed as for *n* = 1. Figures 4 shows the load as a function of
blister radius for *n* = 1 for a variety of shaft-tip diameters. All
curves appear to overlap. The graph shows that the relationship between
the load and debond radius is unaffected by the shaft-tip diameter,
which supports the principle that the load-based equation is independent
of plastic deformation at the contact area. Figure 5 shows the
displacement as a function of blister radius for *n* = 1 and varied
shaft-tip diameters. The graph shows that as the shaft-tip diameter
decreases, displacement increases, presumably due to an increase in
plastic deformation at the contact zone. Figure 6 shows the load as a
function of displacement for *n* = 1 and varied shaft-tip diameter. This
graph shows the expected trend, that increasing the shaft-tip diameter
increases the applied loads for a given displacement \[10, 14\].

The effects of varying the film thickness are shown in Figures 7 and 8.
Figure 7 shows the load as a function of blister radius for different
values of *n* and for all shaft-tip diameters. Figure 8 shows the
displacement as a function of blister radius for different values of n
and the smallest shaft-tip diameter. Figures 7 and 8 illustrate that
increasing the film stiffness (*n*) increases the applied load, but
reduces the displacement and overall reduces plastic yielding. In this
case, the increase in load and reduced displacement is due to the
increase in available stored elastic energy. In addition, Figure 7 again
shows that the load-displacement curves are independent of the plastic
deformation at the contact area.

Figure 4. The load as a function of blister radius for *n* = 1 and
varied shaft-tip diameter. Symbols are: small diameter (\*), medium
diameter (▲), and large diameter (○).

![](media/image43.wmf){width="5.3381944444444445in"
height="3.558333333333333in"}

Figure 5. The displacement as a function of blister radius for *n* = 1
and varied shaft-tip diameter. Symbols are: small diameter (\*), medium
diameter (▲), and large diameter (○).

![](media/image44.wmf){width="5.354166666666667in"
height="3.5833333333333335in"}

Figures (4 -- 8) show that the relationship among *P*, *w*, and *a*
change as a function of the shaft-tip diameter and film thickness, but
the question remains whether G is also affected. Tables 2, 3, and 4 list
the calculated values of G as a function of film thickness and shaft-tip
diameter for *n* = 1, 2 and 3, respectively. The average and standard
deviation were calculated from 7 samples each. The expected trend was
observed in Table 2 for *n* = 1, where decreasing the shaft-tip

Figure 6. The load as a function of displacement for *n* = 1 and varied
shaft-tip diameter. Symbols are: small diameter (\*), medium diameter
(▲), and large diameter (○).

![](media/image45.wmf){width="5.34375in" height="3.5729166666666665in"}

Figure 7. The load as a function of blister radius for different values
of *n*. Data sets from all three shaft-tip sizes are shown. Lines are
drawn by hand to aid the eye.

![](media/image46.wmf){width="5.3625in" height="3.5791666666666666in"}

diameter increased the yielding at the contact area and affected
calculations of G that incorporated the displacement in the equation. As
seen in the study of the effect of the substrate hole size (Table 1),
the consistent trend was that values of G calculated from the hybrid,
displacement, and combination were lower, much greater, and greater,
respectively, relative to the "correct" load-based equation. The only
exception was for the *n* = 1 medium shaft-tip where the values of G
between the load-based equation and combination equation were equal.

Figure 8. The displacement as a function of blister radius for different
values of *n*. Data sets from the smallest shaft-tip size are shown.
Lines are drawn by hand to aid the eye.

![](media/image47.wmf){width="5.383333333333334in"
height="3.6034722222222224in"}

The effects of the shaft-tip diameter and yielding are most apparent for
the thinnest film (*n* = 1) (Table 2) and between the smallest and
largest shaft-tip size. As the shaft-tip diameter increased, the values
of G calculated from the load-based equation remain constant, while they
decreased for the hybrid equation, increased for the displacement-based
equation, and exhibited no trend for the combination equation. The size
of the shaft-tip diameter does not affect the values of G calculated
from the load-based equation. This supports the idea that the load-based
equation is independent of plastic deformation at the contact area and
is the most preferred expression to calculate G.

**Table 2.** Applied strain energy release rate, G, (J/m^2^) determined
from the load-based, hybrid, displacement-based, and combination
equation as a function of the shaft-tip diameter for *n* = 1. The mean ±
one standard deviation about the mean is shown.

  -------------- -------------- -------------- ---------------- ---------------
  *n = 1*        *load*         *hybrid*       *displacement*   *combination*

  *small*        34.1 ± 2.2     17.7 ± 2.0     123.4 ± 14.8     46.8 ± 7.4

  *medium*       34.1 ± 4.6     21.3 ± 2.5     83.5 ± 22.9      34.3 ± 3.8

  *large*        32.9 ± 3.7     25.0 ± 3.9     57.6 ± 3.9       40.4 ± 3.2
  -------------- -------------- -------------- ---------------- ---------------

For *n* = 2 and 3 (Tables 3 and 4), and similar to *n* = 1, the value of
G calculated from the load-based equation is not affected by the
shaft-tip diameter. However, increasing the film thickness reduces the
value of G calculated from the load-based equation, presumable due to an
increase in the bending moment and a reduction of plastic deformation of
the adhesive film. The peel test behaves similarly where stiffening of
the peel arm \[26\] (or an increase in tensile residual stress \[27\])
can cause a reduction in peel force. The values of G calculated from the
hybrid equation also decrease as the film thickness increases,
presumably due to an increase in bending moment. In fact the reduction
in displacement due to an increase in *n*, which would result in an
increase of the value calculated from the hybrid equation, is not enough
to overwhelm the effects of increased bending moment.

**Table 3**. Applied strain energy release rate, G, (J/m^2^) determined
from the load-based, hybrid, displacement-based, and combination
equation as a function of the shaft-tip diameter for *n* = 2. The mean ±
one standard deviation about the mean is shown.

  -------------- -------------- -------------- ---------------- ---------------
  *n = 2*        *load*         *hybrid*       *displacement*   *combination*

  *small*        28.3 ± 2.0     16.9 ± 5.1     92.2 ± 59.6      48.2 ± 11.2

  *medium*       25.2 ± 3.9     16.7 ± 4.3     56.4 ± 10.8      38.3 ± 5.0

  *large*        25.5 ± 5.1     17.3 ± 3.4     59.8 ± 11.4      36.8 ± 3.1
  -------------- -------------- -------------- ---------------- ---------------

**Table 4**. Applied strain energy release rate, G, (J/m^2^) determined
from the load-based, hybrid, displacement-based, and combination
equation as a function of the shaft-tip diameter for *n* = 3. The mean ±
one standard deviation about the mean is shown.

  -------------- -------------- -------------- ---------------- ---------------
  *n = 3*        *load*         *hybrid*       *displacement*   *combination*

  *small*        24.3 ± 5.9     11.7 ± 2.7     94.7 ± 43.7      42.2 ± 19.2

  *medium*       22.8 ± 5.0     13.8 ± 4.7     56.5 ± 8.8       35.2 ± 9.8

  *large*        22.0 ± 3.7     13.1 ± 3.8     56.7 ± 12.3      35.7 ± 3.1
  -------------- -------------- -------------- ---------------- ---------------

For the hybrid and displacement equations, the influence of the
shaft-tip diameter for *n* = 2 and 3 is not as significant as for *n*
= 1. For the smallest shaft-tip diameter and *n* = 2 and 3 the average
and standard deviation of G calculated from the displacement and
combination equation is significantly greater than in any other
condition. This is due to the smallest diameter imparting the most
plastic deformation and the dependence of the displacement equation on
the value of *w* to the fourth power. The increase in plastic
deformation has been is has observed graphically (Figure 5), where
reducing the diameter of the shaft-tip leads to larger values of
displacement. Also, the smallest shaft-tip diameter leaves the deepest
dimple in the center of the blister, indicating plastic deformation.
Note that the size of the dimple is reduced as the film thickness
increases. Furthermore, the difference in both the values of G and the
graphs is much greater between the small diameter and either the medium
or large diameter than the difference between the medium and large
diameter. The influence of the small diameter shaft-tip on the value of
G calculated from the combination equation suggests that the
load-equation is more preferable than the combination equation.

Varying the shaft-tip diameter and film thickness caused different
amounts of plastic deformation which was evident from the differences in
*w* seen graphically (Figures 5 and 8). However, differences among the
values of G due to yielding are small with the exceptions of *n* = 1
(all sizes) and the smallest shaft-tip size for *n* = 2 and 3. Therefore
we have observed that plastic deformation can influence the calculated
value of G in cases where the film is thin or the bearing is small. The
yield stress, plastic deformation, film thickness, or the size of the
shaft-tip can be increased to reduce the undesirable effects. However,
we see that for *n* = 1 and a large bearing, the effects of plastic
deformation are not reduced sufficiently to result in all four
expressions of G to agree.

*Calculation of the Film Tensile Rigidity (Eh)*

The film stiffness of film tensile rigidity (*Eh*) was calculated using
an experimental compliance calibration and equation 5. These results
were compared to the film tensile rigidity calculated from the Young's
modulus determined from stress-strain experiment in a UTM. Ideally, if
linear elasticity holds and equations 1 to 5 are correct, then the
values of *Eh* determined from the UTM and the compliance calibration
should agree. The results for the varied substrate hole size are listed
in Table 5. Table 6 lists the calculated values for the varied film
thickness and shaft-tip diameter. The values calculated from the
stress-strain experiment are 77,500 N/m, 154,900 N/m, and 309,800 N/m
for *n* = 1, 2, and 3, respectively.

**Table 5**. The film tensile rigidity, *Eh*, (N/m) calculated from an
experimental compliance calibration and equation 5. This data set is for
*n* = 1 and varied substrate hole diameters (*small*, *medium*, and
*large*). The value calculated from the stress-strain experiment for a
single ply is 77,500 N/m. The mean ± one standard deviation about the
mean is shown.

  ----------------- ----------------- ----------------- -----------------
                    *small*           *medium*          *large*

  *N* = 1           54,000 ± 5000     48,000 ± 4000     41,000 ± 3000
  ----------------- ----------------- ----------------- -----------------

**Table 6**. The film tensile rigidity, *Eh*, (N/m) calculated from an
experimental compliance calibration and equation 5. This data set is for
*n* = 1, 2, and 3 and the varied shaft-tip diameter (*small*, *medium*,
and *large*). The values calculated from the stress-strain experiment
and UTM are 77,500 N/m, 154,900 N/m, and 309,800 N/m for *n* = 1, 2, and
3, respectively. The mean ± one standard deviation about the mean is
shown.

Note that the values of *Eh* determined from the UTM and the compliance
calibration showed the best agreement for experiments that utilized the
largest shaft-tip.

  ----------------- ----------------- ----------------- -----------------
                    *small*           *medium*          *large*

  *n* = 1           45,000 ± 9000     58,000 ± 8000     83,000 ± 9000

  *n* = 2           96,000 ± 31,000   139,000 ± 32,000  169,000 ± 47,000

  *n* = 3           155,000 ± 25,000  164,000 ± 98,000  242,000 ± 28,000
  ----------------- ----------------- ----------------- -----------------

Examination of Table 5 shows that the calculated film tensile rigidity
did not depend on the size of the substrate hole diameter. This was not
unexpected given the similarity of the curves shown in Figure 3.
However, the calculated film tensile rigidity depended strongly on the
size of the shaft-tip diameter (Table 6). The results also show that the
values of *Eh* determined from the UTM and the compliance calibration
agreed best for experiments that utilized the largest shaft-tip. This is
presumable due to the reduction in both plastic deformation and the
value of displacement. In addition, disagreement between the two methods
may also be due to the multilayer structure of stacked layers of glassy
backing and soft adhesive as well as any anisotropy in the PSAT backing
. See Li *et*. *al*. 2004 for a rigorous treatment of the debonding of
layered structures \[28\].

Begley and Mackin noted that using a point-load solution to measure the
mechanical properties of thin films in a shaft-loaded blister test
geometry resulted in errors and derived analytical expressions to
account for the spherical loading \[14\]. Wan and Liao also derived
expressions to determine the mechanical properties of thin films using
the shaft-loaded blister test geometry and predicted that increasing the
size of the shaft-tip diameter will change the constitutive equation 5
by a factor Ω~1~ \[10\]:

$\text{Pa}^{2} = \left( \frac{\pi\text{Eh}}{4} \right)\Omega_{1}w^{3}$
(8)

where Ω~1~ is a parameter that depends on shaft-tip radius, *R*, contact
radius, *c*, and angle, *θ* (Figure 1). Therefore, it is expected that
plasticity at the shaft-tip should result in decreasing the calculated
film tensile rigidity. This was observed in this work; however, the
decrease in the value of *Eh* was most likely due to plastic deformation
and not solely due to the spherical contact area.

Previous research showed improved agreement among the values of G
calculated from equations 1, 2, and 3 when the value of *Eh* determined
from the compliance calibration was utilized in the calculation \[2\].
This was likely due to the plastic deformation at the contact area and
not because the value of *Eh* determined from the compliance calibration
more closely reflects the mechanical behavior of the film under loading
conditions encountered in shaft-loaded blister test geometry. The
dependence of the value of *Eh* on the shaft-tip diameter, and therefore
the amount of plastic deformation, supports this conclusion.

*Methods to Calculate of the Contact Radius*

There are several methods to calculate the contact radius, *c*, and the
penetration of the sphere into the film, *δ*, at the shaft-tip (Figure
2). The contact radius is related to *δ* by equation 9 \[29\].

> $\delta = c^{2}R$ (9)

In the work of Wan and Liao the contact radius can be calculated from
the following linear elastic expression \[10\]:

> $c = \left\lbrack \frac{3R^{3}P(1 - v)}{\pi\text{Eh}} \right\rbrack^{\frac{1}{4}}$
> (10)

where *v* is Poisson's ratio. This expression assumes a small uniform
membrane strain.

Begley and Mackin derived an approximate closed form solution for the
contact radius that incorporates the effects of residual stress \[14\]:

> $c = \sqrt{\sqrt{\left( \frac{3}{2\pi} \right)\left( \frac{P}{\text{EhR}} + 6\text{πε}_{0} \right)} - 3\varepsilon_{0}}$
> (11)

where *ε*~0~ is the pre-strain in the film attributable to residual
stress.

Wan and Mai developed an expression for the yielding radius, *a*~p~,
that accounted for plastic deformation at the contact area which can be
used to estimate the contact radius (*a*~p~ ≈ c) \[6\]:

> $a_{p} \approx a \cdot \text{exp}\left\lbrack - \left( \alpha \cdot a^{\frac{4}{3}} - \frac{3}{4} \right)^{\frac{1}{2}} \right\rbrack$
> (12)

where

> $\alpha = \left( \frac{4\pi^{2}\sigma_{p}^{3}h^{2}}{P^{2}E} \right)^{\frac{2}{3}}$
> (13)

and *σ*~p~ is the yield stress of the film determined from a
stress-strain experiment.

The actual value of the penetration depth and displacement due to
plastic deformation are unknown; however, the magnitude was estimated to
be about 1mm from examination of Figures 5 and 8. None of the models
discussed previously predict the correct magnitude of the contact radius
and penetration depth. This is not unexpected given that models assume
elastic deformations (except the model of Wan and Mai). However, the
disagreement between the experimental and the model of Wan and Mai is
likely also due to the how plasticity is modeled. Unlike linear
elasticity, the solutions that incorporate plasticity are not unique.
Plastic yielding behavior among polymers can be very different; it may
be rate dependent, time dependent, stress hardening, stress softening
and small variations in behavior can lead to large differences
especially at high strains. Therefore, plasticity models are highly
specific and it is not unexpected that the models may not match the
experimental data; however, there may be many other systems that do
match the model. This suggests that rather than using these models to
predict the contact radius, it is best to actually measure the plastic
contribution to the blister height. The plastic deformation at the
contact area can be measured by loading and unloading the specimen. Just
as in a stress-strain experiment the degree of plastic deformation can
be deduced from the difference between the loading-unloading curves for
successive loadings of the same specimen. For this PSAT, the
loading-unloading process is complicated because the PSAT will reattach
upon regaining contact with the substrate. In adhesive systems where the
adhesive will not re-adhere, like glassy structural adhesives, this
approach is possible. However, measuring the amount of plastic
deformation may not be necessary if one is only interested in the
measuring G and utilizes the load-based equation.

*Effect of Film Thickness and Shaft-Tip Diameter on the Mechanical
Behavior (Stretching Membrane vs. Bending Plate)*

In a peel test geometry the adhesive layer can behave either like a
bending plate, a stretching membrane, or a combination of the two.
Whether the film behaves like plate or membrane determines which linear
elastic equations should be utilized to model the mechanical properties
and delamination of the adhesive. If the load is small or if the film is
thick or stiff, then bending behavior dominates. If the load is large or
if the film is thin or compliant, then stretching behavior dominates
\[14\]. As a consequence there is a predicted bending to stretching
transition when the load is first applied during contact with the shaft,
up to when the debond initiates.

There are several methods to determine mechanical behavior of the film.
A simple method is to plot the logarithmic load as a function of the
logarithmic displacement (*P* ∝ *w^γ^*) during the initial loading of
the film prior to debond initiation. The value of the slope, *γ*,
indicates the mechanical behavior, where *γ* = 1 is characteristic of a
bending plate and a value of *γ* = 3 is characteristic of a stretching
membrane \[10\].

In addition, Wan and Liao derived the expressions to determine the
normalized membrane stress, *β* = (*N* *a*^2^ / *D*)^1/2^, which
indicates the ratio of stretching stress to bending rigidity \[10\]. *N*
is the film stress and *D* is the flexural rigidity. A small value of
*β* (less than 0.1) indicates a pure bending plate and a large *β*
(greater than 20) indicates a stretching membrane.

A similar dimensionless parameter was derived by Komaragiri *et. al.* to
determine if bending can or can not be ignored (for both pressure
loading and point loading) \[15\]:

$\lambda = \left\lbrack \text{12} \cdot (1 - v^{2}) \right\rbrack^{\frac{3}{2}}\left( \frac{\text{Pa}^{2}}{\text{Eh}^{4}} \right)$
(14)

The value of *λ* determines if the film behaves more like a bending
plate or stretching membrane.

The values of the slope, *γ*, of the log load as a function of log
displacement are listed in Tables 7 for the varied substrate hole size.
Table 8 lists the values of *γ* for the varied shaft-tip diameter and
film thickness. Tables 7 and 8 show that for this adhesive the measured
value of *γ* does not depend on the substrate hole size, shaft-tip
diameter and film thickness. This is unexpected given that Wan and Liao
showed analytically and experimentally that increasing the shaft-tip
diameter results in a larger gradient, *γ* \[10\]. However, this work
agrees with the research of Begley and Martin \[14\] which showed
analytically and experimentally that for both a point load and spherical
load of a stretching membrane that it is expected that *P* ∝ *w*^3^.
However, the scatter in the data suggests that UTM, which measures the
load and displacement, may be insensitive to the effects of substrate
hole diameter, shaft-tip diameter and film thickness. The values of *γ*
listed in Tables 7 and 8 is roughly 2.3 ± 0.3 for all test conditions,
which suggests that the film behaves more like a stretching membrane
than a bending plate. The stretching film behavior of this adhesive is
supported by calculations using the methods of Wan and Liao and
Komaragiri *et*. *al*.

**Table 7**. The slope, *γ* , of the log load -- log displacement curve
(*P* ∝ *w^γ^*). This data set is for *n* = 1, and the varied substrate
hole diameter (*small*, *medium*, and *large*). For a pure bending
plate, *γ* = 1, and for a stretching membrane, *γ* = 3. The mean ± one
standard deviation about the mean is shown.

  ----------------- ----------------- ----------------- -----------------
                    *small*           *medium*          *large*

  *n* = 1           2.3 ± 0.3         2.3 ± 0.4         2.4 ± 0.4
  ----------------- ----------------- ----------------- -----------------

**Table 8**. The slope, *γ* , of the log load -- log displacement curve
(*P* ∝ *w^γ^*). This data set is for *n* = 1, 2, and 3 and varied
shaft-tip diameter (*small*, *medium*, and *large*). For a pure bending
plate, *γ* = 1, and for a stretching membrane, *γ* = 3. The mean ± one
standard deviation about the mean is shown.

  ----------------- ----------------- ----------------- -----------------
                    *small*           *medium*          *large*

  *N* = 1           2.2 ± 0.3         2.7 ± 0.4         2.3 ± 0.2

  *N* = 2           2.3 ± 0.3         2.2 ± 0.3         2.3 ± 0.3

  *N* = 3           2.3 ± 0.4         2.4 ± 0.4         2.1 ± 0.2
  ----------------- ----------------- ----------------- -----------------

*Effect of Applying Bending Plate Equations to Calculate* G

It is of interest to compare values of G determined for a bending plate
model to the stretching membrane model we have used previously
(equations 1 to 4). Note that we have shown previously that the adhesive
film behaves more like a stretching membrane (*γ* = 2.3 ± 0.3). Malychev
and Salganik derived the load-based, combination and displacement-based
equations for a bending plate \[30\].

$G = \frac{3(1 - v^{2})}{8\pi^{2}\text{Eh}^{3}}P^{2}$ load-based
equation (15)

$G = \frac{\text{Pw}}{2{\pi a}^{2}}$ combination equation (16)

$G = \frac{2\text{Eh}^{3}}{3(1 - v^{2})}\frac{w^{2}}{a^{4}}$
displacement-based equation (17)

The combination equation (eq 16) is identical to that derived by Wan
\[11\] and Williams \[22\]. For a bending plate, equations 15 to 17 will
be most applicable when the displacement in less than the film thickness
\[31\]. Furthermore, for a bending plate, the load is predicted to be
constant during delamination. In these experimental results, the
displacement is much greater than the film thickness and the load is not
constant. Therefore, the membrane equations are more appropriate for the
adhesive system investigated in this work.

The strain energy release rate calculated from equation 16 varies by as
much as five orders of magnitude from the load-based stretching membrane
equation (eq. 1). Note that this difference is significantly reduced as
the film thickness increases. The combination equation derived for a
bending plate (eq. 16), which does not incorporate the mechanical
properties of the film, differs by a factor of 2 from the membrane
solution of the combination equation (eq. 4). Therefore, the bending
plate equation yields a value of G twice as much as the membrane
solution. The displacement-based equation for the bending plate is also
very sensitive to the film thickness. For *n* = 1 the difference between
the bending plate and stretching membrane case was less than a factor of
two; however, increasing the film thickness increased the difference by
as much as four orders of magnitude.

*Effect of Shaft-Tip Diameter and Film Thickness on Scaling of Equations
1 to 4*

If equations 1 to 4 have been derived correctly and the test specimens
behaved linear elastically, then the data plotted in Figures 3 to 8
should be linear and should interpolate back to the origin (*P* = 0, *w*
= 0 and *a* = 0). Examination of Figures 3 to 8 reveals three trends.
First, graphs of the load as a function of blister radius interpolate
through the origin which suggest linear elasticity occurs and supports
the idea that the load-based equation is independent of the plastic
deformation at the contact area. The second trend is that reducing the
shaft-tip diameter causes the graphs to interpolate more closely through
the origin. This supports the reasoning that the offset between the
interpolated line and origin is due to the finite width of the
shaft-tip, which was suggested by Wan and Mai (Wan and Mai 1995).
Lastly, as the film thickness was increased, the interpolated line
tended to pass further from away from the origin.

*Practical Implications for the Shaft-Loaded Blister Test*

This work has practical implications for the design of a SLBT
experiment. Wan and Liao proposed that to reduce plastic deformation at
the contact area, the radius of the shaft-tip should greater than or
equal to \[10\]:

$R \geq \frac{9P}{2{\pi h\sigma}_{y}}$ (18)

where *σ*~y~ is the yield stress of the adhesive film. In other words,
one should increase the shaft-tip diameter, reduce the applied load and
increase the thickness to reduce the stress and possibility of yielding
in the adhesive film. This work has shown that plastic deformation can
be reduced by increasing the shaft-tip diameter, despite the expected
increase in load. This work has also shown that the size of the
shaft-tip does not affect the load-based equation and so the size of the
shaft-tip seems to be unimportant; however, the chance for film rupture
can be reduced if a larger shaft-tip is utilized and enables the
application of greater loads per given displacements and therefore
greater strain energy release rates. Begley also notes that the greater
applied loads facilitated by a larger shaft-tip diameter provide better
load resolution, which has practical implications for applying atomic
force microscopy to adhesion studies and measuring the mechanical
properties of thin films \[14\]. By reducing the stress in the film, a
thinner film can be utilized, which will more closely follow the
assumption of a thin stretching membrane used to derive the expressions
of G. Furthermore, a larger bearing that fits snuggly into the initial
blister hole enables the shaft-tip and blister to be easily centered and
can help to reduce sample to sample scatter.

Plastic deformation may also be influenced by the cross-head
displacement rate, which affects the strain rate and therefore the yield
stress and yield strain in the adhesive layer. Although no experiments
have been performed to investigate the effect of displacement rate on
plastic deformation at the contact area, effects similar to those
presented in this work could be expected. However, for this PSAT,
increasing the test rate results in larger values of G due to increase
in the debond velocity and viscoelastic effects in the soft pressure
sensitive adhesive layer. Therefore, deconvolution of the effects of
plastic deformation and debond velocity on G could prove difficult.

**Conclusions**

The influence of the film thickness, substrate hole diameter and
shaft-tip diameter on plastic deformation at the contact area and
blister height were measured. Increasing the hole size slightly
increased the amount of plastic deformation, which was evident from the
changes in G, but did not significantly affect the measured *P*, *w* or
*a*. Increasing the film thickness (*n*) increased the applied load and
decreased the displacement. Decreasing the shaft-tip diameter increased
the displacement or blister height due to plastic deformation at the
contact area. The presence of both effects suggests that there are
differences in the amount of plastic deformation among the different
test conditions. Differences in the calculated values of G were observed
when the displacement was incorporated into the calculation. Relative to
the "correct" load-based equation, differences among the equations for G
can be reduced using a large shaft-tip diameter. The value of G
calculated from the load-based equation decreased slightly as the film
thickness increased. This is a trend typically observed in many other
adhesive tests. The film tensile rigidity, *Eh*, calculated from the
experimental compliance calibration agreed best with values determined
from a tensile test of the film when the largest shaft-tip diameter was
used. The contact radius and displacement due to plastic deformation
should be determined experimentally; however, it may be unnecessary if
the load-based equation is utilized. Methods to determine if the film
behaves like a bending plate or stretching membrane were discussed.
Using these techniques it was found that the film behaves mostly like a
thin stretching membrane. The values of G were significantly different
depending on whether the equations for a bending plate or stretching
membrane were used.

**Acknowledgements**

Financial support for Stephanie Goldfarb was provided by the National
Science Foundation through the Summer Undergraduate Research Fellowship
(SURF) program at NIST. The authors thank their colleagues at the
National Institute of Standards and Technology: Jason Garver and Ned
Embree for their mechanical expertise and Xiaohong Gu, Amanda Forster,
Aaron Forster, Peter Drzal, Jon Martin, and Bryan Vogt for providing
helpful comments. We also appreciate the help of the editor and the
comments by the referees.

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A communication submitted to the *International Journal of Adhesion and
Adhesives*

**Comparison** **of Subcritical Adhesion Test Methods: The**
**Shaft-loaded** **Blister** **Test vs. the** **Wedge**
**Test**[]{#__RefHeading___Toc97685946 .anchor}

Emmett P. O'Brien^A,B^ and Christopher C. White^A^

^A^National Institute of Standards and Technology, Buildings and Fire
Research Laboratory

Gaithersburg, MD, USA

^B^Institute of Materials Science, University of Connecticut, Storrs, CT
USA

To whom correspondence should be addressed: Email:
emmett.obrien@nist.gov

**Abstract**

Subcritical adhesion testing is of practical interest to engineers and
scientists because it enables the study of the mechanisms underlying
adhesive failure while closely simulating failure mechanisms and time
scales occurring during service. Furthermore, the results from these
types of experiments provide engineers with parameters for designing
adhesive joints and coatings. Traditionally, subcritical fracture test
specimens have been triple-layered laminated beams, where the adhesive
is bonded between two rectangular rigid adherends. An example of this
type of test specimen is the well known double cantilever beam wedge
(DCB) test. Recently, the shaft-loaded blister test (SLBT) was shown to
be an alternative method for subcritical adhesion testing of adhesive
coatings (O'Brien et. al. *J. of Adhesion* 2005). In this work, the pros
and cons of the SLBT and DCB tests for Subcritical adhesive fracture
testing are discussed. As an example, we investigate the effects of
moisture on the crack growth between an epoxy and a glass substrate.

**1 Introduction**

Subcritical adhesion testing or stress corrosion cracking explores
adhesive debonding in a range of crack velocities and applied strain
energy release rates (SERR), *G*, that are significantly less than are
observed from catastrophic failure. As a consequence, subcritical
adhesion testing can closely simulate the failure occurring in the
real-life application or service life of the adhesive. Information about
the mechanism of failure is gathered from a log-log plot of the average
debond velocity, *v*, as a function of *G*. A change in the slope is
indicative of a change in the rate limiting step for crack advancement
and includes such behavior as threshold behavior, stress-dependent
chemical reaction or reaction-limited, and transport limited mechanism
for debond advancement \[1-3\].

Traditionally, subcritical fracture test specimens have been
triple-layered laminated beams, where the adhesive is bonded between two
rectangular rigid adherends. Examples of the laminated beam type
experiments are the DCB wedge test \[4, 5\], the asymmetric double
cantilever beam test \[6\], the double cleavage drilled compression
specimen \[7, 8\], and the four-point flexure samples \[1\]. The
advantages of laminated beam type specimens are: 1) the adhesive is
loaded elastically away from the crack tip, 2) high strain energy
release rates are obtainable, 3) the fracture mechanics models for
analysis are well understood, and 4) the specimens can be self-loading.
A disadvantage of these type of tests is that sometimes it is difficult
to measure the debond length. For transparent adherends or for a clearly
visible crack propagating at the edge of the specimen, an optical
microscope may be the only instrument needed to measure the debond
length. However, if the debond is not clearly visible, such as for
opaque adherends, the use of sophisticated experimental equipment (video
camera, acoustic or electrical methods) may be necessary \[9, 10\].
Additionally, for an adhesive sandwiched between two impermeable
substrates, diffusion occurs only from the edge and the equilibration
time may be long \[11, 12\]. This can slow down the speed of research as
well as lead to a heterogeneous distribution of diffusant in the
adhesive joint.

With respect to the laminated beam type specimens, there are advantages
to utilizing the shaft-loaded blister test. The time for environmental
saturation is relatively short, due to the exposed face and short
diffusion path. \[11, 12\] In addition, the specimen geometry is
axisymmetric, which reduces any misleading edge effects caused by the
degradation of the interface away from the crack tip. Some disadvantages
of the shaft-loaded blister test are that its fracture mechanics models
have not been studied as extensively as models from the laminated beam
specimens; and, like most coatings tests, the maximum value of the
strain energy release rate before film rupture occurs is limited by the
film's mechanical strength and the intrinsic interfacial toughness.
Plastic yielding of the coating may lead to an overestimated blister
height (relative to the elastic case) \[13\], possibly lead to creep
\[14\] and therefore complicate the analysis. Furthermore, the strain
energy release rate decreases as a function of *a* ^*-4*/3^ and
therefore will approach a threshold value of *G* more slowly than beam
type specimens. For the DCB wedge test, the strain energy release rate
decreases as a function of *a^-^*^4^. Therefore, a wide range of *G*
values can be obtained for a relatively small change in crack length and
the threshold energy can be rapidly approached. Neither the SLBT nor
wedge test are particularly less sensitive than the other to the effects
of residual stresses; in both test methods during subcritical testing
the residual stress driven release rate may be the same magnitude as the
threshold value, *G* ~Th~, and should therefore be considered \[15-18\].

In this work, the subcritical adhesion behavior between an epoxy and
glass as a function of relative humidity (r.h.) was measured using the
DCB wedge test and the SLBT. The results from the two tests are compared
and the disadvantages and advantages of each test method are highlighted
based on the experimental data.

**2. Experimental**[^7]

The epoxy adhesive utilized in this research was D.E.R. 332 epoxy resin
cured with Huntsman Jeffamine T-403. To reduce residual stress in the
adhesive, the specimens were cured for 48 h at room temperature followed
by a 2 h cure at 130 °C. Borosilicate glass cut into the appropriate
dimensions was used as the substrate.

SLBT specimens were (3.5 x 101.6 x 101.6) mm^3^ squares with an 8 mm
diameter hole in the center. A pre-crack was fabricated by placing a
0.95 cm diameter piece of Kapton pressure-sensitive adhesive tape (PSAT)
over the hole in the center of the quartz substrate. The Kapton PSAT
consists of a 25 μm (1 mil) thick Kapton backing and a 37.5 μm (1.5 mil)
thick acrylic pressure sensitive adhesive. The tape also provided
additional mechanical reinforcement to the thin epoxy film at the highly
stressed contact area between the coating and shaft-tip. To prepare the
specimen, first the un-cured model epoxy was coated on to the quartz
substrate. A 50 μm (2 mil) thick piece of Kapton-E film (no PSA) was
then placed on top of the epoxy coating. The Kapton-E film also acts as
a mechanical reinforcing layer for the epoxy coating. The resulting
adhesive coating is therefore a composite of the model epoxy, Kapton
PSAT (located solely in the center) and Kapton-E film. The average epoxy
film thickness of each sample ranged between 100 μm and 150 μm ± 10
(based on one standard deviation and 4 thickness measurements).

To develop a sub-critical blister test specimen the sample must be
self-loading, the integrity of the thin adhesive coating must be
maintained, and the sample must be exposed to the environment. A
schematic of the subcritical SLBT specimen is shown in Figure 1. To
fabricate a simple self-loading constant load SLBT specimen, a hole is
punched in the coating that can accommodate a 2.54 mm (or 4/40")
stainless steel machine screw. The machine screw acts as the fastener
from which to suspend the load (via a flexible copper wire). The punched
hole containing the screw is sealed with a room temperature cure epoxy
(Devcon 2-ton epoxy). The entire SLBT specimen was placed in a sealed
vessel and conditioned at constant r.h. at room temperature using
saturated salt solutions \[19-21\].

![](media/image48.wmf){width="4.241666666666666in"
height="2.4972222222222222in"}

Figure 1. Schematic of the constant load sub-critical shaft-loaded
blister test.

The strain energy release rate or crack driving energy, *G*, was
calculated using the load-based equation (equation 1) \[22\]:

$G = \left( \frac{1}{\text{16}\pi^{4}\text{Eh}} \right)^{\frac{1}{3}}\left( \frac{P}{a} \right)^{\frac{4}{3}}$
Equation 1.

where *P* is the load, *a* is the blister radius, *E* is the Young's
tensile modulus of the composite film, and *h* is the thickness of the
adhesive coating. The modulus of the coating (*E*~c~) for the bi-layer
film (Kapton and epoxy) can be estimated from a simple rule of mixtures
(*E*~c~ = Σ *v*~i~ *E*~i~).

DCB samples were prepared from rectangular glass specimens (0.98 x 25 x
75) mm^3^. To prepare the specimens, a Teflon shim 0.127 mm thick was
used to control the thickness of the adhesive layer and to confine the
adhesive between two glass rectangular adherends. The shim was cut so
that a strip of adhesive (12 x 56) mm^2^ was left in the center in the
DCB once the shim was removed. The strain energy release rate was
calculated using the following expression:

$G = \frac{3\Delta^{2}\text{BEt}^{3}}{8a^{4}w}\frac{B^{2}E^{2}t^{4} + w^{2}E_{a}^{2}h^{4} + 2\text{BwEE}_{a}\text{th}(2t^{2} + 3\text{th} + 2h^{2})}{2B^{2}E^{2}t^{4} + w^{2}E_{a}^{2}h^{4} + \text{BwEE}_{a}\text{th}(5t^{2} + 6\text{th} + 4h^{2})}$
Equation 2.

where ∆ is the end opening, *B* and *w* are the width of the adherends
and adhesive, respectively, *t* and *h* are the thickness of the
adherends and adhesive, respectively, and *E* and *E~a~* are the
corresponding Young's moduli of the adherends and adhesive. A stainless
steel razor (∆ = 0.25 mm) was used as the wedge. For both the SLBT and
DCB sub-critical experiments, a micrometer was utilized to periodically
measure the debond length. Like many adhesive tests, the uncertainty due
to sample to sample variation is much greater than the uncertainty
introduced by measuring the debond length. The average debond velocity,
*v* (*da*/*dt*), was determined from the change in average debond length
(*a*) over the elapsed time between measurements.

**3. Results and Discussion**

The graph of the *v*-*G* curves obtained from the constant-load SLBT for
75 % r.h. and 81 % r.h. is shown in Figure 2. SLBT specimens were tested
at (30, 44, 54, 66, 75, and 81) % r.h.; however, no debonding was
observed for samples tested at 66 % r.h. and below. This is because the
applied SERR was not large enough to cause debonding. More details about
this will be discussed later.

![](media/image49.wmf){width="4.661111111111111in"
height="3.1256944444444446in"}

Figure 2. *v*-*G* curves obtained from the constant-load SLBT. Symbols
are 73 % (□) and 81% (▲) r.h. Note that 100 % r.h. was not tested.
Humidity levels of (30, 44, 54, and 66) % r.h. did not exhibit adhesion
loss over the experiment's time scale. The error bars are not shown for
clarity.

The graphs of the *v*-*G* curves obtained from the DCB test for (15, 33,
43, 66, 81 and 100) % r.h. are shown in Figure 3. Figures 2 and 3 are
shown on the same *y*-scale to facilitate comparison. Error bars are not
shown on the graphs because the uncertainty in *G* and *v* attributable
to measuring the debond length is significantly less than is the sample
to sample variation. Data sets from all specimens are shown in the
graphs.

![](media/image50.wmf){width="4.825694444444444in"
height="3.0229166666666667in"}

Figure 3. *v*-*G* curves obtained from the DCB test. Symbols are: 15%
(■), 33% (•), 43% (▲), 66% (∆), 81% (□) and 100% (\*) r.h. Lines are
drawn in to guide the eye. No line is shown for 81% r.h. and 100% r.h.
due to significant scatter. The error bars are not shown for clarity.

For the DCB experiments, the SERR once the wedge is introduced or the
"initial SERR" is relatively large; in fact, when the wedge is
introduced for a debond length of 1 mm, the value of the SERR is on the
order of 10^6^ J/m^2^. The initial SERR in the wedge test is much
greater than the intrinsic interfacial toughness of the adhesive and
therefore a debond will propagate. As a consequence, debonding is
measurable at much lower relative humidities than seen with the SLBT.
Figure 2 shows a significant difference between the low humidities (15,
33, and 43) % r.h.. and the high humidities (66, 81, and 100) % r.h..
This is characteristic of a critical relative humidity level for
adhesion loss where there is a dramatic loss of adhesion above a
critical relative humidity level which is typically between 40 % r.h and
70% r.h. \[2, 23\]. At 81 % and 100 % r.h.. the debond behaviors are
different. At 81 % r.h., during the early stage of the test, the debond
grows rapidly and then arrests suddenly. At a 100 % r.h. the crack grows
rapidly and then appears to reverse direction. This behavior is probably
caused by swelling of the adhesive and the subsequent change in the
stress state of the adhesive from tensile to compressive.

For the SLBT experiments, the initial applied strain energy release rate
(SERR) was 200 J/m^2^. Therefore, if the intrinsic interfacial fracture
toughness exceeded or met 200 J/m^2^, the debond would not propagate,
and the test will not work. Increasing the suspended load would increase
the SERR; however, the maximum suspended load and hence the SERR is
limited by the strength of the film. Any additional load suspended from
the center of the blister resulted in significant plastic yielding and
rupture of the film. A 100 % r.h. was not tested because it was
suspected that the adhesion level would reach a minimum value above the
critical relative humidity level. Only 75 % and 81 % r.h. are shown,
because at humidity levels below 75 % r.h. no crack growth was observed
over the time frame of the experiment, 4 months. Classic debond behavior
was observed, where the debond propagates presumably by a
stress-controlled reaction at the crack tip, followed by the debond
apparently arresting at a threshold value of the SERR, *G*~Th~. For 75 %
and 81 % r.h. *G*~Th~ was (95 ± 10) J/m^2^ and (60 ± 10) J/m^2^,
respectively. Because no debond growth was observed at low humidity,
this suggests that *G*~Th~ at these moisture levels is greater than 200
J/m^2^.

Ultimately, this study shows that the results from the two tests are
different due to the unusual behavior exhibited by the DCB specimens at
high % r.h. and because the debond velocities seen in the DCB are much
faster than in the SLBT, for an equal applied SERR. However, it is
unclear if these differences are directly attributable to the tests
(thin film vs. bending plate, mode mixing, geometry, etc.) or are some
artifact of the experiment (moisture concentration, residual and
swelling stresses, thickness, etc.).

There are a number of advantages and disadvantages for each test
highlighted by these experiments. A serious problem with the SLBT, and
common to most peel type tests, is the high stress in the film which can
cause yielding in the adhesive. For these SLBT experiments, the maximum
suspended load and therefore SERR was limited by the strength of the
composite film. Furthermore, the applied loads were large enough to
cause visible yielding or creep in the adhesive. This was evident from
the permanent set in the delaminated film. This may render the
expressions for *G* derived from linear elasticity invalid, depending if
elastic conditions at the crack tip exist or not during debond
propagation. Therefore caution must be taken to make sure that creep
does not affect the adhesion results. In addition, the DCB test utilizes
much smaller samples which can occupy significantly less lab space. The
time frame of the DCB test is much less than the SLBT: (1 to 1.5) months
and (3 to 4) months, respectively. Although, the SLBT specimen is an
open-face geometry and should equilibrate in its environment much sooner
than a DCB test specimen (a sandwich-type geometry specimen), the time
frame of the experiment suggests that there is no advantage to using the
SLBT data to increase the rate of environmental degradation during
subcritical testing.

**Conclusions**

The subcritical adhesion test results from the SLBT and DCB were
different; however, it was unclear if the differences were due to the
tests themselves or some experimental artifact. Significantly greater
initial SERR were obtained with the DCB, which facilitated
characterizing the adhesion at a wider range of SERR and moisture levels
than the SLBT. However, the DCB, exhibited some unusual behavior where
the debond apparently reversed direction, probably due to swelling.
Lastly, care must be taken when using the SLBT due to the affects of
creep.

**Acknowledgements**

The authors thank Tom Seery for assistance in acquiring financial
support. The authors also thank Shu Guo, Hitendra Singh, Aaron Forster,
Amanda Forster, Jon Martin, and Don Hunston for their valuable ideas and
The Dow Chemical Company for supplying the epoxy resin.

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**36**, 121-129 (2004)

\[11\] Chang, T., Sproat, E.A., Lai, Y.H., Shephard, N.E., and Dillard,
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**Appendix A. Project Listing for BFRL** **Research and Development for
the** **Safety of Threatened Buildings
Program**[]{#__RefHeading___Toc97685947 .anchor}

Prevention of Progressive Collapse

Fire Safety Design and Retrofit of Structures

Fire Protective Coatings for Structural Steel

Standard Test Methods for Evaluating the Fire Resistance of Structural
Steel

Methodology for Fire Resistance Determination and Simulation of Building
Partitions

Emergency Use of Elevators

Occupant Behavior and Egress

Equipment Standards for First Responders

Guidelines and Technologies for CBR Attacks

Standard Building Information Models

Cost-Effective Risk Management Tools

More information can be found at:
<http://www.bfrl.nist.gov/goals_programs/prgmSTB.htm>

The program is managed by Dr. William Grosshandler
(<william.grosshandler@nist.gov>).

[^1]: Certain commercial products are identified in this paper to
    specify the materials used and procedures employed. In no case does
    such identification imply endorsement by the National Institute of
    Standards and Technology, nor does it indicate that the products are
    necessarily the best available for the purpose.

[^2]: Certain commercial products are identified in this paper to
    specify the materials used and procedures employed. In no case does
    such identification imply endorsement by the National Institute of
    Standards and Technology, nor does it indicate that the products are
    necessarily the best available for the purpose.

[^3]: MetSys Corporation, Millwood VA 22646-0317.

[^4]: Photonics System Team, Korea Photonics Technology Inst., #459-3
    Bonchon-Dong, Buk-Gu, Gwangju, 500-210 Republic of Korea.

[^5]: Certain commercial products are identified in this paper to
    specify the materials used and procedures employed. In no case does
    such identification imply endorsement by the National Institute of
    Standards and Technology, nor does it indicate that the products are
    necessarily the best available for the purpose.

[^6]: ^‡^ Certain commercial equipment and materials are identified in
    this paper in order to specify adequately the experimental
    procedure. In no case does such identification imply recommendations
    by the National Institute of Standards and Technology nor does it
    imply that the material or equipment identified is necessarily the
    best available for this purpose.

[^7]: Certain commercial equipment and materials are identified in this
    paper in order to specify adequately the experimental procedure. In
    no case does such identification imply recommendations by the
    national Institute of Standards and Technology nor does it imply
    that the material or equipment identified is necessarily the best
    available for this purpose.