July 2001

NASA/TM-2001-211030

ARL-TR-2540

Influence of Specimen Preparation and

Specimen Size on Composite Transverse

Tensile Strength and Scatter

T. Kevin O’Brien

U. S. Army Research Laboratory

Vehicle Technology Directorate

Langley Research Center, Hampton, Virginia

Arun D. Chawan

Syracuse University, Syracuse, New York

Kevin DeMarco

Virginia Polytechnic Institute & State University, Blacksburg, Virginia

Isabelle Paris

Langley Research Center, Hampton, Virginia
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July 2001

NASA/TM-2001-211030

ARL-TR-2540

Influence of Specimen Preparation and

Specimen Size on Composite Transverse

Tensile Strength and Scatter

T. Kevin O’Brien

U. S. Army Research Laboratory

Vehicle Technology Directorate

Langley Research Center, Hampton, Virginia

Arun D. Chawan

Syracuse University, Syracuse, New York

Kevin DeMarco

Virginia Polytechnic Institute & State University, Blacksburg, Virginia

Isabelle Paris

Langley Research Center, Hampton, Virginia
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and Space Administration or the U.S. Army.
1

INFLUENCE OF SPECIMEN PREPARATION AND

SPECIMEN SIZE ON COMPOSITE

TRANSVERSE TENSILE STRENGTH AND SCATTER

T. Kevin O’Brien

U.S. Army Research Laboratory

 Vehicle Technology Directorate

NASA Langley Research Center

Hampton, Virginia

Arun D. Chawan

Syracuse University

Syracuse, New York

Kevin DeMarco

Virginia Polytechnic Institute & State University

Blacksburg, Virginia

Isabelle Paris

National Research Council

NASA Langley Research Center

Hampton, Virginia

ABSTRACT

The influence of specimen polishing, configuration, and size on the

transverse tension strength of two glass-epoxy materials, and one carbonepoxy material, loaded in three and four point bending was evaluated.

Polishing machined edges, and/or tension side failure surfaces, was

detrimental to specimen strength characterization instead of yielding a

higher, more accurate, strength as a result of removing inherent

manufacture and handling flaws. Transverse tension strength was typically

lower for longer span lengths due to the classical weakest link effect.

However, strength was less sensitive to volume changes achieved by

increasing specimen width. The Weibull scaling law typically overpredicted changes in transverse tension strengths in three point bend tests

and under-predicted changes in transverse tension strengths in four point

bend tests. Furthermore, the Weibull slope varied with specimen

configuration, volume, and sample size. Hence, this scaling law was not

adequate for predicting transverse tension strength of heterogeneous, fiberreinforced, polymer matrix composites.
2

KEYWORDS: Transverse Tensile Strength, matrix cracking, Weibull

distribution, scale effects, glass-epoxy, carbon-epoxy, bending tests

INTRODUCTION

Matrix ply cracking is a common initial damage mechanism in fiber

reinforced composites. Because matrix ply cracking is seldom catastrophic

for laminates subjected to membrane loading, few researchers have tried to

identify and overcome the difficulties involved in characterizing transverse

tensile strength, one of the fundamental material properties associated with

matrix ply crack formation. However, for composite structures that undergo

bending, or other out-of-plane loading, the formation of matrix cracks may

lead to immediate delamination formation and unstable growth [1,2].

Hence, accurate characterization of the transverse tensile strength of

composite materials may be required to accurately predict matrix ply

cracking in these structures.

The influence of material volume, in the form of a ply thickness

dependence on matrix crack formation, is well established. Hence, for a

strength-based characterization to be truly generic, volume scaling must be

achieved through a Weibull Scaling Law [3]. Early attempts to achieve this

characterization were performed using 90-degree laminate tension tests [4].

However, a large percentage of the failures occurred at the grips. An

alternate technique would be to create transverse tension failures in 90-

degree laminates subjected to bending loads. This type of loading has the

added benefits of requiring simple fixtures and relatively small specimen

sizes. Hence, a greater number of specimens may be tested for a given

specimen size for the same amount of material required to perform uniaxial tension tests. These larger sample sizes facilitate the generation of the

large number of replicates required for statistical characterization and

generation of the parameters required for the Weibull scaling law.

In this study, 90-degree unidirectional glass-epoxy and carbon-epoxy

laminates were tested in three and four point bending to characterize the

composite transverse tensile strength. The influence of edge flaws due to

machining, and surface flaws due to manufacture and handling, were

assessed by testing specimens in both the natural (as-manufactured and

machined) condition as well as testing specimens with polished edges,

polished bottom failure surfaces, or both. Furthermore, the dependence of

transverse tensile strength on volume was assessed by testing specimens with

different widths and spans. A large number of specimens were tested for

each unique combination of specimen preparation, geometry, and loading.
3

MATERIALS

Three different fiber reinforced polymer matrix composites were

tested. These included two glass-epoxy materials (S2/F584 and S2/8552)

and a carbon-epoxy material (IM7/8552) with two different laminate

thicknesses (24-ply and 36-ply).

S2/F584 glass-epoxy

Two sets of panels were supplied by the Boeing Company, Mesa,

Arizona. The original prepreg material used to manufacture the first set was

flagged by the material supplier, Hexcel Corporation, as having

contaminates in the form of small spots of aluminum silicate (i.e. grease,

etc.). This material was replaced by new prepreg material to manufacture

the second set. However, because no significant flaws were detected in

ultrasonic inspection, both sets of panels were tested in this study. The S2

glass fiber density for both panels was 2.48 g/cm3. The fiber aerial weight

was 218 g/m2 for the original prepreg material and 223 g/m2 for the new

prepreg material.

All panels from both materials were cured in an autoclave using the

manufacturer’s recommended curing cycle. This consisted of a temperature

rise of 3.5 K (7°F) per minute up to 451 K (350°F) at a pressure of 689

KPa (100 psi). This was followed a 120 minute hold, then cooling down at

the same rate while maintaining pressure until the temperature was less than

334 K (140°F). The panels were made with 24 plies of prepreg and were

406 mm (16 in) long in the fiber direction and 305 mm (12 in) wide in the

direction transverse to the fibers. The nominal panel thickness was 4.45 mm

(0.175 in), corresponding to a nominal ply thickness of 0.185 mm (0.0073

in). Nominal fiber volume fraction was 47.3% and 48.4% for the original

and new panels, respectively, as estimated from the following equation

 %Vf =

N(FAW)

t(FD)

x100 (1)

where N is the number of plies, t is the panel thickness, FAW is the fiber

aerial weight and FD is the fiber density. This fiber volume fraction

compares well with the average volume fraction measured using ASTM

standard D3171 for fiber volume fraction by digestion of the polymer

matrix. This technique was used on the thinnest and thickest specimen from

each test configuration. Fourteen samples from two panels of the original

prepreg material, and 24 samples from three panels of the new prepreg
4

material, were digested using concentrated sulfuric acid and 30% hydrogen

peroxide until no resin remained. The average fiber volume fraction

determined this way was 48.0% for the original prepreg material and 48.1%

for the new prepreg material. The volume fraction measurement coefficient

of variation was 4.8% and 4.5%, respectively, for the original and new

prepreg material.

S2/8552 glass-epoxy

A single panel was manufactured from unidirectional prepreg tape by

Bell Helicopter Company, Fort Worth, Texas. The S2 glass fiber density

was 2.48 g/cm3. The Fiber aerial weight was 295 g/m2. The uncured resin

content was 34% by weight.

The panel was cured in an autoclave using the manufacturer’s

recommended curing cycle. This consisted of 120 minutes at 454 K (355°F)

and 621 KPa (90 psi) pressure. The panel consisted of 24 plies of

unidirectional prepreg tape and measured 762 mm (30 in) square. The

nominal panel thickness was 5.56 mm (0.219 in), corresponding to a

nominal ply thickness of 0.231 mm (0.0091 in). No significant flaws were

detected in ultrasonic inspection of this panel.

Nominal fiber volume fraction was 51.3 %, as estimated from

equation (1). This fiber volume fraction compares well with the average

volume fraction measured using the ASTM standard D3171 for fiber

volume fraction by digestion of the polymer matrix. This technique was

used on the thinnest and thickest specimen from each test configuration.

Eighteen samples were digested using concentrated sulfuric acid and 30%

hydrogen peroxide until no resin remained. The average fiber volume

fraction determined this way was 49.8%. The volume fraction measurement

coefficient of variation was 2.5%.

IM7/8552 carbon-epoxy

Three panels were manufactured from IM7/8552 unidirectional

prepreg by the Boeing Company, Philadelphia, Pennsylvania. The IM7

carbon fiber density was 1.75 g/cm3. The Fiber aerial weight was 148 g/m2.

The uncured resin content was 34% by weight.

The panels were cured in an autoclave using the manufacturer’s

recommended curing cycle. This consisted of a 2 hours hold at 454 K

(355°F) under 621 KPa (90 psi) pressure. Two of the panels consisted of 24

plies of unidirectional prepreg tape and the third panel consisted of 36 plies
5

of unidirectional prepreg tape. All three panels measured 610 mm (24 in)

by 305 mm (12 in). For the 24-ply panels, the nominal panel thickness was

3.32 mm (0.1305 in), corresponding to a nominal ply thickness of 0.137

mm (0.0054 in). For the 36-ply panel, the nominal panel thickness was 4.93

mm (0.194 in), corresponding to a nominal ply thickness of 0.137 mm

(0.0054 in). No significant flaws were detected in ultrasonic inspection of

these panels.

Nominal fiber volume fraction, as estimated from equation (1), was

62.1 % for both the 24-ply and 36-ply laminates. This fiber volume

fraction compares well with the average volume fraction measured using the

ASTM standard D3171 for fiber volume fraction by digestion of the

polymer matrix. This technique was used on the thinnest and thickest

specimen from each test configuration. For both the 24-ply and 36-ply

laminates, fourteen samples were digested using concentrated sulfuric acid

and 30% hydrogen peroxide until no resin remained. The average fiber

volume fraction determined this way was 63.0% for the 24-ply laminates

and 62.6% for the 36-ply laminates. The volume fraction measurement

coefficient of variation was 6.2% and 6.4%, respectively, for the 24-ply

and 36-ply laminates.

SPECIMEN PREPARATION

Specimen cutting

Test specimens with fibers oriented at ninety degrees to the

longitudinal axis were cut from the panels fabricated for all three materials.

All specimens were cut from panels using a diamond saw. A 6.35 mm (0.25

in) plexi-glass sheet was placed beneath each panel during the machining to

minimize any fiber spalling on the back side of the saw cut.

S2/F584 glass-epoxy test specimens

Specimens were cut from two panels (TO3 and TO5) made from the

original prepreg material and three panels (TN2, TN3, and TN6) from the

new prepreg material (table 1). Panels TO3, TO5, and TN2 were cut into 5

columns, 57.2 mm (2.25 in) wide. Hence, test specimens cut from these

columns were 57.2 mm (2.25 in) long (B configurations, table 1). All test

specimens cut from panel TO3 columns were 6.35 mm (0.25 in) wide

(Configurations B-2, B-3, and B-4 in table 1). For the columns from panels

TO5 and TN2, specimens were cut in a repeated pattern consisting of

repeated sets of two specimens 6.35 mm (0.25 in) wide (configurations B-A
6

and B-B), one specimen 12.7 mm (0.5 in) wide (configuration B-C), and

one specimen 19.1 mm (0.75 in) wide (configuration B-D). This cutting

pattern was chosen to minimize any strength dependence on specimen panel

position. Selected specimen configurations from panels TO3, TO5, and

TN2 were polished on the edges, bottom surface, or both, prior to testing

(table 1). Panel TN3 was cut into four columns with four different widths.

Specimens cut from these columns had lengths of 31.8 mm (1.25 in) for

configuration A, 57.2 mm (2.25 in) for configuration B, 82.6 mm (3.25 in)

for configuration C, and 108 mm (4.25 in) for configuration B3. Panel

TN6 was cut into four columns, two with widths of 57.2 mm (2.25 in) and

two with widths of 82.6 mm (3.25 in). Specimens cut from these columns

had lengths of 57.2 mm (2.25 in) for configurations B and A1 and 82.6 mm

(3.25 in) for configurations A2 and B2. All test specimens cut from panels

TN3 and TN6 were 6.35 mm (0.25 in) wide (table 1). All specimens cut

from panels TN3 and TN6 were polished on the edges only.

S2/8552 glass-epoxy test specimens

The large 762 mm (30 in) square panel was first cut into four 381

mm (15 in) square panels to facilitate further cutting into test specimens.

These four smaller panels were then cut into columns with different widths.

These columns were cut into test specimens with lengths of 31.8 mm (1.25

in) for configuration A, 57.2 mm (2.25 in) for all B configurations and

configuration A1, 82.6 mm (3.25 in) for configurations C, A2, and B2, and

108 mm (4.25 in) for configuration B3 (table 2). One of the 57.2 mm (2.25

in) columns from each of the four quadrants (I-IV) of the original large

panel were cut into specimens using a repeated pattern. This pattern

consisted of repeated sets of two specimens 6.35 mm (0.25 in) wide

(configurations B-A and B-B), one specimen 12.7 mm (0.5 in) wide

(configuration B-C), and one specimen 19.1 mm (0.75 in) wide

(configuration B-D). This cutting pattern was chosen to minimize any

strength dependence on specimen panel position. One set of the 6.35 mm

(0.25 in) wide specimens (configuration B-B) was polished on the edges

and bottom surface (table 2). In addition, a set of 57.2 mm (2.25 in) long

by 6.35 mm (0.25 in) wide specimens (configuration B-2) from a column

in a single quadrant of the original panel was also polished on the edges

only. All remaining specimens were tested in their as-cut, unpolished,

condition.
7

IM7/8552 carbon-epoxy test specimens

24-Ply Panels

The two 610 mm (24 in) by 305 mm (12 in) panels were each cut

into two 305 mm (12 in) square panels to facilitate further cutting into test

specimens. The first panel (24-1) was cut into five 57.2 mm (2.25 in) wide

columns yielding 57.2 mm (2.25 in) long specimens. Test specimens of

three different widths were cut from these columns (table 3). Columns were

cut in a pattern consisting of repeated sets of four specimens 6.35 mm (0.25

in) wide (configurations B-A to B-D), one specimen 12.7 mm (0.50 in)

wide (configuration B-E), and one specimen 19.1 mm (0.75 in) wide

(configuration B-F). This cutting pattern was chosen to minimize any

strength dependence on specimen panel position. Selected configurations

were polished on the edges, bottom surface, or both, prior to testing (table

3). The second panel (24-2) was cut into columns with four different

widths. These columns were cut into 6.35 mm (0.25 in) wide test specimens

with lengths of 31.8 mm (1.25 in) for configuration A, 57.15 mm (2.25 in)

for configurations B and A1 and 82.55 mm (3.25 in) for configurations C,

A2 and B2 (table 3).. All specimens from the second panel were tested in

their as-cut, unpolished, condition.

36-Ply Panel

One 610 mm (24 in) by 305 mm (12 in) panel was first cut into two

305 mm (12 in) square panels to facilitate further cutting into test

specimens. These two smaller panels were then cut into columns with four

different widths. These columns were cut into 6.35 mm (0.25 in) wide test

specimens with lengths of 31.8 mm (1.25 in) for configuration A; 57.2 mm

(2.25 in) for configurations B and A1; 82.6 mm (3.25 in) for

configurations C, A2 and B2; and 108 mm (4.25 in) for configuration B3

(table 3). All specimens from this panel were tested in their as-cut,

unpolished, condition.

Polishing procedure

Specimen edges and bottom surfaces were polished for selected

specimens using the following procedure. Specimens were first sanded on a

Buhler Ecomet III Polisher/Grinder using 600 grit Buhler carbiMet paper

discs. Next, specimens were polished on this same machine using 1200 grit

Lapmaster international Silicon Carbide paper discs. Finally, specimens

were polished using a very fine nap cloth (Chem-met) and Buehlers
8

Masterprep (.05 micron Alumina suspension solution) with a lubricant of

soapy water (pH 7). Polished surfaces had a mirror image finish upon

completion of this polishing process. In some cases, this process was also

performed on specimens that had been tested without previous polishing to

facilitate post-mortem microscopic observation of the failure orientation.

Thickness and width measurement

The thickness and width of each specimen was measured at three

points along the specimen length using flat nose digital calipers. The

average of these three measurements, as well as the percentage variation in

thickness and width along the specimen length, were calculated and

tabulated along with the individual measurements. For specimens that were

polished, thickness and width measurements were performed after polishing

and before testing. For each test configuration on each material, the average

thickness and coefficient of variation are shown in tables 1-3.

EXPERIMENTAL PROCEDURE

Test apparatus

Three and four point bending tests were performed on an MTS model

858 table-top hydraulic load frame with an MTS model 458 controller

(figure 1). This load frame was equipped with a 22.2 kN (5000 lb) load

cell. An additional 2.22 kN (500 lb) load cell was placed in series with this

standard load cell to more accurately measure the small loads anticipated.

This smaller load cell was typically run at the 50% range corresponding to a

1.1 kN (250 lb) load at full scale. Both load cells, and the internal LVDT

that controlled the stroke of the ram, were calibrated according to NIST

traceable ISO 9001 specifications just before the test series was begun.

The load frame was equipped with three and four point bending

fixtures that were designed and built at NASA Langley (figure 2). The

fixtures consisted of individual upper and lower pieces that included the

load point supports. These supports were machined to a radius of 3.18 mm

(0.125 in), and were bolted to the cross member so that the span length

could be adjusted between 25.4 mm (1 in) and 102 mm (4 in). An angle

bracket and a set of metal strips, clamped to the bracket, were used to center

the specimen width on the load point supports.
9

Bending test configurations

Three-point bending tests were performed in three configurations, A,

B, and C, shown in figure 3a with span lengths of 25.4 mm (1.0 in), 50.8

mm (2.0 in), and 76.2 mm (3.0 in). Four point bending tests were

performed using four configurations (A1, A2, B2, B3) also shown in figure

3a. These configurations had combinations of inner spans ,s-l, of 25.4 mm

(1.0 in) or 50.8 mm (2.0 in) and outer spans, s, of 50.8 mm (2.0 in) to 102

mm (4.0 in).

Test Procedure

Tests were performed in stroke control using a programmed loading

ramp. Stroke rates were determined by estimating the maximum center

point displacement at failure using beam theory and programming a stroke

rate so that specimen failure would occur in approximately one minute.

Hence, different specimen configurations were tested at different stroke

rates so that the time to failure would be similar for all specimens tested.

Tables 1-3 show the stroke rates used for each test configuration and

material. For each unique configuration for a given material, all tests were

completed on the same day, by the same operator, under the same ambient

laboratory environmental conditions.

Failure loads were recorded using peak detectors in the MTS 458

controller. In addition, for each test a continuous plot of load versus loadpoint displacement was recorded using an analog X-Y recorder. Specimens

were removed from the load frame as it was unloaded. Immediately

thereafter, the distance from the failure location along the length to the

center load point in the three point tests, and to the center of the specimen

span in the four point tests, was measured and recorded. For each

configuration tested, the maximum mid-span deflection, δ max, normalized

by the average specimen thickness, t avg, were recorded (tables 4-6). For

most of the configurations tested, δ max, was less than t avg , and hence,

δ max / t avg < 1.

Data Reduction

For the three point bending tests shown in figure 3b, with span

length, s and width, b, specimen strengths were determined from the beam

theory expression for the maximum tension stress, σmax, under the center

load nose using the maximum load at failure, Pc, and the average specimen

thickness, tavg,
1 0

σ max = 3

2 2

P s

bt

c

avg

(2)

For the four point bending tests shown in figure 3b, with outer span,

s, inner span, s-l, and width, b, specimen strengths were determined from

the beam theory expression for the maximum uniform tension stress, σmax,

between the inner load points using the maximum load at failure, Pc, and

the average specimen thickness, tavg,

σ max = 3

2 2

P

bt

c

avg

l

(3)

Figure 4 shows a failed S2/8552 glass-epoxy specimen that was tested

in 3-point bending configuration A. This is the shortest span and thickest

specimen tested, and hence, would be the most prone to fail in transverse

shear as opposed to transverse tension. Figure 4 shows the crack that formed

at 90 degrees to the bottom of the beam, illustrating that the failure was due

to transverse tension. This same failure pattern was observed for all three

materials for all of the 3-point and 4-point bend configurations.

TRANSVERSE STRENGTH CHARACTERIZATION

The strength of a material is typically characterized assuming either a

symmetric (normal) distribution or a skewed (Weibull) distribution. For the

normal distribution, the mean strength and coefficient of variation, CV,

(standard deviation divided by the mean strength) are calculated. The mean

strength characterizes the central tendency of the strength distribution,

whereas the CV quantifies the scatter in the strength distribution. However,

since most strength data is not normally distributed, a Weibull distribution

is often assumed as an alternative.

Weibull assumed an extreme value, or “weakest link”, distribution for

material strength by developing a two parameter function for the

probability of failure at a given stress level, P(σ), of the form

 P c

m

σ e σ σ ( ) = −1 −( ) / (4)
1 1

Where σc is the location parameter known as the characteristic strength, and

m is the shape parameter known as the Weibull slope [3]. The location

parameter, σc, provides a measure of the central tendency of the

distribution, similar to the mean for a normal distribution. The Weibull

slope, m, provides a measure of the scatter in the distribution, with a small

value of m corresponding to a large amount of scatter in the data.

Therefore, the amount of scatter is inversely proportional to m. Hence, as

the magnitude of m increases, the scatter decreases. Equation 4 may also be

recast into an equation of the form

 ym b = + lnσ (5)

Where

 y P = −





 



 



 



 ln ln

( )

1

1 σ

 (6)

And

 b m = − c lnσ (7)

Then by assuming a probability of failure corresponding to a median

ranking of the data

 P i

n

( ) ( ).

. σ =

− +

+

1 07

0 4 (8)

Where n is the total number of data points in the sample and i is the number

of the data points in ascending order from 1 to n; a least squares regression

fit of the logarithmic equation 5 may be performed to determine m and σc.

For each least squares regression analysis, the goodness of the fit was

quantified using Pearson’s “r” value given by

r

i i

i i

i

N

i

N

i

N

x x y y

x x y y

=

− 





 − 



 

 ∑ 

− 

  ∑ − 





 ∑

_ _

_ _ 2 2 (9)
1 2

An “r” value close to 1.0 indicates a good fit to the data.

In addition to characterizing the strength distribution for a given

material, Weibull postulated that the characteristic strengths for two

different volumes, V1 and V2, of the same material will obey the following

scale law [3]

 σ

σ

c

c

m

V

V

( )

( ) = 



 



 1

2

2

1

1/

 (10)

This scaling law was used previously to characterize transverse tension

strength via tension testing of 90 degree unidirectional carbon fiber epoxy

laminate [4].

For all three materials tested, characterization of the transverse

tension strength for each configuration was performed assuming both a

normal distribution and a Weibull distribution. Because of the inverse

relationship between the Weibull slope and the degree of scatter in the data,

the inverse of the Weibull slope, 1/m, was tabulated and plotted to allow a

more intuitive feeling for the trends observed. In addition, it is the inverse

Weibull slope that appears as the exponent in the Weibull volume scale law

in equation 10. Furthermore, the decimal value of CV and the inverse

Weibull slope, 1/m, have similar magnitudes. Hence, these quantities were

tabulated and plotted together.

The scaling law in equation 10 assumes that the two volumes being

compared are subjected to a uniform tensile stress throughout the volume.

However, the stress distributions in the three and four point bend tests are

not uniform (fig.3b). Hence, the scaling law was modified in reference 5

for 3-point bending as

σ

σ

f

pt

t

t

f

pt

m

m

V

V

3

2

3

1

= + 2 1 ( ) 



 



 (11)

Where the subscript “f” corresponds to the stress and volume in the flexure

test and the subscript “t” corresponds to the stress and volume under

uniform tension. A similar expression was derived in reference 5 for 4-

point bending as
1 3

σ

σ

f

pt

t

t

f

pt

m

m

m

V

V

4 2

4

1

4 1

2 = ( + )

( + )





 



 (12)

Equation (12) is applicable for quadrant point loading only. Hence, this

would apply for configurations A1 and B3 only. Similar expressions were

derived in the appendix for configurations A2 and B2.

The relationship between the 4-point quadrant point loading and 3-point

bending cases may be expressed by combining equations 11 and 12 to yield

σ

σ

f

pt

f

pt

f

pt

f

pt

m

m

V

V

4

3

3

4

1

2

2 = +



 





 



 (13)

Equation (13) is applicable for quadrant point loading only. Hence, this

would apply for configurations A1 and B3 only. Similar expressions were

derived in the appendix for configurations A2 and B2.

EXPERIMENTAL RESULTS

Results for the strength and scatter, as characterized using both a

normal and Weibull distribution, are given in tables 4-6 for the three

materials tested. Strengths and scatter parameters were also recalculated for

smaller sample sizes than the total n tested to determine the influence of

sample size on the results. All populations were evaluated starting from the

first specimen tested up to the desired number in the order of testing as

determined by random number generation. Results for each of the three

materials tested are described in detail in the following sections. The figures

will show results in SI units only. Results are also tabulated in English units

in tables 4-6.

S2/F584 Glass-epoxy

Influence of Specimen Preparation

Figure 5a shows the mean and characteristic strengths for

configuration B specimens from panel TO3 and TO5 that had different

specimen preparation. There was less than 2% difference in the strengths of

the unpolished specimens, B-2, and specimens with polished edges, B-3.
14

Therefore, any flaws created due to cutting the plate do not appear to

significantly affect the specimen strength. However, specimens with

polished bottom (tension side) surfaces, either with (B-B) or without (B-4)

polished edges, had 5.7% and 10.6% lower strengths, respectively. Hence,

instead of increasing the measured strength as a result of removing inherent

flaws in the material due to manufacture and handling, polishing appears to

be detrimental to specimen strength. In addition, for 2 of the 3 polished

configurations (B-3 and B-B), polishing the edges resulted in greater scatter

than was obtained in tests with unpolished edges, as indicated when

comparing the values of CV and 1/m in figure 5b.

In order to eliminate the influence of sample size on these

comparisons, strengths and scatter for each of these configurations were

recalculated with a common sample size of n=35. This number was chosen

because it is the smallest common sample size for the configurations being

compared. In all cases, the first 35 specimens tested were used in the

calculation. As shown in figure 6a, the smaller sample size resulted in some

numerical differences, but the same relative comparisons noted previously

were still observed. The only exception was for configuration B-B where

the CV for this polished configuration was 2.5% lower than the CV for the

unpolished configuration B-2 (fig. 6b).

Figure 7a shows the mean and characteristic strengths for

configuration B specimens from panel TN2 made with the new prepreg

material. Both configurations had polished edges, but just as was observed

with specimens made from the original prepreg material, edge polished

specimens with polished bottom surfaces (configuration B-B) had lower

strengths than the edge polished specimens with unpolished bottom surface

specimens (configuration B-A). Furthermore, the specimens with polished

bottom surfaces had greater scatter, as shown in figure 7b.

Influence of Specimen Width

Figure 8a shows the mean and characteristic strengths for original

prepreg configuration B specimens from panels TO3 and TO5 with three

different widths: 6.35 mm (configuration B-2), 12.7 mm (configuration BC), and 19.7 mm (configuration B-D). Results are presented for a common

sample size of n=35. No trend is apparent, as the strength appears to

decrease by 6.2% between the 6.35 mm (0.25 in ) and 12.7 mm (0.50 in)

wide specimens, then increases by 2.3% between the 12.7 mm (0.50 in) and

19.7 mm (0.75 in) wide specimens. Similarly, there is no apparent trend in

the scatter with specimen width, as shown in figure 8b.
15

Figure 9a shows the mean and characteristic strengths for new

prepreg configuration B specimens from panel TN2 with three different

widths: 6.35 mm (configuration B-A), 12.7 mm (configuration B-C), and

19.7 mm (configuration B-D). Results are presented for a common sample

size of n=35. As was the case with the original prepreg material specimens,

no significant trend is apparent, with only a 2.2% increase in strength with

increasing specimen width. Hence, the anticipated trend of decreasing

strength with increasing width, and hence increasing volume, that would be

anticipated from the Weibull scaling law was not observed for specimens

from either the original, or new prepreg materials. As shown in figure 9b,

for the new material (panel TN2) specimens, the scatter increases with

increasing specimen width, with the CV for the widest configuration (B-D)

being 1.7% greater than the CV for the narrowest configuration (B-A),.

Influence of panel-to-panel variability

Figure 10a shows the mean and characteristic strengths for identical

configuration B specimens with polished edges from different panels (TO3,

TN2, TN3, TN6) calculated for a common sample size of n=35. There is

clearly some variability in strength from panel to panel. This variability is

fairly small (4.2%) compared to the absolute strength, but it is greater than

the 2.2% variability found with increasing specimen width for panel TN2

(fig.9a). There is a greater variability in scatter between panels, as shown in

figure 10b, with the panel from the original prepreg material (TO3)

showing the greatest scatter. This could possibly be due to the

contamination found in the prepreg.

Influence of Span Length

Figure 11a shows the mean and characteristic strengths for three point

bending configurations with three different span lengths of 25.4 mm (1.0

in), 50.8 mm (2.0 in), and 76.2 mm (3.0 in) calculated for a common

sample size of n=47. Specimens tested in each of these configurations were

from a single panel (TN2) and had polished edges. There is a slight

decrease (1.8%) in strength with increasing span length, and hence

increasing volume, as anticipated based on the Weibull scaling law. In

addition, there is a noticeable trend of decreasing scatter with increasing

span length as shown in figure 11b. Similar trends in strength and scatter

dependence with span length were obtained for a smaller common sample

size of n=35.
16

Figure 12a shows the mean and characteristic strengths calculated for

a common sample size of n=47, for four-point bending configurations with

different span length combinations. Specimens tested in each of these

configurations had polished edges. There is an 11% decrease in strength

with increasing outer span length, s, from configuration A1 to A2 and an

8.3% decrease in strength with increasing inner span, s-l, from

configuration A2 to B2. Specimens for all three of these configurations

were cut from the same panel (TN6). However, strength increased by

almost 10% with increasing outer span length, s, from configuration B2

(panel TN6) to configuration B3 (panel TN3). Hence, the anticipated trend

of decreasing strength with increasing volume may be masked by significant

panel-to-panel variability. In addition, unlike the three point bending case,

there is a noticeable trend of increasing scatter with increasing span length

for the three configurations from the same panel (TN6), as shown in figure

12b. However, the scatter for specimens from panel TN3 did not follow this

trend. Similar strength and scatter dependence with span length were

obtained for a smaller common sample size of n=35.

S2/8552 Glass-epoxy

Influence of Specimen Preparation

Figure 13a shows the mean and characteristic strengths for

configuration B specimens that had different specimen preparation.

For the configurations that were tested with specimens from all four

quadrants of the original large panel (B-A, B-B), strengths for polished

specimens were slightly lower (1.5%) than strengths for unpolished

specimens. Similarly, for the configurations that were tested with specimens

from a single quadrant of the original large panel (B-1, B-2), strengths for

polished specimens were also slightly lower (0.8%) than strengths for

unpolished specimens. Hence, instead of increasing the measured strength as

a result of removing inherent flaws in the material due to manufacture and

handling, polishing appears to be detrimental to specimen strength. For the

specimens from all four quadrants of the original large panel (B-A, B-B)

polishing resulted in 1.15% greater CV than obtained in tests with

unpolished edges, as shown in figure 13b. However, the opposite was true

for specimens cut from a single quadrant of the original large panel, with

polished specimens (B-2) having 0.88% lower CV than unpolished

specimens (B-1).
17

Influence of Specimen Width

Figure 14a shows the mean and characteristic strengths for

configuration B specimens with three different widths: 6.35 mm (0.25 in ),

12.7 mm (0.50 in), and 19.1 mm (0.75 in). Results are presented for a

common sample size of n=25. No trend is apparent, as the strength

decreases by 3.2% between configurations B-A and B-C, then increases by

0.9% between configurations B-C and B-D. Hence, the anticipated trend of

decreasing strength with increasing width, and hence increasing volume,

that would be anticipated from the Weibull scaling law was not observed.

However, the scatter increased with increasing specimen width, as shown in

figure 14b.

Influence of Span Length

Figure 15a shows the mean and characteristic strengths for three point

bending configurations with three different span lengths of 25.4 mm (1.0

in), 50.8 mm (2.0 in), and 76.2 mm (3.0 in). All specimens tested in each

of these configurations were unpolished. There is no decrease in strength

between span lengths of 25.4 mm (1.0 in) and 50.8 mm (2.0 in), however,

there is a 6.0% decrease in strength between span lengths of 50.8 mm (2.0

in) and 76.2 mm (3.0 in), as anticipated based on the Weibull scaling law.

In addition, there is a noticeable trend of decreasing scatter with increasing

span length as shown in figure 15b. Similar trends in strength and scatter

dependence with span length were obtained for a smaller common sample

size of n=35.

Figure 16a shows the mean and characteristic strengths for four-point

bending configurations with different span length combinations. All

specimens tested in each of these configurations were unpolished. There is a

noticeable decrease in strength with increasing inner (s-l) or outer (s) span

length for these configurations. In addition, strength decreases as the inner

span length is increased relative to a constant outer span length (i.e., from

configuration A2 to B2), thereby increasing the volume of material

subjected to the maximum bending stress. These observations are consistent

with the anticipated trend of decreasing strength with increasing volume

based on the Weibull scaling law. However, the scatter appeared to increase

with span length for all but the longest span configuration B3, as shown in

figure 16b.
18

IM7/8552 Carbon-epoxy

Influence of Specimen Preparation

Figure 17a shows the mean and characteristic strengths for 24-ply,

configuration B specimens that had different specimen preparation.

Strengths for specimens polished on the edges or bottom only were slightly

lower (1-2%) than strengths for unpolished specimens. Strengths for

specimens polished on both the edges and bottom surface were nearly

identical (within 0.5%) to the strengths for unpolished specimens. Hence,

polishing does not appear to significantly increase the measured strength as

a result of removing inherent flaws in the material due to manufacture and

handling. As shown in figure 17b, with the exception of configuration B-C,

polished specimens (B-A and B-B) had greater scatter than obtained in tests

with unpolished edges (B-D).

Influence of Specimen Width

Figure 18a shows the mean and characteristic strengths for 24-ply,

configuration B specimens with three different widths: B-D, 6.35 mm (0.25

in), B-E, 12.7 mm (0.50 in), and B-F, 19.7 mm (0.75 in). Strengths

decreased with increasing width, with a maximum difference of 5.4%

between configurations B-F and B-D. This is consistent with the anticipated

trend of decreasing strength with increasing width, and hence increasing

volume, that would be anticipated from the Weibull scaling law. However,

the scatter increased with increasing specimen width, as shown in figure

18b, with a maximum rise in CV of 2.36% from configurations B-D to BF. Similar trends in strength and scatter dependence with span length were

obtained for a smaller common sample size of n=35.

Influence of panel-to-panel variability

Figure 19a shows the mean and characteristic strengths for unpolished

24 ply, configuration B specimens from different panels. There is clearly

some variability in strength (4.7%) between the two panels. The variability

in scatter between panels was small, as shown in Figure 19b, with a

difference of 0.8% in CV.
19

Influence of Span Length

24-ply panel

Figure 20a shows the mean and characteristic strengths for three point

bending configurations with three different span lengths of 25.4 mm (1.0

in), 50.8 mm (2.0 in), and 76.2 mm (3.0 in). All specimens tested in each

of these configurations were unpolished. Strength decreased by almost 10%

between span lengths of 25.4 mm (1.0 in) and 50.8 mm (2.0 in). However,

strength increased by 7.3% between span lengths of 50.8 mm (2.0 in) and

76.2 mm (3.0 in). In addition, there is a noticeable trend of decreasing

scatter with increasing span length as shown in figure 20b. Similar trends in

strength and scatter dependence with span length were obtained for a

smaller common sample size of n=35.

Figure 21a shows the mean and characteristic strengths for four-point

bending configurations with different span length combinations. All

specimens tested in each of these configurations were unpolished. There is a

noticeable decrease in strength (4.2%) with increasing outer span length, s,

from configurations A1 to A2. However, strength increased by 2.5% from

configuration A2 to B2 as the inner span length, s-l, was increased relative

to a constant outer span length, s, thereby increasing the volume of material

subjected to the maximum bending stress. Similar trends were observed for

strengths calculated for a smaller common sample size of n=35.

Furthermore, as shown in figure 22b, the scatter exhibited trends similar to

those observed for strength.

36-ply panel

Figure 22a shows the mean and characteristic strengths for three point

bending configurations with three different span lengths of 25.4 mm (1.0

in), 50.8 mm (2.0 in), and 76.2 mm (3.0 in). Specimens tested in each of

these configurations were unpolished. There is a significant decrease (4.8-

9.3%) in strength with increasing span length, and hence increasing volume,

as anticipated based on the Weibull scaling law. In addition, there is a

noticeable trend of decreasing scatter with increasing span length as shown

in figure 22b. Similar trends in strength and scatter dependence with span

length were obtained for a smaller common sample size of n=35.

Figure 23a shows the mean and characteristic strengths for four-point

bending configurations with different span length combinations. All

specimens tested in each of these configurations were unpolished. There is a
20

3.4% increase in strength with increasing outer span length, s, between

configurations A1 and A2. However, strength decreases by 14.1% with

increasing outer span length, s, between configurations B2 and B3. In

addition, strength increased by 3.4% as the inner span length, s-l, was

increased relative to a constant outer span length, s, from configuration A2

to B2. Similar trends were observed for strengths calculated for a smaller

common sample size of n=35. Scatter appeared to increase with both inner

and outer span length for all but the shortest span configuration (A1) as

shown in figure 23b.

Influence of Specimen Thickness

Figures 24a and 24b compare mean strengths for identical

configurations of 24-ply and 36-ply IM7/8552 specimens tested in 3-point

and 4-point bending, respectively. For specimens subjected to uniform

tension, the weakest link theory would predict a lower strength for the

thicker specimen. However, for the specimens tested in flexure in this

study, the thicker specimen was weaker for only one of the three 3-point

bend configurations (C) and for only one of the three 4-point bend

configurations (A1). Failure initiates on the bottom surface in these flexure

tests. Hence, the differences in strength observed for specimens with

different thicknesses may be attributed more to variability between panels

than to the classical weakest link effect, which assumes a greater probability

of a defect causing failure in a thick laminate with a large volume.

Discussion of Experimental Results

In order to summarize the comparisons made in the previous section,

results were plotted for all four material and thickness combinations for

each effect studied (width, span, etc.).

The trend of decreasing strength with increasing specimen width, and

hence increasing volume, that would be anticipated from the Weibull

scaling law was not clearly apparent (fig.25). In contrast, a small decrease

in strength with increasing 3-point span was observed for all three materials

(fig.26). In addition, for the 4-point bending tests, a decrease in strength

with increasing inner and outer span length was typically observed for the

two glass-epoxy materials (fig.27). However, this expected scaling was

occasionally masked by more significant panel-to-panel variability

(S2/F584 configuration B3). The variation in strength with span length was

not as consistent for the carbon-epoxy materials (fig.27).
21

For all three materials tested in 3-point bending, scatter typically

increased with increasing specimen width (fig.25). However, scatter

typically decreased with increasing 3-point span for all three materials

(fig.26). For all three materials, scatter in the 4-point bending tests typically

increased with increasing span length (fig.27). However, this trend was not

consistent for all four configurations tested.

HISTOGRAMS OF FAILURE LOCATIONS

3-point bending

Histograms showing the frequency of occurrence of failure locations,

relative to the center load nose, for the 3-point bend configurations are

shown for (1) S2/F584 (panel TN3) glass-epoxy in figures 28 a-c, (2) for

the S2/8552 glass-epoxy in figures 29 a-c, (3) for the 24-ply IM7/8552

carbon-epoxy in figures 30 a-c, and (4) for the 36-ply IM7/8552 carbonepoxy in figures 31 a-c. Failure occurs near, but not always directly under,

the center load nose where the beam theory indicates the tension stress is a

maximum (fig.3b), thus illustrating the sensitive to flaws in the

microstructure.

4-point bending

Histograms showing the frequency of occurrence of failure locations,

relative to the inner load noses, for the 4-point bend configurations are

shown for (1) S2/F584 (panel TN3) glass-epoxy in figures 32 a-d, (2) for

the S2/8552 glass-epoxy in figures 33 a-d, (3) for the 24-ply IM7/8552

carbon-epoxy in figures 34 a-c, and (4) for the 36-ply IM7/8552 carbonepoxy in figures 35 a-d. Failures occurred primarily between the inner load

noses. However, some failures also occurred under these load points, and

between the inner and outer load noses, reflecting the sensitive to flaws in

the microstructure. For the S2/8552 glass-epoxy, failures were concentrated

more toward one load nose for the longest span (configuration B3). For the

24-ply IM7/8552 carbon-epoxy, failures were concentrated more toward

one load nose for the smallest span configurations A1 and A2. No tests were

performed on configuration B3 for this thin material because of the large

deflections that would occur. For the 36-ply IM7/8552 carbon-epoxy, more

failures where concentrated near one load nose than the other for three of

the four configurations tested.
22

POST MORTEM EXAMINATION

After failure had occurred, selected specimens were potted in epoxy,

polished on the edges and examined in a light microscope to identify the

details of the failure location. Figure 36 shows the photomicrographs taken

at the failure location for two of the S2/8552 3-point bend specimens. The

left and right sides of the specimen are shown at the failure location for

each specimen.

For the specimen that had a low strength, there is a pocket of resin on

the bottom surface at the failure location. This resin pocket was not present

at the failure location for the other specimen that had a high strength.

Hence, transverse tension strength may be influenced by the presence of a

resin pocket. However, a larger sampling of photomicrographs is needed to

determine if this is a real trend or simply coincidence.

EVALUATION OF WEIBULL SCALING LAW

Goodness of fit

Before applying the Weibull scaling law, it is prudent to first

establish if the strength data fits an extreme value Weibull distribution.

Figures 37 a-d show the Pearson’s “r” value from equation (9) for the

S2/F584, S2/8552, and IM7/8552 materials three and four point bend

configurations used to evaluate span effects on transverse tension strength.

These data fit the Weibull distribution well. Only two configurations had an

“r” value less than 0.95. Most configurations had “r” values greater than

0.96. As noted earlier, an “r” value close to 1.0 indicates a good fit to the

data.

In order to verify that the Weibull Scaling law is applicable for fiber

reinforced composites, measured data from one volume should be used with

this scaling law to accurately predict the strength of any other volume of the

same material with the same failure mode. The following section documents

attempts to do this for transverse tension strength measurement using the 3-

point and 4-point bending tests utilized in this study.

Three Point Bend Tests

For S2/F584, S2/8552, and IM7/8552 configuration B specimens

tested in three point bending, strengths of the wider specimens were

predicted (fig.38 a-c) using the characteristic strength, σc, and 1/m for the

6.35 mm (0.25 in) wide specimens and the relative volumes of the
23

specimens in tension. This volume consisted of the product of the test span,

specimen width, and one half of the specimen thickness. In addition, as

shown in figure 39 a-d, configuration B specimens were used to predict the

strengths of specimens with identical widths of 6.35 mm (0.25 in) but with

shorter and longer spans (configurations A & C). Because all the

configurations were tested in three point bending, and hence have similar

tensile stress distributions (fig.3b), predictions were made using equation

10. For these cases, the predicted strength decrease with increasing width or

span was between 1.6% and 6.5%.

At first glance, the predictions in figures 38 and 39 appear reasonably

close to the measured strengths. However, as noted earlier, the anticipated

trends in the measured data do not always follow the trends anticipated by

the Weibull theory. In most cases, the Weibull scaling law over predicted

changes in transverse tension strengths in three point bend tests. For the

S2/F584 and S2/8552 glass-epoxy materials, the predicted strength variation

was typically greater than the measured variation in strength with width or

span length. The maximum variation in measured strength with specimen

width was only 1.4%. The maximum variation in measured strength with

span length for the S2/F584 material was only 1.9%. However, the

maximum variation in measured strength with span length for the S2/8552

material was 6.7%. For the IM7/8552 carbon-epoxy, the predicted strength

variation was also greater than the measured variation in strength with

width, but less than the measured variation in strength with span length.

The maximum variation in measured strength with specimen width was

only 0.5%, whereas the maximum variation in measured strength with span

length was 10.4%.

Four Point Bend Tests

The strength of S2/F584, S2/8552, and IM7/8552 four point bend

configurations A2, B2, and B3 were predicted using, σc, and 1/m for

configuration A1 and the relative volumes of the specimens in tension

(fig.40 a-d). This volume consisted of the product of the test span, s, width,

and one half of the specimen thickness. Scaling coefficients were derived in

the appendix for predicting the strengths of configurations A2 and B2 using

the measured strength of quadrant point loading configuration A1. Equation

10 was used to predict the strength of quadrant point loading configuration

B3.

Unlike the 3-point bend cases, the strength predictions for 4-point

bending, shown in figure 40, do not always appear close to the measured

strengths. Also, as noted earlier, the anticipated trends in the measured data
24

do not always follow the trends anticipated by the Weibull theory.

Furthermore, Unlike the three point bending tests, predicted strength

variations between the 4-point bending configurations were often

significantly smaller than the measured variation in strengths.

 For the S2/F584 glass-epoxy materials, predicted strengths for the

four configurations differed by 4 percent or less, whereas measured

strengths for the four configurations differed by 10-17 percent. For the

S2/8552 glass-epoxy materials, predicted strengths for the four

configurations differed by 4 percent or less, whereas measured strengths for

the four configurations differed by 4-22 percent. For the 24-ply IM7/8552

carbon-epoxy material, predicted strengths for the four configurations

differed by 4 percent or less, whereas measured strengths for the four

configurations differed by 1-5 percent. For the 36-ply IM7/8552 carbonepoxy material, predicted strengths for the four configurations differed by 5

percent or less, whereas measured strengths for the four configurations

differed by 2-7 percent. However, for the 36-ply IM7/8552 material,

measured strengths for two configurations (A2 and B2) exceeded the

reference strength for configuration A1.

In addition, 24-ply data were used in equation 10 to predict the

strengths of the 36-ply data for each of the IM7/8552 carbon-epoxy 4-point

bend configurations A1, A2, and B2 (fig. 41). Predicted strengths were

greater than measured strengths for all three configurations.

Comparison of three and four point bend test results

The strengths of S2/F584, S2/8552 and IM7/8552 four point bend

configurations A1, A2, B2, and B3 were predicted using, σc, and 1/m from

the three point bend configuration B. As before, the volume consisted of the

product of the test span, s, width, and one half of the specimen thickness for

each configuration. Equation 13 was used to predict the strength of

quadrant point loading configurations A1 and B3 using the measured

strength of 3-point bending configuration B. Scaling coefficients were

derived in the appendix for predicting the strengths of configurations A2

and B2 using the measured strength of 3-point bending configuration B.

Results for the S2/F584 and S2/8552 glass-epoxy materials are shown

in figures 42 a-b. For both materials, predicted strengths decreased with

increasing span lengths. This trend was also observed for the measured

strengths of the S2/8552 material (figure 42b). However, the change in

strength with span length predicted by the Weibull scaling law was

significantly less than the measured changes in strength with increasing
25

span. For the S2/8552 glass-epoxy materials, predicted strengths for the

four configurations differed from the reference 3-point bend configuration

B strength by 12-15 percent, whereas measured strengths for the four

configurations differed from the reference 3-point bend configuration B

strength by 9-30 percent. For the S2/F584 material, measured strengths also

decreased with increasing span length except for the longest span

configuration B3 (fig.42a). However, configuration B3 specimens were cut

from a different panel (TN3) than the other three configurations tested

(TN6). Hence, this difference may simply reflect the panel-to-panel

variability. However, for the three shortest span configurations that

exhibited the expected trend, the change in strength with span length

predicted by the Weibull scaling law was also significantly less than the

measured changes in strength with increasing span. For the S2/F584 glassepoxy materials, predicted strengths for the three configurations from the

same panel differed from the reference 3-point bend configuration B

strength by 10-13 percent, whereas measured strengths for the four

configurations differed from the reference 3-point bend configuration B

strength by 2-19 percent.

Results for the 24-ply and 36-ply IM7/8552 carbon-epoxy materials

are shown in figures 42 c-d. For both the 24-ply and 36-ply specimens,

predicted strengths decreased with increasing span lengths. However, no

trend was apparent for the measured strengths of either thickness.

Discussion of Weibull Scaling law

As noted earlier, because failure initiates on the bottom surface in

these flexure tests, the differences in strength observed for specimens with

different thicknesses may be attributed more to variability between panels

than to the classical weakest link effect, which assumes a greater probability

of a defect causing failure in a thicker laminate with a larger volume.

Furthermore, equations 10-13 assume that the inverse Weibull slope

parameter (1/m) is a material constant, independent of volume. However,

the three and four point bend test data indicate that the parameter (1/m),

and hence the scatter in the data, varies with specimen size (tables 4-6). For

the three point bend tests, 1/m increased with increasing specimen width

(fig.25) for configuration B specimens; but for the 6.35 mm wide

specimens, the parameter (1/m) decreased with increasing span length

(fig.26). In contrast, for the four point bend specimens, 1/m typically

increased with increasing span length (fig.27). In addition, the parameter

(1/m), also varied to some degree with sample size (see figure 43, for

example). Hence, this scaling law was not adequate for predicting transverse
26

tension strength of heterogeneous, fiber-reinforced, polymer matrix

composites.

CONCLUSIONS

The influence of specimen polishing, specimen configuration, and

specimen size on the transverse tension strength of two glass-epoxy

materials, and one carbon-epoxy material, loaded in three and four point

bending was evaluated. Polishing specimen edges had little, or no, effect on

the transverse tension strength of 90-degree laminate tested in three and

four point bending. However, polishing bottom (tension side) surfaces

resulted in lower strengths. Furthermore, in most cases, specimens with

polished edges and bottom surfaces had greater scatter than unpolished

specimens. Hence, polishing appears to be detrimental to specimen strength

characterization instead of yielding a higher, more accurate, strength as a

result of removing inherent manufacture and handling flaws in the material.

The trend of decreasing strength with increasing specimen width, and

hence increasing volume, that would be anticipated from the Weibull

scaling law was not clearly apparent. In contrast, a decrease in strength with

increasing span was observed for 3-point and 4-point bending for all three

materials. However, this expected scaling was occasionally masked by more

significant panel-to-panel variability. In addition, for the 4-point bending

tests, a decrease in strength with increasing inner and outer span length was

also observed for the two glass-epoxy materials. However, the variation in

strength with span length was not as consistent for the carbon-epoxy

materials. Because failure initiates on the bottom surface in these flexure

tests, the differences in strength observed for specimens with different

thicknesses may be attributed more to variability between panels than to the

classical weakest link effect, which assumes a greater probability of a defect

causing failure in a thicker laminate with a larger volume.

For all three materials, scatter increased with increasing width for

specimens tested in 3-point bending. However, scatter decreased with

increasing 3-point span for all three materials. For all three materials,

scatter in the 4-point bending tests typically increased with increasing span

length. However, this trend was not consistent for all four configurations

tested.

Histograms were plotted showing the frequency of occurrence of the

failure locations relative to the center load nose in 3-point bending and

relative to the inner load noses where the tension stress is a maximum in 4-

point bending. For 3-point bending, failure occurred near, but not always
27

directly under, the center load nose where the beam theory indicates the

tension stress is a maximum, thus illustrating the sensitive to flaws in the

microstructure. For 4-point bending, failures occurred primarily between

the inner load noses, where the beam theory indicates the tension stress is a

maximum. However, some failures also occurred under these load points,

and between the inner and outer load noses, reflecting the sensitive to flaws

in the microstructure. In addition, failures were concentrated more toward

one load nose for the longest span of the S2/8552 glass-epoxy material and

for most configurations of the IM7/8552 carbon-epoxy material.

In most cases, the Weibull scaling law over predicted changes in

transverse tension strengths in three point bend tests and under predicted

changes in transverse tension strengths in four point bend tests.

Furthermore, the Weibull slope varied with specimen configuration, volume

and sample size. Hence, this scaling law was not adequate for predicting

transverse tension strength of heterogeneous, fiber-reinforced, polymer

matrix composites.

REFERENCES

1) Minguet, P.J, and O'Brien, T.K., “Analysis of Test Methods for

Characterizing Skin/Stringer Debonding Failures in Reinforced Composite

Panels”, Composite Materials: Testing and Design, Twelfth Volume, ASTM

STP 1274, August, 1996, p.105-124.

2) O'Brien, T.K., and Sen, J.K., “Tension-Torsion Behavior of Glassepoxy Flexbeam Laminatetes”, ASTM Journal of Composites Technology

and Research, JCTRER, Vol. 20, No.4, October, 1998, pp. 221-226.

3) Weibull, W., “A Statistical Theory of the Strength of Materials”, Ing.

Vetenskaps Akad. Handl. (Royal Swedish Institute Engineering Research

Proceedings) NR151, 1939.

4) O'Brien, T. K. and Salpekar, S. A., “Scale Effects on the Transverse

Tensile Strength of Carbon-epoxy Composites”, Composite Materials:

Testing and Design, Eleventh Volume, ASTM STP 1206, 1993, pp.23-52.

5) Bullock, R.E., “Strength Ratios of Composite Materials in Flexure and

in Tension“, Journal of Composite Materials, Vol.8, April. 1974, p.200.
28

ACKNOWLEDGEMENTS

The authors wish to thank the following individuals who supplied panels for

this study as part of Cooperative Research and Development Agreements

(CRDA) between their companies and the U.S. Army Research Laboratory,

Vehicle Technology Directorate, located at NASA Langley Research

Center.

1) Dr. Joy Sen of the Boeing CoMPany, Mesa, Arizona, for supplying the

S2/F584 panels.

2) Dr. Carl Rousseau of Bell Helicopter, Fort Worth, Texas, for supplying

the S2/8552 panels.

3) Dr. Pierre Minguet, of the Boeing CoMPany, Philadelphia,

Pennsylvania, for supplying the IM7/8552 panels.

In addition, the authors wish to thank Mr. Louis Simmons, of NASA

Langley, for his diligent help in cutting specimens from the panels for all

three materials tested. The authors also wish to thank Mr. Scott Young of

NASA Langley for his help in setting up the small load cell testing

machines. The authors would also like to thank Mr. James Baughman of

Analytical Services and Materials, Inc., for training the co-authors in the

techniques for polishing composite specimens, and Dr. Isabelle Paris for

help in taking photomicrographs of the test specimens.
29

APPENDIX

The Weibull theory was used to describe the probability of survival of a

specimen containing a distribution of flaws throughout its volume and

subjected to a stress distribution σ (x, y, z):

S xyz dxdydz u

o

m

V = −  ( ) −



 























 exp ∫ σ σ , ,

σ

(A.1)

where

m is the Weibull slope,

σo is the characteristic strength,

σu is the threshold stress below which the material will never fail,

V is the volume of the specimen that is being stressed.

The probability of survival for a specimen subjected to a uniform tensile

stress throughout the volume was derived as:

S V t t

t

o

m

= − 



 























 exp

σ

σ

(A.2)

and that the probability of survival for a rectangular specimen under threepoint bending was derived as:

S V

m pt f

pt f

pt

o

m

3

3

3

2

1

2 1 = − 



 



 ( + )





 























 exp

σ

σ

(A.3)

where σf

3pt is the maximum tensile stress at the central point load and Vf3pt is

the volume of the specimen between the supports. Therefore, the ratio of the

median failure stresses in three-point bending and tension was obtained by

setting S3pt=St in equation A.2 and A.3, yielding:

σ

σ

f

pt

t

t

f

pt

m

m

V

V

3

2

3

1

= + 2 1 ( ) 



 



 (A.4)
30

The probability of survival may also be calculated for a rectangular

specimen under four-point loading. The dimensions are defined in Figure

A.1

L

L-l l

2

l

2

x

y

2h

Figure A.1 Four-point bending specimen geometry

The stress distribution in the part of the specimen subjected to tension

(bottom half of the specimen) is:

 

σ

σ

σ

σ

x y

xy

h if x

y

h if x L

x Ly

h if L x L

f

f

f

( , ) =

< <

<<−

− − ( ) −<<



















2

0

2

2 2

2

2

l

l

l l

l

l

(A.5)

Placing equation A.5 into equation A.1 and integrating over the volume of

the specimen that is under tensile stress, yields:

 

S V

m

m

L

m pt f

pt f

pt

o

m

4

4

4

2

1

2 1 = − 



 





+ − 

 

( + )





















exp

σ

σ

l

(A.6)

where Vf

4pt is the volume of the specimen between the support:
31

V bhL f

4pt = 2 (A.7)

Therefore, the ratio of the median failure stress in four-point bending and

tension is obtained by setting S4pt=St in equations A.2 and A.6, yielding:

 

σ

σ

f

pt

t

t

f

pt

m

m

m

m

L

V

V

4 2

4

1

2 1

1

= ( + )

+ − 

























 l (A.8)

The ratio of the median failure stress in three-point and four-point bending is

obtained by setting S3pt=S4pt in equations A.3 and A.6, yielding:

 

σ

σ

f

pt

f

pt

f

pt

f

pt

m

m

m

L

V

V

4

3

3

4

1

1

1

=

+ −







































 l (A.9)

In our study, configuration A1 and B3 are quadrant-point loading

configurations, i.e. l =L/2. Therefore, equation A.8 and A.9 become:

σ

σ

f

pt

t

t

f

pt

m

m

m

V

V

4 2

4

1

4 1

2 = ( + )

( + )





 



 (A.10)

and

σ

σ

f

pt

f

pt

f

pt

f

pt

m

m

V

V

4

3

3

4

1

2

2 = +



 





 



 (A.11)

Equation A.10 and A.11 are shown as equation 12 and 13 in the text and

agree with note 1 concerning quadrant-point loading in reference [5].
32

For configuration A2, 

l

L = 23

 and equation A.9 becomes:

σ

σ

f

pt

f

pt

f

pt

f

pt

m

m

V

V

4

3

3

4

1

3

3 = +













 



 (A.12)

For configuration B2, 

l

L = 13

 and equation A.9 becomes:

σ

σ

f

pt

f

pt

f

pt

f

pt

m

m

V

V

4

3

3

4

1

3

2 3 = +



 





 



 (A.13)

Four-point bending configurations A2 and A1 may be compared by taking

the ratio of equations A.11 and A.12:

σ σ A

pt m

A

m pt

m

2

4

1

1

3 4

2

2

3 = ++













 



 (A.14)

Similarly, for A1 and B2:

σ σ B

pt m

A

m pt

m

2

4

1

1

3 4

2

2

2 3 = ++













 



 (A.15)
Table 1. S2/F584 glass epoxy test sets

Panel (•)Config.&

set number

Length

mm (in)

Polished

surfaces

Average t,

mm (in)

thickness

CV, %m

TO3 B-2 57.2 (2.25) none 4.50 (0.177) 3.2 

B-3 57.2 (2.25) edges 4.67 (0.184) 1.5 

B-4 57.2 (2.25) bottom 4.57 (0.180) 1.8 

TO5 B-B 57.2 (2.25) edges+bottom 4.67 (0.184) 3.7 

*B-C 57.2 (2.25) none 4.75 (0.187) 3.7 

**B-D 57.2 (2.25) none 4.75 (0.187) 3.7 

TN2 B-A 57.2 (2.25) edges 4.37 (0.172) 2.7 

B-B 57.2 (2.25) edges+bottom 4.39 (0.173) 3.1 

*B-C 57.2 (2.25) edges 4.39 (0.173) 2.7 

**B-D 57.2 (2.25) edges 4.39 (0.173) 2.4 

TN3 A 31.8 (1.25) edges 4.37 (0.172) 1.6 

B 57.2 (2.25) edges 4.11 (0.162) 1.5 

C 82.6 (3.25) edges 4.32 (0.170) 1.5 

B3 108 (4.25) edges 4.44 (0.175) 1.7 

TN6 B 57.2 (2.25) edges 4.19 (0.165) 3.0 

A1 57.2 (2.25) edges 4.42 (0.174) 2.9 

A2 82.6 (3.25) edges 4.39 (0.173) 3.1 

B2 82.6 (3.25) edges 4.42 (0.174) 2.8 

All specimens 6.35 mm (0.25 in) wide, except * 12.7 mm (0.5 in) wide and ** 19.1 mm (

(•) see figure 3

33
Table 2. S2/8552 glass epoxy test sets

Panel

Quad

(•) Config.&

set number

Length,

mm (in)

Polished

surfaces

Average t,

mm (in)

thickness

CV, %

S

mm

I-IV B-A 57.2 (2.25) none 5.59 (0.220) 2.5 1

I-IV B-B 57.2 (2.25) edges+bottom 5.54 (0.218) 2.4 1

I-IV *B-C 57.2 (2.25) none 5.59 (0.220) 2.5 1

I-IV **B-D 57.2 (2.25) none 5.59 (0.220) 2.4 1

I B-1 57.2 (2.25) none 5.54 (0.218) 1.1 1

II B-2 57.2 (2.25) edges 5.61 (0.221) 1.4 1

III A 31.8 (1.25) none 5.61 (0.221) 1.5 0.

IV B 57.2 (2.25) none 5.28 (0.208) 1.8 1

I C 82.6 (3.25) none 5.56 (0.219) 1.3 1

II A1 57.2 (2.25) none 5.59 (0.220) 1.5 1

II A2 82.6 (3.25) none 5.64 (0.222) 1.6 5

III B2 82.6 (3.25) none 5.61 (0.221) 1.6 1

IV B3 108 (4.25) none 5.56 (0.219) 1.7 4

All specimens 6.35 mm (0.25 in) wide, except * 12.7 mm (0.5 in) wide and ** 19.1 mm (0.7

(•) see figure 3

34
Table 3. IM7/8552 Carbon epoxy test sets

Panel (•) Config.&

set number

Length,

mm (in)

Polished

surfaces

Average t,

mm (in)

thickness

CV, %

S

mm

24-1 B-A 57.2 (2.25) edges 3.30 (0.130) 4.3 2

B-B 57.2 (2.25) bottom 3.30 (0.130) 4.0 2

B-C 57.2 (2.25) edges+bottom 3.33 (0.131) 2.6 2

B-D 57.2 (2.25) none 3.35 (0.132) 2.9 2

*B-E 57.2 (2.25) none 3.35 (0.132) 3.8 2

**B-F 57.2 (2.25) none 3.33 (0.131) 3.4 2

24-2 A 31.8 (1.25) none 3.35 (0.132) 2.3 0

B 57.2 (2.25) none 3.17 (0.125) 2.7 2

C 82.6 (3.25) none 3.25 (0.128) 2.3 4

A1 57.2 (2.25) none 3.17 (0.125) 4.4 2

A2 82.6 (3.25) none 3.43 (0.135) 2.0 4

B2 82.6 (3.25) none 3.43 (0.135) 2.0 

36-1 A 31.8 (1.25) none 4.44 (0.175) 1.9 

B 57.2 (2.25) none 5.21 (0.205) 1.2 

C 82.6 (3.25) none 4.75 (0.187) 2.3 2

A1 57.2 (2.25) none 5.13 (0.202) 1.4 

A2 82.6 (3.25) none 4.93 (0.194) 2.8 2

B2 82.6 (3.25) none 4.98 (0.196) 2.3 2

B3 108 (4.25) none 5.08 (0.200) 2.1 4

All specimens 6.35 mm (0.25 in) wide, except * 12.7 mm (0.5 in) wide and ** 19.1 mm (0.7

(•) see figure 3

35
Table 4. S2/F584 glass epoxy strength and scatter

Panel Configuration

& set number

Number

tested, n

δmax / tavg Mean Strength,

MPa (Ksi)

CV,

%

Characteris

Strength,

MPa (Ksi

TO3 B-2 35 0.19 102 (14.79) 6.50 104 (15.14

B-3 38 0.19 100 (14.51) 9.30 104 (15.13

B-4 38 0.18 91.1 (13.22) 6.40 93.8 (13.6

TO5 B-B 44 0.17 96.2 (13.95) 7.40 99.3 (14.40

B-C 40 0.21 96.7 (14.02) 8.70 101 (14.59

B-D 35 0.18 97.6 (14.15) 7.50 101 (14.62

TN2 B-A 42 0.21 103 (14.87) 5.70 105 (15.24

B-B 43 0.20 96.9 (14.06) 7.60 101 (14.59

B-C 40 0.21 102 (14.82) 5.50 105 (15.18

B-D 35 0.20 102 (14.85) 6.30 105 (15.27

TN3 A 47 0.07 106 (15.35) 7.80 109 (15.88

B 47 0.23 105 (15.26) 7.40 109 (15.77

C 47 0.47 104 (15.08) 5.80 107 (15.48

B3 48 1.13 89.0 (12.91) 6.20 91.6 (13.28

TN6 B 47 0.21 101 (14.65) 5.60 104 (15.02

A1 47 0.32 98.7 (14.31) 6.60 102 (14.74

A2 47 0.67 87.8 (12.74) 6.90 90.5 (13.13

B2 48 0.62 80.5 (11.68) 10.1 84.3 (12.22

36
Table 5. S2/8552 glass epoxy strength and scatter

Panel

Quad

Config.&

set number

Number

tested, n

δmax / tavg Mean Strength,

MPa (Ksi)

CV,

%

Characteristic

Strength,

MPa (Ksi)

I-IV B-A 35 0.21 140 (20.30) 5.85 144 (20.84) 

I-IV B-B 33 0.21 138 (20.00) 7.00 142 (20.61) 

I-IV B-C 34 0.21 141 (20.43) 8.46 146 (21.21) 

I-IV B-D 27 0.21 139 (20.10) 8.27 144 (20.84) 

I B-1 51 0.21 145 (21.10) 6.99 150 (21.78) 

II B-2 51 0.21 144 (20.94) 6.11 148 (21.51) 

III A 49 0.05 145 (21.03) 7.98 150 (21.78) 

IV B 48 0.33 145 (21.05) 6.31 149 (21.65) 

I C 50 0.45 136 (19.78) 6.25 140 (20.33) 

II A1 52 0.26 131 (18.99) 6.54 135 (19.55) 

II A2 51 0.52 125 (18.07) 7.39 129 (18.69) 

III B2 43 0.55 115 (16.64) 12.17 121 (17.50) 

IV B3 52 0.83 101 (14.67) 8.61 105 (15.22) 

37
Table 6. IM7/8552 Carbon epoxy strength and scatter

Panel Config. &

set number

Number

tested, n

δmax/t

avg MeanStrength,

MPa (Ksi)

CV,

%

Characteristic

Strength,

MPa (Ksi)

24-1 B-A 51 0.49 121 (17.58) 6.76 125 (18.11) 

B-B 46 0.51 120 (17.41) 8.44 125 (18.07) 

B-C 42 0.51 123 (17.85) 5.23 126 (18.27) 

B-D 41 0.54 122 (17.76) 5.57 126 (18.21) 

B-E 44 0.51 117 (16.95) 6.91 120 (17.47) 

B-F 44 0.49 116 (16.80) 7.93 120 (17.39) 

24-2 A 37 0.13 129 (18.71) 6.90 133 (19.29) 

B 37 0.51 117 (16.92) 4.77 119 (17.28) 

C 37 1.24 126 (18.26) 4.26 128 (18.61) 

A1 37 0.72 115 (16.62) 6.17 118 (17.08) 

A2 37 1.34 110 (15.93) 4.88 112 (16.28) 

B2 37 1.44 113 (16.34) 7.80 117 (16.91) 

36-1 A 41 0.11 134 (19.43) 7.20 138 (20.05) 

B 43 0.26 127 (18.49) 6.24 131 (19.01) 

C 43 0.67 121 (17.62) 4.10 124 (17.98) 

A1 43 0.30 107 (15.57) 8.61 111 (16.17) 

A2 43 0.63 111 (16.11) 5.59 114 (16.52) 

B2 43 0.70 115 (16.68) 7.16 119 (17.21) 

B3 42 0.98 98.8 (14.33) 10.40 103 (14.99) 

38
Fig.1 Hydraulic Load Frame

500 lb

Load

cell

39
Fig.2. Test apparatus and specimens

40
41

Configuration s, mm

A 25.4

B 50.8

C 76.2

Config. s, mm /2, mm s- , mm

A1 50.8 12.7 25.4

A2 76.2 25.4 25.4

B2 76.2 12.7 50.8

B3 102 25.4 50.8

s

P/2 P/2

P/2 P/2

 /2 s- /2

P

P/2 P/2

s

(a) 3-point bending (b) 4-point bending

P

P/2 P/2

s s

P/2 P/2

P/2 P/2

(a) 3-point bending (b) 4-point bending

 /2 s- /2

0 0

σmax σmax

Figure 3 – (a) Bending Test Configurations and

 (b)Beam Theory Stress Distributions

3-Point Bending 4-Point Bending
Fig. 4 - Failure Orientation for Three Point Bend Test Sp

Configuration A

Transverse tension

failure oriented at

90 degrees to 

maximum bending stress

42
43

Fig. 5 – Effect of Polishing on (a) Transverse Tension Strength and (b) Scatter

S2/F584, 3-Point bending, Panels TO3 and TO5

0

20

40

60

80

100

120

140 Sig char

Sig mean

Strength,

Mpa

Specimen Type

Unpolished Polished

Edges Polished

Bottom

Polished edges

and bottom

B-2 B-3 B-4 B-B

(n=35) (n=38)

(n=38) (n=44)

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

Scatter

Specimen Type

Unpolished

Polished

Edges

Polished

Bottom

Polished edges

and bottom

B-2 B-3 B-4 B-B

(n=35)

(n=38)

(n=38)

(n=44)
44

Fig. 6 – Effect of Polishing on (a) Transverse Tension Strength and (b) Scatter

S2/F584, 3-Point bending, Panels TO3 and TO5, n=35

0

20

40

60

80

100

120

140 Sig char

Sig mean

Strength,

MPa

Specimen Type

Unpolished Polished

Edges Polished

Bottom

Polished edges

and bottom

n=35

B-2 B-3 B-4 B-B

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

Scatter

Specimen Type

Unpolished

Polished

Edges

Polished

Bottom

Polished edges

and bottom

n=35

B-2 B-3 B-4 B-B
45

Fig. 7 – Effect of Polishing on (a) Transverse Tension Strength and (b) Scatter

S2/F584, 3-Point bending, Panel TN2

0

20

40

60

80

100

120

140

B-A B-B

Sig char

Sig mean

Strength,

MPa

Specimen Type

Polished

Edges Polished edges

and bottom

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

Scatter

Specimen Type

Polished

Edges

Polished edges

and bottom

B-A B-B
46

Fig. 8 – Effect of Specimen Width on (a) Transverse Tension Strength and

(b) Scatter : S2/F584, 3-Point bending, Panels TO3 and TO5, n=35

0

20

40

60

80

100

120

140 Sig char

Sig mean

Strength,

MPa

Specimen Type

Unpolished

6.35 mm

width 12.7 mm

width

19.1 mm 

width

n=35

TO3 B-2 TO5 B-C TO5 B-D

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

Scatter

Specimen Type

Unpolished

6.35 mm

width

19.1 mm

width

12.7 mm

width

n=35

TO3 B-2 TO5 B-C TO5 B-D
47

Fig. 9 – Effect of Specimen Width on (a) Transverse Tension Strength and

(b) Scatter : S2/F584, 3-Point bending, Panel TN2, n=35

0

20

40

60

80

100

120

140 Sig char

Sig mean

Strength,

Mpa

Specimen Type

polished 

edges

6.35 mm

width

12.7 mm

width

19.1 mm

width

n=35

B-A B-C B-D

0.0

0.020

0.040

0.060

0.080

0.10

1/m

CV dec

Scatter

Specimen Type

polished

edges

6.35 mm

width

19.1mm

width

12.7 mm

width

n=35

B-A B-C B-D
48

Fig. 10 – Effect of Panel Variability on (a) Transverse Tension Strength and

(b) Scatter : S2/F584, 3-Point bending, n=35

0

20

40

60

80

100

120

140 Sig char

Sig mean

Strength,

MPa

Specimen Type

Polished

Edges

original

material

new 

material

n=35

T03 B-3 TN2 B-A TN3 B TN6 B

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

Scatter

Specimen Type

Polished

Edges

original

material

new

material

n=35

T03 B-3 TN2 B-A TN3 B TN6 B
49

Fig. 11 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : S2/F584, 3-Point bending, Panel TN3

0

20

40

60

80

100

120

140

A B C

Sig char

Sig mean

Strength,

MPa

Specimen Type

polished 

edges

25.4 mm

span

50.8 mm

span

76.2 mm

span

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

Scatter

Specimen Type

polished

edges

25.4 mm

span

76.2 mm

span

50.8 mm

span

A B C
50

Fig. 12 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : S2/F584, 4-Point bending

0

20

40

60

80

100

120

140

TN6 A1 TN6 A2 TN6 B2 TN3 B3

Sig char

Sig mean

Strength,

MPa

Specimen Type

polished 

edges

s-l = 25.4 mm

s = 50.8 mm s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 101.6 mm

s-l = 50.8 mm

s = 76.2 mm

0.0

0.020

0.040

0.060

0.080

0.10

0.12

1/m

CV dec

TN6 A1 TN6 A2 TN6 B2 TN3 B3

Scatter

Specimen Type

polished

edges

s-l = 25.4 mm

s = 50.8 mm

s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm

s-l = 50.8 mm

s = 101.6 mm
51

Fig. 13 – Effect of Polishing on (a) Transverse Tension Strength and (b) Scatter

S2/8552, 3-Point bending, n=35

0

50

100

150

200

B-A B-B B-1 B-2

Sig char

Sig mean

Strength,

MPa

Specimen Type

Unpolished Polished

Edges Polished edges Unpolished

and bottom

n=35

0.0

0.020

0.040

0.060

0.080

0.10

0.12

B-A B-B B-1 B-2

1/m

CV dec

Scatter

Specimen Type

Unpolished Polished

Edges

Polished edges

and bottom

Unpolished

n=35
52

Fig. 14 – Effect of Specimen Width on (a) Transverse Tension Strength and

(b) Scatter : S2/8552, 3-Point bending, n=25

0

50

100

150

200

B-A B-C B-D

Sig char

Sig mean

Strength,

Mpa

Specimen Type

Unpolished

6.35 mm

width

12.7 mm

width

19.1 mm

width

n=25

0.0

0.020

0.040

0.060

0.080

0.10

0.12

B-A B-C B-D

1/m

CV dec

Scatter

Specimen Type

Unpolished

6.35 mm

width

19.1 mm

12.7 mm width

width

n=25
53

Fig. 15 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : S2/8552, 3-Point bending

0

50

100

150

200

A B C

Sig char

Sig mean

Strength,

Mpa

Specimen Type

unpolished 

25.4 mm

span

50.8 mm

span

76.2 mm

span

0.0

0.020

0.040

0.060

0.080

0.10

0.12

A B C

1/m

CV dec

Scatter

Specimen Type

unpolished

25.4 mm

span

76.2 mm

span

50.8 mm

span
54

Fig. 16 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : S2/8552, 4-Point bending, n=35

0

50

100

150

200

Sig char

Sig mean

Strength,

MPa

Specimen Type

unpolished 

n=35

s-l = 25.4 mm

s = 50.8 mm s-l = 25.4 mm

s = 76.2 mm s-l = 50.8 mm

s = 76.2 mm

s-l = 50.8 mm

s = 101.6 mm

A1 A2 B2 B3

0.0

0.020

0.040

0.060

0.080

0.10

0.12

0.14

0.16

A1 A2 B2 B3

1/m

CV dec

Scatter

Specimen Type

unpolished

n=35

s-l = 25.4 mm

s = 50.8 mm

s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm

s-l = 50.8 mm

s = 101.6 mm
55

Fig. 17 – Effect of Polishing on (a) Transverse Tension Strength and (b) Scatter

24-ply, IM7/8552, 3-Point bending

0

50

100

150

200

B-D B-A B-B B-C

Sig char

Sig mean

Strength,

MPa

Specimen Type

Unpolished Polished

edges

Polished

bottom

Polished edges

and bottom

0.0

0.020

0.040

0.060

0.080

0.10

0.12

B-D B-A B-B B-C

1/m

CV dec

Scatter

Specimen Type

Unpolished

Polished

Edges

Polished edges

and bottom

Polished

Bottom
56

Fig. 18 – Effect of Specimen Width on (a) Transverse Tension Strength and

(b) Scatter : 24-ply, IM7/8552, 3-Point bending

0

20

40

60

80

100

120

140

160

B-D B-E B-F

Sig char

Sig mean

Strength,

MPa

Specimen Type

Unpolished

6.35 mm

width 12.7 mm

width

19.1 mm

width

0.0

0.020

0.040

0.060

0.080

0.10

0.12

B-D B-E B-F

1/m

CV dec

Scatter

Specimen Type

Unpolished

6.35 mm

width

19.1 mm

width

12.7 mm

width
57

Fig. 19 – Effect of Panel Variability on (a) Transverse Tension Strength and

(b) Scatter : 24-ply, IM7/8552, 3-Point bending

0

50

100

150

200

B-D B

Sig char

Sig mean

Strength,

Mpa

Specimen Type

Unpolished

0.0

0.020

0.040

0.060

0.080

0.10

B-D B

1/m

CV dec

Scatter

Specimen Type

Unpolished
58

Fig. 20 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : 24-ply, IM7/8552, 3-Point bending

0

50

100

150

200

A B C

Sig char

Sig mean

Strength,

MPa

Specimen Type

unpolished 

25.4 mm

span 50.8 mm

span

76.2 mm

span

0.0

0.020

0.040

0.060

0.080

0.10

A B C

1/m

CV dec

Scatter

Specimen Type

unpolished

25.4 mm

span

76.2 mm

span

50.8 mm

span
59

Fig. 21 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : 24-ply, IM7/8552, 4-Point bending

0

20

40

60

80

100

120

140

160

A1 A2 B2

Sig char

Sig mean

Strength,

MPa

Specimen Type

unpolished 

s-l = 25.4 mm

s = 50.8 mm s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm

0.0

0.020

0.040

0.060

0.080

0.10

A1 A2 B2

1/m

CV dec

Scatter

Specimen Type

unpolished

s-l = 25.4 mm

s = 50.8 mm

s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm
60

Fig. 22 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : 36-ply, IM7/8552, 3-Point bending

0

50

100

150

200

A B C

Sig char

Sig mean

Strength,

MPa

Specimen Type

unpolished 

25.4 mm

Span 50.8 mm

Span 76.2 mm

Span

0.0

0.020

0.040

0.060

0.080

0.10

1/m

CV dec

Scatter

Specimen Type

unpolished

A B C

25.4 mm

Span

50.8 mm

Span

76.2 mm

Span
61

Fig. 23 – Effect of Span Length on (a) Transverse Tension Strength and

(b) Scatter : 36-ply, IM7/8552, 4-Point bending

0

50

100

150

200

A1 A2 B2 B3

Sig char

Sig mean

Strength,

MPa

Specimen Type

unpolished 

s-l = 25.4 mm

s = 50.8 mm

s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm

s-l = 50.8 mm

s = 101.6 mm

0.0

0.020

0.040

0.060

0.080

0.10

0.12

0.14

A1 A2 B2 B3

1/m

CV dec

Scatter

Specimen Type

unpolished

s-l = 25.4 mm

s = 50.8 mm

s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm

s-l = 50.8 mm

s = 101.6 mm
62

Fig. 24 – Effect of Thickness on Transverse Tension Strength of IM7/8552

(a) 3-Point bending, (b) 4-Point bending

0

50

100

150

200

A B C

24 ply 

36 ply

Strength,

MPa

Specimen Type

unpolished 

25.4 mm

span 50.8 mm

span

76.2 mm

span

0

50

100

150

200

A1 A2 B2

24ply

36ply

Strength,

MPa

Specimen Type

unpolished 

s-l = 25.4 mm

s = 50.8 mm

s-l = 25.4 mm

s = 76.2 mm

s-l = 50.8 mm

s = 76.2 mm
100

110

120

130

140

150

0 5 10 15 20

S2/F584

S2/8552

24pIM7/8552

Strength,

MPa

Width, mm

Fig.25 Influence of Specimen Width on Characteristic Strength

and Scatter for 3-point bending Configuration B

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0 5 10 15 20

S2/F584

S2/8552

24pIM7/8552

1/m

Width, mm

63
Fig.26 Influence of Span Length on Characteristic Strength 

and Scatter for 3-point bending

100

110

120

130

140

150

160

A B C

S2/F584

S2/8552

24pIM7/8552

36pIM7/8552

Strength,

MPa

Configuration

0.000

0.020

0.040

0.060

0.080

0.100

A B C

S2/F584

S2/8552

24pIM7/8552

36pIM7/8552

1/m

Configuration

64
Fig.27 Influence of Span Length on Characteristic Strength 

and Scatter for 4-point bending

80

90

100

110

120

130

140

A1 A2 B2 B3

S2/F584

S2/8552

24pIM7/8552

36pIM7/8552

Strength,

MPa

Configuration

0.000

0.020

0.040

0.060

0.080

0.100

0.120

A1 A2 B2 B3

S2/F584

S2/8552

24pIM7/8552

36pIM7/8552

1/m

Configuration

65
66

0.0

5.0

10.0

15.0

20.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 47

(a) Configuration A

0.0

5.0

10.0

15.0

20.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 47

(b) Configuration B

0.0

5.0

10.0

15.0

20.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 47

( c ) Configuration C

Fig. 28 – Histogram of Failure Locations, S2/F584, 3-point Bending, Panel TN3
67

(a) Configuration A (b) Configuration B

( c ) Configuration C

Fig. 29 – Histogram of Failure Locations, S2/8552, 3-point Bending

0.0

5.0

10.0

15.0

20.0

25.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 49

0.0

5.0

10.0

15.0

20.0

25.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 48

0.0

5.0

10.0

15.0

20.0

25.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 50
68

(a) Configuration A (b) Configuration B

( c ) Configuration C

Fig. 30 – Histogram of Failure Locations, 24-ply IM7/8552, 3-point Bending

0.0

5.0

10.0

15.0

20.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

n = 37

- +

0.0

5.0

10.0

15.0

20.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 37

0.0

5.0

10.0

15.0

20.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 37
69

(a) Configuration A (b) Configuration B

( c ) Configuration C

Fig. 31 – Histogram of Failure Locations, 36-ply IM7/8552, 3-point Bending

0.0

5.0

10.0

15.0

20.0

25.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

n = 41

- +

0.0

5.0

10.0

15.0

20.0

25.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 43

0.0

5.0

10.0

15.0

20.0

25.0

-10 -5 0 5 10

Count

Distance from center load point (mm)

- +

n = 43
70

(a) Configuration A1 (b) Configuration A2

( c ) Configuration B2

Fig. 32 – Histogram of Failure Locations, S2/F584, 4-point Bending

(d) Configuration B3

0.0

2.0

4.0

6.0

8.0

10.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 47

25.4 mm 

inner span

0.0

2.0

4.0

6.0

8.0

10.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 47

25.4 mm

inner span

0.0

2.0

4.0

6.0

8.0

10.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 48

50.8 mm

inner span

0.0

2.0

4.0

6.0

8.0

10.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 48

50.8 mm

inner span
71

(a) Configuration A1 (b) Configuration A2

( c ) Configuration B2

Fig. 33 – Histogram of Failure Locations, S2/8552, 4-point Bending

(d) Configuration B3

0.0

5.0

10.0

15.0

20.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 52

50.8 mm

inner span

0.0

2.0

4.0

6.0

8.0

10.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 52

25.4 mm

inner span

0.0

5.0

10.0

15.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 51

25.4 mm

inner span

0.0

2.0

4.0

6.0

8.0

10.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 43

50.8 mm

inner span
72

(a) Configuration A1 (b) Configuration A2

( c ) Configuration B2

Fig. 34 – Histogram of Failure Locations, 24-ply IM7/8552, 4-point bending

(d) Configuration B3

0.0

5.0

10.0

15.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 37

25.4 mm

inner span

Not

tested

0.0

5.0

10.0

15.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 37

50.8 mm

inner span

0.0

5.0

10.0

15.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 37

25.4 mm

inner span
73

(a) Configuration A1 (b) Configuration A2

( c ) Configuration B2

Fig. 35 – Histogram of Failure Locations, 36-ply IM7/8552, 4-point bending

(d) Configuration B3

0.0

5.0

10.0

15.0

20.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 43

25.4 mm

inner span

0.0

5.0

10.0

15.0

20.0

-40 -30 -20 -10 0 10 20 30

Count

Distance from center (mm)

n = 43

25.4 mm

inner span

0.0

5.0

10.0

15.0

20.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 43

50.8 mm

inner span

0.0

5.0

10.0

15.0

20.0

-40 -30 -20 -10 0 10 20 30 40

Count

Distance from center (mm)

n = 42

50.8 mm

inner span
3-pt, static, polished edge and bottom, high str

3-pt, static, polished edge and bottom, low stre

Resin

pocket

Fig. 36 - Photomicrographs of specimen failure loc

S2/8552 Configuration B

74
75

(a) S2/F584 (b) S2/8552

( c ) 24-ply IM7/8552

Fig. 37 – Weibull Distribution fit, Pearson’s “r” value

(d) 36-ply IM7/8552

0.90

0.92

0.94

0.96

0.98

1.0

A B C A1 A2 B2 B3

all n

n=35

r

Specimen Configuration

0.90

0.92

0.94

0.96

0.98

1.0

A B C A1 A2 B2 B3

all n

n=35

r

Specimen Configuration

0.90

0.92

0.94

0.96

0.98

1.0

A B C A1 A2 B2

all n

n=35

r

Specimen Configuration

0.90

0.92

0.94

0.96

0.98

1.0

A B C A1 A2 B2 B3

all n

n=35

r

Specimen Configuration
76

(a) S2/F584 (TN2) (b) S2/8552

( c ) 24-ply IM7/8552

Fig. 38 – Weibull Strength Prediction, Width Effect, 3-point bending

0

20

40

60

80

100

120

140

160

B-C B-D

Measured

Predicted

Strength,

Mpa

Specimen Type

B-A 

reference

strength

0

50

100

150

200

B-C B-D

Measured

Predicted

Strength,

MPa

Specimen Type

B-A

reference

strength

0

20

40

60

80

100

120

140

160

B-E B-F

Measured

Predicted

Strength,

MPa

Specimen Type

B-D

reference

strength
77

(a) S2/F584 (TN3) (b) S2/8552

( c ) 24-ply IM7/8552

Fig. 39 – Weibull Strength Prediction, Span Effect, 3-point bending

(d) 36-ply IM7/8552

0

20

40

60

80

100

120

140

160

A C

Measured

Predicted

Strength,

Mpa

Specimen Type

B 

reference

strength

0

50

100

150

200

Measured

Predicted

A C

Strength,

MPa

Specimen Type

B

reference

strength

0

20

40

60

80

100

120

140

160

Measured

Predicted

Strength,

MPa

Specimen Type

B

reference

strength

A C

0

50

100

150

200

Measured

Predicted

Strength,

MPa

Specimen Type

B

reference

strength

A C
78

 (a) S2/F584 (b) S2/8552

( c ) 24-ply IM7/8552

Fig. 40 – Weibull Strength Prediction, Span Effect, 4-point bending

(d) 36-ply IM7/8552

0

20

40

60

80

100

120

140

160 measured

predicted

Strength,

MPa

Specimen Type

A1

reference

strength

A2 B2 B3

0

20

40

60

80

100

120

140

160

measured

predicted

Strength,

Mpa

Specimen Type

A1

reference

strength

A2 B2

0

20

40

60

80

100

120

140

160

measured

predicted

Strength,

Mpa

Specimen Type

A1

reference

strength

A2 B2 B3

0

20

40

60

80

100

120

A2 B2 B3

Measured

Predicted

Strength,

Mpa

Specimen Type

A1 

reference

strength
79

 

Fig. 41– Weibull 4-point bending Strength Prediction for 36-ply IM7/8552

0

20

40

60

80

100

120

140

160

Measured

Predicted

Strength,

Mpa

Specimen Type

24-ply

reference

strength

A1 A2 B2
80

 (a) S2/F584 (b) S2/8552

( c ) 24-ply IM7/8552

Fig. 42– Weibull 4-point bending Strength Prediction

(d) 36-ply IM7/8552

0

20

40

60

80

100

120

A1 A2 B2 B3

Measured

Predicted

Strength,

Mpa

Specimen Type

3pt bend Configuration B (TN6)

reference strength

0

20

40

60

80

100

120

140

A1 A2 B2 B3

measured

predicted

Strength,

MPa

Specimen Type

3pt Bend Configuration B

reference strength

0

20

40

60

80

100

120

140

A1 A2 B2

measured

predicted

Strength,

MPa

Specimen Type

3pt Bend Configuration B

reference strength

0

20

40

60

80

100

120

140

A1 A2 B2 B3

measured

predicted

Strength,

MPa

Specimen Type

3pt Bend Configuration B

reference strength
0.10

0.08

0.06

0.04

0.02

0.00

0 10 20 30 40 50 

Fig. 43 - Influence of Sample Size on Scatter 

1/m

CV

CV,

1/m

Sample Size, n

S2/8552 Unpolished

 Configuration A2 

81
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Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

July 2001

3. REPORT TYPE AND DATES COVERED

Technical Memorandum

4. TITLE AND SUBTITLE

Influence of Specimen Preparation and Specimen Size on Composite

Transverse Tensile Strength and Scatter

5. FUNDING NUMBERS

WU 712-10-21-01

6. AUTHOR(S)

T. Kevin O’Brien, Arun D. Chawan, Kevin DeMarco, Isabelle Paris 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center U.S. Army Research Laboratory

Hampton, VA 23681-2199 Vehicle Technology Directorate

 NASA Langley Research Center

 Hampton, VA 23681-2199

8. PERFORMING ORGANIZATION

REPORT NUMBER

 L-18092

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

 National Aeronautics and Space Administration

Washington, DC 20546-0001

 and

 U.S. Army Research Laboratory

 Adelphi, MD 20783-1145

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA/TM-2001-211030

ARL-TR-2540

11. SUPPLEMENTARY NOTES

Chawan: Syracuse University, Syracuse, New York

DeMarco: Virginia Polytechnic Institute & State University, Blacksburg, VA

Paris: National Research Council Associate, NASA Langley Research Center, Hampton, VA

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 24 Distribution: Standard

Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

The influence of specimen polishing, configuration, and size on the transverse tension strength of two glassepoxy materials, and one carbon-epoxy material, loaded in three and four point bending was evaluated. Polishing

machined edges, and/or tension side failure surfaces, was detrimental to specimen strength characterization

instead of yielding a higher, more accurate, strength as a result of removing inherent manufacture and handling

flaws. Transverse tension strength was typically lower for longer span lengths due to the classical weakest link

effect. However, strength was less sensitive to volume changes achieved by increasing specimen width. The

Weibull scaling law typically over-predicted changes in transverse tension strengths in three point bend tests and

under-predicted changes in transverse tension strengths in four point bend tests. Furthermore, the Weibull slope

varied with specimen configuration, volume, and sample size. Hence, this scaling law was not adequate for

predicting transverse tension strength of heterogeneous, fiber-reinforced, polymer matrix composites.

14. SUBJECT TERMS

Composite Materials, Transverse Tensile Strength, matrix cracking, Weibull

15. NUMBER OF PAGES

86

distribution 16. PRICE CODE

A05

1 7. S E CURI TY CLASS IFI CATI O N

O F RE P ORT

Unclassified

1 8. S E CURI TY CLASS IFI CATI O N

O F THI S PAG E

Unclassified

19. SECURITY CLASSIFICATION

 OF ABSTRACT

Unclassified

20. LIMITATION

 OF ABSTRACT

 UL

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z-39-18

298-102