Mechanical Testing of Composites and
their Constituents
• Tests done to determine intrinsic material
properties such as modulus and strength for use in
design and analysis (major emphasis here)
• Tests done to determine quality or acceptability of
specific components during manufacturing (minor
emphasis here)
American Society for Testing and
Materials (ASTM) Standards
• Test standards for polymer matrix and metal
matrix composites - ASTM Vol. 15.03 Space
Simulation; Aerospace and Aircraft; Composite
Materials
• Test standards for ceramic matrix composites –
ASTM Vol. 15.01 – Refractories; Activated
Carbon; Advanced Ceramics
TM
HI-NICALON
Type S
CERAMIC FIBER
Direct measurement of fiber
longitudinal properties Ef1 and Sf1(+)
Different ways of mounting fiber specimens on backing strip. (From ASTM
Standard C 1557-03R08. Copyright ASTM International. With permission.)
Different failure modes for resin-impregnated strand test specimens. (From ASTM
Standard D4018-99(2008). Copyright ASTM International. Reprinted with permission.)
Indirect measurement of fiber
transverse modulus Ef2
P = load
P
Prediction
Experimental data
Δ
Δ = deflection
Diametral compression of fiber for measurement of fiber transverse Young’s
modulus. (From Kawabata, S. 1989. In Vinson, J.R. ed., Proceedings of the 4th
Japan–U.S. Conference on Composite Materials, pp. 253–262. CRC Press,
Boca Raton, FL. With permission.)
Tensile measurement of neat resin
properties Em and Sm1(+)
ASTM D638-10 Type I, II, III, IV and V neat resin tensile specimen geometries.
(From ASTM Standard D638-10. Copyright ASTM International. Reprinted
with permission).
ASTM 618-05 Conditioning Plastics and
Electrical Insulating Materials for Testing
Standard Laboratory Atmosphere:
Temperature of 23C (73.4F) and
relative humidity of 50%
Specimen for measurement of neat resin
compressive properties Em and Sm1(-)
Neat resin compressive test specimen. (From ASTM Standard D695-10.
Copyright ASTM International. Reprinted with permission.)
Neat resin compression specimen support jig
Support jig for D695-10 compressive test specimen. (From ASTM Standard
D695-02a. Copyright ASTM International. Reprinted with permission.)
Compression test fixture for neat resin specimen
Compression fixture with ball-and-socket joint to minimize bending.
(From ASTM Standard D695-10. Copyright ASTM International.
Reprinted with permission.)
Three-point bending specimen for flexural properties of neat resin or composite.
(From ASTM Standard D790-10. Copyright ASTM International. Reprinted with
permission.)
M
Bending moment diagram
Constituent Volume Fraction Measurement
• Removal of resin matrix from composite sample
by either chemical digestion with acids or other
chemicals (carbon fiber composites), or resin
burn-off in a furnace (glass fiber composites)
according to ASTM Standard D3171-09
• Computer-aided image analysis of digital
photomicrographs to determine fiber area fractions
of polished composite specimens
Composite tensile specimen for measurement of
longitudinal properties E1 and SL(+)
Tab
Bevel
Angle
Overall Length
Tab
Thickness
Specimen
Thickness
Width
Tab Length
Specimen geometry for ASTM D3039/D3039M-08 standard tensile test.
(Dimensions from ASTM D3039/D3039M-08. Copyright ASTM
International. Reprinted with permission.)
Typical stress-strain curves from D3039 specimen
Longitudinal and transverse strain data at different stresses for [0]8 graphite/epoxy tensile
specimen. (From Carlsson, L.A. and Pipes, R.B. 1989. Experimental Characterization of
Advanced Composite Materials. Prentice-Hall, Inc., Englewood Cliffs, NJ. Reprinted by
permission of Prentice-Hall, Englewood Cliffs, NJ.)
End constraints can cause bending of off-axis
tensile specimens due to shear coupling
Effect of end conditions on deformation of an off-axis tensile specimen
exhibiting shear coupling. (From Pagano, N.J. and Halpin, J.C 1968.
Journal of Composite Materials, 2, 18–31. With permission.)
Importance of specimen length-to-width ratio
 y  xy  0
 x  Ex x
 y   xy  0
 x Q x
11
Ex  Q !!!!!
11
Ex
"Apparent" Modulus (GPa)
140
120
100
80
60
Ex
Series1
40
Series2
Q11
20
0
0
20
40
60
80
100
θ (Degrees)
Variation of “apparent moduli” and with fiber orientation for off-axis tensile test of a
unidirectional T300/934 carbon/epoxy lamina. Lamina engineering constants are
taken from Table 2.2. Conclusion: E x  Q11 except at   0o and   90o
Lamina tensile strength can be “backed out”
from laminate tensile test data
“Backed out” tensile strength data from seven different laminates of IM7G/8551-7
graphite/epoxy. (From Rawlinson, R.A. 1991. Proceedings of the 36th International
SAMPE Symposium and Exhibition, Book 1, pp. 1058–1068. Reprinted by permission
of the Society for the Advancement of Material and Process Engineering.)
Compression test specimen for
ASTM D3410/D3410M-03
D3410 fixtures produce
side-loading rather than
end-loading as in D695
Geometry for tabbed compression test specimen. (From ASTM Standard
D3410/D3410M-03 (Reapproved 2008). Copyright ASTM International.
Reprinted with permission.)
Cutaway view of compression test fixture for ASTM
D3410/D3410M-03
Cross-section view of ASTM D3410/D3410M-03 (Reapproved 2008)
compression test fixture. (From ASTM Standard D3410/D3410M-03
(Reapproved 2008). Copyright ASTM International. Reprinted with permission.)
Sandwich beam specimen for face sheet compression
ASTM D5467/D5467M-97 (Reapproved 2004) sandwich beam specimen
for face sheet compression. (From ASTM Standard D5467/D5467M-97
(Reapproved 2004). Copyright ASTM International. Reprinted with permission.)
Test fixture for ASTM D 6641/D 6641M- 09
combined loading compression (CLC) test method
Test fixture for ASTM D6641/D6641M-09 CLC test method. (From ASTM
Standard D6641/D6641M-09. Copyright ASTM International. Reprinted
with permission.)
Test fixture for compressive residual strength of polymer
composite plates. (From ASTM D 7137/D 7137M-07)
Test fixture for compressive residual strength of polymer composite plates.
(From ASTM D7137/D7137M-07. Copyright ASTM International.
Reprinted with permission.)
Comparison of shear test methods for composites.
(From Adams, D.F., 2005 High Performance Composites, 13(5), pp. 9–10)
Iosipescu test fixture for shear strength
and stiffness in all three shear stress states
(ASTM D5379)
Test fixture for V-notched rail shear test
Test fixture for V-notched rail shear test. (From ASTM Standard
D7078/D7078M-05. Copyright ASTM International. Reprinted with permission.)
Different test specimen arrangements for
V-notched rail shear test. (From ASTM
Standard D7078/D7078M-05. Copyright
ASTM International. Reprinted with
permission.)
Rail shear test fixtures, ASTM D4255/D4255M-01
(Methods A and B)
Rail shear test fixtures. (From ASTM Standard D4255/D4255M-01(2007).
Copyright ASTM. Reprinted with permission.)
Analysis of Rail Shear Test Procedure A
Shear stress along loading axes x,y)
 xy
P

Lt
(10.8)
Strain transformation from normal strain along strain
gage axis x’ oriented at 45o from x to shear strain along
(x,y) axes
 xy  2 x '
(10.10)
Therefore the shear modulus along loading axes is
 xy
P
Gxy 

 xy 2 Lt x '
where P, L, t, and εx’ are all measured quantities.
If the specimen is unidirectional, and (x,y) are aligned
with (1,2), then Gxy  G12 and if this specimen is
loaded to failure
 xy  S LT
 450 Laminate test for in-plane shear modulus G12
x


Shear stress from applied stress: 12 2
Shear strain from measured normal strains: 12   xo  oy
Shear modulus:

G  12
12 12
Off-axis tensile test for indirect
measurement of G12
x
Ex 
x
When  x  0,  y   xy  0
x
1
(2.39)
 Ex 

S 11 x S 11
Young’s modulus, Ex
2
y
x
x
1
or
Ex 
1
1 4  2v12
1  2 2 1 4
c  

c s 
s

E1
E2
 E1 G12 
(2.40)
Off-axis tensile test for indirect
measurement of G12
• Conduct off-axis tensile test to measure Ex at
some fiber orientation θ
• Conduct longitudinal tension test to measure E1
and υ12
• Conduct transverse tension test to measure E2
• Use above results in Eq. 2.40 to calculate G12
Limitation of the off-axis tensile test for measurement of
shear properties of an orthotropic lamina
The off-axis tensile test of the orthotropic lamina shown below can be used to determine the
shear modulus, 𝐺12 , by using the first of the transformation equations for elastic constants
(Equations (2.40)) if the properties E1, E2, and ν12 are known from separate tensile tests along the
1 and 2 axes, and Ex is determined from the off-axis test at angle θ.
strain gages
y
1
2
x
o
45
x
Alternatively, 𝐺12 can be determined from the off-axis tensile test data by using the definition
𝐺12 =
𝜏 12
𝛾12
where the shear stress 𝜏12 and the shear strain 𝛾12 can be determined from applied stress, x,
along with the measured strains from the strain gages and the stress and strain transformation
equations. This is true even though there is a biaxial stress state (𝜎1 , 𝜎2 , 𝜏12 ) acting along the 1,2
axes.
Limitation of the off-axis tensile test for measurement of
shear properties of an orthotropic lamina (continued)
Usually, however, the purpose of such a mechanical test is to determine not only the
slope of the linear part of the stress-strain curve (in this case, the shear modulus, 𝐺12 ), but
the failure stress, or strength (in this case, the shear strength, 𝑆𝐿𝑇 ). The off-axis tensile
test cannot be expected to yield accurate measurement of 𝑆𝐿𝑇 because of the biaxial stress
state (𝜎1 , 𝜎2 , 𝜏12 ). For example, if we apply the Tsai-Hill failure criterion for the biaxial
stress state along the 1,2 axes, the failure condition is given by
𝜎12
𝑆𝐿2
-
𝜎1 𝜎2
𝑆𝐿2
+
𝜎22
𝑆𝑇2
+
2
𝜏 12
2
𝑆𝐿𝑇
=1
Clearly, the failure here is due to all three stress components (𝜎1 , 𝜎2 , 𝜏12 ), and we can
only have an accurate measurement of the shear strength 𝑆𝐿𝑇 when we have the pure
shear condition 𝜎1 = 𝜎2 = 0, 𝜏12 ≠ 0, in which case the Tsai-Hill criterion reduces to
𝜏12 = 𝑆𝐿𝑇 . Such a pure shear condition is not possible with the off-axis tensile test.
ASTM D2344/D2344M-00 Short beam shear test
for interlaminar strength (parallel fibers only)
P
d
b
L
Note: not recommended for measurement of intrinsic
properties, only for quality control and specification
Short beam test specimen with
shear and moment diagrams
Mechanics of
materials stresses
Shear stress
 xy
VQ

Ib
Bending stress
Mz
x 
I yy
Short beam shear test
• Short beam fails due to interlaminar shear stress
• Long beam fails due to either tensile or
compressive normal stress on bottom or top of
beam, respectively
• Questions about accuracy of mechanics of
materials beam theory equations for stresses in
short beams where support effects may not be
negligible (Whitney’s theory of elasticity analysis)
Whitney’s conclusion: Stress distributions from mechanics of materials
beam theory are only accurate far away from loads and supports
Comparison of predicted interlaminar shear stress distributions from theory of
elasticity (solid curves) and beam theory (dotted curve) for a 50 ply short beam shear
specimen with length-to-depth ratio of 4. Differences are particularly large near
loading point (section C) and support points (section A). (From Whitney, J. M. 1985.
Composites Science and Technology, 22, 167-184. With permission)
Interlaminar Fracture Tests
DCB analysis – treat one half of DCB as cantilever beam
(ASTM D5528-01 (2007)e3)
Mode I strain energy release rate
P 2 s 96P 2a 2
GI 

2t a Efxt 2h3
(10.16)
Mixed mode bending (MMB) test for Mode I
and Mode II delamination testing
(ASTM Standard D6671)
Test fixture for MMB test. (From ASTM Standard D6671/D6671M-06.
Copyright ASTM International. Reprinted with permission.)
Single fiber fragmentation specimen for
measurement of fiber/matrix interfacial
shear strength
Test procedure: Load specimen until fiber starts to break up into
fragments, then measure “critical lengths” of fragments, then
calculate interfacial shear strength from theory of discontinuous
fiber composites developed in Chap. 6
Single-fiber fragmentation specimen developed by Drzal et al. (From Drzal, L.T.,
Rich, M.J., and Lloyd, P.F. 1982. Journal of Adhesion, 16, 1–30.; Drzal, L.T., Rich, M.J.,
Koenig, M.F., and Lloyd, P.F. 1983. Journal of Adhesion 16, 133–152. With permission.)
Microindenter test for fiber/matrix
interfacial shear strength
Test procedure: Load end of fiber in compression with microindenter
probe until fiber slips with respect to matrix, then use finite element
analysis of specimen to estimatefiber/matrix interfacial shear strength
Microindenter test for fiber/matrix interfacial strength. (From Mandell, J.F., Grande, D.H.,
Tsiang, T.H., and McGarry, F.J. 1986. Composite Materials: Testing and Design (Seventh
Conference), ASTM STP 893, pp. 87–108. American Society for Testing and Materials,
Philadelphia, PA. Copyright ASTM. Reprinted with permission.)
Microbond test for fiber/matrix
interfacial shear strength
resin droplet
fiber embedded in
resin droplet
applied tensile force
Problem: Difficult to reproduce the composite
resin matrix cure condition in a small droplet.
Source: From McDonough, W.G., Herrera-Franco, P.J., Wu, W.L., Drzal, L.T., and
Hunston, D.L. 1991. In Advanced Materials/Affordable Processes, Proceedings of
23rd International SAMPE Technical Conference, Kiamesha Lake, NY, pp. 247–258.
Society for Advancement of Material and Process Engineering, Covina, CA. Reprinted
by permission of the Society for the Advancement of Material and Process Engineering.
ASTM D5766 open hole tension test – similar to
ASTM D3039 tensile test, but with central hole
(a)
(b)
(c)
(d)
Acceptable test failure modes for ASTM D 5766/D 5766M-07 standard test method
for open hole tensile strength (a) failure mode codes (b) LGM (c) AGM (d) MGM.
(From ASTM D5766/D5766M-07. 2009. Copyright ASTM International. Reprinted
with permission.)
ASTM D5961 bearing test – Procedure A
Fixture assembly for ASTM D5961/D5961M-08 (Procedure A) double shear test
method for bearing response of polymer matrix composite laminates. (From
ASTM D5961/D5961M-08. 2009. Copyright ASTM International. Reprinted
with permission.)
ASTM D7332 fastener pull-through test
Test fixture and specimen for ASTM standard test method for measuring the fastener
pull-through resistance of a fiber-reinforced polymer matrix composite, Procedure B.
(From ASTM D 7332/D 7332M-07e1. Copyright ASTM International. Reprinted
with permission.)
Measurement of Viscoelastic and
Dynamic Properties
Creep test parameters
Total strain = εo+ε(t)
Strain
gage
Strain, ε
Test
specimen
Creep strain, ε(t)
Initial elastic strain, εo
Time, t
Constant applied stress, σo
Elastic compliance = εo/ σo
Creep compliance = ε(t)/σo
Measurement of orthotropic creep compliances
Measurement of orthotropic creep compliances
Apply constant stresses and measure time-dependent strains
for applied longitudinal stress,  1 :
S11 (t ) 
1 (t )
1
where strain 1 (t ) is measured
S21 (t ) 
 2 (t )
1
where strain  2 (t ) is measured
For applied transverse stress  2 :
S22 (t ) 
 2 (t )
2
where strain  2 (t ) is measured
S12 (t ) 
1 (t )
2
where strain 1 (t ) is measured
For off-axis creep test with applied stress  x and measured
strains  x and  y at   45o
Stress transformation equation:
12   cos(45o )sin(45o ) x  0.5 x
Strain transformation equation:
 12
2
  cos(45o )sin(45o ) x  cos(45o )sin(45o ) y

x y
2
Therefore for time-dependent strains:  12 (t )   x (t )   y (t )
and the measured shear creep compliance is
S66 (t ) 
[ x (t )   y (t )]
 12 (t )
2
12
x
Empirical power law for creep compliance
S(t)  S0  S1t
n
where S(t) is the creep compliance, S0 the initial elastic
compliance, and S1 and n the empirically determined parameters
Important modes of specimen deformation
for vibration tests
Flexural
Torsional
Longitudinal
Natural frequencies of flexural and torsional modes of vibration are usually
in the range of typical excitation frequencies, but longitudinal modes are
usually well above this range. Automated Dynamic Mechanical Analyzers
(DMA) typically operate in the flexural mode.
Range of typical
excitation frequencies
Longitudinal
modes
Response
Flexural and
torsional modes
Frequency
Representation of automated DMA plot showing storage
modulus, loss modulus and loss factor (tan δ) vs. temperature.
Storage Modulus, E’
Loss Modulus, E”
Loss Factor, η = tan δ
Temperature
Material Damping
• Energy dissipation within a material under cyclic or oscillatory stress
• Characterized by stress-strain hysteresis loop under steady-state
vibration and decaying oscillation under free vibration
• Area enclosed by hysteresis loop and rate of decay are proportional to
damping factor
• Damping is linear if it is independent of oscillation amplitude
Hysteresis loop in
steady state vibration
Free vibration decay
Complex modulus of linear viscoelastic material from stressstrain hysteresis loop ( assuming perfectly elliptical loop)
Energy dissipated per cycle
D cd   a cos 
2

Energy stored at maximum
displacement
U  1 b d cos
22
Loss factor
  D  ad cos
a
2U 2 2  1 b d cos b


22
Storage Modulus
b
E'  2  b
d cos 2d cos
Free vibration decay method
xo
1
Logarithmic decrement   n ln x
n
Loss factor   
(for light damping)
Impulse-frequency response method
Impulse-frequency response apparatus for
flexural vibration of cantilever beam specimens
Modal frequencies
0
-20
FRF
-40
-60
-80
-100
0
400
800
1200
Frequency (Hz)
1600
2000
Modal frequencies and loss factors found by curve-fitting
to frequency response curve at peak frequencies
Single Degree of Freedom Curve Fit to Peak in Frequency
Response Curve by Half Power Bandwidth Method
f
Amplitude
Peak for
nth mode


X
0.707 X
fn
Damping Loss Factor 
Frequency
 
f
fn
f n = natural frequency of nth mode
f
= bandwidth at half power points
(10.36)
Measurement of Hygrothermal Properties
Measurement of glass transition temperature, Tg
ASTM D7028-07e1 test for determination of DMA Tg
from storage modulus vs. temperature plot
B
DMA Tg
A
E’
Temperature
ASTM 696-08 test for measurement of
coefficient of thermal expansion, CTE
Measure thermal strain,  T , or the change in length, L,
of a specimen of original length Lo which is subjected
to a temperature change T in an environmental chamber
Measured coefficient of thermal expansion is
T
L
CTE   

T L0 T
(10.37)
Variation of measured longitudinal and transverse thermal strains for
unidirectional Kevlar 49/epoxy and S-glass/epoxy with temperature.
(From Adams, D.F., Carlsson, L.A., and Pipes, R.B., 2003. Experimental
Characterization of Advanced Composite Materials. CRC Press, Boca
Raton, FL. With permission.)
Measured CTEs for undirectional orthotropic lamina
Measured longitudinal CTE
1T
L1 1
1 

T
L01 T
Measured transverse CTE

L2 1
2 

T
L02 T
T
2
Weight % absorbed
moisture, M
ASTM D5229 test for measurement of
moisture absorption properties
M2
Saturation moisture content, Mm
Through-thickness Diffusivity
 h   M 2  M1
Dz   
 
 4M m   t2  t1
2
M1




2
(10.40)
Example of test done to determine quality or acceptability
of specific components during manufacturing
ASTM D2290 Split Disk Test for tensile strength
of filamentwound composite rings
Load
Composite ring specimen
Split disk loading fixtures
Exploded view of test fixture for ASTM D2290
Split Disk Test for Rings