HIGH STRAIN-RATE COMPRESSIVE BEHAVIOR OF
A UNIDIRECTIONAL CARBON/EPOXY COMPOSITE
: EFFECT OF LOADING DIRECTIONS
T. Yokoyama, K. Nakai and T. Odamura
Department of Mechanical Engineering
Okayama University of Science, Okayama 700-0005, Japan
ABSTRACT
The high strain-rate compressive characteristics of a unidirectional carbon/epoxy (T700/2521) composite in all three principal
material directions (or fiber, in-plane transverse and thickness directions) are determined using the conventional split
Hopkinson pressure bar. To avoid uncertainties related to size effects, the specimens in all the tests have the same geometry,
i.e., cubic specimen of nominal size 10 mm. The low and medium strain-rate compressive characteristics are measured using
an Instron testing machine. It is shown that the ultimate compressive strength exhibits the positive sensitivity, while the ultimate
compressive strain (or failure strain) and the absorbed energy up to failure exhibit the negative one in all three directions.
Failure mechanisms of the test composite are also discussed. The present study provides important data for the design of
composite structures in high strain-rate applications.
Introduction
Recently, composite materials have been widely used in a variety of structures, because of their high specific stiffness and
strength, long fatigue life and superior corrosion resistance. Some applications of composite materials involve dynamically
loaded components and structures. The analysis and design of such structures needs precise knowledge of the dynamic
behavior of composite materials. However, the high strain-rate properties of composite materials have been much less
understood, due to the experimental difficulties associated with impact testing. Cantwell/Morton[1], Sierakowski[2],
Hamouda/Hashmi [3] and Al-Hassani/Kaddour [4] have reviewed the experimental set-ups for impact testing of composite
materials, such as gas-gun, drop-weight, Charpy or Izod pendulum, flyer plate and split Hopkinson pressure bars (SHPB). Most
of these testing techniques were designed to conduct lateral impact testing of laminated composites with emphasis on the
evaluation of impact energy and damage modes. The constitutive properties required for accurate material modeling are not
available from the results of these lateral impact tests. The SHPB, originally developed by Kolsky [5], has been widely used and
modified to measure the dynamic properties of engineering materials. More recently, the SHPB has often been applied to
characterize the dynamic behavior of various polymeric composites under compressive, tensile and shear loading conditions.
Most of the experimental studies with the SHPB have been concerned with the strain-rate effects, specimen geometry effects,
reinforcement geometry (or structure) effects, fiber orientation effects and so on.
In the present study, we attempt to examine the effects of strain rate and loading directions along the three principal material
axes on the compressive stress-strain behavior of a unidirectional carbon/epoxy composite. The high strain-rate tests are
performed in the standard SHPB. The low and medium strain-rate tests are performed in an Instron 5500R testing machine. To
avoid uncertainties related to size effects, the identical cubic specimens are used in all compression tests. The effects of strain
rate and loading directions on the overall compressive properties are investigated in detail. Furthermore, failure mechanisms of
the test composite are discussed.
Experimental Details
Test Composite and Specimen Preparation
A 42-ply unidirectional carbon/epoxy (T700/2521) composite laminate with a nominal thickness of 10.04 mm was chosen for
2
testing. The laminates were prepared from pre-impregnated tapes of size 500 x 500 mm and processed in a heat press, i.e.,
o
o
the laminates were heated at a rate of about 2 C/min to a temperature of 125 C held for 1 hr at this temperature under a
pressure of 0.98 MPa and then cooled. The types of reinforcing fiber, matrix resin and fiber volume fraction are given in Table1.
The cylindrical geometry has been usually used in the standard compression tests (see, e.g., ASTM E8). However, the
cylindrical specimens are not machinable from the unidirectional composites, except along the 3-direction, because the
interlaminar and in-plane shear strength are very low. It is, therefore, decided to use a cubic geometry [6], in an attempt to avoid
uncertainties related to size effects. The cubic specimens were cut from the composite laminate and were carefully polished to
ensure smooth surfaces. The longitudinal (or fiber) and in-plane transverse directions are defined as 1 and 2, and the throughthickness direction is defined as 3 (see Figure 1). Compression loading was applied in the 1-, 2- and 3- directions.
Table 2. In-plane tensile properties of unidirectional
carbon/epoxy composite
Table 1. Type of reinforcing fiber and matrix resin used
in unidirectional carbon/epoxy composite
UD-CFRP
L
T
Young's modulus E (GPa) 135
8.6
Tensile strength σＢ (MPa) 2016 37
Fracture strain
εF (%)
1.8
0.5
Mass density ρ(kg/m 3)
1500
L
Property
T
Basic Tensile Properties and Preliminary Testing
The basic in-plane tensile and physical properties of the test composite are given in Table 2. Note that the differences in the
tensile properties between the longitudinal (or fiber) and transverse directions are very significant. To study the effect of
specimen geometry on the compressive stress-strain behavior, preliminary quasi-static tests were carried out on two different
designs of specimen geometry (cylindrical and cubic) in the Instron 5500R testing machine at a crosshead speeds of 1 mm/min.
Figure 2 shows the compressive stress-strain curves in the 3-direction from the two specimens. Both stress-strain curves
coincide well with each other, except for the ultimate compressive strain or failure strain. Consequently, it is confirmed that the
compressive stress-strain curves can accurately be measured from the cubic specimen geometry.
800
3
UD-CFRP
CROSSHEAD VELOCITY : V = 1mm/min
3-DIRECTION
600
CUBIC (10
10
3
10 mm )
CYLINDRICAL (d = 10 mm, h =10 mm)
1 (FIBER)
400
2
X: FAILURE
d = 10 mm
3
200
3 (THICKNESS)
2 (TRANSVERSE)
3 (THICKNESS)
0
2 0
1
Figure 1. Cubic specimen and three loading directions along
three principal material axes
2
1
4
XX
6
COMPRESSIVE STRAIN
8
ε
10
(%)
Figure 2. Static compressive stress-strain curves in 3 (thickness)direction for unidirectional carbon/epoxy composite from two
different designs of specimen
High Strain-Rate Testing
A schematic diagram of the conventional SHPB apparatus is shown in Figure 3. The apparatus consists principally of a steel
striker bar, a gun barrel, two steel Hopkinson bars and associated recording system (not shown). The cubic specimen is
sandwiched between the two Hopkinson bars. Details of the test procedure are given elsewhere [7]. By applying the elementary
theory of elastic wave propagation, we can determine the average nominal strain ε , strain rate ε˙ and stress σ along the gage
length of the cubic specimen from the SHPB test records as [8] (where subscripts 1 and 2 denote the left and right interfaces,
see, the insert in Fig. 3)
ε (t) =
ε˙ (t) =
€
€
u1 (t) − u 2 (t) 2c o
=
h
h
t
∫ {ε (t€′) − ε (t′)} dt′ €
i
t
(1)
0
u˙1 (t) − u˙ 2 (t) 2c o
=
{ε i (t) − ε t (t)}
h
h
(2)
σ (t) =
P2 (t) AE
=
ε t (t)
AS
AS
(3)
under the assumption of dynamic force (or stress) equilibrium across the specimen. Here E, A and co are Young's modulus
2
(=209GPa), the cross-sectional area (64π mm ), the longitudinal elastic wave velocity (= 5205m/s) in the Hopkinson bars,
2
respectively; h and As are the original gage length (=10mm) and cross-sectional area (=100mm ) of the specimen; t is the time
€
from the start of the pulse. Equations (1) to (3), respectively, provide the nominal strain, strain rate and stress in the specimen
as a function of time. Eliminating time t through Eqs. (1) to (3) yields the nominal (or engineering) compressive stress-strain and
strain rate-strain relations for the specimen. Note that the stress and strain are assumed positive in compression.
Figure 3. Schematic diagram of conventional SHPB set-up (recording system not shown)
Results and Discussion
Low and Medium Strain-Rate Tests
The low and medium strain-rate compression tests were conduced in the Instron 5500R testing machine at two different
crosshead velocities of 1mm/min and 100 mm/min. Only under the 1-direction loading, the cubic specimens failed by kink
(shear) band formation or local micro-buckling. Therefore, steel endcaps or rings [9] were attached at both ends of the cubic
specimen to prevent premature kink band formation or longitudinal splitting near the specimen ends.
High Strain-Rate Tests
A number of high strain-rate compression tests were performed with the conventional SHPB. Figure 4 shows typical
GAGE NO.1
εi
εr
800
UD-CFRP
1-DIRECTION
FRONT STRESS
σ1
BACK STRESS
σ2
600
GAGE NO.2
εt
Sweep rate: 100 µs/div
Vertical sensitivity:
Upper trace : 500 mV/div (1130 µε/div)
Lower trace : 500 mV/div (1119 µε/div)
Figure 4. Oscilloscope records from SHPB test on unidirectional
carbon/epoxy composite in fiber (1-) direction
400
200
0
STRIKER BAR VELOCITY :V =15.7 (m/s)
0
100
50
150
TIME t (μs)
Figure 5. Dynamic compressive stress histories at
both ends of specimen
oscilloscope traces from the SHPB test on the specimen in the 1-direction. Figure 5 presents the resulting axial stress histories
at the front and back ends of the specimen. Both stress histories agree well with each other, that is, the assumption of the
dynamic stress equilibrium across the specimen is verified experimentally. Figure 6 shows the resulting compressive stressstrain and strain rate-strain relations from the 1-direction test. Note that there is an abrupt increase in the strain rate at a X on
the dynamic stress-strain curve, corresponding to the failure initiation. After the peak stress, or the ultimate compressive
strength designated as σB, a residual stress of about 200 MPa is visible. This is caused by the sections of the axially split
specimen still being able to carry a compressive load. The final unloading pattern suggests elastic recovery of the specimen.
The compressive stress-strain curves in the 1-direction at three different strain rates are shown in Figure 7. It is observed that
the initial modulus increases remarkably with increasing strain rate, which is consistent with the SHPB test results by Li and
Lambros [10]. This is due to the viscoelastic nature of the epoxy resin matrix itself [11]. The compressive stress-strain curves in
the 2- and 3- directions from the cubic specimens at three different strain rates are given in Figures 8 and 9, respectively. As in
the 1-direction test, the compressive stress-strain curve shows stiffening behavior with increasing strain rate. However, the flow
stress level in the 2- and 3- directions is much lower than that in the 1-direction. In order to evaluate the effects of strain rate and
loading directions on the overall compressive properties, the ultimate compressive strength and strain (or failure strain), and the
absorbed energy up to failure strain are plotted against the strain rate at failure in Figures 10 to 12, where the strain rate at
failure is defined as ε˙f = ε B / t f (tf: failure initiation time), which considers almost linear elastic behavior of the test composite
before failure.
1600
€ €
800
.
UD-CFRP
STRIKER BAR VELOCITY :V =15.7 (m/s)
ε. = 410
ε. =1.5
ε =1.5
1-DIRECTION
1200
σB
ε
B
X
600
800
400
400
200
X: FAILURE
10 -3 (1/s)
X
X
=1.80 (%)
0
0
2
ε(%)
Figure 6. Dynamic compressive stress-strain and strain
rate-strain relations in fiber (1-) direction for unidirectional
carbon/epoxy composite
800
2-DIRECTION
8
ε
10
(%)
Figure 7. Compressive stress-strain curves in fiber (1-)
direction for unidirectional carbon/epoxy composite at
three different strain rates
.
UD-CFRP
ε. = 1030 (1/s)
ε. =1.5 10 -1 (1/s)
ε =1.5 10 -3 (1/s)
600
4
6
COMPRESSIVE STRAIN
800
.
UD-CFRP
ε. = 1150 (1/s)
ε. =1.5 10 -1 (1/s)
ε =1.5 10 -3 (1/s)
3-DIRECTION
600
X: FAILURE
X: FAILURE
400
400
X
200
0
(1/s)
10 -1 (1/s)
0
2
4
6
COMPRESSIVE STRAIN
X
200
X X
8
ε
10
(%)
Figure 8. Compressive stress-strain curves in
transverse (2-) direction for unidirectional
carbon/epoxy composite at three different strain rates
0
0
2
X X
4
6
COMPRESSIVE STRAIN
8
ε
10
(%)
Figure 9. Compressive stress-strain curves in thickness (3-)
direction for unidirectional carbon/epoxy composite at
three different strain rates
In an attempt to quantitatively express the rate dependence of the compressive properties, a straight line was fitted to the data
points in Figures 10 to 12 using linear regression analysis. This resulted in the following three relations:
log σ B = m log ε˙f + log σ 0
log ε B = m log ε˙f + log ε 0
logU B = m log ε˙f + logU 0
(4)
(5)
(6)
€
where m is a strain-rate sensitivity parameter, and σ0, ε0 and U0 are material parameters. The respective parameters in Eqs. (4)
to (6) are determined and summarized €
in Table 3. It is clearly seen that the ultimate compressive strength σB exhibits the
positive strain-rate sensitivity in all three€ directions, whereas the failure strain εB and the absorbed energy UB exhibit the
negative one. The three relations in each column of Table 3 are depicted as the solid lines in each of Figures 10 to 12.
1000
12
INSTRON
É
Ç
Ñ
1-DIRECTION
800
2-DIRECTION
3-DIRECTION
UD-CFRP
SHPB
UD-CFRP
10
H
B
INSTRON
SHPB
É
Ç
Ñ
H
B
1-DIRECTION
2-DIRECTION
3-DIRECTION
8
600
6
400
4
200
2
0
0
10-4
10-3
10-2
10-1
10 0
10 1
10 2
・
10 3
10 4
10-3
10-1
10 0
10 1
102
10 3
10 4
・
εf （1/s）
Figure 11. Effect of strain rate at failure on ultimate
strain of unidirectional carbon/epoxy composite in
three different directions
40
UD-CFRP
10-2
STRAIN RATE AT FAILURE
Figure 10. Effect of strain rate at failure on ultimate
strength of unidirectional carbon/epoxy composite
in three different directions
INSTRON
SHPB
É
Ç
Ñ
Table 3. Parameters of fitted curves for rate dependence of
compressive properties of test composite
H
B
σ B = σ 0 ε˙f m ; εB = ε0 ε˙f m ; U B = U 0 ε˙f m
1-DIRECTION
2-DIRECTION
30
10-4
εf （1/s）
STRAIN RATE AT FAILURE
3-DIRECTION
σB (MPa)
εB (%)
3
UB (MJ/m )
20
σ0
€
10
0
-4
10
-3
10
-2
10
-1
10
10
0
10
STRAIN RATE AT FAILURE
1
10
2
10
3
10
(MPa)
ε0
m
U0
3
(MJ/m )
m
4.38
-0.12
11.13
-0.099
-3
4.12
-0.0564
3.7
-0.0121
-3
4.65
-0.0488
4.45
-0.0206
m
(%)
-3
1-d
550
7.7X10
2-d
185
5.55X10
3-d
183
2.22X10
4
・
εf （1/s）
Figure 12. Effect of strain rate at failure on absorbed energy
up to failure strain of unidirectional carbon/epoxy composite
in three different directions
Failure Modes
The failure modes in the cubic specimens in the three principal material directions under static and impact compression loading
are given in Figure 13. Visual inspections of the statically tested specimens show that in the 1-direction, the specimen failed
mainly by axial splitting, while in the 2-direction, the failure initiated at both edges of the loaded face of the specimen, and
traversed through the length of the specimen at nearly 25 degrees to the free surfaces, and in the 3-direction, the specimen was
split into two parts along a direction that was about 45 degrees from the loading axis. It can be said that static failures of the
specimens in the 2- and 3- directions are mainly dominated by transverse matrix cracking. In the conventional SHPB tests, the
specimen is subjected to repeated compressive loading by the elastic waves traveling back and forth in the input bar after
failure initiation took place in the specimen. Consequently, the dynamically tested specimens are catastrophically disintegrated
into several small pieces and the dynamic failure modes are distributed in several planes. Failure appearance suggests that
longitudinal splitting, interlaminar delamination and transverse matrix cracking are the dominant failure modes in the
dynamically tested specimens.
LOADING DIRECTION
STATIC
1 (FIBER) DIRECTION
IMPACT
3
1
3
2
3
1
2
2 (TRANSVERSE) DIRECTION
3
2
3 (THICKNESS) DIRECTION
Figure 13. Different failure modes in cubic specimens under static and impact compression loading
Conclusions
The influences of strain rate and loading directions on the compressive stress-strain behavior of the unidirectional carbon/epoxy
composite have been studied using the cubic specimens. High strain-rate compression tests were performed with the standard
SHPB over a strain-rate range of 400 to 1200/s. From the present test results, we can draw the following conclusions:
1. The ultimate compressive strength in the 1-direction is 2.5 to 3 times as high as that in other two directions at any strain
rates. However, the ultimate compressive strength in all three directions is very insensitive to strain rate.
2. The ultimate compressive strain (or failure strain) in all three directions greatly decreases with increasing strain rate at
failure.
3. The absorbed energy up to failure strain in the 1-direction significantly decreases with increasing strain rate at failure. In
contrast, that in other two directions remains almost constant.
4. The failure modes in the cubic specimens significantly vary with strain rate and loading directions.
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2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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