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Measurement of shear properties of fibre composites
Measurement of shear properties of fibre composites Part 1. Evaluation of test methods C.C. CHIAO, R.L. MOORE, and "1-.7-. CHIAO
Six methods have been evaluated of measuring the shear properties of a fibre composite consisting of a 65-volume % aramid fibre in an epoxy. The shear data obtained from each of the methods was compared with the 90°-wound thin-walled tube torsion test, which was used as the standard. Based on that comparison, it is recommended, for the present, that the -+ 45 ° off-axis laminate tensile shear test be used for determining the shear properties of composites. The method is simple, inexpensive, and reliable, and its shear stress/strain response is the closest to that of the 90 ° wound thin-walled tube torsion test.
A knowledge of shear properties is invaluable whenever the interfacial bonding or matrix failure of a composite is critical - such as in a composite structure subjected to compression loading. However, because so many methods have been developed to measure shear, there is a great deal of confusion as to which shear method to use. Ideally, a test method should produce pure shear. However, this is difficult to attain because of coupling effects. In addition to producing pure shear, the authors felt that a good shear test method should
Torsional shear of a thin-walled tube
•
give reproducible results;
•
provide all shear properties;
•
require no special equipment for specimen preparation;
In this test, a torque is applied to a thin-walled circular cross-section tube about its longitudinal axis (Fig. la). Care must be taken to ensure that only pure torque is applied to the specimen. The applied torque subjects the wall of the specimen to a pure shear stress, which is uniform around the circumference and along the length of the specimen. Since the wall thickness is small compared to the mean radius of the tube, the shear strain gradient through the thickness is negligible. The specimen must be mounted concentrically to prevent the development of bending moments, and must be free to move axially to avoid the introduction of axial force. Bert and co-workers ~,2 described how to prevent buckling during testing.
•
be capable of being tested on readily available testing machines;
The shear stress r, shear strain % and shear modulus G, can be calculated from the following expressions:
•
have a simple data reduction procedure.
The objective of this study is to evaluate a number of selected shear testing methods based on the above criteria and to recommend a good method for measuring shear properties of fibre composites.
T
r --z
"r
=
a
-
~n"Trr~t
a45o
--
(1)
e-4so
(2)
SELECTED METHODS
Numerous methods are available for measuring shear properties, a few simple and promising ones were selected for evaluation. They are described below. R.L. Moore and T.T. Chiao are with the Lawrence Livermore Laboratory, University of California, Livermore, California 94550 and C.C. Chiao is with the Dow Chemical Co, Walnut Creek, California
COMPOSITES . JULY 1977
7"
(3)
7 where T is the applied torque, t is the wall thickness, rm = (ri + ro)/2 (Fig. l a), and e+45o and e-45o are the strains measured at + 45 ° and --45 ° to the longitudinal direction of the tube. Whitney and co-workers 3 found that
161
dad irection
Fibr dire
a
90 °- wound thin-walled tube, torsional shear
10* off-axis laminate tensile shear
d Load direction same as fibre direction
SJ
00- wound composite rod, torsional shear
b
Fibre directions
e - - . ~
Load direction
Unidirectional grooved laminate, interlominor tensile shear
g
Midplane
Midplone symmetry
~'450 off-axis laminate, tensile shear
P/2
C
Fig. 1
Schematic representations of specimens for various shear tests
tensile test of a + 45 ° laminate which is symmetrically laminated about the midplane (Fig. 1c).
the torsion tube is the most desirable shear test specimen from the viewpoint of applied mechanics. Torsional shear o f a unidirectional composite rod
In Adams and Thomas's method, a torque is applied to a moulded rod to determine the shear properties of a composite (Fig. lb). The same care has to be taken as in torsional shear of a tube to ensure that only pure torque is applied to the specimen. Also, the rod radius must be kept small.
The shear stress r for a solid rod is maximum (rmax) at the surface of the rod. The values of "rmax and shear strain (7) can be calculated from
Petit derived the relations from laminated plate theory and presented expressions that allow the shear stress/strain curve to be incrementally reproduced from the + 45 ° laminate stress/strain curve. The data reduction was simplified by Rosen. 7 He showed that the shear stress/strain relation could be obtained directly from the average applied tensile stress (Ox) and the resulting strains (ex, ey) by using the transformation law between components in different coordinates. Thus,
r 2T 7"max
--
?ira
Or =
- -
l
(5)
where T is the applied torque, r is the radius of the rod, I is the length of the specimen between clamps, and 0 is the angle of the twist. These equations can be used for unidirectional composites up to the torsional proportionality limit s if fibres are oriented parallel to the axis of the specimen, as shown in Fig. 1b. Tensile shear o f +- 4 5 ° off-axis laminates
Petit's 6 technique for determining the shear stress/strain relation is based on the stress/strain results of a uniaxial
OX
(6)
2
(4) ')'
162
P/2
Short-beam interlominor shear
(7)
----- Ex - - e y
Hahn 8 further verified and defined the conditions under which the above expressions hold.
Tensile shear o f 10 ° off-axis laminates
Chamis and Sinclair 9 proposed the 10 ° off-axis tensile test to determine the in-plane shear stress/strain diagram, modulus, and fracture stress. The specimens can be cut from a unidirectional laminate sheet. Fig. 1d shows the schematic representation of the test specimen. The shear properties can be calculated using the following expressions: r
= 0.171 Ox
(8)
COMPOSITES. JULY 1977
7
=
EXPERIMENTAL MATERIALS AND PROCEDURES
-- 0.456 %° -- 0.857 el2OO + 1.313 e2aoo
(9)
(60 ° delta rosette) or
7
=
-- 1.282 %° + 1.879 e45o
-
-
0.598 eseo
(rectangular rosette)
(10)
Reference 9 also gives tile advantages and disadvantages of this test method.
Materials
An aramid fibre, poly(p-phenylene terephthalamide) (commercially called Kevlar 49) was used in the composites. The fibre is a 1420 denier yarn (filament diameter 11.9/am) without sizing. It was vacuum-dried and stored in a desiccator until used. The fibre surface is smooth, but the microstructure of single filaments is not homogeneous, la' Table 1 summarizes the two epoxy systems used in this study. Epoxy system No. 1 was used for all the composites unless otherwise indicated.
Interlaminar tensile shear of a grooved laminate
The tensile-shear of a flat plate specimen that has two grooves cut on opposite faces (Fig. le) is described in detail in ASTM D - 2 7 3 3 J ° The mean values of the shear stress over the central plane are obtained by
Specimen preparation
All fibre composite specimens had a nominal fibre content of 65 volume %. 1. Flat laminates
r
P -wl
=
(11)
where P is the applied stress, w is the width of the specimen, and ! is the length between the grooves. Markham and Dawson 11 made a theoretical analysis of this method. The analysis included the consideration of the stress distribution between the grooves rather than the mean shear stress. Using a series of specimens with various groove spacings, they calculated the shear stress after deriving a material constant, k, by a process of successive approximation. See Reference 11 for data reduction. Interlaminar shear of a short beam
This method, based on elementary beam theory, has been used to obtain the interlaminar shear strength of unidirectional reinforced plasticsJ 2 The concept is illustrated in Fig. 1 f where a short beam specimen is supported by two rods; P is the applied load. The shear stress distribution along the thickness of the specimen is a parabolic function which reaches a maximum value at the centre of the thickness (neutral axis) of the specimen and zero at the upper and lower surfaces. Thus,
Flat laminates were formed by winding fibres on fiat mandrels with a filament winding machine; the fibres were impregnated with the epoxy resin during the winding operation. After winding, fiat plates were placed on each side of the mandrel, shimmed to the desired thickness, and cured in a heated press with just enough pressure to force out excess resin and press the plates down to the shims. The 10 ° offaxis specimens and interlaminar shear specimens were wound as unidirectional laminates while the -+ 45 ° off-axis laminate specimens were wound with alternate layers at 90 ° to each other. Specimens were cut from the cured laminates with a carborundum friction-type saw that was water cooled. The saw was lowered to the laminate and passed over the surface in successive steps cutting a little deeper each pass until the material was parted. Cutting in this manner produced speciments with smooth sides and stable dimensions. 2. Tubular specimens
The tubular specimens were wound on cylindrical mandrels on which the steel end fittings were secured. In this way the end fittings became an integral part of the composite tube. After clare, the mandrel was drawn from the tube with a hydraulic ram.
3P "rul t
=
--
(12)
4A
where P is the load at failure, Tult is the shear strength, and A is the cross-sectional area. Table 1. Formulations and cure cycles of the two epoxy systems used in the fibre composites tested in this study
Epoxy No 1
Epoxy system (wt ratio)
Cure cycle
Dow DER-332/Jefferson Jeffamine T-403 (100/39)
24 h at 60°C
Dow XD-7818/Union Carbide ER L-4206/Uniroyal Tonox 6040 (80/20/29.1)
2.5 h at 80°C, plus 2 h at 160°C,
COMPOSITES. JU LY 1977
3. Rod specimens
The round rod specimens were wound on a special fourpiece mandrel that formed the unidirectionally wound part into a cylindrical rod when cured in a press. After cure the rods were cut to length and bonded in the fixtures with a structural adhesive. Testing
All specimens were conditioned for 24 hours at 23°C and 50% relative humidity and were tested under the same temperature and relative humidity. 1. Tensile shear
The + 45 ° tensile shear specimens were made by cutting a 90 ° laminate on the diagonal. Specimens were 25 mm wide, 300 mm long, and 2 mm thick. Strain gauges were bonded in the centre of the specimen at 0 ° and 90 °. The specimens
163
were tested in tension at a crosshead speed of 5 mm/min and in most cases were tested to a point where the strain gauges failed when surface cracks developed. Fig. 2a shows a typical specimen after testing.
...........
_ ......
i.....
The 10 ° off-axis laminate specimens were cut from a unidirectional laminate at an angle of 10 ° to the fibre direction; specimens were 12.5 mm wide, 250 mm long, and 2 mm thick. Thin aluminium end tabs were bonded to the ends leaving a gauge length of 180 mm. The edges of one set of specimens were coated with a more flexible epoxy resin. Three strain gauges were bonded to the specimens at either 0 °, 90 °, and 45 °, or 0 °, 120 °, and 240 ° to the specimen direction and then the specimens were tested in tension to failure at a crosshead speed of 2 mm/min. Fig. 2b shows typical specimens after failure. The grooved laminate specimens for interlaminar tensile shear testing were cut from a unidirectional laminate. The specimens were 150 mm long, 20 mm wide, and 2 mm thick with grooves cut from opposite sides half way through the thickness o f the specimens. These grooves were spaced at different lengths (l) between the slots for each group of specimens (Fig. le). The specimens were tested in tension to failure at a crosshead speed of 5 mm/min. 2. Torsional shear
The torsional shear tubes had an internal diameter of 38 mm and a wall thickness of ~ 1 mm. The tubes were ~ 90 mm long between transition build-up points. Strain gauges were bonded at the centre of the specimen at -+ 45 °. The specimens were tested in torsion on a servo-controlled, hydraulically powered torsion machine which maintained a zero load in the axial direction. The specimens were loaded at a rotational rate of 2°/min and tested to failure. Fig. 2c shows a specimen after testing. The unidirectional rods were 6.35 mm in diameter with a length of ~ 180 mm between end fixtures. Strain gauges were bonded to the specimens in the centre at -+ 45 °. The rod specimens were tested in torsion at a rotational rate of 5°/min on the same machine as above to a point where the load dropped off, indicating a failure of the matrix or of the fibre/resin bond. Fig. 2d shows a rod specimen after shear failure. 3. Short-beam shear
The short-beam interlaminar shear test has been studied previously. 14
EXPERIMENTAL RESULTS
d Fig. 2 Typical specimens after shear failure (a) + 45 ° off-axis laminate, tensile shear; (b) 10 ° off-axis laminate, tensile shear (the top specimen has coated edges, the bottom one does not); (c) 90°-wound thin-walled tube, torsional shear; (d) O°-wound composite rod, torsional shear
164
Tables 2 - 4 and Figs 3 - 9 present the experimental results of all six methods. In the tables, the secant modulus values at 0.5% shear strain are used, which are the same as the initial modulus because the shear stress/strain curves are all linear at this small strain (see Figs 3 - 9 ) . The failure stresses for the thin-walled tube and the 10 ° off-axis specimens corresponded to their actual fracture stresses. The rod and the -+ 45 ° off-axis specimens do not actually break apart at the point of shear failure; they simply lose their integrity. Therefore, the shear failure stresses for the rod and the -+ 45 ° laminates were arbitrarily chosen using the 0.2% offset method (Fig. 10). The in-plane shear stress/strain curves are compared in Figs 1 1 - 1 3 . (Interlaminar shear testing does not produce a stress/strain curve.)
C O M P O S I T E S . JU L Y 1977
Table 2. Comparison of shear properties obtained from various test methods (material: 65 volume % aramid fibre in epoxy No 1) Shear failure stress MPaa CV*, % Torsional shear of 90°wound thin tube
Shear strain a at failure stress % CV*, %
Shear modulus at 0.5% shear strain, MPa CV*, %
No of specimens
31.3±2.0
6.0
2.02±0.20
9.4
1744±39
2.1
6
31.3±2.8 32.5±3.0
7.2 7.5
1.82±0.20 2.06±0.17
8.8 6.8
1965±89 1758±21
3.6 1.0
5 5
29.4±0.7
2.0
1.73±0.05
2.3
1923±113
4.7
5
27.9±1.6 31.7±1.4
2.4 3.6
t.68±0.05 1.89±0.06
2.4 2.6
1889±20 1875±90
0.8 3.9
5
Tensile shear of 10° off-axis laminates Coated edges Bare edges
19.4±1.1 19.1±2.9
3.6 9.4
0.97±0.08 1.03±0.21
5.2 12.6
2082±188 1903±191
5.7 6.3
4 4
Interlaminar shear of a short beam b Flat specimen Curved specimen
36.8±0.9 38.4±0.9
5.1 4.1
Interlaminar tensile shear of grooved laminates
7.7 to 23.5 °
Torsional shear of a 0°wound composite rod Strain measured with gauges Strain from angle of twist Tensile shear of ± 45 ° off-axis lamintes Midplane symmetry (7-layer) Midplane symmetry (7-layers repeated) Nonsymmetrical (8-layer)
18 15 See
a Plus or minus (+-) values indicate 95% confidence limits b Data f r o m Reference 14
Table 4 c See Table 4 for details * Coefficient of variation
Table 3. Shear data from rod torsion shear test (material: 65 volume % aramid fibre in epoxy No 2) Shear strain at failure stress as measured by
Shear modulus at 0.5% shear strain as measured by
Specimen No
Shear failure stress, MPa
Angle of twist, %
Strain gauges, %
Angle of twist, MPa
Strain gauges, MPa
1
29.2
2.33
1.52
1110
2034
2
29.4
2.37
1.49
1448
2179
3
33.2
2.26
1.75
1340
1999
4
26.4
1.75
1.55
1531
1779
5
30.4
1.97
1.59
1462
1999
Mean
29.7
2.14
1.58
1378
1998
2.5
0.27
0.10
165
143
Standard deviation
DISCUSSION
The torsional shear of a thin-walled tube can theoretically produce the desired state of pure shear. However, it is not a simple test that can be used easily. Therefore, a simple
COMPOSITES . JULY 1977
method has been sought that can provide shear properties comparable to those obtained from thin-tube torsion. With this in mind, the shear stress/strain curves from various methods were compared with those from the thin-tube torsion test (Fig. 11 ). The shear modulus for all methods is
165
Table 4. Effect of groove depth on the maximum interlaminar shear stress calculated from tensile shear of grooved laminates Mean shear stress between grooves,
Specimen
1/t a
Maximum shear stress,
MPa
C.V., %
No of specimens
With grooves cut to centre ply or slightly under
5.43 8.12 11.94 12.58 15.67
15.2 16.7 14.0 10.9 10.7
5.8 10.0 22.0 12.3 8.1
5 5 4 5 5
With grooves cut through centre ply or slightly over
3.94 5.87 7.87 9.73 10.98
14.14 11.73 8.49 8.18 7.44
6.2 6.6 7.8 4.3 11.0
3 4 4 4 3
4.41 6.03 8.21 10.40 11.61
5.20 5.42 5.05 4.12 3.76
13.5 7.2 6.4 2.8 4.2
5 5 5 5 5
With over-cut grooves
k
MPa
0.17
14.03 23.05 28.42 23.31 28.50
Av = 23.46
0.22
12.26 15.15 14.70 17.51 17.97
Av = 15.52
0.21
4.82 6.86 8.71 9.00 9.17
Av = 7.71
a See Fig. 2e
generally higher than that of the thin-tube torsion tests. However, the shear failure stresses from rod torsion and -+45 ° off-axis laminate tensile shear tests are comparable to those of the thin-tube torsion tests; the shear failure stress from the 10 ° off-axis laminate tensile shear tests is significantly lower. For torsional shear of a unidirectional composite rod, the shear strain was measured with both angle of twist and strain gauges. For a given shear stress, the shear strains calculated from angles of twist are consistently higher than 40
X Fracture
50
o o;E 20
/
g,
//
I0
/ Six specimens
,# o"
o15
,'5
215
Shear strain (%) Fig. 3 Shear stress/strain diagram f r o m torsional shear of 90°-wound thin-walled tube
166
those from strain gauges. This, in turn, affects the calculated shear modulus (Fig. 12). Rod torsion tests of the aramid in another resin system show the same trend (Table 3). Although the shear stress/strain curve calculated from the angle of twist is closer to that of the thin-tube torsion result, it may very well be coincidence. It is very possible that shear of the adhesives between the rod specimen and its end fixtures contributed in some degree to the angle of twist. By using strain guage measurements, the calculated shear modulus was found to be about 13% higher and the failure stress about the same as that obtained from the thintube torsion test (Fig. 11). The rod torsion test is subjected to the same equipment and test restrictions as the thinwalled tube torsion test. In addition, a special mould is needed for winding the composite rod specimens. The tensile shear of 10 ° off-axis laminates does not require special equipment. In the first attempt to evaluate this method specimens with bare-cut edges were used. The resulting fracture strength was approximately two-thirds of that from thin-walled tube torsion tests. A second evaluation was therefore performed. This time the edges of the speciments were coated with flexible epoxy with the intention of eliminating the possibility of cracks starting at the edges. The results did not show significant improvement in strength (Table 2). The tensile shear test of 10 ° off-axis laminates (coated edges) shows that the shear modulus is approximately 19% higher and the fracture stress 38% lower than that of the thin-walled tube torsion test. Hahn and Whitney Is compared this method with the tensile shear test of -+ 45 ° off-axis laminates using graphite/epoxy composites. They found that the 10 ° off-axis tensile shear test resulted in significant shear coupling, and that it gave a higher shear modulus, lower failure stress, and lower failure strain than the -+ 45 ° off-axis laminate tensile shear test. This is consistent with the results of the present study (Table 2 and Fig. 11).
COMPOSITES. JULY 1977
40
40
X Sheor foilure ® m
X Frocture
3o
3O
(3_
n
~ 2c
-'- 2C in
N
u)
IC
/ ~ /
7` from str.oin
gouges
F~ve spemmens
o
' 0.5
I'0
I'5
%/o/ 0% ,'c
2 0'
2 I5
1
2!o
1.0 15 Sheor strain (%)
Shear stroin(%) Fig. 4 Shear stress/strain diagram f r o m torsional shear o f 0 ° unidirectional composite rods; shear strain was obtained f r o m strain gauge measurements
Four specimens Edges cooled
i
2.5
Fig. 6 Shear stress/strain diagram f r o m 10 ° off-axis tensile shear test o f specimens with coated edges
40
4o r It[]
i
X Shear foilure i 30
X Fracture
30F
o_ :E 20
/
v)
/
I0
o_ v a~
/
/"
V
2o
113
/ 7" from ongle of lwist Five specimens
[m
Four specimens Edges not coated
S
o~
o15
~i 0
,15
zlo
25t
Sheor stroin (%)
0'5
,15
li.O Shear stroin (%)
21o
215
Fig. 5 Shear stress/strain diagram f r o m torsional shear o f 0 ° unidirectional composite rods; shear strain was obtained f r o m angle o f twist
Fig. 7 Shear stress/strain diagram from 10 ° off-axis tensile shear test o f specimens with uncoated edges
The -+ 45 ° off-axis laminate tensile shear test results in a shear modulus about 10% higher and a shear failure stress about 6% lower than that of the thin-walled tube torsion test. As can be seen in Fig. 11, its shear stress/strain response is closest to that of the thin-walled tube torsion shear test. Sims 16 compared this method with published thin-wall tube torsion data of graphite/epoxy composites and also found good agreement in shear stress/strain responses. Midplane symmetry should be observed in fabricating the test specimen to avoid bending-stretching coupling. However, in many cases this symmetry condition is either inconvenient or impossible to achieve. Whitney ~7 showed that the severity of coupling effects is inversely proportional to the number
of plies of the composite. For nonsymmetrical lay-ups, Chiao and Hamstad is recommended eight or more plies to minimize this coupling effect. Therefore, in this study, both 7-layer (midplane symmetry) and 8-layer (nonsymmetrical) specimens were used. The resulting stress/strain responses were practically the same (Fig. 13). After completing this test, the authors of the present work concluded that the -+45° off-axis laminate tensile shear test was simple and reproducible.
COMPOSITES
. JULY
1977
The interlaminar tensile shear of grooved laminates was evaluated and the interlaminar shear strength was claculated by Markham and Dawson's method. ~1 As can be seen in
167
34 5
Table 4, the shear strengths vary depending on the cut of the grooves. It is very difficult to cut the grooves to the depth of precisely half the specimen thickness. A slight undercut gives a higher shear strength than an overcut (Table 4). Some tearing in the fibre was observed during the testing of the undercut specimens. Bending and peeling were also observed during testing, especially for the overcut specimens. This may be the reason for the low shear strength obtained. Although this method is relatively simple, it provides only shear strength data - not the shear stress/ strain curve. Moreover, even the shear strength data is unreliable.
29 27.2
j-
Shear failure
Stress-sfram curve
The shear strength of the specimens, as measured by the short-beam interlaminar shear test, was approximately 20%
Shear fatlure
X
Shear Fig. 10 Obtaining stress/strain curve
I
I
I
05
1.0 Shear
Fig. 8 off-axis
I
strain
I%)
shear failure stress from a * 45” using the 0.2% off-set method
25
(%I
Shear stress/strain diagram from tensile laminates with midplane symmetry
shear
of
f 45’
X Shear failure
Shear **
Q
w
k”
30-
failure
X Thin-wall
paint tube.tarsian
A
Unidlrectlanaf rod, torsion
0
i
0
05
Fig.
Eight-layer-laminate specimens
d I
05
I
I
IO
I5 Shear
Fig. 9 off-axis
168
Shear stress/strain laminates without
diagram midplane
_I
20
25
s1raln (%) from tensile symmetry
shear
Comparison
tensile
tensile
I.5 Shear sk6in (%)
of shear
stress/strain
20
25
curves
higher than that measured by the thin-walled tube torsion test (Table 2). The method is simple and inexpensive but again provides only shear strength data. In a separate report l4 the authors evaluated this method and found that the results often could not be reproduced even for specimens made by the same process and tested by the same person.
IO-
FIW
11
IO
composite
45O off -axis
0 IO0 off-axis
Oo
off-axis
1
20
1.5
strain
of
+ 45”
Despite the above noted advantages and reliability of the + 45” off-axis laminate tensile shear test, some qualifications should be noted. Rather complicated failure mechanisms may be involved in the test in an interactive manner. That is, the sources of failure may include the combined effects
COMPOSITES.
JULY 1977
40
40
Strain measured with gouges t
Strain from angle of twist
\
,,
3oi
30
o/
n
= 20
o 20
a
g I0
I0
0 Seven-layer A
015
ItO ' 15 Shear strain (%)
2 0'
I
O~
2.5
Fig. 12 Comparison of torsional shear stress/strain curves o f 0 ° unidirectional composite rods obtained f r o m different strain measuring devices
RECOMMENDA TION
5
Based on the experimental results obtained in this study it is recommended that the + 45 ° off-axis laminate tensile shear test be used for the measurement of the shear properties of fibre composites. Although this method gives a slightly higher shear modulus, it has the following merits:
6
•
simple specimen fabrication;
•
conventional tensile test;
•
no end tab required;
•
simpledata reduction;
•
inexpensive.
2
3
7 8 9 10 11 12 13
A C K N O W L E D G E M E N TS
The authors would like to thank R.M. Christensen for the helpful discussion and critical review of the manuscript. It should be noted that reference to a company or product name does not imply approval or recommendation of the product by the University of California or the US Energy Research and Development Administration to the exclusion of others that may be suitable.
REFERENCES 1
Bert, C.W., Mayberry, B.L., and Ray, J.D. 'Behaviour of Fiber
C O M P O S I T E S . JU L Y 1977
15
210
I
25
Fig. 13 Comparison of shear stress/strain curves f r o m tensile shear of -+ 45 ° off-axis lamiantes o f 7 and 8 layers
4
good reproducibility;
II0
Sheor stroin (%)
of fibre/matrix debonding, failure in matrix phase, and (on a larger scale) debonding of lamina. Also, it must be recognized that no single test method provides general failure information on composites in all possible states of stress. For this reason recourse must be made to the ultilization of a general failure criterion, with its basis established by several different types of tests. Despite these qualifications the -+ 45 ° off-axis laminate tensile shear test does seem to provide pertinent and reliable special failure information.
•
0 5~
Eight~loyer
14 15 16 17 18
Reinforced Plastic Laminates Under Uniaxial, Biaxial and Shear Loadings', US Army Aviation Materials Lab, A YLABS-TR-6886, AD-684321 (1971) Bert, C.W. 'Experimental Characterization of Composites in 'Structural Design and Analysis', Part II', Composite Mater 8 edited by Broutman, L.J. and Krock, V.H. (Academic Press, New York, 1975) Whitney, J.M., Stansbarger, D.L., and Howell, H.B. 'Analysis of the Rail Shear Test - Applications and Limitations', J Composite Mater 5 (1971) p 24 Adams,D.F. and Thomas, R.L 'Advances in Structural Composites', Nat Soc Aerospace Mater Process Eng Syrup 12, paper A C-5 'Proposed Method of Test for Torsional Shear Properties of Reinforced Plastics, ASTM Committee working document Petit, P.H. 'A Simplified Method of Determining the Inplane Shear Stress-Strain Response of Unidirectional Composites', ASTMSTP460, (1969) p 83 Rosen, B.W. 'A Simple Procedure for Experimental Determination of the Longitudinal Shear Modulus of Unidirectional Composites', J Composite Mater 6 (1972) p 552 Hahn, H.T. 'A Note on Determination of the Shear Stress-Strain Response of Unidirectional Composites, J Composite Mater 7 (1973) p 383 Chamis,C.C. and Sinclair, J.H.'10 ° Off-Axis Tensile Test for lnterlaminar Shear Characterization of Fiber Composites' NASA Tech Note D-8215 (1976) ASTM Designation D-2733 Part 30 (1974) Markham,M.F. and Dawson, D. Composites 6 (1975) p 173 ASTM Designation D-2344 (1972) Chiao, T.T., Hamstad, M.A., Marcon, M.A. and Hanafee, J.E. 'Filament Wound Kevlar 49/Epoxy Press Vessels', Lawrence Livermore Laboratory, Livermore, California, Report NASACR-134506 (UCRL-51466) (1973) Chiao, C.C. and Moore, R.L. 'Evaluation of Interlaminar Shear Test for Fiber Composites', Lawrence Livermore Laboratory, Livermore, California Report UCRL-51 766 (1975) Hahn, H.T. and Whitney, J.M. Air Force Materials Laboratory Wright-Patterson AFB, Ohio, private communication (1976) Sims,D.F. 'In-Plane Shear Stress-Strain Repsonse of Unidirectional Composite Materials,J Composite Mater 7 (1973) p 124 Whitney, J.M. 'Bending-Extensional Coupling in Laminated Plate Under Transverse Loading', J Composite Mater 3 (1969) p 20 Chiao, T.T. and Hamstad, M.A. 'Testing of Fiber Composite Materials', Proc Int Conf on Composite Mater, AIME {Geneva, April 1975} Vol 2 (1976) p 884
169
Six methods have been evaluated of measuring the shear properties of a fibre composite consisting of a 65-volume % aramid fibre in an epoxy. The shear data obtained from each of the methods was compared with the 90°-wound thin-walled tube torsion test, which was used as the standard. Based on that comparison, it is recommended, for the present, that the -+ 45 ° off-axis laminate tensile shear test be used for determining the shear properties of composites. The method is simple, inexpensive, and reliable, and its shear stress/strain response is the closest to that of the 90 ° wound thin-walled tube torsion test.
A knowledge of shear properties is invaluable whenever the interfacial bonding or matrix failure of a composite is critical - such as in a composite structure subjected to compression loading. However, because so many methods have been developed to measure shear, there is a great deal of confusion as to which shear method to use. Ideally, a test method should produce pure shear. However, this is difficult to attain because of coupling effects. In addition to producing pure shear, the authors felt that a good shear test method should
Torsional shear of a thin-walled tube
•
give reproducible results;
•
provide all shear properties;
•
require no special equipment for specimen preparation;
In this test, a torque is applied to a thin-walled circular cross-section tube about its longitudinal axis (Fig. la). Care must be taken to ensure that only pure torque is applied to the specimen. The applied torque subjects the wall of the specimen to a pure shear stress, which is uniform around the circumference and along the length of the specimen. Since the wall thickness is small compared to the mean radius of the tube, the shear strain gradient through the thickness is negligible. The specimen must be mounted concentrically to prevent the development of bending moments, and must be free to move axially to avoid the introduction of axial force. Bert and co-workers ~,2 described how to prevent buckling during testing.
•
be capable of being tested on readily available testing machines;
The shear stress r, shear strain % and shear modulus G, can be calculated from the following expressions:
•
have a simple data reduction procedure.
The objective of this study is to evaluate a number of selected shear testing methods based on the above criteria and to recommend a good method for measuring shear properties of fibre composites.
T
r --z
"r
=
a
-
~n"Trr~t
a45o
--
(1)
e-4so
(2)
SELECTED METHODS
Numerous methods are available for measuring shear properties, a few simple and promising ones were selected for evaluation. They are described below. R.L. Moore and T.T. Chiao are with the Lawrence Livermore Laboratory, University of California, Livermore, California 94550 and C.C. Chiao is with the Dow Chemical Co, Walnut Creek, California
COMPOSITES . JULY 1977
7"
(3)
7 where T is the applied torque, t is the wall thickness, rm = (ri + ro)/2 (Fig. l a), and e+45o and e-45o are the strains measured at + 45 ° and --45 ° to the longitudinal direction of the tube. Whitney and co-workers 3 found that
161
dad irection
Fibr dire
a
90 °- wound thin-walled tube, torsional shear
10* off-axis laminate tensile shear
d Load direction same as fibre direction
SJ
00- wound composite rod, torsional shear
b
Fibre directions
e - - . ~
Load direction
Unidirectional grooved laminate, interlominor tensile shear
g
Midplane
Midplone symmetry
~'450 off-axis laminate, tensile shear
P/2
C
Fig. 1
Schematic representations of specimens for various shear tests
tensile test of a + 45 ° laminate which is symmetrically laminated about the midplane (Fig. 1c).
the torsion tube is the most desirable shear test specimen from the viewpoint of applied mechanics. Torsional shear o f a unidirectional composite rod
In Adams and Thomas's method, a torque is applied to a moulded rod to determine the shear properties of a composite (Fig. lb). The same care has to be taken as in torsional shear of a tube to ensure that only pure torque is applied to the specimen. Also, the rod radius must be kept small.
The shear stress r for a solid rod is maximum (rmax) at the surface of the rod. The values of "rmax and shear strain (7) can be calculated from
Petit derived the relations from laminated plate theory and presented expressions that allow the shear stress/strain curve to be incrementally reproduced from the + 45 ° laminate stress/strain curve. The data reduction was simplified by Rosen. 7 He showed that the shear stress/strain relation could be obtained directly from the average applied tensile stress (Ox) and the resulting strains (ex, ey) by using the transformation law between components in different coordinates. Thus,
r 2T 7"max
--
?ira
Or =
- -
l
(5)
where T is the applied torque, r is the radius of the rod, I is the length of the specimen between clamps, and 0 is the angle of the twist. These equations can be used for unidirectional composites up to the torsional proportionality limit s if fibres are oriented parallel to the axis of the specimen, as shown in Fig. 1b. Tensile shear o f +- 4 5 ° off-axis laminates
Petit's 6 technique for determining the shear stress/strain relation is based on the stress/strain results of a uniaxial
OX
(6)
2
(4) ')'
162
P/2
Short-beam interlominor shear
(7)
----- Ex - - e y
Hahn 8 further verified and defined the conditions under which the above expressions hold.
Tensile shear o f 10 ° off-axis laminates
Chamis and Sinclair 9 proposed the 10 ° off-axis tensile test to determine the in-plane shear stress/strain diagram, modulus, and fracture stress. The specimens can be cut from a unidirectional laminate sheet. Fig. 1d shows the schematic representation of the test specimen. The shear properties can be calculated using the following expressions: r
= 0.171 Ox
(8)
COMPOSITES. JULY 1977
7
=
EXPERIMENTAL MATERIALS AND PROCEDURES
-- 0.456 %° -- 0.857 el2OO + 1.313 e2aoo
(9)
(60 ° delta rosette) or
7
=
-- 1.282 %° + 1.879 e45o
-
-
0.598 eseo
(rectangular rosette)
(10)
Reference 9 also gives tile advantages and disadvantages of this test method.
Materials
An aramid fibre, poly(p-phenylene terephthalamide) (commercially called Kevlar 49) was used in the composites. The fibre is a 1420 denier yarn (filament diameter 11.9/am) without sizing. It was vacuum-dried and stored in a desiccator until used. The fibre surface is smooth, but the microstructure of single filaments is not homogeneous, la' Table 1 summarizes the two epoxy systems used in this study. Epoxy system No. 1 was used for all the composites unless otherwise indicated.
Interlaminar tensile shear of a grooved laminate
The tensile-shear of a flat plate specimen that has two grooves cut on opposite faces (Fig. le) is described in detail in ASTM D - 2 7 3 3 J ° The mean values of the shear stress over the central plane are obtained by
Specimen preparation
All fibre composite specimens had a nominal fibre content of 65 volume %. 1. Flat laminates
r
P -wl
=
(11)
where P is the applied stress, w is the width of the specimen, and ! is the length between the grooves. Markham and Dawson 11 made a theoretical analysis of this method. The analysis included the consideration of the stress distribution between the grooves rather than the mean shear stress. Using a series of specimens with various groove spacings, they calculated the shear stress after deriving a material constant, k, by a process of successive approximation. See Reference 11 for data reduction. Interlaminar shear of a short beam
This method, based on elementary beam theory, has been used to obtain the interlaminar shear strength of unidirectional reinforced plasticsJ 2 The concept is illustrated in Fig. 1 f where a short beam specimen is supported by two rods; P is the applied load. The shear stress distribution along the thickness of the specimen is a parabolic function which reaches a maximum value at the centre of the thickness (neutral axis) of the specimen and zero at the upper and lower surfaces. Thus,
Flat laminates were formed by winding fibres on fiat mandrels with a filament winding machine; the fibres were impregnated with the epoxy resin during the winding operation. After winding, fiat plates were placed on each side of the mandrel, shimmed to the desired thickness, and cured in a heated press with just enough pressure to force out excess resin and press the plates down to the shims. The 10 ° offaxis specimens and interlaminar shear specimens were wound as unidirectional laminates while the -+ 45 ° off-axis laminate specimens were wound with alternate layers at 90 ° to each other. Specimens were cut from the cured laminates with a carborundum friction-type saw that was water cooled. The saw was lowered to the laminate and passed over the surface in successive steps cutting a little deeper each pass until the material was parted. Cutting in this manner produced speciments with smooth sides and stable dimensions. 2. Tubular specimens
The tubular specimens were wound on cylindrical mandrels on which the steel end fittings were secured. In this way the end fittings became an integral part of the composite tube. After clare, the mandrel was drawn from the tube with a hydraulic ram.
3P "rul t
=
--
(12)
4A
where P is the load at failure, Tult is the shear strength, and A is the cross-sectional area. Table 1. Formulations and cure cycles of the two epoxy systems used in the fibre composites tested in this study
Epoxy No 1
Epoxy system (wt ratio)
Cure cycle
Dow DER-332/Jefferson Jeffamine T-403 (100/39)
24 h at 60°C
Dow XD-7818/Union Carbide ER L-4206/Uniroyal Tonox 6040 (80/20/29.1)
2.5 h at 80°C, plus 2 h at 160°C,
COMPOSITES. JU LY 1977
3. Rod specimens
The round rod specimens were wound on a special fourpiece mandrel that formed the unidirectionally wound part into a cylindrical rod when cured in a press. After cure the rods were cut to length and bonded in the fixtures with a structural adhesive. Testing
All specimens were conditioned for 24 hours at 23°C and 50% relative humidity and were tested under the same temperature and relative humidity. 1. Tensile shear
The + 45 ° tensile shear specimens were made by cutting a 90 ° laminate on the diagonal. Specimens were 25 mm wide, 300 mm long, and 2 mm thick. Strain gauges were bonded in the centre of the specimen at 0 ° and 90 °. The specimens
163
were tested in tension at a crosshead speed of 5 mm/min and in most cases were tested to a point where the strain gauges failed when surface cracks developed. Fig. 2a shows a typical specimen after testing.
...........
_ ......
i.....
The 10 ° off-axis laminate specimens were cut from a unidirectional laminate at an angle of 10 ° to the fibre direction; specimens were 12.5 mm wide, 250 mm long, and 2 mm thick. Thin aluminium end tabs were bonded to the ends leaving a gauge length of 180 mm. The edges of one set of specimens were coated with a more flexible epoxy resin. Three strain gauges were bonded to the specimens at either 0 °, 90 °, and 45 °, or 0 °, 120 °, and 240 ° to the specimen direction and then the specimens were tested in tension to failure at a crosshead speed of 2 mm/min. Fig. 2b shows typical specimens after failure. The grooved laminate specimens for interlaminar tensile shear testing were cut from a unidirectional laminate. The specimens were 150 mm long, 20 mm wide, and 2 mm thick with grooves cut from opposite sides half way through the thickness o f the specimens. These grooves were spaced at different lengths (l) between the slots for each group of specimens (Fig. le). The specimens were tested in tension to failure at a crosshead speed of 5 mm/min. 2. Torsional shear
The torsional shear tubes had an internal diameter of 38 mm and a wall thickness of ~ 1 mm. The tubes were ~ 90 mm long between transition build-up points. Strain gauges were bonded at the centre of the specimen at -+ 45 °. The specimens were tested in torsion on a servo-controlled, hydraulically powered torsion machine which maintained a zero load in the axial direction. The specimens were loaded at a rotational rate of 2°/min and tested to failure. Fig. 2c shows a specimen after testing. The unidirectional rods were 6.35 mm in diameter with a length of ~ 180 mm between end fixtures. Strain gauges were bonded to the specimens in the centre at -+ 45 °. The rod specimens were tested in torsion at a rotational rate of 5°/min on the same machine as above to a point where the load dropped off, indicating a failure of the matrix or of the fibre/resin bond. Fig. 2d shows a rod specimen after shear failure. 3. Short-beam shear
The short-beam interlaminar shear test has been studied previously. 14
EXPERIMENTAL RESULTS
d Fig. 2 Typical specimens after shear failure (a) + 45 ° off-axis laminate, tensile shear; (b) 10 ° off-axis laminate, tensile shear (the top specimen has coated edges, the bottom one does not); (c) 90°-wound thin-walled tube, torsional shear; (d) O°-wound composite rod, torsional shear
164
Tables 2 - 4 and Figs 3 - 9 present the experimental results of all six methods. In the tables, the secant modulus values at 0.5% shear strain are used, which are the same as the initial modulus because the shear stress/strain curves are all linear at this small strain (see Figs 3 - 9 ) . The failure stresses for the thin-walled tube and the 10 ° off-axis specimens corresponded to their actual fracture stresses. The rod and the -+ 45 ° off-axis specimens do not actually break apart at the point of shear failure; they simply lose their integrity. Therefore, the shear failure stresses for the rod and the -+ 45 ° laminates were arbitrarily chosen using the 0.2% offset method (Fig. 10). The in-plane shear stress/strain curves are compared in Figs 1 1 - 1 3 . (Interlaminar shear testing does not produce a stress/strain curve.)
C O M P O S I T E S . JU L Y 1977
Table 2. Comparison of shear properties obtained from various test methods (material: 65 volume % aramid fibre in epoxy No 1) Shear failure stress MPaa CV*, % Torsional shear of 90°wound thin tube
Shear strain a at failure stress % CV*, %
Shear modulus at 0.5% shear strain, MPa CV*, %
No of specimens
31.3±2.0
6.0
2.02±0.20
9.4
1744±39
2.1
6
31.3±2.8 32.5±3.0
7.2 7.5
1.82±0.20 2.06±0.17
8.8 6.8
1965±89 1758±21
3.6 1.0
5 5
29.4±0.7
2.0
1.73±0.05
2.3
1923±113
4.7
5
27.9±1.6 31.7±1.4
2.4 3.6
t.68±0.05 1.89±0.06
2.4 2.6
1889±20 1875±90
0.8 3.9
5
Tensile shear of 10° off-axis laminates Coated edges Bare edges
19.4±1.1 19.1±2.9
3.6 9.4
0.97±0.08 1.03±0.21
5.2 12.6
2082±188 1903±191
5.7 6.3
4 4
Interlaminar shear of a short beam b Flat specimen Curved specimen
36.8±0.9 38.4±0.9
5.1 4.1
Interlaminar tensile shear of grooved laminates
7.7 to 23.5 °
Torsional shear of a 0°wound composite rod Strain measured with gauges Strain from angle of twist Tensile shear of ± 45 ° off-axis lamintes Midplane symmetry (7-layer) Midplane symmetry (7-layers repeated) Nonsymmetrical (8-layer)
18 15 See
a Plus or minus (+-) values indicate 95% confidence limits b Data f r o m Reference 14
Table 4 c See Table 4 for details * Coefficient of variation
Table 3. Shear data from rod torsion shear test (material: 65 volume % aramid fibre in epoxy No 2) Shear strain at failure stress as measured by
Shear modulus at 0.5% shear strain as measured by
Specimen No
Shear failure stress, MPa
Angle of twist, %
Strain gauges, %
Angle of twist, MPa
Strain gauges, MPa
1
29.2
2.33
1.52
1110
2034
2
29.4
2.37
1.49
1448
2179
3
33.2
2.26
1.75
1340
1999
4
26.4
1.75
1.55
1531
1779
5
30.4
1.97
1.59
1462
1999
Mean
29.7
2.14
1.58
1378
1998
2.5
0.27
0.10
165
143
Standard deviation
DISCUSSION
The torsional shear of a thin-walled tube can theoretically produce the desired state of pure shear. However, it is not a simple test that can be used easily. Therefore, a simple
COMPOSITES . JULY 1977
method has been sought that can provide shear properties comparable to those obtained from thin-tube torsion. With this in mind, the shear stress/strain curves from various methods were compared with those from the thin-tube torsion test (Fig. 11 ). The shear modulus for all methods is
165
Table 4. Effect of groove depth on the maximum interlaminar shear stress calculated from tensile shear of grooved laminates Mean shear stress between grooves,
Specimen
1/t a
Maximum shear stress,
MPa
C.V., %
No of specimens
With grooves cut to centre ply or slightly under
5.43 8.12 11.94 12.58 15.67
15.2 16.7 14.0 10.9 10.7
5.8 10.0 22.0 12.3 8.1
5 5 4 5 5
With grooves cut through centre ply or slightly over
3.94 5.87 7.87 9.73 10.98
14.14 11.73 8.49 8.18 7.44
6.2 6.6 7.8 4.3 11.0
3 4 4 4 3
4.41 6.03 8.21 10.40 11.61
5.20 5.42 5.05 4.12 3.76
13.5 7.2 6.4 2.8 4.2
5 5 5 5 5
With over-cut grooves
k
MPa
0.17
14.03 23.05 28.42 23.31 28.50
Av = 23.46
0.22
12.26 15.15 14.70 17.51 17.97
Av = 15.52
0.21
4.82 6.86 8.71 9.00 9.17
Av = 7.71
a See Fig. 2e
generally higher than that of the thin-tube torsion tests. However, the shear failure stresses from rod torsion and -+45 ° off-axis laminate tensile shear tests are comparable to those of the thin-tube torsion tests; the shear failure stress from the 10 ° off-axis laminate tensile shear tests is significantly lower. For torsional shear of a unidirectional composite rod, the shear strain was measured with both angle of twist and strain gauges. For a given shear stress, the shear strains calculated from angles of twist are consistently higher than 40
X Fracture
50
o o;E 20
/
g,
//
I0
/ Six specimens
,# o"
o15
,'5
215
Shear strain (%) Fig. 3 Shear stress/strain diagram f r o m torsional shear of 90°-wound thin-walled tube
166
those from strain gauges. This, in turn, affects the calculated shear modulus (Fig. 12). Rod torsion tests of the aramid in another resin system show the same trend (Table 3). Although the shear stress/strain curve calculated from the angle of twist is closer to that of the thin-tube torsion result, it may very well be coincidence. It is very possible that shear of the adhesives between the rod specimen and its end fixtures contributed in some degree to the angle of twist. By using strain guage measurements, the calculated shear modulus was found to be about 13% higher and the failure stress about the same as that obtained from the thintube torsion test (Fig. 11). The rod torsion test is subjected to the same equipment and test restrictions as the thinwalled tube torsion test. In addition, a special mould is needed for winding the composite rod specimens. The tensile shear of 10 ° off-axis laminates does not require special equipment. In the first attempt to evaluate this method specimens with bare-cut edges were used. The resulting fracture strength was approximately two-thirds of that from thin-walled tube torsion tests. A second evaluation was therefore performed. This time the edges of the speciments were coated with flexible epoxy with the intention of eliminating the possibility of cracks starting at the edges. The results did not show significant improvement in strength (Table 2). The tensile shear test of 10 ° off-axis laminates (coated edges) shows that the shear modulus is approximately 19% higher and the fracture stress 38% lower than that of the thin-walled tube torsion test. Hahn and Whitney Is compared this method with the tensile shear test of -+ 45 ° off-axis laminates using graphite/epoxy composites. They found that the 10 ° off-axis tensile shear test resulted in significant shear coupling, and that it gave a higher shear modulus, lower failure stress, and lower failure strain than the -+ 45 ° off-axis laminate tensile shear test. This is consistent with the results of the present study (Table 2 and Fig. 11).
COMPOSITES. JULY 1977
40
40
X Sheor foilure ® m
X Frocture
3o
3O
(3_
n
~ 2c
-'- 2C in
N
u)
IC
/ ~ /
7` from str.oin
gouges
F~ve spemmens
o
' 0.5
I'0
I'5
%/o/ 0% ,'c
2 0'
2 I5
1
2!o
1.0 15 Sheor strain (%)
Shear stroin(%) Fig. 4 Shear stress/strain diagram f r o m torsional shear o f 0 ° unidirectional composite rods; shear strain was obtained f r o m strain gauge measurements
Four specimens Edges cooled
i
2.5
Fig. 6 Shear stress/strain diagram f r o m 10 ° off-axis tensile shear test o f specimens with coated edges
40
4o r It[]
i
X Shear foilure i 30
X Fracture
30F
o_ :E 20
/
v)
/
I0
o_ v a~
/
/"
V
2o
113
/ 7" from ongle of lwist Five specimens
[m
Four specimens Edges not coated
S
o~
o15
~i 0
,15
zlo
25t
Sheor stroin (%)
0'5
,15
li.O Shear stroin (%)
21o
215
Fig. 5 Shear stress/strain diagram f r o m torsional shear o f 0 ° unidirectional composite rods; shear strain was obtained f r o m angle o f twist
Fig. 7 Shear stress/strain diagram from 10 ° off-axis tensile shear test o f specimens with uncoated edges
The -+ 45 ° off-axis laminate tensile shear test results in a shear modulus about 10% higher and a shear failure stress about 6% lower than that of the thin-walled tube torsion test. As can be seen in Fig. 11, its shear stress/strain response is closest to that of the thin-walled tube torsion shear test. Sims 16 compared this method with published thin-wall tube torsion data of graphite/epoxy composites and also found good agreement in shear stress/strain responses. Midplane symmetry should be observed in fabricating the test specimen to avoid bending-stretching coupling. However, in many cases this symmetry condition is either inconvenient or impossible to achieve. Whitney ~7 showed that the severity of coupling effects is inversely proportional to the number
of plies of the composite. For nonsymmetrical lay-ups, Chiao and Hamstad is recommended eight or more plies to minimize this coupling effect. Therefore, in this study, both 7-layer (midplane symmetry) and 8-layer (nonsymmetrical) specimens were used. The resulting stress/strain responses were practically the same (Fig. 13). After completing this test, the authors of the present work concluded that the -+45° off-axis laminate tensile shear test was simple and reproducible.
COMPOSITES
. JULY
1977
The interlaminar tensile shear of grooved laminates was evaluated and the interlaminar shear strength was claculated by Markham and Dawson's method. ~1 As can be seen in
167
34 5
Table 4, the shear strengths vary depending on the cut of the grooves. It is very difficult to cut the grooves to the depth of precisely half the specimen thickness. A slight undercut gives a higher shear strength than an overcut (Table 4). Some tearing in the fibre was observed during the testing of the undercut specimens. Bending and peeling were also observed during testing, especially for the overcut specimens. This may be the reason for the low shear strength obtained. Although this method is relatively simple, it provides only shear strength data - not the shear stress/ strain curve. Moreover, even the shear strength data is unreliable.
29 27.2
j-
Shear failure
Stress-sfram curve
The shear strength of the specimens, as measured by the short-beam interlaminar shear test, was approximately 20%
Shear fatlure
X
Shear Fig. 10 Obtaining stress/strain curve
I
I
I
05
1.0 Shear
Fig. 8 off-axis
I
strain
I%)
shear failure stress from a * 45” using the 0.2% off-set method
25
(%I
Shear stress/strain diagram from tensile laminates with midplane symmetry
shear
of
f 45’
X Shear failure
Shear **
Q
w
k”
30-
failure
X Thin-wall
paint tube.tarsian
A
Unidlrectlanaf rod, torsion
0
i
0
05
Fig.
Eight-layer-laminate specimens
d I
05
I
I
IO
I5 Shear
Fig. 9 off-axis
168
Shear stress/strain laminates without
diagram midplane
_I
20
25
s1raln (%) from tensile symmetry
shear
Comparison
tensile
tensile
I.5 Shear sk6in (%)
of shear
stress/strain
20
25
curves
higher than that measured by the thin-walled tube torsion test (Table 2). The method is simple and inexpensive but again provides only shear strength data. In a separate report l4 the authors evaluated this method and found that the results often could not be reproduced even for specimens made by the same process and tested by the same person.
IO-
FIW
11
IO
composite
45O off -axis
0 IO0 off-axis
Oo
off-axis
1
20
1.5
strain
of
+ 45”
Despite the above noted advantages and reliability of the + 45” off-axis laminate tensile shear test, some qualifications should be noted. Rather complicated failure mechanisms may be involved in the test in an interactive manner. That is, the sources of failure may include the combined effects
COMPOSITES.
JULY 1977
40
40
Strain measured with gouges t
Strain from angle of twist
\
,,
3oi
30
o/
n
= 20
o 20
a
g I0
I0
0 Seven-layer A
015
ItO ' 15 Shear strain (%)
2 0'
I
O~
2.5
Fig. 12 Comparison of torsional shear stress/strain curves o f 0 ° unidirectional composite rods obtained f r o m different strain measuring devices
RECOMMENDA TION
5
Based on the experimental results obtained in this study it is recommended that the + 45 ° off-axis laminate tensile shear test be used for the measurement of the shear properties of fibre composites. Although this method gives a slightly higher shear modulus, it has the following merits:
6
•
simple specimen fabrication;
•
conventional tensile test;
•
no end tab required;
•
simpledata reduction;
•
inexpensive.
2
3
7 8 9 10 11 12 13
A C K N O W L E D G E M E N TS
The authors would like to thank R.M. Christensen for the helpful discussion and critical review of the manuscript. It should be noted that reference to a company or product name does not imply approval or recommendation of the product by the University of California or the US Energy Research and Development Administration to the exclusion of others that may be suitable.
REFERENCES 1
Bert, C.W., Mayberry, B.L., and Ray, J.D. 'Behaviour of Fiber
C O M P O S I T E S . JU L Y 1977
15
210
I
25
Fig. 13 Comparison of shear stress/strain curves f r o m tensile shear of -+ 45 ° off-axis lamiantes o f 7 and 8 layers
4
good reproducibility;
II0
Sheor stroin (%)
of fibre/matrix debonding, failure in matrix phase, and (on a larger scale) debonding of lamina. Also, it must be recognized that no single test method provides general failure information on composites in all possible states of stress. For this reason recourse must be made to the ultilization of a general failure criterion, with its basis established by several different types of tests. Despite these qualifications the -+ 45 ° off-axis laminate tensile shear test does seem to provide pertinent and reliable special failure information.
•
0 5~
Eight~loyer
14 15 16 17 18
Reinforced Plastic Laminates Under Uniaxial, Biaxial and Shear Loadings', US Army Aviation Materials Lab, A YLABS-TR-6886, AD-684321 (1971) Bert, C.W. 'Experimental Characterization of Composites in 'Structural Design and Analysis', Part II', Composite Mater 8 edited by Broutman, L.J. and Krock, V.H. (Academic Press, New York, 1975) Whitney, J.M., Stansbarger, D.L., and Howell, H.B. 'Analysis of the Rail Shear Test - Applications and Limitations', J Composite Mater 5 (1971) p 24 Adams,D.F. and Thomas, R.L 'Advances in Structural Composites', Nat Soc Aerospace Mater Process Eng Syrup 12, paper A C-5 'Proposed Method of Test for Torsional Shear Properties of Reinforced Plastics, ASTM Committee working document Petit, P.H. 'A Simplified Method of Determining the Inplane Shear Stress-Strain Response of Unidirectional Composites', ASTMSTP460, (1969) p 83 Rosen, B.W. 'A Simple Procedure for Experimental Determination of the Longitudinal Shear Modulus of Unidirectional Composites', J Composite Mater 6 (1972) p 552 Hahn, H.T. 'A Note on Determination of the Shear Stress-Strain Response of Unidirectional Composites, J Composite Mater 7 (1973) p 383 Chamis,C.C. and Sinclair, J.H.'10 ° Off-Axis Tensile Test for lnterlaminar Shear Characterization of Fiber Composites' NASA Tech Note D-8215 (1976) ASTM Designation D-2733 Part 30 (1974) Markham,M.F. and Dawson, D. Composites 6 (1975) p 173 ASTM Designation D-2344 (1972) Chiao, T.T., Hamstad, M.A., Marcon, M.A. and Hanafee, J.E. 'Filament Wound Kevlar 49/Epoxy Press Vessels', Lawrence Livermore Laboratory, Livermore, California, Report NASACR-134506 (UCRL-51466) (1973) Chiao, C.C. and Moore, R.L. 'Evaluation of Interlaminar Shear Test for Fiber Composites', Lawrence Livermore Laboratory, Livermore, California Report UCRL-51 766 (1975) Hahn, H.T. and Whitney, J.M. Air Force Materials Laboratory Wright-Patterson AFB, Ohio, private communication (1976) Sims,D.F. 'In-Plane Shear Stress-Strain Repsonse of Unidirectional Composite Materials,J Composite Mater 7 (1973) p 124 Whitney, J.M. 'Bending-Extensional Coupling in Laminated Plate Under Transverse Loading', J Composite Mater 3 (1969) p 20 Chiao, T.T. and Hamstad, M.A. 'Testing of Fiber Composite Materials', Proc Int Conf on Composite Mater, AIME {Geneva, April 1975} Vol 2 (1976) p 884
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