- Email: [email protected]
epoxy laminates at impact rates of strain
Composites Science and Technology 45 (1992) 161-171
Determination of interlaminar shear strength for glass/epoxy and carbon/epoxy laminates at impact rates of strain J. Harding & Y. L. Li* Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK, OX1 3PJ (Received 31 May 1991; accepted 7 February 1992)
A brief review is given of some of the techniques which have been used to determine the interlaminar shear strength of laminated composites under impact loading. A new technique employing a double-lap shear specimen, where failure occurs on predetermined interfaces, is then described and results are presented for tests on this design of specimen at both a quasi-static and an impact rate of strain. The strain distribution along the failure plane is determined by using a finite element analysis. Large variations in both the shear strain and the normal strain were observed, the magnitude of this variation being sensitive both to the elastic properties of the different reinforcing plies and to the chosen
stacking sequence. Results are presented for the interlaminar shear strength at the interface between (a) two plain-weave glass/epoxy plies, (b) two plain-weave carbon/epoxy plies, and (c) a plain-weave glass/epoxy and a plain-weave carbon/epoxy ply. In each case the mean value of the interlaminar shear stress at failure was found to increase significantly as the loading rate was raised from quasi-static to impact. Keywords: interlaminar shear strength, impact loading, woven reinforcement, fibre/epoxy composites, double-lap shear specimen, finite element analysis
1 INTRODUCTION
reinforced composites when loaded in the reinforcement direction emphasise the significance of the rate dependence of the interlaminar shear strength in determining the failure mode. Thus, while fibre fracture dominates the tensile failure at quasi-static rates, at impact rates failure is almost entirely due to either interlaminar shear, in the woven laminates, or fibre pull-out, in the unidirectionally reinforced specimens. Such behaviour is consistent with the hypothesis that the tensile strength of the fibres increases more rapidly with strain rate than either the interlaminar shear strength or the interfacial bond strength. For this hypothesis to be checked it is necessary to devise techniques which allow the effect of strain rate on each of these various properties to be independently determined. The present paper specifically considers the interlami-
Failure in laminated composite materials frequently involves a complex interaction between a number of different processes amongst which interlaminar shear is one of the most significant. The critical value of the interlaminar shear strength at failure, therefore, is a very important parameter in the design of composite structures and in the analysis of their failure processes. 1 Changes in the failure process which have been observed with increasing strain rate in tensile tests on both woven 2 and unidirectional 3 glass * Present address: P.O. Box 106, Northwestern Polytechnical University, Xian Shaanxi 710072, People's Republic of China.
Composites Science and Technology 0266-3538/92/$05.00 © 1992 Elsevier Science Publishers Ltd. 161
162
J. Harding, Y. L. Li
nar shear strength and reports on an attempt to determine its rate dependence for woven reinforced laminates when measured at the interface between (a) two woven glass plies, (b) two woven carbon plies and (c) a woven glass and a woven carbon ply. In practice there are considerable difficulties to be overcome in the experimental measurement of the interlaminar shear strength. In the main such difficulties are associated with the design of a specimen in which the shear stress on the interlaminar plane is reasonably uniform and sufficiently high to dominate the failure process. Relatively few attempts have been made, therefore, to determine the interlaminar shear strength at the highest rates of loading where these problems are most severe. One of the first of these 4 used the torsional version of the Hopkinson bar and a thin-walled tubular specimen cut with its axis perpendicular to the plane of reinforcement. A significant increase in the interlaminar shear strength with strain rate was found for both plain weave and cross-ply glass/epoxy laminates at strain rates in the range 100-1000/s. In neither case, however, was failure by simple shear entirely on the interlaminar plane. Other types of specimen were used by Chiem and Liu, 5 for woven glass/epoxy, also in the torsional Hopkinson bar, and by Werner and Dharan, 6 for plain-weave carbon/epoxy, in the double-notch shear version of the Hopkinson bar. A marked rate dependence of the interlaminar shear strength was found for the glass/epoxy specimens. In contrast, no effect of strain rate on the interlaminar shear strength was observed in the carbon/epoxy specimens while their transverse shear strength decreased with increasing strain rate. More recently, a double-lap design of shear specimen has been developed for determining the interlaminar shear strength of composite specimens at impact rates of strain. This the tensile version of the Hopkinson bar. Results have been reported for a satin-weave carbon/epoxy laminate 7 and, most recently, for both a unidirectionally reinforced carbon/epoxy laminate 8 and for various plain-weave carbon and glass/epoxy laminates. 9 In all of these studies the interlaminar shear strength was found to increase with strain rate. In view, however, of the considerable variation in the magnitude of the shear stress along the interlaminar failure plane
and the presence of significant levels of normal stress at the ends of this plane, some doubts must remain regarding the specific values of interlaminar shear strength obtained with this design of specimen. The present paper looks in detail at a range of results determined in this way and discusses the significance of the values of interlaminar shear strength so obtained.
2 SPECIMEN DESIGN A double-lap design of shear specimen, as shown schematically in Fig. 1, was used in both quasi-static and impact tests. A tensile load applied across the ends of the specimen is required to give shear failures at the two interfaces over which the reinforcing plies overlap rather than tensile failures in one or more of the arms of the specimen. Since the rate dependence of the tensile strength may not be the same as that of the interlaminar shear strength a ply lay-up which is found to be satisfactory at one rate may not prove to be satisfactory at the other. Thus, while the lay-up shown in Fig. 1, i.e. two reinforcing plies in each of the outer arms and four in the central region, gave good results for the carbon/epoxy laminate at the quasi-static rate, under impact loading tensile failures were obtained in one or more of the arms of the specimen. A modified lay-up, shown in Fig. 2(a), with three reinforcing plies in each outer arm and five in the central region, proved satisfactory at both loading rates, however, for the carbon/epoxy laminate. To determine the interlaminar shear strength at the interface between a carbon reinforced and a glass reinforced ply, a hybrid lay-up is required. A previous finite element study of two such hybrid lay-ups ~° showed that the shear stress variation on the failure plane was minimised
PTFE Input barn .~
\
~20-1~ A
Specimen
,,
IIIII~'III I (II III . . . .
=J i
Outputbar
rT_~ / / /
30
,
+c; \
i
Strain gauge -I
Dimensionsin mm Fig. 1. Double-lap shear specimen.
I
Interlaminar shear strength of laminated composites a) All-carbon toy-up, quasi-static and impact tests
[
t. . .
I
I
I
I
b) Hybrid lay-up, quasi-static tests
I
[
l
I
....
I
the lay-up shown in Fig. 2(c) which gave good results at both loading rates. The lay-up used for the glass/epoxy laminate is shown in Fig. 2(d) and gave shear failures at both rates of loading. At the quasi-static rate specimens were loaded in a standard Instron testing machine, giving a time to failure of about 10 s, while in the impact tests the specimen was fixed between the input and output bars of a split Hopkinson bar apparatus and failure occurred after about 30 jus.
3 SPECIMEN MATERIAL A N D PREPARATION
c) Hybrid lay-up, quasi-static and impact tests
I
163
I
I
I
d) All-glass toy-up, quasi-static and impact tests
Fig. 2. Ply lay-ups in double-lap shear specimens.
when the reinforcing plies with the higher stiffness were in the outer arms of the specimen and when the number of lower stiffness plies was minimised. The first hybrid lay-up to be studied, therefore, was that shown in Fig. 2(b). This proved satisfactory at the quasi-static but not at the impact loading rate and thus was replaced by
To allow as close a comparison as possible with earlier experimental work on the same materials under impact loading in both tensionT M and compression,7 the carbon/epoxy, glass/epoxy and hybrid specimens were prepared from the Ciba-Geigy XD 927 epoxy resin system and dry fabric supplied by Fothergill and Harvey Ltd (Littleborough, Lancashire). The carbon fibre fabric was woven from Toray 3000 filament fibre tows, type T300-3000A, and had a weight of 189g/m 2 and an approximate thickness of 0.28 ram. The fabric was of a relatively coarse weave with only 47 ends and picks per 10 cm. The glass fabric was woven from continuous E-glass fibres, designation 11 x 2EC5, and had a weight of 96g/m 2 and a thickness of about 0.10 mm. With 252 ends and 173 picks per 10 cm the weave was much finer than that for the carbon fabric. To prepare double-lap laminates, aluminium and poly-tetra-fluoro-ethylene (PTFE) spacers were used (see Fig. 3). The lay-up was covered with a Nylon bagging film, breather fabric, Aluminium spacer covered with PTFE
Outer reinforcing plies
Central reinforcing plies
Alurninium spacer covered with PTFE 7ram
~tumlnlum spacer covered with PTFE
-Aluminium base plate covered with PTFE
Outer rein pliers
Fig. 3. Preparation of double-lap shear specimens.
164
J. Harding, Y. L. Li Table 1. Details of plain-weave double-lap shear laminates
Interface t y p e : Resin (%) Total plies Central plies Testing rates
Carbon/carbon 39.0 8 4 Static
45-7 11 5 Static Impact
Carbon/glass 49-1 7 + 4b 3 + 4h Static
Glass/glass
42.0 10 + 4h 4 + 4h Static Impact
52.5° 56.7 25 25 11 11 Static Static I m p a c t Impact
a Delay of 13 h at ambient temperature after lay-up and before curing. b 7 + 4, 7 carbon plies + 4 glass plies.
pin-prick film and peel ply and evacuated to 635 mm of mercury. In order to minimise loss of resin this was then put into an open mould having internal dimensions 160 mm × 90 mm × 10mm. The mould was then placed inside a closed container at an air pressure of 620 kPa and the container placed inside a small oven. The temperature was raised over a period of 1 h to 100°C, held for 16 h and then allowed to cool to room temperature at a rate of 8°C/h. Specimens of l O m m width were cut from the resulting laminate using a diamond saw. Details of the six laminates prepared in this way are given in Table 1.
90 80
T
70 60 ~ so ~ 40 ~ 30 g~ 2o ~0 0 0
J
::}5
7!0
~-5
]&.O
]- - S h e a r zone =i IDistance atong specimen (mm)
Fig. 5. Shear stress distribution on interlaminar failure plane for all-carbon lay-up of Fig. 1. 4 FINITE ELEMENT
ANALYSIS
A two-dimensional finite element analysis was performed for each of the five specimen lay-ups of Figs 1 and 2 with previously determined in-plane elastic properties for the carbon and glass reinforced plies and estimated elastic properties in the through-thickness direction. 1 In all specimens there were geometrical discontinuities at each end of the failure plane leading to a singularity and stress and strain concentrations at each of these points. For the all-carbon lay-up shown in Fig. 1 a finite element mesh consisting of 120 isoparametrical elements, each with eight nodes, was used (see Fig. 4). Since the specimen is symmetrical about the longitudinal axis, only half is modelled. The shear stress variation on the interlaminar plane over the shear zone length of 7 r a m and for a further 3.5 mm on either side was determined and is shown in Fig. 5. The analysis was performed with
Fig. 4. Finite element mesh for all-carbon lay-up of Fig. 1.
the assumption of an external loading of 245 kN, equivalent to an average shear stress on the failure plane of 35 MPa, about the same as that determined experimentally for quasi-static failure of the all-carbon lay-up. As expected, large and almost equal shear stress concentrations were found at each end of the failure plane, giving an apparent maximum variation in the shear stress of about 5.5" 1. For the all-glass lay-up this ratio increased to about 9:1. In practice, however, the actual values of shear stress derived from the finite element analysis close to the points of singularity will be dependent on the mesh size in this region--the finer the mesh the more reliable the estimate of the maximum shear stress. The results shown in Fig. 5, therefore, should only be taken as giving a general indication of the shear stress variation in the all-carbon lay-up. In the hybrid specimens, however, an additional problem arises from the discontinuity in elastic properties due to the different types of reinforcing ply on either side of the failure plane. This leads to a corresponding discontinuity across the interface in the longitudinal stress and the shear and normal strains. However, since the
Interlaminar shear strength of laminated composites shear stress at the interface is directly proportional to the average of the shear strains either side of the interface, as shown in the Appendix, while the longitudinal strain is not discontinuous, the results of the finite element analyses may be more conveniently presented in terms of the strain distribution along the interlaminar failure plane. The variation of shear, longitudinal and normal strain for the all-carbon lay-up is shown in Fig. 6 for an applied longitudinal displacement across the ends of the specimen equivalent to a tensile strain of 1%. The maximum variation in the shear strain, about 5-6: 1, is very similar to the maximum variation in shear stress shown in Fig. 5. The normal strain, due to the Poisson's ratio contraction at the outer ends of the specimen, shows local peak values at each end of the failure plane, indicating the presence of significant levels of normal stress at these points and raising the possibility that failure will initiate here under the combination of the peak shear stress and the peak normal stress. Generally, similar strain distributions were shown by each of the five specimen lay-ups, except that for the modified all-carbon lay-up (Fig. 2(a)) and the all-glass lay-up (Fig. 2(d)) the peak shear and normal strains were increased at the left hand end and reduced at the right hand end of the failure plane. This effect was even more marked for the two hybrid lay-ups--see Fig. 7 where it is the average values of shear and normal strain at the interface which are determined. From these various finite element analyses it is clear that the shear stress on the interlaminar failure plane will be far from 0.04
i
0.035
i
it II II i ~
0.03
al
0"025 .c_
i
I I
0.02
/
I
I
A
I k
I
": o.o15
v)
0"01
x
0.005 o
-ooos
---'
I !, '"
"...
,,,' s /
I
....
!!K ---
x!L
3'.5
7!0 Distance
~d5
~40
along specimen (mm)
Fig. 6. S t r a i n d i s t r i b u t i o n o n i n t e r l a m i n a r f a i l u r e p l a n e f o r a l l - c a r b o n l a y - u p o f Fig. 1. L o n g i t u d i n a l s t r a i n ( e n ) - - ; s h e a r s t r a i n (Y,2) . . . . . . ; n o r m a l s t r a i n ((22) . . . . .
0-07
165
i
i
i
f
0-0(
II
iI
0.0 t,
It
0"0~
I| I I I I ! I
A'
._~ o
0.0"
J l l ill
0,02
o ...... _
-0.01
o
', "..
. . . ._/.~, : ,
,,
/',A t~ . ~~,-~ ... . . . . . . .
....................
3'.5 Distance
i
7'0 along
specimen
10-5
~4.0
(ram)
Fig. 7. Strain distribution on interlaminar failure plane for hybrid lay-up of Fig. 2(c). Longitudinal strain (E,I) ; shear strain (Y12) ; normal strain (e22). . . . . uniform and that normal stresses at the ends of the interlaminar plane will be likely to play a part in the initiation of failure. However, until a better design of specimen, which is suitable for testing at both quasi-static and impact rates, is developed the double-lap shear specimen does allow comparative data to be obtained for different lay-ups and different rates of loading.
5 RESULTS Quasi-static tests
In the quasi-static tests the load was obtained from a load cell in series with the specimen, and the displacement across the ends of the specimen was derived from the integrated output of a pair of velocity transducers in parallel with the specimen. Typical load/time and displacement/time signals for a test on an all-glass specimen are shown in Fig. 8. By assuming that failure occurs at the peak load and that the two failure planes are equally loaded, a mean shear stress on the interlaminar plane at failure may be determined. Table 2 lists the shear stresses obtained in this way for the all-carbon, all-glass and hybrid carbon/glass lay-ups. The displacement signal in Fig. 8 gives a measure of the overall extension of the specimen and relates, therefore, to an apparent average tensile strain. The actual shear strain in the interlaminar region will depend on what proportion of the total displacement appears across the shear zone and on the effective thickness of this region, neither of which are known. However,
J. Harding, Y. L. Li
166
30
200
.,~ ,/
25
~
150
~~ ......Displ~acement
20
Load
~ 0
~
tOO
~0
s ~s
oE
z 5
0 0
10
30
20
Time
/
40
;~
50
(seconds)
¢.0
¢.~
---
2.0
Nomina[ Shear Strain (*/,)
Fig. 8. Load versus time and displacement versus time signals for quasi-static test on all-glass specimen.
the finite element analyses of Figs 6 and 7 show that although the shear strain on the interlaminar plane varies by almost an order of magnitude the mean value is of the same order as the 1% overall applied tensile strain. It is possible, therefore, to derive a nominal shear stress versus nominal shear strain curve from load and displacement signals such as those in Fig. 8. Curves for four tests on plain weave all-carbon specimens are given in Fig. 9 and show a reasonably repeatable behaviour. Impact tests The load supported by the specimen in the impact test is derived from the output bar strain gauge signal while calculation of the overall extension of the specimen requires, in addition, signals from two sets of gauges on the input bar. In order to allow a more direct estimate of the deformation of the specimen, strain gauges were also attached to the specimen itself on the outer surfaces in the 7 mm overlap region, as shown in Fig. 1. Typical load/time and strain/time signals,
Fig, 9. Nominal shear stress versus nominal shear strain curves for quasi-static tests on all-carbon specimens.
as obtained from the output bar and the specimen strain gauges and stored in a dual-channel high-speed transient recorder, are shown in Fig. 10 for a test on an all-carbon specimen. Allowance has been made for the time taken by the loading wave to travel between the two strain gauge positions. With the same assumptions as in the quasi-static tests, the mean shear stress and shear strain on the interlaminar plane may be determined from the load/time curve, obtained from the output bar strain gauges and the overall specimen extension, derived from the standard Hopkinson bar analysis. Mean interlaminar shear strengths calculated from the peak values of load for the four specimen types are listed in Table 3 and a set of nominal shear stress versus nominal shear strain curves for the four impact tests on the all-carbon specimens and the corresponding
u]
150
Specimen Strain Gauge
/~
el
Table 2. Average interlaminar shear strengths (ILSS) in quasi-static tests Specimen type
Fibre fraction
No. of tests
Average ILSS (MPa)
(wt%)
~
o ID ~
All-carbon
39 45
3 4
26.2 + 1-3 26.4 + 1.7
.,~
Carbon/glass
42 49
5 6
26.6 + 3.9 27.1 + 3.0
~
53 57
3 5
20.8 + 0.5 20-2 + 3.2
All-glass
7oo
5o
o
i
t
10
20
Time
.
L
30
40
5O
(microseconds)
Fig. 10. Specimen and output bar strain gauge signals for impact test on all-carbon specimen.
Interlaminar shear strength of laminated composites
167
Table 3. Average intedsminar shear strengths (ILSS) in impsct tests Specimen type
Fibre fraction
No. of Average ILSS tests (MPa)
(%wt)
All-carbon
45
6
45.0 + 4.2
Carbon/glass
42
5
41.4 + 4.7
All-glass
53 57
3 3
33.4 + 2.0 37-4 + 0-3
curves of nominal shear strain rate versus shear strain are shown in Fig. 11. Fracture behaviour
Macrographs of a failed hybrid specimen after quasi-static loading are shown in Fig. 12. Both the fine-weave glass fabric and the trace in the resin matrix of the coarse-weave carbon fabric are visible on the interlaminar failure plane, implying that there is a step in the resin across the failure plane, as shown schematically in Fig. 50
~,\ 3O
/S
5 U3
2O ,
1
2
.x\"
'¢,\
3
Nominal Shear Strain (*/,1
(a) 2000
Fig. 12. Macrographs of quasi-statically tested hybrid specimen (x2-2).
13. A similar behaviour was observed in both quasi-static and impact tests on all plain-weave specimen lay-ups. Scanning electron micrographs of the failure surface for a quasi-statically tested all-glass specimen show the bare glass fibres in the region below the step (Fig. 14(a)) and the resin matrix bearing the imprint of the glass fabric in the region above the step (Fig. 14(b)). A scanning electron micrograph of the step itself for an impacted all-glass specimen (Fig. 14(c)) shows both these regions. In the impact tests all the specimens for which results are given in Table 3 failed by shear on both the interlaminar planes. However, one of the five hybrid specimens also failed simultaneously in tension, at section (a) in Fig. 15, and three of the six all-carbon specimens showed similar behaviour, two failing at section (b) and one at section (c). Only in the all-glass specimens were simultaneous tensile failures entirely absent under impact loading.
1500
Carbon plies
c
I000
5oo Glass plies Nominal Shear Strain (*/,)
(b) Fig. U . Nominal shear stress versus nominal shear strain curves for impact tests on all-carbon specimens.
Path of fracture
(Y-points of maximum initiate)
shear strain
y layer where cracks
Fig. 13. Schematic model of failure process in hybrid specimen.
J. H a r d i n g ,
168
Y. L. L i
TensiLeFailures (c) [b) (a) {[=__Xj
F~l"u'~r\els(all tests) I,,
Shear
I
Fig. 15. Types of failure in impact tests.
(a)
(b)
performed on two different laminates with slightly different lay-ups, and hence strain distributions on the interlaminar plane, and slightly different fibre weight fractions. In neither case, however, was there any significant effect on the measured interlaminar shear strength. Two different laminates were also used for the all-glass specimens. In this case both had the same lay-up but there was a slight difference in the curing treatment they had received. Again, no significant effect on the interlaminar shear strength was apparent. Under impact loading (Table 3) only for the all-glass specimens were tests performed on two different laminatae. Of these the correctly cured laminates, which also had the slightly higher fibre weight fraction, showed a significantly increased interlaminar shear strength, by about 12%. This increase was greater than the combined experimental scatter on both sets of measurements and suggests that a difference in the rate dependence of the resin following the different curing treatments may have been the determining factor. However, despite this extra effect, the average nominal interlaminar shear-stress/shearstrain curves shown in Fig. 16 almost certainly give a general indication of the shear strength of the three types of interface under impact loading. 50
(c) Fig. 14. Scanning electron micrographs of fracture surface for all-glass specimens. (a) Bare fibres below the step in a quasi-static test (x-500); (b) bare matrix above the step in a quasi-static test (x-500); (c) step region for an impact
.I '
30
,,,"
j ~"
i.!"
'\
".
test ( x - 1 0 0 0 ) u~ 20
Interface type ,~/,"
6 DISCUSSION Effect of fibre weight fraction and ply lay-up Quasi-static tests on both the all-carbon and the hybrid carbon/glass specimens (Table 2) were
E
/ 10 ~ ' / / /.
.1.1"
/" . / . / " I"""'"''"" I 1
--
carbon/carbon
....... carbon/glass .....
glass/glass
L I 2 3 Nominal Shear Strain (o/°)
Fig. 16. Effect of interface type on nominal interlaminar shear stress versus strain curves under impact loading.
Interlaminar shear strength of laminated composites Process of fracture
50
ca
Impact m
20~ asi
E o 7
-
static
10
I 1 Nominal
I 2
3
Shear S t r a i n (,/o)
Fig. 17. Effect of loading rate on n o m i n a l interlaminar shear stress versus strain curves for c a r b o n / c a r b o n interface.
Effect of strain rate
Average shear-stress/shear-strain curves for the all-carbon specimens at the two loading rates, derived from the results given in Figs 9 and 11, are shown in Fig. 17. Table 4 collates data on the average interlaminar shear strength for the three types of interface. In each case there is a significant increase in the shear strength between the quasi-static and the impact rates of loading, by about 70% for the all-carbon and all-glass interfaces and by about 50% for the hybrid interface. At both rates the carbon/carbon interface has a higher failure strength than the glass/glass interface. This could be either because the bonding with the matrix is better for the carbon than the glass fibres or because the carbon fabric has a much coarser weave than the glass fabric, allowing a stronger mechanical interaction across the interface between two carbon plies. Whichever mechanism controls the interlaminar failure, it has the same rate dependence for the two types of interface. However, as will be discussed in the next section, comparison of results for the different types of interface is complicated by the different strain distributions along the interlaminar plane. Table 4. Effect .of loading rate on interlaminar shear strength (MPa) Interface type Carbon/carbon Carbon/glass Glass/glass
169
Quasi-static tests 26.3 -t- 1.7 (7 tests) 26.8 + 3.9 (11 tests) 20.5 -t- 3.2 (8 tests)
Impact tests 45.0 + 4.2 (6 tests) 41-4 + 4-7 (5 tests) 35-4 + 2.9 (6 tests)
In all cases where interlaminar shear failure was obtained, a step was observed across the fracture surface. This is very clearly shown in Fig. 12 for a quasi-static test on a hybrid specimen. Scanning electron micrographs of the fracture surfaces on either side of this step for all-glass specimens tested at both quasi-static and impact rates of loading (see Fig. 14) showed a change from mainly the bare fibres of the lower ply on the input side to mainly the bare resin matrix carrying the imprint of the fibres of the upper ply on the output side. These observations support the proposed failure process illustrated schematically in Fig. 13 for the hybrid lay-up. Cracks are thought to be initiated at the points of high strain concentration at each end of the failure plane and to propagate inwards, forming a step across the resin layer where they first overlap. Further support for this proposed failure process comes from the signals obtained in all impact tests from strain gauges attached directly to the specimen. As shown in Fig. 10, which compares the specimen strain gauge signal with that derived from the ouput bar strain gauges for an impact test on an all-carbon specimen, although the load transmitted through the specimen, as recorded by the output bar gauges, increases monotonically to a single peak value, the specimen gauges show a double peak separated by a region where the strain decreases slightly. The time between the two peaks, - 1 0 #s, is too long to be due to reflected waves within the overlap region of the specimen. It seems more likely that this small decrease in strain results from the initiation and limited propagation of cracks from points Y at the left hand end of the interlaminar plane (cracks propagating from the right hand ends of the interlaminar planes would be much less likely to reduce the longitudinal strain at the gauge positions). It is significant, therefore, that in all of the specimen lay-ups used for tests at the impact loading rate, both the shear and the normal strain concentrations were greater at the input end than at the output end of the interlaminar plane. Although for the all-carbon lay-up the difference in strain concentration between the ends of the interlaminar plane was relatively small, for the all-glass and, particularly, the hybrid lay-ups (see Fig. 7) the difference was much greater. Here, therefore, cracks initiating
170
J. Harding, Y. L. L i
'~
90
~
80
~
7O
~d so O ~
50 4O
09
3O
b-"
10
I I0
t 20
i 30
i 40
,a_ 50
60
Time (microseconds) (a) 130 .~
120 110
¢~ 1 0 0 ~
9O
~"
8O
~ @ 0
7O 60
~
5O
~
4o
"~
30
t~
,? O 10
f o
i
i
i
i
~
i
5
,o
,5
zo
zs
so
s5
40
(microseconds) (b) Fig. 18. Effect of failure mode on specimen strain gauge signal. (a) Hybrid lay-up of Fig. 2(c) failing by interlaminar shear; (b) hybrid lay-up of Fig. 2(b) failing in tension. Time
at this point are likely to propagate further, giving a much more marked decrease in the specimen strain gauge signal, such as is shown in Fig. 18(a). This contrasts with the impact response of a hybrid specimen having the lay-up shown in Fig. 2(b). Under impact loading this failed in tension in the central arm at position (b) in Fig. 15. A crack had initiated and propagated a short distance from the left hand end of the interlaminar plane. In this, and similar, cases, as shown in Fig. 18b, no double peak was apparent on the specimen strain gauge signal, presumably because the tensile failure occurred at a lower load than that required to initiate the crack at the right hand end of the interlaminar plane.
7 CONCLUSIONS
A new testing technique is described for determining the interlaminar shear strength of
fibre-reinforced polymer matrix composites. A double-lap shear specimen is used in which failure occurs on a predetermined plane. Finite element studies reveal large stress and strain concentrations at each end of the failure plane so that only mean values of the shear stress at failure may be determined by this method. Using different ply lay-ups in the double-lap shear specimen, results are obtained for the effect of loading rate on the shear strength at the interface between (a) two plain-weave carbon/ epoxy plies, (b) two plain-weave glass/epoxy plies, and (c) a plain-weave carbon/epoxy ply and a plain-weave glass/epoxy ply. The stress and strain distribution on the failure plane is sensitive to the precise ply lay-up so the specific values of strength determined at the different types of interface are not directly comparable. The same general trends in mechanical response, however, were shown by each interface. An increase in loading rate of about six orders of magnitude was found to raise the average value of the shear stress on the failure plane by about 70%, for the carbon/carbon and glass/glass interfaces and by about 50% for the hybrid carbon/glass interface. Fracture is by crack propagation along the fibre matrix interface from each end of the interlaminar failure plane and final failure occurs when the two cracks overlap and produce a step across the intervening matrix region.
ACKNOWLEDGEMENTS
This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant no. AFOSR-870129.
REFERENCES 1. Li, Y. L., Ruiz, C. & Harding, J., Failure analysis of woven hybrid composites using a finite element method. Comp. Sci. & Technol., 41 (1991) 129-46. 2. Welsh, L. M. & Harding, J., Effect of strain rate on the
tensile failure of woven-reinforced polyester resin composites. In Proc. DYMAT 85, Int. Conf. on Mechanical and Physical Behaviour o f Materials under Dynamic Loading, Les Editions de Physique, Paris,
CoUoque C5, 1985, pp. 405-14. 3. Welsh, L. M. & Harding, J., Proc. Composite Materials, ICCM V,
1517-31.
5th Int. Conf. on TMS-AIME (1985)
Interlaminar shear strength of laminated composites 4. Parry, T. & Harding, J., The failure of glass-reinforced composites under dynamic torsional loading. In Colloque Int. du CNRS No. 319, Plastic Behaviour of Aniaotropic Solids, ed. J. P. Boehler. CNRS, Paris, 1988, pp. 271-88. 5. Chiem, C. Y. & Liu, Z. G., Modelling of dynamic behaviour of composite materials. In Impact Loading and Dynamic Behaviour of Materials, Vol. 2, ed. C. Y. Chiem, H.-D. Kunze & L. W. Meyer. DGM Informationsgesellschaft mbH, Oberursel, 1988, pp. 579-86. 6. Werner, S. M. & Dharan, C. K. H., The dynamic response of graphite fibre/epoxy laminate at high shear strain rate. J. Comp. Mater., 20 (1986) 365-74. 7. Harding, J., Li, Y. L., Saka, K. & Taylor, M. E. C., Characterisation of the impact strength of woven carbon fibre/epoxy laminates. In 4th Oxford Int. Conf. on Mech. Props. of Materials at High Rates of Strain. Inst. Phys. Conf. Series No. 102, Institute of Physics, London, 1989, pp. 403-10. 8. Bouette, B., Cazeneuve, C. & Oytana, C., Shear in carbon/epoxy laminates at various strain rates. In Developments in the Science and Technology of Composite Materials. Elsevier Applied Science, London, 1990, pp. 937-42. 9. Harding, J., Li, Y. L. & Taylor, M. E. C., The ettect of strain rate on the interlaminar shear strength of woven reinforced laminates. In Developments in the Science and Technology of Composite Materials. Elsevier Applied Science, London, 1990, pp. 967-72. 10. Li, Y. L., Harding, J. & Ruiz, C., A new type of shear specimen for measuring the interlaminar shear strength under impact loading. Appendix II, Oxford University Engineering Laboratory Report No. OUEL 1863/90, 1990. 11. Harding, J., Saka, K. & Taylor, M. E. C., The effect of strain rate on the tensile failure of woven-reinforced carbon/glass hybrid composites. In IMPACT 87, Impact Loading and Dynamic Behaviour of Materials, Vol. 1, ed. C. Y. Chiem, H.-D. Kunze & L. W. Meyer. DGM
171
Informationsgesellschaft mbH, Oberursel, 1988, pp. 515-22.
APPENDIX: SHEAR STRESS A N D SHEAR STRAIN ON INTERLAMINAR PLANE The average shear and normal strains on the interlaminar plane m a y be defined by the relations: (Y12)~ = ½{(Y,2), + (rl2)c)
(A1)
(e22)a = ½{(ez2)g + (e22)c}
(A2)
and
w h e r e subscripts 'g' and 'c' refer to glass and carbon reinforced plies, respectively. Continuity of shear stress across the interlaminar plane requires that: (G12)¢(]/12)¢ = (G12)g(Yl2)g = l=12
(A3)
where G12 is the shear m o d u l u s of the c a r b o n or glass reinforced ply and ~12 is the interlaminar shear stress. Solving for ~lz b e t w e e n eqns (A1) and (A3) gives:
~2 = { 2( G,E)~(G,2)g/[ ( G,2)~ + (G,E)gl}(Y,2)~ (A4) i.e. the interlaminar shear stress is directly proportional to the average interlaminar shear strain.
Determination of interlaminar shear strength for glass/epoxy and carbon/epoxy laminates at impact rates of strain J. Harding & Y. L. Li* Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK, OX1 3PJ (Received 31 May 1991; accepted 7 February 1992)
A brief review is given of some of the techniques which have been used to determine the interlaminar shear strength of laminated composites under impact loading. A new technique employing a double-lap shear specimen, where failure occurs on predetermined interfaces, is then described and results are presented for tests on this design of specimen at both a quasi-static and an impact rate of strain. The strain distribution along the failure plane is determined by using a finite element analysis. Large variations in both the shear strain and the normal strain were observed, the magnitude of this variation being sensitive both to the elastic properties of the different reinforcing plies and to the chosen
stacking sequence. Results are presented for the interlaminar shear strength at the interface between (a) two plain-weave glass/epoxy plies, (b) two plain-weave carbon/epoxy plies, and (c) a plain-weave glass/epoxy and a plain-weave carbon/epoxy ply. In each case the mean value of the interlaminar shear stress at failure was found to increase significantly as the loading rate was raised from quasi-static to impact. Keywords: interlaminar shear strength, impact loading, woven reinforcement, fibre/epoxy composites, double-lap shear specimen, finite element analysis
1 INTRODUCTION
reinforced composites when loaded in the reinforcement direction emphasise the significance of the rate dependence of the interlaminar shear strength in determining the failure mode. Thus, while fibre fracture dominates the tensile failure at quasi-static rates, at impact rates failure is almost entirely due to either interlaminar shear, in the woven laminates, or fibre pull-out, in the unidirectionally reinforced specimens. Such behaviour is consistent with the hypothesis that the tensile strength of the fibres increases more rapidly with strain rate than either the interlaminar shear strength or the interfacial bond strength. For this hypothesis to be checked it is necessary to devise techniques which allow the effect of strain rate on each of these various properties to be independently determined. The present paper specifically considers the interlami-
Failure in laminated composite materials frequently involves a complex interaction between a number of different processes amongst which interlaminar shear is one of the most significant. The critical value of the interlaminar shear strength at failure, therefore, is a very important parameter in the design of composite structures and in the analysis of their failure processes. 1 Changes in the failure process which have been observed with increasing strain rate in tensile tests on both woven 2 and unidirectional 3 glass * Present address: P.O. Box 106, Northwestern Polytechnical University, Xian Shaanxi 710072, People's Republic of China.
Composites Science and Technology 0266-3538/92/$05.00 © 1992 Elsevier Science Publishers Ltd. 161
162
J. Harding, Y. L. Li
nar shear strength and reports on an attempt to determine its rate dependence for woven reinforced laminates when measured at the interface between (a) two woven glass plies, (b) two woven carbon plies and (c) a woven glass and a woven carbon ply. In practice there are considerable difficulties to be overcome in the experimental measurement of the interlaminar shear strength. In the main such difficulties are associated with the design of a specimen in which the shear stress on the interlaminar plane is reasonably uniform and sufficiently high to dominate the failure process. Relatively few attempts have been made, therefore, to determine the interlaminar shear strength at the highest rates of loading where these problems are most severe. One of the first of these 4 used the torsional version of the Hopkinson bar and a thin-walled tubular specimen cut with its axis perpendicular to the plane of reinforcement. A significant increase in the interlaminar shear strength with strain rate was found for both plain weave and cross-ply glass/epoxy laminates at strain rates in the range 100-1000/s. In neither case, however, was failure by simple shear entirely on the interlaminar plane. Other types of specimen were used by Chiem and Liu, 5 for woven glass/epoxy, also in the torsional Hopkinson bar, and by Werner and Dharan, 6 for plain-weave carbon/epoxy, in the double-notch shear version of the Hopkinson bar. A marked rate dependence of the interlaminar shear strength was found for the glass/epoxy specimens. In contrast, no effect of strain rate on the interlaminar shear strength was observed in the carbon/epoxy specimens while their transverse shear strength decreased with increasing strain rate. More recently, a double-lap design of shear specimen has been developed for determining the interlaminar shear strength of composite specimens at impact rates of strain. This the tensile version of the Hopkinson bar. Results have been reported for a satin-weave carbon/epoxy laminate 7 and, most recently, for both a unidirectionally reinforced carbon/epoxy laminate 8 and for various plain-weave carbon and glass/epoxy laminates. 9 In all of these studies the interlaminar shear strength was found to increase with strain rate. In view, however, of the considerable variation in the magnitude of the shear stress along the interlaminar failure plane
and the presence of significant levels of normal stress at the ends of this plane, some doubts must remain regarding the specific values of interlaminar shear strength obtained with this design of specimen. The present paper looks in detail at a range of results determined in this way and discusses the significance of the values of interlaminar shear strength so obtained.
2 SPECIMEN DESIGN A double-lap design of shear specimen, as shown schematically in Fig. 1, was used in both quasi-static and impact tests. A tensile load applied across the ends of the specimen is required to give shear failures at the two interfaces over which the reinforcing plies overlap rather than tensile failures in one or more of the arms of the specimen. Since the rate dependence of the tensile strength may not be the same as that of the interlaminar shear strength a ply lay-up which is found to be satisfactory at one rate may not prove to be satisfactory at the other. Thus, while the lay-up shown in Fig. 1, i.e. two reinforcing plies in each of the outer arms and four in the central region, gave good results for the carbon/epoxy laminate at the quasi-static rate, under impact loading tensile failures were obtained in one or more of the arms of the specimen. A modified lay-up, shown in Fig. 2(a), with three reinforcing plies in each outer arm and five in the central region, proved satisfactory at both loading rates, however, for the carbon/epoxy laminate. To determine the interlaminar shear strength at the interface between a carbon reinforced and a glass reinforced ply, a hybrid lay-up is required. A previous finite element study of two such hybrid lay-ups ~° showed that the shear stress variation on the failure plane was minimised
PTFE Input barn .~
\
~20-1~ A
Specimen
,,
IIIII~'III I (II III . . . .
=J i
Outputbar
rT_~ / / /
30
,
+c; \
i
Strain gauge -I
Dimensionsin mm Fig. 1. Double-lap shear specimen.
I
Interlaminar shear strength of laminated composites a) All-carbon toy-up, quasi-static and impact tests
[
t. . .
I
I
I
I
b) Hybrid lay-up, quasi-static tests
I
[
l
I
....
I
the lay-up shown in Fig. 2(c) which gave good results at both loading rates. The lay-up used for the glass/epoxy laminate is shown in Fig. 2(d) and gave shear failures at both rates of loading. At the quasi-static rate specimens were loaded in a standard Instron testing machine, giving a time to failure of about 10 s, while in the impact tests the specimen was fixed between the input and output bars of a split Hopkinson bar apparatus and failure occurred after about 30 jus.
3 SPECIMEN MATERIAL A N D PREPARATION
c) Hybrid lay-up, quasi-static and impact tests
I
163
I
I
I
d) All-glass toy-up, quasi-static and impact tests
Fig. 2. Ply lay-ups in double-lap shear specimens.
when the reinforcing plies with the higher stiffness were in the outer arms of the specimen and when the number of lower stiffness plies was minimised. The first hybrid lay-up to be studied, therefore, was that shown in Fig. 2(b). This proved satisfactory at the quasi-static but not at the impact loading rate and thus was replaced by
To allow as close a comparison as possible with earlier experimental work on the same materials under impact loading in both tensionT M and compression,7 the carbon/epoxy, glass/epoxy and hybrid specimens were prepared from the Ciba-Geigy XD 927 epoxy resin system and dry fabric supplied by Fothergill and Harvey Ltd (Littleborough, Lancashire). The carbon fibre fabric was woven from Toray 3000 filament fibre tows, type T300-3000A, and had a weight of 189g/m 2 and an approximate thickness of 0.28 ram. The fabric was of a relatively coarse weave with only 47 ends and picks per 10 cm. The glass fabric was woven from continuous E-glass fibres, designation 11 x 2EC5, and had a weight of 96g/m 2 and a thickness of about 0.10 mm. With 252 ends and 173 picks per 10 cm the weave was much finer than that for the carbon fabric. To prepare double-lap laminates, aluminium and poly-tetra-fluoro-ethylene (PTFE) spacers were used (see Fig. 3). The lay-up was covered with a Nylon bagging film, breather fabric, Aluminium spacer covered with PTFE
Outer reinforcing plies
Central reinforcing plies
Alurninium spacer covered with PTFE 7ram
~tumlnlum spacer covered with PTFE
-Aluminium base plate covered with PTFE
Outer rein pliers
Fig. 3. Preparation of double-lap shear specimens.
164
J. Harding, Y. L. Li Table 1. Details of plain-weave double-lap shear laminates
Interface t y p e : Resin (%) Total plies Central plies Testing rates
Carbon/carbon 39.0 8 4 Static
45-7 11 5 Static Impact
Carbon/glass 49-1 7 + 4b 3 + 4h Static
Glass/glass
42.0 10 + 4h 4 + 4h Static Impact
52.5° 56.7 25 25 11 11 Static Static I m p a c t Impact
a Delay of 13 h at ambient temperature after lay-up and before curing. b 7 + 4, 7 carbon plies + 4 glass plies.
pin-prick film and peel ply and evacuated to 635 mm of mercury. In order to minimise loss of resin this was then put into an open mould having internal dimensions 160 mm × 90 mm × 10mm. The mould was then placed inside a closed container at an air pressure of 620 kPa and the container placed inside a small oven. The temperature was raised over a period of 1 h to 100°C, held for 16 h and then allowed to cool to room temperature at a rate of 8°C/h. Specimens of l O m m width were cut from the resulting laminate using a diamond saw. Details of the six laminates prepared in this way are given in Table 1.
90 80
T
70 60 ~ so ~ 40 ~ 30 g~ 2o ~0 0 0
J
::}5
7!0
~-5
]&.O
]- - S h e a r zone =i IDistance atong specimen (mm)
Fig. 5. Shear stress distribution on interlaminar failure plane for all-carbon lay-up of Fig. 1. 4 FINITE ELEMENT
ANALYSIS
A two-dimensional finite element analysis was performed for each of the five specimen lay-ups of Figs 1 and 2 with previously determined in-plane elastic properties for the carbon and glass reinforced plies and estimated elastic properties in the through-thickness direction. 1 In all specimens there were geometrical discontinuities at each end of the failure plane leading to a singularity and stress and strain concentrations at each of these points. For the all-carbon lay-up shown in Fig. 1 a finite element mesh consisting of 120 isoparametrical elements, each with eight nodes, was used (see Fig. 4). Since the specimen is symmetrical about the longitudinal axis, only half is modelled. The shear stress variation on the interlaminar plane over the shear zone length of 7 r a m and for a further 3.5 mm on either side was determined and is shown in Fig. 5. The analysis was performed with
Fig. 4. Finite element mesh for all-carbon lay-up of Fig. 1.
the assumption of an external loading of 245 kN, equivalent to an average shear stress on the failure plane of 35 MPa, about the same as that determined experimentally for quasi-static failure of the all-carbon lay-up. As expected, large and almost equal shear stress concentrations were found at each end of the failure plane, giving an apparent maximum variation in the shear stress of about 5.5" 1. For the all-glass lay-up this ratio increased to about 9:1. In practice, however, the actual values of shear stress derived from the finite element analysis close to the points of singularity will be dependent on the mesh size in this region--the finer the mesh the more reliable the estimate of the maximum shear stress. The results shown in Fig. 5, therefore, should only be taken as giving a general indication of the shear stress variation in the all-carbon lay-up. In the hybrid specimens, however, an additional problem arises from the discontinuity in elastic properties due to the different types of reinforcing ply on either side of the failure plane. This leads to a corresponding discontinuity across the interface in the longitudinal stress and the shear and normal strains. However, since the
Interlaminar shear strength of laminated composites shear stress at the interface is directly proportional to the average of the shear strains either side of the interface, as shown in the Appendix, while the longitudinal strain is not discontinuous, the results of the finite element analyses may be more conveniently presented in terms of the strain distribution along the interlaminar failure plane. The variation of shear, longitudinal and normal strain for the all-carbon lay-up is shown in Fig. 6 for an applied longitudinal displacement across the ends of the specimen equivalent to a tensile strain of 1%. The maximum variation in the shear strain, about 5-6: 1, is very similar to the maximum variation in shear stress shown in Fig. 5. The normal strain, due to the Poisson's ratio contraction at the outer ends of the specimen, shows local peak values at each end of the failure plane, indicating the presence of significant levels of normal stress at these points and raising the possibility that failure will initiate here under the combination of the peak shear stress and the peak normal stress. Generally, similar strain distributions were shown by each of the five specimen lay-ups, except that for the modified all-carbon lay-up (Fig. 2(a)) and the all-glass lay-up (Fig. 2(d)) the peak shear and normal strains were increased at the left hand end and reduced at the right hand end of the failure plane. This effect was even more marked for the two hybrid lay-ups--see Fig. 7 where it is the average values of shear and normal strain at the interface which are determined. From these various finite element analyses it is clear that the shear stress on the interlaminar failure plane will be far from 0.04
i
0.035
i
it II II i ~
0.03
al
0"025 .c_
i
I I
0.02
/
I
I
A
I k
I
": o.o15
v)
0"01
x
0.005 o
-ooos
---'
I !, '"
"...
,,,' s /
I
....
!!K ---
x!L
3'.5
7!0 Distance
~d5
~40
along specimen (mm)
Fig. 6. S t r a i n d i s t r i b u t i o n o n i n t e r l a m i n a r f a i l u r e p l a n e f o r a l l - c a r b o n l a y - u p o f Fig. 1. L o n g i t u d i n a l s t r a i n ( e n ) - - ; s h e a r s t r a i n (Y,2) . . . . . . ; n o r m a l s t r a i n ((22) . . . . .
0-07
165
i
i
i
f
0-0(
II
iI
0.0 t,
It
0"0~
I| I I I I ! I
A'
._~ o
0.0"
J l l ill
0,02
o ...... _
-0.01
o
', "..
. . . ._/.~, : ,
,,
/',A t~ . ~~,-~ ... . . . . . . .
....................
3'.5 Distance
i
7'0 along
specimen
10-5
~4.0
(ram)
Fig. 7. Strain distribution on interlaminar failure plane for hybrid lay-up of Fig. 2(c). Longitudinal strain (E,I) ; shear strain (Y12) ; normal strain (e22). . . . . uniform and that normal stresses at the ends of the interlaminar plane will be likely to play a part in the initiation of failure. However, until a better design of specimen, which is suitable for testing at both quasi-static and impact rates, is developed the double-lap shear specimen does allow comparative data to be obtained for different lay-ups and different rates of loading.
5 RESULTS Quasi-static tests
In the quasi-static tests the load was obtained from a load cell in series with the specimen, and the displacement across the ends of the specimen was derived from the integrated output of a pair of velocity transducers in parallel with the specimen. Typical load/time and displacement/time signals for a test on an all-glass specimen are shown in Fig. 8. By assuming that failure occurs at the peak load and that the two failure planes are equally loaded, a mean shear stress on the interlaminar plane at failure may be determined. Table 2 lists the shear stresses obtained in this way for the all-carbon, all-glass and hybrid carbon/glass lay-ups. The displacement signal in Fig. 8 gives a measure of the overall extension of the specimen and relates, therefore, to an apparent average tensile strain. The actual shear strain in the interlaminar region will depend on what proportion of the total displacement appears across the shear zone and on the effective thickness of this region, neither of which are known. However,
J. Harding, Y. L. Li
166
30
200
.,~ ,/
25
~
150
~~ ......Displ~acement
20
Load
~ 0
~
tOO
~0
s ~s
oE
z 5
0 0
10
30
20
Time
/
40
;~
50
(seconds)
¢.0
¢.~
---
2.0
Nomina[ Shear Strain (*/,)
Fig. 8. Load versus time and displacement versus time signals for quasi-static test on all-glass specimen.
the finite element analyses of Figs 6 and 7 show that although the shear strain on the interlaminar plane varies by almost an order of magnitude the mean value is of the same order as the 1% overall applied tensile strain. It is possible, therefore, to derive a nominal shear stress versus nominal shear strain curve from load and displacement signals such as those in Fig. 8. Curves for four tests on plain weave all-carbon specimens are given in Fig. 9 and show a reasonably repeatable behaviour. Impact tests The load supported by the specimen in the impact test is derived from the output bar strain gauge signal while calculation of the overall extension of the specimen requires, in addition, signals from two sets of gauges on the input bar. In order to allow a more direct estimate of the deformation of the specimen, strain gauges were also attached to the specimen itself on the outer surfaces in the 7 mm overlap region, as shown in Fig. 1. Typical load/time and strain/time signals,
Fig, 9. Nominal shear stress versus nominal shear strain curves for quasi-static tests on all-carbon specimens.
as obtained from the output bar and the specimen strain gauges and stored in a dual-channel high-speed transient recorder, are shown in Fig. 10 for a test on an all-carbon specimen. Allowance has been made for the time taken by the loading wave to travel between the two strain gauge positions. With the same assumptions as in the quasi-static tests, the mean shear stress and shear strain on the interlaminar plane may be determined from the load/time curve, obtained from the output bar strain gauges and the overall specimen extension, derived from the standard Hopkinson bar analysis. Mean interlaminar shear strengths calculated from the peak values of load for the four specimen types are listed in Table 3 and a set of nominal shear stress versus nominal shear strain curves for the four impact tests on the all-carbon specimens and the corresponding
u]
150
Specimen Strain Gauge
/~
el
Table 2. Average interlaminar shear strengths (ILSS) in quasi-static tests Specimen type
Fibre fraction
No. of tests
Average ILSS (MPa)
(wt%)
~
o ID ~
All-carbon
39 45
3 4
26.2 + 1-3 26.4 + 1.7
.,~
Carbon/glass
42 49
5 6
26.6 + 3.9 27.1 + 3.0
~
53 57
3 5
20.8 + 0.5 20-2 + 3.2
All-glass
7oo
5o
o
i
t
10
20
Time
.
L
30
40
5O
(microseconds)
Fig. 10. Specimen and output bar strain gauge signals for impact test on all-carbon specimen.
Interlaminar shear strength of laminated composites
167
Table 3. Average intedsminar shear strengths (ILSS) in impsct tests Specimen type
Fibre fraction
No. of Average ILSS tests (MPa)
(%wt)
All-carbon
45
6
45.0 + 4.2
Carbon/glass
42
5
41.4 + 4.7
All-glass
53 57
3 3
33.4 + 2.0 37-4 + 0-3
curves of nominal shear strain rate versus shear strain are shown in Fig. 11. Fracture behaviour
Macrographs of a failed hybrid specimen after quasi-static loading are shown in Fig. 12. Both the fine-weave glass fabric and the trace in the resin matrix of the coarse-weave carbon fabric are visible on the interlaminar failure plane, implying that there is a step in the resin across the failure plane, as shown schematically in Fig. 50
~,\ 3O
/S
5 U3
2O ,
1
2
.x\"
'¢,\
3
Nominal Shear Strain (*/,1
(a) 2000
Fig. 12. Macrographs of quasi-statically tested hybrid specimen (x2-2).
13. A similar behaviour was observed in both quasi-static and impact tests on all plain-weave specimen lay-ups. Scanning electron micrographs of the failure surface for a quasi-statically tested all-glass specimen show the bare glass fibres in the region below the step (Fig. 14(a)) and the resin matrix bearing the imprint of the glass fabric in the region above the step (Fig. 14(b)). A scanning electron micrograph of the step itself for an impacted all-glass specimen (Fig. 14(c)) shows both these regions. In the impact tests all the specimens for which results are given in Table 3 failed by shear on both the interlaminar planes. However, one of the five hybrid specimens also failed simultaneously in tension, at section (a) in Fig. 15, and three of the six all-carbon specimens showed similar behaviour, two failing at section (b) and one at section (c). Only in the all-glass specimens were simultaneous tensile failures entirely absent under impact loading.
1500
Carbon plies
c
I000
5oo Glass plies Nominal Shear Strain (*/,)
(b) Fig. U . Nominal shear stress versus nominal shear strain curves for impact tests on all-carbon specimens.
Path of fracture
(Y-points of maximum initiate)
shear strain
y layer where cracks
Fig. 13. Schematic model of failure process in hybrid specimen.
J. H a r d i n g ,
168
Y. L. L i
TensiLeFailures (c) [b) (a) {[=__Xj
F~l"u'~r\els(all tests) I,,
Shear
I
Fig. 15. Types of failure in impact tests.
(a)
(b)
performed on two different laminates with slightly different lay-ups, and hence strain distributions on the interlaminar plane, and slightly different fibre weight fractions. In neither case, however, was there any significant effect on the measured interlaminar shear strength. Two different laminates were also used for the all-glass specimens. In this case both had the same lay-up but there was a slight difference in the curing treatment they had received. Again, no significant effect on the interlaminar shear strength was apparent. Under impact loading (Table 3) only for the all-glass specimens were tests performed on two different laminatae. Of these the correctly cured laminates, which also had the slightly higher fibre weight fraction, showed a significantly increased interlaminar shear strength, by about 12%. This increase was greater than the combined experimental scatter on both sets of measurements and suggests that a difference in the rate dependence of the resin following the different curing treatments may have been the determining factor. However, despite this extra effect, the average nominal interlaminar shear-stress/shearstrain curves shown in Fig. 16 almost certainly give a general indication of the shear strength of the three types of interface under impact loading. 50
(c) Fig. 14. Scanning electron micrographs of fracture surface for all-glass specimens. (a) Bare fibres below the step in a quasi-static test (x-500); (b) bare matrix above the step in a quasi-static test (x-500); (c) step region for an impact
.I '
30
,,,"
j ~"
i.!"
'\
".
test ( x - 1 0 0 0 ) u~ 20
Interface type ,~/,"
6 DISCUSSION Effect of fibre weight fraction and ply lay-up Quasi-static tests on both the all-carbon and the hybrid carbon/glass specimens (Table 2) were
E
/ 10 ~ ' / / /.
.1.1"
/" . / . / " I"""'"''"" I 1
--
carbon/carbon
....... carbon/glass .....
glass/glass
L I 2 3 Nominal Shear Strain (o/°)
Fig. 16. Effect of interface type on nominal interlaminar shear stress versus strain curves under impact loading.
Interlaminar shear strength of laminated composites Process of fracture
50
ca
Impact m
20~ asi
E o 7
-
static
10
I 1 Nominal
I 2
3
Shear S t r a i n (,/o)
Fig. 17. Effect of loading rate on n o m i n a l interlaminar shear stress versus strain curves for c a r b o n / c a r b o n interface.
Effect of strain rate
Average shear-stress/shear-strain curves for the all-carbon specimens at the two loading rates, derived from the results given in Figs 9 and 11, are shown in Fig. 17. Table 4 collates data on the average interlaminar shear strength for the three types of interface. In each case there is a significant increase in the shear strength between the quasi-static and the impact rates of loading, by about 70% for the all-carbon and all-glass interfaces and by about 50% for the hybrid interface. At both rates the carbon/carbon interface has a higher failure strength than the glass/glass interface. This could be either because the bonding with the matrix is better for the carbon than the glass fibres or because the carbon fabric has a much coarser weave than the glass fabric, allowing a stronger mechanical interaction across the interface between two carbon plies. Whichever mechanism controls the interlaminar failure, it has the same rate dependence for the two types of interface. However, as will be discussed in the next section, comparison of results for the different types of interface is complicated by the different strain distributions along the interlaminar plane. Table 4. Effect .of loading rate on interlaminar shear strength (MPa) Interface type Carbon/carbon Carbon/glass Glass/glass
169
Quasi-static tests 26.3 -t- 1.7 (7 tests) 26.8 + 3.9 (11 tests) 20.5 -t- 3.2 (8 tests)
Impact tests 45.0 + 4.2 (6 tests) 41-4 + 4-7 (5 tests) 35-4 + 2.9 (6 tests)
In all cases where interlaminar shear failure was obtained, a step was observed across the fracture surface. This is very clearly shown in Fig. 12 for a quasi-static test on a hybrid specimen. Scanning electron micrographs of the fracture surfaces on either side of this step for all-glass specimens tested at both quasi-static and impact rates of loading (see Fig. 14) showed a change from mainly the bare fibres of the lower ply on the input side to mainly the bare resin matrix carrying the imprint of the fibres of the upper ply on the output side. These observations support the proposed failure process illustrated schematically in Fig. 13 for the hybrid lay-up. Cracks are thought to be initiated at the points of high strain concentration at each end of the failure plane and to propagate inwards, forming a step across the resin layer where they first overlap. Further support for this proposed failure process comes from the signals obtained in all impact tests from strain gauges attached directly to the specimen. As shown in Fig. 10, which compares the specimen strain gauge signal with that derived from the ouput bar strain gauges for an impact test on an all-carbon specimen, although the load transmitted through the specimen, as recorded by the output bar gauges, increases monotonically to a single peak value, the specimen gauges show a double peak separated by a region where the strain decreases slightly. The time between the two peaks, - 1 0 #s, is too long to be due to reflected waves within the overlap region of the specimen. It seems more likely that this small decrease in strain results from the initiation and limited propagation of cracks from points Y at the left hand end of the interlaminar plane (cracks propagating from the right hand ends of the interlaminar planes would be much less likely to reduce the longitudinal strain at the gauge positions). It is significant, therefore, that in all of the specimen lay-ups used for tests at the impact loading rate, both the shear and the normal strain concentrations were greater at the input end than at the output end of the interlaminar plane. Although for the all-carbon lay-up the difference in strain concentration between the ends of the interlaminar plane was relatively small, for the all-glass and, particularly, the hybrid lay-ups (see Fig. 7) the difference was much greater. Here, therefore, cracks initiating
170
J. Harding, Y. L. L i
'~
90
~
80
~
7O
~d so O ~
50 4O
09
3O
b-"
10
I I0
t 20
i 30
i 40
,a_ 50
60
Time (microseconds) (a) 130 .~
120 110
¢~ 1 0 0 ~
9O
~"
8O
~ @ 0
7O 60
~
5O
~
4o
"~
30
t~
,? O 10
f o
i
i
i
i
~
i
5
,o
,5
zo
zs
so
s5
40
(microseconds) (b) Fig. 18. Effect of failure mode on specimen strain gauge signal. (a) Hybrid lay-up of Fig. 2(c) failing by interlaminar shear; (b) hybrid lay-up of Fig. 2(b) failing in tension. Time
at this point are likely to propagate further, giving a much more marked decrease in the specimen strain gauge signal, such as is shown in Fig. 18(a). This contrasts with the impact response of a hybrid specimen having the lay-up shown in Fig. 2(b). Under impact loading this failed in tension in the central arm at position (b) in Fig. 15. A crack had initiated and propagated a short distance from the left hand end of the interlaminar plane. In this, and similar, cases, as shown in Fig. 18b, no double peak was apparent on the specimen strain gauge signal, presumably because the tensile failure occurred at a lower load than that required to initiate the crack at the right hand end of the interlaminar plane.
7 CONCLUSIONS
A new testing technique is described for determining the interlaminar shear strength of
fibre-reinforced polymer matrix composites. A double-lap shear specimen is used in which failure occurs on a predetermined plane. Finite element studies reveal large stress and strain concentrations at each end of the failure plane so that only mean values of the shear stress at failure may be determined by this method. Using different ply lay-ups in the double-lap shear specimen, results are obtained for the effect of loading rate on the shear strength at the interface between (a) two plain-weave carbon/ epoxy plies, (b) two plain-weave glass/epoxy plies, and (c) a plain-weave carbon/epoxy ply and a plain-weave glass/epoxy ply. The stress and strain distribution on the failure plane is sensitive to the precise ply lay-up so the specific values of strength determined at the different types of interface are not directly comparable. The same general trends in mechanical response, however, were shown by each interface. An increase in loading rate of about six orders of magnitude was found to raise the average value of the shear stress on the failure plane by about 70%, for the carbon/carbon and glass/glass interfaces and by about 50% for the hybrid carbon/glass interface. Fracture is by crack propagation along the fibre matrix interface from each end of the interlaminar failure plane and final failure occurs when the two cracks overlap and produce a step across the intervening matrix region.
ACKNOWLEDGEMENTS
This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant no. AFOSR-870129.
REFERENCES 1. Li, Y. L., Ruiz, C. & Harding, J., Failure analysis of woven hybrid composites using a finite element method. Comp. Sci. & Technol., 41 (1991) 129-46. 2. Welsh, L. M. & Harding, J., Effect of strain rate on the
tensile failure of woven-reinforced polyester resin composites. In Proc. DYMAT 85, Int. Conf. on Mechanical and Physical Behaviour o f Materials under Dynamic Loading, Les Editions de Physique, Paris,
CoUoque C5, 1985, pp. 405-14. 3. Welsh, L. M. & Harding, J., Proc. Composite Materials, ICCM V,
1517-31.
5th Int. Conf. on TMS-AIME (1985)
Interlaminar shear strength of laminated composites 4. Parry, T. & Harding, J., The failure of glass-reinforced composites under dynamic torsional loading. In Colloque Int. du CNRS No. 319, Plastic Behaviour of Aniaotropic Solids, ed. J. P. Boehler. CNRS, Paris, 1988, pp. 271-88. 5. Chiem, C. Y. & Liu, Z. G., Modelling of dynamic behaviour of composite materials. In Impact Loading and Dynamic Behaviour of Materials, Vol. 2, ed. C. Y. Chiem, H.-D. Kunze & L. W. Meyer. DGM Informationsgesellschaft mbH, Oberursel, 1988, pp. 579-86. 6. Werner, S. M. & Dharan, C. K. H., The dynamic response of graphite fibre/epoxy laminate at high shear strain rate. J. Comp. Mater., 20 (1986) 365-74. 7. Harding, J., Li, Y. L., Saka, K. & Taylor, M. E. C., Characterisation of the impact strength of woven carbon fibre/epoxy laminates. In 4th Oxford Int. Conf. on Mech. Props. of Materials at High Rates of Strain. Inst. Phys. Conf. Series No. 102, Institute of Physics, London, 1989, pp. 403-10. 8. Bouette, B., Cazeneuve, C. & Oytana, C., Shear in carbon/epoxy laminates at various strain rates. In Developments in the Science and Technology of Composite Materials. Elsevier Applied Science, London, 1990, pp. 937-42. 9. Harding, J., Li, Y. L. & Taylor, M. E. C., The ettect of strain rate on the interlaminar shear strength of woven reinforced laminates. In Developments in the Science and Technology of Composite Materials. Elsevier Applied Science, London, 1990, pp. 967-72. 10. Li, Y. L., Harding, J. & Ruiz, C., A new type of shear specimen for measuring the interlaminar shear strength under impact loading. Appendix II, Oxford University Engineering Laboratory Report No. OUEL 1863/90, 1990. 11. Harding, J., Saka, K. & Taylor, M. E. C., The effect of strain rate on the tensile failure of woven-reinforced carbon/glass hybrid composites. In IMPACT 87, Impact Loading and Dynamic Behaviour of Materials, Vol. 1, ed. C. Y. Chiem, H.-D. Kunze & L. W. Meyer. DGM
171
Informationsgesellschaft mbH, Oberursel, 1988, pp. 515-22.
APPENDIX: SHEAR STRESS A N D SHEAR STRAIN ON INTERLAMINAR PLANE The average shear and normal strains on the interlaminar plane m a y be defined by the relations: (Y12)~ = ½{(Y,2), + (rl2)c)
(A1)
(e22)a = ½{(ez2)g + (e22)c}
(A2)
and
w h e r e subscripts 'g' and 'c' refer to glass and carbon reinforced plies, respectively. Continuity of shear stress across the interlaminar plane requires that: (G12)¢(]/12)¢ = (G12)g(Yl2)g = l=12
(A3)
where G12 is the shear m o d u l u s of the c a r b o n or glass reinforced ply and ~12 is the interlaminar shear stress. Solving for ~lz b e t w e e n eqns (A1) and (A3) gives:
~2 = { 2( G,E)~(G,2)g/[ ( G,2)~ + (G,E)gl}(Y,2)~ (A4) i.e. the interlaminar shear stress is directly proportional to the average interlaminar shear strain.