Initiation of damage in composite plates under
transverse central static loading
N.K. Naik *, Bulliraju Nemani
Department of Aerospace Engineering, Indian Institute of Technology, Powai, Mumbai 400 076, India
Abstract
Experimental and analytical studies have been carried out on transverse static central load threshold for damage initiation.
Experiments have been carried out on a typical plain weave E-glass/epoxy laminated plate. A good correlation is observed between
the experimental results and ®nite element analysis predictions. Further, analytical studies have been carried out on the e€ect of
reinforcement architecture on the load threshold for damage initiation. It is observed that transverse static central load threshold for
damage initiation is higher for woven fabric composites compared to those of cross-ply laminates made of unidirectional layers and
unidirectional composites.
Keywords: Damage initiation; Transverse static loading; Experimental results; Prediction; Woven fabric composites
1. Introduction
Polymer matrix composite materials are ®nding increasing use in high performance applications because
of their high inplane speci®c sti€ness and speci®c
strength. For e€ective use of composite structures, they
should be able to withstand multidirectional loading
also. Composite structures under transverse static
loading are one of the important design requirements.
For laminated composites made of unidirectional (UD)
layers di€erent failure modes are: matrix cracking/
lamina splitting, ®bre debonding, delamination and ®bre breakage. Normally, the macro damage initiation
takes place in the form of matrix cracking/lamina
splitting and delamination.
Stress analysis of laminated composite plates subjected to transverse loading has received considerable
attention of researchers, and many articles are available
[1±8]. The objective of the present work is to look into
the initiation of damage in composite plates under
transverse central static loading. Experimental studies
have been carried out on a typical plain weave E-glass/
epoxy laminate. The damage initiation has also been
predicted using the inhouse ®nite element analysis code.
Further, a parametric study has been carried out on
damage initiation with di€erent reinforcement architectures. Speci®cally, the studies have been carried out on
balanced symmetric cross-ply laminates made of UD
layers, woven fabric (WF) composites and three-dimensional (3D) composites.
2. Stress and damage analysis
A three-dimensional linear elastic ®nite element
analysis has been used to predict the initiation of damage in composite plates. A 3D eight-noded brick element
was used in the analysis, with three degrees of freedom
at each node …u; v; w†. The aspect ratio considered in the
present analysis is inbetween 1 and 2. By taking symmetry into consideration, quarter plate analysis was
used for the present study. Convergence study was carried out for the mesh size. Based on this study, a mesh
size of 32 32 5 was chosen for the quarter plate. The
co-ordinate system for the composite plate is shown in
Fig. 1. The boundary conditions for quarter plate are as
given below:
(a) Simply supported boundary conditions:
At X ˆ 0;
u 6ˆ 0; v ˆ 0; w ˆ 0;
At X ˆ LX =2;
u ˆ 0; v 6ˆ 0; w 6ˆ 0;
At Y ˆ 0;
u ˆ 0; v 6ˆ 0; w ˆ 0;
At Y ˆ LY =2;
u 6ˆ 0; v ˆ 0; w 6ˆ 0:
168
3. Damage evolution during transverse central quasi-static
loading
Fig. 1. Composite plate co-ordinate system.
(b) Clamped boundary conditions:
At X ˆ 0;
At X ˆ LX =2;
u ˆ 0; v ˆ 0; w ˆ 0;
u ˆ 0; v ˆ
6 0; w ˆ
6 0;
At Y ˆ 0;
u ˆ 0; v ˆ 0; w ˆ 0;
At Y ˆ LY =2;
u 6ˆ 0; v ˆ 0; w 6ˆ 0:
Based on the nodal displacements obtained, the stress
state has been evaluated throughout the composite
plate.
An inplane failure criterion by Tsai±Hill [9] has been
used for damage initiation studies. An inplane failure
function, I based on Tsai±Hill criterion is de®ned as
follows:
2 2 2 r1
r2
s12
r1
r2
‡
‡
ˆ 1:
XT
YT
S12
XT
XT
Here r1 ; r2 , and s12 are the induced inplane stress
components and XT ; YT , and S12 are the normal and inplane shear strength values. The damage initiation takes
place in the form of matrix cracking/lamina failure when
the value of the inplane failure function, I just exceeds
unity.
Initiation of delamination due to rZ and other interlaminar shear stresses is determined using an interlaminar failure function. For this, an interlaminar failure
function based on through-the-thickness quadratic failure criterion as proposed by Brewer±Lagace has been
used [10]. An interlaminar failure function is de®ned as
follows:
2 2 2 2
r3t
r3c
s23
s31
‡
‡
‡
ˆ 1:
Zt
Zc
S23
S31
Here, r3 ; s23 and s31 are the induced stress components and Z, S23 and S31 are the corresponding strength
values. Subscripts t and c indicate tensile and compressive, respectively. Superscript indicates average values
over a certain area. The delamination initiates when the
value of the interlaminar failure function, I just exceeds
unity.
The damage initiation in laminated composite plates
subjected to transverse loading can be in the form of
matrix cracking/lamina splitting, debonding and initiation of delamination. Upon further loading, the major
damage propagation mode can be the delamination
growth, and the cracking of the adjacent layers, ®nally
leading to ®bre breakage and ®bre pull out. Matrix
micro-cracking and the debonding are the micro-failure
mechanisms, and can take place at very early stages. For
UD-laminated composites the ®rst macro damage occurs in the form of lamina splitting on the tensile side of
the laminates during transverse loading because of the
inplane stresses [11]. This is because of the lower
transverse tensile strength properties of the UD lamina.
Lammerant and Verpoest [11] carried out transverse
quasi-static loading experiments on cross-ply laminate
‰904 =04 ŠS made of toughened carbon/epoxy prepreg
HTA/6376. In the experiments, they used plate-like
composite specimens clamped in a square ®xture and
loaded at a speed of 0.01 mm/sec with a hemispherical
tup at a central loading point. The laminates could still
slide in the ®xture because of the ¯at polished surface of
the ®xture. So, at the edges the ®xture only prevented
the plate from translating in the loading direction or
rotating. The unsupported area of the composite plate
was 80 mm 80 mm and the thickness 1.8 mm. Using
the acoustic emission technique and ultrasonic testing,
they monitored initiation and propagation of damage.
They observed that the ®rst damage in the laminate was
matrix cracking/lamina splitting in the bottom layer
right under the loading point at a displacement of 1 mm.
They experimentally observed that the ®rst matrix crack
initiated only a small delamination in the centre of the
plate at the lower interface.
The WF composites are characterised by balanced
inplane properties. Hence, inplane elastic and strength
properties are equal along both warp and ®ll directions.
Hence, early lamina splitting may not take place. It was
observed that the failure initiates in the top layer for WF
laminates because of inplane stresses [12]. This is because of lower inplane compressive strength of the WF
laminate compared to its inplane tensile strength. The
damage can also initiate in the form of delamination at
di€erent interfaces because of interlaminar stresses for
WF composites.
4. Experimental studies: transverse quasi-static loading
Composite plates of dimension 150 mm 150 mm 5 mm made of a typical plain weave E-glass/epoxy
laminate GLE-12 were used for the experimental studies
under transverse quasi-static loading. Loading was
169
Fig. 2. Experimental load±displacement behaviour for E-glass/epoxy,
WF, …0†s , GLE-12 under transverse static central loading-clamped.
performed on the clamped specimen at the rate of 0.2
mm/min. The unsupported area of the plate was 128 mm
128 mm. Loading was continued till the damage initiated. Tests were planned at loads at which the damage
just initiated and at loads at which substantial damage
occurred. Experimental load±displacement behaviour is
presented in Fig. 2.
In the ®rst test, loading was continued till a substantial damage was visible on the top and bottom
surfaces of the specimen. The maximum load in this case
was 5.12 kN. In the second test, loading of the specimen
was continued until damage was clearly visible on the
top surface. The corresponding load was 4.06 kN. Cscans also showed damage at this load. The other two
tests were carried out at comparatively lesser loads of
2.3 and 2.56 kN. No clear damage was visible on any of
the surfaces. However when viewed against a strong
source of light, these specimens showed a dense region
below the point of contact. The C-scans did not show
any damage. It can be taken that the point damage
initiated at a load below 2.3 kN. Typical C-scans are
shown in Fig. 3.
4.1. Validation
Using the inhouse ®nite element analysis code [13,14],
the central point displacement and the inplane failure
function have been evaluated in the present study for the
composite plate used in [11]. It was observed that, the
failure had just initiated in the form of matrix cracking/
lamina splitting in the bottommost layer as in the case of
Lammerant and Verpoest experimental observations.
Lammerant and Verpoest considered quasi-static load-
Fig. 3. Damage shapes and sizes under transverse quasi-static central
loading: C-scan results.
ing condition, whereas in the analytical predictions static
loading is considered. For the plate geometry and materials considered, inplane failure function at the bottom
(at point b), I1 ˆ 1:049 at a central static load of 380 N
for simply supported case. The corresponding displacement of the plate at the centre, dm ˆ 1.221 mm. Again,
for the simply supported boundary condition, dm ˆ 1:06
mm at a load of 330 N. The corresponding inplane failure function, I1 ˆ 0:791. On the other hand, for clamped
boundary condition, inplane failure function, I1 ˆ 1:042
at a central static load of 460 N. The corresponding
displacement of the plate at the centre, dm ˆ 0:57 mm.
As seen earlier, the boundary condition was not
simply supported or clamped realistically for the experimental studies of Lammerant and Verpoest [11].
Hence, the displacement predicted should be in between
the limiting case of 1.221 mm for simply supported case
and 0.57 mm for the clamped case at I1 ˆ 1:04.
Realistically, the transverse central loading can be
treated as a small patch load rather than a point load.
Hence the transverse load was distributed over a central
patch for the predictions. The patch area considered was
0.097% of the plate area.
Further, the experimental and predicted results have
been compared for plain weave E-glass/epoxy laminate
GLE-12. The prediction was carried out with mechani-
170
Table 1
Elastic properties of composites: E-glass/epoxya
Material
E11
(GPa)
E22
(GPa)
E33
(GPa)
G12
(GPa)
G13
(GPa)
G23
(GPa)
m12
m13
m23
Vf0
q (kg/m3 )
UD
UD
GLE-12
WG02G
3D-O
3D-OO
48.0
30.9
20.8
20.8
20.1
16.9
15.3
8.3
20.8
20.8
19.9
19.5
15.3
8.3
8.7
8.7
14.0
11.7
5.1
2.8
3.92
3.9
4.0
3.9
5.1
2.8
4.2
4.2
4.0
3.9
5.8
3.0
4.2
4.2
4.0
3.9
0.32
0.33
0.17
0.17
0.20
0.19
0.32
0.33
0.28
0.28
0.29
0.36
0.33
0.40
0.28
0.28
0.30
0.36
0.65
0.40
0.44
0.40
0.40
0.40
2112
1750
1808
1750
1750
1750
6.9b
6.9b
3.2
0.28b
0.28b
0.39b
Toughened carbon/epoxy HTA/6376
148.0
9.9
a
b
9.9b
1430b
Densities of E-glass ®bre ˆ 2620 kg/m3 and epoxy resin ˆ 1170 kg/m3 ; 3D-OO: considering possible undulations in stu€ers, ®llers and warp weavers.
Estimated values.
Table 2
Strength properties of composites: E-glass/epoxya
Material
XT
(MPa)
YT
(MPa)
ZT
(MPa)
UD
UD
GLE-12
WG02G
3D-O
3D-OO
1297
798
360
250b
359
253
27.8
27.1
360
250b
340
333
27.8
27.1
32.0
27.1
83.0
22.0
Toughened carbon/epoxy HTA/6376
2000
70
70c
YC
(MPa)
ZC
(MPa)
Vfo
820
480
225
183
215
152
150
140
225
183
204
200
150
140
445
140
170
170
0.65
0.4
0.44
0.4
0.4
0.4
1892c
260c
260c
)
S12
(MPa)
S13
(MPa)
S23
(MPa)
XC
(MPa)
39.2
36.8
28.0
28.0
36.8
36.8
39.2
36.8
28.0
28.0
36.8
36.8
38
36
28
28
36
36
100c
105
105c
a
3D-OO: considering possible undulations in stu€ers, ®llers and warp weavers.
At pure matrix block failure.
c
Estimated values.
b
cal properties given in Tables 1 and 2 [12]. Peak stresses
were at the top layer right below the point of loading.
With a load of 2 kN and clamped boundary condition
on all the four sides, the following stress state has been
obtained:
rX ˆ
227 MPa;
rZ ˆ
140 MPa:
rY ˆ
227 MPa;
The maximum tensile rZ at some distance away from
the point of loading is 6 MPa, and the central de¯ection
d ˆ 1 mm.
The same plate was analysed for simply supported
boundary condition on all the four sides with a central
load of 2 kN. The results are:
rX ˆ
263 MPa;
rZ ˆ
140 MPa:
rY ˆ
263 MPa;
The maximum tensile rZ at some distance away from
the point of loading is 6 MPa, and the central de¯ection
d ˆ 2:28 mm.
For the clamped boundary condition, rX or rY is
)227 MPa. The corresponding strength value YC is 225
MPa. So, this indicates that the damage would initiate at
a load of 2 kN on the upper surface right below the
point of loading.
For static loading, the predictions showed that the
point damage initiates at a transverse central patch
loading of 2 kN. The experimental study also showed
that the point damage would initiate at about 2 kN load.
The corresponding central de¯ection, d was 1.7 mm. The
prediction shows d ˆ 1:0 mm for clamped boundary
condition and d ˆ 2:28 mm for simply supported
boundary condition. It was observed during experimentation that the composite plate could still slide even
though clamped boundary condition was adopted. At
the edges the clamping ®xture only prevented the composite plate from translating in the loading direction or
rotating. Hence, during experimentation, the boundary
condition was not exactly clamped. The prediction of
central de¯ection is based on clamped boundary condition. Hence, the central de¯ection predicted should be
in between the limiting cases of 1.0 mm for clamped case
and 2.28 mm for simply supported case.
5. Parametric studies
A parametric study has been carried out on the e€ect
of reinforcement architecture on transverse static central
load for damage initiation. Studies have been carried
171
Table 3
Stress and failure behaviour of composites under transverse central static loadinga
Material
Load, P
(kN)
Central
displacement,
dm (mm)
UD1b
UD2c
CP1b
CP2c
GLE-12
WG02G
3D-O
3D-OO
0.49
0.51
0.55
0.58
2.00
1.60
1.85
1.40
0.172
0.301
0.189
0.334
1.006
0.805
0.938
0.767
rX
(MPa)
51.2
55.8
56.8
62.5
())227.0
())182.0
())206.0
())154.0
rY
(MPa)
rZ
(MPa)
27.6
27.5
27.8
27.4
())227.0
())182.0
())204.0
())165.0
())16.3
())1.8
())2.3
())2.5
())139.0
())112.0
())136.0
())102.0
Failure
function I1
Failure
function I2
0.99
1.03
1.00
1.03
±
±
±
±
±
±
±
±
1.02
0.99
1.00
1.01
a
Plate dimensions: LX ˆ 128 mm, LY ˆ 128 mm, LZ ˆ 5 mm, clamped.
1. Vf0 ˆ 0.65.
c
2. Vf0 ˆ 0.40.
b
3D composites. This is because of lower inplane compressive strength of WF and 3D composites compared
to the corresponding tensile strength. It may be noted
that through-the-thickness stress rZ does not lead to
initiation of delamination.
From Table 3 and Fig. 4 it can be seen that transverse
static central load threshold for damage initiation is
higher for WF and 3D composites compared to those of
CP laminates made of UD layers and UD composites.
This is because of balanced inplane properties of WF
and 3D composites.
6. Conclusions
Fig. 4. Transverse static central load threshold for damage initiation
for E-glass/epoxy composites ± clamped.
out on E-glass/epoxy composites clamped on all four
sides using the inhouse ®nite element analysis code
[13,14]. The plate dimension: 128 mm 128 mm 5
mm. The central patch area is 0.097% of the plate area.
Studies have been carried out on balanced symmetric
cross-ply laminate (CP) made of UD layers and UD
composites with ®bre volume fraction, Vf0 ˆ 0:65 and
0.4. Studies have also been carried out on two types of
plain weave E-glass/epoxy composites (GLE-12 and
WG02G) and two types of 3D orthogonal through-thethickness interlock woven composites (3D-O and 3DOO). The mechanical properties are given in Tables 1
and 2 [12,15].
Transverse static central load threshold for damage
initiation (P), central displacement …dm ) and peak stress
values …rX ; rY and rZ ) are given in Table 3 and Fig. 4. It
may be noted that the corresponding failure function
values are equal to one. Damage initiates at the bottom
surface (Fig. 1, point b) for CP and UD composites.
This is because of lower transverse tensile strength of the
unidirectional composites. On the other hand, failure
initiates at the top surface (Fig. 1, point a) for WF and
Experimental studies have been carried out on a
typical plain weave E-glass/epoxy composite, and the
transverse quasi-static central load threshold for damage
initiation has been determined. The damage initiation
has been predicted using the inhouse ®nite element
analysis code. A good correlation is observed between
the experimental and predicted results.
The transverse static central load threshold for
damage initiation is higher for WF and 3D composites
compared to those of CP laminates made of UD layers
and UD composites.
Acknowledgements
This work was supported by the Structures Panel,
Aeronautics Research and Development Board, Ministry of Defence, Government of India, Grant No. Aero/
RD-134/100/10/95-96/890.
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