Influence of ply orientation on mode I interlaminar fracture toughness of woven carbon and glass composites/Angliaplastikio ir stiklaplastikio sluoksniu armavimo kampu itaka irimo tarpsluoksnyje tasumui atplesiant.
Kersiene, N. ; Ziliukas, A. ; Kersys, A. 等
1. Introduction
The problems of toughness of steels, metal alloys, plastics and
composite, and strain mechanics that are tackled show up during extreme
loads. Various tests predicting behavior of materials and structures
[1-3] were performed trying to manage the mechanical characteristics of
materials and the best of them in developing innovative mechanical
systems and technologies. Therefore investigation of the most widely
used composite materials is relevant.
Because composite laminates are high performance structural
materials, there is a need of accurate evaluation of the interlaminar
fracture toughness for optimal design and material selection of
composite structures. Various test methods were developed to measure
critical strain energy release rate [G.sub.Ic]: the double cantilever
beam test (DCB), is used for Mode I, the 3 point end notch flexure test
(3 ENF) or the 4 point end notch flexure test (4 ENF) is used for Mode
II and the mixed-mode bending test (MMB) is used for mixed-mode I/II
[4-7]. The specimen usually contains an implanted delamination in the
form of a nonadhesive insert and is used for unidirectional fiber
reinforced composites. However, the most practical applications involve
woven reinforced and cross-ply multidirectional laminates where
delaminations occur between the plies of different orientations.
Therefore, it is essential to characterize the delamination resistance
[G.sub.Ic] with various stacking sequence along the interface for the
development of more accurate design methods. Several studies were
already performed on the mode I and mode II fracture of multidirectional
laminates [8, 9] and the majority of those results were affected by
intraply damage and crack jumping to another interface.
The aim of this paper is to study the effects of ply orientation on
the interlaminar fracture behavior of mode I in woven carbon and glass
composites. For defining the exact instant of crack initiation the
nonlinearity (NL), 5% offset or maximum force criteria were used.
2. Double cantilever beam (DCB) test details
The specimens of woven carbon and glass composites were used in DCB
tests to determine critical strain energy release rate Gc. Mode I (DCB)
test were performed on twill woven carbon/epoxy and glass/epoxy
composite systems. The specimens (width 25 mm, length 150 mm) were made
in an enterprise "Sportine Aviacija" (Fig. 1). The matrix of
laminar composite was reinforced with glass 92 125 and carbon 98 131
fibre 2/2 twill woven fabrics. Tenax HTA type filaments were used in
carbon fibre fabrics. Epoxy/hardener system L285/287 was used to
manufacture laminar composites. The initial fracture was made by
inserting aluminium foil of 30 Lim thickness into the middle of the
sample edge. Under the critical load applied this crack propagates into
the specimens' delamination plane. To determine the influence of
reinforced angles of the layers between inserts on critical strain
energy release rate [G.sub.Ic], the layer reinforced angles in four
specimens (I-IV) groups of woven carbon and glass composites were
arranged as follows:
I - [[([0.sub.2]/90).sub.3]/[0.sub.2]//[([0.sub.2]/90).sub.3]/
[0.sub.2]],
II - [[([0.sub.2]/90).sub.3]/ [0.sub.2]//90/[([0.sub.2]/90).sub.3]/
[0.sub.2]],
III - [[([0.sub.2]/90).sub.3]/ [0.sub.2]/ + 45//-
45/[([0.sub.2]/90).sub.3]/ [0.sub.2]],
iv - [[([0.sub.2]/90).sub.3]/ [0.sub.2]//+
45/[([0.sub.2]/90).sub.3]/ [0.sub.2]].
With such layout of the layer reinforcement angles the extreme
influence of the elasticity bonds on the [G.sub.c] should be reduced
because they generate asymmetrical delamination front. Such sequence of
ply layout was chosen to meet the obligatory condition, i.e., to avoid
great shifts in the layer of plastic deformations and damages.
Delamination spread in middle part of the sample marked with a symbol
"//" in parallel direction to the adjacent layers. The layer
reinforcement angles in the middle part of the specimen are 0//0, 0//90,
+ 45//- 45 and 0//+ 45.
Cantilever made from aluminum alloy was glued to the specimens with
the cold-welding type adhesive during DCB test. The pull force of
cantilever of aluminium foil-absent was 3 kN, i.e., 30 times exceeding
the required proper adhesion. For better visual observation of the crack
front propagation the measure was drawn on the white background on the
specimen side beginning from the end of aluminum foil (Fig. 1).
Tests were made in the Centre for Strength and Fracture Mechanics
of Kaunas University of Technology using the universal tension and
compression test bench produced by Swiss company "Amsler" (the
greatest load 50 kN). DCB test was made in accordance with standard ASTM
D5528 [5] crack is opened by tearing in the woven carbon and glass
composite specimens. During this test the specimen was loaded by tension
in the direction perpendicular to middle plane of the specimen while the
force was distributed in cantilevers (Fig. 2).
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Delamination developed in accordance with the mode I crack in the
middle plane of the specimen. Crack opening displacement
[[delta].sub.1]--the crack opening height was measured during the
experiment. Crack length a was visually determined during the test. The
push was from 0.5 to 1.0 mm/min. Because stable crack increase (dG/da
< 0) was observed in the course of DCB test, the unloading was done
at the beginning of the test at 2.0 and 3.0 mm, and later increments of
5.0 mm.
In conformity with the tests results the critical values of force
[F.sub.c], displacement [[delta].sub.c], crack length [a.sub.c] and
compliance C were defined. Alternative nonlinearity (NL) and 5% offset
from the initial curve rise or the maximum force (MF) criteria [8, 9]
were used in practice to estimate the inter-laminar critical strain
energy release rate to precisely determine the fracture initiation (Fig.
3). NL characterized the crack advance at the moment when the
force-displacement curve diverged from the linearity.
Because DCB test was used to determine the mode I fracture
toughness [G.sub.c] may be found from the force and deflection data by
compliance calibration using the fundamental Eq. (1)
[G.sub.c] = [F.sup.2]/2 dC/dA = [F.sup.2]/2b dC/da (1)
where b is the specimens width.
A compliance calibration is therefore required and this can be
performed using one of two modified beam theory expressions
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [[DELTA].sub.I] is the correction to the crack length to take
account of imperfectly clamped beam boundary condition, and is defined
as the intercept on the x axis of a plot of cube root of compliance
([delta]/F) versus crack length. For Berry method the compliance as a
function of crack length may be obtained for each specimen from the
slope of its load versus deflection data. The method of least squares
can be used to obtain the coefficients k and n from C - [ka.sup.n] into
equation
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
where FI and 8 are the load and deflection, respectively, at the
onset of crack advance.
[FIGURE 3 OMITTED]
When the load-displacement curves for the cracked specimens exhibit
a linear elastic response, the change in total energy in the body due to
crack extension from a to (a + [DELTA]a) is simply the area A between
the loading and unloading curves. Thus [G.sub.Ic] is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where [[delta].sub.1] and [[delta].sub.2]--displacement, estimated
respectively by loading and unloading cracked specimens.
3. Influence of ply orientation on fracture toughness
Relationships of the force F and crack opening displacement
[[delta].sub.I] of the specimen with initial crack were obtained during
the test (Fig. 4 and Fig. 5).
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
The investigation results showed that in the case of carbon/epoxy
specimen when compared with lass/epoxy, the smaller offset of the
relationship of load force displacement and crack opening displacement
from the linearity was determined. In glass/epoxy composite relationship
nonlinearity from 10 to 20 times greater could be visually observed.
[FIGURE 6 OMITTED]
The increase of load force value at the beginning of fracture in
glass/epoxy specimens had an influence on the sharp increase of critical
strain energy release rate. This determined the formation of great
plastic zone in the crack tip depending on the type of reinforced
material. Unstable crack propagation was noticed in carbon/epoxy
specimen during the experiment due to the influence of brittle fabric of
carbon fibre on the crack propagation in the epoxy resin. This
consistent pattern was reflected in the nature of relationships between
F and [delta] (see the vertical apexes in Fig. 4).
Test results were processed on the basis of Eqs. 2-4 using the
crack length correction and Berry methods, estimating the compliance C
and beam theory (F, a) and area integration methods. The crack length a
was determined visually after each unloading of the specimen until its
general predetermined value was reached. [G.sub.Ic] is required for
crack propagation for some particular value [a.sub.i] expressed by the
area limited with load-offset curve excluding elastic energy, and
estimated as the beam compliance C (mm/N).
[FIGURE 7 OMITTED]
But in glass/epoxy specimen during crack propagation the
significant increase of [G.sub.Ic] was obtained as the result of the
initial delamination branching into additional layer of the specimen
delamination plane. The increase of the values of [G.sub.Ic] during
crack propagation was set in most of glass/epoxy specimen. It was
specified that when the layers were reinforced at the angles + 45//- 45
in the delamination plane, the crack was branching into the adjacent
0//+ 45 layers after the area a - a0 = 30 - 40 mm was reached. When the
reinforced angles of the layers in delamination plane were arranged as
0//0 and 0//90, the increase of [G.sub.Ic] was noticed when the value
a-a0 reached 30 mm length.
During crack opening, the values [G.sub.Ic] were calculated at the
points of crack initiation, i.e., NL and MF. The values of critical
strain energy release rate during crack initiation were determined with
the help of initial crack length. Analogous variation in amplitude
response of the [G.sub.Ic] of carbon/epoxy and glass/epoxy specimens was
obtained using the method of crack length correction and Berry method.
Figs. 6 and 7 show the results of [G.sub.Ic] of delamination in the
middle plane of carbon/epoxy and glass/epoxy specimen at the angle of
0//90 by using maximum force criteria. The values of [G.sub.Ic], defined
by the nonlinearity criterion to values of [G.sub.Ic], defined by
maximum force criteria were compared. In the case of carbon/epoxy the
nature of relationships of [G.sub.Ic] and crack growth for all four
groups of the reinforced angles in the middle plane during crack
propagation remained constant.
[FIGURE 8 OMITTED]
The application of area integration method resulted in significant
variation of estimated values. Beam theory method used in case of
glass/epoxy specimens showed the variation of relationships analogous to
the crack length correction and Berry method. But the values determined
with the help of nonlinearity and maximum force criteria in Beam theory
method significantly exceeded the values of [G.sub.Ic] obtained with
more conservative methods (Figs. 8 - 11).
On the basis of nonlinearity criterion in Berry method, the
following [G.sub.Ic] values of mode I and mode II were obtained for
glass/epoxy specimen types: [G.sub.Ic] = 0.577 kJ/[m.sup.2] [0//0] and
[G.sub.Ic] = 0.591 kJ/[m.sup.2] [0//90].
DCB test defined the relationships of the critical strain energy
release rate of composite materials and crack increase describing the
character of the crack propagation and [G.sub.Ic-prop] values (Table).
The values of [G.sub.Ic] in carbon/epoxy and glass/epoxy specimens were
calculated. They were estimated in relation to the reinforced angles of
the layers in the delamination plane and the calculation methods of the
crack initiation and crack propagation in various change areas (NL and
MF).
In carbon/epoxy specimens when the angles 0//0 were used to
reinforce layers in delamination plane and using the method of crack
length correction the values of [G.sub.Ic] in the delaminating area were
0.28 - 0.42 kJ/[m.sup.2] and using Berry method the values were 0.20 -
0.23 kJ/[m.sup.2]. [G.sub.Ic] values in the maximum force (MF) area were
0.32 and 0.23 kJ/[m.sup.2], approximately.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
When [G.sub.Ic] values of the specimen were estimated at the
maximum force equal to [0//0] using the crack length correction method,
the critical strain energy release rate values of glass/epoxy specimens
were 0.83 and 0.77 kJ/[m.sup.2] when Berry method was used. [G.sub.Ic]
values of the carbon/epoxy specimen changed by 33% in the
initiation-propagation area of maximum force when the crack correction
method was used, and by 1.3% when Berry method was used, thus this made
significantly smaller part if compared with the change of the [G.sub.Ic]
values of the polymer composites reinforced with glass fibre fabric.
[FIGURE 11 OMITTED]
For glass/epoxy specimens 52 % change was determined in the first
instance, and 18 % variation was defined in the second instance. The
estimated significant increase of the [G.sub.Ic] determines the greater
than actual values in many specimen types, especially mode I [0//0]. But
the most conservative Berry method was chosen for the more precise
values of the [G.sub.Ic]. Table and Fig. 12 demonstrated the values of
compliance C (mm/N) and coefficient n used in this method.
Figs. 13 and 14 demonstrated the relationships of [G.sub.Ic] values
of the carbon/epoxy and glass/epoxy specimen groups of modes I-IV on the
angles that reinforced the layers in the delamination plane using Berry
method.
The values of [G.sub.Ic] of the critical strain energy release rate
of glass/epoxy specimens by 2.8, 2.76, 1.78 and 2.21 times are greater
if compared with the [G.sub.Ic] values of carbon/epoxy specimens using
NL criterion at the corresponding angles of layer reinforcement in
delamination area: 0//0, 0//90, 0//+ 45 ir + 45//- 45. The more
significant variation of specimens was obtained for MF criterion, i.e.,
3.96, 5.01, 2.37 and 2.06 times, respectively. This showed greater
resistance of glass/epoxy specimens to delamination when the crack was
opened by tearing (mode I) and especially, in the case of mode II
[0//90] and mode I [0//0] specimen groups at NL and MF load.
[FIGURE 12 OMITTED]
[G.sub.Ic] values of carbon/epoxy and glass/epoxy specimen were the
greatest in the interlayer of + 45//- 45. It has been determined that
the variation of the angle [theta] in the sequence of 0 [degrees], 45
[degrees] and 90 [degrees] in the delamination plane of layer
reinforcement, the equivalent change of the [G.sub.Ic] in the
glass/epoxy specimens was obtained when the difference of the crack
length was 20-30 mm.
But this consistent pattern could not be used with carbon/epoxy
specimens. Great result variation was obtained during the trail in
carbon/epoxy specimen due to unstable crack propagation (dG/da > 0,
[a.sub.0] < L/[cube root of 3]). Thus the estimation of more precise
[G.sub.Ic] values was impossible to determine.
[FIGURE 13 OMITTED]
[FIGURE 14 OMITTED]
After the layer reinforcement angles in the delamination plane were
arranged in + 45//- 45 the extremely great variation from 0.91 to 0.54 J
of [G.sub.Ic] values was obtained. If compared with the values of
critical strain energy release rate obtained at the angle 0//0
arrangement that varied in the range from 0.3 to 0.13 J, the variation
was by 2.5 to 4 times greater. With such result variation in the crack
propagation area, it was appropriate to determine [G.sub.Ic] values in
the zone of initial fracture where the actual delamination in the sample
interlayer started.
3. Conclusions
In order to determine the influence of angles used to reinforce the
layers between inserts on the critical strain energy release rate, the
quasi-stationary test analysis was used to open the crack by tearing the
woven carbon and glass composites. In accordance with the test results
with carbon/epoxy composites from 10 to 20 times less deflection from
linearity was defined for the relationships between load force and the
crack opening displacement. The increase of the load force value in
glass/epoxy specimens at the fracture initiation has significant
influence to the increase of [G.sub.Ic] that determined the formation on
the great plastic zone on the crack tip determined by the type of
reinforcement material.
When nonlinearity criterion was used the value of [G.sub.Ic] of
glass/epoxy specimen was by 2.8, 2.76, 1.78 and 2.21 times greater if
compared with [G.sub.Ic] values of carbon/epoxy specimen of the
corresponding angles of layer reinforcement in delamination area: 0//0,
0//90, 0//+ 45 and + 45//- 45. This showed greater resistance of
glass/epoxy specimens to delamination when the crack opened by tearing.
It was determined that [G.sub.Ic] in glass/epoxy significantly
increased when the crack branching in the delamination plane occurred.
The variation of critical strain energy release rate was obtained in
crack propagation area due to unstable crack propagation in carbon
plastics; thus this energy in the crack propagation area should be
defined in the initial crack zone.
The values of critical strain energy release rate determined with
area integration method showed great variation of results. For this
reason the conservative Berry method (mode I) and nonlinearity criterion
were chosen for the result estimation. NL criterion made it possible to
predict the increase of the damages in the microlevel.
After the estimation of the influence of the angles used to
reinforce the layers on [G.sub.Ic] the conclusion was made that the
reinforcement at the angles of 0//0 and especially 90//0 was the most
dangerous. Thus in the structures the layers should be reinforced at the
angles of 0//+45 because [G.sub.Ic] was by 1.4 times greater if compared
with the instance of 0//0 angles.
Received February 03, 2010 Accepted April 15, 2010
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N. Kersiene *, A. Ziliukas **, A. Kersys ***
* Kaunas University of Technology, Kqstucio 27, 44312 Kaunas,
Lithuania, E-mail: neringa.kersiene@ktu.lt
** Kaunas University of Technology, Kqstucio 27, 44312 Kaunas,
Lithuania, E-mail: antanas.ziliukas@ktu.lt
*** Kaunas University of Technology, Kqstucio 27, 44312 Kaunas,
Lithuania, E-mail: arturas.kersys@ktu.lt
Table
Critical strain energy release rate employing Berry method
MFC
Composite [G.sub.Ic-init.],
system Interlayer C, mm/N kJ/[m.sup.2]
Glass/epoxy 0//0 0.100 0.774
92 125// 0//90 0.091 0.919
L285/287 0//+ 45 0.085 1.030
+ 45//- 45 0.070 1.274
Carbon/epoxy 0//0 0.085 0.227
98 131// 0//90 0.069 0.247
L285/287 0//+ 45 0.070 0.292
+ 45//- 45 0.037 0.405
NLC
Composite [G.sub.Ic-init.],
system Interlayer C, mm/N kJ/[m.sup.2]
Glass/epoxy 0//0 0.094 0.577
92 125// 0//90 0.075 0.591
L285/287 0//+ 45 0.074 0.721
+ 45//- 45 0.068 0.895
Carbon/epoxy 0//0 0.079 0.205
98 131// 0//90 0.061 0.214
L285/287 0//+ 45 0.070 0.292
+ 45//- 45 0.037 0.405
Composite [G.sub.Ic-prop.],
system Interlayer kJ/[m.sup.2]
Glass/epoxy 0//0 0.911
92 125// 0//90 1.178
L285/287 0//+ 45 1.130
+ 45//- 45 1.554
Carbon/epoxy 0//0 0.230
98 131// 0//90 0.355
L285/287 0//+ 45 0.477
+ 45//- 45 0.754
