1
Effect of reinforcement material on damage caused by low speed impact
of 2D braided composite plates
2nd February 2011
MPF Sutcliffe, C Monroy Aceves, WJ Stronge, RS Choudhry, AE Scott, L Lobo
Cambridge University Engineering Department, Trumpington Street, Cambridge, CB2 1PZ
Northwest Composites Centre, University of Manchester, Sackville Street, Manchester, M60
1QD, U.K
University of Southampton
Laser Optical Engineering Ltd
2
Summary
This report brings together various results for the Dowty braided fabrics impacted by gas guns
at Cambridge following the formal completion of the project at the end of 2009. Three 2Dbraided glass-carbon hybrids, with 50, 75 and 100% of carbon reinforcement, were tested
using vibrations, static tests and gas-gun impact. [revise]
1. Introduction
Composite materials are widely used in applications requiring good specific stiffness and
strength. However, there is a tendency for these materials to suffer more damage as a result of
impact than equivalent metallic materials, either in the form of fracture of the relatively brittle
fibres or due to cracking in the matrix [1]. Woven materials have traditionally been used in
impact-critical applications due to their superior ability, relative to unidirectional composites,
to maintain structural integrity under significant impact energies.
[needs augmenting…]
Impact damage results in a reduction of the composite in–plane compressive strength mainly
due to delamination [?]. Delamination between plies occurs in the interlaminar (resin rich)
regions where the extensional and bending stiffness differs due mainly to different fibre
orientation between the layers or, in some cases, different materials [6, 7]. Further
investigations have suggested that delamination is initiated by matrix cracks in both opening
and shear modes [8, 9].
In general there are at least two phases of impact damage in composites: (1) dynamic
compaction of the composite plate which is being compressed ahead of any colliding missile;
and (2) delamination of plies in the neighbourhood of the impact site [2]. The exact nature of
damage will depend on the composite weave architecture, resin properties and the properties
of the colliding missile [?, 3]. However, for low speed impact, damage modes which are
observed are bending damage on the distal surface and an approximately circular internal
delamination, followed by fibre splitting and perforation or shear failure at high incident
energies [4]. Moreover, the impact damage tends to initiate on the distal surface if the ratio of
plate thickness to projectile nose radius is less than one (i.e. thin plates) and on the impact
surface if the plate thickness is greater than the projectile nose radius (thick plates) [3, 5].
High speed impacts trigger different failure mechanisms because the deformation field
induced by the impact induces higher frequency modes in addition to the fundamental (quasistatic) mode of deformation [6].
Tougher resins or three dimensional woven composites can be used to increase the
delamination toughness and so improve the composite impact resistance. With tougher
matrices and stronger interfaces, larger impact energies are required to initiate delamination
[10]. Through thickness tows in three-dimensional weaves act as crack stoppers by altering
the fracture paths from intra-tow mode to inter-ply mode; this approximately doubles the
fracture toughness [11].
Hybrid materials containing a mixture of ductile glass fibres and relatively brittle carbon
fibres can be used to increase the strain to failure of the composite and hence potentially
3
increase the impact resistance, at the expense of increased weight and reduced stiffness.
Previous work by the authors [4] has presented preliminary results for braided and 3D woven
material. In this paper we explore the effect of the proportion of glass on the impact behaviour
of 2D braided materials.
2. Materials
Dry fabrics were braided using a 2×2 bias braid from tows of glass and carbon1200 tex Eglass (Owens Corning) and 800 tex 12k HTA 40 carbon (Tenex). Densities for the glass and
carbon, taken from data sheets, are 2550 and 1760 kg/m3, respectively. Three fabrics were
woven, containing 50, 75 or 100% of carbon tows. The nominal volume percentage of carbon
in the dry fabrics was estimated from the nominal fibre density and tex to be very close to the
tow percentage.
Flat plates were resin transfer moulded from 9 layers of the braided material with a ±45° layup, using an epoxy resin ( Huntsman Araldite LY 564 with Aradur 2954 hardener), to give a
plate thickness of 4.34±0.02 mm. The panels were C-scanned (see details below) to identify
and exclude any poor quality regions. Square samples with side length approximately 130 mm
were cut out for testing with tows running across the plate diagonals. Plate thicknesses were
measured from at least three samples, taking four measurements per sample. The fibre volume
fraction was estimated from the pre-form areal densities, the nominal dry-fabric density (to
give the volume of dry fibre per unit area) and the final sample thickness. For all three
materials the fibre volume fraction was estimated as 0.54. Samples were measured and
weighed, and from this the mass density was deduced to be 1668, 1587 and 1461 kg/m 3 for
the 50, 75 and 100% carbon plates, respectively. The densities were very consistent, within
1.5% of the mean value for the three samples per panel measured.
3. Plate elastic property measurement
3.1 Vibration measurements
The elastic properties of the plates were estimated from their vibration response, using the
method described in [5?]. The 130×130 mm samples were suspended from two corners using
light thread and then lightly tapped with an instrumented impact hammer. The response of the
samples was measured using a light accelerometer attached to the plate.
Table 1 gives the resonant frequencies for the undamaged samples. The first three resonances
were used to extract plate stiffness parameters, using the methodology described by McIntyre
and Woodhouse [?]. Table 1 gives the plate stiffness constants, with xy properties referred to
the plate edges (along the bias direction) and 12 properties referred to the tow directions.
Standard rotation matrices are used to relate these properties.
To measure mode shapes the 50% carbon undamaged specimens were lightly tapped on a
5 × 5 grid, centred on the centre of the specimen, with a nominal 25 mm spacing between grid
points. Q factor results were taken from averaging these grid data (excluding outliers
associated with loading on nodes). Mode shapes for the first three modes are given in Fig. 1,
corresponding to cross (X), George cross (+) and ring (o) modes.
4
% carbon
Mode
50
75
100
1
2
3
4
5
723
712
701
757
752
904
902
878
1023
1153
1281
1268
1222
1394
1540
1977
1972
1916
2188
2391
2720
2678
2628
3024
3167
Table 1. Undamaged sample resonant frequencies (Hz)
%carbon Ex
(GPa)
14.9
50
14.9
15.7
75
15.7
100
14.3
yx
Gxy
(GPa)
17.4
17.8
18.5
21.4
24.9
E1
(GPa)
38.8
39.3
40.4
46.2
53.2
0.66
0.66
0.65
0.68
0.75
12
G12
(GPa)
4.50
4.47
4.78
4.66
4.07
0.11
0.11
0.094
0.078
0.068
Table 2. Plate elastic properties
690 Hz
1206 Hz
856 Hz
(b)
(a)
(c)
100
80
100
40
50
60-80
50-100
50
20 0-50
0
S5
S4
-50
S3
-100
1
2
S2
4
S1
5
40-60
50-100
20-40
0 -50-0
0-50
0 0-20
-20-100--50
-50-0
-20-0
-40
S5
-50 -40--20
-60
S5
-80
S3
-100
3
80-100
100
60
1
2
3
4
S1
5
-100
S
-60--40
S
-80--60
1
-100--80
2
S
3
4
S1
5
Figure 1. Mode shapes; (a) mode 1 – Cross (690 Hz), (b) mode 2 - George cross (856 Hz),
(c) mode 3 - ring (1206 Hz).
3.2 Static tests
Static centrally-loaded tests were undertaken on 50% and 100% carbon samples, using a
screw driven universal testing machine at a slow speed of 0.5 mm/min. The deflection was
measured from the bottom surface, so that local deformation at the contact was excluded. The
plate was supported along a square of side length 100 mm, either simply-supported or using
the same clamping conditions as for the impact test.
The plate stiffness k = /F, where  is the central displacement and F the force, was
calculated from the slope of the force-displacement curve. Values for the free and clamped
conditions are given in Table 3. An effective elastic modulus can be derived using the plate
bending formulae from Roark [?], who gives the stiffness of a centrally-loaded square plate of
side length L and thickness t, made of isotropic material with an elastic modulus E and
Poisson’s ratio 0.3 as
-100--50
5
k
Et 3
 L2
(8)
The corresponding values of  are 0.0611 and 0.1267 for fully clamped and simplysupported cases. Taking L = 100 mm, t = 4.357 mm (assumed the same for both plates), gives
the effective moduli included in Table 3. The higher effective stiffness for the simply
supported plates indicates that the clamped condition is not perfect. The values of 22.9 and
28.8 GPa for effective moduli for the simply-supported 50% and 100% carbon plates,
respectively, are between the corresponding values inferred from the vibration tests (Table 2)
for Exy and E1 along the bias and tow directions of 14.9 / 39 and 14.3 / 53 GPa for the 50%
and 100% carbon plates, respectively.
50 % carbon
100 % carbon
k (MN/m) E (GPa) k (MN/m) E (GPa)
Simply supported
1.49
22.9
1.87
28.8
Clamped
1.61
12.0
2.08
15.4
Table 3. Plate stiffness k and effective modulus E for centrally loaded static test.
4. Strength test methodologies
4.1. Impact testing
The samples of size 130×130 mm were mounted in a steel support frame with a square
window of 100×100 mmm for impact testing. The edges of the sample were clamped onto the
support frame using a thick steel plate, which also containing a window and additionally a
small gap to allow a side-on view of the impact site. A steel hemispherical-ended impactor of
tip radius 6.25 mm and mass of either 12.5 or 44.5 g was projected normally at the plates
using a gas gun. Energies up to 50 J were used, with corresponding peak velocities of 83 and
46 m/s for the light and heavy impactors, respectively. High speed photography was used to
measure indirectly the impact and rebound speeds as well as the contact force. The trailing
edge of the impactor was identified from the camera images using an image detection
algorithm to track the position of the impactor as a function of time. Velocity and acceleration
were taken by numerically differentiating this displacement. The contact force was inferred
from the deceleration of the impactor. It is assumed that the contact time is sufficient to allow
stress waves to propagate through the impactor and for it to reach equilibrium. For the longer
impactor a typical contact time of 300 µs corresponds to stress waves travelling 31 times the
length of the longer impactor, so that this assumption is reasonable.
4.2 Compression after impact testing
Braided panels containing 50:50 glass/carbon were tested in compression after being
impacted. Because of the relatively small specimen sizes (130×130 mm) compared with the
extent of the damage it was not considered appropriate to cut the panels down to allow testing
along the fibre direction (recall that the panels were cut with their sides along the bias
direction). Hence these specimens were loaded along the bias direction. The loading faces
were ground flat and parallel before testing. A purpose-built jig was constructed to support
the edges of the panels and prevent macro-buckling, in a similar way to the standard
compression after impact specimen []. The specimen was compressed in a screw-driven
6
Instron testing machine at a loading rate of 1 mm/min with the load introduced using flat
platens. The end compression of the specimens was calculated from the cross-head
displacement. A relatively small correction was made for the machine compliance, measured
using a massive steel block in place of the specimen.
5. Impact damage assessment methods
A range of methods, both destructive and non-destructive, were used to assess the damage
incurred in the impact. As well as providing useful and complementary information about the
damage, this spread of tests provides the opportunity to compare and correlate the
observations obtained with the various test methods.
5.1 Ultrasonic C-scanning
Ultrasonic C-scanning was undertaken using a MIDAS NDT water-jet inspection system,
using an unfocussed 5 MHz probe in transmission mode and a 50 mm/s scan rate. The
damage area was found from the region above a suitable intensity threshold.
5.2 Contact profilometry
Contact profilometry was performed using a Taylor Hobson Form Talysurf 120 to measure
the maximum crater depth at the impact site.
5.3 Visual observation
A standard flat bed optical scanner was used to record the visual appearance of the specimens
on their impact and distal faces at a resolution of 300 dpi.
5.4 Sectioning
Selected specimens were sliced using a Struers Accutom-50 to make a series of sections
through the damage area. The samples were polished, and imaged using a BX51 Olympus
microscope with an automatic stage.
5.5 Micro-CT X-ray imaging.
[Needs completing – Anna] Two 75% carbon samples, which had been impacted at the same
nominal energy of 35 J but with the different masses, were examined using X-ray
tomography. These samples had C-scan damage areas of 1744 and 798 mm2 for the low and
high mass impactors respectively, to give corresponding effective c-scan damage diameters of
47 and 32 mm.
5.6 Shearography
Braided samples of the three materials impacted either with the 45 g impactor at 12 J or with
the 12.5 g impactor at 35 J were examined for damage using shearography. The extent of
damage was estimated by thresholding the raw signal. The maximum of the impact and distal
areas was chosen as characteristic. [Needs more detail - Leon]
5.7 Vibration measurements
More extensive measurements of frequency and Q factor, similar to the measurements for
elastic properties as described in section ?, were made on the 50% carbon material, for both
undamaged and impacted samples, to explore the effect of damage on the vibration response.
The damaged samples had been impacted by a gas gun (see section ?) with an impactor of
either 12.5 or 44.5 g. None of the plate measurements were ‘before-and-after’ comparisons,
making results prone to differences in plates, e.g. tow orientation differences.
7
6. Impact damage assessment results
6.1 C-scan results
There was a clear division in the C-scan intensity between the undamaged regions of the plate
and a roughly circular region around the impact site. Figure 3 plot the measured damage area
as a function of impact energy for the three plates and two impactor masses. The damage area
increases roughly linearly with the impact energy for a given material and impactor mass.
However there are significant differences between sets of data, with the damage area being
significantly smaller for the heavier impactor at the same energy. The 50% carbon material
showed the smallest damage area, with the 75 and 100% carbon braids having roughly similar
damage. Only one sample was perforated, the 100% carbon braid with the highest impact
energy of around 50 J, impacted by the heavier impactor.
3000
C-scan damage area (mm2)
2500
50% carbon
75% carbon
100% carbon
2000
50% carbon - low mass
50% carbon - high mass
75% carbon - low mass
75% carbon - high mass
100% carbon - low mass
100% carbon - high mass
1500
1000
500
0
0
10
20
30
Impact Energy (J)
40
50
Fig. 3. Effect of impact energy on measured damage area using c-scanning
6.2 Profilometry
Figure 4 plots the dent depth, measured by contact profilometry, as a function of impact
energy. The dent depth increases roughly linearly with impactor energy with similar
behaviour for different materials and impactor masses, with the exception of two 100%
carbon high mass samples and one high energy, high mass 75% carbon sample. These
samples suffered much more extensive denting than the other tests (e.g. severe visible damage
on the distal surface at nominal impact energies of 35 and 50 J), and the 100% carbon highmass highest-energy sample was perforated.
8
Perforated
1000
900
Dent depth (µm)
800
700
50% carbon - low mass
50% carbon - high mass
75% carbon - low mass
75% carbon - high mass
100% carbon - low mass
100% carbon - high mass
600
500
400
300
200
100
0
0
10
20
30
40
50
Impact Energy (J)
Fig. 4. Effect of impact energy on measured damage depth using profilometry.
6.3 Observations: visual images, sectioning and X-ray imaging
[Needs modifying in light of CT images] Figure 6 compares cross-sections of two 100%
carbon braids under the impact site, for the same impact energy, but with different impactor
masses. The impact site was near the top of each figure. Damage with the heavier impactor
Fig. 6 (a), although smaller in c-scan area, is characterized by more severe tow damage, while
the lighter impactor, Fig. 6(b), causes more widespread delamination damage. This is
consistent with the dent measurements, showing in some cases a deeper dent with the heavier
impactor at corresponding energies.
(a)
(b)
0.5 mm
Figure 6. Sections at impact site
(a) heavy impactor (b) light impactor.
for
35 J
impact,
100%
carbon
braid,
9
Figure 7 compares the C-scan results and the scanner visual images of the distal surface of
50% carbon braids, with the two impactor masses at an impact energy of 50 J. With the glass
tows, significant matrix damage, probably in the form of matrix debonding, is clearly seen as
a significant whitening. Corresponding damage which would presumably also be present in
the carbon tows is not visible. This whitening appears to be more intense for the heavier
impactor, at comparative impact energies, but not as widespread as for the lighter impactor.
The area detected as damage by c-scanning (approximated by the circles superimposed on the
figures), corresponds reasonably closely to the observed areas of whitening. The threshold
used for the C-scan images has excluded some areas where whitening is seen around the
edges of the damage patch.
20 mm
Figure 8. Comparison of optical (distal face) and c-scan images, 50 % carbon material,
nominal impact energy of 50 J:
left - optical, right – C-scan, upper - 12.5g impactor, lower - 44.5 g impactor.
All images are to the same scale. The circles superimposed on the images have an area equal
to that derived from the C-scan thresholding procedure.
6.4 Shearography
Figure 3 compares the damage area identified by shearography with that measured by cscanning, for the six samples impacted either with the 45 g impactor at 12 J or with the 12.5 g
impactor at 35 J. There is a good correlation between the two methods. It seems likely that the
damage seen in the scanner images of the distal surface (see Fig. ?) corresponds to that
detected by shearography.
10
50% carbon
75%
100%
Shearography (mm2)
Shearography area (mm2)
2000
1500
1000
500
0
0
500
1000
Cscan area (mm2)
1500
2000
Figure ?. Comparison of damage estimated using shearography and c-scanning.
6.5 Vibration measurements
Although we would expect a drop in resonant frequency which increases with damage energy,
this was not observed. Instead results were characterised by random variations between
measurements, probably associated with geometric and material differences between samples.
Probably ‘before and after’ measurements would be needed to give the accuracy required for
such a study. However there does seem to be a consistent drop in Q factor (and so increased
damping) with increasing impact energy, for the ring mode 3, see Fig. ?. Note that these Q
factor data have been normalised by a mean Q factor for the undamaged samples, which had
values of 62, 287 and 131 for modes 1, 2 and 3, respectively. It is interesting to note that the
ring mode excited by the impact event is the one associated with the drop in Q factor. One
data point at an impact energy of 13 J appears to be anomalous, probably reflecting
difficulties with measuring the Q factor accurately.
1.2
Mode 1 - low mass
Mode 1 - high mass
Mode 2 - low mass
Mode 2 - high mass
Mode 3 - low mass
Mode 3 - high mass
Normalised Q factor
Normalised Q factor
1.1
1
0.9
0.8
0
10
20
30
Impact Energy (J)
40
50
Fig 2. Effect of impact damage on modal Q factors, normalised by undamaged plate data.
11
6. Compression after impact results
Figure 1 shows a typical failure response for compression-after-impact testing. Failure of the
panels was progressive, but with a marked maximum. A clip gauge was inserted into the side
of some panels, and showed a similar stress strain response to the overall response, up to the
point of failure. Failure occurred at the impact site, where this was present, with some bulging
observed and considerable shear both at the impact site and running at 45° from there.
Figure 2 plots the maximum stress as a function of impact energy (note that the y-axis scale
does not start at zero). Because the material is loaded on the bias direction the failure stresses
are relatively low. There is a significant fall in compressive strength with increasing impact
energy, with a similar behaviour for the small and large impactor masses. Note that the
specimens with no impact damage (zero impact energy) could have suffered from some stress
concentration effects at the loading points, so these values represent ‘lower bounds’.
80
Compressive stress (kN)
Force (kN)
70
60
Undamaged
50
40
30
20
46 J impact,
heavy impactor
10
0
0
1
2
3
4
5
End compression (mm)
6
7
Figure 1. Typical compression-after-impact failure response
12
140
Maximum stress (MPa)
Light impactor
Heavy impactor
120
100
80
60
0
0
10
20
30
Impact Energy (J)
40
50
Figure 2. Compression after impact strength, 50% carbon panels
7. Impact mechanics
In this section further details about what is happening during the impact event are explored, to
understand better factors controlling the impact damage incurred.
The videos were used to identify the time of compression, from first contact to maximum
plate deflection. This was around 130 and 260 µs for the light and heavy impactors,
respectively, independent of the material. There was only a relatively modest increase of
contact time with impact energy (changing by around 30% over the range of impact energies
considered).
Figure 8 plots the rebound energy as a function of impact energy. There appear to be two sets
of trends. In the main the curves follow two straight lines, as included, with more energy
retained with the high mass than with the low mass impactor. The straight dashed lines fitted
through the data represent proportions of the impact energy retained as rebound energy for the
high and low mass indentors as 40 and 22%, respectively. Three data points off these linear
fits, identified in the figure, correspond to cases where severe dents and fibre damage was
observed. For these cases it is assumed that the damage absorbed in the plate during the
impact event is significant.
13
40
35
Rebound Energy (J)
30
50% carbon - low mass
50% carbon - high mass
75% carbon - low mass
75% carbon - high mass
100% carbon - low mass
100% carbon - high mass
25
20
large
dents
15
10
5
0
0
10
20
30
40
Impact Energy (J)
50
60
Fig. 8. Effect of impact energy on measured rebound energy.
Figure 9 plots the variation of inferred contact force with impact energy for the different tests.
The peak contact force is roughly independent of material and projectile mass, increasing with
impact energy.
Assuming that the plate behaves in a linear elastic manner, with a stiffness k relating the
contact force F and the central plate deflection , equating the impact kinetic energy TI with
the stored elastic energy in the plate at maximum deflection gives a relationship for the
maximum contact Fm as
(9)
Fm  2k TI
The measured plate stiffnesses for clamped conditions taken from the static tests with 50%
and 100% carbon are used to plot theoretical curves on Fig. 9. The relatively slight change in
modulus and stiffness between the different materials results in only a slight change in the
predicted contact force. However the measured contact force falls significantly below the
elastic prediction. This matches the observation from the static tests that damage was
observed even at a load of 5 kN. Local deformation and damage at the impactor site will
cause a reduction in effective stiffness, while dynamic effects associated with vibration of the
plate will also affect the contact response. Future work will explore further details of the
impact event to quantify these factors.
14
15
Contact force (kN)
Mass
50% carbon
Heavy Light
75% carbon
50% carbon
100%75%
carbon
carbon
100% carbon
Elastic response
100% carbon
50% carbon
Co 10
nta
ct
Fo
rce
(k
N)
5
0
0
10
20
30
Impact Energy (J)
40
50
Fig. 9. Effect of impact energy on peak contact force inferred from videos.
Figure 5 plots maximum force versus dent depth. The solid line is an approximate best fit line
to all but the three high-dent points, with F  0.57 0.5 where the maximum force F is in kN
and dent  is in micrometres. Note that a maximum force of 8 kN and an indent depth of
200 µm corresponds to a contact pressure of 1 GPa, assuming that the indent is spherical with
radius equal to the impactor. It is not surprising that damage is occurring at these pressures.
15
Maximum force (kN)
Contact force (kN)
15
10
50% carbon - low mass
50% carbon - high mass
75% carbon - low mass
75% carbon - high mass
100% carbon - low mass
100% carbon - high mass
5
0
0
200
400
600
Dent depth ( m)
800
1000
Figure 5. Relationship between maximum contact force and dent depth.
5. Discussion
[this section needs sharpening up/revising]
5.1 Damage area
A range of damage detection methods have been used to identify the effect of material and
impact energy on damage. Ultrasound C-scanning provides a useful and reliable way of
assessing damage, as would be expected from its widespread use. For samples where glass
tows were present, visual inspection of the surface revealed a similar extent of damage as that
seen in the c-scanning, presumably due to matrix debonding. Shearography also correlated
well with the c-scan data, for the range of samples used. Similarly vibration measurements
showed a drop in Q factor with increased impact energy. Although this method does not
quantify the impact area, nevertheless it is a simple non-destructive tool which can provide
useful data. These detection techniques were effective at picking up the diffuse damage
evident in most of the samples, particularly at the distal surface associated with bending of the
specimen on impact and extension of the tows.
To identify the form of internal damage [add something about x-ray results and sectioning].
The observed damage area increases with increasing impact energy as expected, but the
damage area is smaller and more severe for the heavier impactor as compared with the light
impactor, despite the contact forces being comparable. Nevertheless the compression-afterimpact response is similar for the two impactor masses, at equal energies. Apparently the less
severe more diffuse damage for the lighter impactor is equivalent to the more localised and
severe damage for the heavier impactor in these cases.
16
A number of factors might explain the effect of impactor mass on damage. Plate inertia
effects would tend to cause more localisation of damage at high speeds (low mass, in this
case), contrary to what is observed. Moreover the lack of change of peak contact force with
mass also suggests that this effect is not significant.
Alternatively there is consistent evidence that matrix material exhibits strain rate sensitivity,
being stronger/stiffer at higher strain rates []. Hence we can expect the longer contact time for
the low-speed high-mass impactor to result in more matrix damage. This is consistent with the
deeper dents observed in some cases, giving damage akin to that seen in static loading. [It is
presumed that tow failure is associated with matrix shear under the impactor.]
Impact causes a compressive stress wave to travel to the distal face of the plate and reflect as
a tensile wave of equal magnitude. A rough estimate of this stress wave amplitude w is given
by assuming plane conditions and taking the impactor as rigid, to give
(12)
 w  v c cc
where v is the impact velocity, c and cc  Ec  c are the plate density and wave speed. As
the compressive stress wave emanating from the impact site decays with time, then the
magnitude of the tensile stress generated by the reflected wave will be of this order. Taking
typical values of c = 1587 kg/m3 and Ec = 5 GPa (i.e. a through-thickness, matrix-dominated
value) for the 75% carbon specimen gives an order-of-magnitude estimated stress of 225 MPa
for an impact speed of 80 m/s. This would be typical of the tensile through-thickness strength,
indicating that such tensile waves could lead to delamination and tensile spallation damage,
particularly at the distal surface. This is consistent with the observed damage. Less
delamination damage is expected for the high-mass low-speed tests where the stress wave will
be of smaller magnitude (see equation 12).
5.2 Energy lost in impact [maybe omit, awaiting more sophisticated model, or put very
small detail in earlier impact mechanics section]
Observations of the rebound energy show a linearity between impact energy and rebound
energy for all but a few tests. This suggests that a simple model of the impact which ignores
plasticity effects may be appropriate.
Two estimates can be made of energy lost during the impact (in addition to energy lost to
damage). When a rigid projectile of mass M hits a stationary mass m, then momentum
considerations, assuming that the two masses instantaneously merge, gives the fraction energy
lost in the collision Ti as
m M
Ti 
(10)
1 m M
Taking an effective plate mass as 1/3 of the unsupported plate (typically one third of 69 g for
the 75% carbon braid) the prediction of this model for fractional energy lost for the 12.5 and
44.5 g impactors is 65 and 34 %, respectively. This model correctly predicts the observation
that the lighter mass retains a greater proportion of its energy on rebounding. However the
measured energy lost (estimated as 78 and 60%, respectively, see Fig. 8) is significantly
greater than this estimate. Moreover the observed change in impactor velocity with time does
not resemble the hypothetical step change in velocity, making such a simple model
questionable.
17
Alternatively, it can be assumed that the collision is perfectly elastic. In a simplified onedegree-of-freedom model, assume that unloading is elastic, with the impactor and plate
travelling at the same speed. Then the maximum plate velocity equals the impactor rebound
velocity. The ratio of plate kinetic energy to impactor rebound kinetic energy is in proportion
to the plate and impactor effective masses m and M. Assuming that all the energy of the
impactor is either retained in the plate kinetic energy or the impactor rebound kinetic energy,
the amount of the impact kinetic energy transferred to plate kinetic energy TPKE (and so
hypothetically lost from the impactor) is given by
m
TPKE 
(11)
mM
which is identical to the expression for energy lost using the above impact model,
equation 10. This model suggests that significant energy is retained in the plate kinetic
energy. Perhaps the actual energy lost in the collision is a result of some energy lost due to
impact as per the momentum calculation, plus some energy retained by the plate kinetic
energy. Further work modelling the dynamics of the plate during impact is... In addition, of
course, further energy associated with inelastic deformation will be lost during the impact.
Conclusions
[add]
Acknowledgements
Contributions are gratefully acknowledged from the EPSRC (grant EP/C538145/1),
University of Nottingham, Cranfield University, Rolls-Royce plc., Dowty Propellers (Part of
GE's Aviation Business), Carr Reinforcements Ltd. and JR Technology Ltd. The authors are
indebted to Prof. Woodhouse and Mr Mohagheghian for assistance with vibration testing.