J. Phys. IV France 134 (2006) 995–1001
C EDP Sciences, Les Ulis
DOI: 10.1051/jp4:2006134152
Dynamic strength of cylindrical fiber-glass shells
and basalt plastic shells under multiple explosive loading
M.A. Syrunin1 and A.G. Fedorenko1
1
Russian Federal Nuclear Center – VNIIEF, Russia
Abstract. We have shown experimentally that, for cylindrical shells made of oriented fiberglass platic and
basalt plastic there exists a critical level of deformations, at which a structure sustains a given number of
explosions from the inside. The magnitude of critical deformation for cylindrical fiberglass shells depends
linearly on the logarithm of the number of loads that cause failure. For a given type of fiberglass, there is a
limiting level of explosive action, at which the number of loads that do not lead to failure can be sufficiently
large (more than ∼ 102 ). This level is attained under loads, which are an order of magnitude lower than the
limiting loads under a single explosive action. Basalt plastic shells can be repeatedly used even at the loads,
which cause deformation by ∼30-50% lower than the safe value ∼3.3.5% at single loading.
1. INTRODUCTION
In works [1-7, 13, 14] we have studied distinctive features of dynamic reaction and failure of fiberglass
shells and basalt plastic shells under explosive loading. It has been shown that on the basis of these
materials, one can create explosion-resistant vessels (explosion chambers) with the unique strength-toweight ratio: the ratio of the mass of an explosive substance that explodes within a vessel to the mass of
its load-bearing shell can be equal to ∼ 0.05 [7, 8]. However, the problem of fatigue explosion strength
of shells under explosive loading, which is of significance from the viewpoint of the widening of the
range of applicability of fiberglasses and basalt plastics in load-bearing shells of explosion-resistant
structures, has not yet been studied closely. The dynamic strength and deformability of glass epoxide
(glass cloth impregnated by an epoxy binder) have been shown (s. [1, 3]) to depend strongly on the
level of explosive loading and the number of loads N [1]. For example, for N = 1, 3-4, and 23, through
cracks appear under maximum circumferential strain of the shell ey = 2.5, 2, and 1-1.2%, respectively.
In studying wound fibrous fiberglasses the experts have noted a decrease in the limiting (breaking)
deformation in the case of repeat loading [5]. For a class of fibrous fiberglasses, the effects that are
associated with the number of loads, however, have been studied only in a narrow interval of loads close
to the limiting values when the initial components (strength fibers and a binder) were strongly damaged
during a first loading. Subsequent loading caused immediately failure of the entire laminated package
of composite.
2. RESEARCH RESULTS
In the present paper we have generalized the results of the studies performed earlier regarding the effect
of the number of loads of various levels on the limiting breaking deformation of cylindrical shells
composed of wound fibrous fiberglass in a wide range of explosive loads. [13]. Analogous experimental
data are presented for basalt plastic shells, including data from [14] with regard to single loading of
shells made of the above-mentioned materials.
The objects of trials were cylindrical annular fiberglass shells [13] and basalt plastic shells [14],
which were fabricated by the method of wet winding of RVMN-1260-80 roving (from filaments on
the basis of VM-1 fiber 10 m in diameter) or RB9-1200 (from basalt filaments 9 m in diameter),
impregnated by an EDT-10 epoxy binder. The shells have a combined pattern of reinforcement with
Article published by EDP Sciences and available at http://www.edpsciences.org/jp4 or http://dx.doi.org/10.1051/jp4:2006134152
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JOURNAL DE PHYSIQUE IV
alternation of double spiral (angle of reinforcement ± 45◦ (fiberglass)) or ±35◦ (basalt plastic) and
annular layers ( = 90◦ ) with thickness ratio 1:1. The internal shell radius was R = 150 mm – for the
fiberglass shell, R = 75 mm – for the basalt plastic shell, the length was L=4R, the wall thickness was
h1 , the relative wall thickness was h1 /R = 4.5 — 6.7 %, and the shell mass was M. After fabrication, the
specimens were measured and weighed. Besides, the mean fiberglass density was determined using
the method of hydrostatic weighing. The mean density of basalt plastic specimens– 2.1 g/cm3 , what is
close to the mean fiberglass density ∼1.9. . . 2.0 g/cm3 . Prior to testing a steel shell with thickness h2 = 1
mm was inserted into a basalt plastic shell without a gap.
An open-sided shell was loaded by detonation of a spherical charge of an explosive substance from
TG 50/50 alloy of mass mwhich was placed in the geometrical center of its hollow.
In experiments, the shell strain in time (t) was measured in the most intensely loaded central cross
section by the methods of speed photographing and tensometry. The maximum circumferential strain 1 ,
the time of its achievement from the onset of wall shift and the maximum velocity of radial displacement
V , on the basis of which the maximum strain rate 1 = V /RH , where RH = R + h1 was calculated, were
found from measurement results. The residual circumferential strain res was measured in the central
cross-section. The error in determination of the indicated quantities did not exceed 10%.
The appearance of even one through micro crack was regarded as damage of a shell in the
experiment. The appearance of other defects such as exfoliation, detachment of some filaments, and
failure of the binder were regarded as damage of a shell that does not hinder subsequent loadings. The
quantity = m/M was used as a conditional characteristic of the specific explosive load of a shell,
as was previously done in [1-7]. For double-layer shells M = M1 + M2 – mass of a double-layer shell,
4(RH -h1 -h2 ) in length (the value M was used for calculation of in the experiments, where the quantity
RH was changed at the expense of the residual strain, without regard for this change of RH ). Some basic
initial data and the basic experimental results with fiberglass shells and basalt plastic shells are given in
tables 1, 2.
Table 1. Results of Explosive Loading Trials for Fiberglass Shells [13].
/R,% N Mex , g · 103
6.7
5.8
6.5
4.8
6.6
6.2
6.2
6.8
4.9
1
1
1
1
2
1
2
1
3*
1
5*
1
2
9*
15*
1
2
3
44*
81*
303
205
209
169
169
171
167
137
137
110
110
64.8
63.3
63.5
62.5
21
29.9
29
29
29
28.6
21.3
20.0
19.3
19.3
14.2
13.8
12.6
12.6
10.1
10.1
5.3
5.2
5.2
5.1
2.4
3.4
3.3
3.3
3.3
V,
m/sec
110
78
76
80
—
71
—
62
—
52
64
39
31
28
—
17
19
18
16
20
1 ,
1/sec
686
490
475
509
—
444
—
387
—
324
400
244
194
175
—
108
127
112
102
127
1 , %
State of a shell
4.7
Failed in the tensile phase
3.2 Failed in the 1st period of oscillations in the compression phase
3.3 Failed in the sixth period of oscillations in the compression phase
3.1
Did not fail, but damaged
—
Failed
2.5
Did not fail, but damaged
—
Failed
2.0
Did not fail, but damaged
—
Failed
1.8
Did not fail
2.15
Failed
1.15
Did not fail
1.1
“”
0.9
Did not fail, but damaged
—
Failed
0.45
Did not fail
0.73
“”
0.63
“”
0.65
Did not fail, but damaged
0.55
“”
*-We omit the results of the remaining trials (previous to this trial with the same loading). The results are close to
the results of the trials with a lesser number of loading.
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Table 2. Results of Explosive Loading Trials for Basalt Plastic Shells.
1
2
3
4
5
6
7
8
9
10
mex ,
g
30.1
29.6
29.5
29.7
29.9
29.9
29.8
29.8
30.0
29.8
·
103
9.63
9.58
9.55
9.60
9.67
9.67
9.64
9.64
9.70
9.64
1.7
2.3
2.2
2.4
2.6
2.4
≈ 2.5
2.8
11
29.9
9.67
2.6
1 ,
1/sec
492
623
721
-
83.2
12
29.6
9.57
4.1
516
85.2
13
29.7
9.47
751
14
29.9
9.54
1.9
(4.5)
2.4
(4.2)
15
30.0
9.57
3.6
(7.6)
928
1
46.0
15.7
2.9
891
2
62.2
21.2
3.7
1188
1
90.7
30.1
>4.7
1498
RH ,
mm
81.8
N
87.1
89.5
81.6
81.8
1 , %
551
State of a shell after a trial
Did not fail.
“”
“”
“”
“”
“”
Did not fail, abruption of two separate filaments
Did not fail, abruption of five filaments
Did not fail, abruption of two bands.
Did not fail, detachment of external bands for a
width of ∼30mm
External annular layers failed for a width of h = 40mm, a
basalt plastic shell has res = 1.8 %
Abruption of annular layers for a width
of ∼62mm, a
basalt plastic shell has res = 2.3, res = 4.1%
Abruption of annular layers for a widthof ∼70 mm, a
basalt plastic shell has res = 2.3%, OCT = 6.4%.
Abruption of external annular and spiral layers for a
width of h = 80mm, a basalt
plastic shell has res = 2.8
%, res = 9.3%.
Abruption of external annular layer and bands in a
spiral layer for a width of ∼90mm, a basalt plastic
shell has res = 3.0 %; res = 12.7%
Did not fail.
The onset of basalt plastic shell failure, abruption of
exterior annular layer 45mm, loosening of a spiral
layer.
A basalt plastic shell failed in the first expansion
phase, res = 30%in a central ring of width ∼31mm.
Figure 1 shows the experimental dependence of the circumferential breaking strain 1 on lg N for
fiberglass shells [13], where N–a number of loads before failure of a shell. The previous results of
work [1] were also given for cylindrical shells from glass epoxide based on glass cloth and the belowmentioned data on multiple explosive loadings of basalt plastic shells.
An analysis of the data obtained has shown that all the experimental points within the interval
0 < lg N < 1.18 are described by the linear function 1 = 0.0361 — 0.02361·lg N. Later on, for
Figure 1. Dependence of limiting breaking circumferential strain 1 on lg N , -fiberglass shells, data from [13],
— failure, — no failure at 80 loads, thin dashed curve refers to a linear approximation from black plotted
points; -glass epoxide based on glass cloth, data [1]; •-basalt plastic shells [14] and the present work, the dashed
line refers to a linear approximation of this dependence.
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JOURNAL DE PHYSIQUE IV
Figure 2. Oscillogram of the circumferential strain of the central cross section of a shell [13].
1 = 0.6 % a marked deviation from the linear dependence is observed. The character of the curve
corresponds qualitatively to the curves of glass epoxy fatigue during cyclic tests [10, 11] and is close to
data of [1]. It is worth noting that high-speed explosive loading of a shell causes periodic oscillations of
its walls with an approximately equal frequency of the basic mode of free radial oscillations (see Fig. 2).
This frequency (∼5 kHz) is much higher than the frequency of load variation in cyclic quasi-static tests
(no more than a few hertz). In addition, these oscillations are like beats because of close frequencies
of the excited types of natural oscillations of the shell and are of a weakly damping character [2, 5].
Because of this, it is impossible to make a direct quantitative comparison of the known results of cyclic
trials with the explosive experimental data obtained. Special trials should be performed of reusable
fiberglass structures exposed to explosive loads.
Air-filled fiberglass shells are deformed elastically up to the onset of failure, which is in agreement
with data of the previous publications [1-7]. In dynamic response, their walls undergo radial and
bending-meridional oscillations with periods of the basic mode T1 = 215–245 sec and T2 = 450–
495 sec respectively [5, 7].
Under specific load ≥ 28.6 · 10-3 the shell fails in the first phase of tension at the maximum
circumferential strain 1 ≥ 4.7 %, which is in agreement with the results of [5-7], where 1 =
(4.8 ± 0.4) %. Loads within the interval 19.3 · 10-3 < < 21.3 · 10 − 3 caused failure of the shell
during a first load after one or a few radial oscillations with a maximum initial strain in the limits
3.1 < 1 < 3.3 %, which is considerably lower than the limiting magnitude of the strain 1 of the
material (see above). In this case, the shell failed because of the dynamic loss of stability of radial
axisymmetric oscillations and the development of bending modes (similarly to [2, 5, 7]). For specific
loads = 14 · 10−3 . . . 19, 3 · 10−3 no shell failure occurred during the first load. However, repeat
loading of the same level has already caused failure of the shell for 1 = 2.5 . . . 3.1%. For a shell that
is similar in structure and dimensions it was noted in [5] that failure of the shell caused by a repeat
explosive action occurred for = 18.5 · 10−3 and 1 = 2.9 % (the first load: = 7 · 10−3 , 1 = 1 %),
i.e., the effect of damage caused by the first loading is evident. A further decrease in the levels of leads
to an increase in the number of loads sustained by the shell before failure. For = 3.3 · 10−3 (1 = 0.6%)
the shell did not fail completely after more than 80 loads. Note that after this, the character of shell
damage displays its considerable strength capacity. It is not ruled out that the limit of fatigue of the
material is not reached at this level of strains, and the number of cyclic explosive loads can increase
substantially. Such a possibility is also supported by the data obtained by Fujii and Dzako in [10], where,
for fiberglass epoxide, during cyclic pulsating tension with a frequency of 1000-2000 cycle/min, for the
maximum stress of the cycle of ∼12 kgf/mm2 (e ∼ 0.5%), the fatigue curve stabilizes, i.e., the number
of cycles grows abruptly and exceeds 105 . However, this assumption of explosive loading should be
checked experimentally, because the pulse pressure of reflection of a shock wave applied to the internal
shell wall along the normal to it loads the material additionally and can cause damage as well.
The laminate package of composite being studied consists of reinforcing lines from fibers arranged
into layers and of a polymer epoxide binder. After multiple loading, the character of failure of the shells
of a combined-structure fiberglass corresponds to the results obtained previously under single loading
[4-7]. The binder whose strength and deformation characteristics are smaller than those of fiberglasses
first cracks in the material and the lighter regions are formed [5, 12]; separate filaments from fibers are
EURODYMAT 2006
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tabl. 2
999
Photochronograms
1
8
11
15
Figure 3. Photochronograms of radial expansion of a basalt plastic specimen depending on a number of loads.
a)
b)
Figure 4. View of a basalt plastic specimen after the 11-th loading a) and 15-th loading b).
then detached and fail, separate layers are damaged, and, finally, a through crack with loose edges is
formed (see Fig. 3).
Thus, the experiments performed have shown that, for shells from oriented fiberglass, there is a
critical level of strains under which the material sustains a prescribed number of explosive loads; the
presence of a limiting level of explosive loading for which the number of loads can be greater than 102
most likely exists. For the given kind of fiberglass this level is attained under loads approximately an
order of magnitude smaller than the limiting loads under single explosive loading.
Fig. 3 shows some examples of photochronograms of radial expansion of a basalt plastic shell in the
central cross section of a specimen depending on a number of blast loads. Figures 4 show the state of
the specimen after 11 loads and 15 loads.
An analysis of the results of the experiments (table 2) has shown that basalt plastic shells having
an inner steel layer can endure no less than 7-8 loads with the levels of circumferential strains 1 ∼
1.7-2.6 %, (this is by ∼30-50 % lower than a limiting-safe strain ∼3.5 % for single loading) without
visible evidence of failure of basalt plastic. In this case, an inserted steel layer fails practically during the
first loading along its weld seam (at the welding defect site), so its damping properties are deteriorated
in subsequent experiments. The failure of an inner shell as well as accumulation of defects in composite
material structure from one experiment to another, obviously, influence on rigidity and damping capacity
of a composite shell layer. Because of this, values of the maximum circumferential strain increase at
repeat loads and excited radial oscillations die out more rapidly after the eighth loading (fig.3).
Basalt plastic shells are subject to elastic deformation practically after each loading down to the onset
of failure of a laminate package structure as well as fiberglass shells are subject to elastic deformation
under single and multiple loads. Its walls are subject to more pronounced radial oscillations during
a dynamic reaction. Oscillation period is ∼120 sec. The relation between this period and average
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JOURNAL DE PHYSIQUE IV
oscillation period of fiber-glass shells, which are twice as large (230 sec), bears witness to the similarity
of sound velocity and elastic properties in materials under study. When comparing oscillation periods
in each experiment at repeat loads of one specimen, its marked increase begins already after the seventh
loading at a selected level of blast loads, namely from this point on irreversible changes occur in material
structure and properties.
From the eighth to the tenth loading a basalt plastic shell starts losing continuity of a laminate
package owing to cracking of a binder. We observe also failure of bands in external layers. By starting
with the eleventh loading, when continuity/solidity of a composite layer is broken in a thickness in a
central zone, and layers of a reinforcing fiber are not connected with each other, residual strains appear
in a shell owing to a partial damage of the most loaded annular layers and a shear displacement of
spiral layers. The appearance of a failed basalt plastic shell under multiple loading is in agreement
with the results obtained previously under single loading as a whole. This appearance is similar to
analogous damages of fiber-glass shells. At first, a binder is cracked in a material and it is gone out of
a material composition, separate filaments are detached and fail. Then, separate annular layers fail after
ten loadings (fig. 4à). Finally, the whole laminate package fails with rupture of mostly annular layers
and partial shift of spiral layers, as a result of which a material bulges (fig. 4a).
The similarity of the character of failure of fiber-glass and basalt plastic shells under single or
multiple loading indicates that damage that appears in the composite depends weakly on a type of
load-bearing fibers, the strain rate and even, probably, on the level of loading. But, the kinetics of their
accumulation and attainment of the critical (failure) level of damage depends strongly on these factors
and the duration of load-unload phases.
So, the obtained data on dynamic strength under multiple loading, when transferring data to shells
for example, having other (increased) sizes, can be used only in terms of proper corrections that are
obtained based on an adequate kinetic model of damage growth both of a binder and fibers of a concrete
composite.
Linear approximation of experimental data for multiple loading of basalt plastic shells (fig.1) takes
the form: 1 (Lg N) = 0,0425-0.0188· Lg N, namely a small distinction is seen from fiber-glass both in
the value of maximum breaking strain under single loading, and in a slope. In this case, evidently, the
availability of a steel shell tells on to some extent. This steel shell is inserted into a basalt plastic shell for
its support. This steel shell is absent in the experiments with fiber-glass shells. Another possible reason
for these distinctions may be a scale effect of the statistical nature that was studied experimentally in
[15] for composite samples (carbon fiber reinforced plastic) having various schemes of reinforcement.
This scale effect reduces material resistance in samples having a larger size (in our case a diameter
of fiberglass samples was twice as large of a diameter of basalt plastic samples or fiberglass samples
had a eight times larger volume of a body under stress at geometrical similarity). It should be noted
that basalt plastic has somewhat smaller values of elastic modulus and failing stress than fiberglass at
close values of ultimate strain along the reinforcement direction: E1 = 5360 kgf/mm2, 1 = 121 kgf
/mm2 1 = 2, 4% - basalt plastic and E2 = 5500 kgf /mm2 , 1 = 150 kgf/mm21 = 2, 33% (no less) –
fiber-glass.
3. CONCLUSION
The performed experiments show that the principal possibility exists of reusing basalt plastic shells
under loads that lead to strain by∼30-50% lower than an ultimate level under single loading that makes
up ∼3,5%. In that case, basalt plastic shells with an inner steel layer stand up to no less than 8 loadings
at levels of circumferential strains 1 ∼ 1.7-2.6% without evidence of failure of a composite.
Therefore, under multiple and single loading [14] basalt plastic practically does not exceed fiberglass in dynamic strength based on an epoxy binder and high-modulus fibers of the BM and BMP types
[4-7, 13].
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1001
The data obtained can be used as estimates in developing composite shells of protective chambers
and structures made of fiber-glass and basalt plastic intended for multiple applications of explosive
loads.
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