aluminium shells under hydrostatic pressure

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Science and Technology

0266-3538(95)00086-O

BORON/ALUMINIUM

Institute of Solid State Physics, Russian Academy

0266-3538/95/$09.50

SHELLS UNDER PRESSURE

S. T. Mileiko

55 (1995) 25-32

0 1995 Elsevier Science Limited in Northern Ireland. All rights reserved

HYDROSTATIC

& A. A. Khvostunkov

of Sciences, Chernogolovka

Moscow District, 142 432 Moscow, Russia

(Received 4 October 1994; revised version received 19 April 1995; accepted 19 May 1995) Abstract

behaviour of shells made of polymer-matrix composites as the stress/strain behaviour of MMCs differs essentially from that of polymer-matrix composites. First, the elastic anisotropy of MMCs is much less than that inherent to fibre-reinforced plastics. Therefore, the usual problems which arise when simplified shell theories based on either the Love-Kirchhoff or Timoshenko hypotheses are applied2 are of little importance. On the other hand, the non-linearity of the stress/strain curve of a MMC can be significant at small deformations.3 Sufficiently rigorous buckling theories for anisoshells loaded by external tropic elastic/plastic hydrostatic pressure,4,5 can supply a means for analysing dependencies of the critical pressure upon both structural parameters of the shell and elastic/plastic characteristics of the material. Howfor appropriate ever, when one is searching fabrication parameters for making shells it is clearly desirable to connect the output parameter, which is the critical pressure in the case under consideration, to input technological parameters, which are the temperature, pressure, and time in the case of making composite shells by hot pressing a blank. Such an analysis will obviously give an approximate result, so the next step should be a correction of the results by using a rigorous theory. This can give the necessary structural parameters of the shell, namely the wall thickness, distance between the ribs, etc. We base the approximate analysis on an expansion of a simple Papkovich formula,6 obtained originally for an isotropic elastic shell, to the elastic/plastic region7 and on further expansion of the Papkovich formula to an elastic/plastic anisotropic shell.8 The basic fabrication technology for MMC cylindrical shells studied in the present work is the hot isostatic pressing of a blank prepared by the plasma spraying of a matrix alloy. Boron/aluminium composite was chosen as a material for model shells with diameters of 122 mm and lengths up to 200 mm. With a modified Papkovich formula being the first base point of the analysis, we shall use as the second

Model cylindrical boron/aluminium shells have been produced by the hot isostatic pressing of plasmasprayed blanks and tested by external hydrostatic pressure. The dependence of the critical pressure on geometrical sizes of shells and material properties is shown to be described by a simple Papkovich formula modified to account for anisotropic and elastic/plastic behaviour of the shell material. The analysis yields a correlation between the shell performance and fabrication regime. A procedure for quantitative comparison of the critical pressures for the shells of various reinforcement schemes are suggested. Keywords:

metal-matrix composites, boron/aluminium, cylindrical shell, critical pressure, fabrication regime 1 INTRODUCTION Mechanical behaviour of composite structural elements is analysed most effectively if a dependence of the critical load of an element on fabrication parameters emerges as a result of the analysis. This is of special importance when we are dealing with elements produced under conditions which are different, in important features, from those observed in producing material specimens for mechanical testing. If a corresponding procedure of the analysis is established, the path from a specimen to an effective structure can be shortened. At the same time, the real effectiveness of a structure made of a new material can be better understood. Thin-walled cylindrical shells made of metal-matrix composites (MMCs) like boron/aluminium are obviously very effective in terms of weight saving. With the geometrical parameters changing in the direction of the enhanced rigidity, plasticity of the matrix begins to play a role and the applicability of theories of elastic shells made of fibre-reinforced plastics’,* therefore becomes questionable. The buckling behaviour of MMC shells differs from the intrinsic 25

S. T. Mileiko, A. A. Khvostunkov

26

base point the dependence of a characteristic strength of a metal matrix obtained by plasma spraying and subsequent hot pressing upon hot pressing parameters suggested previously’ after analysing experimental data given elsewhere.”

2 FABRICATION

AND

STRUCTURE

The fabrication route includes two main steps, namely preparation of a blank and consolidation of the blank. When dealing with thick fibres like boron filaments and aiming at sufficiently large-scale structures, a solid-state consolidation process seems to be preferable to liquid-state methods. Therefore, the blank for a future shell has to be suitable for solid-state consolidation. The blank can be produced in a number of ways: (i) plasma spraying of a matrix alloy on layer-by-layer wound fibres; (ii) winding plasma-sprayed tapes on a mandrel; (iii) winding fibres on a matrix foil, etc. The first of these methods appears to be less time consuming, and was used for making shells with circumferential reinforcement. A combination of the

first and second methods was used for shells with both circumferential and longitudinal reinforcements. For consolidation of structural elements like shells and tubes, a ‘soft’ die should be used’ to follow changes in the curvature of the blank surface during the consolidation process. A scheme used previously” was based on the use of a gas autoclave (Fig. l(a)) and this scheme can still be exploited in straightforward fabrication processes of composites of the boron/aluminium type. Such a scheme has been accepted for this work, despite the fact it brings a danger of excessive fibre breakage during densification of the blank with the external diameter being constant. It should be noted that the scheme of densification with the internal diameter being constant (Fig. l(b)) leads to kinking of fibres’* which seems to be a more difficult problem to overcome. The plasma-spraying process was performed by using a commercially available machine with argon gas as plasma precursor. The blank after plasma spraying is encapsulated into a container shown schematically in Fig. 2. Winding the fibres and spraying the matrix are carried out on a shell mandrel made of 18-8

Fig. 1. Scheme’ for making a composite shell in a gas isostat: (a) densification at the inner rigid wall.

of a blank with the outer rigid wall; (b) the same

Boronlaluminium

Segmented

shells under hydrostatic pressure

Internal steel shell

die

/Blank External / steel shell

Fig. 2. The container

/

with a blank.

stainless steel. The wall thickness of the shell mandrel is about 1.5 mm. The blank after spraying is inserted, with a minimal gap, into a segmented die (Fig. 2) two halves of which are kept together by the end rings. The whole set is then inserted into the external shell which encapsulates the blank hermetically by welding. The container with a blank is then subjected to hot pressing in a gas isostat. The extraction of the boron/aluminium shell from the container is performed by turning the shell mandrel and sealing welds and cutting the external shell in the longitudinal direction. The quality of a shell obtained depends particularly on fabrication parameters. They determine the properties of the matrix and fibre/matrix interface as well as the configuration of the fibre break system. When a set of parameters is chosen appropriately, then the fibre breaks which occur during consolidation of the blank are distributed homogeneously, so they do not influence the shell performance. Otherwise, in a sufficiently thick shell, the fibre breaks are concentrated along one plane, as can be seen in Fig. 3, where specimen 1006 (second from right) exhibits white spots showing the breaks. In the case of densification of a blank with the

27

external diameter being kept constant, the fibres in the internal layer experience a strain E = (h/r)P where h, r, and P are the wall thickness, internal radius and porosity of the blank, respectively. Hence, for usual values of the porosity, P = 0.2, and ultimate fibre strain, E* = 0.007, we have a maximum relative thickness of the shell wall h/r = 0.035 to be densified without danger of fibre breaks. Actually, because of the presence of rough defects in fibres and gaps in the set-up shown in Fig. 2, the maximum wall thickness appears to be even smaller. Consequently, one should be looking for a densification route that will exclude the possibility of collective fibre breaks and provide a structure with random fibre breakage. Obviously, to stimulate random fibre breakage the main densification stage should be performed when the fibre/matrix interface strength is relatively low. Experiments with various pressure/time and temperature/time routes (Fig. 4) were carried out on shells with h/r = 0.07 to choose a consolidation regime. The results are as follows. If the initial pressure in the gas isostat, pO, which is applied before heating, is low, say between 15 and 30MPa, i.e. about half the pressure, pS, at the stationary stage of the fabrication process, during which the temperature T, = 460 - 500°C (ts = O-5 - 1 h) then there occur either collective fibre breaks, as revealed by X-ray microscopy,13 or longitudinal cracks (Fig. 3, specimen 995 (far left)). By increasing the initial pressure to 40MPa and keeping the pressure pS at a reasonable level, i.e. 55 MPa, we obtained shorter cracks as well as collective fibre breaks along some lines (Fig. 3, specimen 1006). At po=ps = 55 MPa, T, = 460-500°C random fibre breakage occurs as shown in Fig. 3 (specimen 1008 (far right)). The same is observed by X-ray microscopy.‘3

P

I

TIME

Fig. 3. Boron/aluminium

shells with external diameters of 122 mm and wall thicknesses between 3 and 4 mm. The white spots on the shell surface identify the collective fibre breaks.

Fig. 4. Scheme the fabrication

of possible pressure/temperature cycles for of composite shells in a gas isostat. See text for details.

S. T. Mileiko,

28

4. A. Khvostunkov

Table 1. Fabrication parameters (pressure, temperature and time) used for making boron/aluminium cylindrical shells, and the effective matrix yield stress, a”,

Number

1 2 3 4

Matrix alloy

(M?‘a)

Al-Mg-Zn Al-Mg-Zn Al-Mg-Zn Al-6% Mg

550 550 460 550

& 520 460 500 500

(min) 20 120 30 30

3-o

H f

0 000000000 000000000 00000000

000000000 000000000

imp

$a)

000000000

AND

‘-I

189 239 191 -

Therefore, regimes (2) and (3) were accepted as the basic ones for producing boron/aluminium shells, the former being tolerable for shells of a relative wall thickness less than 0.07. The actual fabrication parameters used are shown in Table 1. RESULTS

f&”

0000000000 0000

0000

1

000000000

I

=;-“,“,;“,

-c

L Fig.

3-F

I?

CP

3 TESTING

t

c

000000000 000000000

5. Schemes

of the reinforcement aluminium shell walls.

of

the

boron/

DISCUSSION

3.1 Testing results Boron/aluminium shells of four reinforcement schemes (Fig. 5) were obtained and tested13 under hydrostatic pressure. The external diameter of the shells was 122mm, and the length of a specimen, L, varied from 50 to 200mm. Values of the critical pressure obtained in testing the shells with circumferential homogeneous reinforcement (scheme H in Fig. 5) are given in Table 2, those for two-dimensional reinforcement (schemes CP, 3-F and 3-O in Fig. 5) are given in Table 3. 3.2 Modification of the Papkovich formula Papkovich6 presented a simple formula for the critical pressure of an elastic shell under hydrostatic loading: p.+ = kE(R/L)‘+j(h/R)2’5”

(1)

where R, L, and h are the shell sizes, k is a constant which depends on the end conditions. Rewritten as p* = kE,(RlL)“(hlR)”

(2)

the formula was applied to the analysis of the studied behaviour of elastic/plastic shells experimentally’ on carefully made aluminium models. Equation (1) could be written directly from dimensional considerations. However the authors are basing their analysis on eqn (1) to acknowledge the contribution made to shell theory by P. F. Papkovich, a great Russian ship-builder. To apply eqn (2) to the classification of testing results, we need to modify it to account for the anisotropy of the material. Following previous work* we assume the effective modulus for the homogeneous reinforcement scheme to be: E, = (E;)2’3(E;)1’3

(3)

where E’, and E’, are the secant moduli of the composite in the circumferential and longitudinal

directions, respectively. Because the fibre volume fraction changes in these experiments, we have to calculate the stress/strain dependencies for corresponding values of I+. An approximate nature of eqns (2) and (3) calls for an approximate determination of the elastic and secant moduli involved in the corresponding calculations. Hence, we use simple averaging for the values of moduli: E, = E,v, + E,v,

(4)

Table 2. Boron/aluminium cylindrical shells with unidirectional homogeneous reinforcement of the wall in the circumferential direction (the matrix is Al-Zn-Mg a110y)13

Specimen number 979 976.1 976.2 978 975.1 975.2 964 963.1 963.2 950 1002 1003 1004 1005 953 1244“ 1493” 1494” 114 1890 937b 938’ 1492h 173h

Fabrication regime 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4

RIL

hlR

0.3362 1.1518 0.5650 0.3326 1.1738 0.5701 0.3380 1.2547 0.5791 0.3383 0.3314 0.3313 0.3283 0.3276 0.4309 0.3184 0.3236 0.3253 0.3224 0.3275 0.3380 0.3380 0.3270 0.3270

0.0384 0.0369 0.0369 0.0376 0.0379 0.0379 0.0276 0.0257 0.0257 0.0376 0.0451 0.0458 0.0530 0.0460 0.0518 0.0384 0.0379 0.0384 0.0453 0.0470 0.0460 0.0451 0.0364 0.0361

n Fibre diameter is 140 pm. ’ Matrix is Al-6% Mg alloy.

0.394 0.410 0.410 0.402 0.400 0.400 0.328 0.350 0.350 0.345 0.277 0.266 0.287 0.330 0.393 0.460 0.370 0.360 0.290 0.340 0.296 0.296 0.380 0.380

10.98 24.72 16.18 11.18 21.77 14.12 5.29 10.79 5.59 10.00 12.85 14.22 15.79 14.81 21.58 11.77 13.43 12.55 12.65 14.12 17.45 12.75 10.30 9.70

Boron laluminium Table 3. Boron/aluminium

cylindrical

shells under hydrostatic shells with two-dimensional Al-Zn-Mg alloy)”

Structure of the wall Specimen number

Fabrication regime

Scheme (Fig. 5)

N,

924 955 954 1014 1015 1012 1008 1009 1011 1007 1013.1 1013.2 1742

1 1 1 1 2 2 2 2 2 2 2 2 1

CP CP 3-F 3-F 3-F 3-F 3-o 3-o 3-o 3-o 3-F 3-F 3-F

10 15 14 13 12 10 4 4 4 8 10 10 10

NL

29

pressure reinforcement

(the matrix is

Geometry Uf

hlR

RIL

@%a) 5 4 4 6 6 8 8 8 4

0.35 0.40 0.38 0.43 0.43 044 0.15 0.15 0.16 0.31 0.45 0.45 0.34

0.0449 0.0470 0.0473 0.0461 0.0436 0.0430 0.0544 0.0554 0.0566 0.0521 0.0410 0.0410 0.0359

0.331 0.341 0.304 0.331 0.330 0.332 0.328 0.330 0.328 0.391 1.172 0.623 0.333

(&a)

13.73 19.62 16.78 18.84 15.89 16.78 18.25 19.42 19.72 21.38 32.37 23.54 9.71

14.3 17.2 15.8 17.0 15.3 15.1 14.3 14.3 15.8 19.7 29.1 20.2 9.2

Subscripts cpand L relate to values in circumferential and longitudinal directions, respectively.

and EL = E,F,

(5)

whereI

3.3 Matrix

as well as for the stress/strain region:

curve in the plastic

u = Efevf + (T&V,

(7)

where vf, v~, and ug are the Poisson ratios for the fibre and matrix and the matrix yield stress, respectively. So the secant modulus in the circumferential direction is:

Note that in the case under consideration we may take the value of E, as the elastic modulus since the longitudinal stress is just a half of that in the circumferential direction. Therefore, eqn (2) can be rewritten as: p* = kEfv;‘3

which exceeds the elastic limit of the composite; otherwise eqn (2) should be used directly.

I-

%&f)-“‘F;f3@“i~)”

(9)

which is an algebraic equation for the critical pressure of a MMC shell containing elastic fibres unidirectionally and homogeneously distributed in a perfect elastoplastic matrix according to H in Fig. 5. The equation is valid provided the solution yields the stress

properties

To connect the effective matrix stress, ug, which determines the composite secant modulus according to eqn (S), to the fabrication parameters, we shall use the presentation of experimental dependencies of the matrix strength, u$, on consolidation parameters pressure, 4, temperature, T, and time, t, by introducing the equivalent time:9

-$)

T=t(:rexp(

(10)

where n, u*, and T, are constants, the latter being determined by the activation energy of a process to determine the matrix structure. The matrix for a majority of the shells was Al-Zn-Mg alloy. The structure and strength of this matrix obtained for various hot-pressing parameters of a plasma-sprayed precursor are presented elsewhere.‘” The data presented were analysed’ and the dependence of the matrix strength, u& on the equivalent time of hot pressing, z, given by eqn (lo), was obtained. The result shown in Fig. 6 corrects a mistake in the dimension of the equivalent time in Fig. 37 of Ref. 9. The experimental dependence calls for either a power or an exponential approximation, The power approximation shown in Fig. 6, i.e. *_ urn-u,

z

r

(1 -

70

fits the experimental 1 min, and r = 0.1254.

data if u, = 153.9 MPa,

(11) r, =

S. T. Mileiko, A. A. Khvostunkov

30

L/R=3, h/R=O.O5

,004 0

100 200 300 EQUIVALENT TIME / min

400

Fig. 6. Dependence Al-Zn-Mg

of the strength of a plasma-sprayed alloy matrix on equivalent time of hot pressing. Experimental data from Ref. 10.

3.4 Classification

of the testing results and some

conclusions

Consider now the behaviour of shells reinforced homogeneously in the circumferential direction only (Table 2). First, we need to accept values of the effective matrix yield stress, a& to obtain corresponding stress/strain curves for the composites. Having the dependence of the tensile matrix strength, a;, on the equivalent time shown in Fig. 6 we can assume that g; = au2 where CYis to be chosen from consideration of the stress/strain curve of the matrix. However, (Y can be seen as a free parameter which can be

100 0.5

:.: FIBRE

V&&E

FRACTION

Fig. 8. The critical pressure of boron/aluminium shells versus fibre volume fraction according to eqn (2). The shell wall is reinforced in the circumferential direction. The experimental points are brought to the values of (L/R), and (h/R), shown by the correction procedure outlined in the text. For the Al-Zn-Mg alloy matrix, the corresponding values of &, are shown in Table 1, for the Al-6% Mg alloy matrix, u”, = 100 MPa was assumed.

Fig. 7. Approximate surface corresponding to eqn (2) with k = 0.07296, m = 1.938, and II = 0.58. The lower point of a vertical

line indicates the experimental value for a shell with the Al-Zn-Mg alloy matrix.

arbitrarily chosen within a reasonable range, and the final result is expected to fit the experimental data if an appropriate choice of the constant in the modified Papkovich formula, eqn (2), is made. Assuming (Y= 2/3 for the Al-Zn-Mg alloy matrix (the corresponding values of a: are shown in Table 1) we calculate the effective modulus, E,, by using eqns (3), (11) and (lo), for each shell in Table 2. Then a procedure of fitting the experimental values of p*, normalized with respect to the corresponding values of E, obtained by using eqn (3), to the dependence given by eqn (2) yields the following values of the

Boronlaluminium

shells under hydrostatic pressure

constants: k = O-07296, m = l-938, and n = 0.58. Figure 7 is an attempt to visualize the corresponding surface, pJE, = F(hIR, R/L), together with the experimental data. The approximation evolved allows us to systematize the experimental data and draw some quantitative conclusions. Because in a series of physical experiments it is really impossible to keep the fibre volume fraction and geometrical parameters of the shells strictly constant, small variations of these values are to be either neglected, and that is a source of the inevitable scatter, or taken into account by a correction procedure. The approximation given by a means for the correction eqn (2) provides procedure. Let us determine the dependence of the critical pressure on the fibre volume fraction making use of eqn (2) to bring all the data to some sets of values of (L/R), and (h/R),. First, we obtain corrected values of the critical pressure, p*, applying to the

experimental transformation:

31

values

p*,

of

the

following

P* =p*((RIL),I(RIL))“((hlR),l(hlR))” Then, calculating a new value of the stress in the shell wall, uF= p,/(hlR),, we obtain: _ j$* =p,%

where i?, is the calculated value of the effective modulus corresponding to the corrected value of the wall stress, ‘TV. The dependencies calculated according to eqn (2) and experimental data corrected according to the procedure just outlined are presented in Fig. 8. Note that all of the experimental data, except those for three specimens, relate to the dependencies calculated sufficiently well. Note also that the higher the geometrical rigidity of the shell (this means increasing h/R and/or decreasing L/R) the stronger is the

Ja* 1.10

-

? & 1.05

-

E

:

i

-

215

E 4

0

0 0

8

-

0

_

_ 10

E & u

(b)

-

0

-

5

-

0.00

,

,

,

,

,

0.25

,

,

,

,

:

0.50

ho/h Fig. 9. The critical pressure of a boron/aluminium shell reinforced according to scheme 3-O (h/R -0.05, L/R ~3) versus relative thickness of the unreinforced part of the shell wall. (a) Normalized by the critical pressure of a shell with homogeneous distribution of the same quantity of the fibres. (b) Absolute values of the critical pressure. The theoretical line is from Ref. 4.

Fig. 10. The critical pressure of a boron/aluminium shell reinforced according to scheme 3-F (the values of h/R and L/R are given in Table 3) versus relative thickness of the wall part reinforced in the longitudinal direction. (a) Normalized by the critical pressure of a shell with homogeneous distribution of the same quantity of the fibres. (b) Absolute values of the critical pressure.

32

S. T. Mileiko,

geometrical rigidity of the shell (this means increasing h/R and/or decreasing L/R) the stronger is the dependence of the critical pressure on the fibre volume fraction. Consider now the behaviour of shells reinforced according to schemes CP, 3-F, and 3-O (Table 3). From the viewpoint of the use of an expensive reinforcement like boron fibres, the effectiveness of a reinforcement scheme is given by the ratio of the critical pressure of a shell of a particular reinforceto that of a shell with the same ment scheme, p*, geometrical parameters and the same fibre volume fraction but of reinforcement scheme H, pt. The values of pt are calculated and shown in Table 3. The first conclusion is nearly obvious. A homogeneous two-dimensional reinforcement (scheme CP) does not yield any fibre saving. The second conclusion is obvious in qualitative terms. It is worthwhile to dispose fibres in the periphery of the wall (scheme 3-O). The experimental data presented in Fig. 9(a) give the quantitative measure of the effectiveness of fibre reinforcement according to scheme 3-O. These data are to be considered together with the dependence of the critical pressure on relative height of the unreinforced part of the wall, h”/h, presented in Fig. 9(b). These two dependencies allow us to choose a compromise in designing the shell. Note that increasing the value of ho/h to about 0.5 and keeping the fibre volume fraction in the reinforced zones constant yield just a small decrease in the critical pressure. The third conclusion concerns shells with partial reinforcement in the longitudinal direction (scheme 3-F). The experimental data presented in Fig. 10(a) show the quantitative measure of the advantage of such a reinforcement scheme as compared to the homogeneous fibre distribution. However, if one compares these data with those shown in Fig. 9(a) one can see that these data with those shown in Fig. 9(a) one can see that the former scheme looks more attractive from the viewpoint of fibre saving. In terms of the absolute values, the substitution of the longitudinal reinforcement for a circumferential one in a central part of the wall yields a small increase in the critical pressure (Fig. 10(b)).

A. A. Khvostunkov

REFERENCES 1. Bert, C. W., Analysis of shells. In Structural Design and Analysis, Part I, ed. C. C. Chamis. Academic Press, New York, 1975, pp. 207-58. 2. Guz’, A. N. & Babich, I. Yu., A three-dimensional buckling theory of shells. In Mechanics of Composite Materials and Structural Elements, Vol. 2, ed. Ya. M. Grigorenko. Naukova Dumka, Kiev, 1983, pp. 305-18 (in Russian). S. T., Mechanics of metal-matrix fibrous 3. Mileiko, composites. In Mechanics of Composites, ed. I. F. Obraztsov & V. V. Vasiliev. Mir Publishers, Moscow, 1982, pp. 129-65. 4. Dymkov, I. A., An investigation of the ultimate state of boron-aluminium cylindrical shells loaded by external pressure. PhD thesis, Moscow High Technical Bauman School, Moscow, 1982 (in Russian). I. A. & Trofimov, V. V., Stability of 5. Dymkov, cylindrical shells made of metal matrix composites under external pressure. Trans. Moscow High Tech. Bauman School, 24112 (1977) 39-47 (in Russian). 6. Papkovich, P. F., Collection of Works on Ship Strength. Sudpromgiz Publishers, Leningrad, 1956 (in Russian). 7. Kondakov, S. F. & Mileiko, S. T., An experimental study of elastic-plastic buckling of a cylindrical shell loaded by hydrostatic external pressure. Mechanika Twerdogo Tela, 6 (1974) 171-4 (in Russian). 8. Mileiko, S. T., Metal-matrix composite structural elements under compressive loads. Theor. Appl. Fract. Mech. (submitted). 9. Mileiko, S. T., Fabrication of metal-matrix composites. In Fabrication of Composites (Handbook of Composites, Vol. 4), ed. A. Kelly & S. T. Mileiko. North-Holland, Amsterdam, 1983, pp. 221-94. 10. Alipova, A. A., Ivanov, V. V., Ivanov, V. G., Kuchkin, V. V. & Khvostunkov, A. A., Mechanical properties of a plasma sprayed Al-Mg-Zn matrix alloy. Physica and Khimija Obrabotki Materialou, 6 (1979) 116-20 (in

Russian). 11. Weisinger, M. D., US Patent 3,788,926 (1972). 12. Mileiko, S. T. & Kondakov, S. F., Buckling of fibre-reinforced cylindrical shells under hydrostatic external pressure. Mechanika Polymerov, 1 (1977) 90-S (in Russian). 13. Mileiko, S. T., Khvostunkov, A. A., Zolotarevsky, Yu. S., Ivanov, V. V., Kuchkin, V. V., Ivanov, V. G. & Melnichuk, 0. Ya., Fabrication, structure and mechanical behaviour of boron-aluminium shells (in prep.). 14. Bolotin, V. V., A plane problem of the elasticity theory for structural elements made of fibre-reinforced materials. In Strength Analysis, Vol. 12. Mashinostroenie, Moscow, 1966, pp. 3-31 (in Russian).