composite pressure hulls for deep ocean submersibles
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Composite Structures 32 (199.5) 331343 Ekvier Science Limited Printed in Great Britain 02638223I95lS9.50 02638223(95)000283
Composite pressure hulls for deep ocean submersiblesDerek GrahamDRA, Dunfennline, Fife KY11 2XR, Scotland UK
DRA Dunfermline first became involved in the development of a composite pressure hull for a deep ocean submersible with the NERC Autosub project and this work has continued under the European MAST II programme. This paper describes the analysis which has been carried out in support of an extensive programme of model testing. An anisotropic Lame solution has been developed for the analysis of cylindrical components under external pressure and this was used to evaluate some of the popular failure criteria. Extensive use was also made of the Finite Element method.
INTRODUCTIONTethered remotely operated vehicles (ROVs) are routinely used in the offshore industry but there are many potential applications for a completely autonomous underwater vehicle (AUV) with full ocean depth capability. DRA Dunfermlines fnst involvement in the development of such a vehicle came with the NERC (Natural Environment Research Council) AUTOSUB project. This was originally prompted by contern about climatic changes such as global warming and the need to understand fully the influence of the oceans in climatic behaviour. The ultimate objective is to develop a free swimming robotic instrument which is capable of repeated dives to full ocean depth, while continuously monitoring its surroundings. Other applications include the exploration and exploitation of resources from the ocean bed or perhaps under ice covered polar seas which are inaccessible by other means. Submersibles which are capable of reaching great depths have of course been around for some time. The pressure hulls of These vessels are typically constructed of high strength steels or alloys of aluminium or titanium. This gives high weight to displacement ratios which makes them unsuitable for use in an autonomous vehicle with limited energy carrying capability, which has long endurance requirements. New materials such as solid glass, ceramics, ceramic331
composites and metal matrix composites have great potential but are considered technically unfeasible at present. This leaves glass or carbon fibre reinforced polymers as the only current option which will provide a pressure hull with a low enough weight to displacement ratio to allow the required payload to be carried. Most authors appear to favour the theoretically stronger carbon fibre composites, see for example Smith and Stachiw & Frame.2 Experimental work for both the AUTOSUB and the European Marine Science and Technology MAST II programmes has been carried out using the high pressure test facilities at DRA Dunfermline. A range of small scale (typically about onesixth) fibre wound specimens have been tested under hydrostatic pressure as cylinders in the UltraHigh Pressure Vessel or as short ring specimens in a specially developed ring tester. Over a period of time a range of specimens have been produced by different manufacturers. Glass fibres and a variety of carbon fibres have been used in different epoxy resins, specimen wall thickness has been varied and alternative winding configurations have been employed. All specimens were fully strain gauged and the resulting data was used to provide measured values of material elastic properties and strengths. The main topic of this paper is the associated analysis, which has been carried out in parallel with the programme of testing.
332
D. Graham
ANALfYSIS A theoretical solution has been developed for an externally pressurised, thick walled composite cylinder with uniform, nonzero axial strain. This was initially developed for a cylinder consisting of orthotropic layers, described by Graham & Anderson,3 but has been extended to include shear coupling and thermal effects in individual laminae in a similar manner to that described by Tzeng & Chien.4 Extensive use has also been made of the Finite Element Method to investigate the fully three dimensional behaviour of test cylinders. The package ASASNL was used. Theoretical solution For a single lamina with one axis of material symmetry the constitutive relations in cylindrical coordinates arecl, Cl2 Cl3 0 0 Cl, Cl2 c22 c23 0 0 C26 Cl3 c23 c33 0 0 C36 0 0 0 c44 c45 0 0 0 0 c 45 c55 0 Cl6 C26 C36 0 0 C66
Using eqns (1) and (2), eqn (3) can be written in terms of the displacements as
r2where
+r i3r2
a%
A2u=@(r,AT,E,) ar
au
(4)
C p=22 C 33 and qb(r, AT,.?,) is the forcing general solution of eqn (4) isu=c&+pr+Y(r,AT,&)
function.
The(9
where a and /3 are unknown coefficients and Y(r, AT,&) is the known particular solution. Equations (l), (2) and (5) can be used to express strains and stresses in terms of the coefficients M.and p, for example the radial stress becomeso,=car~dBr_~+ee,+gAT (6)
X
E,ci,AT .
(1)
where the suffices z, 8 and r denote the axial, circumferential and radial directions, respectively. Assuming that all shear strain components vanish, the remaining strain components relate to the displacement field thus
auEl=%,
U
i3W
se= r and E,==E
a.2
z
(2)
where E, is the assumed constant axial strain. For the condition of axisymmetry and uniform axial behaviour the appropriate equilibrium equation is+
aorar
crtJeY
=O.
(3)
where c, d and e are functions of the stiffness coefficients and g is a function of the stiffness coefficients and the coefficients of thermal expansion. The coefficients a and /? are found for each layer by applying the boundary conditions cr,=O on the inner surface and rsr= P on the outer surface, and the compatibility of radial stress and displacement at each interface between layers. Once these coefficients have been determined, the radial displacements are obtained from eqn (5), strains are obtained from eqns (5) and (2) and stresses are obtained from equations similar to eqn (6). This analysis has been programmed in FORTRAN for a PC and provides a rapid solution to the problem of an externally pressurised filament wound cylinder. Input data required by the program includes the nine elastic constants and three coefficients of thermal expansion of a single lamina in the lamina coordinate system (e.g., El is the Youngs modulus in the fibre direction and E2 the transverse direction, etc.) as well as the radius, thickness and details of the layup of the cylinder. Loading consists of the external pressure, a constant axial strain and a temperature difference, any of which can be set to zero. Imposed axial strain was chosen as an input since this was directly measured during tests,
Composite pressure hulls however, as a check, the resulting axial load and equivalent end pressure were included in the output for comparison with the actual applied pressure. To provide a more general analysis tool it is intended to provide the facility to specify both internal pressure and axial load as input conditions. The lamina elastic properties are transformed, using the layup information, to give the stiffness matrix C in eqn (l), in cylindrical coordinates. The stresses and strains can then be calculated, in cylindrical coordinates, as described above. For each lamina the stresses can be transformed from the global cylindrical coordinate system to the local lamina axes using 611022 =
333

1 S+
1 _~22
1~32 611g22

1 1 _z+S32 1 1
1
1
i
Cl2
iiX
0, i ifJB bze
m2 n2 mn
n2 m2 mn
2mn 2mn (mn)
1(7)
(9
Again, tensile or compressive strengths are used as appropriate. The most general polynomial criterion is that of Tsai & WU,~ given by Fioi+FqaiQj=l where i,j= 1,2,. . .6 and 1 1 F1=_SlT Sic 1 F3~s371 ; F2~
(10)
where m =cosO and n =sin 19.The through thickness stress, c33 is assumed to remain equal to the radial stress or. In theory the stresses in lamina coordinates can be used in conjunction with a failure criterion to predict the failure pressure of a cylinder, provided buckling does not occur. Some of the popular failure criteria have been investigated. The maximum stress or maximum strain criteria can be useful in situations where stresses are highly unidirectional but for general loading some form of polynomial criterion is generally considered more suitable. A number of possibilities have been considered and programmed for comparison. The first, and simplest, was a version of the AzziTsai criterion, given in eqn (8)._
1
1 s2c
S2T 1 s3c
* )
1;F22=
F11=
SlrSlc
s27S2c
;
1F33=
s37S3c
;
dl
fJllC22

0222
62
S12
SlS2
+ s22 +s=
1
(8)
1 1 F&$=; Fss=s132 S232 F12= 1 1 2 Js 17Sl~S27S2~ Fi3= 1 1 2 Jsl~sl~s3*s3~ F23= _ 1 2 &2TS2cS3TS3c
;
1 F@j=s122
*
(11)
where Sl is the strength in the fibre direction, S 2 the strength transverse to the fibres and S 12 the in plane shear strength. If these strengths are different in tension and compression then the appropriate value is used depending on the sign of each stress component. The TsaiHill criterion accounts for a fully threedimensional stress system and is shown in eqn (9) (from Ochoa & Reddy6).
334
D. Graham250 1
Subscripts T and C denote strengths in tension and compression. This was used in two forms; its twodimensional plane stress form (1) and its full threedimens