How do i calculate maximum hull pressure resistance?

Question

I am designing a submersibal and i need to know how much stress my hull can handle so i can calculate maximum divig depths.

Answer 1

Here is a cached page from an MIT project that contains info. and formulas. You will need to go to the page to see the formulas because they are images and cannot be cut and pasted here.

http://216.239.51.104/search?q=cache:tTGUiKMyOvsJ:web.mit.edu/12.000/www/m2005/a2/finalwebsite/equipment/transport/Hull.shtml+submersible+hull+pressure+resistance&hl=en&gl=us&ct=clnk&cd=1&client=firefox-a
Pressure Hull
Pressure Hulls – the structure that provides the occupants of an underwater submersible with a dry, pressure resistant habitat.

1. Shape - The pressure hull consists of spherical or cylindrical shapes in various combinations. Table 1 illustrates the advantages and disadvantages of various pressure hull shapes.

Table 1. Advantages and Disadvantages of Submersible Pressure Hull Shapes
Shape

Advantages


Disadvantages
Sphere

1. Most favorable weight to displacement ratio
2. Thru-hull penetrations easily made
3. Stress analyses more accurate and less complex

1. Difficult and inefficient interior arrangements
2. Large hydrodynamic drag
Ellipse

1. Moderate weight to displacement ratio
2. More efficient interior arrangements than in sphere
3. Thru-hull penetrations easily incorporated

1. Expensive to construct
2. Difficult to perform accurate structural analysis
Cylinder

1. Inexpensive to construct
2. More efficient interior arrangements than in ellipse
3. Low hydrodynamic drag

1. Least efficient weight to displacement ratio
2. Interior frames required to increase strength

2. Materials

The selection of an appropriate pressure hull material is based on the following criteria:

1. Corrosion Resistance – the ability of a material to resist its deterioration by chemical or electrochemical action within its environment.
2. Resistance to Stress-Corrosion and Cracking – the ability of a material to resist failures caused by the combined action of a flaw (e.g. a crack) and tensile stress.
3. Resistance to Low Cycle Fatigue – the ability of a material to withstand localized fluctuating stress.
4. Creep Resistance – the ability of a material t withstand permanent deformation over time.
5. Stress Relief Embrittlement – the process by which localized residual stresses in a metal are reduced by the reduction in the normal ductility when a metal is heated to a suitable temperature and slowly cooled.
6. Resistance to Brittle Fractures – the ability of a material to resist failures with little or no plastic deformation.
7. High Strength to Density Ratio – the material must be strong and light.
8. High Ductility – the ability of a material to deform plastically without fracturing.
9. Fracture Toughness – the ability of a cracked material to resist catastrophic propagation of cracks.
10. Weldability – the property of a material which allows it to be welded under normal conditions.
11. Formability – the ability of a metal to be shaped through plastic deformation.

Submarine pressure hull are usually made of steel, aluminum, titanium, acrylic plastic and glass. However, the most widely used material is steel, because of a high degree of knowledge available to designers and manufacturers as well as of its outstanding performance in the ocean.

Aluminum is generally considered unacceptable as a pressure hull material because it is unweldable and is subject to stress-corrosion cracking. Nevertheless one solution would be to bolt the hull together instead of welding and anodize it to resist stress-corrosion cracking. Pure titanium is too susceptible to stress-corrosion at high tensile stress levels, but titanium graphite alloys do not exhibit this problem.

Despite of its weaknesses, such as its brittleness, high sensitivity to surface abrasion, and considerable strength degradation at joints, glass and glass-reinforced plastic has a low weight/displacement ratio.

3. Calculations

For pressure hulls, collapse can occur at wall stress levels below the elastic limit. This is called elastic buckling or instability failure. Failure at stress levels above the elastic limit is usually due to plastic yielding of the material.

The following equations are used to calculate the thickness of each pressure hull [Sharp, 1981].
1. Elastic Buckling Collapse Pressure: The classical elastic buckling pressure for an ideal sphere

Poisson's ratio is a measure of the simultaneous change in elongation and in cross-sectional area within the elastic range during a tensile or compressive test. During a tensile test, the reduction in cross-sectional area is proportional to the increase in length in the elastic range by a dimensionless factor, Poisson's ratio [O'Brien, 1996].

The elastic modulus of a material represents the relative stiffness of the material within the elastic range and can be determined from a stress-strain curve by calculating the ratio of stress to strain. Unless indicated otherwise, values were determined in tension [O'Brien, 1996].

According to Arnold G. Sharp, experimental studies have shown a wide disagreement with the above equation. This is probably due to imperfections in geometry and material. Extensive recent testing at the David Taylor Naval Ship Research and Development Center (DTNSRDC) has indicated that the coefficient 1.22 can be attained in an ideal spherical shell, but in most cases, even when imperfections are almost immeasurably small, the coefficient more properly should be about 70% of the theoretical value. DTNSRDC has recommended that the classical equation be modified for near-perfect spherical shells to be:

2. Inelastic Failure

Failure is considered to occur when Smax is equal to the yield strength of the material (ie. Ti-6A1-4V).

4. LEEAMITe's Spherical Hulls

LEEAMITe's pressure hulls are designed to withstand pressure at a depth of 5400 m. The operational depth of each pressure hull is approximately 3000 m. The yield strength of the Titanium Alloy 6A1-4V, the chosen alloy for both pressure hulls, is 828 MPa (120,000 psi) [Sharp, 1981].

At the depth of 5400 m, the ratio between the wall thickness and outside diameter is 0.017 [Sharp, 1981].

Passenger Pressure Hull: Inside diameter = 3.00 m
0.017 = x / (3.00 + 2x) , where x is the wall thickness
Therefore, x = 0.053 m Pilot

Pressure Hull: Inside diameter = 1.75 m
0.017 = y / (1.75 + 2y), where y is the wall thickness
Therefore, y = 0.031 m

Volume of Titanium Alloy 6A1-4V in the Passenger Pressure Hull = 1.552 cu. m
Volume of Titanium Alloy 6A1-4V in the Pilot Pressure Hull = 0.309 cu. m
Density of Titanium Alloy 6A1-4V = 4500 kg/(cu. m)

Mass of Passenger Pressure Hull = 6984 kg
Mass of Pilot Pressure Hull = 1391 kg
Total mass of both pressure hulls: 8375 kg

Cost of Titanium Alloy 6A1-4V and fabrication: $220.00/kg
Estimated cost of both pressure hulls: $1,842,500.00

5. Exostructure

Outer Shell of LEEAMITe: NS90 - high-strength steel

- C < 0.1%
- Si : 0.15% - 0.40%
- Mn : 0.35% - 0.80%
- P < 0.010%
- S < 0.010%
- Cu < 0.10%
- Ni : 5.00% - 5.50%
- Cr : 0.30% - 0.80%
- Mo : 0.20% - 0.60%
- V : 0.03% - 0.10%
- Yield strength: > 90kg/(sq. mm)

The advantages of this steel alloy are its great strength and high corrosion resistance. Although it is rather heavy heavy, the outer shell is not required to be thick. In fact, the exostructure does not have to withstand enormous amounts of pressure because the empty spaces within are filled with mineral oil. Certain types of mineral oil have comparable density to sea water and the substance is an electric insulator, which protects the electric connectors and equipment.
6. References

1. Sharp, A. G., Design curves for oceanographic pressure-resistant housings, Technical Memorandum, 3, Issue 81, 1981.
2. Bever, M. B., (ed). Encyclopedia of Materials Science and Engineering. New York: Pergamon Press, 1986, p. 1059.
3. Lide, D.R. (ed.) CRC Handbook of Chemistry and Physics. 73rd ed., Boca Raton, Fla.: The Chemical Rubber Co., 1993.
4. O'Brien, W. J., Biomaterials Properties Database, University of Michigan, Quintessence Publishing, 1996.

Answer 2

R=V/I so find where the ratio V/I is highest and that's your maximum resistance in that range