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ADVANCED MATERIALS AND MATERIAL SELECTION

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ADVANCED MATERIALS AND MATERIAL SELECTION

QUESTION 1

Part 1

The cost for the pressure vessel C is given by the product of mass and cost per kilogram Cm of material

Failure of material due to yielding

Allowable stress needs to be less than yield material strength, to prevent material yielding

The cylindrical pressure vessel designed need to withstand both circumferential and longitudinal stress. The design material to withstand circumferential stress must be higher than longitudinal stress (Ashby, 2013)

Stress in walls of pressure vessel caused by pressure p needs not be exceed

Substituting the equation to eliminate t which is a free variable (Abdullah, 2012)

Material cost

Material cost

The material performance index for Yielding;

The mass of material is minimized through selecting materials with largest index values

The cost of material is minimized through selecting materials with largest index values

Material failure due to fast fracture

Substituting the value t which is a free variable in the equation;

And the cost is given by

Material performance Index for Fast Fracture

The mass is minimized through selecting materials with largest index value (Cavallini, 2013)

The mass is minimized through selecting materials with largest index value.

Conditions for buckling prevention requirement

Substituting the equations

Based on mass

Mass is minimized through selecting materials with largest index value

Cost is minimized through selecting materials with largest index value

The two performance index for material selection results to multiple problem constraint .Some materials may comprise of extra mass of fast fracture which may result to fail due to yielding while other may fail through yielding due to their thickness that may be excess for fracture. Depending on the initial largest crack size the 2 cost equations () will represent the precise material with minimum cost and fail on the same time by yielding fracture chosen and this can be achieved by coupling the two costs i.e. (.

For the 1st material index-

For the 2nd

The equation form which is a straight line (Banerjee, 2015)

The cost of the vessel, of the material

The mass of the material is minimized through selection materials with largest index value (Chakraborty, 2011)

The material cost is minimized through selection of material with largest index value

The conditions for fast fracture prevention it requires